The Computer Aided Optimization For The Design Of Spur Face Gear Drives With Multi-objective Optimization

Face gear drives are used for power transmission between unparallel shafts.Its tooth surface equation is complex and prone to edge contact.Especially in the case of loading and installation errors,it is usually necessary to modify(optimize)the design parameters repeatedly to meet the design requirements.The idea of optimal design of face gear drives is to determine the initial design parameters according to the working conditions,and then conduct the tooth surface contact analysis.Judge whether it meets the design requirements according to the analysis results.If not,modify the tooth surface modification parameters until it meets the requirements.The key technology in this process is tooth surface contact analysis,which can adopt analytical method or finite element method.When using analytical method,the calculation time is usually less than that of finite element method,but the calculation of stress and contact area is usually not as accurate as that of finite element method,and the calculation may be unstable in complex cases.When using the finite element method,although the calculation is stable and the result is accurate,the optimization process involves many software operation steps and usually requires a lot of manual operation,which makes the automation of the whole optimization process(the corresponding technology is computer-aided optimization technology)very difficult.In the previous research,computer-aided optimization technology is only applied to simple gear design.For complex gear pairs,the three-dimensional modeling,meshing and meshing analysis of tooth surfaces are more complex in the process of computer-aided optimization,and there is a lack of corresponding technical system at present.Therefore,the computeraided optimization design technology of face gear pair transmission is studied in this paper.The main research contents are as follows:(1)The equation of modified parabola tooth surface of face gears and comprehensive modified tooth surface of pinions are derived.The models of tooth surface contact analysis for the unloaded and loaded face-gear drive are established.(2)The primary design method of face gear drives is given.The recommended design parameters can be given based on the working conditions of face gear drives,the contact and bending fatigue strength are checked,and the top-down design software of face gear drives is compiled.(3)The modification optimization analysis of face gear drives is carried out.The optimization model is established with the symmetry of the parabolic geometric transmission error curve,the contact area in the central tooth surface and the minimum contact stress of the tooth surface as the optimization multi-objective.The modification parameters of face gears and pinions are chosen as the optimization variables and the avoidance of edge contact is constrained to the model.The ULH experimental design algorithm provides a uniformly distributed initial optimization space,and the fast optimization algorithm combined with NSGA-II and RSM approximate models are used to find the optimal combination of modification parameters.(4)The module programs of modeling,simulation and optimization analysis of face gear drives are integrated in mode FRONTIER? by compiling Python script program.It can automatically model,assembly,mesh,simulation analysis and data extraction of results based on the design parameters of face gear drives,avoid a mass of repetitive manual operations,shorten the design cycle of face gear pairs.Meantime,the optimal combination of modification parameters meeting the design requirements can be obtained by optimization calculation to improve the contact performance of tooth surface.(5)The correctness of the contact area of face gear pairs with the optimal combination of modification parameters is verified by experiments.It turns out that: The optimal combination of modification parameters can be obtained using the tooth surface modification design method of face gear pairs,which can avoid edge contact,reduce contact stress by 31.12%,and improve the contact performance of face gear drives.Meantime,the computer-aided optimization design system of face gear transmission based on contact simulation analysis based on finite element method is realized,It avoids a large number of manual operations and improves the efficiency of optimal design of face gear drives.The research can provide a reference for optimization design of the tooth surface modification of face gear drives.