基于ANSYS的直齿轮接触问题的齿向形状优化研究
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摘要
齿轮传动由于受制造和安装误差、齿轮弹性变形及热变形等因素的影响,在啮合过程中不可避免地会产生冲击、振动和偏载,从而导致齿轮早期失效的概率增大。如果对轮齿齿向作适当的修形,对改善其运转性能、提高其承载能力、延长其使用寿命有着明显的效果。因此利用先进的计算分析软件——ANSYS对轮齿的齿向修形进行研究具有特别重要的意义。本文利用有限元方法,就直齿圆柱齿轮的修形参数对轮齿啮合过程中接触线上载荷分布的影响进行了认真深入的分析,建立了一种寻求最优齿向修形参数以获得合理齿向形状使齿向载荷分布均匀的方法。
本文利用ANSYS有限元软件,建立直齿圆柱齿轮三维参数化有限元模型。整个三维模型通过APDL自动生成,实现了有限元分析模型的参数化,可以快捷方便地对不同修形参数的齿向形状进行有限元计算和分析。
对直齿圆柱齿轮接触线上的应力分析表明,接触应力沿接触线方向分布不均匀,且在接触母线的端点处存在较大的应力。为使在接触区内应力沿接触线方向分布较均匀,需改变不同的齿向形状参数,对齿向形状进行优化分析。
本文采用二次曲线作为鼓形齿的修形曲线,考虑鼓形量对曲线的约束,运用零阶优化算法,建立了修形齿轮的数学模型,对接触轮齿进行形状优化。优化结果显示:进行接触轮齿齿向方向的形状优化后,最大应力值减小并且应力分布比较均匀,大大提高了轮齿的接触强度,为工程设计提供了有力的依据。本文还采用文献[2]中的中央鼓形曲线对接触轮齿进行形状优化,其优化结果与二次修形曲线的优化结果进行比较。得出结论:采用二次曲线对轮齿进行优化的优化结果要略优于用中央鼓形曲线对轮齿进行优化的优化结果。从而验证了用二次曲线对轮齿进行优化的优越性。
Shock, vibration and offset load are generated unavoidably during gear transmission period due to the influence of manufacturing error and setting up error, elastic deformation of gear, hot deformation and so on, which lead to increase probability of early failure of gear. If shape of gear along gear trace were modified , transmission performance and bearing capacity would have been improved and service life would have been prolonged. Therefore, it is very important to study shape optimization of gear by means of modern computer analysis software—ANSYS. According to the effect of the parameters to the load distribution along the contact line of spur gear,this paper applies the finite element method(FEM) to analysis and study further,in order to establish a method of the correct shape along contact line by finding the optimum shape parameters.
In this paper, the three dimensional parameterized FEM model of spur gear is established by ANSYS. The three dimensional model is generated automatically by APDL, which accomplish the parameterized FEA model. It can be analyzed by FEM efficiently and conveniently on the shape along gear width of different shape parameters.
According to stress analysis of contact line, contact stress along contact line is not equally distributed, and the bigger stress concentration is produced on the two sides of the contact line. In order to distribute equally stress on the contact line, the shape parameters are changed and the shape of tooth trace is optimized.
Shape of contcact gear is optimized using zero-stepped method by adopting quadratic curve as shape-modified curve, considering restriction of the drum-shaped quantity to it and establishing the mathematical model .The result of optimization is displayed : the max stress value of contact line is decreased and stress value is equally distributed on contact line after optimization the shape of gear,which enhanced contact strength of gear and providing the evidence for engineering design .the paper also adopt the central drum-shaped curve of document [2] to optimize the shape. Compared with the optimization result of quadratic shape-modified curve, the optimization result of quadratic shape-modified curve is predominant in the stress distribution of contact line.
本文利用ANSYS有限元软件,建立直齿圆柱齿轮三维参数化有限元模型。整个三维模型通过APDL自动生成,实现了有限元分析模型的参数化,可以快捷方便地对不同修形参数的齿向形状进行有限元计算和分析。
对直齿圆柱齿轮接触线上的应力分析表明,接触应力沿接触线方向分布不均匀,且在接触母线的端点处存在较大的应力。为使在接触区内应力沿接触线方向分布较均匀,需改变不同的齿向形状参数,对齿向形状进行优化分析。
本文采用二次曲线作为鼓形齿的修形曲线,考虑鼓形量对曲线的约束,运用零阶优化算法,建立了修形齿轮的数学模型,对接触轮齿进行形状优化。优化结果显示:进行接触轮齿齿向方向的形状优化后,最大应力值减小并且应力分布比较均匀,大大提高了轮齿的接触强度,为工程设计提供了有力的依据。本文还采用文献[2]中的中央鼓形曲线对接触轮齿进行形状优化,其优化结果与二次修形曲线的优化结果进行比较。得出结论:采用二次曲线对轮齿进行优化的优化结果要略优于用中央鼓形曲线对轮齿进行优化的优化结果。从而验证了用二次曲线对轮齿进行优化的优越性。
Shock, vibration and offset load are generated unavoidably during gear transmission period due to the influence of manufacturing error and setting up error, elastic deformation of gear, hot deformation and so on, which lead to increase probability of early failure of gear. If shape of gear along gear trace were modified , transmission performance and bearing capacity would have been improved and service life would have been prolonged. Therefore, it is very important to study shape optimization of gear by means of modern computer analysis software—ANSYS. According to the effect of the parameters to the load distribution along the contact line of spur gear,this paper applies the finite element method(FEM) to analysis and study further,in order to establish a method of the correct shape along contact line by finding the optimum shape parameters.
In this paper, the three dimensional parameterized FEM model of spur gear is established by ANSYS. The three dimensional model is generated automatically by APDL, which accomplish the parameterized FEA model. It can be analyzed by FEM efficiently and conveniently on the shape along gear width of different shape parameters.
According to stress analysis of contact line, contact stress along contact line is not equally distributed, and the bigger stress concentration is produced on the two sides of the contact line. In order to distribute equally stress on the contact line, the shape parameters are changed and the shape of tooth trace is optimized.
Shape of contcact gear is optimized using zero-stepped method by adopting quadratic curve as shape-modified curve, considering restriction of the drum-shaped quantity to it and establishing the mathematical model .The result of optimization is displayed : the max stress value of contact line is decreased and stress value is equally distributed on contact line after optimization the shape of gear,which enhanced contact strength of gear and providing the evidence for engineering design .the paper also adopt the central drum-shaped curve of document [2] to optimize the shape. Compared with the optimization result of quadratic shape-modified curve, the optimization result of quadratic shape-modified curve is predominant in the stress distribution of contact line.
引文
[1]姚英姿,齿轮的精确建模及其接触应力有限元分析,现在机械,2004年第6期,16-17
[2]王丽彪,三维弹性接触问题形状优化及应用,[学位论文],太原理工大学,2001
[3]尉小霞,斜齿轮接触问题的形状优化研究,[学位论文],太原理工大学,2002年4月
[4]CruseT.A,Development on Boundary Element,J.Num.Math Comput.Appl,NO.1,1988
[5]Oguz Kayabasi,Shape optimization of tooth profile of a flexspline for a harmonic drive by finite element modelling,Materials & Design,Volume 28,Issue 2,2007,441-447
[6]程耿东,汪溜,连续体形状优化数值方法的若干改进,大连工学院学报,Vol.23,No.2,1986
[7]刘英卫,三维形状优化设计,计算结构力学及其应用,Vol.2,No.1,1985
[8]程耿东,汪溜,形状优化数值方法与自适应运动极限,计算结构力学及其应用,Vol.2,No.2,1985.8
[9]武凯,二维弹性接触问题的形状优化,[学位论文],太原理工大学,1999
[10]马新武,多型腔锻造过程预锻模形状优化设计,中国机械工程,2001年8月第12卷第8期,865-867
[11]王莉静,双圆弧齿轮的啮合特性及有限元分析,[学位论文],太原理工大学,2004
[12]崔海涛,轴对称有限元的结构形状优化分析,机械科学与技术,Vol.21第3期,2002年5月,376-379
[13]张静,双圆弧齿轮齿形参数的有限元分析与优化设计,[学位论文],太原理工大学,2002
[14]周到,基于接触的捞雷具夹紧爪接触面形状优化,海军工程大学学报,2006年6月,第18卷第三期,70-72
[15]关振群,离心式叶轮三维参数化形状优化设计方法,机械强度,2006,28(6):p833-838
[16]晏红文,一种新型弹性联轴节的形状优化设计,铁道车辆,第45卷第5期,2007年5月, 4-6
[17]刘旭,柔性机构尺寸与形状优化新方法及实现,微纳电子技术,2007年第7/8期,34-36
[18]钟佩思,基于AWE的自行车车架的CAE分析,人工智能与识别技术,p1710-1713
[19]张玉梅,双压力角非对称齿轮啮合特性及应力分析研究,[学位论文],南京航空航天大学,2005
[20]Shuting Li,Centrifugal load and its effects on bending strength and contact strength of a high speed thin-walled spur gear with offset web,Mechanism and Machine Theory
[21]Faydor L.Litvin,New version of Novikov-Wildhaber helical gears,computerized design,simulation of meshing and stress analysis,Computer Methods in Applied Mechanics and Engineering,Volume 191,Issues 49-50,6 December 2002,5707-5740
[22]Peter Groche,Application and modelling of flow forming manufacturing processes for internally geared wheels,International Journal of Machine Tools and Manufacture,Volume 46,Issue 11,September 2006,1261-1265
[23]Faydor L.Litvin,Reduction of noise of loaded and unloaded misaligned gear drives,Computer Methods in Applied Mechanics and Engineering,Volume 195,Issues 41-43,15August 2006,5523-5536
[24]Song He,Effect of sliding friction on the dynamics of spur gear pair with realistic timevarying stiffness,Journal of Sound and Vibration,Volume 301,Issues 3-5,3 April 2007,927-949
[25]Vijaya Kumar Ambarisha,Nonlinear dynamics of planetary gears using analytical and finite element models,Journal of Sound and Vibration,Volume 302,Issue 3,8 May 2007,577-595
[26]D.Mundo,Kinematic optimization of ball-screw transmission mechanisms,Mechanism and Machine Theory,Volume 42,Issue 1,January 2007,34-47
[27]Chien-Hsing Li,integration of finite element analysis and optimum design on gear systems,Finite Elements in Analysis and Design,38(2002)179-192
[28]屈文涛,沈允文,徐建宁,基于ANSYS的双圆弧齿轮接触应力有限元分析,农业机械学报,2006年10月,第37卷第10期
[29]陈秀宁编,机械优化设计[M],浙江:浙江大学出版社,1999
[30]王龙宝,齿轮刚度计算及其有限元分析,[学位论文],江苏大学,2007
[31]陈建辉,圆柱齿轮的三维参数化建模与应力分析,[学位论文],西北工业大学,2005
[32]周长江,齿轮应力与变形精确分析中的有限元建模研究,[学位论文],中南大学,2004年5月
[33]李金澎,大模数直齿轮轮齿弯曲强度与齿面接触研究,[学位论文],大连理工大学,2007年5月
[34]李建宜,齿轮扭转啮合刚度的研究,[学位论文],太原理工大学,2007
[35]孙桓,陈作模.机械原理,北京,高等教育出版社,2004
[36]吴继泽,王统.齿根过渡曲线与齿根应力,北京,国防工业出版社,1989
[37]东方人华,ANSYS7.0入门与提高,北京,清华大学出版社,2004
[38]雷镭,武宝林等,基于ANSYS有限元软件的直齿轮接触应力分析[J],机械传动,2006第3卷第2期,50-51
[39]刘洁,张和平,基于ANSYS参数化语言的机械结构优化设计[J],沈阳化工学院学报,2004(9)第18卷第3期,204-207
[40]李宏雁,ANSYS的设计优化理论及应用[J],一重技术,2003年第2期,24-26
[2]王丽彪,三维弹性接触问题形状优化及应用,[学位论文],太原理工大学,2001
[3]尉小霞,斜齿轮接触问题的形状优化研究,[学位论文],太原理工大学,2002年4月
[4]CruseT.A,Development on Boundary Element,J.Num.Math Comput.Appl,NO.1,1988
[5]Oguz Kayabasi,Shape optimization of tooth profile of a flexspline for a harmonic drive by finite element modelling,Materials & Design,Volume 28,Issue 2,2007,441-447
[6]程耿东,汪溜,连续体形状优化数值方法的若干改进,大连工学院学报,Vol.23,No.2,1986
[7]刘英卫,三维形状优化设计,计算结构力学及其应用,Vol.2,No.1,1985
[8]程耿东,汪溜,形状优化数值方法与自适应运动极限,计算结构力学及其应用,Vol.2,No.2,1985.8
[9]武凯,二维弹性接触问题的形状优化,[学位论文],太原理工大学,1999
[10]马新武,多型腔锻造过程预锻模形状优化设计,中国机械工程,2001年8月第12卷第8期,865-867
[11]王莉静,双圆弧齿轮的啮合特性及有限元分析,[学位论文],太原理工大学,2004
[12]崔海涛,轴对称有限元的结构形状优化分析,机械科学与技术,Vol.21第3期,2002年5月,376-379
[13]张静,双圆弧齿轮齿形参数的有限元分析与优化设计,[学位论文],太原理工大学,2002
[14]周到,基于接触的捞雷具夹紧爪接触面形状优化,海军工程大学学报,2006年6月,第18卷第三期,70-72
[15]关振群,离心式叶轮三维参数化形状优化设计方法,机械强度,2006,28(6):p833-838
[16]晏红文,一种新型弹性联轴节的形状优化设计,铁道车辆,第45卷第5期,2007年5月, 4-6
[17]刘旭,柔性机构尺寸与形状优化新方法及实现,微纳电子技术,2007年第7/8期,34-36
[18]钟佩思,基于AWE的自行车车架的CAE分析,人工智能与识别技术,p1710-1713
[19]张玉梅,双压力角非对称齿轮啮合特性及应力分析研究,[学位论文],南京航空航天大学,2005
[20]Shuting Li,Centrifugal load and its effects on bending strength and contact strength of a high speed thin-walled spur gear with offset web,Mechanism and Machine Theory
[21]Faydor L.Litvin,New version of Novikov-Wildhaber helical gears,computerized design,simulation of meshing and stress analysis,Computer Methods in Applied Mechanics and Engineering,Volume 191,Issues 49-50,6 December 2002,5707-5740
[22]Peter Groche,Application and modelling of flow forming manufacturing processes for internally geared wheels,International Journal of Machine Tools and Manufacture,Volume 46,Issue 11,September 2006,1261-1265
[23]Faydor L.Litvin,Reduction of noise of loaded and unloaded misaligned gear drives,Computer Methods in Applied Mechanics and Engineering,Volume 195,Issues 41-43,15August 2006,5523-5536
[24]Song He,Effect of sliding friction on the dynamics of spur gear pair with realistic timevarying stiffness,Journal of Sound and Vibration,Volume 301,Issues 3-5,3 April 2007,927-949
[25]Vijaya Kumar Ambarisha,Nonlinear dynamics of planetary gears using analytical and finite element models,Journal of Sound and Vibration,Volume 302,Issue 3,8 May 2007,577-595
[26]D.Mundo,Kinematic optimization of ball-screw transmission mechanisms,Mechanism and Machine Theory,Volume 42,Issue 1,January 2007,34-47
[27]Chien-Hsing Li,integration of finite element analysis and optimum design on gear systems,Finite Elements in Analysis and Design,38(2002)179-192
[28]屈文涛,沈允文,徐建宁,基于ANSYS的双圆弧齿轮接触应力有限元分析,农业机械学报,2006年10月,第37卷第10期
[29]陈秀宁编,机械优化设计[M],浙江:浙江大学出版社,1999
[30]王龙宝,齿轮刚度计算及其有限元分析,[学位论文],江苏大学,2007
[31]陈建辉,圆柱齿轮的三维参数化建模与应力分析,[学位论文],西北工业大学,2005
[32]周长江,齿轮应力与变形精确分析中的有限元建模研究,[学位论文],中南大学,2004年5月
[33]李金澎,大模数直齿轮轮齿弯曲强度与齿面接触研究,[学位论文],大连理工大学,2007年5月
[34]李建宜,齿轮扭转啮合刚度的研究,[学位论文],太原理工大学,2007
[35]孙桓,陈作模.机械原理,北京,高等教育出版社,2004
[36]吴继泽,王统.齿根过渡曲线与齿根应力,北京,国防工业出版社,1989
[37]东方人华,ANSYS7.0入门与提高,北京,清华大学出版社,2004
[38]雷镭,武宝林等,基于ANSYS有限元软件的直齿轮接触应力分析[J],机械传动,2006第3卷第2期,50-51
[39]刘洁,张和平,基于ANSYS参数化语言的机械结构优化设计[J],沈阳化工学院学报,2004(9)第18卷第3期,204-207
[40]李宏雁,ANSYS的设计优化理论及应用[J],一重技术,2003年第2期,24-26