基于数字化齿面的弧齿锥齿轮柔性多体接触动力学分析
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摘要
基于弧齿锥齿轮局部综合法,计算弧齿齿面的精确空间数字化坐标点,建立了弧齿齿面的四边形面片有限元网格模型。基于弧齿齿面的四边形面片接触块模型,运用弧齿齿面的包围盒全域搜索方法和结点-目标面的主从面局部搜索方法,实现高精度数字化真实弧齿齿面的动态接触搜索计算。以四边形面片单元中心的外法向矢量来计算弧齿齿面的从结点到目标单元面的接触变形量,采用罚函数法计算弧齿齿面的动态接触作用力,提出了多柔性体、多界面动态接触的弧齿锥齿轮动力学分析方法。计算分析了弧齿锥齿轮的传动误差、动态接触力、等效约束力、弧齿边缘动态接触、最大应力值等动态接触特性。研究表明:忽略多柔性体、多界面动态接触特性,会低估弧齿齿轮的传动误差、动态接触力和等效约束力。新方法较好地模拟了弧齿锥齿轮传动动态接触特性,对弧齿锥齿轮系统动态设计提供了理论参考。
Based on spiral bevel gears' local synthesis method, gear tooth surface accurate spatial digital coordinates were calculated to build quad patch finite element grid model of spiral bevel gears. Based on gear tooth surface quad patch contact block model, dynamic contact searching calculation of high-precision digital actual gear tooth surfaces was realized using the global search method for bounding boxes and the local search method of node-target surface based on master and slave surface. The quad patch element center external normal vector was used to calculate gear tooth surface's contact deformation from node to target surface. The penalty function method was used to calculate dynamic contact force of gear tooth surfaces. The dynamic analysis method was proposed for spiral bevel gears with multi-flexible body and multi-interface dynamic contact to calculate and analyze spiral bevel gears' transmission errors, dynamic contact forces, equivalent constraint forces, tooth edge dynamic contact and maximum stresses. The results showed that spiral bevel gear transmission errors, dynamic contact forces, equivalent constraint forces may be underestimated if neglecting multi-flexible body and multi-interface dynamic contact features; the new method can be used to better simulate spiral bevel gear transmission's dynamic contact characteristics and provide a theoretical reference for dynamic design of spiral bevel gear transmission systems.
Based on spiral bevel gears' local synthesis method, gear tooth surface accurate spatial digital coordinates were calculated to build quad patch finite element grid model of spiral bevel gears. Based on gear tooth surface quad patch contact block model, dynamic contact searching calculation of high-precision digital actual gear tooth surfaces was realized using the global search method for bounding boxes and the local search method of node-target surface based on master and slave surface. The quad patch element center external normal vector was used to calculate gear tooth surface's contact deformation from node to target surface. The penalty function method was used to calculate dynamic contact force of gear tooth surfaces. The dynamic analysis method was proposed for spiral bevel gears with multi-flexible body and multi-interface dynamic contact to calculate and analyze spiral bevel gears' transmission errors, dynamic contact forces, equivalent constraint forces, tooth edge dynamic contact and maximum stresses. The results showed that spiral bevel gear transmission errors, dynamic contact forces, equivalent constraint forces may be underestimated if neglecting multi-flexible body and multi-interface dynamic contact features; the new method can be used to better simulate spiral bevel gear transmission's dynamic contact characteristics and provide a theoretical reference for dynamic design of spiral bevel gear transmission systems.
引文
[1] 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):1203-1206.WANG Zhonghou,ZHOU Xiaoling.Simulation methods and developments of dynamics for spiral bevel gear[J].China Mechanical Engineering,2006,17(11):1203-1206.
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[3] LITVIN F L,FTENTES A,HAYASAKA K.Design,mamufacture,stress analysis,and experimental tests of low noise high endurance spiral bevel gears[J].Mechanism and Maehinetheory,2006,41(1):83-118.
[4] LITVIN F L,FUENTES A,FAN Q,et al.Computerized design,simulation of meshing,and contact and stress analysis of face-milled formate generated spiral bevel gears[J].Mechanism & Machine Theory,2002,37(5):441-459.
[5] CHENG Y,LIM T C.Vibration analysis of hypoid transmissions applying an exact geometry-based gear mesh theory[J].Journal of Sound and Vibration,2001,240(3):519-543.
[6] ZHANG Y,LITVIN F L,MARYUAMA N,et al.Computerized analysis of meshing and contact of gear real tooth surfaces[J].J.Mech.Des,ASME,1994,116 (3):677-682.
[7] SHEVELEVA G I,VOLKOV A E,MEDYEDEV V I.Algorithms for analysis of meshing and contact of spiral bevel gear[J].Mechanism and Machine Theory,2007,42(2):198-215.
[8] 汪中厚,李刚,久保爱三.基于数字化真实齿面的螺旋锥齿轮齿面接触分析[J].机械工程学报,2015,50(15):1-11.WANG Zhonghou,LI Gang,KUBO Aizoh.Tooth contact analysis of spiral bevel gear Based on digital real tooth surfaces[J].Journal of Mechanical Engineering,2015,50(15):1-11.
[9] 唐进元,曹康,杜晋.含过渡曲面的弧齿锥齿轮齿面精确建模[J].机械科学与技术,2009,28(3):317-321.TANG Jinyuan,CAO Kang,DU Jin,et al.Accurate modeling of the tooth-surface of a spiral bevel gear with fillet[J].Mechanical Science and Technology,2009,28(3):317-321.
[10] 刘光磊,樊红卫.含齿根过渡曲面的弧齿锥齿轮有限元精确建模[J].机械科学与技术,2010,29(12):1595-1601.LIU Guanglei,FAN Hongwei.Precise finite element modeling of spiral bevel gears with fillet[J].Mechanical Science and Technology,2010,29(12):1595-1601.
[11] 郭伟超.某航空发动机中心轴弧齿锥齿轮传动系统的动力学特性研究[D].西安:西北工业大学,2006.
[12] 苏进展,方宗德,蔡香伟.弧齿锥齿轮数字化齿面啮合仿真分析与试验[J].西北工业大学,2012,30(4):565-569.SU Jinzhan,FANG Zongde,CAI Xiangwei.A useful computerized meshing analysis of numerical tooth surfaces for spiral bevel gears[J].Journal of Northwestern Polytechnical University,2012,30(4):565-569.
[13] 刘光磊,常凯.弧齿锥齿轮高精度离散数值齿面啮合分析[J].航空发动机,2013,39(2):19-24.LIU Guanglei,CHANG Kai.Discrete numerical tooth contact analysis of high precision for spiral bevel gears[J].Aeroengine,2013,39(2):19-24.
[14] LIN C H,FONG Z H.Numerical tooth contact analysis of a bevel gear set by using measured tooth geometry data[J].Mechanism and Machine Theory,2015,84:1-24.
[15] 张金良,方宗德,曹雪梅,等.弧齿锥齿轮齿面接触应力分析[J].机械科学与技术,2007,10(10):1268-1272.ZHANG Jinliang,FANG Zongde,CAO Xuemei,et al.Analysis of a spiral bevel gear’s tooth contact stress[J].Mechanical Science and Technology,2007,10(10):1268-1272.
[16] 唐进元,蒲太平.弧齿锥齿轮动态啮合有限元数值分析.机械科学与技术,2009,28(8):981-985.TANG Jinyuan,PU Taiping.FEM numerical analysis of the dynamic engagement of spiral bevel gears[J].Mechanical Science and Technology,2009,28(8):981-985.
[17] 唐进元,彭方进.惯性载荷对螺旋锥齿轮动态啮合特性的影响研究[J].振动与冲击,2011,30(3):161-164.TANG Jinyuan,PENG Fangjin.Influence of inertial load in dynamic meshing analysis of spiral bevel gears[J].Journal of Vibration and Shock,2011,30(3):161-164.
[18] 汪中厚,王杰,王巧玲,等.基于有限元法的螺旋锥齿轮传动误差研究[J].振动与冲击,2014,33(14):165-170.WANG Zhonghou,WANG Jie,WANG Qiaoling,et al.Transmission error of spiral bevel gear based on finite element method[J].Journal of Vibration and Shock,2014,33(14):165-170.
[19] 汪中厚,王杰,马鹏程,等.真实齿面的螺旋锥齿轮动传动误差研究[J].振动与冲击,2014,33(15):138-143.WANG Zhonghou,WANG Jie,MA Pengcheng,et al.Dynamic transmission error analysis of spiral bevel gears with actual tooth surfaces[J].Journal of Vibration and Shock,2014,33(15):138-143.
[20] 侯祥颖,方宗德,邓效忠.弧齿锥齿轮有限元建模与接触分析[J].哈尔滨工程大学学报,2015,36(6):826-829.HOU Xiangying,FANG Zongde,DENG Xiaozhong,et al.Contact analysis of spiral bevel gears based on finite element model[J].Journal of Harbin Engineering University,2015,36(6):826-829.
[21] 高建平,方宗德,杨宏斌.螺旋锥齿轮边缘接触分析[J].航空动力学报,1998,13(3):289-292.GAO Jianping,FANG Zongde,YANG Hongbin.Analysis of edge contact for hypoid gear and spiral bevel gears[J].Journal of Aerospace Power,1998,13(3):289-292.
[22] 方宗德,邓效忠,任东锋,等.考虑边缘接触的弧齿锥齿轮承载接触分析[J].机械工程学报,2002,38(9):69-72.FANG Zongde,DENG Xiaozhong,REN Dongfeng,et al.Loaded tooth contact analysis of spiral bevel gears considering edge contact[J].Journal of Mechanical Engineering,2002,38(9):69-72.
[23] 侯祥颖,方宗德.考虑边缘接触的弧齿锥齿轮有限元接触分析[J].西安交通大学学报,2016,50(11):69-74.HOU Xiangying,FANG Zongde.Tooth contact analysis of spiral bevel gears considering edge contact with finite element method[J].Journal of Xi’an Jiaotong University,2016,50(11):69-74.
[24] 姚廷强,王立华,谭阳.圆弧齿锥齿轮接触动力学分析[J].振动与冲击,2012,31(9):128-134.YAO Tingqiang,WANG Lihua,TAN Yang.Contact dynamics analysis of spiral bevel gear[J].Journal of Vibration and Shock,2012,31(9):128-134.
[25] SHABANA A A.Dynamics of multibody systems[M].Cambridge University Press,Third Edition,2005.
[26] ZHONG Z H.Finite element procedures for contact-impact problems[M].New York:Oxford University Press Inc.,1993.
[27] LING W C,STOLARSKIT H K.A contact algorithm for problems involving quadrilateral approximation of surfaces[J].Compurers & Structures,1997,63(5):963-975.
[2] LITVIN F L.Gear geometry and applied theory[M].New Jersey:Prentice Hall,second virsion,2004.
[3] LITVIN F L,FTENTES A,HAYASAKA K.Design,mamufacture,stress analysis,and experimental tests of low noise high endurance spiral bevel gears[J].Mechanism and Maehinetheory,2006,41(1):83-118.
[4] LITVIN F L,FUENTES A,FAN Q,et al.Computerized design,simulation of meshing,and contact and stress analysis of face-milled formate generated spiral bevel gears[J].Mechanism & Machine Theory,2002,37(5):441-459.
[5] CHENG Y,LIM T C.Vibration analysis of hypoid transmissions applying an exact geometry-based gear mesh theory[J].Journal of Sound and Vibration,2001,240(3):519-543.
[6] ZHANG Y,LITVIN F L,MARYUAMA N,et al.Computerized analysis of meshing and contact of gear real tooth surfaces[J].J.Mech.Des,ASME,1994,116 (3):677-682.
[7] SHEVELEVA G I,VOLKOV A E,MEDYEDEV V I.Algorithms for analysis of meshing and contact of spiral bevel gear[J].Mechanism and Machine Theory,2007,42(2):198-215.
[8] 汪中厚,李刚,久保爱三.基于数字化真实齿面的螺旋锥齿轮齿面接触分析[J].机械工程学报,2015,50(15):1-11.WANG Zhonghou,LI Gang,KUBO Aizoh.Tooth contact analysis of spiral bevel gear Based on digital real tooth surfaces[J].Journal of Mechanical Engineering,2015,50(15):1-11.
[9] 唐进元,曹康,杜晋.含过渡曲面的弧齿锥齿轮齿面精确建模[J].机械科学与技术,2009,28(3):317-321.TANG Jinyuan,CAO Kang,DU Jin,et al.Accurate modeling of the tooth-surface of a spiral bevel gear with fillet[J].Mechanical Science and Technology,2009,28(3):317-321.
[10] 刘光磊,樊红卫.含齿根过渡曲面的弧齿锥齿轮有限元精确建模[J].机械科学与技术,2010,29(12):1595-1601.LIU Guanglei,FAN Hongwei.Precise finite element modeling of spiral bevel gears with fillet[J].Mechanical Science and Technology,2010,29(12):1595-1601.
[11] 郭伟超.某航空发动机中心轴弧齿锥齿轮传动系统的动力学特性研究[D].西安:西北工业大学,2006.
[12] 苏进展,方宗德,蔡香伟.弧齿锥齿轮数字化齿面啮合仿真分析与试验[J].西北工业大学,2012,30(4):565-569.SU Jinzhan,FANG Zongde,CAI Xiangwei.A useful computerized meshing analysis of numerical tooth surfaces for spiral bevel gears[J].Journal of Northwestern Polytechnical University,2012,30(4):565-569.
[13] 刘光磊,常凯.弧齿锥齿轮高精度离散数值齿面啮合分析[J].航空发动机,2013,39(2):19-24.LIU Guanglei,CHANG Kai.Discrete numerical tooth contact analysis of high precision for spiral bevel gears[J].Aeroengine,2013,39(2):19-24.
[14] LIN C H,FONG Z H.Numerical tooth contact analysis of a bevel gear set by using measured tooth geometry data[J].Mechanism and Machine Theory,2015,84:1-24.
[15] 张金良,方宗德,曹雪梅,等.弧齿锥齿轮齿面接触应力分析[J].机械科学与技术,2007,10(10):1268-1272.ZHANG Jinliang,FANG Zongde,CAO Xuemei,et al.Analysis of a spiral bevel gear’s tooth contact stress[J].Mechanical Science and Technology,2007,10(10):1268-1272.
[16] 唐进元,蒲太平.弧齿锥齿轮动态啮合有限元数值分析.机械科学与技术,2009,28(8):981-985.TANG Jinyuan,PU Taiping.FEM numerical analysis of the dynamic engagement of spiral bevel gears[J].Mechanical Science and Technology,2009,28(8):981-985.
[17] 唐进元,彭方进.惯性载荷对螺旋锥齿轮动态啮合特性的影响研究[J].振动与冲击,2011,30(3):161-164.TANG Jinyuan,PENG Fangjin.Influence of inertial load in dynamic meshing analysis of spiral bevel gears[J].Journal of Vibration and Shock,2011,30(3):161-164.
[18] 汪中厚,王杰,王巧玲,等.基于有限元法的螺旋锥齿轮传动误差研究[J].振动与冲击,2014,33(14):165-170.WANG Zhonghou,WANG Jie,WANG Qiaoling,et al.Transmission error of spiral bevel gear based on finite element method[J].Journal of Vibration and Shock,2014,33(14):165-170.
[19] 汪中厚,王杰,马鹏程,等.真实齿面的螺旋锥齿轮动传动误差研究[J].振动与冲击,2014,33(15):138-143.WANG Zhonghou,WANG Jie,MA Pengcheng,et al.Dynamic transmission error analysis of spiral bevel gears with actual tooth surfaces[J].Journal of Vibration and Shock,2014,33(15):138-143.
[20] 侯祥颖,方宗德,邓效忠.弧齿锥齿轮有限元建模与接触分析[J].哈尔滨工程大学学报,2015,36(6):826-829.HOU Xiangying,FANG Zongde,DENG Xiaozhong,et al.Contact analysis of spiral bevel gears based on finite element model[J].Journal of Harbin Engineering University,2015,36(6):826-829.
[21] 高建平,方宗德,杨宏斌.螺旋锥齿轮边缘接触分析[J].航空动力学报,1998,13(3):289-292.GAO Jianping,FANG Zongde,YANG Hongbin.Analysis of edge contact for hypoid gear and spiral bevel gears[J].Journal of Aerospace Power,1998,13(3):289-292.
[22] 方宗德,邓效忠,任东锋,等.考虑边缘接触的弧齿锥齿轮承载接触分析[J].机械工程学报,2002,38(9):69-72.FANG Zongde,DENG Xiaozhong,REN Dongfeng,et al.Loaded tooth contact analysis of spiral bevel gears considering edge contact[J].Journal of Mechanical Engineering,2002,38(9):69-72.
[23] 侯祥颖,方宗德.考虑边缘接触的弧齿锥齿轮有限元接触分析[J].西安交通大学学报,2016,50(11):69-74.HOU Xiangying,FANG Zongde.Tooth contact analysis of spiral bevel gears considering edge contact with finite element method[J].Journal of Xi’an Jiaotong University,2016,50(11):69-74.
[24] 姚廷强,王立华,谭阳.圆弧齿锥齿轮接触动力学分析[J].振动与冲击,2012,31(9):128-134.YAO Tingqiang,WANG Lihua,TAN Yang.Contact dynamics analysis of spiral bevel gear[J].Journal of Vibration and Shock,2012,31(9):128-134.
[25] SHABANA A A.Dynamics of multibody systems[M].Cambridge University Press,Third Edition,2005.
[26] ZHONG Z H.Finite element procedures for contact-impact problems[M].New York:Oxford University Press Inc.,1993.
[27] LING W C,STOLARSKIT H K.A contact algorithm for problems involving quadrilateral approximation of surfaces[J].Compurers & Structures,1997,63(5):963-975.