Curvature analysis of variable pitch lead screws with cylindrical meshing elements

Based on coordinate transformation matrices and theory of gearing, we derive the mathematical expressions of surface geometry and the location of contact point of variable pitch lead screws. According to curvature theory, we obtain the principal curvatures, the principal directions, and the orientation of the contacting line at any contact point. Furthermore, the condition of avoiding undercutting of the screw surface, the reduced radius of curvature along any tangential direction, and the angle between the normal of contact line and the relative velocity are also derived. The result of this work is necessary for the tasks of contact stress analysis and wear/lubrication analysis for variable pitch lead screws with cylindrical meshing elements.