卢志辉 , 孙浩智 , 王和 , 等 . 三轴转动惯量的直立振复摆与圆周扭摆协同测量方法 [J/OL ] . 兵工学报 , 2021 [2022-01-06 ] . DOI: 10.12382/bgxb.2021.0383 https://dx.doi.org/10.12382/bgxb.2021.0383 . DOI: 10.12382/bgxb.2021.0383 http://doi.org/10.12382/bgxb.2021.0383

LU Z H , SUN H Z , WANG H , et al. The collaborative measuring method of triaxial moment of inertia based on vertical vibration compound pendulum and circular torsion pendulum [J/OL ] . Acta Armamentarii , 2021 [2022-01-06 ] . DOI: 10.12382/bgxb.2021.0383 https://dx.doi.org/10.12382/bgxb.2021.0383 . (in Chinese) DOI: 10.12382/bgxb.2021.0383 http://doi.org/10.12382/bgxb.2021.0383

KLAUS L . Comparison of two experiments based on a physical and a torsion pendulum to determine the mass moment of inertia including measurement uncertainties [J ] . Measurement Science Review , 2017 , 17 ( 1 ): 9 - 18 . DOI: 10.1515/msr-2017-0002 http://doi.org/10.1515/msr-2017-0002 https://www.sciendo.com/article/10.1515/msr-2017-0002 https://www.sciendo.com/article/10.1515/msr-2017-0002 To determine the mass-moment-of-inertia properties of devices under test with particularly small mass moments of inertia (some 10−4 kg m2), two measurement set-ups based on different measurement principles were developed. One set-up is based on a physical pendulum, the second set-up incorporates a torsion pendulum. Both measurement set-ups and their measurement principles are described in detail, including the chosen data acquisition and analysis. Measurement uncertainty estimations according to the Guide to the Expression of Uncertainty in Measurement (GUM) were carried out for both set-ups by applying Monte Carlo simulations. Both set-ups were compared using the same three devices under test. For each measurement result, the measurement uncertainties were estimated. The measurement results are compared in terms of consistency and the resulting measurement uncertainties. For the given devices under test, the torsion pendulum set-up gave results with smaller measurement uncertainties compared to the set-up incorporating a physical pendulum.

唐文彦 , 李慧鹏 , 张春富 . 扭摆法测量飞行体转动惯量 [J ] . 南京理工大学学报 , 2008 , 32 ( 1 ): 69 - 72 .

TANG W Y , LI H P , ZHANG C F . Measurement of flight object’s moment of inertia using torsion pendulum [J ] . Journal of Nanjing University of Science and Technology , 2008 , 32 ( 1 ): 69 - 72 . (in Chinese)

卢志辉 , 张磊乐 , 武艺泳 , 等 . 用于测量物体质心、转动惯量和惯性积的测量装置: 中国, 201410442687.4 [P ] . 2016-08-17.

LU Z H , ZHANG L L , WU Y Y , et al. Measuring device for measuring center of mass, moment of inertia and inertial product: China, 201410442687.4 [P ] . 2016-08-17. (in Chinese)

张磊乐 . 细长杆件质量特性测量技术及设备研究 [D ] . 郑州 : 郑州机械研究所 , 2008 .

ZHANG L L . Research on the slender bar’s technique and equipment for measurement of parameters about the mass properties [D ] . Zhengzhou : Zhengzhou Research Institute of Mechanical Engineering , 2008 . (in Chinese)

李慧鹏 , 唐文彦 , 张春富 , 等 . 导弹转动惯量测试系统及误差分析 [J ] . 兵工学报 , 2007 , 28 ( 2 ): 206 - 208 . 研制了可精确测量质量在100～1200 kg范围内导弹等飞行体转动惯量的大型测试系统。利用可展开式测量臂结构，实现了一次工装就可以测量出导弹对3个轴的转动惯量，从而有效降低了多次安装带来的定位误差。对影响系统测量精度的误差因素进行了定量分析。对标准样件进行了实测，各轴的转动惯量测量误差均小于0.1%．

LI H P , TANG W Y , ZHANG C F , et al. A measuring system of inertia moment of missile and its error analysis [J ] . Acta Armamentarii , 2007 , 28 ( 2 ): 206 - 208 . (in Chinese)

车英 , 李占国 , 陈礼华 , 等 . 弹丸转动惯量测试系统及其误差分析 [J ] . 兵工学报 , 2000 , 21 ( 1 ): 87 - 89 . 介绍了一种用于测量弹丸转动惯量的高精度测量仪器，该仪器利用双悬丝扭摆机构、光电计时系统提取摆动周期信息，由MCS-51丕列单片机组成的测量系统进行数据处理，并由LED显示器测量结果。文中阐述了仪器的工作原理，推导了所需的计算公式，分析了产生测量误差的因素，进行了定量精度分析，给出了实验结果与测量精度。

CHE Y , LI Z G , CHEN L H , et al. Development and error analysis of an inspecting system for measuring the rotational inertia of bullets [J ] . Acta Armamentarii , 2000 , 21 ( 1 ): 87 - 89 . (in Chinese) An instrument for measuring the rotational inertia of various Dullets and rifle grenades with precision is introduced. In this measuring instrument, a double suspension structure is adopted, and an optoelectronic timing system is used to extract the information of the periods of torsional-oscillation of the measured bullet. The data is processed by the measuring system consisting of MCS-51 series of monolithiccomputers, and the measured results are displayed on displayer LED. In this paper, the working principle of the instrument is expounded, the relevant formulae are derived, and the main factors affecting precision discussed. Precision of the instrument is analysed quantitatively. Experimental results and measuring precision are given.

王德民 , 吴红刚 , 张健 , 等 . 基于扭摆法的三扭杆转动惯量测量装置 [J ] . 机械设计与研究 , 2017 , 33 ( 3 ): 139 - 141 ,145.

WANG D M , WU H G , ZHANG J , et al. Research on torsion pendulum based triple torsion bars device for measuring moment of inertia [J ] . Machine Design and Research , 2017 , 33 ( 3 ): 139 - 141 ,145. (in Chinese)

卢志辉 , 支余吉 . 转动惯量标准件标准值的不确定度研究 [C ] ∥全国计量测试技术学术交流会论文集 . 北京 : 中国计量测试学会 , 2016 : 256 - 261 .

LU Z H , ZHI Y J . Research on uncertainty of standard value of moment of inertia of standard sample [C ] ∥Proceedings of Collection of Essays of National Symposium on Measurement and Testing Technology . Beijing : Chinese Society for Measurement , 2016 : 256 - 261 . (in Chinese)

孙宝光 , 刘春兰 , 罗微 . 扭摆法测定物体的转动惯量实验中的标定研究 [J ] . 大学物理实验 , 2017 , 30 ( 6 ): 53 - 56 .

SUN B G , LIU C L , LUO W . Research on the calibration in measuring objects’ processional moment by torsion pendulum method [J ] . Physical Experiment of College , 2017 , 30 ( 6 ): 53 - 56 . (in Chinese)

宋斌 , 莫德强 , 刘永付 , 等 . 小质量弹丸积转动惯量测试设备设计及其标定方法 [J ] . 长春理工大学学报(自然科学版) , 2021 , 44 ( 6 ): 90 - 95 .

SONG B , MO D Q , LIU Y F , et al. Design of measuring equipment for small mass projectile ole moment of inertia and analysis of calibration method [J ] . Journal of Changchun University of Science and Technology (Natural Science Edition) , 2021 , 44 ( 6 ): 90 - 95 . (in Chinese)

张心明 , 王凌云 , 刘建河 , 等 . 复摆法测量箭弹转动惯量和质偏及其误差分析 [J ] . 兵工学报 , 2008 , 29 ( 4 ): 450 - 453 . 基于复摆原理，阐述了箭弹的质偏和转动惯量的测量方法及装置，推导出了质偏和转动惯量的计算公式。对影响测量精度的因素进行了分析。给出测量结果的不确定度计算公式，在假定各测量参数误差为正态分布条件下，导出了测量结果的极限误差计算公式。同时还进行了实例计算和实验测试。结果表明，用复摆法测量弹箭的质偏和转动惯量是可行有效的，其测量精度可满足工程实际要求。该方法采用刀口支承，且在测试中工装简单，便于操作，特别适用于中小弹体的质偏和转动惯量的测量。

ZHANG X M , WANG L Y , LIU J H , et al. The measurement of inertia moment and centroidal deviation of rocket projectile with compound pendulum method and its error analysis [J ] . Acta Armamentarii , 2008 , 29 ( 4 ): 450 - 453 . (in Chinese)

HOU W , ZHENG B , YANG R F . A measuring method on moment of inertia of large-scale ammunition [J ] . Journal of China Ordnance , 2005 ( 1 ): 41 - 46 .

徐向辉 , 陈平 , 唐一科 , 等 . 弹箭转动惯量的振复摆法测量及误差分析 [J ] . 弹箭与制导学报 , 2016 , 36 ( 1 ): 149 - 153 .

XU X H , CHEN P , TANG Y K , et al. The inertia moment of projectile measured by vibration pendulum method and error analysis [J ] . Journal of Projectiles, Rockets, Missiles and Guidance , 2016 , 36 ( 1 ): 149 - 153 . (in Chinese)

张心明 , 王德民 , 李俊烨 , 等 . 基于复摆测量法阻尼对转动惯量的影响分析 [J ] . 长春理工大学学报(自然科学版) , 2018 , 41 ( 4 ): 54 - 59 .

ZHANG X M , WANG D M , LI J Y , et al. Analysis on the influence of rotational inertia by damping based on compound pendulum measuring method [J ] . Journal of Changchun University of Science and Technology (Natural Science Edition) , 2018 , 41 ( 4 ): 54 - 59 . (in Chinese)

GABL R , DAVEY T , NIXON E , et al. Accuracy analysis of the measurement of centre of gravity and moment of inertia with a swing [J ] . Applied Sciences , 2021 , 11 ( 12 ): 5345 . DOI: 10.3390/app11125345 http://doi.org/10.3390/app11125345 https://www.mdpi.com/2076-3417/11/12/5345 https://www.mdpi.com/2076-3417/11/12/5345 Floating devices under wave and current loads are typically designed based on numerical methods followed by a validation with experimental investigations. This allows an independent check due to the comparison of two different modelling approaches based on different assumptions. At an early stage of the project, numerical simulations are based on theoretical (ideal) values of the centre of gravity (CG) and moment of inertia (MI). The building process of a scaled model results very often in a requested simplification of certain parts, which can influence the CG and also the MI of the scaled model. Knowing those discrepancies allows us to improve the comparability of both approaches but the measurement of those values is connected with either a higher uncertainty or a high level of effort. A significant improvement of such measurements can be reached by the deployment of a specific experimental set-up. This paper presents the classification of the newly designed swing with a high accuracy inertial inclinometer, which was verified by the marker-based motion capturing system. The achieved experiences are useful for the future use of the set-up as well as similar investigations. The comparison with the theoretical values for the swing as well as an example model showed very good agreements and a high accuracy of few millimetres for the CG and an error smaller 1% for MI.

卢志辉 , 孙志扬 , 李祥云 , 等 . 高精度质心测量方法研究 [J ] . 兵工学报 , 2009 , 30 ( 12 ): 1748 - 1752 . 质心测量对于空间飞行器至关重要，新型武器的研制对质心测量精度的要求不断提高。将传统的天平原理与旋转轴结合，利用传感器技术，设计了一种新型质心测量机构，提出了一种能够明显提高质心测量精度的测量方法。描述了具体测量机构的主体结构，给出了机构的测量原理、测量方法，并进行了机构对于质心测量的误差分析。结合测量设备研制，进行了误差估算，理论估算的结果最大误差为0.023 mm.采用标准样件的方法进行了实验验证，具体测量数据显示，最大误差为0.020 mm.结果表明此测量方法理论分析计算与实验结果具有较好的一致性，并达到了较高的测量精度。已采用该方法成功地研制出系列高精度测量设备，配用于相关领域。

LU Z H , SUN Z Y , LI X Y , et al. Research on high precision measurement of centroid [J ] . Acta Armamentarii , 2009 , 30 ( 12 ): 1748 - 1752 . (in Chinese)

张磊乐 , 武艺泳 , 时永华 . 基于立式旋转平衡系统的惯性积测试方法研究 [J ] . 计量学报 , 2020 , 41 ( 12A ): 124 - 128 .

ZHANG L L , WU Y Y , SHI Y H . Research on the method of measuring inertial product based on vertical Rotating balance system [J ] . Acta Metrologica Sinica , 2020 , 41 ( 12A ): 124 - 128 . (in Chinese)