Curvature Interference Characteristics of ZN Worm Wheel

To identify the factors affecting curvature interference during the meshing of a cylindrical worm and worm wheel, we establish a concise, general curvature interference limit curve function in the natural coordinate system based on meshing theory. This function does not require differentiation of the meshing equation with respect to the surface parameters. Taking the meshing of a ZN worm pair as an example, we establish a nonlinear system of equations for the curvature interference limit curve of the ZN worm wheel. The nonlinear system is then reduced by the elimination method to a univariate nonlinear equation containing only one unknown. The correctness of the obtained results is verified using the definition of an envelope surface. The results show that the curvature interference limit line of the ZN worm pair is located below the worm wheel tooth surface, with the lower-left region of the worm wheel tooth root being the most susceptible to undercutting. The risk of curvature interference increases with the number of worm-starts and the worm pitch-circle diameter. For a six-start worm, the worm pitch-circle diameter should therefore be selected as small as possible.