Computerized simulation of meshing and contact of enveloping gear tooth surfaces

Abstract A gear mechanism with enveloping gear tooth surfaces is considered. Initially such surfaces are in line contact at every instant. Due to gear misalignment caused by errors of assembly (change of crossing angle, center distance, axial displacements of gears, etc.), the surfaces start to contact each other at every instant at a point but not a line. A computerized approach is proposed for simulation of meshing and contact, determining (i) the paths of the contact point on gear tooth surfaces, (ii) deviations of the transmission function from the theoretical one (transmission errors), and (iii) the bearing contact that is formed as a set of contact ellipses. Direct relations between principal curvatures and principal directions for enveloping tooth surfaces have been developed. It is proved that the eigenvectors of the matrix curvature represent the directions of extreme relative normal curvature. There are two side-effects of this research: (i) proof that the surface torsions for enveloping surfaces are equal at any point on their contact line (characteristic); (ii) the opportunity to determine the normal component of displacement of a contact point over the tooth surface, although the direction of total displacement is indefinite. The normal component of infinitesimal displacement is perpendicular to the tangent to the contact line. The proposed approaches are illustrated with the example of a gear drive with a ruled surface of the worm.