圆柱斜齿圆弧齿轮根切分析
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摘要
圆柱斜齿圆弧齿轮根切的深入分析和详细数据目前并不多见,影响人们对该齿轮根切产生确切、具体和深刻的认识,以及现有理论的广泛应用。针对圆柱斜齿圆弧齿轮,导出了其根切界限方程和不根切条件,详细研究了根切可能性、齿廓最易根切点的位置、不根切最少齿数的确定。将这些成果应用于纯滚动圆弧齿轮和W-N圆弧齿轮,得到验证、拓展和新结论,并获得齿轮工作者很想得知的根切计算数据。研究为各种具有圆柱圆弧齿的机械零件的不根切设计提供了理论依据。
At present, there are few in-depth analysis and detailed data on undercut of cylindrical helical circular arc gears, which affect people's accurate, specific and profound understanding of this undercut and the extensive application of the existing theories. For cylindrical helical circular arc gears, the undercut boundary equation and no undercut condition are derived,and the undercut probability as well as determination of point most easy to be undercut at tooth profile and minimum number of teeth to avoid undercut are studied in detail. When applied to the pure rolling circular arc gear and W-N circular arc gear, above results are verified and extended, and new conclusions and undercut calculation data that gear workers want to know are obtained. This study provides a theoretical basis for the non-undercut design of various mechanical parts with cylindrical circular arc teeth.
At present, there are few in-depth analysis and detailed data on undercut of cylindrical helical circular arc gears, which affect people's accurate, specific and profound understanding of this undercut and the extensive application of the existing theories. For cylindrical helical circular arc gears, the undercut boundary equation and no undercut condition are derived,and the undercut probability as well as determination of point most easy to be undercut at tooth profile and minimum number of teeth to avoid undercut are studied in detail. When applied to the pure rolling circular arc gear and W-N circular arc gear, above results are verified and extended, and new conclusions and undercut calculation data that gear workers want to know are obtained. This study provides a theoretical basis for the non-undercut design of various mechanical parts with cylindrical circular arc teeth.
引文
[1]李特文ФЛ.齿轮啮合原理[M].卢贤缵,高业田,王树人,译.上海:上海科学技术出版社,1984:52-59.
[2]傅则绍.微分几何与齿轮啮合原理[M].东营:石油大学出版社,1999:104-152.
[3]王树人.齿轮啮合原理简明教程[M].天津:天津大学出版社,2005:95-128.
[4]邵家辉.圆弧齿轮第2册[M].北京:机械工业出版社,1994:25-111.
[5]黄小平,黄爱苹,黄锡恺.齿轮纯滚动啮合的原理与实现[J].机械传动,2001,25(3):5-8.
[6]郭建华,李建博,姜洪源,等.新型人字齿同步带轮根切与齿廓修形[J].机械强度,2017,39(6):1404-1408.
[7]吴大任,骆家舜.齿轮啮合理论(附微分几何简介)[M].北京:科学出版社,1985:64-65.
[8]卢贤缵,尚俊开.圆弧齿轮啮合原理[M].北京:机械工业出版社,2003:36-71.
[9]数学手册编写组.数学手册[M].北京:高等教育出版社,1979:88-90.
[2]傅则绍.微分几何与齿轮啮合原理[M].东营:石油大学出版社,1999:104-152.
[3]王树人.齿轮啮合原理简明教程[M].天津:天津大学出版社,2005:95-128.
[4]邵家辉.圆弧齿轮第2册[M].北京:机械工业出版社,1994:25-111.
[5]黄小平,黄爱苹,黄锡恺.齿轮纯滚动啮合的原理与实现[J].机械传动,2001,25(3):5-8.
[6]郭建华,李建博,姜洪源,等.新型人字齿同步带轮根切与齿廓修形[J].机械强度,2017,39(6):1404-1408.
[7]吴大任,骆家舜.齿轮啮合理论(附微分几何简介)[M].北京:科学出版社,1985:64-65.
[8]卢贤缵,尚俊开.圆弧齿轮啮合原理[M].北京:机械工业出版社,2003:36-71.
[9]数学手册编写组.数学手册[M].北京:高等教育出版社,1979:88-90.