准双曲面齿轮准静态接触分析和试验研究
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摘要
建立了精确的准双曲面齿轮的轮齿面和过渡曲面数学模型;选择用平均接触椭圆长半轴、接触线方向角和传动误差曲线交点来评价齿面接触斑点和传动误差;以一个准双曲面齿轮副为计算实例,建立了适合准静态齿面接触分析的准双曲面齿轮传动系统有限元分析模型;通过准静态加载齿面接触特性分析,得到齿根弯曲应力、接触应力和传动误差的变化规律,分析载荷的影响情况,并比较了有限元结果与经验公式计算结果。开发了准双曲面齿轮试验台,进行齿面接触斑点和齿根弯曲应力检测,试验结果与仿真结果的一致性较好。
The precise mathematical models of tooth surfaces and fillet surfaces of the hypoid gear are established. Three indexes of average semi-major axis of contact ellipses,the direction angle of contact path and the intersection of the transmission error curve are selected to evaluate the tooth contact pattern and the transmission error. Then,taking a hypoid gear for example,the finite element analysis model of hypoid gears transmission system is established which is suitable for tooth contact characteristics analysis under quasistatic condition. By the analysis of quasi-static motion and loaded tooth contact,the variations of bending stresses,contact stresses,and transmission error are investigated. Besides,the results are compared with the calculated results by empirical formula. Finally,a hypoid gear transmission performance test bed is developed,then the tooth contact pattern test and bending stress test are carried out,and the test results are well consistent with the simulation results.
The precise mathematical models of tooth surfaces and fillet surfaces of the hypoid gear are established. Three indexes of average semi-major axis of contact ellipses,the direction angle of contact path and the intersection of the transmission error curve are selected to evaluate the tooth contact pattern and the transmission error. Then,taking a hypoid gear for example,the finite element analysis model of hypoid gears transmission system is established which is suitable for tooth contact characteristics analysis under quasistatic condition. By the analysis of quasi-static motion and loaded tooth contact,the variations of bending stresses,contact stresses,and transmission error are investigated. Besides,the results are compared with the calculated results by empirical formula. Finally,a hypoid gear transmission performance test bed is developed,then the tooth contact pattern test and bending stress test are carried out,and the test results are well consistent with the simulation results.
引文
[1]LITVIN F L,FUENTES A.Gear geometry and applied theory[M].Cambridge:Cambridge University Press,2004.
[2]汪中厚,周晓玲.螺旋锥齿轮动力学研究方法及进展[J].中国机械工程,2006,17(11):1203-1208.WANG ZH H,ZHOU X L.Simulation methods and developments of dynamics for spiral bevel gears[J].China Mechanical Engineering,2006,17(11):1203-1208.
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[4]GUINGAND M,DE VAUJANY J P,JACQUIN C Y.Quasi-static analysis of a face gear under torque[J].Computer Methods in Applied Mechanics and Engineering,2005,194(39):4301-4318.
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[8]HOTAIT M A,KAHRAMAN A.Estimation of bending fatigue life of hypoid gears using a multiaxial fatigue criterion[J].Journal of Mechanical Design,2013,135(10):101005.
[9]屈文涛,沈允文,徐建宁.基于ANSYS的双圆弧齿轮接触应力有限元分析[J].农业机械学报,2006,37(10):139-141.QU W T,SHEN Y W,XU J N.Finite element analysis of contact stress for double-arc gear based on ANSYS[J].Transactions of the Chinese Society for Agricultural Machinery,2006,37(10):139-141.
[10]ZHANG J,FANG Z,CAO X,et al.The modified pitch cone design of the hypoid gear:manufacture,stress analysis and experimental tests[J].Mechanism and Machine Theory,2007,42(2):147-158.
[11]WANG Z,ZHOU X,OGUMA T,et al.Surface error measurement of spiral bevel gears using scanning measurement[J].Chinese Journal of Scientific Instrument,2007,28(2):229-235.
[12]汪中厚,赵东升,久保爱三,等.螺旋锥齿轮齿面测量仪精度评定法[J].仪器仪表学报,2009,30(8):1752-1756.WANG ZH H,ZHAO D SH,KUBO A,et al.Accuracy evaluation method of gear measurement instrument for spiral bevel gears[J].Chinese Journal of Scientific Instrument,2009,30(8):1752-1756.
[13]王峰,方宗德,李声晋,等.考虑安装误差的摆线齿准双曲面齿轮轮齿接触分析[J].农业机械学,2012,43(9):213-218.WANG F,FANG Z D,LI SH J,et al.Tooth contact analysis of epicycloid hypoid gear considering assembly misalignment[J].Transactions of the Chinese Society of Agricultural Machinery,2012,43(9):213-218.
[14]李刚,汪中厚,耿直,等.基于非特征分块插值技术的准双曲面齿轮数字化真实齿面建模方法[J].机械工程学报,2015,51(7):77-84.LI G,WANG ZH H,GENG ZH,et al.Modelingapproach of digital real tooth surfaces of hypoid gears based on non-geometric-feature segmentation and interpolation algorithm[J].Journal of Mechanical Engineering,2015,51(7):77-84.
[15]王志永,刘威,曾韬,等.螺旋锥齿轮大轮齿形误差的在机测量[J].仪器仪表学报,2015,36(5):1047-1053.WANG ZH Y,LIU W,ZENG T,et al.On-machine measurement of tooth profile errors for the spiral bevel gears[J].Chinese Journal of Scientific Instrument,2015,36(5):1047-1053.
[2]汪中厚,周晓玲.螺旋锥齿轮动力学研究方法及进展[J].中国机械工程,2006,17(11):1203-1208.WANG ZH H,ZHOU X L.Simulation methods and developments of dynamics for spiral bevel gears[J].China Mechanical Engineering,2006,17(11):1203-1208.
[3]LITVIN F L,VECCHIATO D,YUKISHIMA K,et al.Reduction of noise of loaded and unloaded misaligned gear drives[J].Computer Methods in Applied Mechanics and Engineering,2006,195(41):5523-5536.
[4]GUINGAND M,DE VAUJANY J P,JACQUIN C Y.Quasi-static analysis of a face gear under torque[J].Computer Methods in Applied Mechanics and Engineering,2005,194(39):4301-4318.
[5]DE VAUJANY J P,GUINGAND M,REMOND D,et al.Numerical and experimental study of the loaded transmission error of a spiral bevel gear[J].Journal of Mechanical Design,2007,129(2):195-200.
[6]SHEVELEVA G I,VOLKOV A E,MEDVEDEV V I.Algorithms for analysis of meshing and contact of spiral bevel gears[J].Mechanism and Machine Theory,2007,42(2):198-215.
[7]SIMON V.Head-cutter for optimal tooth modifications in spiral bevel gears[J].Mechanism and Machine Theory,2009,44(7):1420-1435.
[8]HOTAIT M A,KAHRAMAN A.Estimation of bending fatigue life of hypoid gears using a multiaxial fatigue criterion[J].Journal of Mechanical Design,2013,135(10):101005.
[9]屈文涛,沈允文,徐建宁.基于ANSYS的双圆弧齿轮接触应力有限元分析[J].农业机械学报,2006,37(10):139-141.QU W T,SHEN Y W,XU J N.Finite element analysis of contact stress for double-arc gear based on ANSYS[J].Transactions of the Chinese Society for Agricultural Machinery,2006,37(10):139-141.
[10]ZHANG J,FANG Z,CAO X,et al.The modified pitch cone design of the hypoid gear:manufacture,stress analysis and experimental tests[J].Mechanism and Machine Theory,2007,42(2):147-158.
[11]WANG Z,ZHOU X,OGUMA T,et al.Surface error measurement of spiral bevel gears using scanning measurement[J].Chinese Journal of Scientific Instrument,2007,28(2):229-235.
[12]汪中厚,赵东升,久保爱三,等.螺旋锥齿轮齿面测量仪精度评定法[J].仪器仪表学报,2009,30(8):1752-1756.WANG ZH H,ZHAO D SH,KUBO A,et al.Accuracy evaluation method of gear measurement instrument for spiral bevel gears[J].Chinese Journal of Scientific Instrument,2009,30(8):1752-1756.
[13]王峰,方宗德,李声晋,等.考虑安装误差的摆线齿准双曲面齿轮轮齿接触分析[J].农业机械学,2012,43(9):213-218.WANG F,FANG Z D,LI SH J,et al.Tooth contact analysis of epicycloid hypoid gear considering assembly misalignment[J].Transactions of the Chinese Society of Agricultural Machinery,2012,43(9):213-218.
[14]李刚,汪中厚,耿直,等.基于非特征分块插值技术的准双曲面齿轮数字化真实齿面建模方法[J].机械工程学报,2015,51(7):77-84.LI G,WANG ZH H,GENG ZH,et al.Modelingapproach of digital real tooth surfaces of hypoid gears based on non-geometric-feature segmentation and interpolation algorithm[J].Journal of Mechanical Engineering,2015,51(7):77-84.
[15]王志永,刘威,曾韬,等.螺旋锥齿轮大轮齿形误差的在机测量[J].仪器仪表学报,2015,36(5):1047-1053.WANG ZH Y,LIU W,ZENG T,et al.On-machine measurement of tooth profile errors for the spiral bevel gears[J].Chinese Journal of Scientific Instrument,2015,36(5):1047-1053.