Multiple impacts with friction in rigid multibody systems

An impact model for two-dimensional contact situations is developed which contains the main physical effects of a compliance element in the normal direction and a series of a compliance and Coulomb friction elements in the tangential direction. For systems with multiple impacts a unilateral formulation based on Poisson's hypothesis is used to describe the impulses which are transferred in the normal direction. The event of an impact is divided into two phases. The phase of compression ends with vanishing approaching velocity if normal impulses are transferred and is equivalent to a completely inelastic collision. The phase of expansion allows the bodies to separate under the action of the normal impulses whenever they are large enough. The absolute values of the tangential impulses are bounded by the magnitudes of the normal impulses, due to the Coulomb friction relationship on the impulse level. One part of the transferred tangential impulse during compression is assumed to be partly reversible which may be regarded as an application of Poisson's law. The remaining part is completely irreversible and considered friction. This formulation contains the special case of completely elastic tangential impacts as well as the situation when only Coulomb friction acts. It is proven that the presented impact model is always dissipative or energy preserving. The evaluation of the problem is done by solving one set of complementarity conditions during compression and a nearly identical set of equations during expansion. The theory is applied to some basic examples which demonstrate the difference between Newton's and Poisson's hypotheses.     

Simulation of spatial multibody systems with friction

A formulation for modeling and simulation of friction effects in spatial multibody systems is presented. Constraint reaction forces on rigid bodies that are connected by joints that support friction are derived as functions of Lagrange multipliers, using D’Alembert’s principle. Friction forces acting on bodies are calculated as a function of joint geometry, constraint reaction forces that are functions of Lagrange multipliers, and relative velocities at constraint contact points that are determined by system kinematics. Friction forces are implemented in index 0 differential-algebraic equations of motion that are solved numerically using explicit and implicit numerical integration methods. Spatial examples are presented, yielding accurate results and demonstrating that the systems are not stiff, even in the presence of friction and stiction.     

On chaotic motions of systems with dry friction

The principles of formation of closed and quasiperiodic orbitally stable trajectories in systems with dry friction are formulated. A frictional oscillator with periodic forcing is considered. It is established that random and stable oscillations exist. It is discovered that orbital instability and irregular oscillations are associated with the instability domain near a singular point Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 123–132, September 2008.     

Fractional describing function of systems with Coulomb friction

This paper studies the describing function (DF) of systems constituted by a mass subjected to nonlinear friction. The friction force is decomposed into two components, namely, the viscous and the Coulomb friction. The system dynamics is analyzed in the DF perspective revealing a fractional-order behavior. The reliability of the DF method is evaluated through the signal harmonic contents.     

On models of dynamic systems with dry friction

An approach to the design of models of dynamical systems with high dry friction in the kinematic pair is developed. The members of the kinematic pair are represented by parts of rigid bodies. The system as a whole is considered to have a variable structure. According to this assumption, two modes of motion with different dissipative characteristics are possible. The states in which the modes exchange and the motion switches over into critical modes with dynamic self-locking are established. A system with a variable transfer function between members that form a nonideal constraint is described __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 97–105, May 2007.     

Evaluation of autooscillation parameters in two-mass systems with dey friction

A system of two differential equations is used to describe the motion of a two-mass system subject to a constant force and viscous and dry friction. The relationship between dry friction and the relative sliding force is expressed in terms of an odd nonmonotonic function with a discontinuity of the second kind. The averaging method is used for analytical analysis. The initial system of differential equations is transformed into a system with rapidly rotating phase by introduction of special variables. Partical solutions of the first approximation equations are obtained, and their stability studied. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 32, No. 8, pp. 87–94, August, 1996.     

Phase trajectory determination of oscillatory systems with dry friction

Institute of the Ukrainian Border Forces, Khmel'nitskii. Translated from Prikladnaya Mekhanika, Vol. 29, No. 4, pp. 74–77, April, 1993.     

On self-excited vibrations in friction force measurement systems

Problems of friction force measurement under conditions of cosmic experiment on the orbit are considered. To increase the measurement accuracy, some arrangements should be made for preventing the onset of a self-vibration mode in mechanical systems with movable contact. Two self-vibration modes are studied. One of them occurs in the case of moderate relative slip velocities of the moving element and the indenter, and the other, in the case of small velocities. The existence and stability conditions are obtained in terms of the mass-elastic parameters of the contact pair.     

A controller for 2-DOF underactuated mechanical systems with discontinuous friction

We propose a controller for a class of 2-DOF underactuated mechanical systems with discontinuous friction in the unactuated joint. The control objective is the regulation of the unactuated variable while the position and speed of the actuated joint remain bounded. The unactuated joint is considered as a mechanical system with discontinuous friction but continuous, artificial control input given by a term depending on the actuated positions and velocities. The proposed controller guarantees the convergence of the position error of the unactuated joint to zero, and it is robust with respect to some uncertainty in the discontinuous friction coefficients. We illustrate the technique with its application to two systems.     

Interaction between torsional and lateral vibrations in flexible rotor systems with discontinuous friction

In this paper, we analyze the interaction between friction-induced vibrations and self-sustained lateral vibrations caused by a mass-unbalance in an experimental rotor dynamic setup. This study is performed on the level of both numerical and experimental bifurcation analyses. Numerical analyses show that two types of torsional vibrations can appear: friction-induced torsional vibrations and torsional vibrations due to the coupling between torsional and lateral dynamics in the system. Moreover, both the numerical and experimental results show that a higher level of mass-unbalance, which generally increases the lateral vibrations, can have a stabilizing effect on the torsional dynamics, i.e. friction-induced limit cycling can disappear. Both types of analysis provide insight in the fundamental mechanisms causing self-sustained oscillations in rotor systems with flexibility, mass-unbalance and discontinuous friction which support the design of such flexible rotor systems.     

Discontinuity-induced bifurcations in systems with impacts and friction: Discontinuities in the impact law

This paper concerns the non-smooth dynamics of planar mechanical systems with isolated contact in the presence of Coulomb friction. Following Stronge [Impact Mechanics, Cambridge University Press, Cambridge, 2000], a set of closed-form analytic formulae is derived for a rigid-body impact law based on an energetic coefficient of restitution and a resolution of the impact phase into distinct segments of relative slip and stick. Thus, the impact behavior is consistent both with the assumption of Coulomb friction and with the dissipative nature of impacts. The analysis highlights the presence of boundaries between open regions of initial conditions and parameter values corresponding to distinct forms of the impact law and investigates the smoothness properties of the impact law across these boundaries. It is shown how discontinuities in the impact law are associated with discontinuity-induced bifurcations of periodic trajectories, including non-smooth folds and persistence scenarios. Numerical analysis of an example mechanical model is used to illustrate and validate the conclusions.     

Identification and adaptive robust precision motion control of systems with nonlinear friction

Nonlinear Dynamics - Both accurate system identification and high-performance controller design are necessary for precision motion systems. This paper first considers the unavoidable issue of...     

Rotor whirl damping by dry friction suspension systems

An efficient and automatic attenuation technique for the whirling motion of rotating machinery can be achieved by supporting the journal boxes elastically and providing them with suitable rubbing surfaces subject to dry friction normal to the shaft axis. The critical flexural speeds are easily cut off and the whirl amplitude is minimized throughout the frequency range. Confining the usual operative angular speed of the rotor in the range of adhesive contact between the dry friction surfaces, there is no significant increase of power dissipation or heat production as a whole due to this type of suspension system, whose task is just to suppress the resonant peaks when passing the critical speeds. Moreover, the wear of the rubbing surfaces can be easily compensated by use of suitable spring loading systems for the friction contact. The dry friction damping is also compared with an equivalent viscous damping, where the equivalence has to be understood in terms of work dissipated per single revolution of the rotor. As for other conventional cases, the shaft hysteresis is found to exert a destabilizing effect above the first critical speed, which however can be compensated by the other dissipation sources. The system stability is here studied perturbing the periodic motion and applying the Floquet theory.