火炮自动装填系统摆动机构的运动精度可靠性与灵敏度

doi:10.12382/bgxb.2021.0868

摘要/Abstract

摘要：

为高效准确地分析某自动装填系统摆动机构的运动精度可靠性,并分析其尺寸参数的可靠性灵敏度,构建摆动机构运动学模型。考虑摆动机构尺寸误差以及铰接间隙的影响,利用稀疏网格数值积分方法获得运动学响应变量的前4阶统计矩,通过鞍点估计方法得到运动学响应变量的概率密度函数,获得某自动装填系统摆动机构运动精度可靠度,并以此为条件通过计算得到尺寸参数的可靠性灵敏度分析结果。研究结果表明:新方法的计算结果能够较好地吻合蒙特卡洛方法获得的结果,且所需样本点较少,验证了方法的有效性,同时计算所得的摆动机构运动精度的失效概率较小,运动精度可靠性较高;主动臂长度对运动可靠性影响较大,其余参数影响较小,为摆动机构基于可靠性的设计提供了参考。

关键词: 火炮, 自动装填系统, 摆动机构, 运动精度可靠性, 稀疏网格数值积分, 鞍点估计

Abstract:

This study aims to analyze the kinematic accuracy reliability of a swing mechanism with an automatic loading system and calculate the reliability sensitivity of dimension parameters. A kinematical model of the swing mechanism is thus established. Considering the influence of dimension error of the swing mechanism and joint clearance, the first four statistical moments are obtained by using the spare grid numerical integration method, and the probability density function of the kinematic response variable is obtained using the saddle point estimation method. The kinematic accuracy reliability of the swing mechanism with the automatic loading system is then calculated, and the reliability sensitivity analysis of dimension parameters is performed based on the results. The simulation results show that the calculation results in the study are identical to those acquired using the Monte Carlo method while requiring fewer sample points. The effectiveness of the methods in the paper is verified, and there is less failure probability of the swing mechanism kinematic accuracy, indicating high reliability in kinematic accuracy. The reliability sensitivity analysis of the dimension parameters reveals that the length of the driving arm has a larger influence on the kinematic reliability, while the other parameters have less influence. This provides references for the reliability-based design of the swing mechanism.

Key words: cannon, automatic loading system, swing mechanism, kinematic accuracy reliability, sparse grid numerical integration method, saddle point approximation

翟文宇, 钱林方, 陈光宋. 火炮自动装填系统摆动机构的运动精度可靠性与灵敏度[J]. 兵工学报, 2023, 44(4): 1062-1070.

ZHAI Wenyu, QIAN Linfang, CHEN Guangsong. The Kinematic Accuracy Reliability and Reliability Sensitivity Analysis of a Swing Mechanism with the Automatic Loading System of a Cannon[J]. Acta Armamentarii, 2023, 44(4): 1062-1070.

图/表 14

图1 摆动机构示意图

Fig.1 Schematic diagram of the arm of the swing mechanism

图2 摆动机构坐标系

Fig.2 Coordinate system of the swing mechanism

图3 RJ_1铰间隙

Fig.3 The clearance of hinge RJ_1

图4 RJ_3铰间隙

Fig.4 The clearance of hinge RJ_3

图5 RJ_2铰间隙

Fig.5 The clearance of hinge RJ_2

图6 RJ_4铰间隙

Fig.6 The clearance of hinge RJ_4

图7 摆动机构矢量关系示意图

Fig.7 Vector relations of the swing mechanism

表1 常见分布的CGF

Table 1 CGF of the common distribution

分布类型	f(X)	K_X(t)
均匀分布	f(X)=1/(β-α)	K_X(t)=ln(e^βt-e^αt)- ln(β-α)-ln(t)
正态分布	f(X)= $1 2 π σ e - X - μ 2 σ 2$	K_X(t)=μt+σ²t²/2
指数分布	f(X)= $1 β$ e^-^X/β	K_X(t)=-ln(1-βt)
Ⅰ型极值分布	f(X)= $1 σ e - (X - μ) σ e - e - (X - μ) σ$	K_X(t)=μt+lnΓ(1-σt)
伽玛分布	f(X)= $β α Γ (α)$ X^α^-1e^-^βX	K_X(t)=-αln(1-t/β)
χ² 分布	f(X)= $1 2 n 2 Γ (n 2) X n 2 - 1 e - X 2$	K_X(t)=-nln(1-2t)/2

表1 常见分布的CGF

Table 1 CGF of the common distribution

分布类型	f(X)	K_X(t)
均匀分布	f(X)=1/(β-α)	K_X(t)=ln(e^βt-e^αt)- ln(β-α)-ln(t)
正态分布	f(X)= $1 2 π σ e - X - μ 2 σ 2$	K_X(t)=μt+σ²t²/2
指数分布	f(X)= $1 β$ e^-^X/β	K_X(t)=-ln(1-βt)
Ⅰ型极值分布	f(X)= $1 σ e - (X - μ) σ e - e - (X - μ) σ$	K_X(t)=μt+lnΓ(1-σt)
伽玛分布	f(X)= $β α Γ (α)$ X^α^-1e^-^βX	K_X(t)=-αln(1-t/β)
χ² 分布	f(X)= $1 2 n 2 Γ (n 2) X n 2 - 1 e - X 2$	K_X(t)=-nln(1-2t)/2

图8 摆动机构运动精度可靠性流程

Fig.8 Flowchart for acquiring the kinematic accuracy reliability of the swing mechanism

表2 参数不确定性统计特性

Table 2 Statistical characteristics of parameter uncertainty

变量	分布类型	均值	标准差
L₁/mm	正态	360	0.0333
L₂/mm	正态	397.02	0.0601
L₃/mm	正态	360	0.0333
L₄/mm	正态	397.02	0.0601
r_A/mm	正态	0.0215	0.0072
r_B/mm	正态	0.0330	0.0110
r_C/mm	正态	0.0210	0.0070
r_D/mm	正态	0.0330	0.0110
φ₁/(°)	正态	45	15
φ₂/(°)	正态	45	15
φ₃/(°)	正态	45	15
φ₄/(°)	正态	45	15

图9 θ3概率密度分布情况

Fig.9 Probability density distribution of θ3

图10 θ4概率密度分布情况

Fig.10 Probability density distribution of θ4

表3 响应变量的统计参数

Table 3 Statistical parameters of response variables

方法	参数	均值/ rad	标准差/ 10^-4	偏度	峰度	计算次数
本文方法	θ₃	0.9530	8.514	0.0010	3.007	313
	θ₄	0.2938	0.0002	-0.0003	3.011	313
MC方法	θ₃	0.9530	8.512	0.0013	2.998	1×10⁶
	θ₄	0.2938	0.0002	-0.0013	3.003	1×10⁶

表4 可靠性灵敏度分析

Table 4 Reliability sensitivity analysis

参数	L₁/10^-8	L₂/10^-8	L₃/10^-8	L₄/10^-8
$∂ P f ∂ μ L i$	-1.7661	2.1816	-1.766	-1.766
$∂ P f ∂ σ L i$	448.7	192.9	193.0	192.9

表4 可靠性灵敏度分析

Table 4 Reliability sensitivity analysis

参数	L₁/10^-8	L₂/10^-8	L₃/10^-8	L₄/10^-8
$∂ P f ∂ μ L i$	-1.7661	2.1816	-1.766	-1.766
$∂ P f ∂ σ L i$	448.7	192.9	193.0	192.9

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