By Le Xuan Anh
This e-book addresses the final concept of movement of mechanical structures with Coulomb friction. specifically, the ebook makes a speciality of the next particular difficulties: i) derivation of the equations of movement, ii) Painleve's paradoxes, iii) tangential effect and dynamic seizure, and iiii) frictional self-excited oscillations.
In addition to theoretical effects, the booklet encompasses a specific description of experiments which were played. those express that, normally, the friction strength on the immediate of transition to movement depends on the speed of tangential load and doesn't rely on the period of the former touch. those effects are used to advance the speculation of frictional self-excited oscillations. a couple of industrially suitable mechanisms are thought of, together with the Painleve-Klein scheme, epicyclic mechanisms, crank mechanisms, apparatus transmission, the hyperlink mechanism of a planing desktop, and the slider of metal-cutting desktop tools.
The e-book is meant for researchers, engineers and scholars in mechanical engineering.
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Additional resources for Dynamics of Mechanical Systems with Coulomb Friction
E. the value of x for which Fe = F*. The amplitude and the period of the quasi-harmonic self-excited oscillations in both a transient process and a stationary regime are determined for the above law of friction. It is found that the quasi-harmonic self-excited oscillations occur in a certain interval of the velocity v. A hard excitation of self-excited oscillations with periodic stops is considered in ,  for the original hypothesis of Kaidanovsky and Khaikin. It is shown that the amplitude of the self-excited oscillation increases and the length of the part of the immovable contact decreases with the growth of velocity v.
15) and establish the relationship between the coefficients. dq. When the slider is subjected to small displacements in the tangential and normal directions (dr~/dq)81 and (orr/oh)o 8 2 (8 1 and 82 are arbitrary small quantities) the position of the i-th particle should change by (4/dq)8 1 and (orT/oh)o 82, respectively. Let the prescribed virtual displacement of the slider be 8 * rT = dr~8 dq q + (orr) 8h oh ° which, due to eqs. 14), can be put in the following form * 8rT = d4 dq (8q + >'8h) + (orr) oh °8h.
For example, for the scheme shown in Fig. 3 Painleve proved that under a zero initial velocity X(O) = 0 and the condition for paradoxes Mtan > 2 the equation of motion admits simultaneously staying at rest and transition to motion. A general criterion of this non-uniqueness and the interrelation between this effect and the phenomenon of non-uniqueness and non-existence of motion (under zero initial velocity) have not yet been established. e. if Coulomb's law is expressed in terms of the generalised forces.