关于渐开线标准直齿圆柱齿轮重合度的深入认识
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摘要
根据在教学过程中,学生对重合度知识点的理解存在疑惑,有必要对重合度相关知识进行梳理。根据齿轮传动重合度的基本要求,阐述重合度传统的计算公式,并由此分析满足正确啮合条件的渐开线标准直齿圆柱齿轮最小的重合度;经对传统重合度公式的分析推导,得到新的重合度公式,并由此分析得出非标准安装时重合度下降,并且为保障齿轮连续传动,严格控制中心距的相对误差;根据高等数学的知识对重合度的极值进行详细分析,当两齿轮的齿数趋于无穷大时,重合度达到极大值。
In the teaching process, it's hard for the students to understand the knowledge point of contact ratio, so it's necessary to comb the related knowledge of the contact ratio. According to the basic requirement of contact ratio in gear drive, the traditional equation about contact ratio is expanded, the minimum of contact ratio is analyzed in involute standard straight gears satisfying the correct meshing condition. the new equation of contact ratio is given on the basis of analyzing the traditional one,and the contact ratio for nonstandard installation gear is reduced, so the relative error of center distance must be controlled to ensure gear continuous transmission. In the end,the extremum of contact ratio is gotten according to the knowledge of higher mathematics. When both of tooth numbers tend to infinity, the maximum of contact ratio is obtained.
In the teaching process, it's hard for the students to understand the knowledge point of contact ratio, so it's necessary to comb the related knowledge of the contact ratio. According to the basic requirement of contact ratio in gear drive, the traditional equation about contact ratio is expanded, the minimum of contact ratio is analyzed in involute standard straight gears satisfying the correct meshing condition. the new equation of contact ratio is given on the basis of analyzing the traditional one,and the contact ratio for nonstandard installation gear is reduced, so the relative error of center distance must be controlled to ensure gear continuous transmission. In the end,the extremum of contact ratio is gotten according to the knowledge of higher mathematics. When both of tooth numbers tend to infinity, the maximum of contact ratio is obtained.
引文
[1]孙桓,陈作模,葛文杰.机械原理[M].北京:高等教育出版社,2013.
[2]贺建群,张峥嵘.渐开线圆柱齿轮传动的重合度计算[J].机械设计与制造,2005(9):25-26.
[3]邱纪龙.渐开线圆柱直齿轮传动的重合度计算[J].科学论坛,2013(7):241.
[4]叶素娣,徐敬华,徐圣伦.论重合度与齿轮参数的关系[J].绥化学院学报,2015,35(5):150-152.
[5]唐立山.一种新的渐开线直齿圆柱齿轮传动理论重合度算法[J].机械设计与制造,2012(2):54-55.
[6]钟承鲲,卢华,李刚.渐开线圆柱齿轮副重合度的校核计算[J].装备制造技术,2010(10):51-52.
[7]同济大学数学系.高等数学[M].北京:高等教育出版社,2014.
[2]贺建群,张峥嵘.渐开线圆柱齿轮传动的重合度计算[J].机械设计与制造,2005(9):25-26.
[3]邱纪龙.渐开线圆柱直齿轮传动的重合度计算[J].科学论坛,2013(7):241.
[4]叶素娣,徐敬华,徐圣伦.论重合度与齿轮参数的关系[J].绥化学院学报,2015,35(5):150-152.
[5]唐立山.一种新的渐开线直齿圆柱齿轮传动理论重合度算法[J].机械设计与制造,2012(2):54-55.
[6]钟承鲲,卢华,李刚.渐开线圆柱齿轮副重合度的校核计算[J].装备制造技术,2010(10):51-52.
[7]同济大学数学系.高等数学[M].北京:高等教育出版社,2014.