An Investigation of the Dynamic Response of Spur Gear Teeth with Moving Loads

Two concepts relating to gear dynamics were studied. The first phase of the analysis involved the study of the effect of the speed of a moving load on the dynamic deflections of a gear tooth. A single spur gear tooth modelled using finite elements was subjected to moving loads with variable velocities. The tooth tip deflection time histories were plotted, from which it was seen that the tooth tip deflection consisted of a quasistatic response with an oscillatory response superimposed on it whose amplitude was dependent on the type of load engagement. Including the rim in the analysis added flexibility to the model but did not change the general behavior of the system. The second part of the analysis involved an investigation to determine the effect on the dynamic response of the inertia of the gear tooth. A simplified analysis using meshing cantilever beams was used. In one case, the beams were assumed massless. In the other, the mass (inertia) of the beams was included. From this analysis it was found that the inertia of the tooth did not affect the dynamic response of meshing cantilever beams

An analysis of general chain systems

A general analysis of dynamic systems consisting of connected rigid bodies is presented. The number of bodies and their manner of connection is arbitrary so long as no closed loops are formed. The analysis represents a dynamic finite element method, which is computer-oriented and designed so that nonworking, interval constraint forces are automatically eliminated. The method is based upon Lagrange's form of d'Alembert's principle. Shifter matrix transformations are used with the geometrical aspects of the analysis. The method is illustrated with a space manipulator

Interference detection using barycentric coordinates

In summary algorithms using barycentric coordinates have been presented which allow for the simplified testing of whether or not a point lies inside or outside of a triangle or tetrahedron or whether a given line segment intersects a triangle or tetrahedron. Along with the algorithms two formulas were presented for establishing the perpendicular distance from a point to a given side of a triangle or tetrahedron. Finally it should be pointed out that other algorithms are known for solving the problems posed in this paper. They occur in the literature under the general heading of Computational Geometry [4]. © 1982