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.

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.

В данной магистерской диссертации представлены результаты разработки методов повышения точности преобразователей вращательного движения в поступательное для систем отсчета перемещения рабочих органов станков с ЧПУ, что и является целью выпускной квалификационной работы. Актуальность темы обусловлена тем, что точность машин и механизмов является основной характеристикой их качества. Традиционные механические передачи (зубчатые, реечные и др.) имеют широкое применение во всех отраслях машиностроения. Требования к точности изготавливаемых деталей существенно ужесточаются, поэтому необходимо непрерывно совершенствовать методы повышения точности передач. Научная новизна обусловлена разработкой новых методов повышения точности систем отсчета перемещений путем уменьшения или ликвидирования кинематических погрешностей и погрешностей от износа преобразователей вращательного движения в поступательное. Рассмотрены элементы, применяемые при построении современных систем отсчета перемещений и возникающие в них погрешности. Проведен анализ существующих методов уменьшения кинематических погрешностей и погрешностей от износа преобразователей вращательного движения в поступательное. На его основе разработаны: метод отсчета перемещений рабочего органа станка с компенсацией погрешностей ходового винта; метод снижения износа передачи винт-гайка скольжения; метод снижения износа передачи винт-гайка качения; метод отсчета перемещений рабочего органа станка с коррекцией кинематических погрешностей рейки; метод снижения износа зубчато-реечной передачи; насос, предназначенный для использования при реализации перечисленных методов. В ходе работы над магистерской диссертацией было подано шесть заявок на изобретения. В результате было получено пять патентов: патент на изобретение №2750575 «Насос шестеренный реверсивный», патент на изобретение №2756797 «Передача винт-гайка качения», патент на изобретение №2764105 «Зубчато-реечный привод подачи металлорежущего станка с ЧПУ», патент на изобретение №2768807 «Устройство отсчета перемещений рабочего органа машины с ходовым винтом» и патент на изобретение №2767381 «Передача винт гайка скольжения». На рассмотрении в ФИПС находится заявка на изобретение №2021114570 «Зубчато-реечный привод подачи рабочего органа тяжелого крупногабаритного металлорежущего станка». / This master's thesis presents the results of the development of methods for precision improvement of reference systems for the movement of movable operating element of CNC machines, which is the purpose of the final qualifying work. The relevance of the topic is due to the fact that the precision of machines and mechanisms is the main characteristic of their quality. Traditional mechanical gears (gear, rack and pinion, etc.) are widely used in all branches of mechanical engineering. The requirements for the precision of manufactured parts are significantly tightened, so it is necessary to continuously improve methods for improving the precision of transmissions. The scientific novelty is due to the development of new methods for improving the precision of displacement reference systems by reducing or eliminating kinematic errors and errors from wear of rotary motion converters to translational. The elements used in the construction of modern displacement reference systems and the errors arising in them are considered. The analysis of existing methods for reducing kinematic errors and errors from wear of rotary motion converters to translational motion is carried out. Based on it, the following methods have been developed: the method of counting the movements of the movement of movable operating element of the machine with compensation of errors of the lead screw; the method of reducing the wear of the transmission screw-nut sliding; the method of reducing the wear of the rolling screw-nut transmission; the method of counting the movements of the movement of movable operating element of the machine with correction of kinematic errors of the rail; the method of reducing the wear of rack and pinion transmission; the pump, designed for use in the implementation of the above-mentioned methods. During the work on the master's thesis, six applications for inventions were submitted. As a result, five patents were obtained: patent for invention No. 2750575 "Reversible gear pump", patent for invention No. 2756797 "Rolling screw-nut transmission", patent for invention No. 2764105 "Rack-and-pinion feeding drive of CNC metal cutting machine", patent for invention No. 2768807 "Device for counting the movements of the operating member of a machine with a drive screw" and patent for invention No. 2767381 "Sliding screw-nut gearing". The application for invention No. 2021114570 "Rack-and-pinion feeding drive of the operating member of a heavy large-sized metal-cutting machine" is under consideration in the federal institute of industrial property.