# Method for structural optimization of powertrain mounts: Shape optimization of torque rods to meet static stiffness requirement

## Metod för strukturoptimering av motorupphängningskomponenter: Formoptimering av momentstag för att möta krav på statisk styvhet

Jens Medbo
Göteborg : Chalmers tekniska högskola, 2016. 69 s. Diploma work - Department of Applied Mechanics, Chalmers University of Technology, Göteborg, Sweden, ISSN 1652-8557, 2016.

Volvo Cars is in need of a development method to be used for in-house new product development of powertrain mounts. The current development process includes development of requirements in-house and component design by an external supplier. To reduce the development lead-time and cost Volvo Cars is investigating the possibilities to do component design of powertrain mounts in-house. It is suggested to use structural optimization as a tool in the design work. A method for using structural optimization to design the geometry of powertrain mounts to meet stiffness specifications has been developed in this project. The project focused on shape optimization of torque rods to meet static stiffness requirement. An iterative approach was used, where the optimization method was developed using a simplified torque rod to facilitate the development. It was also studied if it is possible to obtain material parameters to sufficiently accurate model rubber materials by doing tensile tests on rubber from existing components. Finally, the optimization method was applied to a real Volvo torque rod for validation and adjustment. The proposed optimization method is based on finite element (FE) modelling of the mount. A concept geometry and a requirement stiffness curve are needed as input to the method. An FE model of the concept geometry is created and then morphed, creating shapes that are used as design variables. The morphing enables controlled geometry changes that are used in the optimization. An objective function, that represents the sum of the squared distances that a certain design’s displacement values for certain force levels deviates from the required displacement values, is used to determine the goodness of the design. The shape of the FE model is then optimized by changing the shapes to minimizing the value of the objective function. The output from the optimization method is an optimized mount geometry that can be used as basis in final design work. The proposed method is performing well; it is able to optimize a concept geometry far from the final geometry into a shape that has a static stiffness close to the required. It is also able to fine-tune the shape of a full-feature geometry to a static stiffness very close to the requirement. The method is very flexible, and additional optimization constraints can easily be added. The proposed optimization method has potential of being an important tool in new product development of powertrain mounts or other rubber components. A modified version of the method was also shown to be useful for optimizing hyperelastic material parameters to model a certain rubber compound more accurately.

Nyckelord: Structural optimization, shape optimization, rubber, powertrain mounts, torque rods, hyperelasticity, Yeoh hyperelastic model, morphing, finite element analysis

CPL ID: 239490

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