Numerical analysis and three dimensional modelling of worm gearing with localised tooth contact.

摘要

This research has developed a new approach to the design of worm gear drives with localised tooth contact (LTC). It has significant advantages over conventional ones: less sensitivity to errors, higher transmission quality, low manufacturing costs and less production lead-time. The approach consists of three main parts: developing the mathematical model, 3D modelling and simulation process and finite element analysis for the worm gear drive. A mathematical model of the localised conjugate worm gear drive has been established based on differential geometry. The completed model is able to determine the position of the localised contact and to achieve better contact quality. Localised tooth contact is achieved by reducing the worm size and modifying the wheel tooth surface. Moreover, it avoids the re-design and manufacture of the hob. The results of numerical simulation show: in spite of the variation in misalignment, the contact areas of the modified worm gearing stay almost at the same position and the size of the contact area almost remains the same as well. It proves that the modified worm gear drive is insensitive to errors. Three-dimensional simulation of a worm gear transmission has been conducted by applying the advanced CAE package Pro-engineer. The process comprises (1) the establishment of three models: worm model, wheel model and assembly model; (2) simulation of the localised tooth contact; (3) investigation of the contact and refinement of design parameters to further improve the transmission quality. The simulation has shown the contact pattern and its moving direction for worm gear drives, which provides a great visual aid for the designer to investigate the contact. Any interference between the modified tooth surfaces can be detected by the 3D model, and, hence, can be avoided at the design stage. This is a significant achievement in the analysis of localised contact of worm gears, because the previous methods often cause interference and can not detect contact position. The 3D models also lay the foundation for the finite element analysis. The finite element analysis offers a solution to calculating tooth stress and evaluating the load sharing of worm gear drives, which both remain unknown in existing design standards such as ISO, BS. Finite element analyses were conducted using the software package ANSYS and the results have been validated by published experimental work. The important characteristics such as meshing stiffness and loaded transmission error have been investigated with the aid of FEA. The load share of a worm gear drive at every moment of engagement has been solved. The results obtained are the fundamentals for the design of worm gear drives with high contact ratio and compact size.