Mathematical modelling of elliptic helicoid screw transmission systems

Abstract

This paper presents a systematic modelling procedure for producing high precision elliptic helicoid screw transmission systems. The modelling procedure includes both the derivation of the geometric model of the helicoid screw and the construction of profile models for the revolving conjugate elements. The profile models are derived by using several techniques including the theories of differential geometry, coordinate transformation and meshing principles. Since the meshing model of the screw transmission system is constructed systematically by rigorous differential geometry and meshing theories, the lead screw model thus developed can lead to good transmission quality and high system performance. In order to verify the effectiveness of the proposed models and the modelling procedure, the performance of the proposed system is evaluated numerically by several different indices including the transmissivity index, the manipulability index and the lubrication angle. The numerical results obtained by using the proposed modelling procedure are also verified by experimental data taken directly from a sample product produced by the NC machine using the proposed theory. A comparative study is conducted. The results indicate that the proposed elliptic helicoid screw model proposed in this paper is accurate and efficient. The proposed theory and performance indices can be used to design for various screw systems of high performance.

Keywords

helicoid surface coordinate transform differential geometry transmissivity index manipulability index lubrication angle

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