Determination of Motion Parameters for Rod Toothed Gears with Skew Axes

Abstract

Approximated gears are considered in the paper. This work is devoted to determination of motion parameters of a rod toothed gear with skew axes. This development is protected by the patent of the Russian Federation. The urgency of the synthesis of new kinds of meshing with simplified geometry of contacting solids is substantiated. The paper describes the location of coordinate systems applied to obtain the position function of the rod toothed gear consisting of two wheels and the fixed element (rack). For gears with skew axes coordinates of contact points on surfaces of rods are obtained and errors of the position function are calculated at re-conjugation. The position function is obtained by the method of matrix transformation of coordinate systems and by equality of radius vectors and normal unit vectors at the contact point. This gear can be used in mechanical engineering, instrument-making and other branches of national economy. Both gearboxes and multipliers can be synthesized on its basis. It has a high manufacturability (special equipment is not required for its production); and the position function is close to a linear one. This paper describes the influence of changing the gear ratio on quality characteristics of the gear. Minimum allowable gear ratios for different numbers of rods of the driving gearwheel are determined. The values of minimum allowable gear ratios are significantly less than those for the bevel rod gears with intersecting orthogonal axes. The meshing occurs without coming of the contact point to the edge of the rod. Numerical methods of MathCAD software package are applied for solving the obtained system of equations. In future, the author will consider other possible errors of manufacturing and assembly for the rod toothed transmission (such as the pitch error, misalignment, etc.) in order to assess their impact on the qualitative characteristics of the meshing for all types of mutual position of axes.