Investigation On Meshing Theory And Load Capacity Of High Performance Unsymmetric Gear With Double Pressure Angles

With the development of modern scientific technology, the performance of gear transmission is required to improve correspondingly. The traditional involute gear can hardly meet the practical requirements. Because the pressure angles have an effect on load capacity of involute gear, in order to increase load capacity and decrease noise and vibration of gear transmission system, a new-type unsymmetric involute spur gear was designed with double pressure angles on the driving and coast sides. A theoretical and experimental investigation on the load capacity and meshing characteristics of unsymmetric involute gear was made deeply and systematically in this paper. Detailed researches are as below:(1) Involute rack-cutter with unsymmetric teeth and different pressure angles was designed. The total tooth profile equations and transition curve equations of tooth root for the unsymmetric involute gear were proposed as well as the geometry formulas for tooth shape. Then the characteristics of the tooth tip were investigated and the four types of transition curve of tooth root for unsymmetric and symmetric gears were established and compared. Furthermore, the coordinates transition matrix for conjugate tooth profile of unsymmetric gear was given. By developing relevant programs, the tooth profile of unsymmetric and symmetric gear were simulated and provided a theoretical basis for the following research.(2) Through iteration algorithm and optimization strategy, the analytic calculation formulas of tooth root bending stress for unsymmetric gear were presented. The analytic calculation formulas of general curvature radius and the tooth face contact stress for unsymmetric gear with different pressure angles were developed in the upper and lower points of single and double teeth meshing areas and meshing pitch point. The finite element model for calculating tooth root bending stress of unsymmetric gear is built. Based on nonlinear theory of finite element, the calculation model of tooth face contact stress for unsymmetric gear is established. By two types of method, the bending stress and contact stress for unsymmetric gear with different combinations of pressure angles were calculated and compared. And the change of the tooth root bending stress and tooth face contact stress were investigated in one engagement period as well as relevant influence factors. Furthermore, systematical design method of unsymmetric gear transmission was proposed.(3) The nonlinear dynamic model for unsymmetric gear was proposed on the basis of mesh characteristics, the effect of time-variant mesh stiffness and integrated transmission error of unsymmetric gear system. By applying the method of numerical simulation to the research on nonlinear dynamics, vibration characteristics were compared between standard and unsymmetric gear. And the effect of unsymmetric gear system parameters on the dynamic characteristics of transmission system was studied.(4) Based on the theories of gear engagement, tooth contact analysis, friction and heat transfer, the three-dimensional steady and transient models of finite element for unsymmetric gear were established to investigate temperature distributions and variations along the contact path. The transformation courses of bulk temperature for unsymmetric and symmetric gear were investigated before gear transmission system got steady conditions.(5) It was proposed that the process of meshing and contact for unsymmetric gear with double pressure angles in case of modified geometry and alignment errors. Computer programs of tooth contact analysis (TCA) of unsymmetric gear and conventional gear have been developed. The computer programs were applied to analyze and compare contact path and transmission errors for double-crowned pinion with unsymmetric tooth profile and standard symmetric gear where alignment errors exist.(6) A set of manufacture approach for unsymmetric gear was presented based on wire electrical discharge machining (WEDM). The unsymmetric gear and symmetric gear of the same parameters and rough material were manufactured and bending fatigue strength testing was carried on the HF fatigue-testing machine. And the test results demonstrated the validity of theoretical analysis.