Vol.28 No.12 肖望强等：双压力角非对称齿轮传动接触分析 。1173。 求得的结果是一种近似解. 比用有限元法计算所得的结果偏大. 3结论 参考文献 (1)推导出双压力角非对称齿轮在单齿啮合 【刂肖望强。李威韩建友，等.双压力角非对称齿廓渐开线齿 轮的振动分析.中国机械工程200617(6)：645 上、下界点，双齿啮入、啮出点和节点的综合曲率 【②]肖望强。李威李梅.双压力角非对称齿廓齿轮齿弯曲应 半径和齿面接触应力的计算公式，并用解析法对 力的有限元分析.北京科技大学学报.200628(6)：570 给定的参数进行计算.结果表明：单齿啮合上界 3 Deng G,NakanishiT.Bending load capacity enhancement us 点处接触应力最大，非对称齿轮齿面接触应力在 ing an asy mmetric tooth profile.JSME Int J.2003,46(3): 一个啮合周期中的最大值比对称齿轮降低了 1171 13.6%. [4 Kapebvich A.Geometry and design of spur gears with asym- metric teeth.Mech Mach Theory,2000 35:117 (2)根据给定参数，将双压力角非对称与对 [5 Litvin F L Lian Q.Asymmetric modfied gear drives:reduc- 称齿轮全齿模型调入ANSYS进行接触应力有限 tion of noise,localizat ion of contact simulation of meshing and 元分析并进行比较.结果表明：接触应力最大值 stress analysis.Comput Methods Appl Mech Eng 2000. 也出现在单齿啮合上界点处，非对称齿轮齿面接 188:363 触应力在一个啮合周期中的最大值比对称齿轮降 【(欧恒安，李润方，龚剑霞.三维冲击动力接触问题的有限 元混合算法.重庆大学学报.19417(2)：52 低了15.9%.两种方法都证明双压力角非对称齿 [7]Difrancesco G.Marini S.Stmuctural analysis of asy mmetrical 轮能有效的提高轮齿齿面接触强度. teeth:reduction of size and weight.Gear Technol 1997.14 (3)通过解析法与有限元法计算实例，对比 (5):121 了在七个特殊啮合点对称与非对称齿轮系统的齿 【习李华敏，韩元莹，王知行.渐开线齿轮的几何原理与计算。 面接触应力，揭示了由于时变啮合刚度和啮合点 北京：机械工业出版社，1985 【9龚藏义陈式椿，王永洁.渐开线圆柱齿轮强度计算与结 曲率半径的影响齿面接触应力在一个啮合周期的 构设计.北京：机械工业出版社，1986 变化规律.同时发现，由于解析法忽略了摩擦力 【10]田涌涛，李从心佟维，等.基于子结构技术的复杂齿轮系 以及计算法向力偏于保守，用解析法得出的结果 统有限元三维接触分析.机械工程学报。2002(5)：133 Transmission contact analysis of the unsymmetric gear with double pressure an- gles XIAO Wangqiang,LI Wei,Han Jianyou,Duan Mingnan Mechanical Engineering School University of Science and Technology Beijing,Beijing 100083,China ABSTRACT The calculation formulas of general curvature radius and tooth face contact stress of the un- symmetric gear with double pressure angles were proposed at the upper and lower points of single and dou- ble teeth mesh areas and the pitch point.The given parameters were calculated by analy tic method.Para- metric design programs of the total tooth models of unsy mmetric and symmetric involute gears were devel- oped by Autolisp language and the total models were transferred into ANSYS and calulated by finite ele- ment method.Compared with the standard involute gear,the two methods show ed that the unsy mmetric involute gear could efficiently improve the tooth face contact strength.Considering the time-variant mesh stiffness and curvature radius of mesh points,the change of tooth face contact stress in one engagement pe- riod w as demo nstrated. KEY WORDS unsymmetric gear;pressure angle;too th face contact stress;analytic method;finite ele- ment analy sis求得的结果是一种近似解 . 3 结论 (1)推导出双压力角非对称齿轮在单齿啮合 上、下界点, 双齿啮入 、啮出点和节点的综合曲率 半径和齿面接触应力的计算公式, 并用解析法对 给定的参数进行计算 .结果表明:单齿啮合上界 点处接触应力最大 , 非对称齿轮齿面接触应力在 一个啮合周期中的最大值比对称齿轮降低了 13.6 %. (2)根据给定参数 , 将双压力角非对称与对 称齿轮全齿模型调入 ANSYS 进行接触应力有限 元分析并进行比较 .结果表明:接触应力最大值 也出现在单齿啮合上界点处, 非对称齿轮齿面接 触应力在一个啮合周期中的最大值比对称齿轮降 低了 15.9 %.两种方法都证明双压力角非对称齿 轮能有效的提高轮齿齿面接触强度 . (3)通过解析法与有限元法计算实例, 对比 了在七个特殊啮合点对称与非对称齿轮系统的齿 面接触应力 ,揭示了由于时变啮合刚度和啮合点 曲率半径的影响齿面接触应力在一个啮合周期的 变化规律.同时发现 , 由于解析法忽略了摩擦力 以及计算法向力偏于保守 ,用解析法得出的结果 比用有限元法计算所得的结果偏大 . 参 考 文 献 [ 1] 肖望强, 李威, 韩建友, 等.双压力角非对称齿廓渐开线齿 轮的振动分析.中国机械工程,2006 , 17(6):645 [ 2] 肖望强, 李威, 李梅.双压力角非对称齿廓齿轮齿弯曲应 力的有限元分析.北京科技大学学报, 2006 , 28(6):570 [ 3] Deng G , Nakanishi T .Bending load capacity enhancement us￾ing an asymmetric tooth profile.JSME Int J , 2003 , 46(3): 1171 [ 4] Kapelevich A .Geometry and design of spur gears w ith asym￾metric teeth.Mech Mach Theory , 2000 , 35:117 [ 5] Lit vin F L, Lian Q .Asymmetric modified gear drives:reduc￾tion of noise , localization of contact, simulation of meshing and stress analysis.Comput Methods Appl Mech Eng , 2000 , 188:363 [ 6] 欧恒安, 李润方, 龚剑霞.三维冲击-动力接触问题的有限 元混合算法.重庆大学学报, 1994 , 17(2):52 [ 7] Difrancesco G , Marini S .Structural analysis of asymmetrical teeth:reduction of size and w eight .Gear Technol, 1997 , 14 (5):121 [ 8] 李华敏, 韩元莹, 王知行.渐开线齿轮的几何原理与计算. 北京:机械工业出版社, 1985 [ 9] 龚 义, 陈式椿, 王永洁.渐开线圆柱齿轮强度计算与结 构设计.北京:机械工业出版社, 1986 [ 10] 田涌涛, 李从心, 佟维, 等.基于子结构技术的复杂齿轮系 统有限元三维接触分析.机械工程学报, 2002(5):133 T ransmission contact analysis of the unsymmetric gear with double pressure an￾gles X IAO Wangqiang , LI Wei , Han Jianyou , Duan Mingnan Mechanical Engineering School, University of Science and Technology Beijing , Beijing 100083 , China ABSTRACT The calculation formulas of general curvature radius and tooth face contact stress of the un￾symmetric gear w ith double pressure ang les w ere proposed at the upper and lower points of single and dou￾ble teeth mesh areas and the pitch point .The given parameters w ere calculated by analy tic method .Para￾metric design programs of the total too th models of unsymmetric and symmetric involute gears w ere devel￾oped by Autolisp language , and the total models were transferred into ANSYS and calculated by finite ele￾ment method .Compared with the standard involute gear, the tw o methods show ed that the unsymmetric involute gear could efficiently improve the tooth face contact streng th .Considering the time-variant mesh stiffness and curvature radius of mesh points, the change of tooth face contact stress in one engagement pe￾riod w as demo nstrated . KEY WORDS unsymmetric gear ;pressure angle ;too th face contact stress ;analy tic method ;finite ele￾ment analy sis Vol.28 No.12 肖望强等:双压力角非对称齿轮传动接触分析 · 1173 ·