基于最小势能原理的双渐开线齿轮载荷分布研究  

Load distribution of double involute gears based on principle of minimum potential energy

作　　者：姜宇 樊智敏[1] 姜春雷 孙旭睿 闵令竹 JIANG Yu;FAN Zhimin;JIANG Chunlei;SUN Xurui;MIN Lingzhu(College of Electromechanical Engineering,Qingdao University of Science&Technology,Qingdao 266061,China)

机构地区：[1]青岛科技大学机电工程学院,山东青岛266061

出　　处：《机电工程》2024年第4期559-569,共11页Journal of Mechanical & Electrical Engineering

基　　金：国家自然科学基金资助项目(52075279)。

摘　　要：双渐开线齿轮接触线上的载荷非均匀分布,使得载荷计算困难。采用现有的方法或过于简化导致精度不足,或过于复杂使得计算量大、耗时长,并不适用于双渐开线齿轮载荷分布研究。为此,将双渐开线齿轮接触线等分为若干段,建立了双渐开线齿轮载荷分布模型,综合有限元法对轮齿载荷分布进行了研究。首先,根据双渐开线齿轮的啮合特点,求解了时变接触线,将每一啮合时刻下的齿轮接触线“分段”;然后,基于最小势能原理,建立了双渐开线齿轮的载荷分布模型,综合有限元法对齿轮轮齿载荷分布进行了研究;最后,对双渐开线齿轮与普通渐开线齿轮的载荷分布进行了对比分析,并研究了输入扭矩、齿宽对双渐开线齿轮轮齿载荷分布的影响。研究结果表明:载荷分布模型与有限元仿真结果之间的误差在10%之内,载荷分布模型合理可靠;双渐开线齿轮沿接触线方向载荷分布不均匀,节线附近载荷值最大;同参数、同工况下的双渐开线齿轮载荷波动幅度小于普通渐开线齿轮;输入扭矩增加,双渐开线齿轮节线附近载荷分布发生突变;齿宽增加,双渐开线齿轮沿接触线载荷分布不均匀程度增加。The load on the contact line of double involute gear is unevenly distributed,which makes the load calculation difficult.The existing methods are either too simplistic,which leads to insufficient accuracy,or too complicated,which leads to a large amount of calculation and longtime consumption,and are not suitable for the study of load distribution of double involute gears.Therefore,the contact line of double involute gear was divided into several sections,the load distribution model of double involute gear was established,and the load distribution of gear teeth was studied by comprehensive finite element method.Firstly,the time-varying contact line of double involute gear was solved according to its meshing characteristics,and the contact line of each meshing moment was"segmented".Then,based on the principle of minimum potential energy,a load distribution model of double involute gear was established,and the load distribution of gear teeth was studied comprehensively by using finite element method.Finally,a comparative analysis was carried out on the load distribution of double involute gear and ordinary involute gear,and the influence of input torque and tooth width on the load distribution of double involute gear teeth was studied.The research results indicate that the error between the load distribution model and the finite element simulation results is within 10%,which suggests that the load distribution model is reasonable and reliable.The load distribution of double involute gear is found to be uneven along the contact line,with the maximum load value near the involute.Under the same parameters and working conditions,the load fluctuation amplitude of double involute gear is smaller than that of ordinary involute gear.When the input torque increases,the load distribution near the involute of double involute gear undergoes a sudden change.With the increase of tooth width,the unevenness of the load distribution of double involute gear along the contact line increases.

关 键 词：渐开线齿轮 齿轮轮齿接触线载荷分布 时变接触线 分段法 最小势能原理 载荷分布模型 输入扭矩 齿宽 

分 类 号：TH132.41[机械工程—机械制造及自动化]