internship segula technologies - tu/e · pdf filein the automotive industry, the mounting of...

Eindhoven University of Technology

Dynamics & Control

Department of Mechanical Engineering

Internship Segula Technologies

Building a material model of a rubberweatherstrip

DC 2016.014

Author:

W.J.A. Thijssen 0745445

Supervisor:Prof. dr. H. Nijmeijer, TU/e

Coaches:dr. D. Kostic, Segula Technologies NL BVIng. P. Smulders, Segula Technologies NL BV

February 3, 2016

Abstract

In the automotive industry, the mounting of rubber weatherstrips onto 3D curved edges is limitingin the throughput of a complete production line. Therefore, it is desirable to automate this actionwith robots.Automation of the weatherstrip assembling process is although challenging, due to the flexibility ofthe rubber weatherstrips. To still be able to automatically assemble the weatherstrips, the materialbehavior of the rubber weatherstrips should be known. This knowledge is necessary for designingmotion and force controllers. Therefore, experiments are designed and executed from which thematerial behavior can be extracted. The measurement data is used for fitting material modelson. The fitted material models are used in FEM simulations and compared with the performedmeasurements to check the validity of the material models.For three different weatherstrip geometries, the designed experiments are executed and materialmodels are formed. The material models fairly correspond with the measurements. Therefore thesematerial models can be used for designing motion and force controllers to automate the assemblyprocess of a rubber weatherstrip in the automotive industry.

Contents

Abstract i

1 Introduction 1

2 Rubber material properties 32.1 Preliminary assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2.1 Nonlinear material properties . . . . . . . . . . . . . . . . . . . . . . 32.2.2 Viscoelastic material properties . . . . . . . . . . . . . . . . . . . . . 52.2.3 Other . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Measurements 93.1 Weatherstrip selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Test specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.3 Tooling and interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.4 Glue selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.5 Assembly of the test samples . . . . . . . . . . . . . . . . . . . . . . . . . . 133.6 Measurement results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4 Data fitting of material properties 174.1 Geometry 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.2 Geometry 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.3 Geometry 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5 FEM analysis of weatherstrip assembly 235.1 Model verification in Ansys . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.2 Comparison between measurements and simulation of perpendicular com-

pression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.3 Actual weatherstrip assembly . . . . . . . . . . . . . . . . . . . . . . . . . . 255.4 Simulation of realistic weatherstrip assembly . . . . . . . . . . . . . . . . . 265.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

6 Conclusion and recommendations 296.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Bibliography 31

A Measurement scheme 33

B Measurement results geometry 2 & 3 35B.1 Geometry 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35B.2 Geometry 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

C Material properties 41

Internship Segula Technologies Page| iii

1 Introduction

SEGULA TechnologiesSEGULA Technologies Nederland BV is a part of the international SEGULA Technologies Groupwith 7000 employees in 19 countries. SEGULA is one of Europeans leading engineering companieswith a strong experience and position in automotive and aerospace engineering. As developmentpartner for many OEM companies in automotive, health-care, high-tech components and systemsindustry, SEGULA contributes with new concepts and innovative solutions to different highly strate-gic engineering projects.

Development of mechatronics systems featuring interaction of controlled processes is one of pri-orities for SEGULA Technologies Nederland BV. Examples are control of motion, temperature,force, pressure, contamination, humidity, etc. These examples are relevant in many industries anddifferent applications including the production automation [1].

Project descriptionIn the automotive industry, the mounting of rubber seals onto 3D curved edges is limiting in thethroughput of a complete production line. In Figure 1.1, an example of an assembly line is shown.The skilled workers that assemble these rubber seals determine throughput and quality of the endproducts. To ensure permanent throughput and uniform quality, it is desirable to reduce depen-dency on human workers. A possible solution is automatic assembly of the rubber weatherstrips [1].

Figure 1.1: Assembly line car factory

In the MSc project ”Robotic assembly of rubber weatherstrips” [2], a theoretical investigation ismade on feasibility of a robotized sealing system. In this project, a simple rubber weatherstripgeometry is considered with rubber material properties from literature.

This internship project is a continuation of the MSc project [2]. The challenge is to move from

Internship Segula Technologies Page| 1

material properties found in the literature and a simple weatherstrip geometry towards more com-plex weatherstrip geometries and actual material properties belonging to the complex weatherstripgeometries. The particular objective is to develop a mathematical model of a physical weatherstripwhich can be used to design motion and force controllers of a realistic robot arm suitable for theassembly of the considered weatherstrip.

Structure of the report

Since this internship is a continuation of the MSc project [2], an overview of the conclusions drawnin [2] are given about the rubber material properties that are relevant for the weatherstrip assembly.These conclusions are used as a guideline to decide what measurements have to be performed onactual rubber weatherstrips. The measurements are needed to determine realistic parameters of theweatherstrip models. Quality of the resulting models is evaluated by comparing simulation resultsprovided by the model with the measurements. The same models are used to simulate fixationof the actual weatherstrip onto a solid surface. The necessary application force is extracted fromthese simulations.

In Chapter 2, an overview of the conclusions drawn in [2] are given. Chapter 3 specifies testprocedures for measuring characteristics of the physical weatherstrips that are required for theirmodeling. In Chapter 4, realistic parameters of the weatherstrip models are determined based onthe measurements. Chapter 5 compares model-based simulation results with the measurements.The force necessary to apply the weatherstrip to the solid surface is also determined. In Chapter6, conclusions and recommendations are given.


2 Rubber material properties

In this chapter, a literature study is performed using [2] and the references therein as the mainsources. This knowledge is used as a basis to formulate which material properties are important inthe process of weatherstrip assembly and should be measured on the physical weatherstrips.

2.1 Preliminary assumptions

• The weatherstrip is assembled with small stresses and thus small strains are applied on theweatherstrip. Therefore, the stretch ratio

λ = L/L0 (2.1)

with L0 the initial length and L the deformed length of the weatherstrip is assumed to liebetween λ = 0.9 and λ = 1.1.

• The small strains are applied slowly. Therefore, the loading rate

ε =d

dt(∆L/L0) (2.2)

is assumed between ε = 0.01 s−1 and ε = 1 s−1.

• The weatherstrips are assembled in a factory where a constant temperature is maintained.This means that temperature dependent behavior can be ignored.

• The weatherstrip is isotropic and of uniform quality.

• During the assembly of the weatherstrip, non-harmonic stretches are performed. Therefore,harmonic stretches are not considered.

2.2 Material properties

The conclusions given in this section are made based on properties of an EPDM rubber from lit-erature [10]. For the physical weatherstrips, these conclusions could be different, because they aremade from different rubber material.

2.2.1 Nonlinear material properties

Tension stiffnessTo know how much force is necessary to achieve the desired stretch during an elongation, thetension stiffness of the material needs to be known. Therefore, a simple stress-strain experimentneeds to be performed for small stretch ratios between λ = 1.0 and λ = 1.1.Typically, the stress-strain response of a rubber material is nonlinear and covers large deformations.Materials that cover such behavior are called hyper-elastic. An example of a typical hyper-elasticresponse is shown in Figure 2.1 [2].


Figure 2.1: Typical nonlinear stretch-strain response

A stress-strain experiment can be performed to check whether a hyper-elastic response similar tothe one shown in Figure 2.1 occurs in the weatherstrip and whether a linear representation of thematerial properties can be made for the small stretches that are measured during the measurement.

Compression stiffnessTo know how much force is necessary to achieve the desired stretch during compression, the com-pression stiffness of the material needs to be known, because in the process of weatherstrip assemblythe weatherstrip is pressed against a solid surface. Therefore, a compression experiment needs tobe performed for stretch ratios between λ = 0.9 and λ = 1.0.

Mullins effectThe Mullins effect occurs when a sample is loaded and unloaded towards a specific strain multipletimes in a row. During these repetitions, the material parameters change and less stress needs tobe applied on the sample to reach the specific strain. In Figure 2.2, an example of the Mullinseffect is shown [13].

Figure 2.2: Example of Mullins effect [13]

In the assembly of rubber weatherstrips, small stretch ratios and low loading rates are used and inthis configuration, the Mullins effect is negligible according to [2]. This conclusion is drawn based


on the material parameters for the EPDM rubber from literature. For the rubber considered in[13], this conclusion could be different. Therefore, this material property should be investigated onthe actual weatherstrips.

2.2.2 Viscoelastic material properties

HysteresisHysteresis is the phenomenon where mechanical energy is dissipated due to material internal fric-tion. It is noticeable in the stress-strain diagram of a tensile test when harmonic loading andunloading is applied to a rubber sample and these loading and unloading curves behave differentlyas shown in Figure 2.3 [11].

Figure 2.3: Hysteresis of stress and strain [11]

In the assembly of rubber weatherstrips, no harmonic loading and unloading appears, thus hystere-sis is of no importance.

RelaxationWhen a viscoelastic material is subject to a sudden step in strain, the stress exhibits a step aswell, but then decreases towards a steady state value as shown in Figure 2.4. This effect is calledrelaxation [11] [12]. During the assembly of weatherstrips, no sudden step in the strain occurs,but only low loading rates are applied. This would indicate that relaxation can be ignored in theprocess of weatherstrip assembly, but due to the importance of no residual strain in the assembledweatherstrip, this effect should be measured on the actual weatherstrips.

Figure 2.4: Strain step input (left) and the corresponding stress relaxation (right)


CreepCreep is the phenomenon of an increasing strain towards an asymptotic value on a steady statestress input.While creep is often explained as above, it can also have the opposite effect. When a weatherstripis placed around a closed contour with a certain strain and internal stress, the weatherstrip maystart to creep over time resulting in a gap. In [2, p.31], it is suggested that the effect of creep cansafely be ignored in the process of weatherstrip assembly due to the use of low loading rates. Dueto the importance of no residual strain, this material property should be investigated during theexperiment.

Loading rateThe stress-strain characteristics of a rubber material is dependent from the loading rate, as it canbe seen in Figure 2.5 [10]. Although the stress-strain responses seem to overlap at low stretchratios, it is important to investigate this behavior on the actual weatherstrips.

Figure 2.5: Example of loading rate effects [10]

2.2.3 Other

TemperatureRubber material properties are normally influenced by the temperature. Due to the assumptionthat the weatherstrips are assembled at a constant temperature, the mechanical properties of theweatherstrip are not influenced by the temperature.

Aging, chemical influences and moisture absorptionThe assembly of rubber weatherstrips happens in a factory with a conditioned environment. Fur-thermore an uniform quality of the weatherstrip is assumed and thus aging, chemical influencesand moisture absorption are of no importance in the material properties of a weatherstrip.


2.3 Conclusion

Based on [2] and the related literature, the conclusion can be drawn that the viscoelastic andnon-linear rubber effects can be neglected for the EPDM rubber from literature in the case ofweatherstrip assembly under the assumptions given in section 2.1.The actual weatherstrips that are considered in this project, probably consist of completely differentrubber material as the EPDM rubber from the literature. Therefore the nonlinear and viscoelasticmaterial properties of the actual rubber weatherstrips have to be investigated in this project.


3 Measurements

In this chapter, a selection of representative rubber weatherstrips is given first. Then, tests thatare needed to measure properties of these weaterstrips are specified together with the requiredmeasurement equipment. Assembly of the test samples is explained including the designed interfacesand selected glue. Finally, the obtained measurement results are presented.

3.1 Weatherstrip selection

Weatherstrips need to be selected that can actually be used in a realistic assembly process. There-fore, three different weatherstrips are bought from different suppliers. Geometry 1 and 2 are shownin Figures 3.1(a) and 3.1(c) respectively. These geometries are bought from a truck restorer [3]and are a bump stop and a door rubber respectively. Geometry 3 is shown in Figure 3.1(e) and isbought from an after market car roof builder [4]. The weatherstrip is part of a car roof.

(a) Geometry 1 (b) Geometry 1

(c) Geometry 2 (d) Geometry 2 (e) Geometry 3 (f) Geometry 3

Figure 3.1: Geometries and photos of 3 different weatherstrips


3.2 Test specifications

Several tests are specified that are used to measure rubber material properties of physical weather-strips. These tests are based on the conclusions drawn in Chapter 2. For uni-axial test experiments,the length of the sample should be at least 4 times the diameter of the sample [5], which is an in-terpolation of the rational used for metal samples. Every test should be repeated three times witha new sample to average out variations in the sample. The measurement scheme for geometry 1 isshown in Table 3.1. The total measurement scheme is given in Appendix A.

Tensile testsExperiment 1, 2a, 2b and 3 are specified to measure the stress-strain characteristics of the rubberweatherstrips. From these characteristics it can be concluded whether nonlinear effects are presentin the weatherstrips. The characteristics are again needed to determine numerical values of thematerial properties by data fitting in Ansys. The cycle of stretching towards λ = 1.1 and releasingto zero force is repeated 3 times to investigate whether the Mullins effect plays a role. Experiments1, 2a and 3 should all be performed at a different loading rate, to see if the rate influences the ma-terial behavior. Experiment 2b is carried out in a similar way as experiment 2a. The difference isthat the sample is stretched towards λ = 1.25 in experiment 2b instead of λ = 1.1 as in experiment2a. Experiment 2b is needed to investigate whether the material characteristics is influenced by ahigher stretch.

Compression testsExperiment 4 should be performed to investigate the material behavior during compression. Asample whose length and diameter are the same should be used to prevent buckling.

Experiment 5 is specified to mimic the actual assembly process. A sample with a length of 4 timesthe diameter of the weatherstrip is used. The weatherstrip should be suppressed with a round tubetowards a half of its initial width.

Relaxation testsExperiments 6, 7 and 8 are specified to investigate appearance of relaxation at low stretches. Thedesired stretch should be hold for 60 seconds. This test is repeated at different loading rates toinvestigate whether the loading rate influences the material behavior.

Table 3.1: Test specification geometry 1

Exp. Description Lengthsample[mm]

Stretch [-] Loadingrate[strain/s]

Loadingrate[mm/s]

Loadingtime [s]

1 Simple tensile test (z-dir) 102 1.0− > 1.1 0.01 1.02 10

2a Simple tensile test (z-dir) 102 1.0− > 1.1 0.05 5.1 2

2b Simple tensile test (z-dir) 102 1.0− > 1.25 0.05 5.1 5


4 Uni-axial compression (z-dir) 25.5 1.0− > 0.9 0.1 2.55 1

5 Perpendicular compression (y-dir) 102 1.0− > 0.5 0.1 2.55 5

6 Relaxation test (z-dir) 102 1.0− > 1.1 0.01 1.02 10




3.3 Tooling and interfaces

ToolingAll the tensile and compression tests are performed on a calibrated 100 kN Zwick 1475 tensiletester from Parthian Technology, Hengelo, which is shown in Figure 3.2. This machine has forceand displacement as its input and output respectively. An output data point can be taken if theforce changes with ∆N , the displacement changes with ∆mm and the time changes with ∆sec. Avariation of these conditions is also possible.

(a) Tensile test (b) Compression test

Figure 3.2: Zwick 1475 tensile tester

InterfacesThe rubber weatherstrips do not have a geometry that can be clamped in the tensile tester withoutintroducing large initial deformations. Besides that, slip can occur easily.To overcome these problems, two different interfaces are designed for connecting the samples to thetensile tester. Interface 1 is for geometry 1 and interface 2 is for geometries 2 and 3. Both interfacesare designed so that the deformations in the interfaces are negligible compared to the deformationsin the rubber samples. In Figure 3.3 the deformations are shown that are computed using SiemensNastran [19]. The maximal deformations for interface 1 and 2 are 4.1 ∗ 10−4 mm and 8.3 ∗ 10−5

mm respectively which is much smaller than the expected deformations in the samples. Besidescausing minimum deformations, the interfaces should be easily to clamp into the tensile tester.


(a) Interface 1 (b) Interface 2

Figure 3.3: Deformation in the interfaces in millimeter.

3.4 Glue selection

To bond a sample to the interface, a glue should be selected that can withstand the tensile forcewhich is applied to the sample. The particular requirements that the glue has to meet are listedbelow.

• The tensile strength should be much larger than 0.346 N/mm2. This is the tensile strengththat occurs when the weatherstrips is stretched by 10 percent based on material propertiesfound in the literature [2].

• The glue should fill-in a gap of ± 0.5 mm. This is due to the difficulty of cutting the samplesexactly at the desired length.

• The glue should have a good adhesive bond on the rubber.

Several glues are taken under consideration as shown in Table 3.2. Out of these options, LOCTITE3090 is eventually found as the most suitable one.

Table 3.2: Glue selection

Glue Tensile strength[N/mm2]

Bondinggap [mm]

Adhesiveon rubber

LOCTITE 406 [14] 13 0.05 x

LOCTITE 480 [15] 5 to 15 0.15 x

Terostat MS 9380 2C [16] ± 4 2 x

Terostat MS 939 [17] ± 3 - x

LOCTITE 3090 [18] > 6 < 5 x


3.5 Assembly of the test samples

In Figure 3.4, the assembled test samples are shown. Noticeable is that the interfaces are notcompletely in line, which can be explained by an uncertainty in the squareness of the cutting facesand by a curve in the samples. The curve in the samples is a residual deformation due to storingthe weatherstrips in loopings. These small curves do not influence the measurements significantly.

(a) Geometry 1

(b) Geometry 2

(c) Geometry 3

Figure 3.4: Assembled test samples

3.6 Measurement results

In this section, the measurement results for all experiments from Table 3.1 for geometry 1 are shownand all rubber characteristics that are found in the measurements are discussed. In Appendix Bare the measurement results for geometries 2 and 3 shown, where the same characteristics are en-countered.

During the experiments, a data point is taken under three conditions: if the displacement changesby 0.1 mm, the force changes by 10 Newton or the measurement time changes by 0.26 seconds.

Tensile testsIn Figure 3.5 the measurement results for the tensile experiments are shown. From these figures,a hysteresis can be observed since the loading and unloading curves differ from each other. Thisbehavior does not change with an increasing loading rate. The Mullins effect is also present in theweatherstrips and it can be noticed by the decreasing force necessary to achieve the same stretchwhile performing a harmonic loading and unloading curve.Sample 1 from experiment 1, which is shown in Figure 3.5(a), shows a 9 percent higher stiffnessthan samples 2 and 3. A reason for the higher stiffness is not clear, since no differences in themeasurement settings are found between the in the sample three samples.


In Figure 3.5(d), a decreasing stiffness can be noticed at strains above 0.09. This can be explainedby the inertia of the sample, since in this region the tensile tester needs to decelerate from a constantpositive velocity towards a constant negative velocity.

0 0.02 0.04 0.06 0.08 0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Strain [−]

Str

ess

[MP

a]

Geom. 1, Exp. 1

Sample 1Sample 2Sample 3

(a) Experiment 1

0 0.02 0.04 0.06 0.08 0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Strain [−]S

tres

s [M

Pa]

Geom. 1, exp. 2a


(b) Experiment 2a

0 0.05 0.1 0.15 0.2 0.25

0

0.2

0.4

0.6

0.8

1

1.2

Strain [−]

Str

ess

[MP

a]

Geom. 1, exp. 2b


(c) Experiment 2b

0 0.02 0.04 0.06 0.08 0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Strain [−]

Str

ess

[MP

a]

Geom. 1, Exp. 3


(d) Experiment 3

Figure 3.5: Measurement results for tensile tests for the samples of geometry 1

Compression testsFigure 3.6(a) shows results of the axial compression of the weatherstrip as described in Table 3.1.A large difference is noticeable between sample 1 and samples 2 and 3. This difference can beexplained by the unevenness in the cutting face. Sample 1 has the smoothest cutting face andthus earlier a stiff behavior can be noticed, where samples 2 and 3 first settle in before a more stiffbehavior can be noticed. In these experiments, also hysteresis can be observed.

In Figure 3.6(b) results of the perpendicular compression test are shown from which it can be seenthat during the compression a linear force built-up occurs.


The three samples all deviate in stiffness, what could be explained by small differences in their wallthickness. Another reason could be that the samples were not completely perpendicular underneaththe compression tester resulting in a difference of material to be deflected.

The remark needs to be made that for both compression experiments, the upper part of the com-pression tester had to drop slowly with a speed of 1 mm/min until it touched the sample with aforce of 2.5 N and then set the force back to 0 [N]. Hereafter the actual measurement could begin.This procedure was necessary to overcome measuring in air.

−0.1 −0.08 −0.06 −0.04 −0.02 0

−0.5

−0.4

−0.3

−0.2

−0.1

0

Strain [−]

Str

ess

[MP

a]

Geom. 1, exp. 4


(a) Experiment 4

0 2 4 6 8 10 12 140

10

20

30

40

50

60

70

80

Displacement [mm]

For

ce [N

]

Geom. 1, Exp. 5


(b) Experiment 5

Figure 3.6: Measurement results for the compression tests with the samples of geometry 1

Relaxation testsIn Figure 3.7, results of the relaxation tests are shown as described in 3.1. These tests are displace-ment controlled. Small differences between the samples can be noticed, but the overall behavior isthe same. Noticeable is that although the loading rate and strain are relatively low, the relaxationis significant. For the different experiments, the stress relaxes approximately by -15, -20 and -19percents for experiments 6, 7 and 8 respectively, over a time span of 60 seconds. For experiment 8,it was expected that more relaxation would appear than in experiment 7 due to the higher loadingrate, but this is not noticeable. This can be explained by the fact that it is not certain whether thehighest stress is measured due to the low number of measuring points in the peak.Sample 3 in Figure 3.7(c) shows a different behavior than samples 1 and 2, which is likely due toan error in the measurement settings.


0 10 20 30 40 50 60 70 80

0

0.1

0.2

0.3

0.4

0.5

0.6

Time [sec]

Str

ess

[MP

a]Geom. 1, Exp. 6


(a) Experiment 6

0 10 20 30 40 50 60 70

0

0.1

0.2

0.3

0.4

0.5

0.6

Time [sec]

Str

ess

[MP

a]

Geom. 1, Exp. 7


(b) Experiment 7

0 10 20 30 40 50 60

0

0.1

0.2

0.3

0.4

0.5

0.6

Time [sec]

Str

ess

[MP

a]

Geom. 1, Exp. 8


(c) Experiment 8

Figure 3.7: Measurement results for the relaxation tests with samples of geometry 1

3.7 Conclusion

Based on the measurements executed in Chapter 3.6 can be concluded that the viscoelastic materialproperties play a significant role in the material properties of the weatherstrips, even at relativelysmall strains. Hysteresis is present during a loading and unloading curve. Relaxation is present,implying that no strain in the longitudinal direction has to be applied during the actual assemblyprocess. And different loading rates give different material behaviors.


4 Data fitting of material properties

To facilitate design of high-performance robust force and motion controllers, material properties ofthe rubber weatherstrips should be known. These properties can be determined by fitting param-eters of the material models into the measured data.

The measurement results from experiments 1, 2a, 2b, 3 and 4 are used for the parameter fitting.First the measurement data are pre-processed. The first loading curve is extracted out of the totalmeasurement data, the start of the stress-strain curve is put to the origin and for the measurementswith a high loading rate, the last data points are omitted where the sample decelerates. After thepre-processing, the data points from samples 1, 2a and 3 of each experiment are combined to obtainan average model of the three measurements by parameter fitting.

Two types of material models are used for fitting on the measurement data. First, a linear materialmodel is used which is shown by [8]

σ = E ∗ ε (4.1)

This model contains the Young’s modulus E.

Second, a hyper elastic material model represented by the 3-term Ogden model is used for datafitting [9]. The Ogden model describes a strain energy given by

W (λ1, λ2, λ3) =3∑p=1

µpαp

(λαp

1 + λαp

2 + λαp

3 − 3) (4.2)

Here, λi are the strains in the three principal directions and µp and αp are empirically determinedmaterial constants.

The engineering stress under simple tension loading can be determined as follows [10].

σE =σ

λ= ηµ

3∑i=1

µi(λαi−1 − λ−(αi/2)−1) (4.3)

with

η(λ) = 1− 1

rerf [

µ

m

3∑i=1

µiαi

(λαimax − λαi + 2λ−(αi/2)

max − 2λ−(αi/2))] (4.4)

4.1 Geometry 1

For experiment 1 with geometry 1, the first sample is disregarded due to the unexplainable mea-surement result which is discussed in Chapter 3.6.

In Figure 4.1, the data fitting is performed for experiments 1, 2a and 3 where stretches are madefrom λ = 1.0 until λ = 1.1. From these figures it can be seen that with an increasing loading rate,the stiffness of the weatherstrip increases. This means that viscoelastic material properties arepresent in the rubber weatherstrip. It also indicates that for a good representation of the materialparameters during the actual assembly process, the material parameters should be known for theloading rate that is used during the assembly of the weatherstrip.


0 0.02 0.04 0.06 0.08 0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Strain [−]

Str

ess

[MP

a]Geometry 1

Linear [strain/s]=0.01Meas. [strain/s]=0.01Linear [strain/s]=0.05Meas. [strain/s]=0.05Linear [strain/s]=0.1Meas. [strain/s]=0.1

(a) Linear material properties

0 0.02 0.04 0.06 0.08 0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Strain [−]

Str

ess

[MP

a]

Geometry 1

Ogden [strain/s]=0.01Meas. [strain/s]=0.01Ogden [strain/s]=0.05Meas. [strain/s]=0.05Ogden [strain/s]=0.1Meas. [strain/s]=0.1

(b) Ogden material properties

Figure 4.1: Results of data fitting of material properties for geometry 1 at different loading rates

It is questionable whether the material properties that correspond to Figure 4.1 are representativeenough, since these properties are obtained for data that only represent 10 percent strain.To check the validity of the obtained material properties, the measurement data from experiment2b are also considered, since these are obtained for stretches between λ = 1.0 and λ = 1.25. Thecorresponding results are shown in Figure 4.2(a). When the material parameters from experiment2b are compared to the material parameters from experiments 1, 2a and 3, it is noticeable that thematerial parameters from experiment 2b show a lower stiffness. 5.02 MPa for experiment 2b versus6.25, 6.64 and 7.27 MPa for experiments 1, 2a and 3 respectively.

An even larger set of data points could be taken if the tensile test from experiment 2b would becombined with the compression test from experiment 4. These data sets can not be combined, sincetests 2b and 4 are performed at different loading rates.Therefore experiment 3 is combined with experiment 4. This is done to include data from com-pression and tension experiments in the material properties. Both experiments are performed at aloading rate of 0.1 strain/s. In Figure 4.2, these fitted curves are shown. Noticeable is that withthe Ogden model, the stress-strain curve shows lower stiffness characteristics with more compres-sion. These material properties cannot be used in simulations, because it will result in unrealisticbehavior of the simulated model. No clear reason for this behavior could be found.To increase the accuracy of the material models, experiments could be performed in which com-pression and tension are combined. This results in a more correct material model.

The material parameters obtained by data fitting are given in Table C.1 and C.2 for all configura-tions.


0 0.05 0.1 0.15 0.2 0.250

0.2

0.4

0.6

0.8

1

1.2

Strain [−]

Str

ess

[MP

a]Geom. 1, Exp 2b

Measurement dataOgden modelLinear model

(a) Curve fit for λ from 1.0 until 1.25

−0.1 −0.05 0 0.05 0.1

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

Strain [−]

Str

ess

[MP

a]

Geom. 1, Exp 3 & 4


(b) Curve fit for λ from 0.9 until 1.1

Figure 4.2: Results of data fitting material properties for geometry 1 with different data sets

4.2 Geometry 2

In Figure 4.3, the material parameters are estimated for experiments 1, 2a and 3 of geometry 2.The data fitting shows non intuitive results, since the material stiffness is higher in experiment 1(the lowest loading rate) than experiment 2 (higher loading rate) while the other way around wasexpected. No explanation can be thought of that could explain this phenomena. On the otherhand, the material stiffness obtained in experiment 3 (highest loading rate) is the highest, which isto be expected.

0 0.02 0.04 0.06 0.08 0.1

0

0.2

0.4

0.6

0.8

1

1.2

Strain [−]

Str

ess

[MP

a]

Geometry 2



0 0.02 0.04 0.06 0.08 0.1

0

0.2

0.4

0.6

0.8

1

Strain [−]

Str

ess

[MP

a]

Geometry 2



Figure 4.3: Results of data fitted material parameters for geometry 2 at different loading rates


For the data fitting based on the measurements obtained in experiment 2b, only the data recordeduntil the rupture of the glue could be used which was λ = 1.125. The total data is shown in Ap-pendix B. The results of data fitting are shown in Figure 4.4(a). No significant change of materialparameters can be observed.In Figure 4.4(b), the data fitting is shown when measurement from experiments 2b and 4 arecombined. The linear model shows a minor decrease in the stiffness compared to the stiffness de-termined in experiments 2a and 2b. The measured data shows a lower stiffness during compressionwhat is unexpected, but the Ogden model describes this characteristics. The lower stiffness duringthe compression might be the property of the specific rubber material.


0 0.02 0.04 0.06 0.08 0.1 0.120

0.2

0.4

0.6

0.8

1

1.2

Strain [−]

Str

ess

[MP

a]

Geom. 2, Exp 2b



−0.1 −0.05 0 0.05 0.1−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Strain [−]

Str

ess

[MP

a]

Geom. 2, Exp 2b & 4



Figure 4.4: Results of data fitting of material parameters for geometry 2 with different data sets

4.3 Geometry 3

In Figure 4.5, the material parameters estimated based on data measured in experiments 1, 2a and3 with samples of geometry 3 are shown. The stiffness of the material models increases with anincreasing loading rate, which is intuitively expected.


0 0.02 0.04 0.06 0.08 0.1−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Strain [−]

Str

ess

[MP

a]Geometry 3



0 0.02 0.04 0.06 0.08 0.1−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Strain [−]

Str

ess

[MP

a]

Geometry 3



Figure 4.5: Results of data fitted material parameters for geometry 3 at different loading rates

In Figure 4.6(a), the results of data fitting based on measurements obtained in experiment 2b areshown. The resulted material models show a more realistic description of the actual material prop-erties.In Figure 4.6(b), the measurement data from experiments 2b and 4 are combined. The Ogdenmodel fits the measurement data accurately over the entire data set. Even more, both the mea-surement data and the Ogden model show a higher stiffness during compression than during tension.


0 0.05 0.1 0.15 0.2 0.250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Strain [−]

Str

ess

[MP

a]

Geom. 3, Exp 2b



−0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25

−0.4

−0.2

0

0.2

0.4

0.6

Strain [−]

Str

ess

[MP

a]

Geom. 3, Exp 2b & 4



Figure 4.6: Results of data fitting of material parameters for geometry 2 with different data sets


4.4 Conclusion

Linear and hyper elastic material models are used for fitting material properties on the measurementresults. For geometries 1 and 2, the hyper elastic material model which is fitted on experiment2b gives the best match with the measurement data. For geometry 3, the hyper elastic materialmodel which is fitted on a combination of experiment 2b and 4 gives the best corresponding withthe measurements over the largest strain range. In experiment 2b, a larger strain ratio is used incomparison with the other measurements. Hence, a larger strain range is recommended.


5 FEM analysis of weatherstrip assembly

In this chapter, results of FEM simulations performed in Ansys workbench are compared with themeasurements. This comparison should indicate which material model is most representative forthe actual material properties. Also an invest, which can be used in servo control simulations ofthe sealing process.

5.1 Model verification in Ansys

To verify that the Ansys simulations are performed in a correct way, a tensile test is simulatedwith the material parameters extracted from the data measured in experiment 2b. In Figure 5.1, aresult of simulation of the deformed tensile test is shown in which the hyper elastic material modelis used.

Figure 5.1: Deformed sample in the simulation of the tensile test

In Figure 5.2, the Ansys simulation results are compared with the measurements and materialmodels. As it can be seen, the differences between the simulated and modelled stress-strain curvesare very small. The small differences could be caused by round-off errors of the material parameters.

0 0.05 0.1 0.15 0.2 0.250

0.2

0.4

0.6

0.8

1

1.2

Strain [−]

Str

ess

[MP

a]

Geom. 1, Exp 2b

Measurement dataOgden modelLinear modelOgden sim.Linear sim.

(a) Comparison

0.2 0.21 0.22 0.23 0.24 0.25 0.26

1

1.05

1.1

1.15

1.2

1.25

Strain [−]

Str

ess

[MP

a]

Geom. 1, Exp 2b

Measurement dataOgden modelLinear modelOgden sim.Linear sim.

(b) Zoom in

Figure 5.2: Comparison between measured data, results of data fitting and simulation of thetensile test


5.2 Comparison between measurements and simulation of perpen-dicular compression

In this section, the perpendicular compression experiment is simulated for geometries 1 and 2. Theperpendicular compression experiment for geometry 3 is not simulated since during the measure-ments, the sample was squeezed while during the actual assembly it has to be pressed to a solidsurface. Simulation of the squeezing has no practical value and therefore it does not have to besimulated.During the measurements, the samples of geometries 1 and 2 are both compressed with a role of5 millimeters in diameter. For the actual assembly process, a role with twice the diameter of thesample is preferred to make sure that the center axis of the role is always above the top of theweatherstrip. In Figure 5.3, the simulation results are shown with the use of the Ogden materialparameters from experiment 2a. Both geometries are symmetric in two directions, therefore a quartof both geometries are simulated to reduce simulation times. Geometry 1 is compressed with a forceof 15 N and geometry 2 is compressed with a force of 25 N.


Figure 5.3: Simulation of the perpendicular compression experiment using Ansys Workbench

In Figure 5.4, a comparison between the simulation and measurement results is shown for bothgeometries and several material properties. The obtained results are discussed in the next twosubsections.

Geometry 1By inspection of Figure 5.4(a) it can be seen that the simulations performed with the materialproperties from experiment 2a show a higher material stiffness than the measurements, but thatthe Ogden and linear material models give similar results. It is noticeable that the simulations withthe material properties from experiments 2a and 2b deviate much from each other. There is also alarge difference in the simulation results obtained using the linear and Ogden material parametersestimated based on the measurements from experiment 2b. The simulation results with the linearmaterial properties from experiment 2b show initially a good match with the measurements, butthen get too stiff when the deformations increase in the sample. On the other hand, the simulationresult with the Ogden material model shows a lower stiffness than the measurements. The increaseof stiffness at a displacement of 15 mm is due to the fact that the tube is compressed completely.Over the entire perpendicular compression range, the hyper elastic material parameters from ex-periment 2b match the measurements most accurately and is therefore the most suitable model forcontrol design.


The main cause for the differences between the simulations and measurements is the fact that thelocal deformations in the simulations are much larger than the deformations during the measure-ments that correspond to the considered strain ranges. Consequently, the resulting data fittings donot cover the complete deformation ranges that are studied in the simulation.

Geometry 2In Figure 5.4(b), the measurements from the perpendicular compression experiment are comparedwith the simulations. The measurements are shifted 2.5 N upwards and 1.8 mm to the left to com-pensate for the pre-load which was applied to overcome measuring in the air as it is explained inChapter 3.6. Simulations with the linear material models show higher stiffness than the measure-ments. The differences between the simulation results obtained with the linear models are small.Noticeable is that the linear model from experiment 2b shows a lower stiffness than from experi-ment 2a, which is a consequence of the parameter fitting results obtained in Chapter 4. Both hyperelastic material models match the measurements closely. The material parameters from experiment2b match the measurements more accurate during the second part of the compression experiment.Therefore, the hyper elastic material model from experiment 2b is the most suitable one for controldesign.

0 2 4 6 8 10 12 14 16

0

10

20

30

40

50

60

70

80

Displacement [mm]

For

ce [N

]

Geom. 1, exp. 5,

Meas. sample 1Meas. sample 2Meas. sample 3Simulation linear 2aSimulation linear 2bSimulation Ogden 2aSimulation Ogden 2b

(a) Geometry 1

0 1 2 3 4 5 6 7 8

0

20

40

60

80

100

120

Displacement [mm]

For

ce [N

]

Geom. 2, exp. 5,

Meas. Sample 2Meas. sample 2Meas. sample 3Simulation linear 2aSimulation linear 2bSimulation Ogden 2aSimulation Ogden 2b

(b) Geometry 2

Figure 5.4: Comparison between the measurements and simulations

5.3 Actual weatherstrip assembly

Rubber weatherstrips are often assembled using a double-sided tape. These double-sided tapesusually need an application pressure of 100 kPa [6]. In the automatic assembly of rubber weath-erstrips, this application pressure can be achieved using a wheel which rolls over the weatherstrip.To ensure that the wheel rolls easily over the weatherstrip, the diameter of the wheel is chosen astwice the height of the weatherstrip. In this case, the center axis of the wheel is always above theweatherstrip.In Figures 5.5(a), 5.5(b) and 5.5(c) the simulated geometries are shown. Sample 1 and 2 are pressedto a flat surface, where sample 3 is pressed over an edge of the solid object.


(a) Sample 1

(b) Sample 2 (c) Sample 3

Figure 5.5: Weatherstrip assemblies that are simulated

5.4 Simulation of realistic weatherstrip assembly

In all simulations, the application force increases until a pressure of 100 kPa is achieved on thecontact surface between the sample and the solid surrounding. Hyper elastic material parametersfrom experiments 2b are used, since this model shows the best match with the measurement resultsfrom Chapter 4 and 5.2.

In Figure 5.6, the pressure at the contact surface between the weatherstrip and the solid surround-ing is shown. For geometries 1 and 2, a quart of the models from Figures 5.5(a) and 5.5(b) isused, because these models are symmetric in x- and z-directions. For geometry 3, half of the modelfrom Figure 5.5(c) is used, because this model is symmetric in z-direction. With the use of thesesimplified models, the simulation times are reduced.

For geometry 1, an application force of 40 Newton on the quart of the model is needed to achieve acontact pressure of at least 100 kPa over the width of the weatherstrip, as shown in Figure 5.6(a).For geometry 2, an application force of 12 Newton is needed on the quart of the model to achieve


a contact pressure of 100 kPa over the entire width of the weatherstrip, as shown in Figure 5.6(b).Both geometries show a relatively low contact pressure at the x-symmetry line. This is caused bythe curling upwards of the middle of the weatherstrip during a perpendicular compression.For geometry 3, no uniform contact pressure of at least 100 kPa could be achieved over the entirecross-section of the weatherstrip. This is due to the curved edges of the surrounding. The contactpressure that is achieved with an application force of 5 Newton is shown in Figure 5.6(c).


(c) Geometry 3

Figure 5.6: Pressure at the contact surface

5.5 Conclusion

The material models from Chapter 4 are used in simulations wherein the perpendicular compres-sion experiments are simulated. The simulations are compared with the perpendicular compressionexperiments from which is concluded that the hyper elastic material models extracted from experi-ment 2b gave the best correspondence with the measurements for geometries 1 and 2. For geometry3, no comparison between the simulations and measurements could be made.It is also investigated what force is required for application of the weatherstrip. For geometries1 and 2, the application force for the quarter models was 40 and 12 Newton respectively. Forgeometry 3, no uniform contact pressure could be achieved due to the shape of the weatherstrip.


6 Conclusion and recommendations

In this chapter, conclusions and recommendations are given about the building of material modelsfor weatherstrips.

6.1 Conclusion

The goal of this project is to create models that can qualitatively and quantitatively describe ma-terial properties of physical weatherstrips. The resulting models are needed to design motion andforce controllers of a realistic robot arm suitable for the assembly of the considered weatherstrips.To accomplish this goal, several steps needed to be taken.

At first, a literature study is performed on [2] and the literature therein. According to the lit-erature, the most visco- and hyper elastic material properties do not play a role in the assemblyof a weatherstrip when EPDM rubber material from literature is considered. Due to the largevariety of rubber materials, these conclusions could be different for actual rubber weatherstrips.Therefore, several visco- and hyper elastic material properties should be investigated on the actualweatherstrips.

Several experiments are specified in which the material properties of the physical weatherstrips aremeasured. For these experiments, a tensile tester is chosen as the measurement device. Interfacesare designed to clamp the weatherstrips into the tensile tester. To bond the weatherstrips to theinterfaces, glue LOCTITE 3090 suited the requirements best.

Based on the measurement results, it can be noticed that viscoelastic material properties play animportant role in the behavior of the weatherstrips, even for relatively small strains. The viscoelas-tic material properties are encountered, such as hysteresis, loading rate effects and relaxation. Theconsequence of the loading rate effects is that the material properties should be known for thespecific loading rate in which the actual assembly process takes place. The relaxation implies thatno strain in the longitudinal direction has to be applied during the actual assembly process, toprevent viscoelastic effects from appearing.

The measurement results are used to determine material properties by fitting the material modelsinto the measurement data. Linear and hyper elastic material models are used. The hyper elasticmaterial model is the 3-term Ogden model. For geometry 1, the hyper elastic material parametersfitted on the measurement data from experiment 2b gave the best results over the entire stretchratio. For geometry 2, the data fitting on experiment 2b gives the best match with the measurementresults and for geometry 3, the data fitting on the combination of experiment 2b and 4 gives the bestmatch with the measurements over the largest stretch range. In experiment 2b, a larger stretch ratiowas used in comparison with the other measurements. Hence, a larger strain range is recommended.

The material models are used to simulate the perpendicular compression experiment with AnsysWorkbench for two physical weatherstrips (geometries 1 and 2). The simulation of geometry 1with the hyper elastic material model from experiment 2b gives reasonable results, but still somelarge improvement can be made. For geometry 2, the simulations with the hyper elastic materialproperties from experiment 2b match the measurement closely and thus this model can be used forcontrol design.


Finally, it is investigated what force is required for application of the rubber weatherstrips. For theweatherstrips with geometries 1 and 2, the estimated application forces are 40 and 12 Newton re-spectively for the quart models. For the weatherstrip with geometry 3, no uniform contact pressurecould be achieved due to the shape of the weatherstrip. For this geometry should be investigatedor a different bonding technique can be used, for instance gluing to its surroundings.

The transition from a theoretical material model and geometry towards realistic material proper-ties and geometries is achieved. For geometry 3, an accurate mathematical model of the materialproperties is made. The obtained models for geometries 1 and 2 show differences with the mea-surements, which confirms how challenging it is to obtain accurate models of rubber materials.

6.2 Recommendations

To increase the accuracy of the material models, experiments should be performed where compres-sion and tension are combined. This may give more correct material models.

Simulations with different methods to apply the pressure on the weatherstrip should be performedto minimize deformations in the weatherstrip while still reaching the desired contact pressure.When smaller deformations occur in the weatherstrip, a closer match with the strains used in themeasurements is made. Use for instance 3 roles instead of 1 or use a role with a diabolo shape.


Bibliography

[1] D. Kostic, Internship description. Eindhoven, The Netherlands, Segula Technologies, 2015

[2] B. Bastings, Robotic assembly of weatherstrips. Eindhoven, The Netherlands: TU/e, 2015.

[3] wifocarrshop.nl, Goor, The Netherlands

[4] carroofservice.nl, Oisterwijk, The Netherlands

[5] ASM International, Tensile Testing, Second Edition. Ohio, USA: 2004.

[6] Christoph Nagel The tesa Technology Journal, A focus on pressure-sensitive adhesive tape tech-nology. Tesa tape inc. , 2013.

[7] Parthian Technology BV, Hengelo

[8] Piet Schreurs Material Models, The Netherlands: Tu/e, 2011

[9] Beomkeun Kim et al. A comparison among Neo-Hookean model, Mooney-Rivlin model, andOgden model for chloroprene rubber. In: International Journal of Precision Engineering andManufacturing 13.5 (May 1, 2012), pp. 759 − 764.

[10] Ming Cheng and Weinong Chen. Experimental investigation of the stress-stretch behavior ofEPDM rubber with loading rate effects. In: International Journal of Solids and Structures 40.18(Sept. 2003), pp. 4749 − 4768.

[11] Piet Schreurs. Computational Material Models, lecture notes. June 16, 2014.

[12] Fredrik Karlsson and Anders Persson. Modelling Non-Linear Dynamics of Rubber Bushings -Parameter Identification and Validation. PhD thesis. Lund, Sweden: Lund University, Divisionof Structural Mechanics, 2003.

[13] S. Cantournet, R. Desmorat, and J. Besson. Mullins effect and cyclic stress softening of filledelastomers by internal sliding and friction thermodynamics model. In: International Journal ofSolids and Structures 46.1112 (June 1, 2009), pp. 2255 − 2264

[14] Henkel, Technical Data Sheet, LOCTITE 406. February 2012

[15] Henkel, Technical Data Sheet, LOCTITE 480. September 2015

[16] Teroson, Technical Data Sheet, Terostat MS 9380 2C. 23 March 2010

[17] Teroson, Technical Data Sheet, Terostat MS 939. 18 August 2009

[18] Henkel, Technical Data Sheet, LOCTITE 3090. September 2012

[19] Siemens NX Nastran 7.0, 2009


A Measurement scheme

Maximal loading rate = 800 mm/min = 13.33 mm/s

Sample 1 Available length = 2 m Total length necessary = 3 ∗ 739.5 = 2218.5 mm

Table A.1: Test specification geometry 1



Loadingrate[mm/s]

Loadingtime [s]


2a Simple tensile test (z-dir) 102 1.0− > 1.1 0.05 5.1 2

2b Simple tensile test (z-dir) 102 1.0− > 1.25 0.05 5.1 5



5 Perpendicular compression (y-dir) 102 1.0− > 0.5 0.1 2.55 5




Total: 739.5

Sample 2 Available length = 2 m Total length necessary = 3 ∗ 388.6 = 1165.8 mm




Loadingrate[mm/s]

Loadingtime [s]

1 Simple tensile test (z-dir) 53.6 1.0− > 1.1 0.01 0.536 10

2a Simple tensile test (z-dir) 53.6 1.0− > 1.1 0.1 5.36 1

2b Simple tensile test (z-dir) 53.6 1.0− > 1.25 0.1 5.36 2.5

3 Simple tensile test (z-dir) 53.6 1.0− > 1.1 0.2 10.72 0.5


5 Perpendicular compression (y-dir) 53.6 1.0− > 0.5 0.1 1.34 5

6 Relaxation test (z-dir) 53.6 1.0− > 1.1 0.01 0.536 10


8 Relaxation test (z-dir) 53.6 1.0− > 1.1 0.2 10.72 0.5

Total: 388.6


Sample 3 Available length = 1.5 m Total length necessary = 3 ∗ 342.2 = 1026.9 mm




Loadingrate[mm/s]

Loadingtime [s]

1 Simple tensile test (z-dir) 47.2 1.0− > 1.1 0.01 0.472 10

2a Simple tensile test (z-dir) 47.2 1.0− > 1.1 0.1 4.72 1

2b Simple tensile test (z-dir) 47.2 1.0− > 1.25 0.1 4.72 2.5

3 Simple tensile test (z-dir) 47.2 1.0− > 1.1 0.25 11.8 0.4


5 Perpendicular compression (y-dir) 47.2 1.0− > 0.5 0.1 1.18 5



8 Relaxation test (z-dir) 47.2 1.0− > 1.1 0.25 11.8 0.4

Total: 342.2

• Exp 1, 2a and 3: The sample needs to be stretched to λ = 1.1. Afterwards it needs to bebrought back to zero stress. This cycle needs to be repeated 3 times.

• Exp 2b: Experiment 2a needs to be repeated for λ = 1.25.

• Exp 4: The sample needs to be compressed towards λ = 0.9 in z-direction.

• Exp 5: The sample needs to be compressed towards λ = 0.5 in y-direction.

• Exp 6, 7 and 8: The sample needs to be stretched towards λ = 1.1 with the loading rategiven in Table A.3. The stretch needs to be held for 60 seconds, after which the stress can beremoved.


B Measurement results geometry 2 & 3

In this appendix, the measurement results for geometry 2 and 3 are shown. Only the phenomenathat are not explained in Chapter 3.6 are discussed. For these two geometries, a data point is takenif the displacement changed by 0.05 mm, the force changed by 10 Newton or the time changed by0.26 seconds

B.1 Geometry 2

Tensile testsIn Figure B.1(c) the measurement results for experiment 2b are shown. From 12 percent strain andfurther, unexpected behavior can be observed. A jump in the stress can be seen and a decreaseof the stiffness. This can be explained by the fact that half way the measurement, the glue of thesamples ruptured. This happened with all the three samples, meaning that the stresses became toolarge for the glue.

0 0.02 0.04 0.06 0.08 0.1

0

0.2

0.4

0.6

0.8

1

Strain [−]

Str

ess

[MP

a]

Geom. 2, Exp. 1


(a) Experiment 1

0 0.02 0.04 0.06 0.08 0.1

0

0.2

0.4

0.6

0.8

1

Strain [−]

Str

ess

[MP

a]

Geom. 2, exp. 2a


(b) Experiment 2a


0 0.05 0.1 0.15 0.2 0.25

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Strain [−]

Str

ess

[MP

a]Geom. 2, exp. 2b


(c) Experiment 2b

0 0.02 0.04 0.06 0.08 0.1

0

0.2

0.4

0.6

0.8

1

Strain [−]

Str

ess

[MP

a]

Geom. 2, Exp. 3


(d) Experiment 3

Figure B.1: Measurement results for tensile tests with geometry 2

Compression testsIn Figure B.2(b), results of the perpendicular compression experiment are shown. Sample 2 showsthe same behavior as samples 1 and 3, but with a higher displacement. This can be explained bythe fact that with sample 2, a different pre-load was used. In this sample, a pre-load of 1.5 Newtonwas used in stead of 2.5 Newton. This induced that the initial deformation was smaller and a longertrajectory needed to be taken until the stiffer behavior could be encountered.

−0.1 −0.08 −0.06 −0.04 −0.02 0

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0

Strain [−]

Str

ess

[MP

a]

Geom. 2, exp. 4


(a) Experiment 4

0 1 2 3 4 5 6 70

20

40

60

80

100

120

Displacement [mm]

For

ce [N

]

Geom. 2, Exp. 5


(b) Experiment 5

Figure B.2: Measurement results for compression tests with geometry 2

Relaxation testsSample 2 from Figure B.3(a) shows unexpected behavior. It only relaxes for 50 seconds instead ofthe prescribed 60 seconds. This is likely due to a fault in the measurement settings.


0 10 20 30 40 50 60 70 80

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time [sec]

Str

ess

[MP

a]

Geom. 2, Exp. 6


(a) Experiment 6

0 10 20 30 40 50 60

0

0.2

0.4

0.6

0.8

1

Time [sec]

Str

ess

[MP

a]

Geom. 2, Exp. 7


(b) Experiment 7

0 10 20 30 40 50 60

0

0.2

0.4

0.6

0.8

1

Time [sec]

Str

ess

[MP

a]

Geom. 2, Exp. 8


(c) Experiment 8

Figure B.3: Measurement results for the relaxation tests with geometry 2

The stress relaxes approximately by -20, -33 and -32 percents in experiments 6, 7 and 8 respectively.


B.2 Geometry 3

The results of geometry 3 show the largest variations in the measurements. This can be explainedby the low stiffness and the small cross section of the rubber weatherstrip.

Tensile testsFrom Figure B.4 it can be seen that hysteresis and the Mullins effect are relatively small in thisweatherstrip compared with geometries 1 and 2.From experiment 3 it can be seen that the inertia effect of accelerating the rubber is large comparedto geometries 1 and 2, what can be explained by the low stiffness of the weatherstrip.

0 0.02 0.04 0.06 0.08 0.1−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Strain [−]

Str

ess

[MP

a]

Geom. 3, Exp. 1


(a) Experiment 1

0 0.02 0.04 0.06 0.08 0.1−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Strain [−]

Str

ess

[MP

a]

Geom. 3, exp. 2a


(b) Experiment 2a

0 0.05 0.1 0.15 0.2 0.25

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Strain [−]

Str

ess

[MP

a]

Geom. 3, exp. 2b


(c) Experiment 2b

0 0.02 0.04 0.06 0.08 0.1−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Strain [−]

Str

ess

[MP

a]

Geom. 3, Exp. 3


(d) Experiment 3

Figure B.4: Measurement results for tensile tests with geometry 3

Compression testsIn Figure B.5(a), the axial compression test is shown. The three samples show the same behavior,but with a different offset. This can be explained by the inaccuracy of the cutting face.


−0.1 −0.08 −0.06 −0.04 −0.02 0−0.45

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

Strain [−]

Str

ess

[MP

a]Geom. 3, exp. 4


(a) Experiment 4

0 1 2 3 4 5 60

5

10

15

20

25

30

35

40

45

50

Displacement [mm]

For

ce [N

]

Geom. 3, Exp. 5


(b) Experiment 5

Figure B.5: Measurement results for compression tests with geometry 3

Relaxation testsIn Figure B.6(a), the relaxation test with a loading rate of 0.01 stain/s is shown. Noticeable is thatthe relaxation time for sample 1 was wrongly set.The stress relaxation increases with an increasing loading rate. For experiments 6, 7 and 8, thestress relaxation is approximately -13, -18 and -22 percents respectively.


0 10 20 30 40 50 60 70 80−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time [sec]

Str

ess

[MP

a]

Geom. 3, Exp. 6


(a) Experiment 6

0 10 20 30 40 50 60−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time [sec]

Str

ess

[MP

a]

Geom. 3, Exp. 7


(b) Experiment 7

0 10 20 30 40 50 60−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Time [sec]

Str

ess

[MP

a]

Geom. 3, Exp. 8


(c) Experiment 8

Figure B.6: Measurement results for the relaxation tests with geometry 3


C Material properties

In Table C.1, the linear material properties of the three geometries are shown for different sets ofmaterial data.

Table C.1: Linear curve fitted material properties

Geometry Experiment Young’s modulus [Pa]

1 1 6.247e6

2a 6.636e6

2b 5.017e6

3 7.266e6

3 & 4 5.866e6

2 1 11.02e6

2a 10.28e6

2b 10.06e6

3 13.99e6

2b & 4 9.605e6

3 1 4.035e6

2a 4.721e6

2b 3.243e6

3 4.883e6

2b & 4 3.278e6

In Table C.2, the Ogden material parameters of the three geometries are shown for different setsof material data.

Table C.2: Ogden curve fitted material properties

Geometry Experiment µ1 [Pa] a1 [-] µ2 [Pa] a2 [-] µ3 [Pa] a3 [-]

1 1 -1.4842e6 -16.807 1.0516e7 -0.053865 2.9997e8 -0.053527

2a -1.3832e11 0.43264 4.9058e10 0.6795 2.4472e11 0.10835

2b 9.256e5 -0.63967 1.4755e6 0.15179 3.0502e7 0.15178

3 -1.8578e11 0.4288 6.59e10 0.67353 3.2863e11 0.10738

3 & 4 9.25e5 -6.486 1.47e6 0.31428 3.05e7 0.31425

2 1 -2.4e8 0.025276 -3e5 11.856 7.5e8 0.025275

2a -1.2e7 -1.372 2.5e6 -1.372 3.8e6 -1.372

2b -1.2813e7 0.33176 1.6871e6 5.5876 2.9871e6 0.33176

3 -2.3577e11 0.32026 8.3539e10 0.50341 4.1776e11 0.080113

2b & 4 -1.3324e7 -2.1611 1.1765e6 -6.0593 2.4765e6 -6.0593

3 1 -1.2133e7 6.7887 3.811e6 10.112 2.6364e7 1.8158

2a -8.1916e10 0.41305 2.9032e10 0.6488 1.4508e11 0.10342

2b -8.2e10 0.12578 2.9e10 0.19827 1.45e11 0.0315

3 -2.8535e10 0.44138 1.0037e10 0.6924 5.1061e10 0.11065

2b & 4 -8.2e10 -0.00239 2.9e10 0.0053053 1.45e10 -0.0023945


internship segula technologies - tu/e · pdf filein the automotive industry, the mounting of...

Documents