Frictional Contact Analysis Of Joints In Multibody System

Being the most common phenomenon, friction can reduce working efficiency of many mechanism systems. For these systems, friction has to be minimized, so that wear is reduced, the lifetime as well as the efficiency of a dynamic system is increased and more resources are saved. However, for some special systems, friction is used to transmit forces or to reduce vibration amplitudes. A possibility to reduce the vibration of a machine is to use friction contacts to dissipate energy. Therefore, it is imperitive to simulate the dynamical behavior of mechanical systems including frictional contact effect in the joint, which may better serve the mechanism and structral design, and provide scientific basis for reducing or using friction in mechanical systems.While considering the frictional effect in the joint of multibody systems, Lagrange multipliers appears on both sides of the dynamical equation. Therefore, it must be solved iteratively:giving initial values of the joint reaction forces and calculating the acceleration of the system, then re-computing the joint reaction forces. If the joint reaction forces obtained are different from the initial value, then execute the next iteration. It is clear that the dynamical equation of the system needs to be solved at each iteration step, and the convergence can not be guaranteed. In addition, a simplified model for the frictional joint is usually used by the traditional method, which may improve the computational efficiency, but at the cost of the contact details in the joint. According to existing theories, a necessary step of frictional contact analysis is to detect locations of contact. When employed in the contact analysis of a joint, kinematic constraints of the joint have to be released, and should be replaced by a contact-impact pair, no matter how small the clearance in the joint would be. The computational efficiency is very low. If the clearance in the joint is very small, the contact detection becomes unpractical because computational errors and the range of the relative motion between the two bodies linked by the joint are usually in the same order of magnitude.Big clearance in the joint may lead to severe wear, vibration and noise, so the clearances of joints in a great number of mechanical systems are well under control and frictional contact analysis with small clearance in joints of multibody systems is of great importance in the design and control of mechanisms. If the clearance in the joint is tiny, the constraints of the joint are still kept and the effects of impacts are negligible. Based on this fact, a new methodology for the frictional contact analysis in the joint of multibody systems is proposed in this paper: The recursive relations of inertias and forces between the bodies of tree systems are introduced, and the recursive formulations of general multibody system with frictional joints are established by regarding the frictional force as external force, from which the acceleration can be expressed as linear function of the generalized frictional multipliers. Using the generalized inertias and external forces formulated in the recursive progress, the joint reaction force can be expressed as linear function in terms of the unknown frictional multipliers. Combining the formulation provided by the Coulomb's law of friction, implicit nonlinear equations about the frictional multipliers are finally obtained, from which all the unknown parameters can be solved directly. The dimension of the nonlinear equations is significantly reduced, and the computational efficiency is improved accordingly.The frictional contact model of revolute joint, universal joint, spherical joint and cylindrical joint are established, combing the equivalent relations between the joint reaction forces and the contact forces, the equivalent equations of the contact forces are formulated, from which the contact details can be obtained.The frictional contact analysis in the spatial prismatic joint is much more complicated. In this paper, it is proved that all types of contacts in the joint can be converted to point-to-point contacts. At each contact points, two gap functions are introduced. However, in the proposed method, not the values of these gap functions but the relations between them are essential. In view of the non-colliding contacts being predominant when clearances of joints are tiny, we formulate the contact forces in terms of resultant frictional forces in the joint from the geometrical relations of the gap functions, the unilateral constraint in the joint, and the compemenrarity conditions between the gap functions and contact forces, resulting in a linear complementarity problem, which is finally converted to a nonlinear problem, and the frictional contact problem in the spatial prismatic joint is solved effectively.From the comperative results of this paper and ADAMS, it can be concluded that:details about the contact in the joint, including the impact instants, can be obtained although impacts are not taken into consideration explicitly. It is worth mentioned that the kinematic constraints of the joint are not released, so that the computational efficiency is highly improved.Solutions of frictional contact analysis of prismatic joints depend on the coefficient of friction and the contact situation in the joint. It is prooved that:in some contact situations, the solution does not exist when the coefficient of friction exceed the critical value that is given by this paper.