A Reasoned Attempt to Mitigate Vibrations in Non-Linear Flexible Systems Influenced by Tractive-Elastic Rolling Contact Friction Through Input Shaping: A Case Study on a Trolley-Pipe Benchmark Transport System

The well-regarded feedforward control strategy known as Input Shaping is aimed at improving the dynamic response of flexible mechanical systems by reducing overshoot and residual vibration amplitude. Its validity has been confirmed by numerous studies dealing with linear system dynamics. However, its application to nonlinear systems, particularly those influenced by tractive-elastic rolling contact friction, remains a challenging and less explored open research area. This paper investigates whether Input Shaping, without tractive rolling friction compensation, can effectively mitigate vibrations in a trolley-pipe benchmark transport system. In this system, the pipe is modeled as a rolling disk attached to the trolley by a spring at its center of mass, while the trolley itself is connected to a guiding body frame by an additional spring acting as a proportional control. The natural frequencies of the system are analytically estimated and numerically verified from a corresponding well suited multibody model. Thus tailored two-mode shapers are designed based on simultaneous constraints and convolution sum respectively. Through multibody simulations, this study evaluates the performance of Input Shaping under tractive-elastic rolling contact friction conditions. The findings highlight both the potential and limitations of this control method in addressing nonlinear mechanical systems influenced by such tractive-elastic rolling contact friction.