By Le Xuan Anh
This ebook addresses the overall thought of movement of mechanical structures with Coulomb friction. particularly, the booklet makes a speciality of the subsequent particular difficulties: i) derivation of the equations of movement, ii) Painleve's paradoxes, iii) tangential influence and dynamic seizure, and iiii) frictional self-excited oscillations.
In addition to theoretical effects, the e-book encompasses a specified description of experiments which have been played. those exhibit that, usually, the friction strength on the rapid of transition to movement depends on the speed of tangential load and doesn't depend upon the length of the former touch. those effects are used to strengthen the idea of frictional self-excited oscillations. a few industrially appropriate mechanisms are thought of, together with the Painleve-Klein scheme, epicyclic mechanisms, crank mechanisms, equipment transmission, the hyperlink mechanism of a planing desktop, and the slider of metal-cutting laptop tools.
The publication is meant for researchers, engineers and scholars in mechanical engineering.
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Extra info for Dynamics of Mechanical Systems with Coulomb Friction
Example text
As one can see from eq. 60) this coefficient depends on the system configuration. On the other hand, the quantity Lo = c2L = L sign q is invariant under the choice of the generalised coordinate q. In what follows Lo is referred to as influence factor. Let us assume that vector r~ is not constant within any finite interval of the generalised coordinate q, that is dr~ -Idq r O. 3 Equation for the constraint force and Painleve's paradoxes 51 It follows from eq. 60) that . L sIgn . 66) Given a model, the second condition in eq.
Therefore, the phase space (q, q) is separated into three regions: the region of existence and uniqueness of solution, the region of non-existence of solution and the region of non-uniqueness of solution. These regions are determined by the following theorem. Theorem 1. 69) the signs of Rand Ro coincide (El = EO) and the normal reaction force R and the acceleration ij are uniquely determined by eqs. 63). 71) = ± i = ±A) if E2 = -EO signL. 72) 52 2. Systems with a single degree of freedom and a single frictional pair Proof.
Theorem 3. 74) be satisfied. 83) the equation of dynamics admits simultaneously both maintaining immovable contact and transition to motion in the direction of C2 = sign Q1 = co sign L. The sign C1 = -co corresponds to the immovable contact whereas the sign C1 = co corresponds to the motion. Proof. Let us prove the first item of the theorem. Inserting L from eq. 60) into eq. 80) yields Taking into account this inequality in eq. 63) we can find the sign of Ro co = - sign Q2 . 84) 56 2. Systems with a single degree of freedom and a single frictional pair On the other hand, it follows from eq.