考虑动态载荷不确定性的弹协调到位精度

doi:10.12382/bgxb.2024.0658

摘要/Abstract

摘要：

为分析弹协调动态随机过程中不确定性输入参数对协调到位精度的影响,基于直接概率积分法(Direct Probability Integer Method,DPIM)研究弹协调过程的动态不确定性传播。建立弹协调机构的刚柔耦合动力学模型,推导弹协调过程的概率密度积分方程,并采用Karhunen-Loeve(K-L)展开方法实现动态随机驱动载荷的降维,进而基于DPIM量化动态不确定性条件下弹协调臂到位角度的不确定性。与试验对比的结果表明:弹协调到位仿真输出与试验测试结果基本吻合,验证了模型的准确性;与Monte Carlo(MC)结果对比,基于DPIM方法得到的概率密度函数与MC相比误差较小,验证了新方法的有效性;动态随机载荷和不确定性参数影响下的协调到位结果表明:K-L方法有效实现了协调过程动态随机载荷的降维,协调到位误差随协调角度变大而变大。计算结果可为弹药自动装填系统可靠性设计提供有力支撑。

关键词: 弹协调机构, 直接概率积分, Karhunen-Loeve展开, 动态不确定性传播

Abstract:

To analyze the impact of uncertain input parameters on the precision of coordination in the dynamic random process of ammunition coordination, the propagation of dynamic uncertainty in the process of ammunition coordination is studied based on the direct probability integral method (DPIM). A rigid-flexible coupling dynamic model of ammunition coordination mechanism is established, and the probability density integral equation of the coordination process is derived. The Karhunen-Loeve (K-L) expansion method is employed to reduce the dimensionality of dynamic random driving load, thus quantificatying the uncertainty in the positioning angle of ammunition coordination arm under dynamic uncertainty conditions based on DPIM. Comparisons with experimental results indicate that the simulation output of the ammunition coordination positioning aligns basically with the experimental test results, which validates the accuracy of the proposed model. Additionally, the probability density function obtained using the DPIM method shows a smaller error, which confirms the effectiveness of the new method. The coordination positioning results under the effects of dynamic random loads and uncertain parameters demonstrate that the K-L method effectively reduces the dimensionality of dynamic random loads in the coordination process, with positioning errors increasing as the coordination angle increases. The computational results provide strong support for the reliability design of automatic ammunition loading system.

Key words: ammunition coordination mechanism, direct probability integration, Karhunen-Loeve expansion, dynamic uncertainty propagation

中图分类号:

TJ302

张云添, 陈龙淼, 陈光宋, 王明明. 考虑动态载荷不确定性的弹协调到位精度[J]. 兵工学报, 2024, 45(11): 4052-4061.

ZHANG Yuntian, CHEN Longmiao, CHEN Guangsong, WANG Mingming. The Positioning Accuracy of Ammunition Coordination Considering the Uncertainty of Dynamic Loads[J]. Acta Armamentarii, 2024, 45(11): 4052-4061.

图/表 13

图1 弹协调机构简化模型

Fig.1 Simplified model of ammunition coordination mechanism

图2 弹协调试验原理示意图

Fig.2 Schematic diagram of ramming coordination test

图3 协调过程路径规划

Fig.3 Path planning in coordination process

图4 试验协调角位移-时间曲线

Fig.4 Experimental coordination angular displacement-time curve

图5 协调过程仿真曲线结果

Fig.5 Simulation curves of coordination process

表1 弹协调过程中的不确定性参数

Table 1 Uncertainty parameters in the ammunition coordination process

序号	参数名	名义值	特征值	分布类型
1	驱动齿轮与齿弧的接触刚度/(N·m^-1)	7.38×10⁵	5×10⁴	正态
2	驱动齿轮与齿弧的间隙/mm	0	0.01	均匀
3	齿弧与耳轴的径向间隙/mm	0	0.01	均匀
4	协调臂总质量(含弹丸)/kg	100	0.1	正态
5	协调臂转动惯量(含弹丸)/(kg·mm²)	5.67×10⁶	5×10⁵	正态

图6 MC与DPIM到位角度概率分布图对比结果

Fig.6 Comparison of probability distributions of positioning angles of MC and DPIM in place angles

表2 弹协调到位角度统计特性

Table 2 Statistical characteristics of coordination angles of ammunition

均值			均方差
MC	DPIM	误差	MC	DPIM	误差
60.0042	60.0041	1.67×10^-4%	9.0413×10^-4	8.8674×10^-4	1.92%

图7 协调到位65°的随机驱动载荷示意图

Fig.7 Schematic diagram of a randomly driven load coordinated at 65 °

图8 K-L展开前15个特征值结果

Fig.8 First 15 eigenvalues result of K-L expansion

图9 随机驱动载荷下协调到位35°时的概率密度函数结果

Fig.9 Probability density function results for coordination at 35° under random driving load

图10 随机驱动载荷下协调到位65°时的概率密度函数结果

Fig.10 Probability density function results for coordination at 65° under random driving load

表3 弹协调动态角位移统计特性

Table 3 Statistical characteristics of coordinated dynamic angular displacement of ammunition

协调到位35°					协调到位65°
时间/s		均值		均方差	时间/s		均值		均方差
0.30	19.932		0.0018		0.300	22.081		0.0014
0.50	32.2407		2.04×10^-4		0.500	45.094		8.05×10^-4
0.65	35.0091		0.001		0.765	65.0196		0.0047

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