next generation methods, concepts and solutions for …

Contract No. 881803

H2020-S2RJU-2019 /

S2R-OC-IP1-02-2019

23/03/2021

NEXT GENERATION METHODS, CONCEPTS AND SOLUTIONS FOR THE DESIGN OF ROBUST AND

SUSTAINABLE RUNNING GEAR

D3.2 – Feasibility study for a hybrid wheelset for a tram of

light rail vehicle and/or feasibility study for a hybrid wheelset

with composite axle

Due date of deliverable: 30/11/2020

Actual submission date: 22/03/2020

Leader/Responsible of this Deliverable: Andrea Bernasconi, POLIMI

Reviewed: Y

Document status

Revision Date Description

1 10/02/21 Draft/Internal

2 23/02/21 First issue for approval by TMT

3 22/03/21 Final/Public

Project funded from the European Union’s Horizon 2020 research and

innovation programme

Dissemination Level

PU Public X

CO Confidential, restricted under conditions set out in Model Grant

Agreement

CI Classified, information as referred to in Commission Decision

2001/844/EC

Start date of project: 01/12/2019 Duration: 24 months

Ref. Ares(2021)2045506 - 23/03/2021

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REPORT CONTRIBUTORS

Name(s) Institution Details of contribution

Michael Johnson

Richard Evans

Preetum Mistry

UNOTT Chapters 1-7

Chapters 5-7

Chapters 1-7, Editing and reviewing

Andrea Bernasconi

Stefano Bruni

Michele Carboni

Rosemere Lima

Luca Michele Martulli

POLIMI Section 9.2, 9.3, 10.3

Editing and reviewing

Reviewing

Section 10, 10.1, 10.2

Section 9.1

Chapter 9: reviewing

Irene Marazzi/

Steven Cervello

LRS Data provisioning, reviewing.

Reviewing

Davide Formaggioni BERCELLA Chapter 8

Sergio Macchiavello

Edoardo Ferrante

RINA-C Chapter 11

Jordi Viñolas

Ingo Kaiser

UNNE Chapter 12, reviewing

Chapter 12

Jose A. Chover MdM Chapter 12, data provisioning, reviewing

Jose Bertolin UNIFE Reviewing

Sebastian Stichel KTH Reviewing

Contract No. 881803

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EXECUTIVE SUMMARY

The objective of Task 3.2 of the NEXTGEAR project was to assess the feasibility of a hybrid metal-

composite (HMC) wheelset, considering one of the following scenarios:

• a complete metal-composite wheelset for light vehicles, like trams or metros;

• a composite axle of a trailer bogie, with integrated connections with wheel rims, brake discs and

bearings.

In Task 3.1 the second scenario was identified as the best candidate for reaching the desired TRL

level of 2. This deliverable presents a detailed analysis of the feasibility of this hybrid metal-

composite axle, characterized by a metallic collar designed to be connected to metal bearings,

wheels and brake discs.

Concept design of the HMC axle developed in T3.2

The feasibility study started from the optimization of the composite layup presented in D3.1 and a

more detailed geometry was defined. Its structural behaviour was analysed by the finite element

method to ensure that the proposed solution minimizes the mass while preserving its strength and

satisfying all the requirements set by the design standards relevant to solid steel axles.

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Finite element analysis of the HMC axle

The feasibility of the manufacturing process was assessed and, among the manufacturing

processes identified in T3.1, roll wrapping and filament were chosen, assessed and compared. The

analysis combined finite element simulations with process simulations, and it was concluded that

both processes are feasible, allowing similar mechanical performance to be achieved, although

filament winding offers the potential for an automated process, characterized by a high level of

repeatability of the results. To reach higher TRL levels, the need of a comprehensive experimental

characterization of the materials used in the different processes was pointed out.

Numerical simulation of the filament winding process

One of the most critical aspects of a hybrid metal-composite structure is the connection between

metallic and composite parts. The proposed axle presents a metallic collar that needs to be

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connected to an inner and an outer composite tube. Both connections were designed to be

adhesively bonded. This joint was optimized to reduce the stresses in the adhesive and increase

the fatigue life of the joint. An optimized adhesive joint geometry was proposed.

The improved design for the adhesive joint between the steel collar and the composite tube

Reaching a higher TRL would require a comprehensive characterization of the chosen adhesives,

particularly under fatigue loading and in different environmental conditions. Mechanical joining is

not an option that has been considered in this project because of the mass increment involved, but

it could be a valid alternative to adhesive bonding, should future tests demonstrate the unfeasibility

of an adhesively bonded joint.

The proposed design was checked against requirements for inspection during maintenance service

interruption. The feasibility of NDT was assessed, focussing particularly on the use of ultrasonic

testing (UT). By simulation, the feasibility of UT was assessed and some limitations of UT were

identified with respect to the possibility of detecting cracks in the adhesive layer, whereas UT would

allow cracks to be detected in the composite tubes and in the metallic collar. Simulations assumed

ideal conditions, therefore, to switch to higher TRL, experimental verification would be needed to

optimize the setup. To overcome the limitations of inspection of the bond line by UT, a possible

structural health monitoring approach was proposed, based on strain profile monitoring, using fibre

optic strain sensors allowing for distributed sensing.

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Numerical simulation of the response of a UT system in the composite and in the steel parts

Dynamic analyses focused on the simulation of the effect of impact loading and on the effects of

the mass reduction on the train-track interaction. Impact loading typical to railway axles is

represented by ballast impact. An impact by a foreign object was simulated and potential damage

was assessed, consisting mainly in damage of the matrix of the external surface of outer tube due

to high compressive stresses. Although this would not impair the overall structural integrity of the

axle, solutions like a protective coating and the installation of sensors capable to detect severe

impacts should be identified.

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Finite element simulation of the impact of a foreign object and damage in the composite tube

Finally, the effect of the reduction of the un-sprung masses achieved with the hybrid metal-

composite design, onto the wheel-rail interaction forces, and consequently onto the wear of both

wheels and rails was assessed numerically. Dynamic simulations were conducted, comparing the

dynamic behaviour of a standard steel wheelset and a wheelset modified with the substitution of a

steel axle with the proposed HMC axle, when mounted on the same reference bogie. Simulations

considered the dynamic effects of the track irregularities and revealed that the reduction of the un-

sprung mass obtained by the substitution on an all steel axle by the proposed HMC one can have

beneficial effects on the wheel-rail contact forces, particularly at higher speeds (greater than 90

km/h).

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The dynamic model and the comparison between vertical forced of the steel (blue lines) and the composite (orange line) axle

At the end of task T3.2, it can be concluded that the mass reduction of a railway axle has been

achieved by replacement of a hollow steel trailer axle with a HMC equivalent axle. The mass of the

HMC axle is 74 kg, a reduction of 63% compared to the steel axle at 198 kg. The HMC railway axle

permits the existing wheels and bearings to be used.

The stresses in the HMC axle are below the design limits and a safety factor of 2 ensures that

strength requirements can be met by the metallic collars and the composite tube. Maximum

deflection in the HMC axle is larger than in the steel axle, but it could be reduced by increasing the

thickness of the secondary composite tube with a relatively low mass increase (on the order of 5

kg).

The high contact stress between the collar and the primary composite tube has been reduced by

proposing a modified, improved geometry of the collar. A margin of improvement still exists, and

future work should focus on the optimization of this joint. Although more experimental validation is

needed to support simulations, in principle, the proposed HMC axle can be inspected by UT, except

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in the bond line. To overcome this limitation, SHM solutions should be implemented, like for

example the distributed strain profile monitoring studied in this project.

The dynamic behaviour of composite tube in the case of impact by a foreign object like ballast

evidenced the need of identify and implement a protection layer or shield, to avoid any possible

damage in the composite. Future work, aiming at reaching higher TRL should consider this point

in detail.

Finally, the analysis of the dynamical forces at the interaction between rail and wheels showed that

the proposed HMC axle can modify the dynamic forces that are responsible of wear mechanisms

of the wheels and the rails. The reduction of the un-sprung mass offered by the HMC axle provides

benefits in terms of reduced dynamic vertical wheel-rail forces, track shift forces and wear number.

Consequently, a reduction of impact forces, wear and rolling contact fatigue damage can be

expected for both the rails and the rolling surfaces of the wheels. These benefits are particularly

significant when the speed is high (90 km/h on a metro line). A reduction of track damage related

to metal fatigue of rails and to permanent settlement in the ballast + embankment can also be

expected. Results confirm the potential positive impact on maintenance costs offered by a lighter

wheelset.

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ABBREVIATIONS AND ACRONYMS

Word/Acronym Description

NEXTGEAR NEXT generation methods, concepts and solutions for the design of

robust and sustainable running GEAR

TRL Technical readiness level

FRP Fibre reinforced polymer (in reference to a type of composite material)

CFRP Carbon fibre reinforced polymer (in reference to a composite material)

HMC Hybrid metallic/composite (in reference to a rail wheelset)

WP Work package (relating to the NEXTGEAR project)

FEA/FEM Finite element analysis/method

NDT Non-destructive testing

VT Visual testing

UT Ultrasonic testing

MT Magnetic particle testing

PT Liquid penetrant testing

ET Eddy current testing

RT Radiographic testing

CT Computed tomography

SHM Structural health monitoring

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TABLE OF CONTENTS

Report Contributors ................................................................................................................. 2

Executive Summary ................................................................................................................. 3

Abbreviations and Acronyms ................................................................................................. 10

Table of Contents................................................................................................................... 11

List of Figures ......................................................................................................................... 14

List of Tables .......................................................................................................................... 19

1. Introduction ................................................................................................................... 20

2. Benchmark hollow steel axle .......................................................................................... 22

2.1 Definition of critical sections along the railway axle ................................................... 23

3. LOAD CASES .................................................................................................................... 25

3.1 Load case 1 ............................................................................................................... 25

3.2 Load case 2 ............................................................................................................... 26

3.3 final load case ........................................................................................................... 27

4. Loading conditions and structural performance parameters of the wheelset ................... 28

4.1 Position of maximum bending stress ......................................................................... 30

4.2 Position of maximum deflection ................................................................................ 30

4.3 Angular misalignment at the journals ........................................................................ 30

4.4 Back-to-back distance between wheel flanges ........................................................... 31

4.5 First critical speed ..................................................................................................... 32

4.6 Position of maximum transverse stress ..................................................................... 32

4.7 Position of maximum torsional stress ........................................................................ 33

4.8 Maximum angular twist ............................................................................................ 33

5. Finite element analysis (FEA) of the wheelset model ....................................................... 34

5.1 Modelled axle systems .............................................................................................. 34

5.2 Loading conditions .................................................................................................... 36

5.3 Boundary conditions ................................................................................................. 36

5.4 Model verification ..................................................................................................... 37

5.5 Assumptions for the FEA wheelset modelling ............................................................ 38

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6. Structural characterisation of the benchmark, hollow steel axle ...................................... 38

7. HMC railway axle design ................................................................................................. 40

7.1 Design of the metallic collars and primary composite tube due to external pressure loading at the interference fit, Position 𝑨 ........................................................................ 42

7.2 Design of the metallic collar and primary composite tube due to static loading, 𝑴𝒙, at Position 𝑪 ....................................................................................................................... 43

7.3 Design of the primary composite tube due to the resultant moment, MR, at Position 𝑬 ....................................................................................................................................... 44

7.4 Design of the primary composite axle due to torsion, 𝑴𝒚′, at Position 𝑪 ................... 46

7.5 Deflection characteristics of the HMC composite axle due to the bending moment, 𝑴𝑹 ....................................................................................................................................... 47

7.6 Structural performance parameters .......................................................................... 48

7.7 Discussion - structural performance the of HMC railway axle ..................................... 50

8. Assessment of the manufacturability and comparison between various manufacturing methods ................................................................................................................................ 52

8.1 Roll wrapping ............................................................................................................ 52

8.2 Filament winding ...................................................................................................... 54

8.3 Comparison among roll wrapping and filament winding process ................................ 63

9. Analysis of the bonded joints .......................................................................................... 64

9.1 Selection of the adhesive and mechanical characterization ........................................ 64

9.2 FEA of the adhesive joint ........................................................................................... 70

9.3 Discussion ................................................................................................................. 81

10. Assessement of the feasibility of NDT AND SHM ...................................................... 85

10.1 Feasibility of NDT methods ...................................................................................... 85

10.2 Feasibility of UT: results of the simulations using CIVAnde software .......................... 87

10.3 Possible solutions for SHM .................................................................................... 105

11. Analysis of the impact response ............................................................................. 110

11.1 Objective of the impact analyses ........................................................................... 110

11.1.1 EN 13261:2009+A1 - Paragraph 3.2.2 Impact Test Characteristics ................. 110

11.1.2 EN 13261:2009+A1 – Annex C .......................................................................... 111

11.2 Software tool ........................................................................................................ 112

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11.3 Geometrical model ................................................................................................ 112

11.4 Materials............................................................................................................... 113

11.5 Numerical model ................................................................................................... 114

11.6 Loading Conditions ................................................................................................ 117

11.7 Results .................................................................................................................. 117

11.7.1 Impact direction: normal to axle surface ......................................................... 118

11.7.2 Impact direction 45° to axle surface ................................................................ 119

11.8 Mitigation measures / Further Developments........................................................ 121

12. Analysis of the dynamic behaviour ......................................................................... 124

12.1 Vehicle model ....................................................................................................... 124

12.2 Wheelset inertia .................................................................................................... 126

12.3 Scenario “Running on a curved measured track” .................................................... 128

12.4 Scenario “Running on a straight track with measured irregularities” ...................... 139

12.5 Conclusions ........................................................................................................... 146

13. Conclusions ........................................................................................................... 147

References ........................................................................................................................... 149

Appendix A. Material propereties used as input to the fEA ................................................... 152

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LIST OF FIGURES

Figure 1 Concept design of a HMC axle having a primary CFRP tube along the length of the axle, a secondary composite tube in the central section and metallic collars bonded to the ends of the axle. (a) External view (b) Cross section through axle. ............................................................... 21

Figure 2. A typical inboard bearing, trailer wheelset with general dimensions including wheels and a hollow axle (Source: Lucchini RS). .......................................................................................... 22

Figure 3. The benchmark, hollow steel (EA1N), inboard bearing trailer axle showing general dimensions (Source: Lucchini RS). ............................................................................................. 23

Figure 4. Critical section diameters a distance 𝑦 along the axle and defined as positions for evaluation. .................................................................................................................................. 23

Figure 5. A typical railway wheelset with the resultant moment, 𝑀𝑅, applied at the loading planes, 𝐷 and 𝐷’, causing the greatest bending about the x-axis. The static load, 𝑃, is used for calculation

of transverse shear, is applied separately at the same position. The torsional moment, 𝑀𝑦′, is applied uniformly about the y-axis. ............................................................................................. 28

Figure 6. Axle loaded with the resultant moment, 𝑀𝑅. The static load, 𝑃, is superimposed for calculation of transverse shear. The torsional moment, 𝑀𝑦′, is constant across the axle. (a) Shear diagram (b) Moment diagram. .................................................................................................... 29

Figure 7. Diagram showing the amount of angular misalignment, 𝜃, at the journal for the axle undergoing bending. ................................................................................................................... 31

Figure 8. Back-to-back distance, 𝐿𝐵𝑡𝐵, as measured between flanges at rail level. As the axle deflects downwards, the overall back-to-back distance increases by ∆𝐿𝐵𝑡𝐵............................... 31

Figure 9. Calculation of the first moment area of inertia, 𝑄, for a hollow tube at the neutral axis of the axle. ..................................................................................................................................... 33

Figure 10. HMC axle model element mesh. (a) Model 1-3D solid model, showing element mesh for the composite axle with the RHS collar attached. The LHS collar is removed to show cohesive elements beneath representing adhesive. (b) Model 2-Axisymmetric model, with element mesh for the primary composite tube, collar and interfacing wheel. ........................................................... 35

Figure 11. Boundary conditions for the wheelset model applied to the running surfaces where the rail and wheel contact. At Position 𝐴, u3=u2=ur2=0 and Position 𝐴’, u3=ur2=0. ......................... 37

Figure 12. HMC railway axle comprising a full length, primary composite tube, a secondary composite tube and metallic collars as introduced in Figure 1. Abaqus 2018 has been used to size the primary and secondary composite tubes as well as the metallic collars. ............................... 41

Figure 13. Cross section through the HMC axle at the running surface (Position 𝐴) showing the diameters of the metallic collar and the primary composite tube. ................................................ 42

Figure 14. von Mises stress at the wheelseat from external pressure loading due to the interference fit between the wheel hub and steel collar. The resultant stresses within the primary composite tube are minimal. Note that the adhesive is not included as a worst case. ........................................ 43

Figure 15. A cross section through the HMC railway axle at Position C showing the absolute maximum value of transverse the shear stress in the primary composite tube. .......................... 44

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Figure 16. (a) Maximum von Mises stress (170.00 MPa) in the composite axle at Position 𝐸, ply 4, bottom of primary composite tube, due to the moment, 𝑀𝑅. (b) Damage field for Hashin failure

criterion highlighting fibre compression in the primary composite tube at Position 𝐸. The secondary composite tube is included in the analysis, but not shown here for clarity. ................................. 45

Figure 17. (a) von Mises stress at Position 𝐸, ply 27, top of primary tube, due to the moment, 𝑀𝑅, showing the peak stress of 528.10 MPa due to penetration of the collar on the top surface of the primary composite tube. (b) Damage field for Hashin failure criterion highlighting fibre compression in the primary composite tube at Position 𝐸. The secondary composite tube is included in the analysis, but not shown here for clarity. ...................................................................................... 45

Figure 18. von Mises stress, Position 𝐸 , at each ply of the primary composite tube (a) and secondary composite tube (b), due to the moment, MR. The high peak stress in the primary composite tube is due to penetration by the collar. ..................................................................... 46

Figure 19. (a) Torsional stress at the outer diameter, ply 2, of the primary composite at Positions 𝐶, due to the torsional moment, 𝑀𝑦′. (b) Damage field for the Hashin failure criterion highlighting matrix compression in the primary composite tube at Positions 𝐶. The secondary composite tube is included in the analysis, but not shown here for clarity. ........................................................... 47

Figure 20. HMC axle under the bending moment, 𝑀𝑅. (a) Vertical displacement field plot compared against the undeformed state, with a scale factor of 20 applied showing maximum deflection, 𝛿𝑚𝑎𝑥,

at Position 𝐹. (b) Angular misalignment angle 𝜃 at Position 𝐷 caused by the axle deflection at the journal seat, with a scale factor 10 applied. ................................................................................ 48

Figure 21 - Section of a tube end. .............................................................................................. 53

Figure 22 - butt joint generation during the mandrel wrapping. ................................................... 53

Figure 23 Filament winding layup optimization routine ............................................................... 56

Figure 24 Simulation of 45° helical winding ................................................................................ 58

Figure 25 Overconservative initial guess for the FW layup ......................................................... 59

Figure 26 Maximum vertical displacement of the roll-wrapped solution [mm] .............................. 61

Figure 27 Maximum rotation about the axis of the roll-wrapped solution [rad] ............................. 61

Figure 28 Maximum vertical displacement of the filament-wound solution [mm] ......................... 62

Figure 29 Maximum rotation about the axis of the filament-wound solution [rad] ........................ 62

Figure 30. Fatigue S-N diagram of the 3M 9323 B/A adhesive [19] ............................................ 68

Figure 31. The tensile stress-strain curve of the bulk adhesive 9323 B/A ................................... 69

Figure 32. results of mode I fracture test, with FE analysis results superimposed, showing the accuracy of cohesive modelling. ................................................................................................. 70

Figure 33. the portion of the composite wheelset used for modelling of the adhesive joint ......... 71

Figure 34. kinematic couplings, reference points and boundary conditions................................. 71

Figure 35. kinematic couplings, reference points and boundary conditions................................. 72

Figure 36. contour plot of the values of the MAXSCRT variable in the adhesive layers .............. 74

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Figure 37. contour plot of the values of the von Mises stress in the adhesive layer .................... 75

Figure 38. contour plot of the out of plane shear stresses in the adhesive layer ......................... 75

Figure 39. contour plot of the out of plane shear stresses in the adhesive layer ......................... 76

Figure 40. the improved joint between the stub axle and the composite tubes ........................... 76

Figure 41. shape and dimensions of the modified stub axle ....................................................... 77

Figure 42. Detail of the adhesive layer of the improved joint between the stub axle and the composite tubes ......................................................................................................................... 78

Figure 43. contour plot of the values of the out of plane shear stress in the adhesive layers of the improved joint ............................................................................................................................. 78

Figure 44. contour plot of the values of the von Mises stress in the adhesive layers of the improved joint ............................................................................................................................................ 79

Figure 45. contour plot of the values of the shear stress amplitude in the adhesive layers between the inner composite tube and the steel axle ................................................................................ 79

Figure 46. contour plot of the values of the shear stress amplitude in the adhesive layers between the inner composite tube and the steel axle, for the 3M AF-163-2 adhesive ............................... 80

Figure 47. contour plot of the values of the von Mises stress in the stub axle ............................. 81

Figure 48. Four different types of mechanical joints between composite and metal parts in wind turbine blades, from [21] ............................................................................................................. 82

Figure 49. Simplified model of the flanged joint .......................................................................... 83

Figure 50. Cross sectional view of the flanged joint .................................................................... 83

Figure 51. Detail of the “tie” constraint between the flanges ....................................................... 84

Figure 52. contour plot of the von Mises stress distribution in the adhesive layers ..................... 84

Figure 53. Geometry of the central region of the composite axles considered for UT numerical simulations. ................................................................................................................................ 88

Figure 54. Stiffness matrices of the inner and outer composite tubes. ........................................ 89

Figure 55. Slowness curves for the inner and outer composite tubes. ........................................ 90

Figure 56.Model of the adopted UT probe for perpendicular incidence of longitudinal waves in the central region of the composite axle. .......................................................................................... 91

Figure 57.Simulation of the physical sound beam for perpendicular incidence of longitudinal sound waves in the central region of the composite axle. ...................................................................... 92

Figure 58. Circular defect representing a delamination in the composite material....................... 92

Figure 59. Ultrasonic responses of the central region of the composite axle inspected by normal incidence of longitudinal waves. ................................................................................................. 93

Figure 60. Model of the adopted UT probe for angled incidence of shear waves in the central region of the composite axle; the inset image shows the probe from a different angle of view. ............. 94

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Figure 61. Refraction angles of the shear waves used in the central region of the composite axle. ................................................................................................................................................... 95

Figure 62. Simulation of the physical sound beam for angled incidence of shear waves in the central region in the central region of the composite axle. ...................................................................... 96

Figure 63. Concave defect representing a transverse crack in the composite material. .............. 96

Figure 64. Ultrasonic responses of the central region of the composite axle inspected by angled incidence of shear waves. .......................................................................................................... 97

Figure 65. Geometry of the lateral region of the composite axles considered for UT numerical simulations. ................................................................................................................................ 98

Figure 66. Simulation of the physical sound beam for perpendicular incidence of longitudinal sound waves in the lateral region of the composite axle. ....................................................................... 99

Figure 67. Simulation of the physical sound beam for angled incidence of shear waves in the lateral region in the central region of the composite axle. .................................................................... 100

Figure 68. Ultrasonic responses of the lateral region of the composite axle inspected by normal incidence of longitudinal waves. ............................................................................................... 101

Figure 69. Ultrasonic responses of the lateral region of the composite axle inspected by angled incidence of shear waves. ........................................................................................................ 103

Figure 70. Ultrasonic responses of the external surface of the metallic collar inspected by angled incidence of shear waves. ........................................................................................................ 104

Figure 71. Schematic view of the installation of a strain sensing fiber optic .............................. 106

Figure 72. Size and position of the simulated crack (10 mm crack length shown in this picture) 107

Figure 73. The node path used for the extraction of the strain values ....................................... 108

Figure 74. The different strain patterns (longitudinal, with reference to the 1 axis of the local coordinate system shown in yellow) for increasing simulated crack length. .............................. 108

Figure 75. Strain values along the longitudinal path, for different simulated crack lengths ........ 109

Figure 76. Location of test pieces for hollow axles according to EN 13261 2009 +A 1 2010 [29] ................................................................................................................................................. 111

Figure 77. Analysis workflow in Ansys© Workbench 2020 R2 suite. ......................................... 112

Figure 78. Simplified geometrical model considered for impact analyses. ................................ 112

Figure 79. Composite material properties table in Ansys© Workbench 2020 R2 suite. ............. 113

Figure 80. Composite layers stacking sequences considered in the analyses. ......................... 114

Figure 81. Composite tubes mesh in radial and tangential direction ......................................... 115

Figure 82. Discretized model of all components ....................................................................... 116

Figure 83. Discretized model of all components (section view) ................................................. 116

Figure 84. Damage plot in the nearby of the impact region - impact angle 90° ......................... 118

Figure 85. Damage plot in the nearby of the impact region (section view) - impact angle 90° ... 119

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Figure 86. Damage plot in the nearby of the impact region - impact angle 45° ......................... 120

Figure 87. Damage plot in the nearby of the impact region (section view) - impact angle 45° ... 120

Figure 88. Bogie of the ML95 vehicle (source [34]) ................................................................... 124

Figure 89. Substitution track model by Chaar and Berg [35] ..................................................... 125

Figure 90. SIMPACK model of the investigated vehicle ............................................................ 126

Figure 91: Parameters of the used metro line: Curvature 1/𝑅𝐶 (upper diagram), superelevation ℎ (middle diagram), cant deficiency Δℎ for 𝑣0 = 54 km/h and 𝐸 = 1.5 m (lower diagram). ........... 129

Figure 92. Comparison of the dynamic vertical wheel-rail forces Δ𝑄 at the leading bogie; 𝑣0 =54 km/h.; blue: steel wheelset; orange: HMC wheelset. ........................................................... 131

Figure 93. Comparison of the dynamic vertical wheel-rail forces Δ𝑄 at the trailing bogie; 𝑣0 =54 km/h; blue: steel wheelset; orange: HMC wheelset. ............................................................ 132

Figure 94. Comparison of the sliding mean values Σ𝑌2m at the four wheelsets; 𝑣0 = 54 km/h; blue: steel wheelset; orange: HMC wheelset. .................................................................................... 134

Figure 95. Comparison of 𝑇𝛾 values (wear numbers) at the leading bogie; 𝑣0 = 54 km/h; blue: steel wheelset; orange: HMC wheelset; magenta: track curvature. ........................................... 136

Figure 96. Comparison of 𝑇𝛾 values (wear numbers) at the trailing bogie; 𝑣0 = 54 km/h; blue: steel wheelset; orange: HMC wheelset; magenta: track curvature. ................................................... 138

Figure 97. Comparison of the dynamic vertical wheel-rail forces Δ𝑄 at the leading bogie; 𝑣0 =90 km/h; blue: steel wheelset; orange: HMC wheelset. ............................................................ 140

Figure 98. Comparison of the sliding mean values Σ𝑌2m at the leading bogie; 𝑣0 = 90 km/h blue: steel wheelset; orange: HMC wheelset. .................................................................................... 141

Figure 99. Comparison of 𝑇𝛾 values (wear numbers) at the leading bogie; 𝑣0 = 90 km/h.; blue: steel wheelset; orange: HMC wheelset. .................................................................................... 142

Figure 100. Comparison of the dynamic vertical wheel-rail forces Δ𝑄 at the leading bogie; 𝑣0 =90 km/h; mainline irregularity profile; blue: steel wheelset; orange: HMC wheelset. ................. 143

Figure 101. Comparison of the sliding mean values Σ𝑌2m at the leading bogie; 𝑣0 = 90 km/h; 𝑣0 =90 km/h; mainline irregularity profile. ; blue: steel wheelset; orange: HMC wheelset. ............... 144

Figure 102. Comparison of 𝑇𝛾 values (wear numbers) at the leading bogie; 𝑣0 = 90 km/h ; mainline irregularity profile; blue: steel wheelset; orange: HMC wheelset. ................................ 145

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LIST OF TABLES

Table 1. Description of the critical section positions along the axle with distance, 𝒚, from the left-hand side (LHS) and a corresponding outer diameter, 𝑫𝒐. ......................................................... 24

Table 2. Moment values at the critical sections along the axle for load case 1. .......................... 26

Table 3.2. Moment values at the critical sections along the axle for load case 2......................... 27

Table 4. Structural performance of the benchmark hollow steel axle. ......................................... 39

Table 5 Summary of Rw and FW comparison. ........................................................................... 62

Table 6. Adhesives’ mechanical properties. ................................................................................ 65

Table 7:The mechanical properties of the studied adhesive joints. ............................................. 66

Table 8. Coefficients of the proposed traction separation law for the 3M 9323 B/A adhesive ..... 69

Table 9. Elastic properties of the materials ................................................................................. 73

Table 10. Pros and Cons of the impact mitigation solutions ...................................................... 122

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1. INTRODUCTION

This deliverable reports on activities performed in Task 3.2 of the NEXTGEAR project and

describes a feasibility study and preliminary design of a wheelset incorporating hybrid metallic-

composite (HMC) railway axle. The work presented here progresses from the three design concept

solutions investigated in Task 3.1. One of these concepts (concept 3, see below) was selected as

the most promising and is further developed in this report with the aim of defining a feasible

configuration for a lightweight wheelset axle made of composite materials. The analyses performed

in Task 3.2 focus on:

• dimensioning and structural optimisation of the axle, including the detailed definition of the composite layup;

• analysis of the manufacturing process and of its feasibility;

• assessment of the manufacturability and comparison between various manufacturing methods;

• feasibility analysis of non-destructive inspection and structural health monitoring of the composite axle;

• effect of the wheelset with composite axle on railway vehicle dynamics;

• analysis of resistance of the axle to impacts (e.g. from flying ballast).

The three HMC railway axle concepts were based upon a replacement for the benchmark, hollow

steel trailer axle with inboard bearings as supplied by Lucchini RS for WP3. The mass of this axle

is 198 kg. The aim of the HMC railway axle is to demonstrate a significant reduction in the mass

of the benchmark steel axle.

The architecture of the initial, two HMC railway axle concept designs are as follows:

• Concept 1. A wound HMC railway axle solution whereby towpreg is wrapped around radial

pins affixed to the stub axles at each end. Complex fibre geometries were possible for

optimised structural performance. However, the overall mass was 190 kg representing a

minimal mass reduction of 4%.

• Concept 2. A carbon fibre reinforced polymer (CFRP) tube of plain diameter with metallic

stub axles adhesively bonded into either end of the tube. This solution provided

manufacturing simplicity, but the joint was complex. The mass of this HMC concept railway

axle was 152 kg, a mass savings of 23%.

Figure 1 illustrates the third HMC railway axle concept which offered a high structural capability

afforded by semi-tailored fibre placement and the manufacturing robustness achieved through roll

wrapping of CFRP prepreg. Importantly, this concept showed the prospect of mass savings of at

least 60%. This concept is distinguished by a primary composite (CFRP) tube running the length

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of the axle. The thickness of the composite tube is increased between the journals using a

secondary composite (CFRP) tube. Metallic collars are bonded onto the ends of the primary tube

and include surface geometry matched to the existing wheel hub and rolling element bearing inner

diameters.

Figure 1 Concept design of a HMC axle having a primary CFRP tube along the length of the axle, a secondary composite tube in the central section and metallic collars bonded to the ends of the axle. (a) External view (b) Cross section through axle.

The axle is designed such that the majority of bending, shear, torque and higher order loads are

taken up by the primary composite tube. The secondary tube provides additional stiffness so that

deflections are minimised. The collars are sufficient to mitigate the radial and circumferential loads

developed by the interference fits onto the journal and wheel seat without transmission to the

primary composite tube.

A parametric approach was taken to size this concept. While successful in specifying an overall

CFRP layup, this approach was considered overly simplistic as bulk strength properties were used

for the laminate. Furthermore, geometric features were not taken into account. To elevate the

fidelity of this concept, it is necessary to treat the composite as a laminate which is analysed using

classical laminate theory (CLT).

This deliverable report for NEXTGEAR WP3.2 first presents a finite element analysis (FEA) of the

benchmark hollow steel axle. The concept HMC railway axle shown in Figure 1 is subjected to the

same FEA analysis, incorporating CLT. Structural conformance of the HMC railway axle is

assessed against the benchmark steel axle. Then, the feasibility of the axle from the perspective

of manufacturing is assessed and different manufacturing routes are proposed. The bonded joint

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between the metallic collars and the primary composite tube is studied in detail and a solution is

proposed to minimize stresses in the adhesive and ensure the desired fatigue life.

This deliverable report covers also other aspect related to service and inspections. Non Destructive

Testing (NDT) and Structural Health Monitoring (SHM) solutions are presented and discussed.

Finally, the behaviour of the composite axle under dynamic loading is studied. Two dynamic

conditions are considered: impact loading due to impact with a foreign object and dynamic loading

under the action forces resulting from wheel rail interaction.

2. BENCHMARK HOLLOW STEEL AXLE

The inboard bearing, trailer wheelset configuration provided by Lucchini RS is shown in Figure 2.

This wheelset, and in particular the axle, serves as a benchmark against which the HMC railway

axle is designed.

Figure 2. A typical inboard bearing, trailer wheelset with general dimensions including wheels and a hollow axle (Source: Lucchini RS).

The axle, item 1, is made from EA1N grade steel and has a mass of 198 kg. Each wheel, item 2,

is made from ER7 Grade steel and has a mass of 331 kg. Two brake discs (not shown) are attached

to the wheel web with fasteners and have an approximate mass of 100 kg each. Therefore, the

estimated mass of the wheelset, excluding bearings, is approximately 1060 kg. While the majority

of mass is associated with the wheels (62%), the axle mass is significant at 16% of the wheelset

mass.

1500 mm

1360 mm

1 2

ɸ1

50

0 m

m

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Figure 3 shows the trailer axle with overall dimensions. The axle is manufactured by a process of

hot forging with interfacing surfaces being post machined. Lightweighting of the steel axle is

accomplished by boring a through hole of 90 mm diameter, 𝐷𝑖.

Figure 3. The benchmark, hollow steel (EA1N), inboard bearing trailer axle showing general dimensions (Source: Lucchini RS).

2.1 DEFINITION OF CRITICAL SECTIONS ALONG THE RAILWAY AXLE

Figure 4. Critical section diameters a distance 𝑦 along the axle and defined as positions

for evaluation.

The axle includes a number of critical sections along the length as set out in Figure 4 and Table 1.

These represent positions where the shaft diameter requires evaluation in terms of stress or is a

where a deflection is measured. A global, right hand coordinate system is established whereby the

1500 mm

1156 mm

1672 mm

ɸ155 mm OD ɸ177 mmID ɸ90 mm

Plane A: running surface

Plane D: loading plane

A B C D E F A’D’

RHSLHS

Plane A’: running surface

Plane D’: loading plane

y

E’

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axis of the axle is along the y-direction with the x-axis pointing in the direction of wheelset travel

(the xy-plane is parallel to the ground) and the z-axis points vertically upward. The Position 𝑦 of

each section is measured from the left-hand side (LHS) in the direction of the right-hand side (RHS).

The outer diameter, 𝐷𝑜, of the axle is specific to the section at Position 𝑦. The running surfaces

(Positions 𝐴 and 𝐴’) are the locations where the reaction forces from the rails are applied to the

wheels. The loading planes (Positions 𝐷 and 𝐷’) are the locations where the bearing loads are

applied to the axle (at the centre of the journal).

Table 1. Description of the critical section positions along the axle with distance, 𝒚, from the left-

hand side (LHS) and a corresponding outer diameter, 𝑫𝒐.

Position Description 𝒚 (mm) 𝑫𝒐 (mm)

A Theoretical wheel centre defining the running

surface on the LHS

0.0 177.0

B Inner edge of the wheel seat 70.0 177.0

C Bottom of the transition between the wheel seat

and bearing journal

90.0 161.5

D Bearings system centre defining the loading plane

on the LHS

172.0 178.5

E Bottom of the transition between the shoulder and

the axle body on the LHS. For the HMC, the

position where the collar ends and the secondary

composite tube begins on the LHS

326.0 155.0

F Middle section of the axle 750.0 155.0

E’ Bottom of the transition between the shoulder and

the axle body on the RHS. For the HMC, the

position where the collar ends and the secondary

composite tube begins on the RHS

1174.0 155.0

D’ Bearings system centre defining the loading plane

on the RHS

1328.0 178.5

A’ Theoretical wheel centre defining the running

surface on the RHS

1500.0 177.0

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3. LOAD CASES

Axle verification is carried out according to the method described in Standard BS 8535 [1]. The

Standard specifies two load cases for consideration when investigating the structural behaviour of

an axle:

Load case 1 – Straight track and mechanical braking.

Load case 2 – Low speed curving and mechanical braking.

For both cases, the axle undergoes four point bending predominantly about the x-axis due to the

static weight of the train. The Standard refers to this as the “masses in motion,” and the associated

bending moment is designated as 𝑀𝑥. Braking introduces additional bending around the x-axis (𝑀𝑥′ )

with a component of bending around the z-axis (𝑀𝑧′) as the braking force is applied. Additionally,

forces develop at the wheel due to conicity and braking so that a moment about the y-axis, 𝑀𝑦′ , is

produced. The Standard specifies this moment, 𝑀𝑦′ , to be constant along the axle, and

representative of the all bending around the y-axis. Intuitively, this manifests itself as torque, or

torsion so these terms are applied to 𝑀𝑦′ within this document.

Importantly, the bending moments applied to the axle causes fully reversed fatigue loading.

Historically, this is the primary cause of failure of a railway axle [2]. For an axle having a service

life of 30 years, the number of fully reversed bending cycles in fatigue is taken as 109 cycles.

Simple and transverse shear stresses occur under static loading with torsion introduced under

braking creating torsional shear. For powered axles, the torsional shear can be significant. For

example, a pinion gear on the axle in mesh with a traction motor at start up illustrates such a case.

This additional torsional moment would be described as 𝑀𝑦′′. Similarly, traction generates moments

about the x and y-axes, denoted as 𝑀𝑥′′ and 𝑀𝑧

′′ , respectively. For the particular case of the

unpowered trailer axle, traction moments are not included.

Buckling under combined bending and torsion at the middle section of the axle is discounted as the

slenderness ratio (length/diameter) of the axle will be less than 10 and the wall of the axle is

relatively thick compared to the outer diameter (27 mm:169 mm).

The Standard is clear that both load case 1 and 2 require consideration and the worst load case is

used for the axle design.

3.1 LOAD CASE 1

Load case 1 represents a condition where the axle loading is distributed equally on each journal.

Asymmetric loading can occur when un-sprung elements such as brake discs or pinion gears are

attached to the axle. This, in combination with accentuated dynamic effects at high speeds, can

result in load case 1 being the worst-case loading condition.

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For the benchmark hollow steel axle (Figure 3), the moments are provided by Lucchini at the critical

sections listed in Table 2. Between the loading planes, position 𝐷 to 𝐷’, the axle is in pure bending

and bending moment is greatest. As a worst-case, a resultant moment, 𝑀𝑅, is used to combine

the moments about the x and z-axes. Generically, the term bending moment is used for 𝑀𝑅 within

this document particularly where associated axle deflections are discussed. 𝑀𝑅 is calculated as

follows:

𝑀𝑅 = √(𝑀𝑥 + 𝑀′𝑥)2 + 𝑀′𝑧

2

It is noted that this calculation of the resultant moment, 𝑀𝑅, differs from the Standard [1] in that it

does not include the moment about the y-axis, 𝑀𝑦′ .

For the benchmark steel axle under load case 1, the maximum resultant moment, 𝑀𝑅 , is

19,392,335 Nmm with a notional torque, 𝑀𝑦′ , of 6,533,460 Nmm. The static bending about the x-

axis, 𝑀𝑥, occurs, as expected, between loading planes with a magnitude of 15,419,135 Nmm.,

Table 2. Moment values at the critical sections along the axle for load case 1.

Position 𝑀𝑥 (N·mm) 𝑀𝑥′ (N·mm) 𝑀𝑧

′ (N·mm) 𝑀𝑅 (N·mm) 𝑀𝑦′ (N·mm)

A 0 0 0 0 6,533,460

B 6,275,229 1,617,000 751,686 7,927,945 6,533,460

C 8,068,152 2,079,000 966,454 10,193,073 6,533,460

D 15,419,135 3,973,200 1,847,001 19,392,335 6,533,460

E 15,419,135 3,973,200 1,847,001 19,392,335 6,533,460

F 15,419,135 3,973,200 1,847,001 19,392,335 6,533,460

3.2 LOAD CASE 2

Load case 2 occurs infrequently and relates to low-speed curving where dynamic effects are less

pronounced. In this case, the back of the flange of one wheel is constrained laterally by the check

rail. This causes the train to tilt outward and the outside journal (LHS) becomes more heavily loaded

than the inside one.

For the benchmark steel axle, the moments are provided by Lucchini at the critical sections given

in Table 3. At the LHS loading plane, Position 𝐷, the journal is most heavily loaded, and the

resultant moment is greatest. Unique to load case 2, an external load is generated outboard of the

running surface, Position A, so that 𝑀𝑥 is greater than zero at that location.

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For the benchmark hollow steel axle under load case 2, the maximum resultant moment, 𝑀𝑅, is

22,283,141 Nmm with a notional torque, 𝑀𝑦′ , of 6,533,460 Nmm. Note that the torque, 𝑀𝑦

′ , is

unaffected by the non-symmetrical resultant moment and is equivalent to that in load case 1. The

static bending about the x-axis, 𝑀𝑥, is maximum at the loading plane on the LHS, Position 𝐷, with

a magnitude of 18,233,262 Nmm.,

Table 3.3. Moment values at the critical sections along the axle for load case 2.

Position 𝑀𝑥 (Nmm) 𝑀𝑥′ (Nmm) 𝑀𝑧

′ (Nmm) 𝑀𝑅 (Nmm) 𝑀𝑦′ (Nmm)

A 5,597,281 0 0 5,597,281 6,533,460

B 10,739,831 1,617,000 751,686 12,379,673 6,533,460

C 12,209,131 2,079,000 966,454 14,320,779 6,533,460

D 18,233,262 3,973,200 1,847,001 22,283,141 6,533,460

E 18,169,423 3,973,200 1,847,001 22,219,522 6,533,460

F 17,993,660 3,973,200 1,847,001 22,044,372 6,533,460

3.3 FINAL LOAD CASE

As the resultant moment, 𝑀𝑅, is greatest under load case 2, this is used as the worst-case load

condition for the design of an HMC railway axle as a replacement for the benchmark hollow steel

axle. Although load case 2 produces the maximum resultant moment at the LHS loading plane

(Position 𝐷), for the analysis, an 𝑀𝑅 of 22,283,141 Nmm is applied equally at the journal loading

planes on both sides of the axle (Positions 𝐷 and 𝐷′). This will produce pure bending between the

loading planes so that the resultant moment at Position 𝐷 will be the same as that at Positions 𝐸,

𝐹 and 𝐷’. Furthermore, although the resultant moment combines braking loads around the x- and

z-axes, the moment will be applied singularly about the x-axis. This will provide a worst-case

deflection at the centre span in the z-direction (downward) and simplifies conceptualisation of the

axle behaviour. As previously explained, the resultant moment, 𝑀𝑅, is referred to generally as the

bending moment. Under this application of 𝑀𝑅 there is no shear force, 𝑉, in the HMC railway axle.

As a result, there is no transverse shear developed under this condition between the running and

loading planes.

The static load case is defined by the greatest static moment (load case 2), 𝑀𝑥, of 18,233,262

Nmm being resolved into a point load, 𝑃, acting at the journal loading planes on both sides of the

axle (Positions 𝐷 and 𝐷′ ) multiplied by the distance between the running and loading planes

(Positions 𝐴 and 𝐷) of 172 mm. As a result, 𝑃 has a magnitude of 106,007 N, with a corresponding

reaction, 𝑄, at each wheel (Positions 𝐴 and 𝐴′). Under this static loading condition, a constant shear

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force, 𝑉, develops in the HMC axle between the running and loading planes (Positions 𝐴 and 𝐷).

As a result, transverse shear developed under this condition between the running and loading

planes.

For completeness, the clockwise moment, 𝑴𝒚′ , is applied to the axle such that a constant

magnitude of 6,533,460 Nmm developed. This moment about the y-axis, 𝑴𝒚′ , is referred to simply

as the torque or torsional moment.

4. LOADING CONDITIONS AND STRUCTURAL PERFORMANCE PARAMETERS OF THE WHEELSET

For analysis of the wheelset, the resultant moment, 𝑀𝑅 is applied at the loading planes, Positions

𝐷 and 𝐷’ for the bending case. The static load, 𝑃, is used for calculation of the transverse shear.

For torsional loading, the moment, 𝑀𝑦′ , is applied about the y-axis, although this is not done in

combination with the bending moment, 𝑀𝑅, or the static load, 𝑃.

The global loading diagram is shown in Figure 5.

Figure 5. A typical railway wheelset with the resultant moment, 𝑴𝑹, applied at the loading planes, 𝑫

and 𝑫’, causing the greatest bending about the x-axis. The static load, 𝑷, is used for calculation of

transverse shear, is applied separately at the same position. The torsional moment, 𝑴𝒚′ , is applied

uniformly about the y-axis.

A A’

D D’

My’

MR

My’

MR

P P

QQ

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The corresponding shear and moment diagrams are shown in Figure 6.

For the static load case, under load 𝑃 the shear force, 𝑉, is constant and positive between the LHS

running surface (Position 𝐴) and LHS loading plane (Position 𝐷). Between the LHS and RHS

loading planes (Positions 𝐷 and 𝐷’, respectively), the shear force reduces to zero. Between the

RHS loading plane (Position 𝐷’) and the RHS running surface (Position 𝐴’) the shear force is

constant and negative, being equal and opposite to the simple shear on the LHS. The static

moment, 𝑀𝑥, is zero at the LHS running surface (Position 𝐴) and increases linearly to the maximum

value at the LHS loading plane (Position 𝐷). The axle is in pure bending and the moment is constant

between the LHS and RHS loading planes (Positions 𝐷 and 𝐷’ , respectively). The resultant

moment reduces from the maximum to zero between the RHS loading plane (Position 𝐷’) and the

RHS running surface (Position 𝐴’).

For the case where the resultant moment, 𝑀𝑅, is applied, the shear force, 𝑉, is zero across the

entire axle. The moment is zero between Positions 𝐴 and𝐷. At this position the moment is applied

and is constant up to Position 𝐷′. Beyond Position 𝐷′ the moment returns to zero to Position 𝐴′.

The clockwise positive torsional moment, 𝑀𝑦′ , is constant across the axle from the LHS running

surface (Position 𝐴) to the RHS running surface (Position 𝐴’).

Figure 6. Axle loaded with the resultant moment, 𝑴𝑹. The static load, 𝑷, is superimposed for

calculation of transverse shear. The torsional moment, 𝑴𝒚′ , is constant across the axle. (a) Shear

diagram (b) Moment diagram.

A A’D D’

= 106,007 N

= 22,283,141 Nmm

= 6,533,460 Nmm

Static

Loading

Resultant

Loading

= 18,233,262 Nmm

= 106,007 N

0 N

0 Nmm

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Reference to the shear and moment diagrams, Figures 6a and b respectively, along with the critical

sections diagram, Figure 4, allows identification of the positions of maximum stress within the axle.

4.1 POSITION OF MAXIMUM BENDING STRESS

The maximum bending stress, 𝜎𝑅, occurs between the loading planes 𝐷 to 𝐷’ where the resultant

moment, 𝑀𝑅, is constant and at a maximum. The stress is defined as:

𝜎𝑅 =𝑀𝑅 ∙ (

𝐷𝑜2 )

𝐼

The hollow tube has an outer diameter, 𝐷𝑜, and an inner diameter, 𝐷𝑖, and the second area moment

of inertia, 𝐼, is as follows:

𝐼 =𝜋

64(𝐷𝑜

4 − 𝐷𝑖4)

By inspection, the maximum bending stress occurs at the position where the tube is thinnest. This

relates to Position 𝐸 on the axle.

4.2 POSITION OF MAXIMUM DEFLECTION

Associated with the maximum bending moment is the maximum deflection, 𝛿𝑚𝑎𝑥, in the axle that

results. This occurs at the centre of the span, Position 𝐹, and is calculated as:

𝛿𝑚𝑎𝑥 =𝑃 ∙ 𝑎

24 ∙ 𝐸 ∙ 𝐼(3 ∙ 𝐿2 − 4 ∙ 𝑎2)

Where the journal load at Position 𝐷 is denoted as 𝑃 and 𝑎 is the distance between Positions 𝐴

and 𝐷. The length between the running surfaces is indicated by 𝐿. The Young’s modulus is 𝐸 and

𝐼 is calculated as for the maximum bending stress (Section 4.1).

4.3 ANGULAR MISALIGNMENT AT THE JOURNALS

The extent of axle bending leads to an angular misalignment with the bearings. The degree of

angular misalignment, 𝜃, at the loading plane, 𝐷, is important for specifying the bearings that can

be used on the axle. As a guide, a deep groove ball bearing can sustain an angular misalignment

between 4° and 7° [3]. The angular misalignment is the angular distance between the straight axis

of the undeflected axle and the tangent to the curved axis of the deflected axle as depicted in Figure

7.

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Figure 7. Diagram showing the amount of angular misalignment, 𝜽, at the journal for the axle undergoing bending.

The angular misalignment is calculated as:

𝜃 =𝑃 ∙ 𝑎 ∙ (𝐿 − 𝑎)

2 ∙ 𝐸 ∙ 𝐼

4.4 BACK-TO-BACK DISTANCE BETWEEN WHEEL FLANGES

Axle deflection also affects the back-to-back distance between wheel flanges at rail level (Figure

8). The requirement for the allowable back-to-back distance is stated in TSI Loc & Pass 1302 /

2014 (Technical Specification of interoperability “Loc & Pass”), clause 4.2.3.5.2.1 [4]. As a guide,

the back-to-back distance (at rail level) should remain within a 6 mm tolerance in both crush and

tare conditions. As the axle deflects downwards, the wheels splay outwards on each side by

(∆𝐿𝐵𝑡𝐵)/2) so that the total increase in the back-to-back distance is ∆𝐿𝐵𝑡𝐵.

Figure 8. Back-to-back distance, 𝑳𝑩𝒕𝑩, as measured between flanges at rail level. As the axle

deflects downwards, the overall back-to-back distance increases by ∆𝑳𝑩𝒕𝑩.

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4.5 FIRST CRITICAL SPEED

The flexural rigidity of the axle, 𝐸𝐼, influences stability in terms of the critical speed. At the critical

speed, the deflections in the rotating axle would increase to an unbounded limit without restraint by

the bearings. Assuming a maximum trains speed of 200 mph running on a wheel of diameter 850

mm, equates to an angular velocity of 209 rad/s, or 33 Hz. The first critical speed is expressed as:

𝜔1 = (𝜋

𝐿)

2

∙ √𝐸 ∙ 𝐼

𝑚𝑙

Where 𝑚𝑙 is the axle mass per unit length and all other variables are as defined

previously.Standard BS EN 61373 [5], indicates a bending frequency of 90 – 110Hz, a reserve

factor, RF, of 3. For the analysis, the distance between the loading planes, Positions 𝐷 to 𝐷’ is

used for the length, 𝐿.

4.6 POSITION OF MAXIMUM TRANSVERSE STRESS

For the static load case, shear stress occurs between the running surfaces and loading planes (for

example, between Positions 𝐴 and 𝐷, respectively).

The average shear stress, 𝜏𝑎𝑣𝑔, across the diameter of an axle section in this region is calculated

as:

𝜏𝑎𝑣𝑔 =𝑉

𝐴

Where 𝐴 is the cross-sectional area of the hollow axle and is expressed as:

𝐴 =𝜋 ∙ (𝐷𝑜

2 − 𝐷𝑖2)

4

However, the maximum shear stress across the axle section is a transverse stress due to bending

occurring at the neutral axis and is calculated as:

𝜏𝑚𝑎𝑥 =𝑉 ∙ 𝑄

𝐼 ∙ 𝑡

Referring to Figure 9, the first area moment of inertia, 𝑄, for a hollow tube at the neutral axis where

it is greatest can be calculated by subtracting an inner (negative area) semi-circular section from

an outer (positive area) semi-circular section as:

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Figure 9. Calculation of the first moment area of inertia, 𝑸, for a hollow tube at the neutral axis of the axle.

So

𝑄 = 𝑄𝑂𝑢𝑡𝑒𝑟 − 𝑄𝐼𝑛𝑛𝑒𝑟 =1

2∙ 𝜋 (

𝐷𝑜

2)

2

∙4

3𝜋(

𝐷𝑜

2) −

1

2∙ 𝜋 (

𝐷𝑖

2)

2

∙4

3𝜋(

𝐷𝑖

2)

And the thickness of the transverse shear plane, 𝑡, is the total wall thickness along the neutral axis

as shown in Figure 9.

𝑡 = 𝐷𝑜 − 𝐷𝑖

It is clear that for a constant wall thickness, 𝜏𝑚𝑎𝑥 will be greatest where the diameter of the hollow

axle is the least. Within region 𝐴 to 𝐷 this occurs in the stress relief groove at Position 𝐶.

4.7 POSITION OF MAXIMUM TORSIONAL STRESS

The torsional moment, 𝑀𝑦′ , produces a shear stress, 𝜏𝑡𝑜𝑟𝑠𝑖𝑜𝑛, which reaches a maximum at the

outer diameter of the tube and is calculated as:

𝜏𝑡𝑜𝑟𝑠𝑖𝑜𝑛 =𝑀𝑦

′ ∙ (𝐷𝑜2

)

𝐽

Where the polar moment of inertia, 𝐽, for a hollow tube is defined as:

𝐽 =𝜋

2∙ [(

𝐷𝑜

2)

4

− (𝐷𝑖

2)

4

]

Generally, the torsion is constant across the axle from Position 𝐴 to 𝐴′. However, the loading

scenario is taken as a seized bearing at Position 𝐷. Under this condition, the region between

Positions 𝐴 and 𝐷 is subject to 𝑀𝑦′ and the maximum torsional stress would occur at the thinnest

point, Position 𝐶.

4.8 MAXIMUM ANGULAR TWIST

The maximum angular twist, 𝜑, arises due to the torsional moment, 𝑀𝑦′ . As with the torsional

shear stress (Section 4.7) the condition is taken whereby the bearing is seized at Position 𝐷 so

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that the twist occurs between Positions 𝐴 and 𝐷, with a maximum at Position 𝐷. The amount of

twist is calculated as:

𝜑 =𝑀𝑦

′ ∙ 𝐿

𝐽 ∙ 𝐺

The shear modulus is defined as 𝐺 and the other variables are as defined previously. The angular

twist increases per unit increase in axle length.

5. FINITE ELEMENT ANALYSIS (FEA) OF THE WHEELSET MODEL

The benchmark, hollow steel and HMC axles are modelled individually using ABAQUS 2018 [6].

The same loading and boundary conditions are used, defined as a quasi-static analysis, with non-

linearity assumed. For both the steel and HMC axles two finite element approaches are adopted to

assess the structural response against the applied bending moments. These are a 3D continuum

model (Model 1), as well as a separate axisymmetric analysis (Model 2), to assess the axle to hub

interaction. To provide verification, a further beam element model (Model 3) was employed to

confirm the system configuration and accuracy of the 3D stress model. The following section

outlines the modelling approach used for both the hollow steel and HMC axles. To reduce

duplication, the HMC axle is used as a representation.

5.1 MODELLED AXLE SYSTEMS

For the 3D model (Model 1), the wheelset is modelled with only half symmetry along the y-axis.

The axle is modelled as two individual parts. The first part is the composite axle comprising the

primary and secondary tubes. The second part is the steel collar with one at each end of the axle.

The collars are modelled as eight node, linear solid elements (C3D8), with full integration and an

isotropic material definition. The primary composite tube is modelled as four node, linear,

conventional shell elements (S4), with full integration. To allow the use of shell elements, the

secondary tube is simplified to neglect the end tapers. The representative mesh for both the collar

and composite axle is given in Figure 10a with an average element size of 10mm.

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Figure 10. HMC axle model element mesh. (a) Model 1-3D solid model, showing element mesh for the composite axle with the RHS collar attached. The LHS collar is removed to show cohesive elements beneath representing adhesive. (b) Model 2-Axisymmetric model, with element mesh for the primary composite tube, collar and interfacing wheel.

The primary composite tube is defined as a laminate material section, with a single integration point

at the midpoint of each ply through the thickness. The contact and interaction between the primary

tube and the collar is modelled using cohesive elements, with a continuum, isotropic material

response. These solid elements of 0.2 mm thickness represent adhesive and are offset from the

primary tube surface, with the orphan mesh sharing the connected nodes of the base of the shell

elements.

For the interference analysis a separate axisymmetric model (Model 2) is created to perform a

localised detailed assessment of contact interaction between the wheel hub and axle. The

wheelset, shown in Figure 10b, with the axle, consisting of the collar and primary composite tube,

is modelled with 4 node, bilinear, axisymmetric, linear elements (CAX4), with full integration.

Cohesive elements with linear, continuum response (COHAX4) and 0.2 mm height are defined

between the collar and tube to represent the adhesive. To account for the stiffness properties in

the composite tube, classical laminate theory (CLT), developed in MATLAB [7], is used to calculate

the inter-ply (E3) stiffness modulus (17.23 GPa), accounting for the sectional properties of laminate

thickness and ply fibre stacking sequence.

The beam element verification model (Model 3), for both axles, is modelled using three node,

quadratic elements (B32). This approach is used to confirm the boundary conditions and application

of loads by comparing the observed locational displacements and bending moment. The axle is

defined as a thick-walled pipe cross section, with varying representative sectional and material

properties along its length. The effective material properties of the composite tube are calculated

using the same CLT approach to determine the axial tensile stiffness modulus. Using the

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Timoshenko (thick wall) formulation, the B32 element allows for transverse shear deformation, with

the stiffness assumed, calculated by default, to be linear elastic with a fixed modulus [6].

The finite element modal analysis is conducted to confirm initial investigation of the critical axle

speed by analysis the first modal frequency using both the 3D element (Model 1) and beam element

(Model 3) models. Both models are defined for the axle profile considering only the unsupported

length between the journals, D to D’, without any external force, constraint or inertial masses being

considered. The first eigenvalue is evaluated using a linear frequency analysis, with the Lanczos

solver.

5.2 LOADING CONDITIONS

The resultant moment, 𝑀𝑅, and the torsional moment, 𝑀𝑦′ , are applied at the axle journal Positions

𝐷 and 𝐷’, the loading planes. The loads are applied in the 3D model (Model 1) to the surface of the

journal seats using a coupling, defined as kinematic. This coupling types adds rotational degrees

of freedom at the journal surface so that angular (misalignment) values can be extracted. The

surface nodes constrain both the translational and rotational degrees of freedom (DOF) to a single

reference point at the centre line of the bearing where the coordinate x=z=0. Utilising this constraint,

a single moment load is applied to the control node and distributed to the seat surface.

For the axisymmetric model (Model 2), the loading is defined as an interference fit between the

axle and the wheel hub. The surface contact and interaction properties are defined between the

hub and collar edges, with a nodal overlap and finite-sliding, ‘hard’, contact-overclosure. The

interaction tangential behaviour coefficient is given as 0.8. Alternative values in the range 0.5 to 1

showed little sensitivity in the stress result field.

For the beam model, bending moments are simply applied to a single node located at the centre

line point of each journal, where coordinates y=z=0.

5.3 BOUNDARY CONDITIONS

To confirm the back-to-back deflection, the axle is required to be modelled as a wheelset, where

the axle collar is connected to the wheel at the forged hub. Boundary conditions for the wheelset,

annotated in Figure 11, are defined for both wheels. Note that u represents displacement with 1, 2,

and 3 relating to the x, y and z directions, respectively. Furthermore, ur represents rotation with 1,

2, and 3 relating to the x, y, and z axes. The left wheel is constrained along the centre of the wheel

at the running surface, Position 𝐴, with displacement u3=ur2=0 and at a single node where the

wheel rim and rail intersect as u2=0. For the right wheel, the centre line is constrained at the running

surface, Position 𝐴’, in the vertical direction with u3=ur2=0.

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Figure 11. Boundary conditions for the wheelset model applied to the running surfaces where the rail and wheel contact. At Position 𝑨, u3=u2=ur2=0 and Position 𝑨’, u3=ur2=0.

For simplicity and to reduce computational time, when not considering the back-to-back deflection,

the axle was modelled without the wheels. Representative boundary conditions employed through

a kinematic coupling between the axle hub contact surface and a reference point. Here, both

translational and rotational degrees of freedom (DOF) are constrained. The control node located

at the centre line of on the hub (z=x=0) is then constrained as u2=u3=ur2=0 and u3=ur2=0 for the

left and right conditions, respectively.

Both the wheelset and axle configurations adopt symmetry boundary conditions on the half model

in the yz-plane (xsymm) as u1=u3=ur2=0.

For the beam element model, boundary conditions are applied as simply supported, four-point

bending for the axle only. A single node located at the hub centre line, is constrained with z=y=0

and z=0 for the left and right sides, respectively.

5.4 MODEL VERIFICATION

To confirm the boundary conditions and applied bending moments, a simple comparative

verification study was done for the comparisons of the maximum deflection of the wheelset against

both the axle (defined without the wheels) and beam element model. For both comparative results

studies, there was an error percentage difference of less than 0.1 % and 3.2 % for the steel and

HMC axle respectively.

A second verification comparison for the deflection results was made to assess the maximum

central deflection imposed by MR, loaded in the x direction, compared against the individual

application of the bending moments 𝑀𝑥, 𝑀𝑥′ , and 𝑀𝑧

′ in the corresponding axial planes. The MR

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results gave percentage increase in the maximum vertical deflection of 0.45 %. This concludes that

the resultant moment, as defined in BS 8535 [1], is a more conservative approach.

5.5 ASSUMPTIONS FOR THE FEA WHEELSET MODELLING

A number of assumptions are made in the analysis of the benchmark hollow steel axle and

subsequent HMC axle. These include:

• The analysis is assumed to be a quasi-static, linear elastic analysis only, with no dynamic

effects being considered.

• The primary and overwrapped secondary composite tubes are to be manufacture by co-

curing and considered as one component in the model.

• While a 0.2mm adhesive layer is included within the model, the adhesive results are not

considered within the analysis.

• High cycle fatigue will reduce the ultimate strength of the steel and composite materials by

50%.

• Environmental and adiabatic effects, caused by material expansion and contraction, are not

considered.

• Failure analysis, where a linear first point of failure causes the evolution of composite

damage is not considered.

6. STRUCTURAL CHARACTERISATION OF THE BENCHMARK, HOLLOW STEEL AXLE

The FEA model of the hollow steel axle is characterised in relation to the loading conditions defined

Section 5.2 with the boundary condition set out in Section 5.3.

Specific material property inputs to the FEA model are required. The axle is manufactured from

EA1N grade steel (approximated as AISI 1030 steel) with mechanical properties listed in Appendix

A, Table A1. The properties of the wheel are taken as AISI 1050 grade steel to approximate ER7

grade steel and listed in Appendix A, Table A2.

The structural performance parameters of the wheelset identified within Chapter 4 are investigated.

Results from the FEA model of the benchmark hollow steel axle are presented in Table 4.

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Table 4. Structural performance of the benchmark hollow steel axle.

Parameter Position

Figure 4

Simplifying

Equation

FEA Value

Benchmark

Hollow Steel

Axle

(Model 1)

Mass - 𝑚 = 𝜌 ∙ 𝑉 196.3 kg*

Maximum interference stress at

wheelseat, von Mises

A 319.20 MPa

(Model 2)

Maximum bending stress, von

Mises, 𝜎𝑅

E

𝜎𝑅 =𝑀𝑅 (

𝐷𝑜2

)

𝐼

(Section 4.1)

73.64 MPa

MR

Reserve Factor in bending after 107

cycles

E 𝑅𝐹 =𝜎𝑆𝑡,𝑓𝑎𝑡 107

𝜎𝑅

=270 𝑀𝑃𝑎

73.64 𝑀𝑃𝑎

3.7

Maximum deflection, 𝛿𝑚𝑎𝑥 F 𝛿𝑚𝑎𝑥 =

𝑃𝑎

24𝐸𝐼

∙ (3𝐿2 − 4𝑎2)

(Section 4.2)

1.123 mm

MR

Angular misalignment at bearings, 𝜃 D 𝜃 =

𝑃𝑎 ∙ (𝐿 − 𝑎)

2𝐸𝐼

(Section 4.3)

0.134°

MR

Back-to-back displacement, ∆𝐿𝐵𝑡𝐵 Between

wheel

flanges at rail

level

(Section 4.4) 2.017 mm

MR

Maximum transverse shear, 𝜏𝑚𝑎𝑥 C 𝜏𝑚𝑎𝑥 =

𝑉 ∙ 𝑄

𝐼 ∙ 𝑡

(Section 4.6)

14.82 MPa

𝑀𝑥

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Maximum torsional stress, 𝜏𝑡𝑜𝑟𝑠𝑖𝑜𝑛 C 𝜏𝑡𝑜𝑟𝑠𝑖𝑜𝑛

=𝑀𝑦

′ ∙ (𝐷𝑜2

)

𝐽

(Section 4.7)

10.20 MPa

𝑀𝑦′

Maximum angular twist, 𝜑

At D from A

𝜑 =𝑀𝑦

′ ∙ 𝐿

𝐽 ∙ 𝐺

(Section 4.8)

0.008 °

𝑀𝑦′

First critical axle speed, 𝜔1

D to D’

𝜔1 = (𝜋

𝐿)

2

∙ √𝐸𝐼

𝑚𝑙

(Section 4.5)

233.79 Hz

*Mass supplied by Lucchini is 198 kg

7. HMC RAILWAY AXLE DESIGN

Definition of the structural performance parameters of the benchmark, hollow steel axle as

characterised within Table 4 establishes conformance criteria for the design of a replacement HMC

railway axle.

The parametric approach to size this concept shown in Figure 1 was overly simplistic as bulk

strength properties were used for the CF reinforced epoxy laminate. Furthermore, geometric

features were not taken into account. In elevating the design fidelity of the concept, the composite

is treated as a laminae stack (a laminate) and analysed using classical laminate theory (CLT).

Abaqus FEA includes numerical methods for a full CLT analysis to be undertaken. The loading,

boundary conditions and assumptions are applied as used for the benchmark, hollow steel axle

described in Chapter 5. The aim is to achieve conformance with the structural performance of the

hollow steel axle set out in Table 4. The composite material used is a conventional, unidirectional

carbon fibre reinforced epoxy prepreg (UCHM450 SE 84LV) supplied by Gurit. While this prepreg

incorporates high modulus carbon fibre, it can be treated as a generic material whose equivalent

could be sourced from other suppliers. The HMC railway axle resulting from the Abaqus CLT

analysis is presented in Figure 12.

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Figure 12. HMC railway axle comprising a full length, primary composite tube, a secondary composite tube and metallic collars as introduced in Figure 1. Abaqus 2018 has been used to size the primary and secondary composite tubes as well as the metallic collars.

The design methodology for the HMC railway axle is as follows:

• Design the metallic collars so that the wall thickness is sufficient to carry the external

pressure load imposed by the interference fit of the wheel onto the collar.

• Design the primary composite tube of the axle so that the outer diameter is coincident with

the inner diameter of the metallic collar. Specify the ply layup and tube thickness to meet

the maximum bending, torsional and transverse shear stress conditions.

• Design the secondary composite tube so that the inner diameter is coincident with the outer

diameter of the primary composite tube. Specify the ply layup so that the centre deflection

of the axle is minimised. In reducing the deflection of the axle, the secondary composite

tube will serve to further reduce the bending stresses within the primary composite tube,

hence the overall HMC axle.

These design sequences are considered in more detail in the following sections.

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7.1 DESIGN OF THE METALLIC COLLARS AND PRIMARY COMPOSITE TUBE DUE TO

EXTERNAL PRESSURE LOADING AT THE INTERFERENCE FIT, POSITION 𝑨

The requirement is to use the existing wheels and bearings on the HMC railway axle. The axle

diameter at the journal is necessarily larger than that of the wheel seat so that the inboard bearing

arrangement can be assembled. In addition, the interference fit of the rolling element bearing on to

the axle is less than that of the wheel against the axle. Hence, the critical diameter relating to the

interference fit is at Position 𝐴 on the loading plane. A cross section through the axle at this location

is shown in Figure 13.

Figure 13. Cross section through the HMC axle at the running surface (Position 𝑨) showing the diameters of the metallic collar and the primary composite tube.

The outer diameter of the collar is 177 mm and is aligned with the inner diameter of the wheel hub.

The thickness of the collar is modelled as either 17.5 mm when no adhesive is considered and as

17.3 mm when adhesive is present, a 0.2 mm bond line. The overall collar thickness dictated by a

necessity to maintain an existing geometric feature in the end of the axle.

The primary composite axle tube has an outer diameter of 142 mm and inner diameter of 115 mm.

The wall thickness is 13.5 mm. The layup is balanced with 30 plies (see Figure 12). The layup is

apportioned as 40% 0° fibres, 40% +/-45° fibres and 20% 90° fibres.

Figure 14 shows a global representation of the von Mises stresses within the steel collar and

primary composite tube due to the external pressure load introduced by the interference fit between

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the wheel hub and the axle collar. In this case, the resultant moment, 𝑀𝑅, and torque, 𝑀𝑦′ , are not

applied to the model.

Figure 14. von Mises stress at the wheelseat from external pressure loading due to the interference fit between the wheel hub and steel collar. The resultant stresses within the primary composite tube are minimal. Note that the adhesive is not included as a worst case.

The maximum stress occurs within the collar near the interface with the primary composite tube. It

is noted that the adhesive bond (0.2 mm thick) has not been included in the analysis as a worst

case. This indicates that while the radial stress reduces from the outer diameter to the inner

diameter of the collar, the circumferential stress increases and becomes the dominate stress in the

collar. However, at 358.50 MPa the maximum stress is less than the yield strength of the collar

(EA1N grade steel) at 440 MPa. The conclusion is that collar could be further reduced in thickness

from 17.3 mm. However, the required geometric feature within the axle end prevents further

thinning.

Analysis of the primary composite tube at the same location shows a maximum compressive von

Mises stress of 13.65 MPa occurring at the outer diameter of the tube where contact occurs with

the collar. This stress is driven predominately by the circumferential stress imparted by the collar

into the primary composite tube, although a component of radial stress arises as the inner diameter

of the collar deflects inward. The 20% proportion of 90° fibres are aligned with the circumferential

stresses within the tube and provide support due to the compressive strength.

7.2 DESIGN OF THE METALLIC COLLAR AND PRIMARY COMPOSITE TUBE DUE TO

STATIC LOADING, 𝑴𝒙, AT POSITION 𝑪

Application of the static load, 𝑃, at the loading planes, Position 𝐷 and 𝐷′, introduces an internal

shear force, 𝑉. This produces transverse stress within the HMC axle. The shear force is constant

over the region from Positions 𝐴 to 𝐷. For a round, hollow tube, the transverse stress is maximum

at the neutral axis of the cross section.

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The transverse stress will be highest at Position 𝐶 in the collar where the wall thickness is the least.

The same location is chosen to assess the transverse shear stress in the primary composite tube.

Figure 15 shows the values of the transverse stress through the axle cross section at that location.

The 40% proportion of +/-45° fibres are aligned to provide support to the transverse stress within

the tube. The maximum surface shear stress in the primary composite tube is 1.72 MPa at the

outer ply

Figure 15. A cross section through the HMC railway axle at Position C showing the absolute maximum value of transverse the shear stress in the primary composite tube.

7.3 DESIGN OF THE PRIMARY COMPOSITE TUBE DUE TO THE RESULTANT MOMENT, MR, AT POSITION 𝑬

The maximum bending moment arises at the loading plane, Position 𝐷, and is maintained at a

constant value of 𝑀𝑅 between loading planes. The primary composite axle gains bending support

in regions beneath the collar. However, at Position 𝐸, the collar ends and the diameter of the axle

increases due to the additional 13.5 mm thickness of the secondary composite tube. The HMC axle

is analysed at Position 𝐸 just before the diameter increases. As the moment is applied about the

x-axis and purely within the yz-plane, deflection is downward in the negative z direction. This results

in the “top” of the axle being in compression while the “bottom” is in tension (Figure 16). Of

importance is that as the axle rotates, the configuration changes and the axle is subject to fully

reversed bending for each cycle.

A DC

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Figure 16. (a) Maximum von Mises stress (170.00 MPa) in the composite axle at Position 𝑬, ply 4,

bottom of primary composite tube, due to the moment, 𝑴𝑹. (b) Damage field for Hashin failure criterion highlighting fibre compression in the primary composite tube at Position 𝑬. The secondary composite tube is included in the analysis, but not shown here for clarity.

The maximum stress is at Position E and is a combination axle bending coupled with a contact

stress on the outer surface of the axle. The highest tensile stress (170.00 MPa) in the laminate due

to bending by MR is in the 0° fibres near the outer diameter of the primary composite tube at the

bottom (Figure 16, ply 4). The 40% proportion of 0° fibres are aligned to provide strength resisting

this load.

Figure 17. (a) von Mises stress at Position 𝑬, ply 27, top of primary tube, due to the moment, 𝑴𝑹, showing the peak stress of 528.10 MPa due to penetration of the collar on the top surface of the primary composite tube. (b) Damage field for Hashin failure criterion highlighting fibre compression in the primary composite tube at Position 𝑬. The secondary composite tube is included in the analysis, but not shown here for clarity.

A D

E

T

T

Top

Section T

z

x

Bottom

(a) (b)

A D

E

T

T

Top

Section T

z

x

Bottom

(a) (b)

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The peak stress in the HMC axle (528.10 MPa) is at Position 𝐸, shown in Figure 17, occurs where

the collar penetrates the outer surface of the primary composite tube at the top, shown here for ply

27. A refinement study of the mesh around the penetration of the collar and primary tube showed

little variation in the stress field when a finer mesh is adopted.

Figure 18, shows the maximum von Mises stress at Position E for each ply through the thickness

in both the primary (a) and secondary composite (b) tubes. This illustrates that the peak

compressive stress (528.10 MPa) is localised on the outer surface of the primary tube (higher ply

number), and diminishes through the tube thickness towards the inner diameter. The greatest

stress on the adjacent secondary composite tube also occurs in the outer plies (b), however, the

magnitude is less than 100 MPa as there is no collar penetration.

Figure 18. von Mises stress, Position 𝑬, at each ply of the primary composite tube (a) and secondary composite tube (b), due to the moment, MR. The high peak stress in the primary composite tube is due to penetration by the collar.

The Hashin failure criterion is applied to the composite axle at Position 𝐸. Maximum values of 0.44

and 0.39, for matrix tension (HSNMTCRT) and fibre compression (HSNFCCRT) failure,

respectively, suggest that no failure is like to occur in this region.

7.4 DESIGN OF THE PRIMARY COMPOSITE AXLE DUE TO TORSION, 𝑴𝒚′ , AT POSITION

𝑪

Application of torsion, 𝑀𝑦′ , to the HMC railway axle produces torsional stress within the system.

Generally, the torsion is constant across the axle from Position 𝐴 to 𝐴′. However, the loading

(a) (b)

Primary composite tube Secondary composite tube

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scenario is taken as a seized bearing at Position 𝐷. Under this condition, the region between

Positions 𝐴 and 𝐷 is subject to 𝑀𝑦′ and the maximum torsional stress would occur at the thinnest

point, Position 𝐶 . Figure 19 shows the torsional stress at the outer diameter of the primary

composite tube in the first 45° ply (ply 2) with a maximum torsional stress of 7.93 MPa. The 40%

proportion of +/-45° fibres are aligned to provide support to the torsional stress within the tube. The

maximum torsional stress occurring in the steel collar at Position 𝐶 is 17.88 MPa.

Figure 19. (a) Torsional stress at the outer diameter, ply 2, of the primary composite at Positions 𝑪,

due to the torsional moment, 𝑴𝒚′ . (b) Damage field for the Hashin failure criterion highlighting

matrix compression in the primary composite tube at Positions 𝑪. The secondary composite tube is included in the analysis, but not shown here for clarity.

The notional torque, 𝑀𝑦′ , also produces twist in the axle, 𝜑. The maximum angle of twist occurs at

Position 𝐷 under the scenario of a seized bearing at this location and has a value of 0.011°.

7.5 DEFLECTION CHARACTERISTICS OF THE HMC COMPOSITE AXLE DUE TO THE

BENDING MOMENT, 𝑴𝑹

Associated with the bending moment, 𝑀𝑅 , is the deflection of the axle and the angular

misalignment at the journal shown in Figure 20. The deflection is downward bending (z direction)

in the plain section of the HMC axle where the primary composite tube is reinforced by the

secondary composite tube. At Position 𝐹, the deflection is greatest, 𝛿𝑚𝑎𝑥, reaching a value of 1.702

mm. For reference, the maximum deflection of the HMC axle with the primary composite tube only

(secondary composite tube not included) is 4.190 mm. Therefore, including the secondary

composite tube decreases the deflection by 59%.

A DC

Top

Section T

z

x

Bottom

(b)(a)

T

T

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Figure 20. HMC axle under the bending moment, 𝑴𝑹. (a) Vertical displacement field plot compared against the undeformed state, with a scale factor of 20 applied showing maximum deflection, 𝜹𝒎𝒂𝒙,

at Position 𝑭. (b) Angular misalignment angle 𝜽 at Position 𝑫 caused by the axle deflection at the journal seat, with a scale factor 10 applied.

The deflection also increases the back-to-back distance by ∆𝐿𝐵𝑡𝐵 between the wheel flanges at rail

level (Figure 8). For the HMC railway axle, the change in the back-to-back distance increases by

3.212 mm which is within the accepted tolerance of 6 mm [4].

The rolling element bearings can tolerate limited angular misalignment (4-7° for a deep groove ball

bearing) for normal operation [3]. This value is taken as the degree of rotation, 𝜃, (Figure 20b)

calculated from the rotational degree of freedom around the x-axis at the surface nodes of the

journal seat for Position 𝐷. This maximum rotation, 𝜃𝑚𝑎𝑥 is equivalent to 0.212° when subject to

the moment, 𝑀𝑅.

The first critical speed, 𝜔1,of the HMC railway axle as calculated between the loading planes,

Positions 𝐷 and 𝐷′ is 388.93 Hz.

7.6 STRUCTURAL PERFORMANCE PARAMETERS

The structural performance parameters of the wheelset identified within Chapter 4 are investigated.

Results from a the full FEA model of the benchmark hollow steel axle are compared to the HMC

axle and presented in Table 5.

(a) (b)

F

Angular misalignment (b)

Maximum vertical

deflection

Angular

misalignment

D

D

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Table 5. Structural performance of the benchmark hollow steel axle vs the HMC axle.

Parameter Position

Figure 4

Simplifying

Equation

FEA

Value

Benchmark

Hollow Steel

Axle

(Model 1)

FEA

Value

HMC Axle

(Model 1)

Mass - 𝑚 = 𝜌 ∙ 𝑉 196.3 kg* 74.0 kg Total

Collars = 26 kg each

Primary composite tube =

14 kg

Secondary composite

tube = 8 kg

Maximum

interference

stress at

wheelseat, von

Mises

A 319.20 MPa

In collar

(Model 2)

358.80 MPa

In collar

13.65 MPa

In primary composite tube

(Model 2)

Maximum

bending stress,

von Mises, 𝜎𝑅

E

𝜎𝑅 =𝑀𝑅 (

𝐷𝑜

2)

𝐼

(Section 4.1)

73.64 MPa

MR

170.00 MPa


528.10 MPa

Collar penetration

MR

Reserve Factor in

bending after 107

cycles

E 𝑅𝐹 =

𝜎𝑆𝑡,𝑓𝑎𝑡 107

𝜎𝑅

3.7

=270 𝑀𝑃𝑎

73.64 𝑀𝑃𝑎

2.5

=421.7 𝑀𝑃𝑎

170.00 𝑀𝑃𝑎

0.8

=421.7 𝑀𝑃𝑎

528.10 𝑀𝑃𝑎

Hashins Criterion Pass

Maximum

deflection, 𝛿𝑚𝑎𝑥

F 𝛿𝑚𝑎𝑥 =

𝑃𝑎

24𝐸𝐼

∙ (3𝐿2 − 4𝑎2)

(Section 4.2)

1.123 mm

MR

1.702 mm

MR

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Angular misalign-

ment at bearings,

𝜃

D 𝜃 =

𝑃𝑎 ∙ (𝐿 − 𝑎)

2𝐸𝐼

(Section 4.3)

0.134°

MR

0.212°

MR

Back-to-back

displacement,

∆𝐿𝐵𝑡𝐵

Between

wheel flanges

at rail level

(Section 4.4) 2.017 mm

MR

3.212 mm

MR

Maximum

transverse shear,

𝜏𝑚𝑎𝑥

C 𝜏𝑚𝑎𝑥 =

𝑉 ∙ 𝑄

𝐼 ∙ 𝑡

(Section 4.6)

14.82 MPa

𝑀𝑥

23.17 MPa

In collar

1.72 MPa


𝑀𝑥

Maximum

torsional stress,

𝜏𝑡𝑜𝑟𝑠𝑖𝑜𝑛

C

𝜏𝑡𝑜𝑟𝑠𝑖𝑜𝑛 =𝑀𝑦

′ ∙ (𝐷𝑜

2)

𝐽

(Section 4.7)

10.20 MPa

𝑀𝑦′

17.88 MPa

In collar

7.93 MPa


𝑀𝑦′

Maximum

angular twist, 𝜑

At D from A 𝜑 =

𝑀𝑦′ 𝐿

𝐽𝐺

(Section 4.8)

0.008 °

𝑀𝑦′

0.011°*

𝑀𝑦′

First critical shaft

speed, 𝜔1

D to D’

𝜔1 = (𝜋

𝐿)

2

∙ √𝐸𝐼

𝑚𝑙

(Section 4.5)

233.79 Hz 388.93 Hz

*Mass supplied by Lucchini is 198 kg

7.7 DISCUSSION - STRUCTURAL PERFORMANCE THE OF HMC RAILWAY AXLE

A hollow, steel railway axle having inboard bearings has been designed to Standard BS 8535 [1].

The structural performance of this axle has been assessed in relation to a number of critical

sections along the axle (Figure 4) and the results are presented in Table 4. An HMC railway axle

has been designed as a direct replacement for the benchmark hollow steel axle. The performance

of the HMC axle relative to the hollow steel axle is provided within Table 5.

The aim in replacing the steel axle with the HMC axle was to reduce the overall axle mass. The

hollow steel axle has a mass of 198 kg. The HMC railway axle has a mass of 74 kg and is 63%

lighter than the hollow steel axle. The mass of the primary and secondary composite tubes of the

HMC axle is modest at 22 kg, representing 30% of the total HMC axle mass. The steel collars, at

52 kg, account for 70% of the total mass of the HMC axle. Substituting titanium for the steel collars

indicated that a collar mass of 15 kg rather that 26 kg each could be achieved. This would result

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in an overall axle mass of 52 kg, or savings of 74% compared to the benchmark, i.e., a hollow steel

axle. Furthermore, a reduction in the collar wall thickness may be possible if the existing axle end

feature could be removed, thereby making and additional mass savings.

The structural performance of the HMC railway axle compared favourably against the benchmark

hollow steel axle. The maximum deflection of the HMC axle is 1.702 mm. While this was 52%

greater than the steel axle the deflection occurs over a 1156 mm span and is considered small. In

addition, the back to back wheel deflection is 3.312 mm and remains within the 6 mm tolerance for

this parameter. The angular misalignment at the bearings is limited to 0.212°, so the requirement

to use the existing bearings is satisfied. Further reduction in these deflection driven parameters

could be achieved by increasing the thickness of secondary composite tube. While this would add

mass to the HMC axle, the increase is estimated to be no more than 5 kg.

The maximum bending stress in the HMC axle is 170.00 MPa occurring at Position 𝐸 where the

primary composite tube is most affected by the maximum bending moment and the collar. This

results in a reserve factor (RF) of 2.5 for the HMC axle versus 3.7 for the steel axle under the

condition of high cycle (107) reversed bending fatigue. As a reference, the steel axle generally

operates with an RF of at least 2 across the axle. While bending is the predominant load case, the

effect of torsion at Position 𝐶 is also presented. This reflects the case where the bearing has seized

and the torque is driven through the collar and primary composite tube. Here the stress in the HMC

axle (7.93 MPa) is less than that for the steel axle, although the torsional stress in the collar is

greater at 17.88 MPa. The maximum transverse shear occurring in the primary composite tube at

the relief groove between the wheelseat and journal (Position 𝐶) is significantly less for the HMC

axle (1.72 MPa) than the steel axle (14.82 MPa), although the stress level in the collar is higher at

23.12 MPa. The Hashin criterion has been used to assess the likelihood of failure of the HMC axle

and values less than 45% of allowable were determined for the worst case of bending at position

𝐸. While the Hashin criterion provides an acceptable measure of composite laminate failure,

treatment of the stress transfer through the thickness (interlaminar shear stress) may be unreliable.

For this reason, the Tsai-Wu criterion is favoured and the HMC axle would benefit from an analysis

using this failure technique.

A clear area for further study is in the design of the metallic collars. The purpose of the collars is

to support the interference fit of the wheel and bearing onto the axle as well as provide the interface

geometry for attachment of those element. This has been achieved with maximum stresses of

358.50 MPa and 13.65 MPa within the collar and primary composite tube, respectively at the

running surface, Position 𝐴. However, the adhesive bond between the collar and the primary

composite tube requires an engineered solution. As presented, the stress within adhesive exceeds

the allowable. Furthermore, the end feature of the collar imparts a penetrating stress (528.10 MPa)

into the outer surface of the primary composite tube under bending. A discussion of the bonded

collar solution is provided in Chapter 9 of this report.

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8. ASSESSMENT OF THE MANUFACTURABILITY AND COMPARISON BETWEEN VARIOUS MANUFACTURING METHODS

The Wheelset Axle is manufacturable following two different processes: manual roll wrapping (RW)

or filament winding (FW).

In this chapter these processes are described in detail. The typical workflow of each method is

shown along with its pros and cons.

This assessment evaluates the feasibility of the Design Concept 3 of the axle, where the composite

part is formed by a primary tube (PT) and a secondary tube (ST), while the metallic collars are

assembled on the ends of the primary tube.

8.1 ROLL WRAPPING

Making the axle with a manual roll wrapping can be carried out following these steps:

1. Prepreg cutting

The prepreg material is cut into layers with appropriate fiber orientation.

2. Roll wrapping

The prepreg layers, regarding the primary and secondary tube, are rolled by hand on a cylindrical rod, known as mandrel, following the appropriate layup

3. Curing

The wrapped tube is placed in a vacuum bag and cured in an autoclave. Once curing is complete, the mandrel is removed from the tube.

4. Milling of the tube

The primary tube ends are milled on the outer side, in order to provide an accurate cylindrical coupling with the collars

5. Bonding of collars

The two metallic collars are bonded on the tube ends with an epoxy adhesive.

6. NDI

Nondestructive inspection of the bonding interface and composite laminate is carried out to find possible defects like delaminations or debonded areas.

7. Finishing

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The axle is finished by removing burrs and coated (if needed)

The roll wrapping provides the ability to make the stacking sequence more customizable, for

example, it allows the placing of layers with fibers aligned with the tube axis, which are the most

suitable for withstanding pure bending loads. The wrapping of the secondary tube can be done with

a good precision, ensuring the removal of material belonging only to the primary tube during the

milling phase and the clearance gap between the secondary tube and the stub axles.

Figure 21 - Section of a tube end.

Manually placing the layers will inevitably generate a butt joint for each layer. This means that there

is a fiber discontinuity for each layer of the composite tube, that cause a loss of performance of the

axle. Efforts should be made to stagger this butt joint around the circumference of the tube for

subsequent layers.

Figure 22 - butt joint generation during the mandrel wrapping.

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8.2 FILAMENT WINDING

Making the axle with a filament winding process can be carried out following these steps:

1. Machine setting

The bobbins of tow preg material is placed on the rack of filament winding machine.

2. First Winding

Winding of the primary tube on a mandrel following the appropriate layup. An extra layer shall be wounded as to be sure not to damage the fibers of the outermost layer of the primary tube.

3. Curing

The wounded tube is placed in a vacuum bag and cured in an autoclave. Once curing is complete, the mandrel is removed from the tube.

4. Milling of the tube

The primary tube ends are milled on the outer side, in order to provide an accurate cylindrical coupling with the metallic collars.

5. Bonding of collars

The two metallic collars are bonded on the tube ends with an epoxy adhesive.

6. NDI

Nondestructive inspection of the bonding interface is carried out to evaluate the voids quantity and dimensions.

7. Second Winding

The primary tube with bonded collars is the new mandrel on which the secondary tube is wounded.

8. Curing The wounded tube is placed in a vacuum bag and cured in an autoclave.

9. Finishing

The axle is finished by removing burrs and coated (if needed)

In the proposed workflow there are two winding steps because it is not possible to wind the

secondary tube with a precise length over the first winding, so the most practical method is to wind

the secondary tube after bonding the collars. Note that this process involves covering the inner

ends of the collars, eliminating the clearance gap, as modelled in Chapter 9.

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This method has a constraint on winding, i.e. it is not possible to place the fibres on the mandrel at

an angle of less than 10° to the tube axis. Moreover, the thicknesses of the single layers are

different than the plies applied during roll wrapping.

Basically, it is not possible to apply the same layup as used for roll wrapping, so dedicated analyses

are carried out.

Once adoption of filament winding as manufacturing route is discussed in technological terms, it

shall also be studied in terms of resulting mechanical performances. More specifically, because of

the manufacturing constraint presented above, it would require a completely different stacking

sequence with respect to the one proposed for roll-wrapping.

The goal is therefore that of quantitatively determine the mass variation caused by adoption of

filament winding and such analysis requires the development of an alternative and concurrent layup

sequence that performs the same as the proposed roll-wrapped layup sequence.

When aiming at mass reduction, it is easy to state that this latter activity shall be implemented

following an optimality approach: thus, the outcome won’t be an alternative layup but the best

performing alternative layup in terms of mass reduction.

An additional point is considered when switching from roll wrapping to filament winding; this latter

process generates an intertwining among tows being wound in different winding strokes.

Consequently, very local variations of ply thickness, orientation angle and, therefore, lamination

law can be observed. Despite such local variation are relatively small, their summation over the

whole wound item might leverage non-negligible global stiffness losses that shall be quantified.

Obviously, the process relies on a set of material properties describing the elastic behaviour of

each layer and determining the overall tubes stiffnesses; as a consequence, the engineering

constants of the base wound lamina in the principal material directions shall be used as input data

during the optimization process.

Summing up, the following points must be considered when developing the best stacking sequence

that can be manufactured by filament winding and that performs the same as the roll wrapped

tubes:

• Re-orientation of plies at 0 deg to ±10 deg;

• Introduction of orientation-dependant minimum ply thickness;

• Estimation of the stiffness loss due to the winding pattern;

• Determination of engineering constants in the principal material directions generated by

filament winding process.

The optimization flow chart is schematically reported:

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Figure 23 Filament winding layup optimization routine

The starting point is the stacking sequence proposed for the roll wrapping process. The final output

shall be a concurrent layup that can be manufactured by filament winding and that ensures the

same performance in terms of torsional and bending stiffness.

Design constraints for the studied application are stiffness-driven ones, since maximum allowed

deformation (displacements/rotations) are drivers for the presented problem; such a statement

appears self-evident because of the higher specific strength pointed out by laminated composite

items if compared to steel ones. Therefore, it is reasonable to adopt the performances of the

laminated tubes in terms of maximum allowed displacement and rotation as indexes of global

stiffness.

Hence, the first step is the evaluation of the performances of the base roll wrapping layup.

Such preliminary activity is implemented in the same Finite Element environment in which the

optimization of the equivalent filament winding layup is defined, to prevent possible errors or results

misalignment due to the adoption of different solvers. For this reason, the chosen FE solver is

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HyperWorks X, containing the OptiStruct suite; this latter allows for the numerical optimization of

composite laminates both in terms of ply thickness and stacking sequence.

Separate primary and secondary tube are modelled in a simplified bending/torsion loading and

constraint condition and their maximum static displacement and rotation are derived:

• 𝛿𝑗,𝑡𝑎𝑟𝑔𝑒𝑡 = maximum vertical displacement of the roll-wrapped PT or ST

• 𝜑𝑗,𝑡𝑎𝑟𝑔𝑒𝑡 = maximum rotation about the axis of the roll-wrapped PT or ST

• 𝑗 = PT (Primary Tube) or ST (Secondary Tube)

These quantities are relevant for mass optimization process of the FW layup, since they act as

optimization constraints.

Once the preliminary activity regarding the reference RW layup is terminated, the optimization

process begins. It shall be fed with few input data, among which of crucial relevance are:

• Objective function: a quantity to be maximized or minimized according to the design

requirements and which is dependent on design variables. According to the purposes of the

analysis, mass shall be minimized.

• Constraint functions: non-negotiable conditions that the outcome of optimization process

shall respect to be considered acceptable. Indeed, these conditions are highlighted by the

sentence written above: “[…] layup that […] performs the same in terms of bending and

torsional stiffness” which translated in quantitative terms below.

𝛿𝐹𝑊𝑗,𝑖 ≤ 𝐾𝐷𝑗,𝑖, 𝛿 ∙ 𝛿𝑗,𝑡𝑎𝑟𝑔𝑒𝑡

𝜑𝐹𝑊𝑗,𝑖 ≤ 𝐾𝐷𝑗,𝑖,𝜑 ∙ 𝜑𝑗,𝑡𝑎𝑟𝑔𝑒𝑡

Where:

o 𝑗 = Primary tube (PT) or secondary tube (ST) index

o 𝛿𝐹𝑊𝑗,𝑖 = max. vertical displacement of the filament-wound PT or ST (i-th iteration);

o 𝜑𝐹𝑊 𝑗,𝑖 = max. rotation about the axis of the filament-wound PT or ST (i-th iteration);

o 𝐾𝐷𝑗,𝑖,𝛿 = Knock-Down factor for bending stiffness due to fiber intertwining during the

winding process for PT or ST (i-th iteration);

o 𝐾𝐷𝑗,𝑖,𝜑 = Knock-Down factor for torsional stiffness due to fiber intertwining during the

winding process for PT or ST (i-th iteration);

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The definition of these coefficients is needed because fibers weaving during the winding

process could be detrimental for global laminate stiffness. They are directly attributed to the

optimization constraints to implicitly compensate for these stiffness losses during the

optimization process by imposing constraints that are more stringent than the target values by

themselves. Their estimation requires an iterative process since their values are assumed to

be stacking sequence-dependent; their values at the first iteration are set to 1 (i.e. fiber

patterning is initially assumed to have no effect on stiffness).

• Minimum ply thickness: such an information is adopted by the solver to discretize the domain

of the thicknesses that could be assigned to a ply: thus, the solver can assign to a certain ply

only manufacturable thicknesses that are integer multiples of the minimum one. In case of

filament winding, these thicknesses are orientation dependent: different deposition angles carry

out different extent of superposition of fibers and, therefore, slightly different thickness for each

ply. CadWind software has been used to determine these ply thicknesses by simulating the

winding process over the mandrel; the software is fed with material properties coming from a

SigmaPreg datasheet referring to a towpreg with the following properties:

- Flame retardant resin system

- Tape width of 6mm

- 24 K carbon fibers

- Fiber mass content: 67%

- TEX: 1600 g/km

Figure 24 Simulation of 45° helical winding

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Plies at ±10 and ±45 deg are featured by a minimum thickness of 0.29 mm whilst hoop-wound

plies by 0.30 mm. For sake of simplicity, 0.3 mm is assumed for all of the orientation angles.

Concerning the FW layup to be determined, the starting point is the generation of an

overconservative layup that can be manufactured by filament winding manufacturing. Such

operation is carried out referring to the layup proposed for RW by re-orienting plies originally

deposed at 0 deg to ±10 deg, and by increasing the number of plies themselves.

Figure 25 Overconservative initial guess for the FW layup

This latter point is needed because re-orientation of axial plies inescapably harms bending stiffness

and it would probably cause violation of optimization constraint on maximum vertical displacement

for the initial layup guess. Conversely, an excessively conservative initial guess would not harm

the validity of the outcomes since useless plies (providing poor contribution to the overall laminate

stiffness) are assigned of zero thickness and erased during the process. Thus, number of plies is

augmented to let the optimization solver starts from a feasible design (i.e. respecting the

constraints).

Then, according to the routine described in Figure 23, the optimization solver is launched. Once

the algorithm stops its iterations, a trial filament winding layup is proposed; the next step, according

to the routine, is the estimation of the KD factors describing the winding pattern detrimental effect

on overall laminate stiffness. These latter can be estimated thanks to CadWind Software, which

allows for the simulation of the whole winding process of the trial stacking sequence determined in

the previous step. Cadwind also enables the extraction of a meshed finite element shell model

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whose peculiarity is that it accounts for the very local thickness and material orientation variations

due to fibres intertwining and causing the losses of global stiffness mentioned above.

Hence, the strategy to estimate the knockdown factors relies in the comparison of the performances

of the model exported from CadWind with another one, being identical in terms of geometry, mesh

and loading conditions but with global thickness and material orientation assignments.

o 𝐾𝐷𝑗,𝑖,𝛿 = 𝛿𝐿,𝑗,𝑖

𝛿𝐺,𝑗,𝑖⁄

o 𝐾𝐷𝑗,𝑖,𝜑 = 𝜑𝐿,𝑗,𝑖

𝜑𝐺,𝑗,𝑖⁄

Where:

o 𝛿𝐿,𝑗,𝑖 = max. vertical displacement of the “local” PT or ST model (i-th iteration);

o 𝛿𝐺,𝑗,𝑖 = max. vertical displacement of the “global” PT or ST model (i-th iteration);

o 𝜑𝐿,𝑗,𝑖 = max. rotation about the axis of the “local” PT or ST model (i-th iteration);

o 𝜑𝐺,𝑗,𝑖 = max. rotation about the axis of the “global” PT or ST model (i-th iteration);

These KD factors can be defined as relative coefficient expressing the expected stiffness decay

that the laminated tube would experience because of the way it is manufactured.

They are attributed to the target deformation values for the next iteration, and, therefore, to update

the design constraints as they reduce the absolute values of the allowed deflection and rotations.

Indeed, the outcome of the optimization process is a function of the value of the knock-down

factors; however, these coefficients cannot be assumed to be universally valid, being that their

values are probably a product of a specific stacking sequence. Because of such a mutual

dependence, an iterative process on the knock-down factors is issued.

The iterations are stopped when, assuming a certain tolerance, two consecutive iterations point out

the same value of knock-down coefficients, because an additional iteration would have the same

result, since the optimization process would be issued with the same constraint boundary values

for deflections and rotations. A tolerance of 2.00% is assumed.

Another condition causing the interruption of the iterative process consists of output trial stacking

sequences whose stiffness performances (transverse vertical deflection and rotation) already fall

within the range of allowed vertical displacement and rotation for next iteration, updated with the

knock down; in such conditions, in fact, an additional iteration would provide the same output

stacking sequences.

At the end of the proposed concept routine, the equivalent stacking sequence for filament winding

is eventually derived.

• Primary tube: [90/±452/(±10/±45)7/±453]s (23.4 mm thick)

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• Secondary tube: [902/±454/±107]s (14.4 mm thick)

Once the presented method generates a mass-optimized stacking sequence, its validity is checked

against the one developed for roll wrapping with an independent analysis tool. Two complete

wheelset models containing the concurrent roll-wrapped tubes and the filament-wound tubes

respectively are therefore produced in Abaqus CAE; they are subjected to the same loading and

constraint condition and their stiffness performances are compared in terms of maximum vertical

deflection, gauge length increase and rotation about the axis.

Results are displayed and summarized:

Figure 26 Maximum vertical displacement of the roll-wrapped solution [mm]

Figure 27 Maximum rotation about the axis of the roll-wrapped solution [rad]

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Figure 28 Maximum vertical displacement of the filament-wound solution [mm]

Figure 29 Maximum rotation about the axis of the filament-wound solution [rad]

Table 5 Summary of Rw and FW comparison.

Property RW- Layup FW – Layup % variation

massPT 13.65 kg 21.83 kg +59.93%

massST 8.28 kg 8.88 kg +7.25%

U2max 2.582 mm 2.491 mm -3.52%

UR3max 12.3 mrad 8.360 mrad -32.03 %

gauge 4.520 mm 4.360 mm -3.54%

Tsai-Hill FI 0.3512 0.4761 +35.56%

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The total mass increase pointed out by the FW solution is of 8.28 kg; however, the assembly of

primary and secondary tube generates a solution that is still much lighter than traditional EA1N

steel axle. Consequently, in spite of its larger mass with respect to the roll-wrapped solution,

filament winding could provide advantages from the manufacturing point of view that may worth

such mass increment. Therefore, final conclusions are entrusted to a comparison over the two

concurrent manufacturing technologies.

8.3 COMPARISON AMONG ROLL WRAPPING AND FILAMENT WINDING PROCESS

The main difference between the two processes is the performance they provide to the component.

It is not possible to evaluate the effect of the layer butt joints (roll wrapping) during the analysis

since it is not possible to quantify accurately the loss of performance due to fibres discontinuities

without making a test campaign or numerically estimating it with relative coefficient as for the KD

factors for the winding pattern effect. Moreover, filament winding generates a pre-tension in the

fibres whose effect it is not included in the presented simulation and which can be relevant for

overall elastic behaviour of the axle.

Indeed, no conclusion based on the expected mechanical behaviour of the concurrent design (RW

and FW) solutions can be drawn without experimental validation of the models.

However, they can still be compared by the manufacturing point of view. A relevant factor that

differentiates the two processes can be found in repeatability: filament winding is an automated

process, so all the tubes produced with such a technology are expected to have identical

performances and characteristics. Tubes produced by roll wrapping with a manual process,

conversely, will inescapably have operator-dependent quality and, therefore, slightly different

output mechanical performances, since more errors could be expected for this kind of manual

process.

The performances obtained with adoption of filament winding process are higher in terms of

mechanical response because of its better repeatability with respect to the performances that would

probably be obtained with the manual roll wrapping.

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9. ANALYSIS OF THE BONDED JOINTS

In this chapter, the feasibility of a bonded joint between the metal collar and the composite tube is

assessed by FEA, with reference to its fatigue strength for 100 million cycles. First, a brief overview

of the literature about multi-material, adhesive joints is presented, and a structural adhesive is

proposed. Then, the bonded joint between the collar and the tube without modifications of the

geometries shown in Figure 12 is studied. Based on the results of this preliminary analysis, a

refined solution is analysed and discussed.

9.1 SELECTION OF THE ADHESIVE AND MECHANICAL CHARACTERIZATION

The use of adhesive joints in structural applications is particularly suitable for joining dissimilar

materials without adding weight (compared to mechanical joints), achieving good fatigue resistance

and design flexibility [8-16]. Nevertheless, joining multi materials can be a challenging task in the

design and manufacturing steps of these new lightweight structures, becoming even more

important to know/study the effects of dissimilar materials used as substrates, the mechanical

behaviour and environmental resistance of adhesive joints in order to guarantee their safety and

reliability [17,18]. G. Sun et al., 2018, studied the effects of adherend thickness and substrate

material type (Q235 steel, 5182 aluminium alloy and woven of carbon fibre reinforced plastic -

CFRP) in the tensile behaviour of the dissimilar adhesively bonded joints. M. D. Banea et al., 2018,

analysed the mechanical properties of similar and multi material adhesive joints by means of

experimental and numerical tests. For this study three different types of substrates were used: hard

steel, carbon fibre reinforced plastic and aluminium. A. H. Khawaja et al., 2016, studied different

methods for the joining of carbon fibre composite materials and aluminium 6061 T6: double-lap

adhesively bonded joints, hybrid joints (adhesive + rivets) and the use of adhesive pins. For the

analysis tensile and fatigue tests were performed.

A summary of the adhesive types found in these references and the most relevant characteristics

are reported in Table 6. The results of the tests reported in the references are summarized in Table

7.

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Table 6. Adhesives’ mechanical properties.

Reference Adhesive type

Shear

modulus

(MPa)

Shear yield

strength

(MPa)

Shear

strength

(MPa)

Shear

failure

strain (%)

Young's

modulus

(MPa)

[8] Sikaflex 256 1.351 ±

0.04 8.26 ± 0.30

8.26 ±

0.30 330 ± 27 -

AV138-HV998 1559 ± 11 25 ± 0.55 30.2 ±

0.40

5.50 ±

0.44 -

[9]

AV138-HV998 1560 ± 11 26 ± 0.55 30.2 ±

0.41

5.50 ±

0.45 -

Araldite 2015 487 ± 77 17.9 ± 1.80 17.9 ±

1.80

43.9 ±

3.40 -

[10]

AS1805 RTV

silicone rubber

0.68 ±

0.03 -

1.47 ±

0.02 332 ± 17 -

RTV 106 0.55 ±

0.05 -

1.97 ±

0.03 408 ± 21 -

[11] FM 73 - - - - 2160

[12] Araldite 420 A/B - - 27 - 1850

[13] AV138-HV998 1559 ± 11 25.1 ± 0.33 30.2 ±

0.41 7.8 ± 0.7 4890 ± 810

[14] AV138-HV999 1560 ± 10 - - - 4890 ± 810

[15] Betamate 4601 - - - - 2860

[16] SikaForce 7888 - - 22 - 2530 ± 160

[17] Araldite 2015 1000 - - - 1850

[18]

[19] 3M 9323 B/A 2600

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Table 7:The mechanical properties of the studied adhesive joints.

Reference Adhesive

type

Adherend type Overlap

(mm)

Lap shear

strength

(MPa)

Ultimate

tensile

strength

(MPa)

Tensile

failure

Loads

(N)

Impact

failure

loads -

SLJ (N)

Fatigue life equation

(SLJ)

[8] Sikaflex

256

Mild steel 25 - 12 914 around

5500

normalized load = -

0.048* ln (number of

cycles) + 1.0456

AV138-

HV998

25 - 41 2554 around

7000

normalized load = -

0.045* ln (number of

cycles) + 1.0555

[9] AV138-

HV998

Aluminium alloy

AA6082

25 - - around

4250

- 1000000 cycles at

2761 N

Araldite

2015

25 - - 9375 - -

[10] AS1805

RTV

silicone

rubber

Steel and

aluminium alloy

6082-T651

12.5 1.25 ±

0.08

- around

500

- normalized load = -

0.0496* ln (number

of cycles) + 1.0963

25 - - around

900

- -

50 - - 1500 - -

RTV 106 12.5 1.65 ±

0.13

- around

500

- normalized load = -

0.0491* ln (number

of cycles) + 1.0379

25 - - 1000 - -

50 - - 2500 - -

[11] FM 73 Alluminium

alloy

12.5 - - - - At 2000000 of cycles

the maximum tensile

strength of the joint

is around 60 MPa

[12] Araldite

420 A/B

Docol 1000

high strength

steel

12.5 - 35 around

6000

- -

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[13] AV138-

HV998

7075 T76

aluminium alloy

and Cr. D steel

12.5 - 39.45 ±

3.18

4825 - vibration cycle

134784 - peak load

of 4254N; vibration

cycle 67392 - peak

load of 4370N and

vibration cycle 0 -

peak load of 4847N

[14] AV138-

HV999

7075 T76

aluminium alloy

and Cr. D steel

12.5 - - - - vibration cycle

49259 - Young's

modulus of 5.054

MPa; vibration cycle

27462 - Young's

modulus of 9.142

MPa and vibration

cycle 0 - peak load

of 4890 MPa

[15] Betamate

4601

A5754-O

aluminium alloy

12.7 - 64 6500 - Variation of

J=1129.2*(number

of cycles) ^-0.1359

[16] SikaForce

7888

Hard steel (HS) 12.5 - 31.12 ±

1.17

5000 - -

Composite

(CFRP)

25 - 31.12 ±

1.17

15000 - -

Alluminium (Al) 50 - 31.12 ±

1.17

30000 - -

[17] Araldite

2015

Q235 steel,

5182 aluminium

alloy and woven

carbon fibre

reinforced

plastic (CFRP)

25 - 17.9 around

7000

- -

[18] KSR-177 6061-T6

aluminium and

USN 125

carbon epoxy

prepreg

40 80.8 4.86 around

5000

- endurance limit of

1.23 kN

[19] 3M 9323

B/A

40

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From the analysis of the literature, it appears that two-part epoxies are usually employed for the

manufacturing of hybrid metal-CFRP joints. The chosen adhesive for the feasibility analysis of the

metal collar to composite tube on is the epoxy adhesive 3M 9323 B/A studied in [19].

For this adhesive, fatigue test results are available for various joint types and in [19] a local stress

approach is presented. It was shown that the shear stress amplitude constitutes a parameter able

to correlate the fatigue lives for different joint configurations, as shown in Figure 30. The same

approach is proposed for the analysis of the joint between the metal collar and the composite tube.

It has to be pointed out that the range of cycles explored in [19] does not exceed one million cycles,

therefore an extrapolation is needed to obtain the admissible shear stress amplitude for 100 million

cycles. The extrapolation allowed evaluation of an allowable shear stress amplitude of 13 MPa for

a probability of failure of 10%, 16 MPa for a probability of failure of 50%.

Figure 30. Fatigue S-N diagram of the 3M 9323 B/A adhesive [19]

To complement the data reported in the technical data sheet of the chosen adhesive and in [19],

additional tests were performed in the framework of this project. They consisted of the evaluation

of the tensile properties of the bulk adhesive, conducted according to ISO 527 standard using

specimens manufactured according to the French standard NF T 76 – 142, and of mode I fracture

toughness tests, conducted according to ISO 25217 using double cantilever beam tests.

By tensile testing, the value of the Young’s modulus E and of the ultimate tensile strength of the

3M 9323 adhesives were obtained and added to Table 6 and Table 7, respectively.

Based on these tests, the coefficients of a triangular traction separation law were derived, as

reported in Table 8. Finite element simulations of the mode I fracture tests allowed assessment of

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the accuracy of the evaluation of these coefficients. Figure 31 showcases the superposition of the

numerical force-opening curve onto the experimental one.

Figure 31. The tensile stress-strain curve of the bulk adhesive 9323 B/A

Table 8. Coefficients of the proposed traction separation law for the 3M 9323 B/A adhesive

GnC(N/mm) GS

C(N/mm) tI0(MPa) tII

0(MPa) eI0(MPa/mm) eII

0(MPa/mm)

2.8 5.42 30.69 42 8564.3 6117.36

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Figure 32. results of mode I fracture test, with FE analysis results superimposed, showing the accuracy of cohesive modelling.

9.2 FEA OF THE ADHESIVE JOINT

The adhesive joint between the steel collar and the primary composite tube was modelled using

the partial model shown in Figure 33. It consists of one collar (ivory), a portion of the primary (inner)

tube (light gray) and the corresponding portion of the secondary (outer) tube (dark gray).

The wheels were not introduced into the model. Instead, a kinematic coupling between the surface

of the stub axle originally in contact with the inner surface of the wheel’s rim and a reference point

(RP2) was used to simulate the presence of a wheel and the corresponding constraints on the

displacements. The RP2 was constrained not to displace in the z and y directions.

Similarly, a kinematic coupling was used to simulate the presence of a bearing and simulate the

constraints imposed by it onto the displacements and the rotations of the surface of the axle

originally in contact with the bearing. Reference point 3 (RP3) was created and constrained not to

displace along x, y and z directions. Rotational degrees of freedom were left free.

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Figure 33. the portion of the composite wheelset used for modelling of the adhesive joint

A third reference point (RP1 in Figure 34) was used to apply the bending moment. The reference

point was linked to the free end’s cross section of the composite tubes on the right by a kinematic

coupling as well.

The outer tube and the inner tube were connected by another kinematic constraint of the “tie” type,

to simulate the achievement of a monolithic structure by overwrapping and co-curing of the two

tubes.

Figure 34. kinematic couplings, reference points and boundary conditions

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Between the inner surface of the collar and the outer surface of the inner composite tube, a thin

layer of cohesive elements was placed, to simulate the presence of the adhesive, as shown in

Figure 35. The adhesive layer was modelled using 0.3 mm thick cohesive elements of 2 mm edge

length. These elements were connected to the mating surfaces of the inner tube and the stub axle

by tie constraints. An additional layer of cohesive element was placed between the end surfaces

of the secondary tube and the collar, creating a sort of butt joint between them.

Figure 35. kinematic couplings, reference points and boundary conditions

Material properties were assigned to the parts as listed below. The mechanical properties of the

materials are listed in Table 9.

• Steel collar: homogeneous isotropic section, material: steel

• Outer tube: homogeneous orthotropic cross section, material: composite outer layup

• Inner tube: homogeneous orthotropic cross section, material: composite inner layup

• Adhesive: cohesive section; in this case, two definitions of the mechanical behaviour of the

adhesive were used: cohesive continuum formulation, to evaluate elastic stresses only, and

cohesive traction separation law, to assess the static damage induced by the external loads.

The choice of homogenizing the properties of the composite laminates through the thickness was

dictated by the need of modelling tapers with reasonable mesh size and the impossibility of defining

a composite laminate cross section in the presence of tapers. The only feasible option would have

been modelling each single ply as a layer of element stacked on one another, but this would have

increased the number of elements beyond the maximum number that it is possible to handle with

the workstation used for this project. A mesh size of 5 mm average length was defined for the metal

stub axle and for the composite tubes. Quadratic elements were used. Tetrahedral elements were

preferred for the more complex geometry of the stub axle, whereas more regular hexahedra were

employed for the composite tubes.

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The properties of the composite materials were derived from the layups proposed in Chapter 7, by

homogenization of the layup along the thickness, to derive the equivalent properties (engineering

constants) of an orthotropic material. Homogenization was conducted by the partner Bercella using

the software package Autodesk Helius.

Table 9. Elastic properties of the materials

Inner layup

Ex (MPa) 101796,00 xy 0,32

Ey (MPa) 63818,90 yx 0,20

Ez (MPa) 6390,00 xz 0,16

Gxy (MPa) 23654,90 zx 0,01

Gxz (MPa) 3742,00 yz 0,10

Gyz (MPa) 3548,00 zy 0,01

Outer Layup

Ex (MPa) 137328,00 xy 0,32

Ey (MPa) 45958,40 yx 0,11

Ez (MPa) 6390,00 xz 0,22

Gxy (MPa) 17146,60 zx 0,01

Gxz (MPa) 3871,33 yz 0,07

Gyz (MPa) 3418,67 zy 0,01

Adhesive

E 2600 0.35

Steel

E 206000 0.3

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The analysis consisted of a static step, with an applied bending moment equal to the resultant

bending moment of 22,283 Nm. This corresponds to the loading at any instant during one revolution

of the axle. If the conditions for a linear response are satisfied, the stress at the highly stressed

point under static loading should correspond to the maximum stress experienced during one

revolution by any point having the same radial coordinates (with respect to a cylindrical reference

system, having the Z axis coincident with the axle’s axis). This allows for assessing the fatigue

strength of the joint under rotating bending loading without simulating one full revolution. To perform

this assessment, the continuous response of cohesive elements is sufficient. However, it is

necessary to verify that the response can be linear. To verify this, a nonlinear analysis with a

cohesive formulation by a traction separation law was run. Results are presented in Figure 36,

where it clearly appears that the adhesive, in the previously defined butt joint, fails (MAXSCRT

damage variable reaches the limit value of 1, indicating that complete fracture occurs). This causes

a peak stress of 75 MPa (von Mises) in the adhesive layer between the collar and the inner tube,

which corresponds to a shear stress amplitude (out of plane shear stress) exceeding 25 MPa, as

shown in Figures 37 and 38. This largely exceeds the fatigue strength estimated for 100 million

cycles and therefore the nucleation of a crack in the adhesive layer cannot be excluded.

Figure 36. contour plot of the values of the MAXSCRT variable in the adhesive layers

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Figure 37. contour plot of the values of the von Mises stress in the adhesive layer

Figure 38. contour plot of the out of plane shear stresses in the adhesive layer

Moreover, the failure of the butt adhesive joint is likely to propagate during the first loading cycle

over the entire annular surface and therefore the real stress distribution would be obtained with a

model without the butt adhesive joints. The stress distribution obtained with this model is shown in

Figure 39. The out of plane shear stress amplitude is 66 MPa, which significantly exceeds the static

strength of the adhesive.

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Figure 39. contour plot of the out of plane shear stresses in the adhesive layer

The results obtained with the joint configuration of Figure 33 suggested a revision of the detail of

the overlap between the steel collar and the composite tubes. The original geometry of the joint

corresponds to a single lap joint. Other geometries are known to be more efficient in terms of stress

peak reduction, and among them the scarf joint is known to be allow the smoothest stress transfer

between dissimilar materials. A new, improved joint configuration was then proposed, inspired by

scarf joints. It is reported in Figure 40. The detailed drawing of the stub axle with dimensions is

reported in Figure 41.

Figure 40. the improved joint between the stub axle and the composite tubes

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Figure 41. shape and dimensions of the modified stub axle

From the manufacturing point of view, this solution requires careful identification of a suitable

sequence of assembly. A paste adhesive for the joint between the stub axle and the outer tube

does not seem to be the right choice anymore. Instead, a film adhesive seems to be more

appropriate, as the outer tube would be overwrapped onto the stub axle and the cured together

with the already assembled inner tube.

At this stage, two analyses were conducted, one without modifications in the constitutive model of

the adhesive, to check if the proposed solutions allow the stresses to be reduced below the fatigue

strength at 100 million cycles estimated for the 3M 9323 B/A adhesive. Then, a second analysis

was conducted, assigning to the adhesive layer the elastic properties of the 3M AF 163-2 film

adhesive, which appears to be a good candidate, but lacks specific experimental tests.

The new adhesive layer is shown in Figure 42. It covers the tapered part of the collar and it is

modelled like the adhesive layer between the inner tube and the collar. Cohesive elements of 2

mm size are used also in this case. The mesh size for the steel collar and the outer composite tube

was refined and an average element edge of 2 mm was defined in the composite tube and in the

region of the tapered overlap region of the collar. This time, a linear analysis step was defined, and

the constitutive model for the adhesive was elastic (selecting a continuum formulation for the

cohesive elements, without any traction separation law).

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Figure 42. Detail of the adhesive layer of the improved joint between the stub axle and the composite tubes

Results are shown in Figure 43. Shear stress amplitudes are now below 16 MPa and the von Mises

stress does not exceed 28 MPa (Figure 44). The shear stress amplitude is still 3 MPa higher than

the estimated fatigue strength at 100 million cycles, but in the adhesive between the inner

composite tube and the steel collar, stresses are now far below the estimated fatigue strength at

100 million cycles, as show in Figure 45.

Figure 43. contour plot of the values of the out of plane shear stress in the adhesive layers of the improved joint

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Figure 44. contour plot of the values of the von Mises stress in the adhesive layers of the improved joint

Figure 45. contour plot of the values of the shear stress amplitude in the adhesive layers between the inner composite tube and the steel axle

Results were then updated, assigning to the adhesive layer between the stub axle and the outer

tube the properties of the 3M AF 163-2 film, whose Young’s modulus is equal to 1100 MPa.

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Results, reported in Figure 46, show that shear stress amplitude is 13 MPa, a lower value than that

obtained by keeping the properties of the 3M 9323 B/A adhesive, thanks to the reduction of the

elastic modulus of the adhesive. However, for this adhesive, no extensive fatigue characterization

is available, and the only available data in terms of stress-life data are reported in [20]. Based on

the coefficients of the SWT parameter reported in [20], for a fatigue life of 100 million cycles, an

allowable shear stress amplitude of 21 MPa can estimated. However, it must be noted that the

experimental data used to derive the coefficients refer to test durations that do not exceed one

million cycles and therefore a specific test programme should be conducted.

Figure 46. contour plot of the values of the shear stress amplitude in the adhesive layers between the inner composite tube and the steel axle, for the 3M AF-163-2 adhesive

The analysis of the stress distribution in the steel collar, shown in Figure 47, confirms that the new

proposed geometry does not raise the stresses in the collar beyond the fatigue limit of the EA1N

steel of 166 MPa [21]. Moreover, further improvements of the local geometry of the collar are still

possible.

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Figure 47. contour plot of the values of the von Mises stress in the stub axle

9.3 DISCUSSION

The finite analysis of the adhesive joint between the steel collar (stub axle) and the composite tube

in the configuration proposed in Chapter 4 leads to the conclusion that the joint needs modification

to lower the stresses in the adhesive below the fatigue strength of the adhesive for 100 million

cycles of rotating bending.

A new geometry is proposed, which allows to reduce the stresses in the adhesive layer between

the steel collar and the inner tube, below the fatigue strength. In the second adhesive layer between

the stub axle and the outer tube, stresses still exceed the fatigue strength of the 9323 B/A adhesive,

but if the 3M AF 163-2 film adhesive is used, the applied stresses fall below the estimated fatigue

strength. However, the fatigue properties of the AF 163-2 adhesive are not known in depth as those

of the paste 9323 B/A adhesive initially proposed. Therefore, an extensive characterization of the

adhesive is required before proceeding to the approval of a final design of the joint.

Moreover, the accuracy of the estimation of applied stress at the end of the overlap between the

outer tube and the new adhesive layer is affected by the simplification made when the composite

layup was homogenized through the thickness. Coupon specimens and full-scale tests would be

required for both assessing the fatigue performances of the adhesives and calibrating the numerical

models. Development of improved modelling techniques based on fatigue crack growth data is

needed, and models should be refined, considering the layered structure of the composite parts

and the possible phenomena of delamination, particularly in the proximity of the ends of the overlap

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in the adhesive joints, where peel stresses arise. Finally, the environmental effect on the fatigue

behaviour of the chosen adhesives should also be considered for future activities and electrical

insulation between the steel stub axle and the carbon fibre reinforced polymer tubes must be

ensured to avoid corrosion due to the mismatch in the electric potential of the different materials in

contact. An electrically insulating glass fibre woven mat on the outer surface of the tubes would

probably solve the problem.

Being the highly stressed bond-line region the end of the overlap on the upper adhesive layer,

towards the steel collar, the site appears to be appropriate for NDT and/or structural health

monitoring, as fatigue cracks are likely to first appear there, and not in the underlying adhesive

layer between the inner composite tube and the steel collar. More details about this point are

reported in Chapter 10.

It is worth mentioning that the possibility of substituting the adhesive joint with a mechanical joint,

or the combined used of adhesive and mechanical joints has not been investigated thoroughly in

this project. For load bearing applications, like the connection between the wind turbine blades and

the rotor, mechanical joints are often applied [22], as shown in Figure 48.

Figure 48. Four different types of mechanical joints between composite and metal parts in wind turbine blades, from [21]

A preliminary analysis of a mechanical joint inspired by the solution (a) reported in Figure 48 was

conducted. Figure 49 showcases the model of a flanged joint between the stub axle and the outer

composite tube, with a cross section presented in Figure 50. The inner composite tube is meant to

be bonded to the stub axle using the 3M 9323 B/A adhesive. The bolts and the counter-flange

shown in Figure 48 (a) were not modelled. Instead, a simplified tie interaction was established

between the flange on the tube and that on the axle, to assess the effect of this type of connection

onto the stresses in the adhesive layer (Figure 51). As shown in Figure 52, it appears that stresses

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are lower than the estimated fatigue strength at 100 million cycles for the 3M 9323 B/A paste

adhesive. Nevertheless, more refined models should be built to confirm the feasibility of this

solution. At present, the adhesively bonded joint still constitutes the preferred solutions, particularly

because it does not add mass, as a bolted flange would do.

Figure 49. Simplified model of the flanged joint

Figure 50. Cross sectional view of the flanged joint

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Figure 51. Detail of the “tie” constraint between the flanges

Figure 52. contour plot of the von Mises stress distribution in the adhesive layers

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10. ASSESSEMENT OF THE FEASIBILITY OF NDT AND SHM

The assessment of the feasibility of NDT and SHM applied to the composite axle is here carried

out considering the specific axle geometry and configuration named “HMC axle” in the previous

Chapters.

From the point of view of NDT and SHM, the composite axle can be broken down into three different

constituent regions: the central one, characterized by the superposition of two coaxial CFRP

composite tubes, the lateral one, characterized by the inner (primary) CFRP tube and the outer

metallic collar bonded together by an epoxy adhesive, and the bonded joint located between the

central and the lateral regions (the bonded joint considered in the present part of the report is the

scarf joint shown in Figure 40). Due to the features characterizing the three different regions, each

of them requires the application of specific NDT methods and procedures and, possibly, of SHM

approaches.

Generally, the application of NDT to axles adopts different inspection procedures for the

manufacturing stages or for in-service maintenance. This because the accessibility to the inspected

parts is usually different (higher during manufacturing) and because typical manufacturing defects

have different nature, shape and size with respect to those typically originating during service. Here,

it is assumed to be in a scenario related to in-service maintenance.

10.1 FEASIBILITY OF NDT METHODS

During in-service maintenance, the traditional approach (common practice) to employ NDT

inspection of railway axles made of steel is based on the synergic application of three different NDT

methods ([23-24]): visual testing (VT), magnetic particle testing (MT) and ultrasonic testing (UT).

All the three are focused on the detection of service defects (fatigue cracks, corrosion pits and

corrosion fatigue cracks, fretting fatigue cracks, ballast impacts, …) mainly originating at the

surfaces of the inspected axles. Recently, a fourth method (eddy current testing, ET) has been

added in the relevant standards [24] with the same scope.

Considering the application of VT to the composite axle, no relevant or substantial differences can

be highlighted with respect to the case of steel axles. This is because VT is usually applied to get

a first general feedback about the conditions of the inspected part and, possibly, to evaluate local

situations by means of direct (for the external surfaces) or remote (for the internal surfaces by, for

example, endoscopy) visual approaches. The scope and methodology of application, then, remain

the same for all the three regions (central, lateral and the bonded joint) of the composite axle, but

the personnel must be trained to detect the typical defects of composites and adhesive bonding,

along with those of steel.

The possible application of MT to the composite axle is, instead, very limited because composite

parts are not ferromagnetic and, consequently, the method cannot be applied. MT would still remain

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effective for the accessible surface of the metallic collar, but just after the disassembly of wheels

and axle boxes. Possible alternatives could be:

1. liquid penetrant testing (PT): this method can be theoretically applied to the accessible surface

of any materials, provided they are not too porous (and this is not a problem for composite

parts) and they are chemically inert with respect to the products used for inspection. This

second point has to be experimentally and carefully checked, because liquid penetrants are

based on organic derivatives of petroleum and could react with the polymeric resin of the

composites adopted for the axle or with the epoxy adhesive used for manufacturing the bonded

joint. Moreover, the inspection time required by PT is much longer than the one by MT and this

must be considered along with the fact that the presence of coatings is not allowed, on the

inspected surfaces, in order to effectively apply PT. Summarizing: given successful checks on

applicability, PT could be effective for the internal surface of the bore, for the external surface

of the collar (provided the wheels and axle boxed are disassembled), for the external surface

of the central region (provided no coatings prevent accessibility to the base material) and for

the external CFRP-metal tip of the bonded joint (provided no coatings prevent accessibility);

2. eddy current testing (ET): this method has been very recently introduced into the relevant

standards, so its application is not yet very widespread and some technical details, in the

application to axles, have to be still understood. Since this method requires an electrically

conductive material, its applicability to the composite axle depends on the volume fraction of

carbon fibres and this detail has to be experimentally checked. Nevertheless, with respect to

MT and PT, it is more expensive because it requires a more refined equipment, but it can be

very fast and totally automatized. Finally, its sensitivity is typically higher than MT and PT.

Summarizing: given successful checks on applicability, ET could be effective for the internal

surface of the bore, for the external surface of the collar (provided the wheels and axle boxes

are disassembled) and for the external surface of the central region (provided no coatings

prevent accessibility to the base material);

3. tap testing: this method was used, in the past (decades ago), on steel axles, but it was

abandoned in order to introduce more performant NDT methods. On the other hand, today it is

a very effective and widespread method for inspecting the surface and sub surface regions of

composite parts and coatings, so it could be reintroduced for composite axles. With respect to

MT, PT and ET, maybe it is the fastest and cheapest one, but, at the same time, it is not the

most sensitive. Summarizing: tap testing could be effective for the internal surface of the bore,

for the external surface of the central region and for the external CFRP-metal tip of the bonded

joint.

UT is theoretically applicable to composite axles, but, being one of the most complicated NDT

methods, it requires careful design and validation, the latter possibly based on experimental

activities. Section 10.2 presents and describes a detailed feasibility analysis, based on numerical

simulations, of UT applied to the central and lateral regions of the composite axle: anticipating the

results, it seems feasible, but, at the same time, a clear and definitive statement, on the feasibility

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of UT, is not possible without some kind of experimental validation. On the other hand, UT does

not seem to be suitable for application to the bonded scarf joint due to its very complex tapered

geometry and alternation of materials. Possible alternatives to UT for the bonded joint could be, as

described above, PT and tap testing, while for the central and lateral regions:

1. radiographic testing (RT) or computed tomography (CT): these methods could be considered

as a volumetric alternative to UT for the composite parts of the composite axle, but not for the

metallic ones, due to the high thickness value of the involved steel, which could not be

penetrated by the radiation generated by the most powerful commercial radiographic tubes

available today. This is the real reason why, today, RT/CT are not an option for traditional steel

axles, but these methods could gain some attractiveness in the case of a composite axle due

to the higher penetrable thickness values. It remains that RT/CT show some drawbacks with

respect to UT: they are much more expensive, the inspection time is much longer and radio

safety issues arise. As for many other possibilities described in this Chapter, an experimental

activity should be carried out in order to clearly understand the real feasibility of RT/CT applied

to the composite axle.

Concluding, in the case of the considered composite axle, some of the traditional NDT possibilities

for axles seem to be unfeasible, but new ones seem to be worth investigating. It remains that,

generally speaking, the reliability of NDT applied to the considered composite axle seems to be

lower than the one of traditional steel axles. This is because MT cannot be systematically applied

and UT shows lower sensitivity, while the possible alternatives must be still evaluated by suitable

experimental activities. A possible alternative, to NDT, is a shift of paradigm to SHM: a short

discussion on this topic, with the proposal of a possible solution, is give in Section 10.3.

10.2 FEASIBILITY OF UT: RESULTS OF THE SIMULATIONS USING CIVANDE

SOFTWARE

As stated in the previous Section, UT seems to be the most promising volumetric NDT method for

the composite axle. The feasibility of its application was, then, evaluated by means of the specific

software package CIVAnde 2020 SP2 [25], which is a simulation tool for different NDT methods (UT,

ET, RT/CT, …).

It is worth remarking that the main hypothesis assumed in the present feasibility analysis is that the

composite axle is going be inspected, by UT, just from the surface of the longitudinal internal bore.

This is reasonable because such a surface is a smooth cylindrical one, so suitably regular for the

application of the inspecting UT probes, while the external surface of the axle is going to be

characterized by a more complex geometry, by the presence of coatings and wrappings, which

would be detrimental for the application of the inspecting probes, and by the presence of press-

fitted and assembled parts.

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Analyses were carried out considering two different regions of the composite axle: the central one,

characterized by the superposition of the inner (primary) and outer (secondary) composite tubes,

and the lateral one, characterized by the superposition of the inner composite tube, the metallic

collar and an adhesive layer. Each region was evaluated considering both perpendicular incidence

of longitudinal sound waves and angled incidence of shear waves.

Feasibility analysis of UT within the central section of the composite axle

Figure 53 shows the detail of the considered region of the composite axle, characterized by the

superposition of the inner and outer composite tubes. The two tubes are assumed to be joined by

a co-curing process of their matrices, without the help of any adhesive.

Figure 53. Geometry of the central region of the composite axles considered for UT numerical simulations.

The CFRP composite lay-ups of the inner and outer tubes were modelled, treated and implemented

as homogenized orthotropic materials characterized by the same elastic properties and stiffness

matrixes already adopted for structural simulations and analyses (see Section 9.2). For the sake

of completeness, Figure 54 shows the implementation of the stiffness matrices of the inner and

outer composite tubes.

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Inner tube

Outer tube

Figure 54. Stiffness matrices of the inner and outer composite tubes.

The abovementioned stiffness matrices, along with the density of the materials (here assumed to

be equal to 1.75 g/cm3 [26] for both CFRP lay-ups), allows the sound speeds to be determined

within the materials themselves and the slowness curves (Figure 55) representing the anisotropy

of sound propagation. Finally, the structural attenuation of sound pressure during propagation is

the last very important parameter for the application of UT to resin-based materials (plastics or

composites): for both the inner and outer tubes and for both longitudinal and shear waves, the

structural attenuation coefficient was assumed to be, according to the literature [27], equal to 0.8

dB/mm at 4 MHz.

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Inner tube Outer tube

Figure 55. Slowness curves for the inner and outer composite tubes.

Considering, first, the inspections based on the perpendicular incidence of longitudinal sound

waves, Figure 56 shows the modelled probe. Specifically, a conventional circular ultrasonic

transducer, characterized by diameter equal to 10 mm and nominal frequency equal to 4 MHz, was

chosen because it is the typical one adopted for inspecting traditional steel axles. In order to

guarantee a good contact between the transducer and the curvilinear surface of the bore, a

cylindrical convex wedge, made of rexolite, was modelled. Coupling between the probe (wedge)

and the inspected piece was ensured by simulating the presence of a thin layer of mineral SAE oil.

The same figure shows the purely geometrical expected sound beam in terms of a ray-tracing

representation. Such a representation has no real physical meaning, because it is just a qualitative

indication of the sound path.

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Figure 56.Model of the adopted UT probe for perpendicular incidence of longitudinal waves in the central region of the composite axle.

The result of the simulation of the physical sound beam propagating into the inner and outer

composite tubes is shown in Figure 57. As can be seen, the sound beam can be effectively

transmitted from the inner tube to the outer one even if, due to the slight mismatch of acoustic

impedance between the two lay-ups, a discontinuity in sound pressure is evident at the interface

between the two.

Transducer

Wedge

Inner tube

Inner tube

Outer tube

Outer tube Expected geometrical (ray

tracing) sound beam

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Figure 57.Simulation of the physical sound beam for perpendicular incidence of longitudinal sound waves in the central region of the composite axle.

The following step was to introduce circular defects into the inner tube (exemplified in Figure 58),

into the outer one and at their interface. Such defects lay in planes perpendicular to the acoustic

axis of the sound beam, so to represent possible delaminations in the composite materials, and

were characterized by a diameter equal to 5 mm, according to the common practice for traditional

steel axles. Their ultrasonic response, i.e. the amount of sound pressure sent back to the probe

according to a pulse-echo inspection technique, was evaluated.

Figure 58. Circular defect representing a delamination in the composite material.

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Defect within the inner tube

Defect at the interface between the inner and the outer tubes

Defect within the outer tube

Figure 59. Ultrasonic responses of the central region of the composite axle inspected by normal incidence of longitudinal waves.

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Figure 59 gathers the obtained results in terms of B-Scan, i.e. a mapping of the ultrasonic response

along the thickness of the inspected piece, and of the A-Scan, i.e. a section of the B-Scan,

corresponding to the maximum value of the response of the inspected defect. As can be seen, all

of the three defects can be clearly detected, even if, as expected, the farer the defect from the

probe, the lower is the amplitude of its response. Nevertheless, the interface seems not to be a

problem for defect detection and the total thickness of the part seems not to too high to prevent the

same detection due to the structural attenuation of the sound beam. On the other hand, the present

simulations are performed in ideal conditions (no background noise, no sound transfer losses, …)

and the outcome should be validated by suitable experiments.

Moving to the inspections based on the angled incidence of shear sound waves, Figure 60 shows

the modelled probe along with the ray tracing representation of the sound beam. In this case, a

conventional rectangular ultrasonic transducer, characterized by a size equal to 10x9 mm2 and

nominal frequency equal to 4 MHz, was chosen because it is similar to the ones adopted for

inspecting traditional steel axles.

Figure 60. Model of the adopted UT probe for angled incidence of shear waves in the central region of the composite axle; the inset image shows the probe from a different angle of view.

To guarantee a good match between the transducer and the curvilinear surface of the bore, a

cylindrical convex wedge, made of rexolite, was modelled. The same wedge was also used to

suitably incline the sound beam incident at the bore surface and to get, via Snell’s Laws, the shear

waves characterized by the proper refraction angles (Figure 61). It is worth noting that such

refraction angles get modified passing through the interface between the inner and outer tubes.

This is due to the slightly different composite lay-ups of the two tubes. Coupling between the probe

(wedge) and the inspected piece was ensured by simulating the presence of a thin layer of mineral

SAE oil.

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Figure 61. Refraction angles of the shear waves used in the central region of the composite axle.

The result of the simulation of the physical sound beam propagating into the inner and outer

composite tubes is shown in Figure 62. As can be seen, the sound beam can be effectively

transmitted from the inner tube to the outer one even if, due to the slight mismatch of acoustic

impedance between the two lay-ups, a discontinuity in sound pressure is evident at the interface

between the two and, due to the anisotropy of the involved materials, the sound beam is

significantly scattered along many different directions.

In the case of angled incidence of shear waves, the morphology of the inspected defects (Figure

63) consisted of a concave shape, representing a transverse crack in the composite material,

characterized by a 16x3 mm2 size. The different positions of the described defects were three: just

below the interface between the inner and outer tubes, just above the interface between the inner

and outer tubes and at the external surface of the outer tube. The obtained results are summarized

in Figure 64 in terms of S-Scan, i.e. a sectorial mapping of the ultrasonic response, and of the A-

Scan, i.e. a section of the S-Scan, corresponding to the maximum value of the response of the

inspected defect.

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Figure 62. Simulation of the physical sound beam for angled incidence of shear waves in the central region in the central region of the composite axle.

Figure 63. Concave defect representing a transverse crack in the composite material.

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Defect just below the interface between the inner and outer tubes

Defect just above the interface between the inner and outer tubes

Defect at the external surface of the outer tube

Figure 64. Ultrasonic responses of the central region of the composite axle inspected by angled incidence of shear waves.

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As can be seen, all of the three defects can be clearly detected, even if, as expected, the farer the

defect from the probe, the lower is the amplitude of its response. Nevertheless, in one case (defect

just below the interface between the inner and outer tubes), the defect tip diffraction is very well

highlighted, and this helps the possible sizing of the defect, while, in the other two cases (farer than

the interface between the inner and outer tubes), it is much less pronounced, even if the

detectability of the defect still remains relevant. On the other hand, the present simulations are

performed in ideal conditions (no background noise, no sound transfer losses, …) and the outcome

should be validated by suitable experiments.

Feasibility analysis of UT within the lateral section of the composite axle

Figure 65 shows the detail of the considered region of the composite axle, characterized by the

superposition of the inner composite tube, the metallic collar and an adhesive layer. In particular,

the two parts are assumed to be joined by adhesive bonding, adopting a 0.3 mm layer of 9323

epoxy adhesive (see Section 9.1 for details on the chosen adhesive).

Figure 65. Geometry of the lateral region of the composite axles considered for UT numerical simulations.

The involved materials were modelled as follows:

1. the composite CFRP inner tube was modelled exactly as described above;

2. the properties of the 3M 9323 epoxy adhesive were derived from the literature [27]. In particular,

it has density 1.23 g/cm3, longitudinal wave velocity equal to 2488 m/s and transverse wave

velocity equal to 1134 m/s. Structural attenuation is equal to 0.815 dB/mm (longitudinal wave

at 2 MHz) and to 3.885 dB/mm (transverse wave at 2 MHz);

3. the collar, made of carbon steel, has [27] density 7.8 g/cm3, longitudinal wave velocity equal to

5900 m/s and transverse wave velocity equal to 3230 m/s. Structural attenuation is equal to

0.006 dB/mm (longitudinal wave at 4 MHz) and to 0.006 dB/mm (transverse wave at 4 MHz).

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The probes, adopted for perpendicular and angled inspections, and their modelling were exactly

the same already described for the case of the central region of the composite axle. The result of

the simulation of the physical sound beam for perpendicular incidence of longitudinal sound waves

in the lateral region of the composite axle is shown in Figure 66. As can be seen, no big issues are

observed in the transmission of the acoustic energy from the composite inner tube to the adhesive,

while very few of the sound energy is actually transmitted from the adhesive to the metallic stub,

due to the strong mismatch of acoustic impedance between the two materials. This can be a real

trouble during real inspections and should be checked by suitable experiments.

The same can be concluded observing the result of the simulation of the physical sound beam for

angled incidence of shear sound waves in the lateral region of the composite axle shown in Figure

67. In this case, due to the anisotropy of the involved composite material, the sound beam is, again,

significantly scattered along many different directions, as well. Moreover, it is worth noting that

multiple refraction angles have to be taken in to account due to the presence of multiple interfaces.

Figure 66. Simulation of the physical sound beam for perpendicular incidence of longitudinal sound waves in the lateral region of the composite axle.

Inner tube

Steel

Adhesive

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Figure 67. Simulation of the physical sound beam for angled incidence of shear waves in the lateral region in the central region of the composite axle.

Steel

Adhesive

Inner tube

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Defect within the inner tube

Defect within the adhesive

Defect within the metallic stub

Figure 68. Ultrasonic responses of the lateral region of the composite axle inspected by normal incidence of longitudinal waves.

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Figure 68 gathers the results, obtained for perpendicular incidence of longitudinal sound waves in

the lateral region of the composite axle, in terms of B-Scan and of the A-Scan corresponding to the

maximum value of the response of the inspected defect. The adopted defect shape and size were

the same previously described for the central region of the axle. As can be seen, the defect within

the inner tube can be easily detected, the defect within the adhesive cannot be detected due to the

shadowing effect of the high impedance mismatch at the interface between the adhesive and the

metallic collar and the defect within the metallic collar can be detected, but with a very low entity of

reflected sound energy. Actually, the issue arising for the defect within the adhesive has no solution

and, consequently, it has to be considered in the preparation of inspection procedure and

maintenance plans or it requires the development of other approaches, probably based on SHM.

On the other hand, in the case of the defect within the metallic stub, the present simulations are

performed in ideal conditions (no background noise, no sound transfer losses, …) and the outcome

should be validated by suitable experiments.

Figure 69 gathers the results, obtained for angled incidence of shear sound waves in the lateral

region of the composite axle, in terms of S-Scan and of the A-Scan corresponding to the maximum

value of the response of the inspected defect. The adopted defect shape and size were the same

previously described for the central region of the axle. As can be seen, all of the three defects can

be clearly detected, even if the defect tip diffraction is very well highlighted, and this helps the

possible sizing of the defect, in just one case, while, in the other two cases, it is much less

pronounced, even if the detectability of the defect still remains relevant. On the other hand, the

present simulations are performed in ideal conditions (no background noise, no sound transfer

losses, …) and the outcome should be validated by suitable experiments.

Finally, due to the complicated morphology, characterized by the presence of many notched

sections, of the external surface of the metallic collar, a series of analyses were carried out in order

to understand if some of such notched sections could represent an issue for UT inspections. Figure

70 gathers the results of all the considered cases: the conclusion is that no relevant issues seem

to be actually present.

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Defect just below the interface between the inner tube and the metallic stub

Defect just above the interface between the inner tube and the metallic stub

Defect at the external surface of the metallic stub

Figure 69. Ultrasonic responses of the lateral region of the composite axle inspected by angled incidence of shear waves.

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Figure 70. Ultrasonic responses of the external surface of the metallic collar inspected by angled incidence of shear waves.

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Conclusions on the feasibility analysis of UT of the composite axle

Based on the results of the analyses presented so far, the following conclusions on the feasibility

of UT can be drawn:

• UT seems to be effectively applicable to the central and lateral regions, even if it shows

significantly different sensitivity levels: the central region seems to be more inspectable, by

UT, than the lateral one.

• The scarf bonded joint has not been investigated because its features (tapered geometry

and alternate materials) suggest, from the beginning, a very difficult application of UT.

• UT simulations were implemented considering ideal conditions (no background noise, no

transfer losses, …), so careful experimental validation should be considered.

• The optimization of UT set-up should be carried out in terms of Probability of Detection,

which, on the other hand, requires an experimental validation, as well.

10.3 POSSIBLE SOLUTIONS FOR SHM

In this Section, possible solutions for structural health monitoring (SHM) of the HMC axle are

discussed and results of a preliminary assessment of the feasibility of a strain based SHM system

for the bonded joint are presented. The focus is on the adhesively bonded joint, that appears to be

the region less suitable for UT inspections.

A large variety of sensors are available for SHM of bonded joints, like the one present in the HCM

axle studied in this project. These sensors can be divided in the following classes, according to the

physical principle that is exploited:

• Acoustic emission

• Elastic wave based methods (particularly, ultrasonic guided waves)

• Vibration monitoring

• Strain sensing

For the present application, a distributed strain sensing technique is proposed, as it does not

require continuous monitoring during operation, as some the other above-mentioned techniques

do (acoustic emission, vibration monitoring) and does not require additional research for the case

of bonds between dissimilar materials, as guided waves would require.

The principle of crack detection and monitoring based on distributed strain sensing consists of

measuring and recording strain patterns along predefined paths in the critical areas at fixed time

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intervals, under static loads, and compare them with values measured the beginning of the service

life. The expected variations of the strain pattern due to the presence of an advancing crack can

be obtained by FE simulations.

Distributed sensing can be achieved by means of an array of sensors, be them physical or virtual.

Physical sensors can be electrical strain gages or fiber optic sensors, like Fibre Bragg Gratings

[28]. Virtual sensors can be defined along fiber optics interrogated by Optical Backscatter

Techniques. In this case, a spatial resolution up to 0.7 mm can be achieved [29].

The back-face technique is often employed to monitor cracks in adhesively bonded joints, as the

strain values and distributions on the free surface of the adherends are modified by the presence

of an advancing front. The detection and tracking of features of the strain distributions associated

to the presence of a crack can allow to infer the shape and position of the crack front.

Figure 71. Schematic view of the installation of a strain sensing fiber optic

This principle is applied to the bonded joint between the metallic collar and the composite outer

tube. A distributed sensing method by optical fibres and an OBR distributed sensing technique is

designed to monitor the back face strain along longitudinal paths, originating from the beginning of

the overlap of the outer composite tube over the collar, in the configurations shown in Figure 71.

One fibre is bonded onto the surface of the composite tube, and strain can be read during

inspections under static loading. The wheelset needs to be rotated until the fibre coincides with the

highly stresses fibres of the composite tube under bending.

Path of the fiber optic

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Figure 72. Size and position of the simulated crack (10 mm crack length shown in this picture)

The feasibility of this SHM system is assessed by FE simulations. Three models were built, one

with an integer bond-line, and two with an artificial crack of 5 mm and 100 mm length. The crack is

assumed to stem from the beginning of the overall and run parallel to the bond-line. The crack front

is assumed uniform and perpendicular to the axle’s axis, as it can be expected in the case of crack

propagation under rotating bending conditions. Figure 72 showcases a schematic representation

of the crack inserted in the model. The presence of a crack was simulated by modifying the

dimensions and the shape of one slave surface in the surface to surface tie constrains that defines

the adhesion of the adhesive layer to the outer composite tube in the FE model.

Longitudinal strains were extracted from the FE models along the node path shown in Figure 73.

To define longitudinal strains, a local coordinate system was defined with its 1 axis coinciding with

the fiber optic axis. Figure 74 showcases the strain patterns for the three cases considered. It

clearly appears that the strain patterns are modified by the presence of the crack and that the

longitudinal strain pattern translates in the same direction of the advancing crack.

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Figure 73. The node path used for the extraction of the strain values

No crack 5 mm crack 10 mm crack

Figure 74. The different strain patterns (longitudinal, with reference to the 1 axis of the local coordinate system shown in yellow) for increasing simulated crack length.

Figure 75 showcases the three curves corresponding to the values of the longitudinal strains

extracted along the path. It clearly appears that the blue curve, corresponding to the strain values

of the joint without any crack, translate along the path defined to extract strain values by a distance

that is close to the increment of crack length. The relationship between crack length and

displacement of the strain curve does not appear to be linear. Nonlinearity is likely to be due to the

non-uniform thickness of the substrate (scarf joint). Moreover, strain values at the beginning of the

overlap in the integer joint and at a distance close to the position of the crack length are close to

zero as expected, but negative. This is likely to be due to the distortion of the elements, whose size

is too coarse with respect to the scale of the defect.

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Figure 75. Strain values along the longitudinal path, for different simulated crack lengths

In spite of these difficulties that could be overcome by more refined models, it seems that a SHM

technique based on strain values measured along the path identified in Figure 71, after appropriate

calibration based on refined simulations and experimentally validate, can constitute a feasible

solution for periodic SHM of the bonded joint at inspection intervals. The definition of the inspection

intervals would require experiments to define the crack propagation speed as a function of the

crack length and the critical length, i.e. the crack length corresponding to the failure of the joint.

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11. ANALYSIS OF THE IMPACT RESPONSE

To verify in detail the consequences of possible impacts onto the axle of stones raised from the

ballast during the passage of the train, a specific analysis campaign was implemented.

11.1 OBJECTIVE OF THE IMPACT ANALYSES

Impact represents a particularly severe condition for the axle design. The objective of the

implemented impact analyses is to identify potential criticalities in the system design and to suggest

possible countermeasures to be taken in possible following detailed design and optimization

phases. Regulatory scouting was performed to identify the impact characteristics of railway axles.

EN 13261:2009+A1 Railway applications - Wheelsets and bogies - Axles - Product requirements

standard defines axle characteristics, qualification procedures and delivery conditions of axles for

use on European networks. It defines characteristics of forged or rolled solid and hollow axles,

made from vacuum-degassed steel grade EA1-Normalized that is the most used grade on

European networks. For hollow axles, this standard applies only to those that are manufactured by

machining a hole in a forged or rolled solid-axle [30]. The standard foresees two different impact

test methodologies, namely:

- Paragraph 3.2.2 (Impact Test Characteristics) refers to EN 10045-1 Metallic materials-

Charpy impact test - Part 1: Test Method and regards some specific test samples taken

from axles.

- Annex C which analyzes the effect of the impact on the coating of the axle with a specific

described method.

11.1.1 EN 13261:2009+A1 - Paragraph 3.2.2 Impact Test Characteristics

Considering the axle design described in Chapter 2, the test methodology related to solid axles

described in Paragraph 3.2.2 of the abovementioned standard could be neglected, the focus should

be directed to the one related to the hollow axles.

Considering hollow axle design, test pieces for Charpy impact test shall be taken from three levels

in the largest axle section:

1) as near as possible to the external surface;

2) at mid-distance between external and internal surfaces, and near the internal surface of

hollow axles [30].

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Figure 76. Location of test pieces for hollow axles according to EN 13261 2009 +A 1 2010 [29]

The abovementioned test procedure is specifically designed for steel axles, as almost all the

existing axles for railway applications. Since the innovative axle design foresees the use of

composite material, which is non-uniform by definition, the test procedure seems to be hardly

applicable to the present design concept. Furthermore, according to axle design, composite tubes

should not be thick enough to extract specimens of correct dimensions.

11.1.2 EN 13261:2009+A1 – Annex C

Paragraph 3.9.1.4 of the standard describes resistance to impacts which is the ability of a coating

to protect the axle from damage due to impacts from projectiles, e.g. ballast (this characteristic

applies only to class 1 axles sections which are those subject to atmospheric corrosion and

mechanical impacts). The test piece shall be the axle or an axle section covered with the coating

to be evaluated and shall be tested by firing a projectile onto the protected surface following Annex

C of the same standard [30].

The test method is to fire a projectile perpendicular to the protected surface and then to study the

change to the coating and that of the test piece surface. A treated steel projectile (diameter: 32

mm; top angle: 105°; mass: 60 g Vickers hardness: 400) shall be fired by the expansion of a volume

of air compressed at 8 bar to ensure an exit speed of 19,4 m/s. The resistance to the impact is

assessed at – 25 °C and ambient temperature [30].

After the impact, the appearance of the coating surface shall be examined with the naked eye, as

well as the appearance of the test piece surface once the coating has been removed. Changes

shall be recorded and compared to the criteria given by this standard. No hole shall be found in the

coating, nor shall there be any alteration to the test piece surface [30].

Although also this test methodology is conceived for steel axles, especially class 1 axle sections,

it can be considered a first reference to evaluate the impact performance of the developed axle

design. FEM analyses has been set-up to reproduce, as accurately as possible, the test

methodology prescribed by Annex C of EN 13261:2009+A1 standard.

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11.2 SOFTWARE TOOL

The numerical model was set up using the Ansys© Workbench 2020 R2 suite, with the adoption of

the Ansys Composite PrepPost (ACP) tool for the definition of the two composite tubes stacking

sequence. The tool also allows performing the post-processing of results by evaluating the most

used failure criteria for composite materials.

Figure 77. Analysis workflow in Ansys© Workbench 2020 R2 suite.

11.3 GEOMETRICAL MODEL

The geometrical model considered for the analysis is based on the design described in Chapter 2

and comprises:

- the axle, made of two concentric composite tubes and two steel collars at its ends;

- the spherical projectile impacting the axle at its middle.

Figure 78. Simplified geometrical model considered for impact analyses.

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As the analysis objective was to investigate the behaviour of composite parts, the steel collars were

simplified as cylindrical parts in the analyses.

The projectile was considered spherical with a diameter equal to 32 mm. Trial analyses were

performed also with a pyramid-shaped projectile, but convergence problems were encountered due

to its sharp edges.

11.4 MATERIALS

The materials adopted are based on the library implemented in Ansys

- Side collars: Structural steel (E=200 GPa, δ= 7850 kg/m3)

- Spherical projectile: Structural steel with modified density to conform its mass with

requirements from Annex C.3: “Method to assess resistance to the impact of the coating”

(E=200 GPa, δ=3500 kg/m3)

- Composite material: Epoxy Carbon UD (UniDirectional) Prepreg, customized with the

properties included in the latest version of the design guidelines (Gurit UCHM450 SE84 –

UD)

Figure 79. Composite material properties table in Ansys© Workbench 2020 R2 suite.

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11.5 NUMERICAL MODEL

The numerical simulations required a particular fine-tuning for the setting of the composite layers

that constitute the two tubes of the axle, but also more generally for the numerical setup of the

analysis. The analysis is carried out in the form of an implicit transient structural simulation.

The methodology for defining composite layers adopted in Ansys ACP tool allows to:

- Define the fabric characteristics (thickness, material);

- Implement the stacking sequences;

- Define the modelling plies with relative deposition angles;

- Expand the layers to create 3D solid mesh starting from the surfaces of the tubes.

Concerning the axle design described in Chapter 2, the geometry and composite layers stacking

sequences considered in the analyses are those represented in Figure 80 (a restatement of Figure

12).

Figure 80. Composite layers stacking sequences considered in the analyses.

Both tubes are composed by a sequence of 30 plies each, with a ply thickness of 0.45 mm. To

optimize computational efficiency while maintaining adequate results accuracy, the solid mesh is

generated as follows:

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- Primary tube: 5 plies for each mesh layer, a single mesh layer thickness of 2.25 mm, 6

mesh layers in total

- Secondary tube: 3 plies for each mesh layer, a single mesh layer thickness of 1.35 mm, 10

mesh layers in total

Figure 81. Composite tubes mesh in radial and tangential direction

From a global point of view, hexahedral linear elements were adopted for meshing both the

composite tubes and the side collars, except for the spherical projectile, realized with pure

tetrahedrons. Since the area of interest was near the impact with the sphere, a gradual element

refinement from the ends to the centre of the axle was performed, starting from an average

longitudinal size of 10mm the elements, reaching 3mm in the impact area. The sphere represented

3mm tetrahedrons. The total amount of elements was almost 1.5 million.

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Figure 82. Discretized model of all components

Figure 83. Discretized model of all components (section view)

During the analysis set-up, the following assumptions were performed:

- General joints are applied to constrain the collars to the ground, leaving only the rotations

along the vertical axis free;

- Bonded contacts are applied between the metal collars and the composite tube as well as

between primary and secondary tube, as investigation on glued joints is reported in Chapter

8;

- Simple frictionless contact is applied between the secondary tube and the spherical

projectile.

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11.6 LOADING CONDITIONS

Two analyses were performed to evaluate sensitivity to impact angle, namely:

- The first analysis with a spherical projectile moving with adirection normal to the axle

surface (radially concerning the tubes axis), with an initial velocity of 19.4 m/s, as described

in Annex C.4 of [30];

- A second analysis, completely analogous to the previous one with spherical projectile

impacting onto the axle with 45° angle respect to axle surface.

Trial analyses were performed also with a pyramid-shaped projectile, but convergence problems

were encountered due to its sharp edges.

11.7 RESULTS

Post-processing of results was performed to evaluate the structural response of the proposed

design to the impact load previously described. The post-processing of results was performed

within the specific ACP module and was focused on the evaluation of possible occurrence of

failures in the composite material.

In particular, to evaluate the occurrence of a failure in the composite material, the Hashin criterion

was adopted, which is specifically designed for UD composite fabrics and is capable of identifying

the presence of:

- Fibre failure;

- Matrix failure;

- Delamination.

The following plots show the behaviour of the system in terms of damaged elements, the colour

scale does not represent a physical quantity, since it corresponds to a damage parameter which

only defines whether the composite layers present failure. In detail, blue areas indicate values close

to 0 and no occurrence of physical failure. Colours from light blue to orange represent values from

0 to 1, where no occurrence of physical failure is foreseen but safety coefficient reduces

proportionally as the parameter approaches 1. The red areas, which identifies the elements with a

value higher than one, are critical from the point of view of the structural performance and need to

be investigated.

For red coloured elements, ACP provides information about the failure criterion by identifying the

elements with the following code:

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- “hf” indicates fibre failure;

- “hm” indicates matrix failure;

- “hd” indicates delamination.

Furthermore, the software tool provides information about the ply number (in parenthesis) for each

element which is subjected to failure

11.7.1 Impact direction: normal to axle surface

The following plots show the damage contour plots for the load case in which the spherical projectile

impacts the axle surface with normal direction.

Figure 84. Damage plot in the nearby of the impact region - impact angle 90°

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Figure 85. Damage plot in the nearby of the impact region (section view) - impact angle 90°

As shown in Figure 84 and Figure 85, damage occurs only in the secondary tube near the impact

region, while no significant alteration is recorded in the remaining parts of the system.

In detail failure affects the 21 external plies underlying the impact region, corresponding to almost

a 10 mm depth, which is equal to the about the 70% of the thickness of the secondary tube. Failure

involves mainly the composite matrix, as expected, due to the high compression load. Delamination

occurs instead on the external surface of the secondary tube, in the nearby of the “perimeter” of

the impacted region.

11.7.2 Impact direction 45° to axle surface

The following plots show the damage contour plots for the load case in which the spherical projectile

impacts the axle surface with 45° angle respect to the axle surface itself.

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Figure 86. Damage plot in the nearby of the impact region - impact angle 45°

Figure 87. Damage plot in the nearby of the impact region (section view) - impact angle 45°

Also in this load case, as shown in Figure 86 and Figure 87, damage occurs only in the secondary

tube in the nearby of the impact region, while no significant alteration is recorded in the remaining

parts of the system. Damage plot is very similar to the previous load case, as expected damage

pattern is no more symmetric.

In detail failure affects all the 30 external plies underlying the impact region, corresponding to the

whole 13.5 mm thickness of the secondary tube. Failure involves mainly the composite matrix, as

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expected, due to the high compression load. Delamination occurs instead on the external surface

of the secondary tube, in the nearby of the “perimeter” of the impacted region.

11.8 MITIGATION MEASURES / FURTHER DEVELOPMENTS

Taking into account the previous results, it seems clear that the test procedure described in

Appendix C [30] results to be highly severe for the assembly, since it results in local failure, mainly

within the matrix, of a certain amount of plies belonging to the secondary tube. This behaviour

seems to be coherent with the type of load applied since the structure is subjected to a high

compressive load close to the impact point with the projectile. It is likely that the axle will not perform

properly, leading to safety and security problems, after such impact, which could be caused by

stones raised from the ballast during the passage of the train.

These kinds of phenomena indeed occur especially for high-speed trains, which could be the last

applications for composite axles, but mitigation measures shall be considered.

Mitigation measures comprise onboard sensors which record impacts and lead to a condition-

based maintenance approach as wells as, above all, an external protection system which can

absorb the highest amount as possible of impact energy. Due to the many challenges tackled within

the axle design phase, it has not been possible in the current project to perform a detailed design

of external protection systems which could solve this issue.

Among the possible solutions, some include the possibility to apply onto the axle surface an

additional external layer of material with high impact absorbing properties. Another approach could

be to create a fixed (not bonded to the axle) external shield. The following table summarizes the

pros/cons of the two different solutions:

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Table 10. Pros and Cons of the impact mitigation solutions

Solution Pros Cons

Additional layer bonded onto

axle surface

- Limited modifications to

axle and bogie designs

- Limited effect on train

aerodynamic

- Depending on material, it

could also provide fire

protection

- Difficulties in inspection

and maintenance on axles

- Additional rotating and

unsprung mass

Fixed shield - Ease of inspection and

maintenance on axles

- No additional rotating and

unsprung mass

- Aerodynamic drag

- Modifications could be

requested to integrate into

bogie design

To reduce the effect of an impact on the system it could be interesting to implement the effect of a

protective coating on the secondary tube. If adequately thick, an additional external layer could

absorb part of the impact energy, reducing the damaged area in the composite material.

For steel axles, Lursak® is the solution developed by LRS to the increasing demand to guarantee

the total protection of railway axle against corrosion and damages derived from ballast impacts. It

is an epoxy combination reinforced by synthetic fibres applied normally with a thickness of 5mm.

In case of damage to the Lursak surface due to very heavy impact, the coating can be easily and

quickly repaired [32]. As it was conceived for denting protection of steel axles, it should be

investigated its capacity to absorb high impact energy and limit damages to underlying composite

layers. However, it should be removed to inspect the composite secondary tube and therefore it is

not deemed feasible.

Among the various possible alternative solutions, two are promising and worthy of further study:

- Additional composite layer with Kevlar® fibres: Kevlar® is an organic fibre in the

aromatic polyamide family, with a unique combination of high strength, high modulus,

toughness and thermal stability. It was developed for demanding industrial and advanced-

technology applications [31]. The considerable resistance to shear stresses, typical of

Kevlar fibres, could allow a significant increase in terms of impact resistance, limiting the

overall dimensions of the system and ensuring good protection of the underlying layers. An

alternative to Kevlar fibres could be ultra-high molecular weight polyethylene fibres (e.g.

Dyneema®). It is worth pointing out that if tests confirm that ballast impact would result in

matrix damage as shown by simulation, a more compliant protective layer could offer more

protection.

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- Additional foam layer: Metallic (e.g. aluminum) or polymeric foams to be positioned onto

the axle surface which can absorb the most of impact energy. Other compliant materials

could be also considered. An additional metallic thin layer should be positioned onto the

foam layer to protect it from the high shear stress caused by the impact with a sharp ballast

stone. This solution is the most complex, but probably the most effective.

Concerning the approach of fixed shields, it regards the creation of a structure to be fixed to the

bogie frame which protects the axle from the impact of ballasts. This structure could be composed

by metallic (e.g. steel) sheets or a textile layer fixed to a beam metallic structure. Concerning the

latter, RINA-C, in the framework of FLY-BAG2 project (Grant agreement ID: 314560) developed a

high strength and impact resistant multi-layer textile to contain blast and fragments produced by an

explosion. A preliminary feasibility study has been already proposed to an Italian industrial

company in the railway sector to adapt this solution to protect systems located in the lower part of

train vehicles against impacts from ballast.

The aforementioned solutions result to be necessary, especially if the results of the numerical

simulations are considered. It is important to notice that all the mitigation measures previously

described require periodical integrity checks, to ensure the overall structural condition and identify

possible damaged areas, that would need a restoration of the protective structure.

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12. ANALYSIS OF THE DYNAMIC BEHAVIOUR

The wheelset is a component of a railway vehicle; in which it is integrated. Therefore, its running

behaviour can only be considered in a realistic way by simulating the behaviour of the entire vehicle.

12.1 VEHICLE MODEL

The wheelset, which is analysed in this project, is designed for the use in metro vehicles. Therefore,

the multibody system used for the simulation of the running behaviour should represent a vehicle

of such type. Unfortunately, relatively few data, which is required for setting up a multibody model

of a metro vehicle, is publicly available. In several works e.g. by Pombo and Ambrosio [33] and by

Marques [34] the data set for the vehicle of the type ML95 operated by the Lisbon metro company

(Metropolitano de Lisboa) has been published. Unfortunately, the bogie design of this vehicle uses

outboard axle boxes instead of inboard axle boxes as chosen for the design of the wheelset used

in the present project. Nevertheless, this is the publicly available data, which seems to come the

closest to the present application case. Therefore, these parameters are used; the essential

modifications are the adaptation of the lateral distances of the axle boxes and of the primary

suspension to the inboard design and the adaptation of the inertia of the wheelsets, which will be

discussed in the following Section. It should also be noted that each axle box is modelled as a

separate body. The following illustration shows a drawing of the vehicle’s bogie.

Figure 88. Bogie of the ML95 vehicle (source [34])

The wheelset is interacting with the track via the wheel-rail contact, which possess a high stiffness.

Therefore, the running on a completely rigid track may lead to unrealistic results so that at least an

approximate description of the track flexibility and dynamics is required. Such a description can be

implemented by using a substitution track model, which consists of “standard multibody system

elements” like bodies, springs and dampers. Their parameters are chosen in such a way that the

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substitution model reproduces the motions of the rail head as a reaction to a force acting on it.

Usually, such a substitution model supports one wheelset and moves together with it along the

trajectory of the track. A family of such substitution track models has been developed and presented

by Chaar and Berg [35]. In the present project, the track model A presented in this paper has been

implemented into the simulation model, but an extension to more complex models can be done in

a relatively easy way. This model is shown in the following illustration.

Figure 89. Substitution track model by Chaar and Berg [35]

The interaction between a railway vehicle and its infrastructure strongly depends on the trajectory

of the track including e.g. curves and on track irregularities, which are inevitable in real operation.

In the present project, data for the trajectory and for the irregularities of a metro line was provided

by Metro de Madrid. The data for the trajectory includes the curvature, i.e. the reciprocal value of

the curve radius, and the cant or superelevation, i.e. the vertical distance between the outer and

the inner rail in a curve; the data for the irregularity describes the vertical and lateral deviation of

each rail from its ideal position. The wheel profile, which is specific for Metro de Madrid, and the

track geometry using UIC54 rail with an inclination of 1:20 were also provided by Metro de Madrid,

although in the present case the standard gauge of 1435 mm was applied.

The entire vehicle model was developed and created in the multibody system software SIMPACK,

which is widely used in the analysis of the dynamics of railway vehicles. The following image, Figure

90, shows the multibody model. It should be noted that in this model the axle boxes, which are

represented as yellow cuboids, are installed between the wheels.

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Figure 90. SIMPACK model of the investigated vehicle

12.2 WHEELSET INERTIA

The goal of the present investigation is to evaluate the advantages of the new wheelset design.

This is done by simulating the same scenarios for two types of wheelsets, here a wheelset of

conventional design and the wheelset of the new design, and by comparing the results.

In a “classical” multibody system, bodies are elements, which are rigid, i.e. undeformable, and

possess an inertia. Therefore, in the present investigation the two different designs of the wheelsets

are represented by different inertia properties. It should be noted that both wheelsets considered

in this investigation have a reflection symmetry to their middle cross plane, i.e. the xz-plane, and a

rotational symmetry around the 𝑦-axis. As a result, the centre of gravity is located in the geometrical

centre of symmetry. Furthermore, as a result of the rotational symmetry, the moment of inertia with

respect to the centre of gravity is equal for each transversal axis so that the inertia moments 𝐼𝑥𝑥

and 𝐼𝑧𝑧 are equal and no deviation moments occur.

For the new wheelset, the original steel axle is replaced by new axle, while the same wheels are

used. The wheelset axle has the same symmetry properties as the entire wheelset, i.e. the

reflection symmetry to the 𝑥𝑧-plane and the rotational symmetry around the 𝑦-axis, and therefore

also the same position of the centre of gravity.

The inertia data for the conventional steel axle was provided by Lucchini RS. After correcting some

inevitable very small numerical errors, the inertia is described by the following parameters:

• Mass: 𝑚Axle,steel = 197.882 kg

• Mass moment of inertia for transversal axis: 𝐼𝑥𝑥,Axle,steel = 𝐼𝑧𝑧,Axle,steel = 52.8686 kg ∙ m2

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• Moment of inertia for axis of symmetry: 𝐼𝑦𝑦,Axle,steel = 0.893713 kg ∙ m2

For the HMC axle, the following parameters were calculated based on data provided by the

University of Nottingham

• Mass: 𝑚Axle,comp = 78.7489 kg

• Moment of inertia for transversal axis: 𝐼𝑥𝑥,Axle,comp = 𝐼𝑧𝑧,Axle,comp = 27.2336 kg ∙ m2

• Moment of inertia for axis of symmetry: 𝐼𝑦𝑦,Axle,comp = 0.473088 kg ∙ m2

The inertia data for the conventional steel wheelset, which serves as the reference case, was

provided by Lucchini RS. Also here, some inevitable very small numerical errors have been

corrected, so that the inertia is described by the following parameters:

• Mass: 𝑚WS,steel = 859.524 kg

• Moment of inertia for transversal axis: 𝐼𝑥𝑥,WS,steel = 𝐼𝑧𝑧,WS,steel = 457.740 kg ∙ m2

• Moment of inertia for axis of symmetry 𝐼𝑦𝑦,WS,steel, = 73.2372 kg ∙ m2

The inertia parameters of the new wheelset are obtained by subtracting the inertia parameters of

the steel axle from the conventional steel wheelset and adding the inertia parameters of the

composite axle. For instance, the mass of the new wheelset is obtained by:

𝑚WS,comp = 𝑚WS,steel − 𝑚Axle,steel + 𝑚Axle,comp

The moments of inertia are treated in the same way. Since the centres of gravity of the entire

wheelset and of the wheelset axle coincide, no further adaptations are required. Based on this, the

following inertia parameters of the new wheelset are obtained:

• Mass: 𝑚WS,comp = 740.391 kg

• Moment of inertia for transversal axis: 𝐼𝑥𝑥,WS,comp = 𝐼𝑧𝑧,WS,comp = 432.105 kg ∙ m2

• Moment of inertia for axis of symmetry: 𝐼𝑦𝑦,WS,comp = 72.8166 kg ∙ m2

The replacement of the steel axle by the HMC axle mainly affects the mass of the wheelset, which

is reduced from 𝑚WS,steel = 859.524 kg to 𝑚WS,comp = 740.391 kg, i.e. by approximately 14%. In

contrast to this, the wheelset’s rotational inertia described by the moments of inertia is hardly

affected. This can be explained by considering the equations for the moments of inertia:

𝐼𝑥𝑥 = ∫(𝑦2 + 𝑧2)𝑑𝑚 , 𝐼𝑦𝑦 = ∫(𝑥2 + 𝑧2)𝑑𝑚 , 𝐼𝑧𝑧 = ∫(𝑥2 + 𝑦2)𝑑𝑚

A mass particle having a larger distance to the reference point makes a higher contribution to the

moment of inertia. Therefore, in the case of the wheelset the highest contribution to the moments

of inertia results from the wheels, which have a larger radius than the axle and are mounted in a

lateral distance to the wheelset’s centre.

One important motive for using other materials than steel for the wheelset is the reduction of the

unsprung mass, since a reduction of the unsprung mass usually reduces the dynamic forces acting

between the wheel and the rail. However, it has to be noticed that the axle boxes also contribute

to the unsprung mass and to the moment of inertia, which is relevant for the wheelset’s yaw motion.

For the vehicle used in the present case, each axle box has a mass of 𝑚AB = 88 kg. As a result,

the two wheelsets have the following unsprung masses:

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• Steel wheelset: 𝑚unspr,steel = 𝑚WS,steel + 2 ∙ 𝑚AB = 1035.524 kg

• HMC wheelset: 𝑚unspr,comp = 𝑚WS,comp + 2 ∙ 𝑚AB = 916.391 kg

Thereby, the use of the composite axle instead of the steel axle reduced the unsprung mass by

11.5% of the original value. This order of magnitude should be kept in mind with regard to the

evaluation of the running behaviour.

12.3 SCENARIO “RUNNING ON A CURVED MEASURED TRACK”

In the first scenario, the running of the vehicle on a measured track is considered. The measured

data, which were provided by Metro de Madrid, describe the track layout and the track irregularities.

The parameters for the track layout are the curvature, i.e. the reciprocal value of the curve radius,

and the superelevation, i.e. the vertical distance between the outer and the inner rail in the curve.

The irregularities are indicated by the lateral and vertical deviation of each rail from the ideal

position. All these parameters were provided as functions of the distance along the track. Also, the

wheel-rail geometry including the profiles of wheel and rail and the rail inclination were provided by

Metro de Madrid.

The following results were calculated for a running speed of 𝑣0 = 54 km/h. This speed was chosen,

because it permitted the passing through the curves of the track without exceeding the limits for

operation. The maximum absolute value of the curvature is max |1

𝑅𝐶| = 0,0052 m−1 , which is

equivalent to a minimum curve radius of 𝑅𝐶,min = 192.3 m. The ideal superelevation ℎ0, for which

the lateral acceleration is fully compensated, is approximated by

ℎ0 ≈𝐸 ∙ 𝑣2

𝑅𝐶 ∙ 𝑔

Here, the sign of the curvature 1

𝑅𝐶, where positive and negative values describe right and left curves,

respectively, has to be taken into account so that in the present case the ideal superelevation is

positive for right curves and negative for left curves. For the standard track gauge, the lateral

distance between the contact points is 𝐸 ≈ 1.5 m, and the gravitational acceleration is 𝑔 = 9.81 m

s2.

The cant deficiency Δℎ = ℎ0 − ℎ is calculated as the difference between the ideal superelevation

ℎ0 and the real superelevation ℎ, whereby the signs of ℎ0 and ℎ are taken into account. For a

running speed of 𝑣 = 54km

h= 15

m

s the absolute value |Δℎ| of the cant deficiency does not exceed

0.15 m, i.e. |Δℎ| < 0.15 m, which is in accordance with the usual limits for operation. The following

diagrams show the curvature 1

𝑅𝐶 and the superelevation ℎ of the used metro line and the cant

deficiency Δℎ, which is calculated for the running speed of 𝑣0 = 54 km/h and the contact point

distance of 𝐸 = 1.5 m, as functions of the track length 𝑠.

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Figure 91: Parameters of the used metro line: Curvature 𝟏/𝑹𝑪 (upper diagram), superelevation 𝒉

(middle diagram), cant deficiency 𝚫𝒉 for 𝒗𝟎 = 𝟓𝟒 𝐤𝐦/𝐡 and 𝑬 = 𝟏. 𝟓 𝐦 (lower diagram).

The simulation of a relatively complex multibody system provides a lot of data. In the present case,

some quantities will be considered, which characterize the running behaviour of the wheelset and

its interaction with the infrastructure. These quantities are:

• The dynamic vertical contact force Δ𝑄 acting in a wheel-rail contact

• The sliding mean value Σ𝑌2m of the resulting lateral force Σ𝑌 between wheelset and rail over

a distance of Δ𝑠 = 2

• The 𝑇𝛾 value, also known as the wear number, for a wheel-rail contact

The wheelsets are numbered in the scheme that the first digit indicates the bogie and the second

digit indicates the wheelset within the bogie, i.e. the wheelsets 11 and 12 are the leading and the

trailing wheelsets of the leading bogie, respectively, and the wheelsets 21 and 22 are the leading

and the trailing wheelsets of the trailing bogie, respectively. In the analysis, the following colour

code will be used:

• The blue curves denote the results calculated for the conventional steel wheelset.

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• The orange curve denote the results calculated for the new HMC wheelset.

First, the dynamic vertical contact force Δ𝑄 shall be considered. This force is defined in the

following way:

Δ𝑄(𝑡) = 𝑄(𝑡) − 𝑄0

Here, 𝑄(𝑡) denotes the current vertical wheel-rail contact force at the time 𝑡. The static vertical

wheel-rail force, which is constant, is denoted by 𝑄0. This formulation is chosen, because due to

different masses of the two different wheelset types the static force 𝑄0 depends on the used

wheelset type. The values of the static vertical wheel-rail force 𝑄0 are:

• Steel wheelsets: 𝑄0 = 23.725 kN

• HMC wheelsets: 𝑄0 = 23.040 kN

First, the dynamic vertical contact force Δ𝑄 shall be considered for the four wheel-rail contacts of

the leading bogie, i.e. for the contacts of the wheelsets 11 and 12. In the following diagrams, the

dynamic vertical contact force Δ𝑄 is displayed as a function of the curved track-length coordinate

𝑠.

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Figure 92. Comparison of the dynamic vertical wheel-rail forces 𝚫𝑸 at the leading bogie; 𝒗𝟎 =𝟓𝟒 𝐤𝐦/𝐡.; blue: steel wheelset; orange: HMC wheelset.

The orange curves (HMC wheelsets) cover the blue curves (steel wheelsets) nearly completely;

from the blue curves, only the peaks are visible. This indicates that for the new composite wheelsets

the dynamic vertical contact force Δ𝑄 is slightly lower than for the conventional steel wheelsets.

Very few blue peaks are visible; in these cases, the lower mass of the new HMC wheelsets distinctly

reduces the dynamic vertical contact force Δ𝑄. However, in total, the effect of the lower wheelset

mass is rather weak.

The dynamic vertical contact force Δ𝑄 obtained for the wheel-rail contacts of the trailing bogie, i.e.

for the contacts of the wheelsets 21 and 22 are displayed in the following diagrams.

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Figure 93. Comparison of the dynamic vertical wheel-rail forces 𝚫𝑸 at the trailing bogie; 𝒗𝟎 =𝟓𝟒 𝐤𝐦/𝐡; blue: steel wheelset; orange: HMC wheelset.

The diagrams for the wheel-rail contacts indicate a very similar result: The lower mass of the HMC

wheelset slightly reduces the dynamic vertical contact force Δ𝑄, but the effect of the reduced mass

is rather weak.

Next, the sliding mean value Σ𝑌2m of the resulting lateral force Σ𝑌 between wheelset and rail over

a distance of Δ𝑠 = 2 m is considered. It is calculated based on the following equation:

Σ𝑌2m = ∫ Σ𝑌(𝑠) 𝑑𝑠s0+2 m

s0

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Originally, this expression has been developed in order to evaluate the risk of lateral track shifting.

Here, the sliding mean value Σ𝑌2m must not exceed the following limit Σ𝑌max,lim:

Σ𝑌max,lim = 𝑘1 ∙ (10 kN +2 𝑄0

3)

Here, 2 𝑄0 is the static axle load of for each wheelset of the vehicle. In the present case of a

passenger vehicle, a factor of 𝑘1 = 1 has to be used. In the present case, the vehicle has the

following static axle loads for the two types of wheelsets:

• Steel wheelsets: 2 𝑄0 = 47.250 kN ⇒ Σ𝑌max,lim = 25.750 kN

• HMC wheelsets: 2 𝑄0 = 46.081 kN ⇒ Σ𝑌max,lim = 25.360 kN

Besides the evaluation of the risk of track shifting, the sliding mean sliding mean value Σ𝑌2m is also

helpful to obtain an impression of the level of the lateral forces Σ𝑌; these forces can sometimes

reach very high values, but for extremely short periods of time, so that these high values have

relatively little effect.

The following diagrams show the sliding mean values Σ𝑌2m for the four wheelsets.

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Figure 94. Comparison of the sliding mean values 𝚺𝒀𝟐𝐦 at the four wheelsets; 𝒗𝟎 = 𝟓𝟒 𝐤𝐦/𝐡; blue: steel wheelset; orange: HMC wheelset.

For all four wheelsets, the sliding mean values Σ𝑌2m stay distinctly below the limit values of

Σ𝑌max,lim = 25.750 kN (steel wheelsets) and Σ𝑌max,lim = 25.360 kN (HMC wheelsets). Generally, for

the leading wheelsets 11 and 21 higher values are obtained than for the trailing wheelsets 12 and

22. This is plausible, since for the curve entry the guiding force acting at the leading wheelset,

which enters the curve first, has to change the direction of motion of the bogie. The highest values

are observed at the leading wheelset 11. Also here, the blue lines (steel wheelsets) are nearly

completely covered by the orange lines (HMC wheelsets) so that just the blue peaks are visible.

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This indicates that the reduction of the unsprung mass in fact reduces the lateral guiding forces,

but also here the reduction is rather small.

Next, the 𝑇𝛾 value, also known as the wear number, is considered. The 𝑇𝛾 value describes the

energy per track length, which is dissipated in the wheel-rail contact. Therefore, it is an indicator

for the strength of the wear occurring in the wheel-rail contacts.

First, the 𝑇𝛾 values for the wheel-rail contacts of the leading bogie shall be considered. The

following diagrams show the 𝑇𝛾 values for the wheel-rail contacts of the wheelsets 11 and 12. Since

it can be expected that higher friction forces occur in curves, the track curvature is shown for

comparison.

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Figure 95. Comparison of 𝑻𝜸 values (wear numbers) at the leading bogie; 𝒗𝟎 = 𝟓𝟒 𝐤𝐦/𝐡; blue: steel wheelset; orange: HMC wheelset; magenta: track curvature.

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At the wheel-rail contacts of the leading wheelset 11, higher 𝑇𝛾 values are observed than at the

contacts of the trailing wheelsets 12. In the diagrams, only the peaks of the blue curves (steel

wheelsets) are visible, indicating that the 𝑇𝛾 values are lower for the HMC wheelsets than for the

steel wheelsets. The reduction of the 𝑇𝛾 values due to the reduced wheelset mass is slightly

greater than the reduction of the Σ𝑌2m values.

The following diagrams display the 𝑇𝛾 values for the wheel-rail contacts of the trailing bogie, i.e. for

the wheel-rail contacts of the wheelsets 21 and 22. Also here, the track curvature is shown for

comparison,

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Figure 96. Comparison of 𝑻𝜸 values (wear numbers) at the trailing bogie; 𝒗𝟎 = 𝟓𝟒 𝐤𝐦/𝐡; blue: steel

wheelset; orange: HMC wheelset; magenta: track curvature.

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The results are very similar to those obtained for the contacts of the leading bogie. Again, higher

𝑇𝛾 values occur in the contacts of the leading wheelset, here the wheelset 21, than in the contacts

of the trailing wheelset, here the wheelset 22. Also here, the 𝑇𝛾 values obtained for the composite

wheelsets are slightly lower than those obtained for the steel wheelsets.

In total, the comparison qualitatively confirms that a reduction of the unsprung mass reduces the

dynamic vertical contact forces, the lateral guiding forces and the energy dissipated in the wheel-

rail contacts due to friction. Quantitatively, the effect is rather weak, i.e. the values obtained for the

lighter composite wheelsets are only slightly lower than those obtained for the heavier steel

wheelsets.

12.4 SCENARIO “RUNNING ON A STRAIGHT TRACK WITH MEASURED IRREGULARITIES”

In the analysis presented in the previous Section, a running speed of 𝑣0 = 54 km/h was chosen

because of the curvature of the trajectory. The comparison of the results has shown that the

reduction of the unsprung mass reduces the dynamic vertical contact forces, the guiding forces and

the energy dissipated in the contact. It can be expected that the reduction of the unsprung mass

has a stronger effect at higher running speeds, since at higher speeds stronger dynamic

interactions can be expected. Therefore, the running behaviour shall now be investigated at a

higher running speed of 𝑣0 = 90 km/h. However, in order to do so, a straight track is used for the

trajectory, while the same irregularities are applied to the track. In this simulation, the first kilometre

of the track had to be excluded from the calculation because of numerical problems.

The analysis in the previous Section has shown that both bogies show qualitatively the same

behaviour. Therefore, for the sake of brevity, only the wheelsets 11 and 12 of the leading bogie

shall be considered here.

First, the dynamic vertical wheel-rail force Δ𝑄 is considered for the four wheel-rail contacts of the

leading bogie, i.e. the contacts of the wheelsets 11 and 12. It should be pointed out that these

diagrams cover a wider range up to 150 kN for the dynamic vertical wheel-rail force Δ𝑄, while in

the previous Sthis range could be limited to 30 kN.

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Figure 97. Comparison of the dynamic vertical wheel-rail forces 𝚫𝑸 at the leading bogie; 𝒗𝟎 =𝟗𝟎 𝐤𝐦/𝐡; blue: steel wheelset; orange: HMC wheelset.

Also here, the dynamic vertical wheel-rail force Δ𝑄 is generally lower for the new HMC wheelset

than for the conventional steel wheelset. Several peaks of the blue curve, which are not covered

by the orange curve, are clearly visible. This indicates that in these points the lower mass of the

HMC wheelset strongly reduced the dynamic force.

Next, the sliding mean value Σ𝑌2m is considered in order to evaluate the level of the guiding forces.

The results are displayed in the following diagrams.

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Figure 98. Comparison of the sliding mean values 𝚺𝒀𝟐𝐦 at the leading bogie; 𝒗𝟎 = 𝟗𝟎 𝐤𝐦/𝐡 blue: steel wheelset; orange: HMC wheelset.

With the exception of very few peaks occurring at the leading wheelsets 11 and 21, the values for

Σ𝑌2m occur stay far below the limit values limit values Σ𝑌max,lim = 25.750 kN (steel wheelsets) and

Σ𝑌max,lim = 25.360 kN (HMC wheelsets) also for the higher running speed. This can also be seen

as an indicator that the running stability is not yet a critical issue at this higher running speed.

Although in this scenario the running on a straight line is considered, also in this case higher values

Σ𝑌2m occur at the leading wheelset 11 than at the trailing wheelset 12. However, also here, the

peaks of the blue curves (steel wheelsets) hardly exceed those of the orange curve (HMC

wheelsets), so that also here the effect of the reduced un-sprung mass is relatively low.

Finally, the 𝑇𝛾 values, which are displayed in the following diagrams, shall be considered. It should

be pointed out that due to the higher level of the 𝑇𝛾 values the considered range, which has been

limited to 𝑇𝛾 ≤ 500 N, is extended here to 1000 N.

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Figure 99. Comparison of 𝑻𝜸 values (wear numbers) at the leading bogie; 𝒗𝟎 = 𝟗𝟎 𝐤𝐦/𝐡.; blue: steel wheelset; orange: HMC wheelset.

Again, higher 𝑇𝛾 values occur at the wheel-rail contacts of the leading wheelset 11. In these

diagrams, in particular those for the leading wheelset 11, the blue curves (steel wheelsets) are

more visible. This indicates that the reduction of the un-sprung mass mostly affects the energy

dissipated by the friction in the contact.

The results indicate that for higher running speeds in fact a stronger dynamic interaction between

the wheelset and the track can be observed. This becomes particularly evident from the dynamic

vertical wheel-rail forces Δ𝑄 and from the 𝑇𝛾 values. Regarding the lateral guiding forces described

by Σ𝑌2m, it has to be noted that in this scenario a straight line instead of a curved trajectory is used

so that the guiding forces required for curve running are eliminated.

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Of course, the behaviour of the vehicle is strongly influenced by the irregularity profile. In order to

estimate this influence, the scenario of running at 𝑣0 = 90 km/h on a straight track shall also be

considered for a different irregularity profile. In this case, the irregularities are taken from a section

of an upgraded mainline between Dortmund and Hannover in Germany. This upgraded line is

adapted to a regular operational speed of 200 km/h. For this line, only data for a section of 2 km

were available. Again, for the following results, an actual running speed of 𝑣0 = 90 km/h is used

for the metro vehicle. Also, the contact geometry defined by the profiles of wheel and rail and by

the rail inclination is kept unchanged.

Also in this case, the leading bogie shall be considered. In the following diagrams, the dynamic

vertical wheel-rail forces Δ𝑄 are compared for the steel wheelset and for the HMC wheelset.

Figure 100. Comparison of the dynamic vertical wheel-rail forces 𝚫𝑸 at the leading bogie; 𝒗𝟎 =𝟗𝟎 𝐤𝐦/𝐡; mainline irregularity profile; blue: steel wheelset; orange: HMC wheelset.

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Since the higher admissible speed on the upgraded line requires a higher track quality, i.e. a lower

level of irregularities, the dynamic vertical forces are far lower than those obtained for the metro

line. Therefore, a different scaling is applied here. Nevertheless, the diagrams show that many

peaks of the blue lines (steel wheelset) are not covered by the orange lines (HMC wheelset), but

clearly visible. This indicates that the percentage, by which the dynamic vertical forces are reduced

for the HMC wheelset, is higher in this case.

Next, the sliding mean values Σ𝑌2m of the lateral forces acting between the wheelsets 11 and 12

and the track shall be considered; they are displayed in the following diagrams.

Figure 101. Comparison of the sliding mean values 𝚺𝒀𝟐𝐦 at the leading bogie; 𝒗𝟎 = 𝟗𝟎 𝐤𝐦/𝐡; 𝒗𝟎 =𝟗𝟎 𝐤𝐦/𝐡; mainline irregularity profile. ; blue: steel wheelset; orange: HMC wheelset.

The absolute values for Σ𝑌2m hardly exceed 2 kN indicating a very low level of guiding forces. The

blue curves are hardly visible so that the impact of the reduced wheelset mass on the guiding forces

is rather weak.

Finally, the 𝑇𝛾 values for the four wheel-rail contacts of the leading bogie’s wheelsets shall be

considered. The results obtained for the two wheelset types are compared in the following

diagrams.

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Figure 102. Comparison of 𝑻𝜸 values (wear numbers) at the leading bogie; 𝒗𝟎 = 𝟗𝟎 𝐤𝐦/𝐡; mainline irregularity profile; blue: steel wheelset; orange: HMC wheelset.

Here, the 𝑇𝛾 values hardly exceed 0.8 N, which indicates an extremely low level. Again, great parts

of the blue curves are covered by the orange ones so that also here the impact of the reduced

wheelset mass is very weak.

Of course, a mainline, which is adapted to a regular operational speed of 200 km/h, requires a high

track quality in the form a very low levels of track irregularities, while for a metro line with a lower

operational speed higher levels of irregularities may be admissible. Therefore, applying these

mainline irregularities to a metro vehicle, which is operated at lower speeds, may appear a bit

arguable; this also explains the extremely low values for Σ𝑌2m and 𝑇𝛾. Nevertheless, the results

obtained for these irregularities clearly show that use of the HMC wheelsets distinctly reduces the

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dynamic vertical force Δ𝑄. For future work, it may therefore be worthwhile to consider also other

vehicle types as application cases for the HMC wheelset.

12.5 CONCLUSIONS

Based on the results of multibody simulations performed considering a metro vehicle in which the

wheelset with composite axle could be realistically used, the following conclusions can be drawn:

• The results of multi-body simulations confirm that the reduction of the un-sprung mass

offered by the HMC axle provides benefits in terms of reduced dynamic vertical wheel-rail

forces Δ𝑄, track shift forces Σ𝑌2m and wear number 𝑇𝛾. This means less impact forces, less

wear and a reduction of rolling contact fatigue damage can be expected for both the rails

and the rolling surfaces of the wheels. Furthermore, a reduction of track damage related to

metal fatigue of rails and to permanent settlement in the ballast + embankment can be

expected as a positive outcome of using the wheelset with HMC in place of the benchmark

one. Additionally, the reduction of un-sprung mass will have an effect on vibrations

transmitted to the ground.

• The benefits mentioned above will be much higher when the vehicle speed is increased,

whereas they are limited at low speed, e.g. the case when the vehicle negotiates a short

radius curve. The fact that 90 km/h was chosen was to be consistent with the wheelset that

has been designed (metro vehicle). Higher benefits are expected in case the HMC axle is

used in a high-speed vehicle, for which service speeds would be much higher than the ones

considered here.

• When assessing the positive impact provided by the use of the HMC axle, it should be borne

in mind that the axle takes a relatively small share of the total un-sprung mass, so even a

design of the HMC axle providing a strong reduction of the axle mass like concept 3

considered in this study leads to a relatively small reduction of the total un-sprung mass

(11.5% approximately in the case considered here). This is the reason why in some of the

results presented in this Chapter only a rather slight reduction of the vertical and lateral

forces and of the wear number is observed.

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13. CONCLUSIONS

The objective of Task 3.2 of the NEXTGEAR project was to assess the feasibility of a HMC

wheelset. In Task 3.1, a composite axle of a trailer bogie, with integrated connections with wheel

rims, brake discs and bearings, was identified as the best candidate for substituting a steel axle,

reaching the desired TRL level of 2.

The aim to reduce the mass of the hollow steel trailer axle by replacement with a HMC equivalent

axle has been achieved. The mass of the HMC axle is 74 kg, a reduction of 63% over the steel axle

at 198 kg. There is the potential to further reduce the mass by altering the collar material and

potentially reducing the wall thickness.

The HMC railway axle permits the existing wheels and bearings to be used. The interference fits

between these components and the axle are met by the metallic collars. There is little load

transmission through the collars to the primary composite tube.

The maximum bending stress in the HMC axle is 170.00 MPa as compared to 73.64 MPa in the

steel axle representing safety factors of 2.5 and 3.7 respectively. A safety factor of 2 was the

threshold being maintained in the design so the higher stress within the HMC axle was considered

acceptable. The maximum torsional stress in the HMC axle (7.93 MPa) is less than that of the steel

axle (10.20 MPa), although the torsional stress in the collar is greater at 17.88 MPa . Maximum

transverse shear stress in the HMC axle is less than in the steel axle at 23.12 MPa (collar).

Maximum deflection in the HMC axle is 1.702 mm versus 1.119 mm for the steel axle over a span

of 1156 mm. The deflection in the HMC axle could be reduced by increasing the thickness of the

secondary composite tube. As the HMC axle remained within tolerance for the allowable back to

back deflection (<6 mm) no further stiffening was proposed.

In the current configuration the metallic collar imparts a high contact stress (528.10 MPa) into the

primary composite tube. An improved solution for the collar has been proposed to reduce the

stresses in the adhesive and increase the fatigue life of the joint. Reaching a higher TRL would

require a comprehensive characterization of the chosen adhesives, particularly under fatigue

loading and in different environmental conditions. Mechanical joining is not an option that has been

considered in this project because of the mass increment involved, but it could be a valid alternative

to adhesive bonding, should future tests demonstrate the unfeasibility of an adhesively bonded

joint.

The feasibility of the manufacturing process has been assessed for roll wrapping and filament

winding, by finite element simulations combined with process simulations. Both processes allow

similar mechanical performance to be achieved, although filament winding offers the potential for

an automated process, characterized by a high level of repeatability of the results. To reach higher

TRL levels, the need of a comprehensive experimental characterization of the materials used in

the different processes has been pointed out.

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The proposed design has been checked against requirements for inspection during maintenance

service interruption. The feasibility of NDT has been assessed, focussing particularly on the use of

ultrasonic testing (UT), by simulation. Some limitations of UT have been identified with respect to

the possibility of detecting cracks in the adhesive layer, whereas UT would allow to detect cracks

in the composite tubes and in the metallic collar. Simulations assumed ideal conditions, therefore,

to switch to higher TRL, experimental verification would be needed to optimize the setup. To

overcome the limitations of inspection of the bond line by UT, a possible structural health monitoring

approach has been proposed, based on strain profile monitoring, using fibre optic strain sensors

allowing for distributed sensing.

Dynamic analyses have shown the effect of impact loading by a foreign object (.e.g ballast stone)

Damage consists mainly in matrix failure of the external surface of outer tube due to high

compressive stresses. Although this would not impair the overall structural integrity of the axle,

solution like a protective coating and the installation of sensors capable to detect severe impacts

should be identified in future works.

Finally, the analysis of the dynamical forces at the interaction between rail and wheels has shown

that the proposed HMC axle can contribute to reduce the dynamic forces that are responsible of

wear mechanisms of the wheels and the rails, particularly at high speeds, thus confirming the

potential positive impact on maintenance costs offered by a lighter wheelset.

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[11] S. Kumar et al. 2011, Fatigue life prediction of adhesively boded single lap joints. Int. Journal

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[12] A. M. Pereira et al. 2013, Effect of saline environment on mechanical properties of adhesive

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https://www.nskeurope.com/en/company/news-search/2014-press/prevent-bearing-misalignment.html#:~:text=The%20permissible%20static%20misalignment%20in,7%20degrees)%20under%20normal%20loads.&text=The%20maximum%20allowable%20misalignment%20of,during%20operation%2C%20and%20the%20load




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[14] Y. Du et al. 2014, Effect of vibration fatigue on modal properties of single lap adhesive joints.

Int. Journal of Adhesion & Adhesives. Doi: 10.1016/j.ijadhadh.2014.01.007

[15] Q. Chen et al. 2017, Fatigue performance and life estimation of automotive adhesive joints

using a fracture mechanics approach. Engineering Fracture Mechanics. Doi: 10.1016 / j.

engfracmech. 2017.01.0050013-7944.

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requirements - In-service and off-vehicle wheelset maintenance, CEN, 2016.

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testing on running gear in railway maintenance - Part 1: Wheelsets, CEN, 2018.

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Heinemann, 1999.

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composite adhesively bonded joints using Fiber Bragg Gratings,” Procedia Engineering, vol. 10,

pp. 207–212, 2011, doi: 10.1016/j.proeng.2011.04.037.

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APPENDIX A. MATERIAL PROPERETIES USED AS INPUT TO THE FEA

Material properties used as input to the FEA model of the hollow, steel railway axle (Table A1) and wheel

(Table A2).

Table A1. Mechanical properties of AISI 1030 Plain Carbon 0.3% Steel normalised representing EA1N steel used for the benchmark hollow railway axle (Source: Cambridge Engineering Selector Database).

Mechanical property Symbol Value Unit

Young’s modulus 𝐸𝑆𝑡 200 GPa

Yield strength 𝜎𝑆𝑡,𝑦 440 MPa

Poisson’s ratio 𝑣𝑆𝑡 0.285 -

Density 𝜌𝑆𝑡 7850 kg/m3

Average fatigue strength at 107 cycles 𝜎𝑆𝑡,𝑓𝑎𝑡 107 270 MPa

Average fatigue strength at 109 cycles 𝜎𝑆𝑡,𝑓𝑎𝑡 109 200 MPa

Table A2. Mechanical properties of AISI 1050 steel representing ER7 steel used for the wheels (Source: Cambridge Engineering Selector Database).


Young’s modulus 𝐸𝑇𝑖 115 GPa

Yield strength 𝜎𝑇𝑖,𝑦 850 MPa

Poisson’s ratio 𝑣𝑇𝑖 0.340 -

Density 𝜌𝑇𝑖 4450 kg/m3

Table A3. Mechanical properties of Gurit UCHM450 SE 84LV unidirectional (0°) laminate (Source: Gurit).


Fibre volume fraction 𝑣𝑓 56 %

Ply thickness 𝑡𝑝𝑙𝑦 0.45 mm

Ply weight 𝑊𝑝𝑙𝑦 683 g/m2

Density 𝜌 1498 kg/m3

Longitudinal tensile modulus 𝐸11,𝑡 208.26 GPa

Longitudinal tensile strength 𝜎11,𝑡 1562 MPa

Fatigue strength at 107 cycles (estimated) 𝜎11,𝑡,𝑓𝑎𝑡 107 781 MPa

Longitudinal compressive modulus 𝐸11,𝑐 187.43 GPa

Longitudinal compressive strength 𝜎11,𝑐 843.40 MPa

Fatigue strength at 107 cycles (estimated) 𝜎11,𝑐,𝑓𝑎𝑡 107 421.7 MPa

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Transverse tensile modulus 𝐸22,𝑡 6.39 GPa

Transverse tensile strength 𝜎22,𝑡 28.80 MPa

Transverse compressive modulus 𝐸22,𝑐 6.39 GPa

Transverse compressive strength 𝜎22,𝑐 83.1 MPa

Interlaminar shear modulus 𝐸13 4.31 GPa

Interlaminar shear strength 𝜎13 64.70 MPa

In-plane shear modulus 𝐸12 4.31 GPa

In-plane shear strength (estimated) 𝜎12 64.70 MPa

Poisson’s ratio – longitudinal strain 𝑣12 0.337 -

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