基于解析解的人字齿轮齿廓修形动态分析

郭家舜; 王三民; 王颖

基于解析解的人字齿轮齿廓修形动态分析

西北工业大学机电学院西安 710072

基金项目: 国家高技术研究发展计划(2009AA04Z404)

计量
- 文章访问数: 1510
- HTML浏览量: 62
- PDF量: 1003
- 被引次数: 0
出版历程
- 收稿日期: 2012-03-26
- 刊出日期: 2013-03-28

Dynamic analysis of tooth profile modification to herringbone gears based on analytical solutions

School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China

摘要

摘要: 根据人字齿轮传动的结构,考虑时变啮合刚度、齿侧间隙,并把齿廓修形作为一种时变齿侧间隙计入,建立了单级人字齿轮传动的弯-扭-轴耦合动力学模型和相应的非线性动力学方程.对方程的数值解进行分析,发现合理的修形使人字齿轮传动不发生齿面的完全分离.基于多尺度法对不发生齿面完全分离时的人字齿轮传动系统进行了摄动分析,得到了系统在主共振频率附近幅频响应的近似解析解.相比数值方法,解析法具有很高的求解效率.最后,根据近似解析解研究了修形参数对动载系数幅值的影响.研究发现:螺旋角越大使动载系数最小所需的修形量越大,而所需的修形长度越小.另外,使动载系数最小的最优修形参数解域呈新月形,其随着主动轮支承刚度的增大而先增大后减小;随着被动轮支承刚度的增大而持续减小.
- 人字齿轮 /
- 非线性动力学 /
- 齿廓修形 /
- 多尺度法 /
- 动态分析
Abstract: Based on the structure of a single-stage herringbone gear transmission,a nonlinear lateral-torsional-axial coupling dynamic model and corresponding dynamic equations considering the time-varying mesh stiffness,tooth profile modification and tooth backlash were proposed,for which the tooth profile modification was considered as a time-varying tooth backlash.The numerical solutions were analyzed and the results show that the total tooth separation can be suppressed with rational tooth profile modification.Then,according to the method of multiple scales,perturbation analysis of the dynamic equations finds that appropriate analytical frequency response solutions for the case cause no total tooth separation at primary resonance.Compared to the numerical method,the analytical method is more efficient.At last,the influence of the modification parameters on the amplitude of the dynamic load factor was analyzed on the basis of the analytical solutions.The analysis results present that the magnitude of tip relief decreases as the helical angle increases to reduce the dynamic load factor,while the length of modification increases in this case.In addition,the optimal solution domain of the minimum dynamic load factor is a meniscoid zone,it increases firstly as the support stiffness of the driving gear increases to a value,after that value,it decreases when the support stiffness of the driving gear continues to increase;the optimal solution domain decreases as the support stiffness of the driven gear continuously increases.
- herringbone gears /
- nonlinear dynamics /
- tooth profile modification /
- method of multiple scales /
- dynamic analysis

HTML

参考文献(15)

[1]	吴勇军,王建军,韩勤锴,等.基于接触有限元分析的斜齿轮齿廓修形与实验[J].航空动力学报,2011,26(2):409-415. WU Yongjun,WANG Jianjun,HAN Qinkai,et al.Tooth profile modification of helical gears and experimental study based on finite element contact analysis[J].Journal of Aerospace Power,2011,26(2):409-415.(in Chinese)
[2]	Simon V.Optimal tooth modifications for spur and helical gears[J].Journal of Mechanisms,Transmissions,and Automation in Design,1989,111(12):611-615.
[3]	Wagaj P,Kahraman A.Influence of tooth profile modification on helical gear durability[J].ASME Journal of Mechanical Design,2002,124(9):501-510.
[4]	王成,方宗德,贾海涛,等.人字齿轮修形优化设计[J].航空动力学报,2009,39(2):1432-1436. WANG Cheng,FANG Zongde,JIA Haitao,et al.Modification optimization of double helical gears[J].Journal of Aerospace Power,2009,39(2):1432-1436.(in Chinese)
[5]	孙月海,张策,葛楠.含误差的直齿轮的齿廓修形[J].机械工程学报,2009,39(12):91-94. SUN Yuehai,ZHANG Ce,GE Nan.Tooth profile modification for spur gears with manufacturing error[J].Chinese Journal of Mechanical Engineering,2003,39(12):91-94.(in Chinese)
[6]	Velex P,Ville F.An analytical approach to tooth friction losses in spur and helical gears-influence of profile modifications[J].ASME Journal of Mechanical Design,2009,131(10):101008.1-101008.10.
[7]	Lin H H,Oswald F B,Townsend D P.Dynamic loading of spur gears with linear or parabolic tooth profile modifications[J].Mechanism and Machine Theory,1994,29(8):1115-1129.
[8]	LIU Gang,Parker R G.Dynamic modeling and analysis of tooth profile modification for multimesh gear vibration[J].ASME Journal of Mechanical Design,2008,130(12):121402.1-121402.13.
[9]	Kahraman A.Dynamic analysis of a multi-mesh helical gear train[J].ASME Journal of Mechanical Design,1994,116(9):706-712.
[10]	Kubur M,Kahraman A.Dynamic analysis of a multi-shaft helical gear transmission by finite elements:model and experiment[J].ASME Journal of Vibration and Acoustics,2004,126(7):398-406.
[11]	Kahraman A.Effect of axial vibrations on the dynamics of a helical gear pair[J].ASME Journal of Vibration and Acoustics,1993,115(1):33-39.
[12]	Baud S,Velex P.Static and dynamic tooth loading in spur and helical geared systems-experiments and model validation[J].ASME Journal of Mechanical Design,2002,124(6):334-346.
[13]	Kahraman A,Blankenship G W.Experiments on nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters[J].ASME Journal of Applied Mechanics,1997,64(3):217-226.
[14]	LIN Jian,Parker R G.Mesh stiffness variation instabilities in two-stage gear systems[J].ASME Journal of Vibration and Acoustics,2002,124(12):68-76.
[15]	Bahk C J,Parker R G.Analytical solution for the nonlinear dynamics of planetary gears[J].ASME Journal of Computational and Nonlinear Dynamics,2011,6(4):021007.1-021007.15.