渐开线圆柱齿轮接触分析和修形设计
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摘要
渐开线圆柱齿轮被广泛地应用在制造业、矿山、冶金等各个行业领域。其轮齿的接触状态对齿轮的啮合和动力学性能影响很大,因此研究渐开线圆柱齿轮的静态和动态接触性能有着重要意义。
根据渐开线圆柱齿轮的齿廓方程表达式,推导计算了各轮齿参数,同时建立了齿轮的参数化模型。考虑了重合度和摩擦系数的变化的影响,应用ANSYS有限元分析软件分析了齿轮的静态接触应力分布的情况。与传统的赫兹公式相对照,结果相当准确。
利用APDL的程序语言组织ANSYS的有限元分析命令,实现了施加参数化载荷、参数化求解以及参数化后处理结果的显示。有限元分析的全过程都实现了参数化,这是ANSYS批处理分析的最高技术。在参数化的分析过程中可以简单的修改其中的参数达到反复分析各种尺寸、不同载荷大小的目的,从而极大的提高分析效率,减少分析成本。
基于显式动力分析有限元软件ANSYS/LS-DYNA,建立了渐开线圆柱齿轮的动态分析模型,并得出随时间变化的齿轮动态接触应力分布。相对于静态接触分析而言,动态接触分析的结果更直观,实时性更强。
基于啮合原理和坐标变换理论,求解出误差状态下的齿轮啮合位置。并在此基础上,详细分析了误差状态下的齿轮接触应力分布情况。分析表明,考虑了中心误差和齿轮轴偏心误差状态下的齿轮静、动态接触应力分析结果更符合实际情况。
基于齿轮修形的基本原理,引入ANSYS有限元分析软件,进行含误差的渐开线圆柱齿轮齿轮的齿廓修形研究,得出不同修形量下的啮合线上接触应力分布和啮合线变形情况,可据此确定渐开线圆柱齿轮的最佳修形量。
The involutes gear is used in many industries such as the manufacturing, mining, and metallurgy. The contact state of gear teeth seriously affects the mesh between gears and dynamics capability, so it is very important to study the static and dynamic contact performance of the involutes gear.
Based on the equation of tooth outlines, gear tooth parameters are computed, and a parameter modeling method in ANSYS software is also proposed. Changed with contact ratio and friction parameter, the static contact stress distributing of involutes gears is discussed in details. Compared with the Hertz method, the result is perfectly accurate.
The parametric loadings, solutions and displays of post-treatment are implemented by using FEM commands of ANSYS which are managed by the APDL program language. All the procedures of analysis are parameterized, which is the most advanced technique of batch. During the whole process, repeatedly analyzing different dimensions and loads can be conveniently realized by modifying parameters, which is more efficiently and economically.
Based on the explicit dynamical program ANSYS/LS-DYNA, the dynamic contact analysis model of gears is built. The changed tooth contact stress along with the contact time is obtained. The result of the dynamic contact analysis is more obvious than the static contact analysis.
According to the meshing theory and coordinate transformation, the responds of meshing point on the condition of error meshing is obtained. Based on the above analysis results, the contact stress distributing characteristics in fixing error and manufacture error is discussed in details. And it shows that the result is perfectly coincident with the fact of involutes gear contact.
Furthermore, formula is provided for determining the profile modification parameters of meshing teeth for spur gears with manufacturing error. Corresponding method for determining the parameters is also proposed. After analyzing the contact stress trend and the meshing line deformation by using the finite element program ANSYS/LS-DYNA, it is obviously that the contact status of gears can be improved.
根据渐开线圆柱齿轮的齿廓方程表达式,推导计算了各轮齿参数,同时建立了齿轮的参数化模型。考虑了重合度和摩擦系数的变化的影响,应用ANSYS有限元分析软件分析了齿轮的静态接触应力分布的情况。与传统的赫兹公式相对照,结果相当准确。
利用APDL的程序语言组织ANSYS的有限元分析命令,实现了施加参数化载荷、参数化求解以及参数化后处理结果的显示。有限元分析的全过程都实现了参数化,这是ANSYS批处理分析的最高技术。在参数化的分析过程中可以简单的修改其中的参数达到反复分析各种尺寸、不同载荷大小的目的,从而极大的提高分析效率,减少分析成本。
基于显式动力分析有限元软件ANSYS/LS-DYNA,建立了渐开线圆柱齿轮的动态分析模型,并得出随时间变化的齿轮动态接触应力分布。相对于静态接触分析而言,动态接触分析的结果更直观,实时性更强。
基于啮合原理和坐标变换理论,求解出误差状态下的齿轮啮合位置。并在此基础上,详细分析了误差状态下的齿轮接触应力分布情况。分析表明,考虑了中心误差和齿轮轴偏心误差状态下的齿轮静、动态接触应力分析结果更符合实际情况。
基于齿轮修形的基本原理,引入ANSYS有限元分析软件,进行含误差的渐开线圆柱齿轮齿轮的齿廓修形研究,得出不同修形量下的啮合线上接触应力分布和啮合线变形情况,可据此确定渐开线圆柱齿轮的最佳修形量。
The involutes gear is used in many industries such as the manufacturing, mining, and metallurgy. The contact state of gear teeth seriously affects the mesh between gears and dynamics capability, so it is very important to study the static and dynamic contact performance of the involutes gear.
Based on the equation of tooth outlines, gear tooth parameters are computed, and a parameter modeling method in ANSYS software is also proposed. Changed with contact ratio and friction parameter, the static contact stress distributing of involutes gears is discussed in details. Compared with the Hertz method, the result is perfectly accurate.
The parametric loadings, solutions and displays of post-treatment are implemented by using FEM commands of ANSYS which are managed by the APDL program language. All the procedures of analysis are parameterized, which is the most advanced technique of batch. During the whole process, repeatedly analyzing different dimensions and loads can be conveniently realized by modifying parameters, which is more efficiently and economically.
Based on the explicit dynamical program ANSYS/LS-DYNA, the dynamic contact analysis model of gears is built. The changed tooth contact stress along with the contact time is obtained. The result of the dynamic contact analysis is more obvious than the static contact analysis.
According to the meshing theory and coordinate transformation, the responds of meshing point on the condition of error meshing is obtained. Based on the above analysis results, the contact stress distributing characteristics in fixing error and manufacture error is discussed in details. And it shows that the result is perfectly coincident with the fact of involutes gear contact.
Furthermore, formula is provided for determining the profile modification parameters of meshing teeth for spur gears with manufacturing error. Corresponding method for determining the parameters is also proposed. After analyzing the contact stress trend and the meshing line deformation by using the finite element program ANSYS/LS-DYNA, it is obviously that the contact status of gears can be improved.
引文
[1]Johnson K L.接触力学[M].徐秉业等译,高等教育出版社,1992.
[2]王勖成,邵敏.有限单元法基本原理和数值方法(第二版)[M].清华大学出版社,1997.
[3]李润方,王建军.齿轮系统动力学[M].北京:科学出版社,1997
[4]Buekinghanm E.Analytical mechanics of gears[M].Dover Publications,1949:312-320.
[5]Duldey D W.Gear handbook[M].McGraw-Hill Book Co.,1962.
[6]Duldey D W.Gear technology-past,present and future.Prodeedings of international conference on gearing.Zheng Zhou,1988.
[7]Coy J J,Townsend D P,Zaretsky V.Gearing[M].NASA-RP-1152,1985.
[8]林朝桧,李云堂,高居胜,林薇.齿轮强度计算简史[C].中国第二届机械史学术会议论文,1991.
[9]潘升材,郭学谦.齿轮强度计算简史初探及其在机械课程中教学的建议[C].第五届全国机械设计及其制造专业教学言探会议论文集.机械工业出版社,1995:105-110.
[10]日本机械学会《齿轮强度设计资料》出版分科会.齿轮强度设计资料.李茹贞,赵请惠译.机械工业出版社,1984.
[11]孙桓,陈作模主编.机械原理[M].高等教育出版社,1995.
[12]杨永才,倪忠仁等.机械设计新标准应用手册[M].北京科学技术出版社,1993:556-584.
[13]国际齿轮装置与传动会议文选.洛阳矿上机械研究所,1997.
[14]成万植.有限元分析在常规强度计算工作中的地位和作用.飞机设计[J].2002,(4):19-22.
[15]杨生华.有限元法在计算根应力和轮齿变形中的应用,煤矿机电[J],1998(6):8-10.
[16]王统.有限元对齿根部位应力分布形状的研究.上海交通大学学报[J],1981(1):17-37.
[17]王建明,刘才山,周学军.内、外啮合斜齿轮三维接触应力有限元分析.机械传动[J],1998,22(3):15-18.
[18]刘更,吴立言.内啮合齿轮的三维接触应力分析.计算结构力学及其应用[J],1994,11(1):63-67.
[19]夏延秋,丁津原,马先贵.摩擦系数对齿轮接触疲劳寿命的影响.机械传动[J], 2002,26(1):48-50.
[20]高创宽,周谋.齿面摩擦力对齿轮接触应力的影响.机械强度[J],2003,25(6):642-645.
[21]乐晓斌,胡宗武,范祖尧.渐开线齿轮接触疲劳可靠度计算.起重运输机械[J],1994,12(1):7-13.
[22]Oswald F B,Townsend D P.Tooth modification and spur gear tooth strain.Gear Technology[J],1996,13(5):1124-1129.
[23]Lin H H,Oswald F B,Townsend D P,Dynamic loading of spur gears with linear or parabolic tooth profile modifications.Mechanism&Theory[J].1994,29(8):1678-1687.
[24]Yoshino H,Muta Y,Studies on 3-D tooth surface modification of helical gears.Transactions of the Japan Society of Mechanical Engineers.Part C[C],1996,62(2):595-598.
[25]Hoyashita S,Calculation method for profile of helical gear with tooth-trace modification finished by worm-shaped tool or form grinding wheel,Transactions of the Japan Society of Mechanical Engineers,Part c[C],1995,61:593-595.
[26]杨连文,郑殿忠,徐中耀,王志兆.齿轮的电化学修形工艺研究.机械传动[J],1993,17(4):37-40.
[27]张敬武,韩维亮.从国家监督抽查看我国汽车齿轮工业的质量水平及其发展.机械传动[J],1995,19(1):41-44.
[28]张永忠,王洪.关于修形齿轮的试验.齿轮[J],1985,13(3):35-39.
[29]刘德昭.汽车变速器齿轮的齿形修整.传动技术[J],1993,13(5):27-33.
[30]陈超常.汽车齿轮精度与检查简说.传动技术[J],1995,15(1):40-42.
[31]张瑞乾,毛世民,吴序堂.用靠模滚切加上鼓形齿轮的新方法.机械传动[J],1996,20(2):35-39.
[32]王能员,齿向修形CAD/CAM闭环系统的理论分析.农业机械学报[J],1995,26(3):27-31.
[33]Hild P,Laborde P.Quadratic finite element methods for unilateral contact problems.Applied Numerical Mathematics[J],2002,41(1):401-421.
[34]李皓月,周田朋,刘相新.ANSYS工程计算应用教程[M].中国铁道出版社,2003.
[35]王庆五,左肪,胡仁喜等.ANSYS10.0机械设计高级应用实例(第二版)[M].机械工业出版社,2006.
[36]廖伯瑜,周新民,尹志宏.现代机械动力学及其工程应用[M].机械工业出版社,2004.
[37]Kahrman A,Singh R.Non-Linear Dynamics of a Geared Rotor-Bearing System with Multiple Clearances.Journal of Sound and Vibration[J],1991,144(3):1124-1131.
[38]Ping H,Lin H,Hsi L etc.Using DynamicAnalysis for Compact Gear Design.ASME Journal of Mechanical design[J],2003,124(1):245-253.
[39]Yuping C,Teik C L,Dynamics of Hypoid Gear Transmission With Nonlinear Time-Varying Mesh Charactexistics,ASME Journal of Mechanical design[J],2003,125(2):756-763.
[40]Litvin F L,Zhang Y,Wang J C.Design and geometry of face-gear drive.Transaction.ASME Journal of Mechanical Design[J],1992,114(2):642-647.
[41]李裕春,时党勇,赵远.ANSYS10.0/LS-DYNA基础理论与工程实践[M],中国水利水电出版社,2006.
[42]Livemore Software Technology Corporation.1998.LS-DYNA Theoretical Manual
[43]Livemore Software Technology Corporation.2001.LS-DYNA Keyword User's Manual.
[44]刘建,吴序堂.齿轮啮合原理[M].机械工业出版社,1987.
[45]董学朱.齿轮啮合理论基础[M].机械工业出版社,1989.
[46]上海高校互换性与测量技术研究会编写组.机械精度设计基础与质量保证(修订本)[M].上海科学技术文献出版社,2002.
[47]高建平,方宗德,杨洪斌.具有时变刚度、传动误差及间隙的齿轮传动系统动力学分析.航空学报[J],1999,20(5):440-444.
[48]齐宝玲.几何精度设计与检测基础[M].北京理工大学出版社,1999.
[49]仙波正庄.高强度齿轮设计[M].北京:机械工业出版社,1981.
[50]孙月海,张策,葛楠.含误差的直齿轮的齿廓修形.机械工程学报[J],2003,39(12):91-94.
[51]庞振基,黄其圣.精密机械设计[M].机械工业出版社,2004.
[2]王勖成,邵敏.有限单元法基本原理和数值方法(第二版)[M].清华大学出版社,1997.
[3]李润方,王建军.齿轮系统动力学[M].北京:科学出版社,1997
[4]Buekinghanm E.Analytical mechanics of gears[M].Dover Publications,1949:312-320.
[5]Duldey D W.Gear handbook[M].McGraw-Hill Book Co.,1962.
[6]Duldey D W.Gear technology-past,present and future.Prodeedings of international conference on gearing.Zheng Zhou,1988.
[7]Coy J J,Townsend D P,Zaretsky V.Gearing[M].NASA-RP-1152,1985.
[8]林朝桧,李云堂,高居胜,林薇.齿轮强度计算简史[C].中国第二届机械史学术会议论文,1991.
[9]潘升材,郭学谦.齿轮强度计算简史初探及其在机械课程中教学的建议[C].第五届全国机械设计及其制造专业教学言探会议论文集.机械工业出版社,1995:105-110.
[10]日本机械学会《齿轮强度设计资料》出版分科会.齿轮强度设计资料.李茹贞,赵请惠译.机械工业出版社,1984.
[11]孙桓,陈作模主编.机械原理[M].高等教育出版社,1995.
[12]杨永才,倪忠仁等.机械设计新标准应用手册[M].北京科学技术出版社,1993:556-584.
[13]国际齿轮装置与传动会议文选.洛阳矿上机械研究所,1997.
[14]成万植.有限元分析在常规强度计算工作中的地位和作用.飞机设计[J].2002,(4):19-22.
[15]杨生华.有限元法在计算根应力和轮齿变形中的应用,煤矿机电[J],1998(6):8-10.
[16]王统.有限元对齿根部位应力分布形状的研究.上海交通大学学报[J],1981(1):17-37.
[17]王建明,刘才山,周学军.内、外啮合斜齿轮三维接触应力有限元分析.机械传动[J],1998,22(3):15-18.
[18]刘更,吴立言.内啮合齿轮的三维接触应力分析.计算结构力学及其应用[J],1994,11(1):63-67.
[19]夏延秋,丁津原,马先贵.摩擦系数对齿轮接触疲劳寿命的影响.机械传动[J], 2002,26(1):48-50.
[20]高创宽,周谋.齿面摩擦力对齿轮接触应力的影响.机械强度[J],2003,25(6):642-645.
[21]乐晓斌,胡宗武,范祖尧.渐开线齿轮接触疲劳可靠度计算.起重运输机械[J],1994,12(1):7-13.
[22]Oswald F B,Townsend D P.Tooth modification and spur gear tooth strain.Gear Technology[J],1996,13(5):1124-1129.
[23]Lin H H,Oswald F B,Townsend D P,Dynamic loading of spur gears with linear or parabolic tooth profile modifications.Mechanism&Theory[J].1994,29(8):1678-1687.
[24]Yoshino H,Muta Y,Studies on 3-D tooth surface modification of helical gears.Transactions of the Japan Society of Mechanical Engineers.Part C[C],1996,62(2):595-598.
[25]Hoyashita S,Calculation method for profile of helical gear with tooth-trace modification finished by worm-shaped tool or form grinding wheel,Transactions of the Japan Society of Mechanical Engineers,Part c[C],1995,61:593-595.
[26]杨连文,郑殿忠,徐中耀,王志兆.齿轮的电化学修形工艺研究.机械传动[J],1993,17(4):37-40.
[27]张敬武,韩维亮.从国家监督抽查看我国汽车齿轮工业的质量水平及其发展.机械传动[J],1995,19(1):41-44.
[28]张永忠,王洪.关于修形齿轮的试验.齿轮[J],1985,13(3):35-39.
[29]刘德昭.汽车变速器齿轮的齿形修整.传动技术[J],1993,13(5):27-33.
[30]陈超常.汽车齿轮精度与检查简说.传动技术[J],1995,15(1):40-42.
[31]张瑞乾,毛世民,吴序堂.用靠模滚切加上鼓形齿轮的新方法.机械传动[J],1996,20(2):35-39.
[32]王能员,齿向修形CAD/CAM闭环系统的理论分析.农业机械学报[J],1995,26(3):27-31.
[33]Hild P,Laborde P.Quadratic finite element methods for unilateral contact problems.Applied Numerical Mathematics[J],2002,41(1):401-421.
[34]李皓月,周田朋,刘相新.ANSYS工程计算应用教程[M].中国铁道出版社,2003.
[35]王庆五,左肪,胡仁喜等.ANSYS10.0机械设计高级应用实例(第二版)[M].机械工业出版社,2006.
[36]廖伯瑜,周新民,尹志宏.现代机械动力学及其工程应用[M].机械工业出版社,2004.
[37]Kahrman A,Singh R.Non-Linear Dynamics of a Geared Rotor-Bearing System with Multiple Clearances.Journal of Sound and Vibration[J],1991,144(3):1124-1131.
[38]Ping H,Lin H,Hsi L etc.Using DynamicAnalysis for Compact Gear Design.ASME Journal of Mechanical design[J],2003,124(1):245-253.
[39]Yuping C,Teik C L,Dynamics of Hypoid Gear Transmission With Nonlinear Time-Varying Mesh Charactexistics,ASME Journal of Mechanical design[J],2003,125(2):756-763.
[40]Litvin F L,Zhang Y,Wang J C.Design and geometry of face-gear drive.Transaction.ASME Journal of Mechanical Design[J],1992,114(2):642-647.
[41]李裕春,时党勇,赵远.ANSYS10.0/LS-DYNA基础理论与工程实践[M],中国水利水电出版社,2006.
[42]Livemore Software Technology Corporation.1998.LS-DYNA Theoretical Manual
[43]Livemore Software Technology Corporation.2001.LS-DYNA Keyword User's Manual.
[44]刘建,吴序堂.齿轮啮合原理[M].机械工业出版社,1987.
[45]董学朱.齿轮啮合理论基础[M].机械工业出版社,1989.
[46]上海高校互换性与测量技术研究会编写组.机械精度设计基础与质量保证(修订本)[M].上海科学技术文献出版社,2002.
[47]高建平,方宗德,杨洪斌.具有时变刚度、传动误差及间隙的齿轮传动系统动力学分析.航空学报[J],1999,20(5):440-444.
[48]齐宝玲.几何精度设计与检测基础[M].北京理工大学出版社,1999.
[49]仙波正庄.高强度齿轮设计[M].北京:机械工业出版社,1981.
[50]孙月海,张策,葛楠.含误差的直齿轮的齿廓修形.机械工程学报[J],2003,39(12):91-94.
[51]庞振基,黄其圣.精密机械设计[M].机械工业出版社,2004.