A High-Precision Circular Helicoidal Surface Meshing Model for Producing High-Performance Lead Screws

Abstract

This paper presents a new circular helicoidal surface meshing model for producing high transmission performance lead screws. The formulation of the meshing model includes the analytical derivation of the helicoidal surface equation and the profile equations of revolving and non-revolving conjugate elements. These surface profile equations are derived and presented using several different theories and techniques including coordinate transformation, differential geometry and meshing principles. Since the meshing model is constructed systematically by rigorous differential geometry and meshing theories instead of the simple techniques of analytical geometry, the lead screw model thus built can lead to better transmission quality and higher system performance. In order to verify the effectiveness of the proposed models and the systematic modelling procedure, the performance of the system is evaluated numerically by three major indices including the transmissivity index, the manipulability index and the lubrication angle. The results obtained by using the proposed modelling procedure are also verified by experimental data taken directly from a sample product produced on an NC machine using the proposed theory. The comparative study further indicates that the proposed circular helicoidal surface meshing model presented in this paper is accurate and efficient. The proposed theory and performance indices presented in this paper can thus be used to design for various high transmission performance lead screw systems.