Optimization of zero-tooth-difference internal gear mechanism based on particle swarm algorithm

WANG Shijie; YANG Zhe

doi:10.7688/j.issn.1000-1646.2025.01.08

Abstract：[Objective]To address the problems of low overlap,unstable internal and external gear thickness coefficients,and easy breaking of gear teeth due to thin tooth thickness in the zero-tooth-difference internal gear mechanism of the coupling device in the oil extraction system of submersible screw pump,a method of optimizing the modification coefficient in the mechanism to improve the degree of overlap was proposed,and the corresponding optimization model was designed.[Methods]The design defect regarding the modification coefficient of zero-tooth-difference mechanism in the traditional design method was analyzed.The objective function and constraints were determined,the design variables were defined.The linearly decreasing inertia weight method in the particle swarm optimization(PSO)algorithm was adopted to improve the local and global optimization ability of the particles.The shrinkage factor was introduced,and the convergence time was shortened by updating the speed iteration formula.The degree of overlap and tooth thickness coefficients were taken as the optimized objective functions.The optimization model was designed by combining the gear constraints of the zero-tooth-difference internal gear mechanism.[Results]To ensure the stability of the algorithm,the user's initial input parameters are used for optimization analysis:the internal and external gear module is 6;the tooth number is 12;the pressure angle of the reference circle is 20°;the width of the external gear tooth is 30 mm;the width of the internal gear tooth is 28 mm;the eccentricity range is 2.5-5 mm.The improved PSO algorithm achieves the optimal solutions of radial modification coefficient and tangential modification coefficient,namely that it significantly improves the optimization results of modification coefficients.By comparing with the original data and optimization results,it is found that the degree of overlap of the improved PSO algorithm is increased by up to 26.2％.In particular,the degrees of overlap at different eccentricities are significantly enhanced after optimization.[Conclusion]The improved PSO algorithm has both global convergence and precise search ability,and the obtained modification coefficients are more reasonable and effective.The optimized tooth thickness coefficients of the internal and external gears tend to be more stable,which can effectively alleviate the problem of tooth breakage caused by the thinning of the tooth thickness.The optimized modification coefficients not only meet the various constraints but also facilitate the post-processing and improve the computational efficiency.Consequently,good design results are achieved.