kisssoft bearing calculation 1 bearing calculation options...

Customer EES KISSsoft GmbH Weid 10 / P.O. Box 6313 Menzingen Switzerland www.EES-KISSsoft.ch

Title: Bearing calc. KISSsoft No.: Date: Manager: HD Email: [email protected]

Revision: 1 Autor: HD Date: 11.10.2011 Approved: HD Date: 11.10.2011

T:\EES KISSsoft GmbH\KISSsoft\12-Rolling-Bearings\Bearings-Overview-Rev-1.doc 1 of 45

EES KISSsoft GmbH ++41 41 755 09 54 (Phone)

Neudorfstrasse 22 ++41 41 755 09 48 (Fax)

6313 Menzingen P.O. Box 121

Switzerland www.EES-KISSsoft.ch

1 Bearing calculation options in KISSsoft

1.1 Executive summary In KISSsoft, for bearings, the following can be calculated

- Bearing static rating as per ISO76 - Bearing basic rating as per ISO281 - Bearing modified rating considering aISO factor - Bearing reference and modified reference rating as per ISO16281 - Bearing load distribution - Bearing stresses - Rolling element corrections - Non-linear bearing stiffness - Bearing operating clearance

The above calculations are available for single bearings or for bearings which are part of a shaft system. Furthermore, thermal rating of bearings can be conducted. KISSsoft includes a database of bearings and the user can add his own data.

1.2 Table of content 1 Bearing calculation options in KISSsoft ............................................................................ 1

1.1 Executive summary.................................................................................................... 1 1.2 Table of content.......................................................................................................... 1 1.3 Document change record............................................................................................ 3 1.4 Abbreviations ............................................................................................................. 3

2 KISSsoft modules............................................................................................................... 3 2.1 Single bearing calculation, life and static rating, KISSsoft module WPK................. 3 2.2 Single bearing calculation, with inner geometry, KISSsoft module WB4................. 3

KISSsoft Bearing Calculation


2.3 Shaft-Bearing calculations, module WPK ................................................................. 4 2.4 Module list.................................................................................................................. 4

3 Single bearing calculation, basic life rating and modified life rating ................................ 5 3.1 Calculations................................................................................................................ 5 3.2 Tabs ............................................................................................................................ 5

3.2.1 Module specific settings..................................................................................... 5 3.2.2 Tab “Basic data”................................................................................................. 6 3.2.3 Tab “Thermally admissible service speed.......................................................... 7

3.3 Graphics and results ................................................................................................... 8 3.3.1 Service life vs. impurity of lubricant.................................................................. 8 3.3.2 Service life vs. lubricant temperature................................................................. 9 3.3.3 Reports ............................................................................................................... 9

4 Single bearing calculation, reference and modified reference life rating........................... 9 4.1 Calculations................................................................................................................ 9 4.2 Tabs ............................................................................................................................ 9

4.2.1 Module specific settings..................................................................................... 9 4.2.2 Tab “Basic data”............................................................................................... 10

4.3 Graphics and results ................................................................................................. 11 4.3.1 Stiffness curve .................................................................................................. 11 4.3.2 Load distribution .............................................................................................. 12 4.3.3 Pressure curve .................................................................................................. 12

5 Bearing-shaft systems rating ............................................................................................ 13 5.1 System modeling ...................................................................................................... 13

5.1.1 Single shaft ....................................................................................................... 13 5.1.2 Coaxial shafts ................................................................................................... 14

5.2 Calculations.............................................................................................................. 15 5.2.1 Types of bearings ............................................................................................. 15 5.2.2 Calculation models........................................................................................... 16 5.2.3 Lubrication ....................................................................................................... 16 5.2.4 Bearing clearance and misalignement.............................................................. 16

5.3 Tabs .......................................................................................................................... 17 5.3.1 Module specific settings................................................................................... 17 5.3.2 Tab “Shaft editor” ............................................................................................ 18 5.3.3 Tab “Basic data”............................................................................................... 19

5.4 Graphics and results ................................................................................................. 20 6 Bearing database .............................................................................................................. 20

6.1 Database tool ............................................................................................................ 20 6.2 Input of basic data .................................................................................................... 21 6.3 Input of inner geometry............................................................................................ 22 6.4 Input of rolling element crowning............................................................................ 22

7 Appendices ....................................................................................................................... 23 7.1 Single bearing calculation, basic and modified life rating ....................................... 23

7.1.1 General report................................................................................................... 23 7.1.2 Report on thermally admissible speed ............................................................. 25

7.2 Single bearing calculation, reference and modified reference life rating................. 26 7.2.1 General report................................................................................................... 26

7.3 Bearing-shaft systems rating .................................................................................... 29 7.3.1 Bearing report................................................................................................... 29


1.3 Document change record Revision Dated Who Comments 0 11.10.2011 HD Original document 1 11.10.2011 HD Updated

1.4 Abbreviations [ ] Units

2 KISSsoft modules

2.1 Single bearing calculation, life and static rating, KISSsoft module WPK

This module may be used in case - a single or a pair of bearings is to be calculated for given forces

This module allows for the calculation of one or two bearings. The static safety factor and the bearing life are calculated based on static and dynamic load capacity numbers C0 and C as per ISO76 and ISO281. Load data has to be given by the user as radial and axial bearing force. Besides the basic life rating, the modified life rating can be done, considering the effect of lubrication. The calculation module can be found here:

Figure 2.1-1 Calculation module

2.2 Single bearing calculation, with inner geometry, KISSsoft module WB4

This module may be used in case - of slewing bearings - detailed analysis of a single bearing with known loads in a gearbox

This module allows for the calculation of one bearing considering the inner geometry of the bearing. Reference and modified reference life are calculated along ISO TS 16281. The force per rolling element is calculated considering the external loads, the bearing inner geometry and the clearance. Also, the contact stresses between rolling element and inner / outer raceway is shown. Furthermore, the rolling element modifications (e.g. crowning) may be defined by the user to study the influence of different modifications on the stresses / lifetime.



2.3 Shaft-Bearing calculations, module WPK This module may be used in case

- the bearing is arranged on a shaft - the bearing is part of a complex transmission - forces on the bearing are to be calculated from the shaft loads

This module is the most powerful and most widely used of the three modules presented here. Note that WPK is required at least, the modules WA1, WB1, WB2 should also be used.


2.4 Module list The relevant shaft and bearing modules from the module list are shown below: WPK Shafts and bearing standard package

Calculation of deformations also for statically overdetermined systems / multiple supports, and line loads, Input of linear stiffness, pressure angle and transverse shear roller bearing service life (ISO281, L10) One strength calculation (static and endurance): either according to DIN 743, FKM or according to Hänchen & Decker Smith and Haigh diagram Rights: W01, W01c, W03, W03a, W05, W06a (or W06b, W06c), K07b

WA1 System of shafts composed of various coaxial shafts Calculation of the deformation in the shaft system (taking in account the bearing offset, bearing clearance, non linear stiffness calculated from the inner geometry, thermal expansion, linked shafts) Rights: W01a, W01b, W03b, W03c, W03d

The above are the two modules for shaft calculation. WPK allows for modelling of a single shaft and for basic bearing rating. WA1 allows for modelling of shafts systems with several shafts. WB1 Enhanced bearing calculation (L10m, Lnm)

Influence of lubrication according to ISO281-1 Thermally permissible service speed acc. DIN732 Rights: W05a


WB2 Reference service life calculation, with inner geometry according to ISO16281 (L10r or Lnmr if combined with Module WB1) Diagram of the load distribution in the bearing Diagram of the load distribution over the rolling bodies User specified input of roller profiles , Rights: W05b, W05c This Module requires WA1

WB4

Calculation of a single bearing with inner geometry according to ISO16281 Own input of the inner and outer ring deformation (possible without the WPK) User specified input of roller profiles Rights: W51

Module WB1 allows for modified bearing rating. WB2 allows for calculation with inner geometry when using the shaft calculation for the bearing calculation WB4 allows for the single bearing calculation with inner geometry.

3 Single bearing calculation, basic life rating and modified life rating

3.1 Calculations Single bearings (one or two) are calculated as follows

- static rating along ISO76 - basic life rating along ISO281 - modified life rating along ISO281 - thermally admissible speed along DIN732-1 and DIN732-2 - considering a1 factor for probability of failure and aISO factor for lubrication - considering load spectrum - considering axial and radial load

3.2 Tabs

3.2.1 Module specific settings In the module specific settings, the failure probability (determining a1 factor), an upper limit for aISO, the type of lubrication (which has an influence on the friction of the bearing) and the oil level (which has an influence on the friction of the bearing) can be given. Furthermore, the bearing database may be filtered for different suppliers.


Figure 3.2-1 Module specific settings

3.2.2 Tab “Basic data” In the field “Operating data”, general data applicable for both bearings can be given. In the field “Bearing data”, the type of bearing is selected. Also, it has to be defined which bearing accepts the axial loads. Finally, the radial load per bearing is defined.

Figure 3.2-2 Tab "Basic data" In the field “Additional data”, for “Modified rating life”, in button “Details”, the lubrication conditions may be defined as shown below:


Figure 3.2-3 Definition of lubrication for modified life rating In the field “Additional data”, for “Consider load spectra”, in button “Details”, the load spectrum may be defined which is used to do the bearing rating

Figure 3.2-4 Definition of load spectrum

3.2.3 Tab “Thermally admissible service speed This tab is opened using the menu “Calculation/Thermally permissible service speed”. It allows for the calculation of the thermally permissible service speed along DIN732-1 and DIN732-2


Figure 3.2-5 Tab "Thermally permissible service speed"

3.3 Graphics and results

3.3.1 Service life vs. impurity of lubricant Using menu “Graphics/Service life / Impurity”, a graph can be generated as shown below. It shows the bearing life as a function of the impurity of the lubricant, expressed by ec.


Figure 3.3-1 Bearing life vs. lubricant impurity

3.3.2 Service life vs. lubricant temperature Using menu “Graphics/Service life / lubricant temperature”, a graph can be generated as shown below. It shows the bearing life as a function of the temperature of the lubricant.

Figure 3.3-2 Bearing life vs. lubricant temperature

3.3.3 Reports See 7.1

4 Single bearing calculation, reference and modified reference life rating

4.1 Calculations Single bearings (one) are calculated as follows

- contact force per rolling element - contact pressure per rolling element to outer and inner race - reference life along ISO TS 16281 - modified reference life along ISO TS 16281 - considering a1 factor for probability of failure and aISO factor for lubrication - considering bearing clearance and bearing inner geometry - considering rolling element corrections / modifications

4.2 Tabs

4.2.1 Module specific settings They allow for the input of the failure probability (which is used to determine a1 factor) and an upper limit for aISO factor.



4.2.2 Tab “Basic data” In the field “Bearing data”, the bearing inner geometry is to be defined by the user. Different types of bearings can be analysed as shown below:

Figure 4.2-2 Types of bearings available The conformity of the raceway can be estimated using the sizing buttons for a 52% conformity as shown below:

Figure 4.2-3 Press sizing button to get a value for the raceway radius based on the ball diameter (for 52% conformity) The diametral clearance can be either a constant value or using the plus button, a variable value may be used. Further to the input of the roller length, the roller profile may be given using the plus button.


Figure 4.2-4 Tab "Basic data"

4.3 Graphics and results

4.3.1 Stiffness curve Using menu “Graphics/Stiffness curve”, a graph can be generated as shown below. It shows the non-linear bearing stiffness as a function of the inner geometry and the clearance.

Figure 4.3-1 Non-linear bearing stiffness


4.3.2 Load distribution Using menu “Graphics/Load distribution”, a graph can be generated as shown below. It shows the contact force per rolling element.

Figure 4.3-2 Contact force per rolling element

4.3.3 Pressure curve Using menu “Graphics/Pressure curve”, a graph can be generated as shown below. It shows the contact stress along the rolling element face width for the contact to the inner race and outer race.

Figure 4.3-3 Contact pressure for roller bearing. Select contact to inner or outer race


Figure 4.3-4 Contact stress shown for ball bearing

5 Bearing-shaft systems rating

5.1 System modeling

5.1.1 Single shaft In KISSsoft, single shafts with multiple bearings can be modeled as shown below. Based on the power transmitted and the gear data, the bearing forces and the resulting bearing life are calculated automatically. The basic rating life, the modified rating life, the reference rating life and the modified reference rating life are shown:


5.1.2 Coaxial shafts Furthermore, complete shaft systems can be modeled. Again, all the bearings in the shaft system are calculated.


5.2 Calculations

5.2.1 Types of bearings In the shaft system calculation, many different types of bearings are available as shown in the list below. The most commonly used bearings may be selected:

Figure 5.2-1 Bearing types in KISSsoft The bearing may take radial load or axial load or both by defining the support of the bearings:


Figure 5.2-2 Support of bearings, selection of radial and axial support type

5.2.2 Calculation models Different calculation models for the bearings may be used. The pressure angle may be considered or not and the bearing stiffness can be calculated, neglected or entered directly depending on the below selection:

Figure 5.2-3 Selection of calculation mode

5.2.3 Lubrication Of course, the lubricant, the lubricant temperature and the lubricant purity has an influence on the bearing life in case of modified rating. The below selection below will influence the aISO factor:

Figure 5.2-4 Selection of settings for aISO calcualtion

5.2.4 Bearing clearance and misalignement For the bearing operating clearance and for the calculation of the non-linear bearing stiffness, the setup of the tolerances, bearing play and bearing misalignment, the housing and shaft tolerances are entered. Furthermore, the bearing clearance and accuracy class is required as input. Also, housing deformation from FEM calculation may be given as initial offset of the bearing as shown below:


Figure 5.2-5 Detailed set up of bearing data, including data for operating clearance calcualtion

5.3 Tabs

5.3.1 Module specific settings In the module specific settings, there is one tab particular for the bearings. There, the axial clearance (for bearings with theoretically no axial clearance), the failure probability (to calculate a1 factor), the required service life, an upper limit for aISO and lubrication data may be given (to calculate the bearing friction torque). Also, the surface roughness of the housing can be given which has some influence on the interference fit between outer race and housing which again has an influence on the operating clearance of the bearing. Again, the different bearing suppliers may be filtered.



5.3.2 Tab “Shaft editor” In the shaft editor, the shaft-bearing system is modeled


Figure 5.3-2 Shaft editor

5.3.3 Tab “Basic data” In the tab “Basic data”, the following may be defined with respect to the bearings Position of shaft in space: determines whether the mass of the shaft results in an axial load on the bearings in case of non-horizontal shafts. Speed: determines the bearing relative speed of inner race to outer race Sense of rotation: may affect the forces acting on the bearings Reference temperature: may affect the operating clearance Temperature of housing: may affect the operating clearance Lubricant temperature: may affect aISO factor Load spectra: is considered in bearing life rating Roller bearing: Determines whether the bearings are considered as infinitely stiff or whether bearing stiffness is calculated. Determines whether basic/modified rating is done or whether reference/modified reference rating is done Modified rating life according ISO281: determines whether basic rating / reference rating or modified rating / modified reference rating is done Lubricant: has an influence on aISO factor through viscosity Impurity: determines ec factor which then has an influence on aISO factor


Figure 5.3-3 Tab "Basic data"

5.4 Graphics and results Similar to the figures shown in 4.3, the load distribution, contact stress and bearing stiffness is shown.

6 Bearing database

6.1 Database tool In the database tool, different databases for different types of bearings and bearing tolerances exist and may be edited by the user.

Figure 6.1-1 Databasetool


For example for cylindrical roller bearings, about 3000 different datasets are available:

Figure 6.1-2 Database for CRB

6.2 Input of basic data

Figure 6.2-1 Input of general bearing data in the database


6.3 Input of inner geometry

Figure 6.3-1 Input of the inner geoemtry of a bearing in the database

6.4 Input of rolling element crowning

Figure 6.4-1 Selecting a file for the definition of the rolling element modification In the respective dat file, the profile is defined in the following form:


Figure 6.4-2 Defining the rolling element modifications

7 Appendices

7.1 Single bearing calculation, basic and modified life rating

7.1.1 General report KISSsoft - Release 03-2011H Non commercial version for demo and support purpose s only ! File Name : Unnamed Changed by : Y.Zimmermann on: 11.10.2011 at: 09:19:51 Important hint: At least one warning has occurred d uring the calculation: 1-> Bearing1: The fatigue load limit is not specified in the data base. An approximation equation according to ISO 281 (200 7) B3.3 will be used. 2-> No values for the frictional moment of sliding and rolling are defined for bearing type or dimension series of Bearing1 ! 3-> The required service life of bearing 'Bearing1' is not achieved! The static margin of safety is low (in range 0.5 - 2.0). Please check whether these values are acceptable or not. ROLLER BEARING ANALYSIS


Calculation method: ISO 281 and manufacturer inform ation - With modified rating life according ISO 281 General data: Speed (1/min) 1200.000 Axial force (N) 300.000 Required service life (h) 20000.000 Operating temperature (°C) 70 Type of oil Oil: ISO-VG 220 Lubricant base Mineral-oil base Kinematic viscosity oil at 40 °C (mm²/s) 220.00 Specific density oil at 15 °C (kg/dm³) 0.895 Oil lubrication with filtration, ISO 4406 -/19/16, beta40=75 Lubricant with additive Roller bearing No. 1: Bearing type NSK 6910NR Type Deep groove ball bearing (single r ow) Bearing clearance: C3 Radial and axial load Radial force (N) [Fr] 4500.000 Axial force (N) [Fa] 300.000 Inner diameter (mm) [d] 50.000 External diameter (mm) [D] 72.000 Width (mm) [B] 12.000 Dynamic load number (kN) [C] 14.500 Static load number (kN) [C0] 11.700 Speed limit (oil) (1/min) [n.max] 11000 Dynamic equivalent load (N) [P] 4500.000 Static equivalent load (N) [P0] 4500.000 Operating viscosity (mm²/s) [nu] 48.884 Reference viscosity (mm²/s) [nu1] 16.632 Fatigue load limit (kN) [Cu] 0.532 Impurity characteristic quantity [ec] 0.176 Service life coefficient [aISO] 0.883 Service life (h) [Lh] 410.255 Static safety factor [S0] 2.600 Roller bearing No. 2: Bearing type SKF 61810 Type Deep groove ball bearing (single r ow) Bearing clearance: C3 Only radial load Radial force (N) [Fr] 3600.000 Axial force (N) [Fa] 0.000 Inner diameter (mm) [d] 50.000 External diameter (mm) [D] 65.000 Width (mm) [B] 7.000 Dynamic load number (kN) [C] 6.760 Static load number (kN) [C0] 6.800 Speed limit (oil) (1/min) [n.max] 13000 Dynamic equivalent load (N) [P] 3600.000 Static equivalent load (N) [P0] 3600.000 Operating viscosity (mm²/s) [nu] 48.884 Reference viscosity (mm²/s) [nu1] 17.131 Fatigue load limit (kN) [Cu] 0.285 Impurity characteristic quantity [ec] 0.162 Service life coefficient [aISO] 0.612 Torque of friction (Nmm) [M] 168.104 Service life (h) [Lh] 56.256 Static safety factor [S0] 1.889 Notice: The modified rating life according ISO 281 contains only approximate formulae for the calculation of the fatigue load boundary an d the resulting values for a23 are


sometimes very high.. Torque of friction M is calculated according to the indications in the SKF catalog 2004.. End report lines: 90

7.1.2 Report on thermally admissible speed KISSsoft - Release 03-2011H Non commercial version for demo and support purpose s only ! File Name : Unnamed Changed by : Y.Zimmermann on: 11.10.2011 at: 09:22:34 THERMAL ADMISSIBLE SERVICE SPEED CALCULATION (according to DIN 732-1 and 732-2) Lubricant Oil: ISO-VG 220 Lubrication type: Immersion lubrication - Oil level up to the middle of the lowest rolling element. Mean bearing temperature [Tm] 80.000 °C Temperature of bearing environment [T] 20.000 °C Lubricant - service temperature [TOil] 70.000 °C Speed [n] 1200.000 1/min Bearing 1 : Thermal nominal speed according to DIN 732-1: The required values for this type of support or des ign series are unknown. Thus, no thermal admissible service speed can be calculated for thes e bearings. Bearing 2 : Thermal nominal speed according to DIN 732-1: Type of support Deep groove ball bearing (single row) Bearing number SKF 61810 Design series 618 Coefficient [f0r] 1.500 (Depends upon type of design and lubrication at ref erence conditions) Coefficient [f1r] 0.000100 (Depends upon type of design and load at reference conditions) Heat sink reference surface [As] 2528.982 mm2 Reference load [P1r] 0.340 kN Bearing mean diameter [dm] 57.500 mm Bearing-specific reference heat flow density [qSr] 20.000 kW/m2 Bearing-specific reference heat flow density [qLr] 0.000 kW/m2 kinematic viscosity (for reference conditions) [nyr] 12.000 mm2/s Thermal nominal speed [ntr] 8046.933 1/min Thermal admissible service speed according to DIN 732-2: Coefficient [f0] 1.500 (Depends upon type of design and lubrication) Coefficient [f1] 0.000327 (Depends upon type of design and load) Heat flow (dissipated by the bearing support surfa ce) [QS] 0.061 kW/(m2*K) Total heat flow [Q] 0.061 kW Dynamic equivalent load [P1] 3600.000 N kinematic viscosity at service temperature [ny] 48.884 mm2/s Lubricant film parameter [KL] 2.126 Charge parameter [KP] 0.941 Speed ratio [fn] 0.454 Thermal admissible service speed [nt] 3654.125 1/min End report lines: 61


7.2 Single bearing calculation, reference and modified reference life rating

7.2.1 General report KISSsoft - Release 03-2011H Non commercial version for demo and support purpose s only ! File Name : Unnamed Changed by : Y.Zimmermann on: 11.10.2011 at: 09:52:44 Roller bearing calculation according to ISO/TS 1628 1 (Deep groove ball bearing) Details for bearing inner geometry Number of rolling elements [Z] 90 Diameter of rolling element [Dw] 20.000 mm Reference diameter [Dpw] 750.000 mm Diameter of inner ring [di] 730.000 mm Diameter of outer ring [do] 770.000 mm Radius of curvature inner ring [ri] 10.400 mm Radius of curvature outer ring [ro] 10.400 mm Dynamic load rating [Cr] 222.565 kN Static load rating [C0r] 656.658 kN Fatigue load limit [Cu] 12.143 kN Life modification factor for reliability[a1] 1.000 Limit for factor aISO [aISOmax] 50.000 Oil lubrication with filtration, ISO4406 -/19/16 Contamination factor [eC] 0.304 Viscosity ratio [kappa] 0.358 Displacement of bearing [ux] -0.531 µm Displacement of bearing [uy] 0.560 µm Displacement of bearing [uz] 0.682 µm Misalignment of bearing [ry] 0.966 mrad Misalignment of bearing [rz] 0.000 mrad Bearing reaction force [Fx] -1.000 kN Bearing reaction force [Fy] -2.000 kN Bearing reaction force [Fz] -3.000 kN Bearing reaction moment [My] -50000.025 Nm Bearing reaction moment [Mz] -0.001 Nm Equivalent load [Pref] 239.545 kN Maximum pressure inner ring [pmax_i] 2789.384 N/mm² Maximum pressure outer ring [pmax_o] 2728.535 N/mm² Vickers hardness [HV] 660.000 Static safety [SF] 3.414 Maximum internal contact diameter [dC_i] 735.024 mm Minimum external contact diameter [dC_o] 764.988 mm Effective speed [n] 20.000 1/min Reference rating service life [L10r] 0.802 Reference rating service life [Lh10r] 668.359 h Modified reference rating service life [Lnmr] 0.387 Modified reference rating service life [Lhnmr] 322.578 h Bearing stiffness in operation point dFr/dur = 13379.083 N/µm ,(dFr/dur)_eff = (Fr/ur) = 4085.622 N/µm dMr/drr = 359090.198 Nm/mrad (6267306.261 Nm/°) ,(d Mr/drr)_eff = (Mr/rr) = 51753.601 Nm/mrad (903270.745 Nm/°) [ux] [uy] [uz] [rx] [rz] [Fx] -1745.786 N/µm 0.218 N/µm -2825.919 N/µm -64 9.421 N/mrad 1644.141 N/mrad [Fy] 0.217 N/µm -3573.123 N/µm 0.258 N/µm -1755 .293 N/mrad 567.782 N/mrad [Fz] -2825.801 N/µm 0.260 N/µm -6600.131 N/µm -87 0.497 N/mrad 1744.829 N/mrad [My] -0.656 Nm/µm -1.756 Nm/µm -0.868 Nm/µm -194 596.900 Nm/mrad -1.994 Nm/mrad [Mz] 1.636 Nm/µm 0.589 Nm/µm 1.755 Nm/µm -2. 016 Nm/mrad -52513.965 Nm/mrad Rolling element no. Loading |F|, Fx, Fy, Fz (kN) An gle(°) Hertzian stress(N/mm²) 1 10.420 -4.295 -0.000 -9 .494 -24.34 2789.38 2 10.355 -4.259 -0.659 -9 .415 -24.29 2783.55


3 10.147 -4.148 -1.289 -9 .170 -24.13 2764.83 4 9.802 -3.966 -1.864 -8 .768 -23.87 2733.27 5 9.333 -3.721 -2.360 -8 .227 -23.50 2688.99 6 8.752 -3.423 -2.755 -7 .569 -23.02 2632.13 7 8.078 -3.084 -3.037 -6 .820 -22.45 2562.88 8 7.332 -2.718 -3.197 -6 .012 -21.76 2481.49 9 6.534 -2.339 -3.234 -5 .174 -20.98 2388.23 10 5.710 -1.962 -3.153 -4 .338 -20.09 2283.47 11 4.883 -1.598 -2.967 -3 .535 -19.10 2167.59 12 4.076 -1.260 -2.693 -2 .788 -18.01 2041.07 13 3.311 -0.958 -2.355 -2 .120 -16.82 1904.46 14 2.605 -0.698 -1.978 -1 .545 -15.54 1758.38 15 1.975 -0.484 -1.588 -1 .071 -14.18 1603.54 16 1.433 -0.316 -1.210 -0 .699 -12.72 1440.79 17 0.983 -0.191 -0.867 -0 .423 -11.19 1271.08 18 0.630 -0.105 -0.576 -0 .233 -9.59 1095.59 19 0.368 -0.051 -0.346 -0 .113 -7.93 915.86 20 0.189 -0.020 -0.183 -0 .046 -6.22 734.07 21 0.081 -0.006 -0.080 -0 .014 -4.46 554.17 22 0.027 -0.001 -0.027 -0 .003 -2.67 385.54 23 0.008 -0.000 -0.008 -0 .000 -0.87 258.81 24 0.008 0.000 -0.008 0 .000 0.94 252.86 25 0.025 0.001 -0.025 0 .003 2.75 373.53 26 0.076 0.006 -0.074 0 .013 4.54 540.36 27 0.178 0.020 -0.172 0 .043 6.29 719.62 28 0.350 0.049 -0.330 0 .107 8.01 901.15 29 0.604 0.102 -0.552 0 .223 9.67 1080.77 30 0.949 0.186 -0.837 0 .408 11.27 1256.22 31 1.389 0.308 -1.173 0 .677 12.81 1425.93 32 1.921 0.473 -1.544 1 .041 14.26 1588.71 33 2.540 0.684 -1.928 1 .506 15.63 1743.59 34 3.234 0.941 -2.300 2 .070 16.91 1889.72 35 3.989 1.239 -2.634 2 .727 18.10 2026.38 36 4.785 1.573 -2.905 3 .462 19.19 2152.96 37 5.602 1.933 -3.091 4 .253 20.18 2268.89 38 6.416 2.307 -3.173 5 .077 21.07 2373.71 39 7.204 2.682 -3.139 5 .903 21.86 2467.01 40 7.943 3.045 -2.984 6 .701 22.54 2548.45 41 8.610 3.381 -2.709 7 .440 23.12 2617.74 42 9.184 3.676 -2.320 8 .090 23.60 2674.63 43 9.649 3.919 -1.834 8 .625 23.97 2718.93 44 9.990 4.100 -1.268 9 .021 24.23 2750.51 45 10.196 4.210 -0.648 9 .264 24.39 2769.24 46 10.261 4.246 0.000 9 .341 24.44 2775.07 47 10.182 4.205 0.647 9 .251 24.39 2767.96 48 9.962 4.089 1.265 8 .996 24.23 2747.94 49 9.608 3.904 1.826 8 .587 23.97 2715.05 50 9.130 3.656 2.307 8 .042 23.60 2669.37 51 8.544 3.356 2.688 7 .383 23.13 2611.05 52 7.866 3.017 2.955 6 .636 22.55 2540.25 53 7.118 2.652 3.102 5 .832 21.87 2457.18 54 6.322 2.275 3.127 5 .002 21.09 2362.10 55 5.502 1.900 3.036 4 .177 20.20 2255.33 56 4.681 1.540 2.842 3 .386 19.21 2137.23 57 3.883 1.207 2.564 2 .654 18.12 2008.19 58 3.128 0.911 2.224 2 .002 16.93 1868.69 59 2.435 0.657 1.848 1 .443 15.65 1719.22 60 1.820 0.449 1.462 0 .986 14.28 1560.34 61 1.294 0.287 1.092 0 .631 12.82 1392.61 62 0.862 0.169 0.760 0 .371 11.29 1216.58 63 0.527 0.089 0.482 0 .195 9.68 1032.69 64 0.285 0.040 0.268 0 .087 8.02 841.04 65 0.126 0.014 0.121 0 .030 6.30 640.80 66 0.037 0.003 0.037 0 .006 4.54 427.60 67 0.002 0.000 0.002 0 .000 2.75 170.56 68 0.000 0.000 0.000 0 .000 0.00 0.00 69 0.000 0.000 0.000 0 .000 0.00 0.00 70 0.004 -0.000 0.004 -0 .000 -2.68 195.56 71 0.042 -0.003 0.041 -0 .007 -4.47 444.99 72 0.136 -0.015 0.131 -0 .033 -6.22 657.05 73 0.301 -0.042 0.284 -0 .092 -7.94 856.84 74 0.551 -0.092 0.504 -0 .204 -9.61 1048.25 75 0.895 -0.174 0.789 -0 .385 -11.21 1231.98 76 1.337 -0.295 1.129 -0 .652 -12.74 1407.88 77 1.873 -0.459 1.506 -1 .015 -14.19 1575.49 78 2.499 -0.671 1.898 -1 .482 -15.56 1734.27 79 3.203 -0.928 2.279 -2 .051 -16.84 1883.64 80 3.969 -1.228 2.622 -2 .715 -18.03 2023.05


81 4.779 -1.565 2.903 -3 .459 -19.12 2152.00 82 5.610 -1.929 3.097 -4 .262 -20.11 2270.03 83 6.440 -2.307 3.187 -5 .099 -20.99 2376.73 84 7.245 -2.688 3.159 -5 .940 -21.78 2471.74 85 8.002 -3.057 3.008 -6 .755 -22.46 2554.75 86 8.686 -3.399 2.735 -7 .511 -23.03 2625.50 87 9.279 -3.701 2.346 -8 .179 -23.51 2683.78 88 9.761 -3.950 1.856 -8 .731 -23.87 2729.42 89 10.119 -4.137 1.285 -9 .144 -24.13 2762.28 90 10.341 -4.254 0.658 -9 .402 -24.29 2782.29

Figure: Load distribution


Figure: Pressure curve(Hertzian stress inside)

Figure: Bearing stiffness in operation point End report lines: 165

7.3 Bearing-shaft systems rating

7.3.1 Bearing report KISSsoft - Release 03-2011B Non commercial version for demo and support purpose s only ! File Name : Shafts 1 Description: KISSsoft example Changed by : Y.Zimmermann on: 06.07.2011 at: 14:20:08 Roller bearing calculation according to ISO/TS 1628 1 (2008) Lubricant Oil: ISO-VG 220 Lubricant with additive, effect on bearing lifetime confirmed in tests Lubricant - service temperature [TB] 70.00 °C Oil lubrication with filtration, ISO4406 -/17/14 Shaft 'Shaft' Roller bearing 'Roller bearing 1' Spherical roller bearings (SKF *22208E) Inner diameter [d] 40.000 mm Outer diameter [D] 80.000 mm Width [B] 23.000 mm Dynamic load rating [C] 96.500 kN Static load rating [C0] 90.000 kN Fatigue load limit [Cu] 9.800 kN


Life modification factor for reliability[a1] 1.000 Service life modification factor [aISO] 1.004 Contamination factor [eC] 0.303 Viscosity ratio [kappa] 2.557 Results according to ISO 281: Equivalent load [P] 15.668 kN Equivalent load [P0] 14.009 kN Effective speed [n] 9 80.000 1/min Service life [Lnh] 72 82.646 h Service life [Lnmh] 73 14.907 h static safety factor [S0] 6.425 Calculation with approximate bearings inner geometr y Number of rolling elements [Z] 16 Diameter of rolling element [Dw] 14.817 mm Effective length of roller [Lwe] 6.086 mm Reference diameter [Dpw] 60.000 mm Diameter of inner ring [di] 46.181 mm Diameter of outer ring [do] 75.858 mm Radius of curvature inner ring [ri] 37.932 mm Radius of curvature outer ring [ro] 37.932 mm Radius of curvature of rolling bodies[Rp] 36.794 mm Contact angle [alpha0] 10.620 ° Dynamic load rating [Cr] 96.500 kN Fatigue load limit [Cu] 9.800 kN Life modification factor for reliability[a1] 1.000 Limit for factor aISO [aISOmax] 50.000 Contamination factor [eC] 0.302 Viscosity ratio [kappa] 2.557 Bearing reaction force [Fx] -3.088 kN Bearing reaction force [Fy] 3.264 kN Bearing reaction force [Fz] 4.968 kN Bearing reaction force [Fr] 5.850 kN (-31.87°) Bearing reaction moment [Mx] 0.00 Nm Bearing reaction moment [My] 0.00 Nm Bearing reaction moment [Mz] 0.00 Nm Bearing reaction moment [Mr] 0.00 Nm (0°) Torque of friction [Mloss] 0.745 Nm Displacement of bearing [ux] 25.388 µm Displacement of bearing [uy] -1 83.173 µm Displacement of bearing [uz] 34.144 µm Displacement of bearing [ur] 42.548 µm (36.63°) Misalignment of bearing [rx] -0.571 mrad (-1.96') Misalignment of bearing [ry] -1.652 mrad (-5.68') Misalignment of bearing [rz] 0.019 mrad (0.06') Misalignment of bearing [rr] 0.571 mrad (1.96') Bearing stiffness in operation point dMr/drr = 0.000 Nm/mrad (0.000 Nm/°) ,(dMr/drr)_eff = (Mr/rr) = 0.000 Nm/mrad (0.000 Nm/°) [ux] [uy] [uz] [rx] [rz] [Fx] -662.905 N/µm 17.850 N/µm -5.468 N/µm -1.08 5 N/mrad 113.832 N/mrad [Fy] 17.868 N/µm -63.515 N/µm -39.834 N/µm -11.696 N/mrad -6.032 N/mrad [Fz] -5.459 N/µm -39.585 N/µm -657.513 N/µm -112.5 27 N/mrad 1.085 N/mrad [Mx] -0.000 Nm/µm -0.000 Nm/µm 0.000 Nm/µm 0. 000 Nm/mrad -0.000 Nm/mrad [Mz] -0.000 Nm/µm -0.000 Nm/µm 0.000 Nm/µm 0. 000 Nm/mrad 0.000 Nm/mrad Results according to ISO/TS 16281: Equivalent load [Pref] 9.893 kN Maximum pressure inner ring [pmax_i] 17 59.215 N/mm² Maximum pressure outer ring [pmax_o] 13 78.500 N/mm² Static safety [SF] 5.170 - Service life modification factor [aISO] 1.654 Reference rating service life [Lnrh] 337 22.743 h Modified reference rating service life[Lnmrh] 557 66.760 h Rolling bodies series: 1 Rolling element no. Loading |F|, Fx, Fy, Fz (kN) Angle (°) Hertzian stress(N/mm²) 1 1.285 -1.255 0.275 0.000 12.38 1589.96 2 0.978 -0.882 0.210 -0.366 12.42 1444.91 3 0.686 -0.473 0.149 -0.473 12.57 1276.01 4 0.455 -0.170 0.101 -0.410 12.81 1105.03 5 0.307 -0.000 0.069 -0.299 13.10 961.83 6 0.239 0.089 0.055 -0.215 13.37 881.80


7 0.246 0.169 0.058 -0.169 13.55 891.11 8 0.328 0.295 0.077 -0.122 13.63 986.28 9 0.492 0.478 0.116 -0.000 13.61 1137.41 10 0.735 0.661 0.172 0.274 13.51 1309.66 11 1.033 0.711 0.239 0.711 13.37 1474.98 12 1.336 0.498 0.305 1.202 13.19 1613.30 13 1.581 0.000 0.355 1.541 12.98 1710.90 14 1.714 -0.640 0.379 1.544 12.76 1759.21 15 1.701 -1.174 0.370 1.174 12.57 1754.22 16 1.546 -1.394 0.333 0.578 12.43 1696.22 Section Profile(µm) aIS O 1 0.00 1.49 2 0.00 1.49 3 0.00 1.49 4 0.00 1.50 5 0.00 1.51 6 0.00 1.52 7 0.00 1.54 8 0.00 1.57 9 0.00 1.59 10 0.00 1.63 11 0.00 1.66 12 0.00 1.71 13 0.00 1.76 14 0.00 1.82 15 0.00 1.89 16 0.00 1.98 17 0.00 2.07 18 0.00 2.19 19 0.00 2.32 20 0.00 2.48 21 0.00 2.67 22 0.00 2.90 23 0.00 3.19 24 0.00 3.55 25 0.00 4.02 26 0.00 4.63 27 0.00 5.46 28 0.00 6.64 29 0.00 8.39 30 0.00 11.17 31 0.00 15.97 32 0.00 25.39 33 0.00 47.58 34 0.00 50.00 35 0.00 50.00 36 0.00 50.00 37 0.00 50.00 38 0.00 50.00 39 0.00 1.00 40 0.00 1.00 41 0.00 1.00 Hertzian stress in contact at inner ring (N/mm²) Rolling element no. 1 2 3 4 5 6 7 8 Section 1: 1589.96 1444.91 1276.01 1105.03 961.83 881.80 891.11 986.28 Section 2: 1588.93 1443.99 1275.22 1104.35 961.22 881.21 890.46 985.53 Section 3: 1586.37 1441.42 1272.59 1101.58 958.27 878.10 887.32 982.48 Section 4: 1582.28 1437.18 1268.10 1096.73 952.98 872.47 881.68 977.15 Section 5: 1576.66 1431.28 1261.76 1089.78 945.33 864.30 873.52 969.50 Section 6: 1569.50 1423.70 1253.55 1080.71 935.28 853.53 862.79 959.50 Section 7: 1560.80 1414.44 1243.45 1069.49 922.77 840.10 849.42 947.11 Section 8: 1550.53 1403.47 1231.44 1056.06 907.75 823.92 833.32 932.25 Section 9: 1538.67 1390.76 1217.46 1040.37 890.10 804.85 814.38 914.84 Section 10: 1525.21 1376.28 1201.47 1022.3 4 869.72 782.74 792.43 894.77 Section 11: 1510.11 1359.99 1183.42 1001.8 7 846.45 757.38 767.27 871.89


Section 12: 1493.33 1341.84 1163.22 978.8 5 820.09 728.51 738.65 846.03 Section 13: 1474.83 1321.76 1140.79 953.1 2 790.40 695.76 706.23 816.96 Section 14: 1454.56 1299.70 1116.02 924.5 2 757.07 658.69 669.56 784.39 Section 15: 1432.45 1275.57 1088.78 892.8 0 719.68 616.65 628.05 747.96 Section 16: 1408.44 1249.26 1058.91 857.7 0 677.69 568.76 580.84 707.18 Section 17: 1382.45 1220.67 1026.24 818.8 7 630.36 513.68 526.71 661.39 Section 18: 1354.38 1189.65 990.54 775.8 3 576.61 449.26 463.66 609.68 Section 19: 1324.12 1156.06 951.51 727.9 9 514.79 371.59 388.20 550.67 Section 20: 1291.55 1119.69 908.81 674.4 9 442.16 271.70 292.69 482.20 Section 21: 1256.51 1080.31 862.00 614.1 3 353.33 111.64 150.30 400.30 Section 22: 1218.83 1037.64 810.46 545.0 2 234.17 0.00 0.00 296.17 Section 23: 1178.29 991.32 753.41 463.9 9 0.00 0.00 0.00 135.41 Section 24: 1134.63 940.90 689.72 364.6 2 0.00 0.00 0.00 0.00 Section 25: 1087.54 885.80 617.67 228.8 2 0.00 0.00 0.00 0.00 Section 26: 1036.63 825.24 534.49 0.0 0 0.00 0.00 0.00 0.00 Section 27: 981.39 758.11 434.99 0.0 0 0.00 0.00 0.00 0.00 Section 28: 921.17 682.83 306.68 0.0 0 0.00 0.00 0.00 0.00 Section 29: 855.08 596.82 80.37 0.0 0 0.00 0.00 0.00 0.00 Section 30: 781.90 495.52 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 31: 699.75 368.85 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 32: 605.62 179.60 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 33: 493.90 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 34: 351.33 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 35: 111.22 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 36: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 37: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 38: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 39: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 40: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 41: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Hertzian stress in contact at inner ring (N/mm²) Rolling element no. 9 10 11 12 13 14 15 16 Section 1: 1137.41 1309.66 1474.98 1613.30 1710.90 1759.21 1754.22 1696.22 Section 2: 1136.54 1308.66 1473.88 1612.13 1709.69 1757.99 1753.03 1695.10 Section 3: 1133.63 1305.86 1471.15 1609.44 1707.03 1755.37 1750.43 1692.53 Section 4: 1128.68 1301.25 1466.78 1605.24 1702.94 1751.34 1746.43 1688.51 Section 5: 1121.69 1294.83 1460.79 1599.53 1697.42 1745.92 1741.03 1683.05 Section 6: 1112.64 1286.58 1453.14 1592.31 1690.45 1739.09 1734.21 1676.13 Section 7: 1101.48 1276.49 1443.85 1583.55 1682.04 1730.85 1725.99 1667.76 Section 8: 1088.18 1264.52 1432.87 1573.26 1672.17 1721.18 1716.33


1657.91 Section 9: 1072.68 1250.64 1420.19 1561.40 1660.82 1710.08 1705.24 1646.57 Section 10: 1054.90 1234.81 1405.78 1547.9 6 1647.98 1697.52 1692.68 1633.73 Section 11: 1034.77 1216.96 1389.60 1532.9 0 1633.61 1683.49 1678.64 1619.35 Section 12: 1012.16 1197.03 1371.59 1516.1 9 1617.69 1667.94 1663.09 1603.40 Section 13: 986.95 1174.93 1351.70 1497.7 8 1600.19 1650.86 1646.00 1585.86 Section 14: 958.98 1150.56 1329.88 1477.6 3 1581.05 1632.20 1627.32 1566.67 Section 15: 928.03 1123.81 1306.03 1455.6 8 1560.25 1611.92 1607.02 1545.78 Section 16: 893.87 1094.54 1280.07 1431.8 7 1537.71 1589.97 1585.04 1523.15 Section 17: 856.17 1062.58 1251.88 1406.1 0 1513.37 1566.29 1561.33 1498.71 Section 18: 814.54 1027.71 1221.36 1378.3 0 1487.18 1540.82 1535.82 1472.37 Section 19: 768.45 989.69 1188.33 1348.3 6 1459.03 1513.48 1508.43 1444.06 Section 20: 717.20 948.20 1152.63 1316.1 6 1428.83 1484.19 1479.08 1413.68 Section 21: 659.78 902.86 1114.05 1281.5 5 1396.48 1452.84 1447.66 1381.11 Section 22: 594.75 853.14 1072.32 1244.3 7 1361.84 1419.32 1414.07 1346.22 Section 23: 519.74 798.37 1027.12 1204.4 2 1324.75 1383.49 1378.15 1308.85 Section 24: 430.51 737.62 978.05 1161.4 5 1285.05 1345.20 1339.76 1268.81 Section 25: 317.54 669.54 924.59 1115.1 8 1242.52 1304.27 1298.71 1225.89 Section 26: 143.34 592.03 866.07 1065.2 3 1196.90 1260.47 1254.77 1179.81 Section 27: 0.00 501.52 801.56 1011.1 5 1147.88 1213.54 1207.69 1130.25 Section 28: 0.00 390.72 729.74 952.3 5 1095.07 1163.16 1157.12 1076.81 Section 29: 0.00 238.30 648.59 888.0 4 1037.99 1108.93 1102.67 1018.96 Section 30: 0.00 0.00 554.74 817.1 4 976.00 1050.34 1043.82 956.03 Section 31: 0.00 0.00 441.60 738.0 5 908.25 986.75 979.90 887.12 Section 32: 0.00 0.00 291.82 648.2 9 833.58 917.26 910.02 810.95 Section 33: 0.00 0.00 0.00 543.5 0 750.24 840.67 832.90 725.60 Section 34: 0.00 0.00 0.00 414.5 1 655.50 755.14 746.68 627.97 Section 35: 0.00 0.00 0.00 231.7 0 544.46 657.80 648.35 512.32 Section 36: 0.00 0.00 0.00 0.0 0 406.41 543.42 532.38 365.06 Section 37: 0.00 0.00 0.00 0.0 0 202.57 400.33 386.14 119.21 Section 38: 0.00 0.00 0.00 0.0 0 0.00 182.94 155.05 0.00 Section 39: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 40: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 41: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Rolling bodies series: 2 Rolling element no. Loading |F|, Fx, Fy, Fz (kN) Angle (°) Hertzian stress(N/mm²) 1 0.000 0.000 0.000 0.000 0.00 0.00 2 0.000 0.000 0.000 0.000 0.00 0.00 3 0.000 0.000 0.000 0.000 0.00 0.00 4 0.000 0.000 0.000 0.000 0.00 0.00 5 0.000 0.000 0.000 0.000 0.00 0.00 6 0.000 0.000 0.000 0.000 0.00 0.00


7 0.000 0.000 0.000 0.000 0.00 0.00 8 0.000 0.000 0.000 0.000 0.00 0.00 9 0.000 0.000 0.000 0.000 0.00 0.00 10 0.000 0.000 0.000 0.000 0.00 0.00 11 0.000 0.000 0.000 0.000 0.00 0.00 12 0.000 0.000 0.000 0.000 0.00 0.00 13 0.000 0.000 0.000 0.000 0.00 0.00 14 0.000 0.000 0.000 0.000 0.00 0.00 15 0.000 0.000 0.000 0.000 0.00 0.00 16 0.000 0.000 0.000 0.000 0.00 0.00 Section Profile(µm) aIS O 1 0.00 1.00 2 0.00 1.00 3 0.00 1.00 4 0.00 1.00 5 0.00 1.00 6 0.00 1.00 7 0.00 1.00 8 0.00 1.00 9 0.00 1.00 10 0.00 1.00 11 0.00 1.00 12 0.00 1.00 13 0.00 1.00 14 0.00 1.00 15 0.00 1.00 16 0.00 1.00 17 0.00 1.00 18 0.00 1.00 19 0.00 1.00 20 0.00 1.00 21 0.00 1.00 22 0.00 1.00 23 0.00 1.00 24 0.00 1.00 25 0.00 1.00 26 0.00 1.00 27 0.00 1.00 28 0.00 1.00 29 0.00 1.00 30 0.00 1.00 31 0.00 1.00 32 0.00 1.00 33 0.00 1.00 34 0.00 1.00 35 0.00 1.00 36 0.00 1.00 37 0.00 1.00 38 0.00 1.00 39 0.00 1.00 40 0.00 1.00 41 0.00 1.00 Hertzian stress in contact at inner ring (N/mm²) Rolling element no. 1 2 3 4 5 6 7 8 Section 1: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 2: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 3: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 4: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 5: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 6: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 7: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 8: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 9: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 10: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 11: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00


Section 12: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 13: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 14: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 15: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 16: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 17: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 18: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 19: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 20: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 21: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 22: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 23: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 24: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 25: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 26: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 27: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 28: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 29: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 30: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 31: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 32: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 33: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 34: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 35: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 36: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 37: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 38: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 39: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 40: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 41: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Hertzian stress in contact at inner ring (N/mm²) Rolling element no. 9 10 11 12 13 14 15 16 Section 1: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 2: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 3: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 4: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 5: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 6: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 7: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 8: 0.00 0.00 0.00 0.00 0.00 0.00 0.00


0.00 Section 9: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 10: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 11: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 12: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 13: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 14: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 15: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 16: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 17: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 18: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 19: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 20: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 21: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 22: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 23: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 24: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 25: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 26: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 27: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 28: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 29: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 30: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 31: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 32: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 33: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 34: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 35: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 36: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 37: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 38: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 39: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 40: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 41: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00


Figure: Load distribution (Roller bearing 1)

Figure: Pressure curve (Roller bearing 1, Hertzian stress inside)


Figure: Stiffness curve (Roller bearing 1) Shaft 'Shaft' Roller bearing 'Roller bearing 2' Spherical roller bearings (SKF 21307CC) Inner diameter [d] 35.000 mm Outer diameter [D] 80.000 mm Width [B] 21.000 mm Dynamic load rating [C] 65.600 kN Static load rating [C0] 72.000 kN Fatigue load limit [Cu] 8.150 kN Life modification factor for reliability[a1] 1.000 Service life modification factor [aISO] 1.850 Contamination factor [eC] 0.289 Viscosity ratio [kappa] 2.503 Results according to ISO 281: Equivalent load [P] 7.396 kN Equivalent load [P0] 7.396 kN Effective speed [n] 9 80.000 1/min Service life [Lnh] 245 64.930 h Service life [Lnmh] 454 44.054 h static safety factor [S0] 9.735 Calculation with approximate bearings inner geometr y Number of rolling elements [Z] 12 Diameter of rolling element [Dw] 8.954 mm Effective length of roller [Lwe] 9.148 mm Reference diameter [Dpw] 57.500 mm Diameter of inner ring [di] 49.548 mm Diameter of outer ring [do] 67.456 mm Radius of curvature inner ring [ri] 33.728 mm Radius of curvature outer ring [ro] 33.728 mm Radius of curvature of rolling bodies[Rp] 32.716 mm Contact angle [alpha0] 10.620 ° Dynamic load rating [Cr] 65.600 kN Fatigue load limit [Cu] 8.150 kN Life modification factor for reliability[a1] 1.000 Limit for factor aISO [aISOmax] 50.000 Contamination factor [eC] 0.288 Viscosity ratio [kappa] 2.503 Bearing reaction force [Fx] -1.501 kN Bearing reaction force [Fy] 0.000 kN Bearing reaction force [Fz] 7.242 kN Bearing reaction force [Fr] 7.396 kN (-11.71°)


Displacement of bearing [ux] 3.163 µm Displacement of bearing [uy] -1 83.951 µm Displacement of bearing [uz] - 15.056 µm Displacement of bearing [ur] 15.385 µm (168.14°) Misalignment of bearing [rx] 0.064 mrad (0.22') Misalignment of bearing [ry] -3.214 mrad (-11.05') Misalignment of bearing [rz] 0.280 mrad (0.96') Misalignment of bearing [rr] 0.287 mrad (0.99') Bearing stiffness in operation point dFr/dur = 1562.866 N/µm ,(dFr/dur)_eff = (Fr/ur) = 480.735 N/µm [ux] [uy] [uz] [rx] [rz] [Fx] -511.169 N/µm 0.127 N/µm 60.239 N/µm 0.00 2 N/mrad 0.009 N/mrad [Fy] -0.045 N/µm -49.424 N/µm 0.050 N/µm -6.835 N/mrad -1.407 N/mrad [Fz] 60.239 N/µm 0.050 N/µm -758.268 N/µm -0.01 4 N/mrad -0.002 N/mrad [Mx] 0.000 Nm/µm 0.000 Nm/µm -0.000 Nm/µm 0. 000 Nm/mrad 0.000 Nm/mrad [Mz] 0.000 Nm/µm 0.000 Nm/µm -0.000 Nm/µm 0. 000 Nm/mrad -0.000 Nm/mrad Results according to ISO/TS 16281: Equivalent load [Pref] 6.233 kN Maximum pressure inner ring [pmax_i] 15 88.583 N/mm² Maximum pressure outer ring [pmax_o] 13 61.488 N/mm² Static safety [SF] 6.340 - Service life modification factor [aISO] 2.715 Reference rating service life [Lnrh] 434 57.794 h Modified reference rating service life[Lnmrh] 1179 87.582 h Rolling bodies series: 1 Rolling element no. Loading |F|, Fx, Fy, Fz (kN) Angle (°) Hertzian stress(N/mm²) 1 0.110 -0.108 0.020 0.000 10.60 667.92 2 0.000 0.000 0.000 0.000 0.00 0.00 3 0.000 0.000 0.000 0.000 0.00 0.00 4 0.000 0.000 0.000 0.000 0.00 0.00 5 0.000 0.000 0.000 0.000 0.00 0.00 6 0.000 0.000 0.000 0.000 0.00 0.00 7 0.000 0.000 0.000 0.000 0.00 0.00 8 0.214 0.182 0.039 0.105 10.62 840.92 9 0.869 0.427 0.160 0.740 10.61 1364.97 10 1.348 0.000 0.248 1.325 10.60 1588.58 11 1.286 -0.632 0.236 1.095 10.59 1562.89 12 0.729 -0.620 0.134 0.358 10.59 1284.31 Section Profile(µm) aIS O 1 0.00 1.00 2 0.00 1.00 3 0.00 1.00 4 0.00 50.00 5 0.00 50.00 6 0.00 50.00 7 0.00 28.19 8 0.00 14.44 9 0.00 9.17 10 0.00 6.61 11 0.00 5.16 12 0.00 4.27 13 0.00 3.68 14 0.00 3.26 15 0.00 2.97 16 0.00 2.76 17 0.00 2.61 18 0.00 2.50 19 0.00 2.43 20 0.00 2.39 21 0.00 2.37 22 0.00 2.39 23 0.00 2.43 24 0.00 2.50 25 0.00 2.61 26 0.00 2.76 27 0.00 2.97 28 0.00 3.26 29 0.00 3.66 30 0.00 4.23


31 0.00 5.10 32 0.00 6.48 33 0.00 8.88 34 0.00 13.68 35 0.00 25.63 36 0.00 50.00 37 0.00 50.00 38 0.00 50.00 39 0.00 50.00 40 0.00 1.00 41 0.00 1.00 Hertzian stress in contact at inner ring (N/mm²) Rolling element no. 1 2 3 4 5 6 7 8 Section 1: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 2: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 3: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 4: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 5: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 6: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 7: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 8: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 9: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 10: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 11: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 100.95 Section 12: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 354.16 Section 13: 133.54 0.00 0.00 0.0 0 0.00 0.00 0.00 490.28 Section 14: 328.57 0.00 0.00 0.0 0 0.00 0.00 0.00 588.36 Section 15: 439.98 0.00 0.00 0.0 0 0.00 0.00 0.00 663.40 Section 16: 518.55 0.00 0.00 0.0 0 0.00 0.00 0.00 721.66 Section 17: 576.11 0.00 0.00 0.0 0 0.00 0.00 0.00 766.47 Section 18: 617.73 0.00 0.00 0.0 0 0.00 0.00 0.00 799.81 Section 19: 646.04 0.00 0.00 0.0 0 0.00 0.00 0.00 822.88 Section 20: 662.52 0.00 0.00 0.0 0 0.00 0.00 0.00 836.45 Section 21: 667.92 0.00 0.00 0.0 0 0.00 0.00 0.00 840.92 Section 22: 662.50 0.00 0.00 0.0 0 0.00 0.00 0.00 836.43 Section 23: 646.04 0.00 0.00 0.0 0 0.00 0.00 0.00 822.88 Section 24: 617.83 0.00 0.00 0.0 0 0.00 0.00 0.00 799.89 Section 25: 576.48 0.00 0.00 0.0 0 0.00 0.00 0.00 766.76 Section 26: 519.42 0.00 0.00 0.0 0 0.00 0.00 0.00 722.33 Section 27: 441.79 0.00 0.00 0.0 0 0.00 0.00 0.00 664.71 Section 28: 332.33 0.00 0.00 0.0 0 0.00 0.00 0.00 590.74 Section 29: 145.02 0.00 0.00 0.0 0 0.00 0.00 0.00 494.47 Section 30: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 361.99 Section 31: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 128.07 Section 32: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00


Section 33: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 34: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 35: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 36: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 37: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 38: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 39: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 40: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 41: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Hertzian stress in contact at inner ring (N/mm²) Rolling element no. 9 10 11 12 Section 1: 0.00 0.00 0.00 0.00 Section 2: 0.00 0.00 0.00 0.00 Section 3: 0.00 0.00 0.00 0.00 Section 4: 0.00 426.83 344.49 0.00 Section 5: 0.00 654.06 598.45 0.00 Section 6: 323.36 818.60 772.89 0.00 Section 7: 556.04 950.05 909.85 362.69 Section 8: 715.42 1059.39 1022.79 568.11 Section 9: 839.78 1152.24 1118.21 713.78 Section 10: 941.49 1231.95 1199.84 828.3 1 Section 11: 1026.52 1300.73 1270.09 922.0 2 Section 12: 1098.32 1360.09 1330.62 1000.0 9 Section 13: 1159.10 1411.14 1382.61 1065.5 6 Section 14: 1210.37 1454.72 1426.94 1120.4 4 Section 15: 1253.20 1491.45 1464.28 1166.0 5 Section 16: 1288.37 1521.83 1495.14 1203.3 8 Section 17: 1316.47 1546.22 1519.91 1233.1 2 Section 18: 1337.92 1564.92 1538.88 1255.7 8 Section 19: 1353.02 1578.12 1552.28 1271.7 2 Section 20: 1362.00 1585.98 1560.25 1281.1 8 Section 21: 1364.97 1588.58 1562.89 1284.3 1 Section 22: 1361.99 1585.97 1560.24 1281.1 7 Section 23: 1353.02 1578.12 1552.28 1271.7 2 Section 24: 1337.98 1564.97 1538.93 1255.8 4 Section 25: 1316.66 1546.39 1520.08 1233.3 2 Section 26: 1288.80 1522.20 1495.51 1203.8 3 Section 27: 1253.99 1492.14 1464.98 1166.8 9 Section 28: 1211.70 1455.87 1428.11 1121.8 5 Section 29: 1161.21 1412.94 1384.44 1067.8 2 Section 30: 1101.51 1362.77 1333.35 1003.5 1 Section 31: 1031.19 1304.60 1274.03 927.1 0 Section 32: 948.22 1237.39 1205.39 835.7 6 Section 33: 849.44 1159.75 1125.89 724.7 5 Section 34: 729.47 1069.68 1033.37 584.9 0 Section 35: 577.53 964.17 924.45 392.3 7 Section 36: 363.17 838.26 793.43 0.0 0 Section 37: 0.00 682.62 629.01 0.0 0 Section 38: 0.00 474.19 399.64 0.0 0 Section 39: 0.00 28.86 0.00 0.0 0 Section 40: 0.00 0.00 0.00 0.0 0 Section 41: 0.00 0.00 0.00 0.0 0 Rolling bodies series: 2 Rolling element no. Loading |F|, Fx, Fy, Fz (kN) Angle (°) Hertzian stress(N/mm²) 1 0.109 -0.107 -0.020 0.000 -10.63 667.14 2 0.000 0.000 0.000 0.000 0.00 0.00 3 0.000 0.000 0.000 0.000 0.00 0.00 4 0.000 0.000 0.000 0.000 0.00 0.00 5 0.000 0.000 0.000 0.000 0.00 0.00 6 0.000 0.000 0.000 0.000 0.00 0.00 7 0.000 0.000 0.000 0.000 0.00 0.00 8 0.213 0.181 -0.039 0.105 -10.60 840.33 9 0.869 0.427 -0.160 0.739 -10.60 1364.58 10 1.347 0.000 -0.248 1.324 -10.60 1588.19 11 1.285 -0.632 -0.237 1.094 -10.61 1562.45


12 0.728 -0.619 -0.134 0.358 -10.62 1283.80 Section Profile(µm) aIS O 1 0.00 1.00 2 0.00 1.00 3 0.00 50.00 4 0.00 50.00 5 0.00 50.00 6 0.00 50.00 7 0.00 25.69 8 0.00 13.70 9 0.00 8.89 10 0.00 6.49 11 0.00 5.11 12 0.00 4.24 13 0.00 3.66 14 0.00 3.26 15 0.00 2.97 16 0.00 2.76 17 0.00 2.61 18 0.00 2.50 19 0.00 2.43 20 0.00 2.39 21 0.00 2.37 22 0.00 2.39 23 0.00 2.43 24 0.00 2.50 25 0.00 2.61 26 0.00 2.76 27 0.00 2.98 28 0.00 3.27 29 0.00 3.68 30 0.00 4.28 31 0.00 5.18 32 0.00 6.63 33 0.00 9.20 34 0.00 14.50 35 0.00 28.37 36 0.00 50.00 37 0.00 50.00 38 0.00 50.00 39 0.00 1.00 40 0.00 1.00 41 0.00 1.00 Hertzian stress in contact at inner ring (N/mm²) Rolling element no. 1 2 3 4 5 6 7 8 Section 1: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 2: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 3: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 4: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 5: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 6: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 7: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 8: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 9: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Section 10: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 11: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 126.39 Section 12: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 361.22 Section 13: 143.08 0.00 0.00 0.0 0 0.00 0.00 0.00 493.84 Section 14: 331.29 0.00 0.00 0.0 0 0.00 0.00 0.00 590.17 Section 15: 440.93 0.00 0.00 0.0 0 0.00 0.00 0.00 664.16 Section 16: 518.63 0.00 0.00 0.0 0 0.00 0.00 0.00


721.79 Section 17: 575.72 0.00 0.00 0.0 0 0.00 0.00 0.00 766.23 Section 18: 617.09 0.00 0.00 0.0 0 0.00 0.00 0.00 799.36 Section 19: 645.29 0.00 0.00 0.0 0 0.00 0.00 0.00 822.34 Section 20: 661.74 0.00 0.00 0.0 0 0.00 0.00 0.00 835.87 Section 21: 667.14 0.00 0.00 0.0 0 0.00 0.00 0.00 840.33 Section 22: 661.70 0.00 0.00 0.0 0 0.00 0.00 0.00 835.84 Section 23: 645.18 0.00 0.00 0.0 0 0.00 0.00 0.00 822.24 Section 24: 616.80 0.00 0.00 0.0 0 0.00 0.00 0.00 799.13 Section 25: 575.11 0.00 0.00 0.0 0 0.00 0.00 0.00 765.75 Section 26: 517.42 0.00 0.00 0.0 0 0.00 0.00 0.00 720.87 Section 27: 438.64 0.00 0.00 0.0 0 0.00 0.00 0.00 662.52 Section 28: 326.83 0.00 0.00 0.0 0 0.00 0.00 0.00 587.37 Section 29: 129.82 0.00 0.00 0.0 0 0.00 0.00 0.00 489.10 Section 30: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 352.57 Section 31: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 96.43 Section 32: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 33: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 34: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 35: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 36: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 37: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 38: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 39: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 40: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Section 41: 0.00 0.00 0.00 0.0 0 0.00 0.00 0.00 0.00 Hertzian stress in contact at inner ring (N/mm²) Rolling element no. 9 10 11 12 Section 1: 0.00 0.00 0.00 0.00 Section 2: 0.00 0.00 0.00 0.00 Section 3: 0.00 24.89 0.00 0.00 Section 4: 0.00 473.75 399.05 0.00 Section 5: 0.00 682.26 628.56 0.00 Section 6: 362.65 837.94 793.04 0.00 Section 7: 577.14 963.86 924.07 391.64 Section 8: 729.12 1069.38 1033.01 584.34 Section 9: 849.12 1159.45 1125.54 724.24 Section 10: 947.91 1237.09 1205.03 835.2 8 Section 11: 1030.88 1304.29 1273.68 926.6 5 Section 12: 1101.19 1362.46 1332.99 1003.0 6 Section 13: 1160.89 1412.62 1384.08 1067.3 7 Section 14: 1211.38 1455.54 1427.74 1121.4 0 Section 15: 1253.66 1491.81 1464.60 1166.4 3 Section 16: 1288.46 1521.86 1495.13 1203.3 7 Section 17: 1316.31 1546.04 1519.68 1232.8 6 Section 18: 1337.62 1564.61 1538.53 1255.3 7 Section 19: 1352.66 1577.75 1551.86 1271.2 3 Section 20: 1361.61 1585.59 1559.81 1280.6 7 Section 21: 1364.58 1588.19 1562.45 1283.8 0 Section 22: 1361.59 1585.57 1559.80 1280.6 5 Section 23: 1352.59 1577.70 1551.81 1271.1 7 Section 24: 1337.47 1564.48 1538.39 1255.2 1


Section 25: 1316.00 1545.76 1519.40 1232.5 2 Section 26: 1287.88 1521.35 1494.61 1202.7 5 Section 27: 1252.68 1490.95 1463.73 1165.3 9 Section 28: 1209.81 1454.19 1426.36 1119.7 3 Section 29: 1158.50 1410.58 1382.00 1064.8 1 Section 30: 1097.68 1359.49 1329.97 999.2 6 Section 31: 1025.82 1300.09 1269.40 921.1 2 Section 32: 940.71 1231.27 1199.09 827.3 0 Section 33: 838.91 1151.50 1117.39 712.6 0 Section 34: 714.40 1058.57 1021.89 566.6 5 Section 35: 554.75 949.13 908.82 360.5 3 Section 36: 321.31 817.54 771.68 0.0 0 Section 37: 0.00 652.75 596.93 0.0 0 Section 38: 0.00 424.93 342.04 0.0 0 Section 39: 0.00 0.00 0.00 0.0 0 Section 40: 0.00 0.00 0.00 0.0 0 Section 41: 0.00 0.00 0.00 0.0 0

Figure: Load distribution (Roller bearing 2)


Figure: Pressure curve (Roller bearing 2, Hertzian stress inside)

Figure: Stiffness curve (Roller bearing 2) End report lines: 775

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