三轴转动惯量的振复摆与扭摆法协同测量比例法

doi:10.12382/bgxb.2022.0055

摘要/Abstract

摘要：

空间飞行体在进行三轴转动惯量测量时需要分别沿3个正交方位做圆周摆动,为减少方位调整次数,提出基于振复摆与扭摆法的协同测量比例法。描述了该方法的测量机构,推导了比例法全因计算公式和近似计算公式;对该方法进行了误差分析,并与扭摆法进行了对比;采用模拟件作为测量对象,对提出的测量方法进行了实验研究。实验结果表明:J_z/J_y小于1.02时,协同比例法的全因计算和近似计算精度基本相同且与扭摆法基本相当;J_z/J_y大于1.02时,只能采用协同比例法全因计算公式,同时该方法解决了带翼飞行体三轴转动惯量测量的难题;协同比例法与前期提出的协同差值法组成了完整的测量体系,可以满足一定类型的回转体和带翼异形体三轴转动惯量测量需求。

关键词: 三轴转动惯量, 协同测量, 振复摆, 扭摆法, 协同比例法

Abstract:

A body moving in space needs to do circular swing along three orthogonal directions respectively during the measurement of its triaxial moment of inertia. To reduce the number of azimuth adjustment, a coollaborative proportional method for measuring the triaxial moment of inertia based on vibration compound pendulum and torsion pendulum is proposed. The equipment structure is described, and the full-parameter calculation formula and approximate calculation formula of the proposed method are given. Error analysis is done to this method and a comparison is made with the torsion pendulum method. Simulators are used as the measurement object, and the proposed method is experimentally studied. The experimental results indicate that: the computational results of the two formulas are basically the same when J_z/J_y is less than 1.02; when J_z/J_y is greater than 1.02, only the full-parameter calculation formula can be used, which can also solve the problem of triaxial measurement of the moment of inertia of winged flying bodies; the proposed method and the collaborative difference method previously developed constitute the complete measurement system, which can meet the requirements of certain types of revolving body and heteromorphic body with wings for the triaxial measurement of moment of inertia.

Key words: triaxial moment of inertia, collaborative measurement, vibration compound pendulum, torsion pendulum, collaborative proportional measuring method

杨洪涛, 卢志辉, 孙浩智, 武艺泳, 刘珉, 来颜博. 三轴转动惯量的振复摆与扭摆法协同测量比例法[J]. 兵工学报, 2023, 44(5): 1513-1520.

YANG Hongtao, LU Zhihui, SUN Haozhi, WU Yiyong, LIU Min, LAI Yanbo. Collaborative Proportional Method for Measuring Triaxial Moment of Inertia Based on Vibration Compound Pendulum and Torsion Pendulum[J]. Acta Armamentarii, 2023, 44(5): 1513-1520.

图/表 8

图1 扭摆法和振复摆协同法机构示意图

Fig.1 Schematic diagram of measuring mechanism with torsion pendulum and vibration compound pendulum

表1 协同比例法引起的附加误差值

Table 1 Additional error value caused by the collaborative proportional method

(ΔJ₀+Δ(m_c $h c 2$ )) 相对误差	J_z/J_y
(ΔJ₀+Δ(m_c $h c 2$ )) 相对误差	1.00	1.05	1.10	1.20
0.5%	0	0.2%	0.4%	0.8%
1.0%	0	0.4%	0.8%	1.6%

表1 协同比例法引起的附加误差值

Table 1 Additional error value caused by the collaborative proportional method

(ΔJ₀+Δ(m_c $h c 2$ )) 相对误差	J_z/J_y
(ΔJ₀+Δ(m_c $h c 2$ )) 相对误差	1.00	1.05	1.10	1.20
0.5%	0	0.2%	0.4%	0.8%
1.0%	0	0.4%	0.8%	1.6%

表2 4组模拟件基本参数和三轴转动惯量扭摆法测量结果

Table 2 Basic parameters of 4 groups of simulators and measurement results of triaxial moment of inertia by the torsion pendulum method

组别及其均值	质量/ kg	轴向质心/ mm	横向质心 y_c/mm	横向质心 z_c/mm	扭摆法转动惯量J_y/ (kg·m²)	扭摆法转动惯量J_z/ (kg·m²)
	153.34	727.09	0.07	-0.12	20.41	20.43
第1组	153.30	726.98	0.07	-0.12	20.42	20.43
	153.31	727.21	0.07	-0.13	20.43	20.44
均值	153.32	727.09	0.07	-0.12	20.42	20.43
	161.34	725.59	0.07	-0.03	21.16	21.47
第2组	161.37	726.14	0.07	-0.04	21.19	21.49
	161.34	726.56	0.09	-0.03	21.20	21.53
均值	161.35	726.10	0.08	-0.03	21.18	21.50
	177.44	722.30	0.07	0.04	22.41	23.20
第3组	177.46	722.42	0.06	0.02	22.41	23.20
	177.46	721.93	0.08	0.03	22.40	23.21
均值	177.45	722.22	0.07	0.03	22.41	23.20
	193.21	678.25	0.18	0.15	26.62	28.51
第4组	193.20	678.67	0.21	0.16	26.63	28.53
	193.19	678.68	0.20	0.17	26.62	28.54
均值	193.20	678.53	0.20	0.16	26.62	28.53

表3 设备及4组模拟件基础数据

Table 3 Basic data of equipment and 4 groups of simulators

组别	m_c/kg	h₀/m	x_c/m	h_c/m	轴系J₀/ (kg·m²)	J₀+m_c $h c 2$ / (kg·m²)
第1组	153.32	0.49	0.25	0.74	77.80	160.85
第2组	161.35	0.49	0.25	0.74	77.80	165.44
第3组	177.45	0.49	0.25	0.74	77.80	175.23
第4组	193.20	0.49	0.30	0.79	77.80	196.86

表3 设备及4组模拟件基础数据

Table 3 Basic data of equipment and 4 groups of simulators

组别	m_c/kg	h₀/m	x_c/m	h_c/m	轴系J₀/ (kg·m²)	J₀+m_c $h c 2$ / (kg·m²)
第1组	153.32	0.49	0.25	0.74	77.80	160.85
第2组	161.35	0.49	0.25	0.74	77.80	165.44
第3组	177.45	0.49	0.25	0.74	77.80	175.23
第4组	193.20	0.49	0.30	0.79	77.80	196.86

图2 模拟产品、模拟产品+第1组试块、模拟产品+第2 组试块、模拟产品+翼展模拟组件实验状态示意图

Fig.2 Schematic diagram of experimental state of simulated product, simulated product+the first group of test blocks, simulated product+the second group of test blocks, simulated product+wing unfolding simulation components

表4 4组模拟件周期协同比例法测量结果

Table 4 Measurement results of 4 groups of simulators bythe periodic collaborative proportional method

组别及均值	第1组		第2组		第3组		第4组
组别及均值	振复摆产品周期T_y/s	振复摆产品周期T_z/s	振复摆产品周期T_y/s	振复摆产品周期T_z/s	振复摆产品周期T_y/s	振复摆产品周期T_z/s	振复摆产品周期T_y/s	振复摆产品周期T_z/s
1	0.3350	0.3350	0.3406	0.3410	0.3501	0.3510	0.3722	0.3744
2	0.3350	0.3350	0.3406	0.3410	0.3501	0.3510	0.3723	0.3744
3	0.3350	0.3352	0.3406	0.3410	0.3501	0.3511	0.3724	0.3744
4	0.3351	0.3352	0.3406	0.3411	0.3501	0.3511	0.3723	0.3745
5	0.3351	0.3352	0.3407	0.3411	0.3503	0.3512	0.3727	0.3747
均值	0.33504	0.33512	0.34062	0.34104	0.35014	0.35108	0.37238	0.37448

表5 4组模拟件转动惯量Jz协同比例法测量结果

Table 5 Measurement results of moment of inertia Jz of 4 groups of simulators by the collaborative proportional method

组别	振复摆产品周期T_y/s	振复摆产品周期T_z/s	J₀+m_c $h c 2$	扭摆法转动惯量J_y/ (kg·m²)	扭摆法转动惯量J_z/ (kg·m²)	协同比例法转动惯量 J_z/(kg·m²)	与扭摆法差值/ (kg·m²)	误差率/ %	J_z/J_y
第1组	0.33504	0.33512	160.853	20.42	20.43	20.51	0.08	0.4	1.00
第2组	0.34062	0.34104	165.440	21.18	21.50	21.64	0.14	0.7	1.02
第3组	0.35014	0.35108	175.234	22.44	23.23	23.50	0.27	1.2	1.04
第4组	0.37238	0.37448	196.855	26.62	28.53	29.21	0.68	2.4	1.07

表5 4组模拟件转动惯量Jz协同比例法测量结果

Table 5 Measurement results of moment of inertia Jz of 4 groups of simulators by the collaborative proportional method

组别	振复摆产品周期T_y/s	振复摆产品周期T_z/s	J₀+m_c $h c 2$	扭摆法转动惯量J_y/ (kg·m²)	扭摆法转动惯量J_z/ (kg·m²)	协同比例法转动惯量 J_z/(kg·m²)	与扭摆法差值/ (kg·m²)	误差率/ %	J_z/J_y
第1组	0.33504	0.33512	160.853	20.42	20.43	20.51	0.08	0.4	1.00
第2组	0.34062	0.34104	165.440	21.18	21.50	21.64	0.14	0.7	1.02
第3组	0.35014	0.35108	175.234	22.44	23.23	23.50	0.27	1.2	1.04
第4组	0.37238	0.37448	196.855	26.62	28.53	29.21	0.68	2.4	1.07

表6 4组模拟件协同比例法近似计算结果

Table 6 Approximate results of 4 groups of simulators by the collaborative proportional method

组别	振复摆产品周期T_y/s	振复摆产品周期T_z/s	扭摆法转动惯量J_y/(kg·m²)	扭摆法转动惯量J_z/(kg·m²)	协同比例法转动惯量J_z/(kg·m²)	与扭摆法差值	误差率/ %	与全因法差值
第1组	0.33504	0.33512	20.42	20.43	20.43	0.00	0.0	-0.08
第2组	0.34062	0.34104	21.18	21.50	21.23	-0.27	1.3	-0.41
第3组	0.35014	0.35108	22.44	23.23	22.56	-0.67	2.9	-0.94
第4组	0.37238	0.37448	26.62	28.53	26.92	-1.61	5.6	-2.29

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