The Kinematic Accuracy Reliability and Reliability Sensitivity Analysis of a Swing Mechanism with the Automatic Loading System of a Cannon

doi:10.12382/bgxb.2021.0868

Abstract

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

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.

Figures/Tables 14

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

Fig.2 Coordinate system of the swing mechanism

Fig.3 The clearance of hinge RJ_1

Fig.4 The clearance of hinge RJ_3

Fig.5 The clearance of hinge RJ_2

Fig.6 The clearance of hinge RJ_4

Fig.7 Vector relations of the swing mechanism

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

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

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

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

Fig.9 Probability density distribution of θ3

Fig.10 Probability density distribution of θ4

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

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

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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