Deformation Characteristic of Moulded Vulcanised Rubber Bush

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1 rd International G raduate Conference on Engineering, School of Graduate Studies Universiti Teknologi Malaysia 4 November Deformation Characteristic of Moulded Vulcanised Rubber Bush Yong Tze Mi Faculty of Mechanical Engineering Universiti Teknologi Malaysia Skudai, Johor, Malaysia yongtzemi@yahoo.co.uk Abstract This paper presents the application of finite element analysis to wards rubber to predict its defo rma ion characteristics, ultimately for the purpose of aid of esign of a rubber bush. The testing is done in accordance to British Standards BS 9-5:4. An unknown mixture of rubber, named K6, is prepared fo r this paper, provided by Marutech Elastomers Industries Sdn. Bhd., where material pro perties testing are done onto. I.e. Uniaxial tensile test, compression test and simple shear test as a requiremen to for material modelling by Abacus/CAE 6.8. Only unaxial tensile test data was used as input for material modelling. While a simple compression modelling results using the material model was done to be compared to experimental test data. Good correlatio n o f less than % erro r is given between compressio n model and testing and this verifies the material model. Next, the same material model is used or static modelling of a rubber bush. The same procedural experimental work is done on an existing rubber bush p rt where the part is provided by Marutech Elasto mer Industries Sdn. Bhd. Again the modelling defo rmation results are compared to the experimental deformation results and again bo th results sho w good correlation of less than % error. Keywords-hyperelastic; simulation; rubber I. INTRODUCTIO N Vibration isolators or dampers are among most important components in achieving performance goals for engineered systems that exhibit significant structural dynamic response. Passive damping can be applied more significantly if the damping properties of the materia s are known. Because of the need to achieve better performance of damping and cost efficiency, much effort in the fie d have been pursued with increased damping properties[,]. However, the most common method used today typically involves high-damping viscoelastic polymers or elastomers. The manufacturing of rubber moulds involves processes that affect the internal stresses of the rub hat will affect performance of the rubber during service[]. The performance of rubber dampers is sensitive to tensile stress (not so much if it is in compression). Thus manufacturing process has included post-processing of the moulded rubber to eliminate these stresses. We have here a rubber bush provided by Marutech Elastomer Industries Sdn. Bhd. (Fig ). The possibility of modelling the behaviour of the rubber under static conditions using finite A. Mohd. Nasir b. Tamin Faculty of Mechanical Engineering Universiti Teknologi Malaysia Skudai, Johor, Malaysia taminmn@fkm.utm.my element method will bring much wanted reduction in cost for testing and development procedures. The objective of this paper is to establish the deformation response of reinforced rubber moulds subjected to static loads. The hyperelastic response of the rubber is established in this paper. The hyperelastic material model contributes to establishing a method to model deformation behaviour and predict performance outcomes other than being repeatable for other geometrical stress problems or even other materials of the like. II. METHODOLOGY The scope of the paper covers. Standard testing - Test for properties behaviour of static loading.. Numerical Method - To establish the material properties and behaviour of compound (NR). Numerical method - Finite element modelling of compound for static loading. (uniaxial compression and bending for part.) 4. Experimental - Testing of part PW875 to verify Finite element modelling The material to be tested is a rubber sample with manufacturers identification of K6. The hardness an cure time results are provided by the manufacturer, wh are Shore A 6 hardness and 6 seconds cure time. It should be noted here that all specimens were prepared at the same time while testing were done at different times. The volumetric test data are not required when the material is incompressible. Standard testing The standard testing procedures will be conducted based on British standards [4] due to availability of standards and ease of application. Uniaxial Tensile Test This tensile test complies with BS 9-A:995 or ISO 7:994 [5]. Compression Test This test complies with British Standard BS9-A4 [6].

rd International Graduate Conference on Engineering, School of Graduate Studies Univ ersiti Teknologi Malaysia 4 Nov ember B. Shear Test This Shear test complies with BS 9-A4 99 or ISO 87:99 [7].

2 rd International Graduate Conference on Engineering, School of Graduate Studies Univ ersiti Teknologi Malaysia 4 Nov ember B. Shear Test This Shear test complies with BS 9-A4 99 or ISO 87:99 [7]. Numerical method and Verification of material model Abacus/CAE version 6.8 will be employed because of its ability in handling hyperelastic materials [8]. To do this, the standard testing data i.e. the tensile test data is compared with the strain energy potential curves generated by using existing models one by one of all models. Evaluation is done for Mooney-Rivlin, Arruda Boyce, Polynomial rd degree, Movlow, Reduce Polynomial st degree, Reduce Polynomial rd degree, Ogden and Van Der Waals models. Finally the closest fitting model is chosen to be used as material model to model the rubber part. The model parameters are generated by Abacus/CAE and are noted down. Varification of the material model is then done by simulating the compression test with the model and comparing the results with standard compression test. C. Application of numerical method Numerical simulation of uniaxial compression and bending of bush (Fig. ) is done. A bush with inner pipe and an outer pipe are bounded to the cured rubber by injection moulding. Two homogeneous solid section definitions are created: one named RubberSection that refers to the rubber material and one named SteelSection that refers to the steel material. The steel parts of the model is modelled with linear elastic properties only with modulus Young, E = 9 Pa and Poison ratio,? =.. Assuming load is not large enough to cause inelastic deformations. The mesh used is CD4H a 4-node linear tetrahedron, hybrid, linear pressure element for the r ber section. The steel section is model with CD4 a 4-node linear tetrahedron for simplification. Global seeds fo the rubber sections are.. While the seeds are bigger for the steel parts as the results of simulation in these are not taken into account for this paper. A single general static step defined. Nlgeom toggled on for large deformations. The total step time is set to seconds and the initial time increment to.6, minimum increment is set to. and maximum increment is set to. For the boundary conditions, ENCASTRE is set to fix the outer pipe as in the real applications. The second boundary condition is defined to have type of velocity/angular velocity. And V is set to 8.e-5 or equivalent to 5mm/ minute. Figure. Example of a figure caption. (figure caption) Uuniaxial compression The centre top point of the rod that is tied to the inner pipe is designated the second boundary condition. The direction of loading will be-y direction. Deformation of rubber will be read off on the surface at a diameter of mm depicted in Fig.. Bending Deflection will be caused by a moment by applying frictionless deflection of a pin through the rod 5cm from the nearest edge of the part. Reaction force read off will be inside the hole where the reaction force of the rod onto the pin is. The point of deflection readoff will be on the opposite end of the part, on the rubber. It is as depicted in Fig.. ENCASTRE Point of Loading Point of measured deflection Figure. Boundary condition for uniaxial compression. Point of deflection Point of load read off (inside hole)

rd International Graduate Conference on Engineering, School of Graduate Studies Univ ersiti Teknologi Malaysia 4 Nov ember Figure 4.

RESULTS Uniaxial Tensile Test The tensile test result after conversion to norminal stress vs norminal strain is as shown in Fig. 5. Nominal Stress vs Nominal Strain D.

A jig is made to hold the outer steel pipe of the part while the loading is done on the inner steel pipe.

3 rd International Graduate Conference on Engineering, School of Graduate Studies Univ ersiti Teknologi Malaysia 4 Nov ember Figure 4. The test jig of the uniaxial compression and bending experiment of bush. Figure. Modelling the bending test. Arrows are the direction where the second boundary condition is given. A. Standard testing III. RESULTS Uniaxial Tensile Test The tensile test result after conversion to norminal stress vs norminal strain is as shown in Fig. 5. Nominal Stress vs Nominal Strain D. Experimental Testing 5 The bush that will be worked on is provided by Marutech Elastomer Sdn. Bhd. A jig is made to hold the outer steel pipe of the part while the loading is done on the inner steel pipe. To transfer either uniaxial load or bending load, a rod is sliding fit into the inner tube to translate the loading to the part. A pin and bracket is needed for transferring load for bending. Instron 46 static testing machine is used. A data logger with idenfication TDS is used. The data is saved in a softcopy format via data logger software called Visual log. The test jig is as shown in Fig. 4. Uniaxial compression A negative strain of 5mm/min is given for mm. The displacement rate is equal to the displacement rat of standard shear test. Like compression test the displacement is cycled 4 times. The corresponding load is measured by the load cell and cross head measurement is taken. Two LVDT(s) are placed on the rubber section to measure displacement of the rubber. The LVDT(s) are connected to a data logger. Stress (Pa) Figure 5. Nominal Stress (Pa) vs. Nominal Strain ratio for tensi e test. Compression Test Strain ratio The compression test result after conversion to norminal stress vs norminal strain is as shown in Fig. 6 for loading cycle. 4th Compression Curve from Testing Be nding Displacement is given via tensile mode. A strain of 5mm/min is given for mm at the clamp. Like compression test the displacement is cycled 4 times. One LVDT is placed on the rubber section at the opposite end to measure displacement of the rubber. The LVDT is connected to a data logger. Nominal Stress (MPa) Nominal Strain th Cycle average curve Figure 6. Nominal Stress (Pa) vs. Nominal Strain ratio for compression curve of the last cycle. Shear Test The shear test result after conversion to Simple Shear Stress vs. Simple Shear Strain is as shown in Fig. 7.

rd International G raduate Conference on Engineering, School of Graduate Studies Universiti Teknologi Malaysia 4 November Shear Stress vs % Shear Strain Figure 8.

Error of the FEA results are calculated to be less ten % to the experimental data. Shear Stress (MPa).4... 4 5 6 7 8 % Shear Strain Figure 7. Simple Shear Stress vs. Simple Shear Strain C.

finite element analysis for uniaxial compression is shown in Fig. 9. The largest relative displacement is read off as 8.6e-m. B.

Correlation analysis shows that Polynomial nd Order and Ogden rd Order, correlates best with experimental data. Table I shows the material model parameters evaluated. TABLE I.

4 rd International G raduate Conference on Engineering, School of Graduate Studies Universiti Teknologi Malaysia 4 November Shear Stress vs % Shear Strain Figure 8. Difference between modelling data and experimental dat..6.5 The results show a good correlation between the experimental data and FEA. Error of the FEA results are calculated to be less ten % to the experimental data. Shear Stress (MPa) % Shear Strain Figure 7. Simple Shear Stress vs. Simple Shear Strain C. Application of numerical method Uuniaxial compression Using Polynomial nd Order model with corresponding model parameters, the stress distribution diagram and displacement distribution diagram for finite element analysis for uniaxial compression is shown in Fig. 9. The largest relative displacement is read off as 8.6e-m. B. Numerical method Evaluation of model is done using only uniaxial tensile test data to obtain suitable strain potential energy curves. Correlation analysis shows that Polynomial nd Order and Ogden rd Order, correlates best with experimental data. Table I shows the material model parameters evaluated. TABLE I. MAT ER IA L MO D EL PA RA M ET ER S O F EVA LUA TION O F U NIA X IA L T EN SILE DA TA ONLY ST YLES Model Polynomial N= Ogden, N= Parame te rs D D C C C C C I MU_I ALPHA_I D_I Verification of material model is done by using the material model (polynomial n d Order) to simulate the standard compression test. Comparison of compression curves made by modeling and perimental Figure 9. Von Mises Stress distribution diagram and Displacement distribution diagram for rubber section of the bush only under uniaxial compression loading. Bending The stress distribution diagram and displacement distribution diagram for finite element analysis for bending is shown in Fig.. The largest relative displacement is read off between.965 e-m and.65e Nominal Stress (MPa) Nominal Strain Modeled from uniaxial data only Experimental 4

rd International Graduate Conference on Engineering, Science and Human ities (IGC ES H) Scho ol of Graduate Studies Univ ersit i Teknologi Malaysia 4 Nov ember Displacement vs.

5 rd International Graduate Conference on Engineering, Science and Human ities (IGC ES H) Scho ol of Graduate Studies Univ ersit i Teknologi Malaysia 4 Nov ember Displacement vs. Time for bending exper iment Displacement(mm) Tim e ( Se co nds ) Fi n al cy cle o f LV D T FE M Figure. Displacement vs. Time for bending for LVDT reading and FEA read o ff at Point of Deflection IV. Figure. Von M ises Stress distribution diagram an d Displacement distribution diagram for rubber section of the bush only under bending load. D. Experimental Testing The read off from the LVDT(s) are compared to the History Output from FEA on the Point of deflection is compared in Fig. and Fig. for uniaxial displacement and bending respectfully. From Fig. and Fig., again it has shown there is a good correlation with error less than %. Displacem ent vs time for uniaxial compression 5 Though the results show very little error between FEA and experimental test, the FEA results show larger magnitude then experimental results. This is because the stress-strain curve plot obtained from experimental testing of the compression test specimen and bush is the 4th cycle where the material is assumed to set in. Whereas the finite element material model is evaluated based on the first cycle of a tensile test, where set is not taken into account. Thus this may account for larger magnitude of finite element prediction stress-strain prediction. Comparison of st cycle curves of standard compression testing and the FEA will yield better correlation as the first cycle of compression curves have larger force magnitude. Note that shear data was taken but not used in FEA. Thus the data basically characterizes the unknown rubber for our better understanding and future work. The conclusions of this paper are; 4 Displacement(mm) DISCUSSIONS AND CONCLUSIONS The deformation of the unknown rubber can best be described using Polynomial nd order model. Independent compression test data agrees with finite element prediction of axial deformation of the rubber specimen by less then % t im e (s e c onds ) LV D T VS Tim e L V DT V s Ti m e FEM Both measured and finite element calculated displacement of specific points on the rubber bush are comparable to within % ACKNOWLEDGE MENT Figure. Displacement vs. Time for uniaxial compression for LVDT reading and FE A read off at Point of Deflection Marutech Elastomers Industries Sdn. Bhd. REFERENCES [] [] Jennifer Kadlowec, David Gerrad and Howard Pearlman, o upled axial - torsional behavior of cylindrical elastomer bushings, Polymer Testing (8), doi:.6/j.po lymertesting.8.. A.M.G. de Lima, D.A. R ade, F.P. Lepore Neto, An effic ent mo delling methodology o f structural systems containing viscoelastic dampers based on frequency response function substructuring, Mechanical Systems and Signal Processing ( 8), do i:.6/j.ymssp

6 rd International G raduate Conference on Engineering, School of Graduate Studies Universiti Teknologi Malaysia 4 November [] T. M. Yong, Industrial Training Report, Universiti Tek ologi Malaysia; 8, unpublished. [4] British Standard. Physical testing of rubber Part 5: Guide to the application of rubber testing to finite element analys.s BS 9-5:4 [5] British Standard. Physical testing of rubber Part A: Method for determination of tensile stress-strain properties. BS 9-A: 995 [6] British Standard. Method for Physical testing of rubber Part A4: Determination of compression stress-strain properties. BS 9-A4: 99 [7] British Standard. Physical testing of rubber Part A4: Method for determination of modulus in shear or adhesion to rigid plates Quadruple shear method. BS 9-A4: 99 [8] Abaqus version 6.7, Getting Started with Abaqus Intera tive Edition. 6

CHAPTER 4 MATERIAL CHARACTERISATION. The material characterization of AFNOR 15CDV6 steel and the

94 CHAPTER 4 MATERIAL CHARACTERISATION The material characterization of AFNOR 15CDV6 steel and the natural rubber based elastomer developed for the use in flex nozzle are discussed in this chapter. This