基于粒子群算法的零齿差内啮合机构优化  

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

作　　者：王世杰[1] 杨喆 WANG Shijie;YANG Zhe(School of Mechanical Engineering,Shenyang University of Technology,Shenyang 110870,Liaoning,China)

机构地区：[1]沈阳工业大学机械工程学院,辽宁沈阳110870

出　　处：《沈阳工业大学学报》2025年第1期61-66,共6页Journal of Shenyang University of Technology

基　　金：辽宁省“揭榜挂帅”科技攻关项目(2021JH1/10400097)。

摘　　要：【目的】针对潜油螺杆泵采油系统中联轴装置零齿差内啮合机构重合度低、内外齿轮齿厚系数不稳定以及齿厚偏薄易导致轮齿折断等问题,提出了一种优化机构内变位系数、提高重合度值的方法,并设计了相应的优化模型。【方法】分析了传统设计方法中零齿差机构变位系数的设计缺陷,明确了目标函数和约束条件,定义了设计变量。采用粒子群优化(PSO)算法中的惯性权重线性递减策略提升粒子的局部与全局寻优能力,引入收缩因子并通过改进的速度更新迭代公式缩短收敛时间。以重合度和齿厚系数为优化目标函数,同时结合零齿差内啮合机构的齿轮约束条件建立了优化模型。【结果】为验证算法的稳定性,以用户输入的初始参数(内外齿轮模数为6,齿数为12,分度圆压力角为20°,外齿轮齿宽为30 mm,内齿轮齿宽为28 mm,偏心量范围为2.5~5 mm)进行优化分析。结果表明,通过改进PSO算法得到了径向变位系数和切向变位系数的最优解,即改进PSO算法显著提升了变位系数的优化效果。对比原始数据和优化结果,改进PSO算法的重合度提升了最高达26.2%,特别是在不同偏心量下,优化后的重合度均显著提高。【结论】通过对比改进前后的PSO算法,改进后的算法兼具全局收敛性与精确搜索能力,所得变位系数更加合理有效;优化后的齿厚系数更加平稳,显著降低了轮齿折断风险。最终优化后的变位系数不仅满足各项约束条件,且便于后续加工,提高了计算效率,显现出良好的设计效果。[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 signif

关 键 词：零齿差内啮合 变位系数 重合度 粒子群算法 优化设计 惯性权重 收缩因子 

分 类 号：TH16[机械工程—机械制造及自动化] TH132.4