一种鼓形齿联轴器的侧隙设计方法
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摘要
为了使鼓形齿联轴器在倾角下正常工作,提出了一种快速、精确的侧隙设计方法。首先,采用沿齿宽方向对齿廓形状连续变位的方法形成鼓形齿,建立了鼓形齿齿面模型;模拟插齿刀加工内齿圈,建立了内齿圈轮齿齿面模型。其次,基于空间坐标变换方法,建立了鼓形齿联轴器在倾角下工作时的装配关系,并在此基础上建立了三维有限元分析模型。再次,运用轮齿齿面接触理论,计算出无侧隙下鼓形齿和内齿圈相邻齿间的最小间隙,并给出了最小侧隙的计算公式。最后,以某鼓形齿联轴器参数为算例,对相邻齿面之间最小间隙点轨迹、最小间隙分布与Alfares方法和有限元结果进行了对比,研究结果表明:无侧隙、有倾角时相邻齿面之间均处于干涉状态;最小侧隙设计量随着倾角的增大而增大;最小侧隙设计位置在纯翻转区;文中方法比Alfares方法更精确。
To make crown gear coupling work properly under the limit misalignment angle, a quick and accurate strategy for the backlash amount is proposed. The hub tooth surface is generated by continuous modification for tooth profile along the tooth width direction, and the sleeve tooth surface is processed by a shaping cutter. Then the assembling relationship of the crown gear coupling under misalignment angle is established by the spatial coordinate transform three-dimensional finite element analysis model is thus established. Following tooth contact analysis, the clearance between adjacent teeth of hub and sleeve without considering backlash is determined and the formula for the minimum circumferential backlash of crown gear coupling is achieved. Taking a crown gear coupling as an example, the locations of minimum clearance between adjacent teeth and the minimum clearance distribution gathered by the proposed strategy are compared with the results obtained by Alfares' s method and finite element analysis. The results indicate that the tooth surfaces between adjacent teeth interfere with each other, amount of the minimum clearance design increases with the increasing misalignment angle, the position of the minimum clearance design is located in the pure tilted area, and the accuracy is much higher than that from Alfares.
To make crown gear coupling work properly under the limit misalignment angle, a quick and accurate strategy for the backlash amount is proposed. The hub tooth surface is generated by continuous modification for tooth profile along the tooth width direction, and the sleeve tooth surface is processed by a shaping cutter. Then the assembling relationship of the crown gear coupling under misalignment angle is established by the spatial coordinate transform three-dimensional finite element analysis model is thus established. Following tooth contact analysis, the clearance between adjacent teeth of hub and sleeve without considering backlash is determined and the formula for the minimum circumferential backlash of crown gear coupling is achieved. Taking a crown gear coupling as an example, the locations of minimum clearance between adjacent teeth and the minimum clearance distribution gathered by the proposed strategy are compared with the results obtained by Alfares' s method and finite element analysis. The results indicate that the tooth surfaces between adjacent teeth interfere with each other, amount of the minimum clearance design increases with the increasing misalignment angle, the position of the minimum clearance design is located in the pure tilted area, and the accuracy is much higher than that from Alfares.
引文
[1] LOCKE S R,CORCORAN J P,THORP J,et al.Coupling credible failure modes and owner options to intervene [C]//Proceedings of 42nd Turbomachinery Symposium.College Station,TX,USA:Turbomachinery Laboratory,2013:1-30.
[2] GUO Y,LAMBERT S,WALLEN R,et al.Theoretical and experimental study on gear-coupling contact and loads considering misalignment,torque,and friction influences [J].Mechanism and Machine Theory,2016,98(8):242-262.
[3] 彭艳,孙建亮,张阳,等.板带轧机稳定运行动力学模型体系及其工业应用 [M].北京:机械工业出版社,2018:143-170.
[4] NAKASHIMA K.Teeth contact behavior and load distribution of gear coupling [J].Transactions of the Japan Society of Mechanical Engineers:Part C,1988,54(502):1302-1307.
[5] ALFARES M,FALAH A,ELKHOLY A.Clearance distribution of misaligned gear coupling teeth considering crowning and geometry variations [J].Mechanism and Machine Theory,2006,41(10):1258-1272.
[6] OHSHIMA F,HIRATA S,YOSHINO H.Study on tooth contact of gear couplings [J].Transactions of the Japan Society of Mechanical Engineers:Part C,2012,78(6):639-649.
[7] HAKOZAKI Y,SHIMACHI S.Equalization about the tooth bearing area for the shaft angle of gear coupling [J].Transactions of the Japan Society of Mechanical Engineers:Part C,2007,73(2):594-601.
[8] GUAN Y B,FANG Z D,YANG X H,et al.Tooth contact analysis of crown gear coupling with misalignment [J].Mechanism and Machine Theory,2018,126(8):295-311.
[9] 刘鹄然,楼易,刘全红.成形法加工鼓形齿轮 [J].中国重型装备,2008,25(2):20-24.LIU Huran,LOU Yi,LIU Quanhong.Crowned teeth gear machined by shaping method [J].Heavy Machinery Science and Technology,2008,25(2):20-24.
[10] 毛世民,孟平德,张瑞谦,等.鼓形齿联轴器成形法加工的参数优化及啮合性能 [J].机械科学与技术,1994,13(4):89-93.MAO Shimin,MENG Pingde,ZHANG Ruiqian,et al.Process parameter optimization meshing performance of crown gear coupling [J].Mechanical Science and Technology for Aerospace Engineering,1994,13(4):89-93.
[11] 彭福华,刘梅艳.鼓形齿轮联轴器齿面接触分析与试验 [J].吉林大学学报(工学版),1989,33(2):103-111.PENG Fuhua,LIU Meiyan.Analyses and experiments on tooth surface contact of crown gear coupling [J].Journal of Jilin University (Engineering and Technology Edition),1989,33(2):103-111.
[12] 彭福华,彭书志.鼓形齿轮齿面共轭滚切规律 [J].吉林大学学报(工学版),1992,36(4):82-87.PENG Fuhua,PENG Shuzhi.The rule of tooth surface of the crowned gear on conjugate hobbing [J].Journal of Jilin University (Engineering and Technology Edition),1992,36(4):82-87.
[13] 彭福华,彭书志.共轭滚切联轴器鼓形齿轮齿面的形成 [J].机械工程学报,1994,30(1):183-190.PENG Fuhua,PENG Shuzhi.Study on the form of the tooth surface of crowned gear on conjugate hobbing clutch [J].Journal of Mechanical Engineering,1994,30(1),183-190.
[14] 易传云,杨叔子,杨元山.非共轭齿面鼓形齿联轴器运动分析 [J].华中科技大学学报(自然科学版),1994,22(7):111-116.YI Chuanyun,YANG Shuzi,YANG Yuanshan.A kinematic analysis of non-conjugate crowned teeth coupling [J].Journal of Huazhong University of Science and Technology (Natural Science Edition),1994,22(7):111-116.
[15] YI Chuanyun.Analysis of the meshing of crown gear coupling [J].Journal of Shanghai University,2005,9(6):527-533.
[16] 易传云,孙国正,杨叔子,等.共轭齿面鼓形齿联轴器诱导法曲率和相对滑动系数分析 [J].武汉理工大学学报(交通科学与工程版),1997,39(2):117-123.YI Chuanyun,SUN Guozheng,YANG Shuzi,et al.On the inducing curvature and the relative sliding rate of conjugate crown gear coupling [J].Journal of Wuhan University of Technology (Transportation Science & Engineering),1997,39(2):117-123.
[17] 李月潭,张兰义.鼓形齿轮联轴器渐开线齿廓的理论分析 [J].吉林大学学报(工学版),1997,41(3):67-72.LI Yuetan,ZHANG Lanyi.Theoretical analysis on involute profile of drum tooth coupling [J].Journal of Jilin University (Engineering and Technology Edition),1997,41(3):67-72.
[18] 魏家麒,张开林,姚远.具有轴间倾角的鼓形齿联轴器啮合状态及受力分析 [J].机械传动,2015,39(9):1-6.WEI Jiaqi,ZHANG Kailin,YAO Yuan.Meshing state and force analysis of the crown gear coupling with inter-axial tilt angle [J].Journal of Mechanical Transmission,2015,39(9):1-6.
[2] GUO Y,LAMBERT S,WALLEN R,et al.Theoretical and experimental study on gear-coupling contact and loads considering misalignment,torque,and friction influences [J].Mechanism and Machine Theory,2016,98(8):242-262.
[3] 彭艳,孙建亮,张阳,等.板带轧机稳定运行动力学模型体系及其工业应用 [M].北京:机械工业出版社,2018:143-170.
[4] NAKASHIMA K.Teeth contact behavior and load distribution of gear coupling [J].Transactions of the Japan Society of Mechanical Engineers:Part C,1988,54(502):1302-1307.
[5] ALFARES M,FALAH A,ELKHOLY A.Clearance distribution of misaligned gear coupling teeth considering crowning and geometry variations [J].Mechanism and Machine Theory,2006,41(10):1258-1272.
[6] OHSHIMA F,HIRATA S,YOSHINO H.Study on tooth contact of gear couplings [J].Transactions of the Japan Society of Mechanical Engineers:Part C,2012,78(6):639-649.
[7] HAKOZAKI Y,SHIMACHI S.Equalization about the tooth bearing area for the shaft angle of gear coupling [J].Transactions of the Japan Society of Mechanical Engineers:Part C,2007,73(2):594-601.
[8] GUAN Y B,FANG Z D,YANG X H,et al.Tooth contact analysis of crown gear coupling with misalignment [J].Mechanism and Machine Theory,2018,126(8):295-311.
[9] 刘鹄然,楼易,刘全红.成形法加工鼓形齿轮 [J].中国重型装备,2008,25(2):20-24.LIU Huran,LOU Yi,LIU Quanhong.Crowned teeth gear machined by shaping method [J].Heavy Machinery Science and Technology,2008,25(2):20-24.
[10] 毛世民,孟平德,张瑞谦,等.鼓形齿联轴器成形法加工的参数优化及啮合性能 [J].机械科学与技术,1994,13(4):89-93.MAO Shimin,MENG Pingde,ZHANG Ruiqian,et al.Process parameter optimization meshing performance of crown gear coupling [J].Mechanical Science and Technology for Aerospace Engineering,1994,13(4):89-93.
[11] 彭福华,刘梅艳.鼓形齿轮联轴器齿面接触分析与试验 [J].吉林大学学报(工学版),1989,33(2):103-111.PENG Fuhua,LIU Meiyan.Analyses and experiments on tooth surface contact of crown gear coupling [J].Journal of Jilin University (Engineering and Technology Edition),1989,33(2):103-111.
[12] 彭福华,彭书志.鼓形齿轮齿面共轭滚切规律 [J].吉林大学学报(工学版),1992,36(4):82-87.PENG Fuhua,PENG Shuzhi.The rule of tooth surface of the crowned gear on conjugate hobbing [J].Journal of Jilin University (Engineering and Technology Edition),1992,36(4):82-87.
[13] 彭福华,彭书志.共轭滚切联轴器鼓形齿轮齿面的形成 [J].机械工程学报,1994,30(1):183-190.PENG Fuhua,PENG Shuzhi.Study on the form of the tooth surface of crowned gear on conjugate hobbing clutch [J].Journal of Mechanical Engineering,1994,30(1),183-190.
[14] 易传云,杨叔子,杨元山.非共轭齿面鼓形齿联轴器运动分析 [J].华中科技大学学报(自然科学版),1994,22(7):111-116.YI Chuanyun,YANG Shuzi,YANG Yuanshan.A kinematic analysis of non-conjugate crowned teeth coupling [J].Journal of Huazhong University of Science and Technology (Natural Science Edition),1994,22(7):111-116.
[15] YI Chuanyun.Analysis of the meshing of crown gear coupling [J].Journal of Shanghai University,2005,9(6):527-533.
[16] 易传云,孙国正,杨叔子,等.共轭齿面鼓形齿联轴器诱导法曲率和相对滑动系数分析 [J].武汉理工大学学报(交通科学与工程版),1997,39(2):117-123.YI Chuanyun,SUN Guozheng,YANG Shuzi,et al.On the inducing curvature and the relative sliding rate of conjugate crown gear coupling [J].Journal of Wuhan University of Technology (Transportation Science & Engineering),1997,39(2):117-123.
[17] 李月潭,张兰义.鼓形齿轮联轴器渐开线齿廓的理论分析 [J].吉林大学学报(工学版),1997,41(3):67-72.LI Yuetan,ZHANG Lanyi.Theoretical analysis on involute profile of drum tooth coupling [J].Journal of Jilin University (Engineering and Technology Edition),1997,41(3):67-72.
[18] 魏家麒,张开林,姚远.具有轴间倾角的鼓形齿联轴器啮合状态及受力分析 [J].机械传动,2015,39(9):1-6.WEI Jiaqi,ZHANG Kailin,YAO Yuan.Meshing state and force analysis of the crown gear coupling with inter-axial tilt angle [J].Journal of Mechanical Transmission,2015,39(9):1-6.