Mathematical Modeling of Lead Screw Drives

In this chapter, a collection of mathematical models are developed which are used to study the dynamic behavior of lead screw systems in the subsequent chapters. Depending on the system elements considered and the type of analysis undertaken, different models are developed with varying number of degrees of freedom. 

The velocity-dependent friction model used in this work is discussed in Sect. 5.1. The dynamics of a pair of meshing lead screw and nut threads is studied in Sect. 5.2. Based on the relationships derived in this section, the basic 1-DOF lead screw drive model is developed in Sect. 5.3. This model is used in Chaps. 6 and 8 to study the negative damping and kinematic constraint instability mechanisms, respectively. A model of the lead screw with antibacklash nut is presented in Sect. 5.4, and the role of preloaded nut on the increased friction is highlighted. Additional DOFs are introduced to the basic lead screw model in Sects. 5.5 to 5.8 in order to account for the flexibility of the threads, the axial flexibihty of the lead screw supports, and the rotational flexibility of the nut. These models are used in Chaps. 7 and 8 to investigate the mode coupling and the kinematic constraint instability mechanisms, respectively. Finally, in Sect. 5.9, srane remarks are made regarding the models developed in this chapter. 

The rubbing action of the contacting lead screw threads against the nut threads is assumed to be the main source of friction in the systems considered in this monograph. We start this chapter by presenting a velocity-dependent coefficient of friction model for the lead screw and nut interface. 

Vahid-Araghi and F. Golnaraghi, Friction-Induced Vibration in Lead Screw Drives, DOI 10.1007/978-l-4419-1752-2 5, Springer Science+Business Media, LLC 2011 

5 Mathematical Modeling of Lead Screw Drives y Moving mass 

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A number of mathematical models are developed for lead screw drive systems in Chap. 5. Starting from the basic kinematic model of lead screw and nut, dynamic... 

A practical case study is presented in Chap. 9 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 the parameters of the velocity-dependent coefficient of friction model. The verified mathematical model is then used to study the role of various system parameters on the stability of the system and on the amplitude of vibrations. These smdies lead to possible design modifications that can solve the system s excessive noise problem. 

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