基于全齿廓普遍方程的齿轮时变啮合刚度改进算法
四机械制造四黄金凤,等四基于全齿廓普遍方程的齿轮时变啮合刚度改进算法
作者简介:黄金凤(1991-),女,江西吉安人,硕士研究生,研究方向为机械动力学及信号处理三
DOI:10.19344/https://www.sodocs.net/doc/a51870879.html,ki.issn1671-5276.2019.01.012
基于全齿廓普遍方程的齿轮时变啮合刚度改进算法
黄金凤1,张飞斌2,3,崔玲丽1,陈雄飞3
(1.北京工业大学先进制造技术北京市重点实验室,北京100124;2.清华大学机械工程系,北京100084;
3.江西农业大学工学院,江西南昌330045)
摘 要:时变啮合刚度是齿轮系统振动信号的最主要内部激励源之一,更是故障诊断机理研究的核心参量三针对传统能量法在齿根圆和基圆不重合时存在的问题,提出了基于齿轮全齿廓普遍方程的齿轮时变啮合刚度精确算法;该算法建立了以滚动角φ为统一变量的高精度全齿廓啮合刚度积分公式,并依据齿条刀加工原理明确了滚动角的取值范围三基于新算法研究发现,不同参数下的齿轮副在完整啮合周期过程中,啮合力对轮齿的径向作用存在拉伸区间和压缩区间两种情况,故提出轮齿拉压刚度的概念以更准确地描述轮齿刚度的组成成分,并研究了拉压刚度的齿轮参数临界值三
关键词:啮合刚度;故障诊断;拉压刚度;普遍方程法
中图分类号:TH132.41 文献标志码:B 文章编号:1671-5276(2019)01-0040-05
Improved Algorithm for Time -varying Meshing Stiffness of Gears Based
on General Equation of Whole Gear Profile
HUANG Jinfeng 1,ZHANG Feibin
2,3
,CUI Lingli 1,CHEN Xiongfei
3
(1.Key Laboratory of Advanced Manufacturing Technology ,Beijing University of Technology ,
Beijing 100124,China ;2.Department of Mechanical Engineering ,Tsinghua University ,Beijing 100084,China ;3.Engineering College ,Jiangxi Agricultural University ,Nanchang 330045,China )
Abstract :Time -varying meshing stiffness is one of the most important internal excitation sources of vibration signals in gear system ,
and it is also the core parameter of making research on fault diagnosis mechanism.When the tooth circle does not coincide with the base circle ,an accurate algorithm of gear time -varying meshing stiffness based on the general equation of gear tooth profile is pro-posed on the principle of the traditional energy method in this paper.The integral formula of high precision whole gear profile meshing stiffness with rolling angle φas uniform variable is established in the algorithm ,and the range of rolling angle is clarified according to the principle of rack cutting.Based on the new algorithm ,it is found that the radial force of the meshing force on the teeth exists in the tension interval and compression interval in the complete meshing cycle of the gear pair under different parameters.Therefore ,the concept of tension and compression stiffness are proposed ,as to describe the component of gear stiffness more accurately ,and the critical values of gear parameters for tension and compression stiffness are also studied.
Keywords :meshing stiffness ;fault diagnosis ;tension and compression stiffness ;general equation method
0 引言
因啮合过程中的单双齿交替啮合及啮合点在啮合线上的位置变化导致即使是正常状态下的齿轮,其啮合刚度也是时变的,其计算比较复杂,一般情况下将其简化为规则的方波三当齿轮出现故障时,更增加了齿轮时变啮合刚度计算的难度三时变啮合刚度是齿轮传动系统振动响应的主要动态激励源之一,对齿轮传动的动力学性能有着显著影响三啮合刚度随啮合位置变化规律,尤其是故障状态下啮合刚度的变化规律,是轮齿修形二动态特性二故障诊断以及寿命预测等研究的基础三因此,研究故障齿轮时变啮合刚度精确高效的计算方法有重要的意义三
目前,针对齿轮时变啮合刚度的计算方法有多种三实
验法[1]的求解结果较精确,但操作复杂并且对实验设备要求高,应用的普遍性不高三线性规划法[2]针对正常齿轮啮合刚度求解时结果也较精确,但应用该方法计算故障
齿轮啮合刚度的文献鲜有报道三有限元法[3]能较真实地模拟计算出齿轮的实际啮合情况,但其计算量和计算耗时比其他方法都要大三Yang 和Lin [4]基于Weber [5]提出的能量法给出了关于齿轮转角变化的啮合综合刚度表达式三文中的啮合刚度由赫兹接触刚度二弯曲刚度和压缩刚度3部分组成三Tian [6]在该模型基础上增加了剪切刚度项,使该模型在原理上进一步完善三Wu 等[7]在前两者的基础上对含裂纹轮齿的啮合刚度进行计算,并探讨了轮齿裂纹对于齿轮动力学特性的影响三万志国[8]等在Yang 和Wu 研究的基础上,提出一种考虑齿根圆与基圆不重合时的啮合刚度修正方法,建立齿根裂纹动力学模型并进行其振动
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