Friction-induced Vibration in Lead Screw Systems

Abstract

Lead screw drives are used in various motion delivery systems ranging from manufacturing to high precision medical devices. Lead screws come in many different shapes and sizes; they may be big enough to move a 140 tons theatre stage or small enough to be used in a 10ml liquid dispensing micro-pump. Disproportionate to the popularity of lead screws and their wide range of applications, very little attention has been paid to their dynamical behavior. Only a few works can be found in the literature that touch on the subject of lead screw dynamics and the instabilities caused by friction. The current work aims to fill this gap by presenting a comprehensive study of lead screw dynamics focusing on the friction-induced instability in such systems. In this thesis, a number of mathematical models are developed for lead screw drive systems. Starting from the basic kinematic model of lead screw and nut, dynamic models are developed with varying number of degrees of freedom to reflect different components of a real lead screw drive from the rotary driver (motor) to the translating payload. In these models, velocity-dependent friction between meshing lead screw and nut threads constitute the main source nonlinearity. A practical case study is presented where friction-induced vibration in a lead screw drive is the cause of excessive audible noise. Using a complete dynamical model of this drive, a two-stage system parameter identification and fine-tuning method is developed to estimate parameters of the velocity-dependent coefficient of friction. In this approach the coupling stiffness and damping in the lead screw supports are also estimated. The numerical simulation results using the identified parameters show the applicability of the developed method in reproducing the actual systems behavior when compared with the measurements. The verified mathematical model is then used to study the role of various system parameters on the stability of the system and the amplitude of vibrations. These studies lead to possible design modifications that solve the system’s excessive noise problem. Friction can cause instability in a dynamical system through different mechanisms. In this work, the three mechanisms relevant to the lead screw systems are considered. These mechanisms are: 1. negative damping; 2. kinematic constraint, and; 3. mode coupling. The negative damping instability, which is caused by the negative gradient of friction with respect to sliding velocity, is studied thorough linear eigenvalue analysis of a 1-DOF lead screw drive model. The first order averaging method is applied to this model to gain deeper insight into the role of velocity-dependent coefficient of friction and to analyze the stability of possible periodic solutions. This analysis also is extended to a 2-DOF model. It is also shown that higher order averaging methods can be used to predict the amplitude of vibrations with improved accuracy. Unlike the negative damping instability mechanism, kinematic constraint and mode coupling instability mechanisms can affect a system even when the coefficient of friction is constant. Parametric conditions for these instability mechanisms are found through linear eigenvalue analysis. It is shown that kinematic constraint and mode coupling instability mechanisms can only occur in self-locking lead screws. The experimental case study presented in this work demonstrates the need for active vibration control when eliminating vibration by design fails or when it is not feasible. Using the sliding mode control method, two speed regulators are developed for 1-DOF and 2-DOF lead screw drive system models where torque generated by the motor is the controlled input. In these robust controllers, no knowledge of the actual value of any of the system parameters is required and only the upper and lower bounds of parameters are assumed to be available. Simulation results show the applicability and performance of these controllers. The current work provides a detailed treatment of the dynamics of lead screw drives and the topic of friction-induced vibration in such systems. The reported findings regarding the three instability mechanisms and the friction parameters identification approach can improve the design process of lead screw drives. Furthermore, the developed robust vibration controllers can be used to extend the applicability of lead screws to cases where persistent vibrations caused by negative damping cannot be eliminated by design modifications due to constraints.