基于混合不确定性的螺旋锥齿轮结构可靠性分析

doi:10.13229/j.cnki.jdxbgxb20211134

摘要/Abstract

摘要：

螺旋锥齿轮结构中各设计参数和边界条件往往存在随机类和区间类参数混杂的情况，由于两类不确定参数的测度空间和测度性质不同，基于概率论的传统可靠性建模分析方法将不再适用，为此提出了一种基于随机-区间混合不确定性的二阶可靠性分析方法。利用二阶泰勒级数展开法在最可能失效点（MPP）近似展开极限状态方程，在此基础上引入极坐标，将n维极限状态函数的近似转化为一个新的极坐标二维函数；利用函数梯度向量代替直角坐标系中的失效域质心向量思想，在极坐标空间中推导随机变量和区间变量的极坐标概率密度函数；以二次二阶矩可靠性分析方法为基础，利用积分法推导出失效概率区间。最后，通过某装备综合传动装置的螺旋锥齿轮结构可靠性分析案例验证了本文方法的有效性。

关键词: 系统工程, 混合可靠性分析, 二阶可靠性方法, 极坐标, 螺旋锥齿轮

Abstract:

There is often a mix of random and interval parameters in the design parameters and boundary conditions of spiral bevel gears. Because the measurement space and properties of the two types of uncertain variables are different， the traditional reliability modeling and analysis methods based on probability theory will no longer be applicable. Therefore， a second-order reliability analysis method for hybrid structural analysis with random and interval variables was presented. The limit state function is approximated at the most probable point（MPP） by using the second-order Taylor series expansion method. On this basis， the polar coordinates are introduced and the n-dimensional limit state function is approximately transformed into a new polar coordinate two-dimensional function. By using the gradient vector of the function instead of the failure domain centroid vector， the polar probability density functions of the random variables and the interval variables are derived in polar space. Based on the second-order moment reliability analysis method， the failure probability interval is deduced by the integration method. Finally， the validity of the proposed method is verified by a structural reliability analysis case for spiral bevel gears of a weapon's comprehensive transmission.

Key words: systems engineering, hybrid reliability analysis, second-order reliability method, harmonic reducer, spiral bevel gear

中图分类号:

TB114.3

邱继伟,罗海胜. 基于混合不确定性的螺旋锥齿轮结构可靠性分析[J]. 吉林大学学报(工学版), 2022, 52(2): 466-473.

Ji-wei QIU,Hai-sheng LUO. Structure reliability analysis of spiral bevel gear based on hybrid uncertainties[J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(2): 466-473.

图/表 4

表1

表2

表3

不确定性变量参数分布"

变量	分布参数	变量类型
齿宽b/mm	u=52.521，σ=0.03	正态分布
转矩T/（N $?$ m）	［3580，3660］	区间分布
转速n/（r/min $- 1$ ）	［2140，2260］	区间分布

表3

表4

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参数名称	参数值
齿数比	31/26
大端模数/mm	8.654
螺旋角/（°）	35
压力角/（°）	20
轴交角/（°）	90
齿高/mm	16.746
齿顶高/mm	6.44
锥距/mm	175.07
传递功率/kW	836

参数名称	参数值
密度/10⁴（kg·m^-3）	7.83
杨氏模量/10¹¹Pa	2.07
泊松比	0.29
抗拉强度/MPa	1175
屈服强度/MPa	1080

方法	失效概率波动范围
方法	下边界	上边界	中值	偏差	耗时/s
本文	0.1874	0.3827	0.2851	0.0977	2.3
MC	0.0031	0.5776	0.2904	0.2873	4.2
SORM	0.0051	0.5718	0.2904	0.2834	3.2