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In many industrial applications imbalance is a major cause for unwanted vibrations. One way to compensate for an unknown imbalance is the implementation of an automatic ball balancer. Oil-lubricated automatic ball balancers are applied in hand-held tools and washers. However, in applications such as optical drives fluid lubrication is highly undesirable since it may destroy the optical system upon leakage. Therefore, in this paper, the balancing performance of an automatic ball balancer without fluid lubrication is investigated. The absence of fluid lubrication gives rise to dry friction phenomena which cause the existence of equilibrium sets of the balls in the automatic ball balancer. A model of the system with dry friction, modeled by a set-valued force law, is built based on dedicated experiments. The resulting equilibrium sets and their dependency on system parameters are studied and the consequences for the balancing performance is assessed. Based on these results, it can be concluded that in parts of such equilibrium sets the balancing performance deteriorates when compared to the system without automatic ball balancer; in other words, the balancing performance is endangered by the presence of dry friction. This conclusion is supported by both numerical and experimental results.

In this paper, the stationary response of a van der Pol vibro-impact system with Coulomb friction excited by Gaussian white noise is studied. The Zhuravlev nonsmooth transformation of the state variables is utilized to transform the original system to a new system without the impact term. Then, the stochastic averaging method is applied to the equivalent system to obtain the stationary probability density functions (pdfs). The accuracy of the analytical results obtained from the proposed procedure is verified by those from the Monte Carlo simulation based on the original system. Effects of different damping coefficients, restitution coefficients, amplitudes of friction and noise intensities on the response are discussed. Additionally, stochastic P-bifurcations are explored.

In this paper, upper bound solutions for plane-strain extrusion and plug drawing are presented using rigid-triangle velocity fields, assuming both the shear friction ($\tau =mk$) and the Coulomb friction ($\tau =\mu p$) conditions at the interfaces. For shear friction condition, the solutions are obtained following the classical approach. For this case, the energy dissipation rates of individual triangles are shown to be equal. For Coulomb friction condition, the analysis is carried out by the generalized upper bound formulation proposed by Collins. The energy dissipation rates of the individual triangles, in the deformation zone, for this friction condition, are found to be in geometric progression. Formulae are provided for the calculation of the lengths of contact and the contact pressures at the die/metal and plug/metal interfaces. Results are presented for mean extrusion/drawing stresses, as a function of reduction, for specified friction conditions and die/plug geometry. Values of optimum die/plug angles are determined graphically for given reductions and friction conditions. Finally, results for an alternative velocity field are presented for which the contact pressures on the die and the plug are nearly equal. The theoretical values are compared with some numerical and experimental results available in the literature.

In this paper we announce some new mathematical results on the stability of quasi-static paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle. A quasi-static path is said to be stable at some value of the load parameter if, for some finite interval of the load parameter thereafter, the dynamic solutions behave continuously with respect to the size of the initial perturbations (as in Lyapunov stability) and to the smallness of the rate of application of the external forces, ε (as in singular perturbation problems). In this paper we prove sufficient conditions for stability of quasi-static paths of a single particle linearly elastic system with Coulomb friction and persistent normal contact with a flat obstacle. The present system has the additional difficulty of its non-smoothness: the friction law is a multivalued operator and the dynamic evolutions of this system may have discontinuous accelerations.

The relationship between Coulomb friction and motion is non-smooth, so that the dynamic behavior of vibration with Coulomb friction is more abundant. This paper discusses the effect of Coulomb friction on both free vibration and forced vibration of single degree of freedom system. Analyzing the phase trajectory of the solution of vibration differential equation, we find out some peculiar dynamical behavior of vibration system with dry friction.