Collaborative Proportional Method for Measuring Triaxial Moment of Inertia Based on Vibration Compound Pendulum and Torsion Pendulum

doi:10.12382/bgxb.2022.0055

Abstract

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

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.

Figures/Tables 8

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

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%

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%

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

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

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

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

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

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

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

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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