Compliance in Lead Screw and Nut Threads

Compared with (5.18), the term — + 1J2)/ is the additional resistive torque 

Compared with (5.19), the contact force is increased due to the preload P. 

Note that the above simplified formulation is valid as long as Ni 0. If this condition is violated (i.e., the left contact is lost) for the duration of such motion, the number of DOFs is increased to two. In such cases, which may be caused by large —R 0, the dynamics of the system gets more complicated since the impact of the threads and repeated loss of contact should be considered. 

Conforming to the sign convention defined in Fig. 2.7, the deflection (or interference) of threads can be calculated as 

The simplest way to approximate the contact force is by modeling the force-deflection relationship of the threads as that of linear springs and dampers. Thus 

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