考虑表面柔性接触的陀螺摆加速度计装配位姿偏差计算与分析

doi:10.12382/bgxb.2024.0826

摘要/Abstract

摘要：

针对设计阶段如何准确把握陀螺摆加速度计装配位姿精度的问题,提出考虑非理想配合面柔性接触行为的装配位姿偏差计算方法。依托位姿的试探调整策略,建立基于多自由度力系平衡条件的装配位姿偏差问题模型,提出用于解算此模型的第3代非支配排序遗传算法(Non-dominated Sorting Genetic Algorithms Ⅲ,NSGA-Ⅲ)框架。以陀螺摆加速度计的同轴装配位姿精度预测为例,与经典小位移旋量(Small Displacement Torsor,SDT)方法和主流迭代最近点(Iterative Closest Point,ICP)方法对比,验证所提方法的有效性和准确性。研究结果表明,该方法有能力提高陀螺摆加速度计装配位姿精度预测的准确性,可为保障我国高端惯导产品的精度性能提供帮助。

关键词: 柔性接触行为, 陀螺摆加速度计, 装配精度预测, 位姿偏差, 非理想表面, 第3代非支配排序遗传算法

Abstract:

To precisely control the assembly position-orientation accuracy of gyroscopic pendulum accelerometers at the design stage,this paper proposes an computing method of position and orientation deviations (PODs) considering the flexible contact behaviors of non-ideal mating surfaces.A mathematical model based on multi-degree-of5freedom force equilibrium conditions is established by adopting an iterative trial adjustment strategy for position and orientation,and a non-dominated sorting genetic algorithm Ⅲ (NSGA-Ⅲ) framework is developed for solving the proposed model.The proposed method is comparaed with the classical small displacement torsor (SDT) method and the mainstream iterative closest point (ICP) algorithm,and its effectiveness and accuracy are validated through a case study of coaxial assembly accuracy prediction for gyroscopic pendulum accelerometers.Results indicate that the proposed method can be used to improve the predicting accuracy of assembly position-orientation,offering technical support for ensuring the precision performance in high-end inertial nvigation systems.

Key words: flexible contact behavior, gyroscopic pendulum accelerometer, assembly accuracy prediction, position and orientation deviations, non-ideal surface, non-dominated sorting genetic algorithm III

中图分类号:

张健, 刘检华, 张国锐, 夏焕雄, 张福礼, 沈宏达. 考虑表面柔性接触的陀螺摆加速度计装配位姿偏差计算与分析[J]. 兵工学报, 2025, 46(9): 240826-.

ZHANG Jian, LIU Jianhua, ZHANG Guorui, XIA Huanxiong, ZHANG Fuli, SHEN Hongda. Computation and Analysis of Assembly Position and Orientation Deviations for a Gyroscopic Pendulum Accelerometer Considering Flexible Surface Contact[J]. Acta Armamentarii, 2025, 46(9): 240826-.

图/表 15

图1 非理想表面柔性接触行为引起的陀螺摆加速度计精度问题

Fig.1 Accuracy problem of gyroscopic pendulum accelerometer caused by flexible contact behavior of non-ideal surfaces

图2 产品的装配结构及其关键零件的主要装配关系

Fig.2 Assembly structure of product and key assembly relations of its main components

图3 非理想表面及其柔性接触行为对带端面轴孔零件装配的影响

Fig.3 Impacts of non-ideal surfaces and their flexible contact behaviors on the assembly of shaft and hole with end faces

图4 带端面轴孔零件装配后约束与未约束的自由度

Fig.4 Constrained and unconstrained degrees of freedom after assembling the shaft and hole with end faces

图5 装配位姿偏差的NSGA-III框架

Fig.5 Computation framework of NSGA-III for assembly position and orientation deviations

图6 陀螺摆加速度计同轴装配精度的案例

Fig.6 Case of coaxial assembly accuracy for a gyroscopic pendulum accelerometer

表1 不同周向角工况

Table 1 Computational conditions of different circumferential angles

序号	周向角/(°)	序号	周向角/(°)
1	30	7	210
2	60	8	240
3	90	9	270
4	120	10	300
5	150	11	330
6	180	12	360

表2 不同作用力工况

Table 2 Computational conditions of different applied forces

序号	F_x/N	F_y/N	F_z/N
1	200	500	-800
2	-200	500	-800
3	-200	-500	-800
4	200	-500	-800
5	200	500	-300
6	200	500	-600
7	200	500	-900
8	200	500	-1200

图7 作用力、周向角示意图

Fig.7 Schematical diagrams of the applied force and circumferential angle

表3 算例的计算参数

Table 3 Computation parameters of the case

类型	参数	数值
配合面非理想形貌参数	名义尺寸	见图6
	配合端面公差/mm	⁺⁰^.⁰⁰⁵ ^-0^.⁰⁰⁵
	配合端面离散点数	6×181
	柱面配合	基孔制H7/g6 间隙配合
	柱面配合孔公差/mm	⁺⁰^.⁰¹¹ ⁰^.⁰⁰⁰
	柱面配合轴公差/mm	^-0.002 ^-0.008
	柱面离散点数	181×16
配合面承受作用力和材料参数	配合面承受作用力	见表1和表2
	配合面材料弹性模量/GPa	210
	配合面材料泊松比	0.3
NSGA-III参数	M	100
	P_c	0.9
	P_m	0.005
	T	100
	H	90
	沿x轴移动范围/mm	[-0.02,0.02]
	沿y轴移动范围/mm	[-0.02,0.02]
	沿x轴转动范围/(°)	[-0.03,0.03]
	沿y轴转动范围/(°)	[-0.03,0.03]

图8 不同周向角装配后的距离偏差及轴线夹角偏差

Fig.8 Distance deviations and angle deviations between axises after assembly at different circumferential angles

图9 不同作用力下距离偏差及轴线夹角偏差

Fig.9 Distance deviations and angle deviations between axises after assembly under different applied forces

图10 本文方法、SDT方法、ICP方法计算不同周向角装配后的位姿偏差

Fig.10 Assembly position and orientation deviations at different circumferential angles determined using the proposed method,SDT method,and ICP method

表4 本文方法、SDT方法、ICP方法计算不同周向角装配后的位姿偏差

Table 4 Assembly position and orientation deviations at different circumferential angles determined using the proposed method, SDT method,and ICP method

参数	SDT方法计算结果	ICP方法计算结果	本文方法
参数	SDT方法计算结果	ICP方法计算结果	计算结果	与SDT方法相对误差/%	与ICP方法相对误差/%
沿x轴距离偏差均值/mm	0.0146	0.0152	0.0129	11.6	15.1
沿y轴距离偏差均值/mm	0.0174	0.0163	0.0149	14.4	8.6
沿z轴距离偏差均值/mm	0.0028	0.0029	0.0025	10.7	16.1
轴线夹角偏差均值/(°)	0.0029	0.0029	0.0024	17.2	17.2

表5 本文方法、SDT方法、ICP方法计算不同周向角工况的耗时

Table 5 Computation times of the proposed method,SDT method, and ICP method for different circumferential angles s

周向角工况	SDT方法		ICP方法		本文方法
周向角工况	耗时	均值	耗时	均值	耗时	均值
1	2.80	2.1	1669	1624	3063	3002
2	2.30		1598		2949
3	1.95		1646		3086
4	1.68		1546		2970
5	1.81		1588		2940
6	2.97		1663		2950
7	1.65		1644		3025
8	1.98		1668		2995
9	1.85		1623		2971
10	2.10		1531		3067
11	2.31		1653		3017
12	2.21		1665		3001

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