Contact dynamics with model order reduction and application

Contact arises in many engineering applications. In these applications, in order to control a system more accurately and more effectively it is important to get an insight into what the system dynamics would be when contact happens.;The study of contact dynamics involves several research subjects, including how to model contact bodies appropriately and accurately, developing algorithms to detect contact quickly and accurately, predicting contact force accurately during contact process, and studying dynamic behaviors of a system under effect of contacts. Although a lot of work has been done on these subjects, there is still a long way to go get a comprehensive solution to predict the contact dynamics for general contact cases.;In this study, a normal contact force model which combines the concepts of rigid body contact models and compliant contact models is constructed. This normal force contact model conforms well to the physical contacting process, which makes it more physically sound. A simple simulation example is carried out and simulation results are compared with results from other contact models to demonstrate the validness of this new contact model.;In most contact scenarios friction also plays an important roles and can have a significant effect on a system's dynamic behaviors. For many contact cases, contact happens in just a short time interval from the moment when contact bodies get in touch with each other to the moment when they separate. Therefore, a suitable friction force model is required to be able to model the switching process between the sticking regime and the sliding regime of friction. A 3D friction model, which is an extension of the bristle friction model, is developed. Numerical simulation and experimental tests show that this friction model is suitable for contact dynamic simulation.;The finite element method is generally considered as the most detailed approach for modeling contact systems and is suitable for high fidelity applications. However, one major problem associated with the finite element method for contact dynamics simulation is that it can be computationally very inefficient because the dimension of a finite element model is usually very large for high modeling accuracy and the time step for the corresponding numerical integration has to be very small in order to have a stable simulation of a stiff system. This makes the real-time simulation almost impossible. To deal with the computational inefficiency problem associated with the finite element based contact dynamics simulation, model order reduction (MOR) technology may be used. A model order reduction technique, which is called a modified Lyapunov truncation method, is introduced into the simulation of contact dynamics. Two contact simulation examples are implemented to demonstrate the effectiveness of the model order reduction technique in improving the simulation efficiency of contact dynamics. Simulation results show that simulation time can be significantly reduced by applying model order reduction in contact dynamics simulation while the simulation error due to model order reduction can be kept at a relatively low level.