Simplified transfer function approach for modeling frequency dependency of damping characteristics of rubber bushings

Abstract

Physical systems that consist of parts and vibration isolators such as rubber bushings are usually modeled in multibody simulations, where parts are represented as rigid bodies with their mass and inertia properties and rubber bushings are modeled with Voigt models to represent their stiffness and damping characteristics. Employment of Voigt models in multi-degree-of-freedom systems, however, may result in lower accuracy due to limitations in representing frequency-dependent dynamic characteristics of vibration isolators. To overcome this challenge, in this study, we develop and present a simplified frequency-dependent transfer function model by generating their frequency-dependent complex stiffness and damping from vehicle-level measurements. The damping characteristics of rubber bushings as a function of frequency is represented by a second-order transfer function. Three parameters of the transfer function are determined by solving an optimization problem to minimize the integral of absolute error between the measurement and simplified model’s predictions. Sequential Quadratic Programming, a gradient descent–based algorithm, is selected as the optimization algorithm for this purpose. The proposed methodology is demonstrated on a heavy commercial truck. Truck cabin is represented as a rigid body connected to four rubber bushings, which are modeled to show the frequency dependency of the damping as a simple transfer function. Simulation results are well correlated with the measurements obtained from prototype vehicle tests on various road profiles showing capability improvement over Voigt modeling approach due to a more representative damping characteristic of rubber bushings as a function of frequency. Integration of the proposed method into multibody simulation software is also demonstrated with cosimulation between MSC.ADAMS and MATLAB software.