Friction-induced vibration

Friction-induced vibration, in the most general sense, is the deviation from uniform sliding due to the interaction of friction and system dynamics. This can occur due to surface topography. However, the problem which is of the most concern is self-excited oscillations that occur due to a functional dependence of friction with velocity or 

---

If the vibration of the system (X(cd)) affects the excitation force F(co), this system can be considered to be in closed loop where self-excited vibrations such as chatter and friction-induced vibration may occur. Unstable vibration in servomechanism, which occurs at an excessive serve gain ( Control), can also be considered as the self-excited vibration. Figure 2 shows the closed loop dynamics of this type of vibrating system. 

Numerous researchers have studied self-excited vibration phenomena in a variety of frictional mechanisms (see, e.g., [4-9]). A considerable portion of the research in the field of friction-induced vibration is devoted to the brake systems. See, for example, the review paper by Kinkaid et al. [7]. The major self-excited vibration mechanisms in the systems with friction can be categorized into three types ... 

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

In a case study (Chap. 9), an actual product is studied where friction-induced vibration in the lead screw drives resulted in unacceptable levels of audible noise. An important part of this study is the development of a novel approach to identify system parameters including the velocity-dependent coefficient of friction between lead screw and nut. 

Design factors given in Fig. 2.5 are discussed by the manufacturers as part of their public technical information or product selection guidelines (see, e.g., [41-46]). There is, however, a major exception friction-induced vibration. Only a few published works are found in the literature that discuss the dynamics of lead screw drive systems and the effect of friction on their vibratory behavior. ... 

Wherever sliding motion exists in machines and mechanisms, friction-induced vibration may occur, and when it does, it severely affects the function of the system. Excessive noise, diminished accuracy, and reduced life are some of the adverse consequences of friction-induced vibration. To this end, lead screw systems are no exception the lead screw threads slide against meshing nut threads as the system operates. 

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. 

Nonlinearity The only nonlinear effect considered here comes from friction. However, many other sources of nonUnearity may exist that are excluded from the subsequent analyses to simplify the study of friction-induced vibrations in... 

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. 

In this chapter, the role of friction and the kinematic constraint equation (which defines the relative motion of lead screw and nut) in causing friction-induced vibrations in lead screw drives was investigated. Depending on the system parameters (including friction), the kinematic constraint may lead to instability in two distinct ways Negative damping and the occurrence of Painleve s paradoxes. 

Figure 9.18a shows the results of a sample open-loop test where lead screw exhibited friction induced vibration. It is interesting to notice that, unlike the lead screw angular velocity, motor angular velocity does not exhibit considerable... 

Ibrahim RA (1994) Friction-induced vibration, chatter, squeal, and chaos. Part I mechanics of contact and friction. Appl Mech Rev 47(7) 209-226... 

Popp K (2005) Modelling and control of friction-induced vibrations. Math Comput Model Dyn Syst ll(3) 345-369... 

Sinou J-J, Jezequel F (2007) Mode coupling instability in friction-induced vibrations and its dependency on system parameters including damping. Fur J Mech A Solids 26 106-122... 

Chevillot F, Sinou J-J, Mazet G-B, Hardouin N, Jezequel L (2008) The destabilizatirai paradox applied to friction-induced vibrations in an aircraft braking system. Arch Appl Mech 78 949-963... 

Friction-Induced Vibration in Lead Screw Drives... 

This book is based partly on the first author s Ph.D. research at the University of Waterloo, Ontario which was carried out under the supervision of the second author. The need for a dedicated and detailed study on the friction-induced vibration in lead screws became evident to the authors when they encountered two lead screw noise problems - over a short period of time - from two very different commercial applications which shared many resemblances. One of these two cases is discussed in Chap. 9. 

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. 

---