一种基于小滑动率内齿轮副的理论及实验研究（英文）
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摘要
基于齿轮滑动率,提出一种点啮合内齿轮副,该齿轮副由渐开线内齿轮和齿廓为二次曲线的外齿轮构成,其中,小齿轮为在渐开线齿轮基础上所构建。提出了齿轮成形方法与数学模型。计算该齿轮副滑动率,并与渐开线齿轮进行对比。讨论齿轮副中心距可分性和接触应力。根据设计参数对齿轮副进行加工和检测。为验证模型的正确性,进行效率试验和与渐开线齿轮副的对比实验。此外,通过扫描电子显微镜分析两种类型小齿轮的表面形貌,并用测量中心测量齿轮磨损深度。实验结果表明,所提出的齿轮副效率稳定在97.1%到98.6%之间,磨损程度小于同参数渐开线齿轮的50%。
Aiming at the issue of sliding ratio, an internal gear pair is proposed which consists of an involute internal gear and a pinion with quadratic curve teeth. Particularly, the contact pattern is point contact and the pinion is generated based on an involute gear. The generation method and mathematical models of the gear pair are presented. The sliding ratio is calculated and the general calculation formulas of sliding ratios are developed. Also, the comparison between the involute gear and proposed gear is made. The adaptability of center distance and contact stress are also discussed. In addition, the gear pair was manufactured and inspected according to the exactitude solid model of the gear pair. In order to confirm this model to be effective, the efficiency experiment and the contrast experiment with the involute gear pair were performed. Furthermore, these two types of pinions were analyzed by scanning electron microscope and wear depths were measured by measuring center. The experiment results show that the efficiency of the internal gear pair is stable at a range about 97.1% to 98.6% and wear depth is less than 50% of the involute gear pair. The internal gear pair is expected to have excellent transmission performance.
Aiming at the issue of sliding ratio, an internal gear pair is proposed which consists of an involute internal gear and a pinion with quadratic curve teeth. Particularly, the contact pattern is point contact and the pinion is generated based on an involute gear. The generation method and mathematical models of the gear pair are presented. The sliding ratio is calculated and the general calculation formulas of sliding ratios are developed. Also, the comparison between the involute gear and proposed gear is made. The adaptability of center distance and contact stress are also discussed. In addition, the gear pair was manufactured and inspected according to the exactitude solid model of the gear pair. In order to confirm this model to be effective, the efficiency experiment and the contrast experiment with the involute gear pair were performed. Furthermore, these two types of pinions were analyzed by scanning electron microscope and wear depths were measured by measuring center. The experiment results show that the efficiency of the internal gear pair is stable at a range about 97.1% to 98.6% and wear depth is less than 50% of the involute gear pair. The internal gear pair is expected to have excellent transmission performance.
引文
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[18]LIANG Dong,CHEN Bing-kui,GAO Yan-e.The generation principle and mathematical model of a new involute-helix gear drive[J].Proceedings of Institution of Mechanical Engineers Part C,Journal of Mechanical Engineering Science,2013,227(12):2834-2843.
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[21]DENG Song,HUA Lin,Han Xing-hui,HUANG Song.Finite element analysis of contact fatigue and bending fatigue of a theoretical assembling straight bevel gear pair[J].Journal of Central South University,2013,20(2):279-292.
[22]AOYAMA T.A study on error compensation on high precision machine tool system using a 2D laser holographic scale system[J].Journal of Advanced Mechanical Design Systems&Manufacturing,2012,6(6):999-1014.
[23]TANG Jin-yuan,CUI Wei,ZHOU Heng,YIN Feng.Integrity of grinding face-gear with worm wheel[J].Journal of Central South University,2016,23(1):77-85.
[24]LIN Chao,CAO Xi-jun,FAN Yu,ZENG Dong.Pitch deviation measurement and analysis of curve-face gear pair[J].Measurement,2015,81:95-101.
[2]PATIL S S,KARUPPANAN S,ATANASOVSKA I,WAHAB A A.Contact stress analysis of helical gear pairs,including frictional coefficients[J].International Journal of Mechanical Sciences,2014,85(8):205-211.
[3]SHENG Zhao-hua,TANG Jin-yuan,CHEN Si-yu,HUZe-hua.Modal analysis of double-helical planetary gears with numerical and analytical approach[J].Journal of Dynamic Systems Measurement&Control,2015,137(4):041012.
[4]ZHANG Yu,YAN Hong-zhi,ZENG Tao,ZENG Yi-yu.Tooth surface geometry optimization of spiral bevel and hypoid gears generated by duplex helical method with circular profile blade[J].Journal of Central South University,2016,23(3):544-554.
[5]XIA Ji-qiang,SHI Kan,WANG Chun-jie.High-order involute modified noncircular bevel gears[J].Journal of Advanced Mechanical Design Systems&Manufacturing,2014,8(3):1-15.
[6]SHAO Ren-ping,JIA Pu-rong,DONG Fei-fei.Dynamic characteristics of cracked gear and three-dimensional crack propagation analysis[J].Proceedings of the Institution of Mechanical Engineers Part C,Journal of Mechanical Engineering Science,2013,227(6):1341-1361.
[7]ZHANG Yuan-shen,HU Xiao-han,LIU Yu-bo,LIUXiao-hua,CHEN Lei.The study of straight conjugate internal meshing gear pump[J].Machinery Design&Manufacture,2010(6):138-139.(in Chinese)
[8]XU Wen-bo.Study on the internal meshing and transmission of double-circular-arc gear[D].Zhengzhou:Zhengzhou Research Institute of Mechanical Engineering,2012.(in Chinese)
[9]KAHRAMAN A,VIJAYAKAR S.Effect of internal gear flexibility on the quasi-static behavior of a planetary gear set[J].Journal of Mechanical Design,2001,123(3):408-415.
[10]TUNALIOGLU M?,TUC B.Theoretical and experimental investigation of wear in internal gears[J].Wear,2014,309(1,2):208-215.
[11]LI Ting,PAN Cun-yun,GAO Fu-dong,Wang Xiao-cong.Research on sliding ratios of conjugate surfaces of two degrees of freedom meshing transmission of spherical gear pair[J].Journal of Mechanical Design,2012,134(9):255-274.
[12]WANG Jian,LUO Shan-ming,WU Yue.A method for the preliminary geometric design of gear tooth profiles with small sliding coefficients[J].Journal of Mechanical Design,2010,132(5):1-8.
[13]CHEN Ning-xin.Curvatures and sliding ratios of conjugate surfaces[J].Journal of Mechanical Design,1998,120(1):126-132.
[14]LIANG Dong,CHEN Bing-kui,GAO Yan-e.Calculation method of sliding ratios for conjugate-curve gear pair and its application[J].Journal of Central South University,2015,22(3):946-955.
[15]ZHAO Ya-ping,WEI Wen-jun,DONG Xue-zhu,TANGQiu-hua.Calculation method of sliding ratio for spot contact tooth surfaces and application to crossed helical involute gears[J].China Mechanical Engineering,2006,17(S2):40-43.(in Chinese)
[16]WANG Zheng.Sliding rate analysis of involute gear teeth[J].Virology,1988,164:309-17.(in Chinese)
[17]ZHANG Yi-cheng.Study on relative sliding ratio of involute internal gear pair[J].Journal of Mechanical Transmission,2001,25(2):25-27.(in Chinese)
[18]LIANG Dong,CHEN Bing-kui,GAO Yan-e.The generation principle and mathematical model of a new involute-helix gear drive[J].Proceedings of Institution of Mechanical Engineers Part C,Journal of Mechanical Engineering Science,2013,227(12):2834-2843.
[19]RADZEVICH S P.Theory of gearing:Kinetics[i.e.kinematics],geometry,and synthesis[M].United States:CRC Press/Taylor&Francis,2013.
[20]MICHAELIS K.Gear contact friction[M].Germany:Springer Berlin Heidelberg,2014.
[21]DENG Song,HUA Lin,Han Xing-hui,HUANG Song.Finite element analysis of contact fatigue and bending fatigue of a theoretical assembling straight bevel gear pair[J].Journal of Central South University,2013,20(2):279-292.
[22]AOYAMA T.A study on error compensation on high precision machine tool system using a 2D laser holographic scale system[J].Journal of Advanced Mechanical Design Systems&Manufacturing,2012,6(6):999-1014.
[23]TANG Jin-yuan,CUI Wei,ZHOU Heng,YIN Feng.Integrity of grinding face-gear with worm wheel[J].Journal of Central South University,2016,23(1):77-85.
[24]LIN Chao,CAO Xi-jun,FAN Yu,ZENG Dong.Pitch deviation measurement and analysis of curve-face gear pair[J].Measurement,2015,81:95-101.