渐开线直齿圆柱齿轮磨损的数值计算与分析
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摘要
以标准渐开线直齿圆柱齿轮为研究对象,以Archard磨损计算模型为载体,将齿轮啮合区域的齿廓进行离散化处理,建立齿轮齿廓磨损计算模型。运用数值计算方法模拟齿廓各点的磨损情况,编写相关的计算程序,分析齿廓各啮合点处压力角与滑动系数、磨损率、摩擦距离、磨损量之间的关系,并进行曲线拟合。结果表明:在啮合区域内,齿廓的相对滑动系数、摩擦距离、磨损率、磨损量从齿根到齿顶的变化规律都是先减小后增大,在节点处理论值为0。提出的数值计算方法可实现对不同尺寸、不同材料、不同工况条件下的齿轮副的磨损量的定量计算,从而实现对齿轮使用寿命的预测。
With the standard involute spur gear as the study object,the meshing area of the gears was discretized by using a numerical method,the calculate model of the wear of tooth profile was established based on the Archard wear equation,and the relevant calculation program was compiled. The relationship between the pressure angle and sliding coefficient,wear rate,friction distance and wear loss was analyzed,and the curve fitting was carried out. The results show that the variation law of the relative sliding coefficient,friction distance,wear rate and wear amount of the tooth profile in the meshing area are reduced first and then increased from the tooth root to the tooth top,and the theoretical value is zero at the node. This numerical calculation method can realize the quantitative calculation of wear rate and wear amount of the gear pairs with different sizes,different materials and at different conditions,so as to achieve the prediction of the service life of the gears.
With the standard involute spur gear as the study object,the meshing area of the gears was discretized by using a numerical method,the calculate model of the wear of tooth profile was established based on the Archard wear equation,and the relevant calculation program was compiled. The relationship between the pressure angle and sliding coefficient,wear rate,friction distance and wear loss was analyzed,and the curve fitting was carried out. The results show that the variation law of the relative sliding coefficient,friction distance,wear rate and wear amount of the tooth profile in the meshing area are reduced first and then increased from the tooth root to the tooth top,and the theoretical value is zero at the node. This numerical calculation method can realize the quantitative calculation of wear rate and wear amount of the gear pairs with different sizes,different materials and at different conditions,so as to achieve the prediction of the service life of the gears.
引文
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[9]阎树田,胡赤兵,邬再新,等.齿轮齿廓滑动磨损的数值计算方法[J].机械设计与制造工程,2001,30(4):9-10.YAN S T,HU C B,WU Z X,et al.The calculating method of sliding wear on tooth outline[J].Machine Design and Manufacturing Engineering,2001,30(4):9-10.
[10]江亲瑜,李曼林,董美云,等.渐开线齿轮磨损的数值仿真[J].大连交通大学学报,1999(1):13-18.JIANG Q Y,LI M L,DONG M Y,et al.Numerical simulation of wear of spur gears[J].Journal of Dalian Jiaotong University,1999(1):13-18.
[11]曹劲然,冯毅,陆宝春,等.基于组合核函数OSVR算法的起重机减速齿轮箱磨损趋势预测[J].中国机械工程,2015,26(5):641-646.CAO J R,FENG Y,LU B C,et al.Wear trend prediction of crane gearbox based on OSVR method with combined Kernel functions[J].China Mechanical Engineering,2015,26(5):641-646.
[12]章易程,田红旗,唐进元,等.基于摩擦功原理的高副滑动磨损的研究[J].中国机械工程,2010,21(3):344-347.ZHANG Y C,TIAN H Q,TAN J Y,et al.Study on sliding wear of high pair based on friction work principles[J].China Mechanical Engineering,2010,21(3):344-347.
[13]宋文成.高精度同步传动中斜齿轮磨损的数值计算[D].哈尔滨:哈尔滨工业大学,2011.
[14]FLODIN A,ANDERSSON S.Simulation of mild wear in spur gears[J].Wear,1997,207(1/2):16-23.
[15]FLODIN A,ANDERSSON S.Simulation of mild wear in helical gears[J].Wear,1998,241(2):123-128.
[16]桂长林.Archard的磨损设计计算模型及其应用方法[J].润滑与密封,1990,15(1):12-21.GUI C L.The Archard design calculation model and its application methods[J].Lubrication Engineering,1990,15(1):12-21.
[17]黄平.摩擦学教程[M].北京:高等教育出版社,2008.
[18]И.В.克拉盖尔斯基.摩擦磨损计算原理[M].汪一麟,译.北京:机械工业出版社,1982.
[2]李宝良,江亲瑜.渐开线齿轮轮齿表面磨损规律的理论与实验研究[J].润滑与密封,2006,31(6):26-28.LI B L,JIANG Q Y.Theory and test research on wearing rules for involute gear tooth surface[J].Lubrication Engineering,2006,31(6):26-28.
[3]王淑仁,闫玉涛,丁津原.渐开线直齿圆柱齿轮啮合磨损试验研究[J].东北大学学报(自然科学版),2004,25(2):146-149.WANG S R,YAN Y T,DING J Y.Experimental study on meshwear of involute spur gears[J].Journal of Northeastern University(Nature Science),2004,25(2):146-149.
[4]徐大伟.利用现有齿轮机构传动参数预测所设计齿轮机构轮齿面磨损量[J].航空精密制造技术,2003,39(4):25-28.XU D W.Predicting abrasion values on tooth surfaces of designed gearing through the use of transmission parameters of existing gear mechanism[J].Aviation Precision Manufacturing Technology,2003,39(4):25-28.
[5]潘冬,赵阳,李娜,等.齿轮磨损寿命预测方法[J].哈尔滨工业大学学报,2012,44(9):29-33.PAN D,ZHAO Y,LI N,et al.The wear life prediction method of gear system[J].Journal of Harbin Institute of Technology,2012,44(9):29-33.
[6]WALTON D,GOODWIN A J.The wear of unlubricated metallic spur gears[J].Wear,1998,222(2):103-113.
[7]ZHANG J.Investigation on coupling effects between surface wear and dynamics in a spur gear system[J].Tribology International,2016,101:383-394.
[8]PARK D,KOLIVAND M,KAHRAMAN A.An approximate method to predict surface wear of hypoid gears using surface interpolation[J].Mechanism&Machine Theory,2014,71:64-78.
[9]阎树田,胡赤兵,邬再新,等.齿轮齿廓滑动磨损的数值计算方法[J].机械设计与制造工程,2001,30(4):9-10.YAN S T,HU C B,WU Z X,et al.The calculating method of sliding wear on tooth outline[J].Machine Design and Manufacturing Engineering,2001,30(4):9-10.
[10]江亲瑜,李曼林,董美云,等.渐开线齿轮磨损的数值仿真[J].大连交通大学学报,1999(1):13-18.JIANG Q Y,LI M L,DONG M Y,et al.Numerical simulation of wear of spur gears[J].Journal of Dalian Jiaotong University,1999(1):13-18.
[11]曹劲然,冯毅,陆宝春,等.基于组合核函数OSVR算法的起重机减速齿轮箱磨损趋势预测[J].中国机械工程,2015,26(5):641-646.CAO J R,FENG Y,LU B C,et al.Wear trend prediction of crane gearbox based on OSVR method with combined Kernel functions[J].China Mechanical Engineering,2015,26(5):641-646.
[12]章易程,田红旗,唐进元,等.基于摩擦功原理的高副滑动磨损的研究[J].中国机械工程,2010,21(3):344-347.ZHANG Y C,TIAN H Q,TAN J Y,et al.Study on sliding wear of high pair based on friction work principles[J].China Mechanical Engineering,2010,21(3):344-347.
[13]宋文成.高精度同步传动中斜齿轮磨损的数值计算[D].哈尔滨:哈尔滨工业大学,2011.
[14]FLODIN A,ANDERSSON S.Simulation of mild wear in spur gears[J].Wear,1997,207(1/2):16-23.
[15]FLODIN A,ANDERSSON S.Simulation of mild wear in helical gears[J].Wear,1998,241(2):123-128.
[16]桂长林.Archard的磨损设计计算模型及其应用方法[J].润滑与密封,1990,15(1):12-21.GUI C L.The Archard design calculation model and its application methods[J].Lubrication Engineering,1990,15(1):12-21.
[17]黄平.摩擦学教程[M].北京:高等教育出版社,2008.
[18]И.В.克拉盖尔斯基.摩擦磨损计算原理[M].汪一麟,译.北京:机械工业出版社,1982.