Calculation and Dressing Simulation of the Profile of the Form Grinding Wheel for Modified ZI Worms

Form grinding is a precision machining method for the modified ZI worms, and the grinding accuracy mainly depends on the dressing accuracy of the grinding wheel’s profile. A mathematical model of the modified involute helicoid of ZI worms is established based on the curve superposition method. Subsequently, the normal vector of the tooth surface is derived. After that, space meshing theory and matrix transformation methods are applied. Thus, the meshing equation between the grinding wheel and the tooth surface during the form grinding is constructed. Based on the equal error principle, an interpolation algorithm for the modified involute is proposed. The nonlinear meshing equations are solved using MATLAB R2019b software to obtain the discrete point coordinates of the worm end section profile and the grinding wheel axial section profile. The derivative of the discrete points is calculated by using the difference method, and the motion trajectory of the diamond wheel during the grinding wheel dressing process is solved based on the equidistant curve theory. The proposed methods holds certain reference value for calculating the profile of grinding wheels used in the form grinding of modified ZI worms.