Closed-Form Equations for Contact Force and Moment in Elastic Contact of Rough Surfaces

It is reasonable to expect that, when two nominally flat rough surfaces are brought into contact by an applied resultant force, they must support, in addition to the compressive load, an induced moment. The existence of a net applied moment would imply noneven distribution of contact force so that there are more asperities in contact over one region of the nominal area. In this paper, we consider the contact between two rectangular rough surfaces that provide normal and tangential contact force as well as contact moment to counteract the net moment imposed by the applied forces. The surfaces are permitted to develop slight angular misalignment, and thereby contact moment is derived. Through this scheme, it is possible to also define elastic contribution to friction since the half-plane tangential contact force on one side of an asperity is no longer balanced by the half-plane tangential force component on the opposite side. The elastic friction force, however, is shown to be of a much smaller order than the contact normal force. Approximate closed-form equations are found for contact force and moment for the contact of rough surfaces

Analytical and experimental parametric vibration stability studies in elastic mechanisms

This thesis presents a study of parametric stability of mechanisms with flexible members. Mathematical models are presented to account for shaft and member flexibilities in slider-crank mechanisms. Flexible coupler and crankshaft are considered and equations governing their motions are obtained using a continuous and a lumped parameter model, respectively. The linearization of equations is facilitated by considering the total motion to be comprised of rigid-body and perturbational elastic motions. Efficient methods are devised to solve for the steady-state dynamic response of rigid-body mechanisms. These are shown to result in significant reductions in computation time. A general method for calculating the steady-state response of periodic systems is presented. The effectiveness of the method is demonstrated by its application in determining the response of a slider-crank mechanism with an elastic coupler. Using the above models, a comprehensive study of parametric stability of slider-crank mechanisms with flexible members is presented. Effects of geometric stiffening, relative member weights, offset, internal material damping and balancing on parametric stability is studied. An experimental validation of the response predicted from these models is also included

A Finite Element-Based Elastic-Plastic Model for the Contact of Rough Surfaces

Three-dimensional elastic-plastic contact of two nominally flat rough surfaces is considered. Equations governing the shoulder-shoulder contact of asperities are derived based on the asperity constitutive relations from a finite element model of the elastic-plastic interaction proposed by Kogut and Etsion (2002), in which asperity scale constitutive relations are derived using piecewise approximate functions. An analytical fusion technique is developed to combine the piecewise asperity level constitutive relations. Shoulder-shoulder asperity contact yields a slanted contact force consisting of two components, one in the normal direction and a half-plane tangential component. Statistical summation of the asperity level contact force components and asperity level contact area results in the total contact force and total contact area formulae between two rough surfaces. Approximate equations are developed in closed form for contact force components and contact area

Synthesis of Spatial Slider-Crank Mechanism for High-Speed Applications

ABSTRACT Certain kinematic design constraints can be derived based on requisite dynamic performance requirements of a mechanism. Perhaps a most suitable kinematic synthesis task related to dynamic performance is function generation involving the entire motion cycle of the mechanism. For this purpose the closed-form equation of a spatial slider-crank mechanism is used to obtain approximate equations separating the various harmonics of the crank angle. The approximate equation is in terms of harmonic functions of the crank angle containing coefficients in terms of the linkage geometry. Hence the approximate equations provide an analytical means of relating the harmonic content of the slider position/displacement to the mechanism dimension. The approximate equations are utilized to establish kinematic synthesis constraints that relate to the dynamic behavior of the mechanism. Conditions for optimum dynamic performance are obtained in explicit analytical form in terms of the spatial slider-crank mechanism dimension, and used to demonstrate kinematic synthesis for minimized higher harmonic content in the slider position; thereby reduction of the induced shaking forces

Investigation of Factors Influencing the Structural Vibration in Ball Bearings

Hertzian equation for elastic contact is utilized along with lumped parameter approach to obtain the equations that govern the structural vibration of ball bearings. The lumped parameter formulation is obtained by treating various elements with mass lumped at their centers of gravity and the contact as nonlinear springs with nonlinear spring rates

Investigation the acoustic behavior of poplar and spruce species reaction wood using ultrasonic technique

The acoustic behavior of reaction and normal woods, phase velocity, group velocity and attenuation coefficients in the main directions for two wood species (Populus deltoids & Picea abies), were measured and compared. The results did not show any significant difference between phase velocities of normal and tension wood at the same ring in poplar wood. But in compression wood from spruce, phase velocity in longitudinal direction was lower; while in transverse direction was higher compared to normal wood. Group velocity as an index of speed of wave energy in compression wood also was less than that in normal wood. In radial and tangential directions, there was no significant difference between group velocity of compression and normal woods of spruce. In poplar species, in all main directions, the measured group velocities, both for tension and normal woods were identical. The result also showed that the attenuation coefficients in reaction wood of two wood species (poplar and spruce) were less than those of normal wood in all directions. In compression and tension woods, a high correlation was observed between acoustic radiation and wood density