Some Remarks Regarding the System Models

The equation of motion (5.53) is equivalent to the system given by (5.44) and (5.45). In this representation, the possibility of Painleve s paradox is clearly shown through the appearance of A, (5.51), in the equations. 

Depending on the configuration of an actual lead screw drive, one or more models presented in this chapter may be suitable to accurately capture the most prominent and/or relevant features of the system s dynamical behavior. This is certainly the case in the subsequent chapters. However, many other features are not included in this work. These features include  

Torsional deflection of lead screw. For a long and/or slender lead screw, the frequency of the first few torsional modes of vibration may be low enough to influence the system dynamics. Moreover, the winding/unwinding action of torsional deflections may affect the threads clearance and the overall load distribution causing further deviation from the models considered here. In this monograph, the lead screws are considered to be sufficiently stiff and modeled as rigid bodies. 

Misalignment. Design and/or assembly problems may lead to axial offset of the centerlines of lead screw and nut. The misalignment may also occur in the form of a skewed nut. In both of these cases, thread contact and load distribution may be affected severely. 

Manufacturing issues Depending on the manufacturing method and the quality of the product, lead screws can suffer from lead error (particularly in longer designs). There may be external contaminants or surface defects on the lead screw or the nut. Although these and other similar issues may have significant impact on the function of a lead screw drive, they are excluded from this fundamental study on the friction-induced vibration. 

---