Axial Compliance in Lead Screw Supports

Remark 5.1. For the model of this section, the relative shding velocity is given by Vs = rmd/cosl + (5 tan/I where d is defined by (5.23). However, in practical situations where the lead angle (2) is small, Vs rmd/cosL As a result, it is assumed that sgn(vs) = sgn(0) which simplifies the equations of motion of the 

Although we do not include backlash nonlinearity in our analysis of friction-induced vibration, it is worthwhile presenting a slightly modified version of the above model that enables one to include the effect of backlash, approximately. 

Instead of (5.24), we may consider the following relationship for the contact force which is based on [114]  

Another important source of flexibility in the system may be the compliance in the lead screw supports. To model this feature, as shown in Fig. 5.10, a spring k and a damper c are added to the basic model of Sect. 5.3, which allows the lead screw to move axially. For the sake of simplicity, in the remainder of this Chapter, the damping Cx is neglected. 

Setting Cx = 0, (5.16) and (5.17) give force-acceleration relationships for the lead screw rotation and nut translation, respectively. Moreover, the lead screw translation DOF is governed by 

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