点蚀和剥落对齿轮扭转啮合刚度影响的研究
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摘要
齿轮是机械传动中应用最为广泛的零件,也是最容易出现故障的零件。目前,动力传动齿轮装置正沿着小型化、高速化、标准化方向发展,这对于齿轮传动特性提出了更高的要求。而齿轮啮合传递误差是造成齿轮传动系统噪声和振动的主要原因,其中齿轮扭转啮合刚度的变化加剧了齿轮的传递误差,特别是在齿轮有缺陷的情况下,引起系统的噪音和振动更大。因此,研究齿轮的扭转啮合刚度,对于理解齿轮产生传动误差和系统噪音的原因以及齿轮故障诊断具有深刻的意义。
三维有限元接触模型的建立是正确进行有限元分析的重要前提。本文采用ANSYS的APDL命令参数化建模,选用自底向上建模方式,采用自由划分与映射划分相结合,实现无缺陷与有缺陷直齿3D接触齿轮的精确建模。
计算齿轮的扭转啮合刚度必须分析接触问题。在对齿轮模型进行三维接触分析时,必须对齿轮进行正确加载,边界的约束和载荷施加位置的正确与否关系到问题是否得到求解。
根据扭转啮合刚度定义,分别计算了无齿面缺陷和有齿面缺陷的齿轮模型的扭转啮合刚度,研究了点蚀和剥落对齿轮扭转啮合刚度的影响。本文主要完成了以下几个方面的工作:
1.回顾了最近几十年研究者所建立的不同目的的齿轮数学模型和有限元模型。
2.根据齿轮传动的几何参数完成了齿轮在ANSYS环境下的精确建模,建立了相互啮合齿轮的有限元接触模型,模拟齿轮传动状态。
3.利用赫兹公式对渐开线齿轮的齿面接触应力进行了解析计算,并与渐开线直齿轮的接触应力的有限元分析进行比较,为计算齿轮的扭转啮合刚度奠定了基础。
4.通过连续旋转齿轮,改变其接触位置,计算了两种运行状态下,不同接触位置上的扭转啮合刚度。
5.研究含有局部点蚀和剥落和无局部点蚀和剥落齿轮的扭转啮合刚度的特性,比较有点蚀和剥落和无点蚀和剥落齿轮的扭转啮合刚度变化情况,得出分析结论。
6.建立了16自由度的齿轮副非线性动力学模型,分析了齿轮扭转啮合刚度在齿轮故障诊断中的应用。
最后对全文进行了总结和对以后工作的展望。
The gear is the most widely applying part in mechanical drive, which is also pronest to fault. At present, the driving gearing is developing along miniaturized, high-speed, standardizing direction and high speed, heavy load, low noise and high reliability have been become modern gear development direction , which has brought forward higher request to gear drive characteristic property. The meshing transmission error of the gear is one of the main causes which creates noise and vibration of the gear power transmission system. The change of the gear torsional mesh stiffness intensifies the gear transmission error, specially when the gear included the flaw, in the situation its torsional mesh stiffness to reduce, therefore caused the noise and the vibration of the system is bigger. Studying the torsional mesh stiffness of the gear has a more profound significance, to understand the causes of the transmission error of the gear and the noise of the system and diagnose the gear fault.
It is the important prerequisite to establish 3-D finite element model for the right finite element analysis. In this paper, using the APDL commands of ANSYS, using the bottom-up modeling way and using mapping and freedom of integration established the 3-D with/without defective accuracy model.
Calculated the gear torsional mesh stiffness must analyze the contact question. This paper presents the contact question study on several issues of methods and its range of application, which is very important significance to analyze the gear contact stress. The gear must be carried out the correct loading during the period of analyzing the 3D gear contact model. It has key effects on correct solution whether boundary conditions and loading location are correct.
According to the definition of torsional mesh stiffness, the 3D contact models for defect-free and defective gear transmission were set up respectively, for researching the effect of pitting and spalling on the torsional stiffness of gear. The major work is summarized as follows:
1. This article review mathematical and finite element gear models for different application purposes which researchers had established in recent decades.
2. In accordance with the geometric parameters of the gear transmission, Completed accurate modeling in ANSYS environment for simulating gear transmission state.
3. Calculated the involute gear contact stress by the classical contact theory of Hertz's, and compared with the result by the use of Finite Element Method, which laid the foundation for calculating the gear torsional mesh stiffness
4. Through continuous circumvolving the gears, and changing their contact position, established the stiffness relations of the two contact faces, calculated the torsional mesh stiffness of the gears in different moments.
5. The main research included the torsional mesh stiffness characteristic of the with-pitting and the without-pitting gear, compared the change of the punishment function and the torsional mesh stiffness of the with-pitting and the without-pitting gear.
6. Establishing a 16-DOF gear nonlinear dynamic model, and analyzed the torsional mesh stiffness application in the gear failure diagnosis.
The last part is a summary of this dissertation and prospect of this research
三维有限元接触模型的建立是正确进行有限元分析的重要前提。本文采用ANSYS的APDL命令参数化建模,选用自底向上建模方式,采用自由划分与映射划分相结合,实现无缺陷与有缺陷直齿3D接触齿轮的精确建模。
计算齿轮的扭转啮合刚度必须分析接触问题。在对齿轮模型进行三维接触分析时,必须对齿轮进行正确加载,边界的约束和载荷施加位置的正确与否关系到问题是否得到求解。
根据扭转啮合刚度定义,分别计算了无齿面缺陷和有齿面缺陷的齿轮模型的扭转啮合刚度,研究了点蚀和剥落对齿轮扭转啮合刚度的影响。本文主要完成了以下几个方面的工作:
1.回顾了最近几十年研究者所建立的不同目的的齿轮数学模型和有限元模型。
2.根据齿轮传动的几何参数完成了齿轮在ANSYS环境下的精确建模,建立了相互啮合齿轮的有限元接触模型,模拟齿轮传动状态。
3.利用赫兹公式对渐开线齿轮的齿面接触应力进行了解析计算,并与渐开线直齿轮的接触应力的有限元分析进行比较,为计算齿轮的扭转啮合刚度奠定了基础。
4.通过连续旋转齿轮,改变其接触位置,计算了两种运行状态下,不同接触位置上的扭转啮合刚度。
5.研究含有局部点蚀和剥落和无局部点蚀和剥落齿轮的扭转啮合刚度的特性,比较有点蚀和剥落和无点蚀和剥落齿轮的扭转啮合刚度变化情况,得出分析结论。
6.建立了16自由度的齿轮副非线性动力学模型,分析了齿轮扭转啮合刚度在齿轮故障诊断中的应用。
最后对全文进行了总结和对以后工作的展望。
The gear is the most widely applying part in mechanical drive, which is also pronest to fault. At present, the driving gearing is developing along miniaturized, high-speed, standardizing direction and high speed, heavy load, low noise and high reliability have been become modern gear development direction , which has brought forward higher request to gear drive characteristic property. The meshing transmission error of the gear is one of the main causes which creates noise and vibration of the gear power transmission system. The change of the gear torsional mesh stiffness intensifies the gear transmission error, specially when the gear included the flaw, in the situation its torsional mesh stiffness to reduce, therefore caused the noise and the vibration of the system is bigger. Studying the torsional mesh stiffness of the gear has a more profound significance, to understand the causes of the transmission error of the gear and the noise of the system and diagnose the gear fault.
It is the important prerequisite to establish 3-D finite element model for the right finite element analysis. In this paper, using the APDL commands of ANSYS, using the bottom-up modeling way and using mapping and freedom of integration established the 3-D with/without defective accuracy model.
Calculated the gear torsional mesh stiffness must analyze the contact question. This paper presents the contact question study on several issues of methods and its range of application, which is very important significance to analyze the gear contact stress. The gear must be carried out the correct loading during the period of analyzing the 3D gear contact model. It has key effects on correct solution whether boundary conditions and loading location are correct.
According to the definition of torsional mesh stiffness, the 3D contact models for defect-free and defective gear transmission were set up respectively, for researching the effect of pitting and spalling on the torsional stiffness of gear. The major work is summarized as follows:
1. This article review mathematical and finite element gear models for different application purposes which researchers had established in recent decades.
2. In accordance with the geometric parameters of the gear transmission, Completed accurate modeling in ANSYS environment for simulating gear transmission state.
3. Calculated the involute gear contact stress by the classical contact theory of Hertz's, and compared with the result by the use of Finite Element Method, which laid the foundation for calculating the gear torsional mesh stiffness
4. Through continuous circumvolving the gears, and changing their contact position, established the stiffness relations of the two contact faces, calculated the torsional mesh stiffness of the gears in different moments.
5. The main research included the torsional mesh stiffness characteristic of the with-pitting and the without-pitting gear, compared the change of the punishment function and the torsional mesh stiffness of the with-pitting and the without-pitting gear.
6. Establishing a 16-DOF gear nonlinear dynamic model, and analyzed the torsional mesh stiffness application in the gear failure diagnosis.
The last part is a summary of this dissertation and prospect of this research
引文
[1]李润方,王建军,齿轮系统动力学,北京,科学出版社,1995
[2]李润方,王建军,平面二包蜗杆传动弹性接触有限元分析,计算结构力学及其应用,1984,Vol.1,pp85-90
[3]杨生华,王统,齿轮轮齿变形中的接触有限元仿真分析,煤矿机械,1999,Vol.8,pp9-11
[4]朱坚民,周福章,雷静桃,渐开线斜齿圆柱齿轮弹性变形的三维有限元分析,农业机械学报,1998,Vol.29,pp113-117
[5]Barlam D,Zahavi E,The reliability of solutions in contact problems,Comp & Struct,1999,Vol.70,pp35-45
[6]刘辉,吴昌林,杨叔子,支承系统变形对斜齿轮承载特性的影响,华中理工大学学报,1998,Vol.26,pp72-74
[7]Tuplin W.A.,Gear Tooth Stresses at High Speed,Proceedings of the Institution of Mechanical Engineers,1950,Vol.16,pp 162-167
[8]Kahraman A.,Singh R.,Nonlinear Dynamics of a Spur Gear Pair,Journal of Sound and Vibration,1990,Vol.142,pp 49-75
[9]Ozguven H.N.,A Nonlinear Mathematical Model for Dynamic Analysis of Spur Gears Including Shaft and Bearing Dynamics,Journal of Sound and Vibration,1991,Vol.145,No.2,pp 239-260
[10]Kahraman A.,Singh R.,Interaction Between Time-Varying Mesh Stiffness and Clearance Nonlinearities in a Geared System,Journal of Sound and Vibration,1991,Vol.146,pp 135-156
[11]龙慧,张光辉等,渐开线直齿轮啮合过程中载荷及应力的计算机模拟,机械工程学报,1995,Vol.31,pp39-44
[12]武宝林,杨素君等,齿轮传动中啮合冲击的理论分析,机械科学与技术,2003,Vol.22,pp55-57
[13]包家汉,张玉华等,齿轮啮合过程齿间载荷分配的有限元分析,机械传动,2004,Vol.28,pp14-16
[14]Kuang J H,L in A D,The effect of tooth wear on the vibration spectrum of a spur gear pair[J],ASME Journal of Vibration and Acoustics,2001,Vol.123,pp311-317
[15]邵忍平,郭万林,李春,裂纹齿轮动力特性三维有限元模拟,航空动力学报,2004,Vol.19,pp284-288
[16]邵忍平,黄欣娜,李宗斌,裂纹对齿轮轮齿结构振动的影响,机械强度,2004,Vol.26,pp629-635
[17]Velex P,MaatarM.A mathematical model for analyzing the influence of shape deviations and mounting errors on gear dynamic behavior[J],Journal of Sound and Vibration,1996,Vol.191,pp629-660
[18]Badaoui EM,Antoni J,Guillet F,et al,Use of the moving cepstrum integral to detect and localize tooth spalls in gears[J],Mechanical Systems and Signal Processing,2001,Vol.15,pp873-885
[19]Choy F.K.,etc.,Analysis of the Effects of Surface Pitting and Wear on the Vibrations of a Gear Transmission System,Tribology International,1996
[20]王勖成,有限单元法,北京,清华大学出版社,2003
[21]王国强,实用工程数值模拟技术及其在ANSYS上的实践,西安,西北工业大学出版,1999
[22]雷晓燕,有限元法,北京,中国铁道出版社,2000
[23]高德平,机械工程中的有限元法基础,西北工业大学出版社,1993,12
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[25]倪栋,段进,徐久成,通用有限元分析,电子工业出版社,2003
[26]任辉启,ANSYS7.0工程分析实例,人民邮电出版社,2003.8
[27]李常义,卢耀辉,周继伟,基于ANSYS的渐开线圆柱齿轮参数化造型与有限元建模及分析技术,机械传动,2004,Vol.28,pp25-28
[28]吴继泽,王统编,齿根过渡曲线与齿根应力,国防工业出版社,1989
[29]杜安平,有限元网格划分的基本原则,机械设计与制造
[30]小飒工作室编,最新经ANSYS及Workbench教程,电子工业出版社,2004
[31]Zhong Z.H.,Finite Element Procedures for Contact-Impact Problem,Oxford University Press Inc,1993
[32]杨汾爱,张志强,龙小乐等,基于精确模型的斜齿轮接触应力有限元分析,机械科学与技术,2003,Vol.22,pp206-208
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[42]Tengjiao Lin,H.Ou,Runfang Li.A finite element method for 3D static and dynamic contact/impact analysis of gear drives.Computer Methods in Applied Mechanics and Engineering,2006,9
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[44]Sirichai S.,Finite Element Analysis of Gears in mesh,Fifth International Congress on Sound and Vibration.Australia,1997
[45]Seney Sirichai,Torsional properties of spur gears in mesh using nonlinear finite element analysis,1999
[46]Shengxiang Jia,Ian Howard,Comparison of localized spalling and crack damage from dynamic modeling of spur gear vibrations,2006,332-349
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[53]李润方,王建军,齿轮系统动力学,北京,科学出版社
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[55]El Badaoui M.,Antoni J.,Guillet F.,Use of the Moving Cestrum Integral to Detect and Localize Tooth Spalls in Gears,2001,Vol.15.No.5,pp 873-885
[56]Howard I.,Jia S.,Wang J.,The Dynamic Modeling of a Spur Gear in Mesh Including Friction and a Crack,Mechanical Systems and Signal Processing,2001,Vol.15 No.5,pp 831-853
[57]Sirichai S.,Torsional properties of spur gears in mesh using nonlinear Finite element analysis,Ph.D.thesis,Curtin University of Technology,1999
[2]李润方,王建军,平面二包蜗杆传动弹性接触有限元分析,计算结构力学及其应用,1984,Vol.1,pp85-90
[3]杨生华,王统,齿轮轮齿变形中的接触有限元仿真分析,煤矿机械,1999,Vol.8,pp9-11
[4]朱坚民,周福章,雷静桃,渐开线斜齿圆柱齿轮弹性变形的三维有限元分析,农业机械学报,1998,Vol.29,pp113-117
[5]Barlam D,Zahavi E,The reliability of solutions in contact problems,Comp & Struct,1999,Vol.70,pp35-45
[6]刘辉,吴昌林,杨叔子,支承系统变形对斜齿轮承载特性的影响,华中理工大学学报,1998,Vol.26,pp72-74
[7]Tuplin W.A.,Gear Tooth Stresses at High Speed,Proceedings of the Institution of Mechanical Engineers,1950,Vol.16,pp 162-167
[8]Kahraman A.,Singh R.,Nonlinear Dynamics of a Spur Gear Pair,Journal of Sound and Vibration,1990,Vol.142,pp 49-75
[9]Ozguven H.N.,A Nonlinear Mathematical Model for Dynamic Analysis of Spur Gears Including Shaft and Bearing Dynamics,Journal of Sound and Vibration,1991,Vol.145,No.2,pp 239-260
[10]Kahraman A.,Singh R.,Interaction Between Time-Varying Mesh Stiffness and Clearance Nonlinearities in a Geared System,Journal of Sound and Vibration,1991,Vol.146,pp 135-156
[11]龙慧,张光辉等,渐开线直齿轮啮合过程中载荷及应力的计算机模拟,机械工程学报,1995,Vol.31,pp39-44
[12]武宝林,杨素君等,齿轮传动中啮合冲击的理论分析,机械科学与技术,2003,Vol.22,pp55-57
[13]包家汉,张玉华等,齿轮啮合过程齿间载荷分配的有限元分析,机械传动,2004,Vol.28,pp14-16
[14]Kuang J H,L in A D,The effect of tooth wear on the vibration spectrum of a spur gear pair[J],ASME Journal of Vibration and Acoustics,2001,Vol.123,pp311-317
[15]邵忍平,郭万林,李春,裂纹齿轮动力特性三维有限元模拟,航空动力学报,2004,Vol.19,pp284-288
[16]邵忍平,黄欣娜,李宗斌,裂纹对齿轮轮齿结构振动的影响,机械强度,2004,Vol.26,pp629-635
[17]Velex P,MaatarM.A mathematical model for analyzing the influence of shape deviations and mounting errors on gear dynamic behavior[J],Journal of Sound and Vibration,1996,Vol.191,pp629-660
[18]Badaoui EM,Antoni J,Guillet F,et al,Use of the moving cepstrum integral to detect and localize tooth spalls in gears[J],Mechanical Systems and Signal Processing,2001,Vol.15,pp873-885
[19]Choy F.K.,etc.,Analysis of the Effects of Surface Pitting and Wear on the Vibrations of a Gear Transmission System,Tribology International,1996
[20]王勖成,有限单元法,北京,清华大学出版社,2003
[21]王国强,实用工程数值模拟技术及其在ANSYS上的实践,西安,西北工业大学出版,1999
[22]雷晓燕,有限元法,北京,中国铁道出版社,2000
[23]高德平,机械工程中的有限元法基础,西北工业大学出版社,1993,12
[24]包家汉,张玉华,薛家国,基于ANSYS的齿轮参数化建模及其应用,安徽工业大学学报,2005,Vol.22,pp35-38
[25]倪栋,段进,徐久成,通用有限元分析,电子工业出版社,2003
[26]任辉启,ANSYS7.0工程分析实例,人民邮电出版社,2003.8
[27]李常义,卢耀辉,周继伟,基于ANSYS的渐开线圆柱齿轮参数化造型与有限元建模及分析技术,机械传动,2004,Vol.28,pp25-28
[28]吴继泽,王统编,齿根过渡曲线与齿根应力,国防工业出版社,1989
[29]杜安平,有限元网格划分的基本原则,机械设计与制造
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