双重螺旋法齿面分区修形对降低安装误差敏感性的影响
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摘要
为了降低齿轮副对安装误差的敏感性,将双重螺旋法加工的齿面划分为小端、中间接触区和大端3个区域,并沿啮合线方向对3个区域分别进行抛物线修形,得到修形后的理论齿面;采用有约束最小二乘法求得与修形后理论齿面逼近的修形后实际齿面;通过齿轮承载接触分析(LTCA),得到原始齿面与修形后实际齿面在有安装误差时的齿面接触区、接触应力和齿根弯曲应力。研究结果表明:经过分区修形,正、反车齿面最大接触应力降低,齿面接触应力更加均匀,齿轮副对安装误差的敏感性降低,同时,齿根弯曲应力也有一定程度增大。
To reduce the sensitivity of the gear pair to the installation error, the original tooth surface generated by duplex helical method was divided into three regions, i.e. the toe region, the middle region and the heel region. Modifications of these regions with three parabolic segments were conducted along the meshing line, and then theoretical tooth surfaces were obtained. The constraint least square method was used to minimize the tooth flank form error between the theoretical modified tooth surface and the actual modified tooth surface. Then, the contact area, the contact stress, the bending stress of tooth root of the original tooth surface and the actual modified tooth surface in the presence of installation error were obtained by loaded tooth contact analysis(LTCA). The results show that the maximum contact stress of the drive side and the coast side are both reduced by zoning modification. Meanwhile, the tooth surface contact stress is more uniform. Thus, sensitivity of installation error of gear pair is reduced and the bending stress of the root increases to a certain extent.
To reduce the sensitivity of the gear pair to the installation error, the original tooth surface generated by duplex helical method was divided into three regions, i.e. the toe region, the middle region and the heel region. Modifications of these regions with three parabolic segments were conducted along the meshing line, and then theoretical tooth surfaces were obtained. The constraint least square method was used to minimize the tooth flank form error between the theoretical modified tooth surface and the actual modified tooth surface. Then, the contact area, the contact stress, the bending stress of tooth root of the original tooth surface and the actual modified tooth surface in the presence of installation error were obtained by loaded tooth contact analysis(LTCA). The results show that the maximum contact stress of the drive side and the coast side are both reduced by zoning modification. Meanwhile, the tooth surface contact stress is more uniform. Thus, sensitivity of installation error of gear pair is reduced and the bending stress of the root increases to a certain extent.
引文
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[14]苏进展,方宗德.弧齿锥齿轮误差敏感性优化设计[J].航空动力学报,2012,27(1):181-189.SU Jinzhan,FANG Zongde.Optimization design of the error sensitivity for spiral bevel gears[J].Journal of Aerospace Power,2012,27(1):183-189.
[15]苏进展,方宗德.弧齿锥齿轮低敏感性修形[J].航空动力学报,2012,27(8):1895-1901.SU Jinzhan,FANG Zongde.Low sensitivity modification for spiral bevel gears[J].Journal of Aerospace Power,2012,27(8):1895-1901.
[16]王会良,邓效忠,徐凯,等.考虑安装误差的拓扑修形斜齿轮承载接触分析[J].西北工业大学学报,2014,32(5):781-786.WANG Huiliang,DENG Xiaozhong,XU Kai,et al.Load tooth contact analysis(LTCA)of helical gears using topographic modification and installation errors[J].Journal of Northwestern Polytechnical University,2014,32(5):781-786.
[17]曹雪梅,孙宁,邓效忠.直齿锥齿轮低安装误差敏感性设计与实验验证[J].航空动力学报,2016,31(1):227-232.CAO Xuemei,SUN Ning,DENG Xiaozhong.Design for straight bevel gear based on low installation error sensitivity and experiment tests[J].Journal of Aerospace Power,2016,31(1):227-232.
[2]刘光磊,张瑞庭,赵宁,等.一种弧齿锥齿轮安装误差变动范围的确定方法[J].机械工程学报,2014,48(3):34-40.LIU Guanglei,ZHANG Ruiting,ZHAO Ning,et al.An approach to determine installation errors of spiral bevel gears[J].Chinese Journal of Mechanical Engineering,2014,48(3):34-40.
[3]佟操,孙志礼,马小英,等.考虑安装与制造误差的齿轮动态接触仿真[J].东北大学学报(自然科学版),2014,35(7):996-1000.TONG Cao,SUN Zhili,MA Xiaoying,et al.Dynamic simulation of spur gears with assembly errors and machining errors[J].Journal of Northeastern University(Natural Science),2014,35(7):996-1000.
[4]王小椿,吴序堂.空间点啮合齿面的接触特性对安装误差的敏感性分析[J].西安交通大学学报,1990,24(6):45-58.WANG Xiaochun,WU Xutang.Sensitivity of the contact characteristics of skew point contact surfaces to the mounting errors[J].Journal of Xi’an Jiaotong University,1990,24(6):45-58.
[5]LI Shuting.Effects of machining errors,assembly errors and tooth modifications on loading capacity,load-sharing ratio and transmission error of a pair of spur gears[J].Mechanism&Machine Theory,2007,42(6):698-726.
[6]LI Shuting.Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors,assembly errors and tooth modifications[J].Mechanism&Machine Theory,2007,42(1):88-114.
[7]LI Shuting.Effects of misalignment error,tooth modifications and transmitted torque on tooth engagements of a pair of spur gears[J].Mechanism&Machine Theory,2015,83:125-136.
[8]FALAH A H,ALFARES M A,ELKHOLY A H.Localised tooth contact analysis of single envelope worm gears with assembly errors[J].International Journal of Advanced Manufacturing Technology,2013,68(9/10/11/12):2057-2070.
[9]ZHANG Ruiling,WANG Tie.The influences of installation errors on double circular arc tooth spiral bevel gear using TCA method[J].Journal of Convergence Information Technology,2012,7(1):1-10.
[10]LITVIN F L,FUENTES A,HAYASAKA K.Design,manufacture,stress analysis,and experimental tests of low-noise high endurance spiral bevel gears[J].Mechanism&Machine Theory,2006,41(1):83-118.
[11]ARGYRIS J,FUENTES A,LITVIN F L.Computerized integrated approach for design and stress analysis of spiral bevel gears[J].Computer Methods in Applied Mechanics&Engineering,2002,191(11):1057-1095.
[12]SIMON V V.Machine-tool settings to reduce the sensitivity of spiral bevel gears to tooth errors and misalignments[J].Journal of Mechanical Design,2008,130(8):082603-1-082603-10.
[13]SIMON V V.Influence of tooth errors and misalignments on tooth contact in spiral bevel gears[J].Mechanism&Machine Theory,2008,43(10):1253-1267.
[14]苏进展,方宗德.弧齿锥齿轮误差敏感性优化设计[J].航空动力学报,2012,27(1):181-189.SU Jinzhan,FANG Zongde.Optimization design of the error sensitivity for spiral bevel gears[J].Journal of Aerospace Power,2012,27(1):183-189.
[15]苏进展,方宗德.弧齿锥齿轮低敏感性修形[J].航空动力学报,2012,27(8):1895-1901.SU Jinzhan,FANG Zongde.Low sensitivity modification for spiral bevel gears[J].Journal of Aerospace Power,2012,27(8):1895-1901.
[16]王会良,邓效忠,徐凯,等.考虑安装误差的拓扑修形斜齿轮承载接触分析[J].西北工业大学学报,2014,32(5):781-786.WANG Huiliang,DENG Xiaozhong,XU Kai,et al.Load tooth contact analysis(LTCA)of helical gears using topographic modification and installation errors[J].Journal of Northwestern Polytechnical University,2014,32(5):781-786.
[17]曹雪梅,孙宁,邓效忠.直齿锥齿轮低安装误差敏感性设计与实验验证[J].航空动力学报,2016,31(1):227-232.CAO Xuemei,SUN Ning,DENG Xiaozhong.Design for straight bevel gear based on low installation error sensitivity and experiment tests[J].Journal of Aerospace Power,2016,31(1):227-232.