By Le Xuan Anh

This e-book addresses the final conception of movement of mechanical structures with Coulomb friction. specifically, the publication specializes in the subsequent particular difficulties: i) derivation of the equations of movement, ii) Painleve's paradoxes, iii) tangential impression and dynamic seizure, and iiii) frictional self-excited oscillations.

In addition to theoretical effects, the publication incorporates a special description of experiments which have been played. those exhibit that, normally, the friction strength on the quick of transition to movement is dependent upon the speed of tangential load and doesn't depend upon the period of the former touch. those effects are used to boost the idea of frictional self-excited oscillations. a couple of industrially appropriate mechanisms are thought of, together with the Painleve-Klein scheme, epicyclic mechanisms, crank mechanisms, apparatus transmission, the hyperlink mechanism of a planing computing device, and the slider of metal-cutting computing device tools.

The publication is meant for researchers, engineers and scholars in mechanical engineering.

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Extra resources for Dynamics of Mechanical Systems with Coulomb Friction

Example text

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.

Dq lie in the drawing plane whereas the planes II+, II~and IIi are perpendicular to the drawing plane. Corollary 1. Within and only within the motion angle any nontrivial force Fi at Fk = 0 (k -=I=- i) can cause motion from the rest condition. Proof. 100) would be satisfied. Then, according to the above said, this condition would be satisfied for any force Fi within if> that contradicts the statement. In other words, any nontrivial force within the motion angle if> can initiate the system into motion.

83) that For this reason, the sign of Flo is also determined by eq. 88). Then substituting eqs. 90) into eq. 64) yields the following expressions = signQ1, = EO = sign(LQl). 92) On the other hand, due to Theorem 1 in the case of /LILI > 1 and C2 = sign L parameter C1 can simultaneously take the two values ±l. Then the first equality in eq. 93) Hence, there occur simultaneously two regimes: transition to motion in the direction of C2 sign Q1 for E1 = co, and remaining at rest for E1 = -Eo. The theorem is thus proved.

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