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In rubber bumper design one of the most important technical properties of the product is the force-displacement curve under a compression load, which is a highly nonlinear behavior because of the large deformation, the rubber material and the contacts. Finite element analysis is a good way to evaluate the working characteristics of the rubber part. Fulfillment of customer needs requires a general iterative design method where the objective can be reached with the modification of the product shape. The determination of the optimum requires numerous iterations of finite element analysis which is computationally expensive. With the integration of the Response Surface Method (RSM) into the design process of a two-variable shape optimization task, the optimal design can be achieved more efficiently. Four different Design of Experiments (DOE) methods were used to intelligently chose design points. As a metamodeling technique, Genetic Aggregation was selected to predict the relation between the sampled geometric variables and the nonlinear objective function value. The Nonlinear Programming by Quadratic Lagrangian (NLPQL) and the Mixed-Integer Sequential Quadratic Programming (MISQP) algorithms with different settings were tested to find the optimum of the response surface. As a result, the most accurate and efficient DOE method and optimization algorithm were determined. The introduced Response Surface Method-based optimization is proved to be suitable to determine the shape of the rubber jounce bumper, which meets the technical requirements.

Non-linear finite element calculations are indispensable when important information of the material response under load of a rubber component is desired. Although the material characterization of a rubber component is a demanding engineering task, the changing contact range between the parts and the incompressibility behaviour of the rubber further increase the complexity of the investigations. In this paper the effects of the choice of the numerical material parameters (e.g. bulk modulus) are examined with regard to numerical stability, mesh density and calculation accuracy. As an example, a rubber spring is chosen where contact problem is also handled.

In rubber products design finite element analysis is a widely used technique. In many cases, the pre-defined operating conditions can be achieved by changing the geometric dimensions of the product which is the well-known iterative design method. Using more than one design parameter the number of possible combinations will increase significantly. The application of Support Vector Machine (SVM) can handle the large number of data in a special way and helps to find the optimal design parameters. In this paper an optimization process of a rubber jounce is presented using nonlinear finite element analysis and SVM.

In rubber product design finite element analysis is widely used. The aim of this research is to choose the appropriate material models and to determine the related material parameters for finite element analysis of a rubber jounce. Rubber products can suffer from large deformation upon working conditions while behaving as a non-linearly elastic, isotropic and incompressible material. Hyperelastic material models accurately describe the observed material behaviour. Uniaxial compression test of rubber specimen has been performed to determine the stress-strain curve. Using test data and ANSYS for curve fitting process, the material constants for Mooney-Rivlin and Yeoh model have been established. Finite element analysis of the compression test has been made to validate the specified material constants. It can be stated that three term Yeoh model showed better agreement with the test data than the one term formula. Two term Mooney-Rivlin model showed good match with the measurement data, thereby it is also recommended for the future investigations of rubber jounce.

Non-linear FEM calculations are indispensable when important technical information like operating performance of a rubber component is desired. For example rubber bumpers built into air-spring structures may undergo large deformations under load, which in itself shows non-linear behavior. The changing contact range between the parts and the incompressibility of the rubber increases this non-linear behavior further. The material characterization of an elastomeric component is also a demanding engineering task. The shape optimization problem of rubber parts led to the study of FEM based calculation processes. This type of problems was posed and investigated by several authors. In this paper the time demand of certain calculation methods are studied and the possibilities of time reduction is presented., {"references":["J. J. Kim, H. Y. Kim, \"Shape design of an engine mount by a method of\nparameter optimization,\" Computers and Structures, vol. 65, no. 5, pp.\n725-731, 1997.","K. K. Choi, W. Duan, \"Design sensitivity analysis and shape\noptimization of structural components with hyperelastic material,\"\nComputer Methods in Applied Mechanics and Engineering, vol. 187, pp.\n219-243, 2000.","J. S. Lee, S. C. Kim, \"Optimal design of engine mount rubber\nconsidering stiffness and fatigue strength,\" Journal of Automobile\nEngineering, vol. 221, no. 7, pp. 823-835, 2007.","V. T. Vu, \"Minimum weight design for toroidal pressure vessels using\ndifferential evolution and particle swarm optimization,\" Structural and\nMultidisciplinary Optimization, vol. 42, no. 3, pp. 351-359, 2010.","T. Mankovits, I. Kocsis, T. Portik, T. Szabó, I. Páczelt, \"Shape Design\nof Rubber Part Using FEM,\" International Review of Applied Sciences\nand Engineering, vol. 4, no. 2, pp. 85-94, 2013.","N. Kaya, \"Shape optimization of rubber bushing using differential\nevolution algorithm,\" The Scientific World Journal, ID 379196, pp. 1-9,\n2014.","K. Shintani, H. Azegami, \"Shape optimization of rubber bushing,\" 11th\nWorld Congress on Computational Mechanics, 20-25 July, Barcelona,\nSpain, 2014.","T. Mankovits, T. Szabó, I. Kocsis, I. Páczelt, \"Optimization of the Shape\nof Axi-Symmetric Rubber Bumpers,\" Strojniski vestnik-Journal of\nMechanical Engineering, vol. 60, no. 1, pp. 61-71, 2014.","ISO 7743 \"Rubber, vulcanized or thermoplastic – Determination of\ncompression stress-strain properties\", 2008."]}

Non-linear FEM calculations are indispensable when important technical information like operating performance of a rubber component is desired. Rubber bumpers built into air-spring structures may undergo large deformations under load, which in itself shows non-linear behavior. The changing contact range between the parts and the incompressibility of the rubber increases this non-linear behavior further. The material characterization of an elastomeric component is also a demanding engineering task. In this paper a comprehensive investigation is introduced including laboratory measurements, mesh density analysis and complex finite element simulations to obtain the load-displacement curve of the chosen rubber bumper. Contact and friction effects are also taken into consideration. The aim of this research is to elaborate a FEM model which is accurate and competitive for a future shape optimization task., {"references":["T. Mankovits, T. Szabó, I. Kocsis, I. Páczelt, \"Optimization of the Shape of Axi-Symmetric Rubber Bumpers,\" Strojniski vestnik-Journal of Mechanical Engineering, vol. 60, no. 1, pp. 61-71, 2014.","T. Mankovits, T. Szabó, \"Finite Element Analysis of Rubber Bumper Used in Air-Springs,\" Procedia Engineering, vol. 48, pp. 388-395, 2012.","T. Mankovits, I. Kocsis, T. Portik, T. Szabó, I. Páczelt, \"Shape Design of Rubber Part Using FEM,\" International Review of Applied Sciences and Engineering, vol. 4, no. 2, 85-94, 2013.","R.K. Luo, W.X. Wu, \"Fatigue Failure Analysis of Antivibration Rubber Spring,\" Engineering Failure Analysis, vol. 13, no. 1, pp. 110-116, 2006.","Q. Li, J. Zhao, B. Zhao, \"Fatigue Life Prediction of a Rubber Mount Based on Test of Material Properties and Finite Element Analysis,\" Engineering Failure Analysis, vol. 16, no. 7, pp. 2304-2310, 2009.","S. Oman, M. Fajdiga, M. Nagode, \"Estimation of Air-Spring Life Based on Accelerated Experiments,\" Materials and Design, vol. 31, no. 8, pp. 3859-3868, 2010.","S. Oman, M. Nagode, \"On the Influence of Cord Angle on Air-Spring Fatigue Life,\" Engineering Failure Analysis, vol. 27, pp. 61-73, 2013.","L.R. Wang, J.C. Wang, I. Hagiwara, \"An Integrated Characteristic Simulation Method for Hydraulically Damped Rubber Mount of Vehicle Engines,\" Journal of Sound and Vibration, vol. 286, no. 4-5, pp. 673-696, 2005.","ISO 7743 \"Rubber, vulcanized or thermoplastic – Determination of compression stress-strain properties\", 2008."]}