摩擦阻力矩对卧式扭摆法测量弹箭极转动惯量精度的影响
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摘要
针对摩擦阻力矩对卧式扭摆法测量弹箭极转动惯量精度的影响,对测量方法进行了修正。给出了摩擦阻力矩的计算方法,对摩擦阻力矩进行了近似常数化处理,推导出考虑摩擦阻力矩影响的扭摆系统运动微分方程,在此基础上分析了摩擦阻力矩对摆动周期、摆动次数、系统静平衡位置的影响。通过对运动微分方程进行数值求解,定性分析了光电传感器位于两静平衡位置之间不同位置时周期测量的变化趋势,进而优化了光电传感器的安装位置。算例结果表明,摩擦阻力矩对弹箭极转动惯量测量精度的影响不可忽略,采用该文修正方法可将卧式扭摆法对弹箭极转动惯量的测量误差降低一个数量级。
In view of the effect of the friction resistance moment on the measurement accuracy of polar moment of inertia of projectiles by the torsion pendulum method,the measurement method is modified.The calculation method and the approximate constant processing of the friction resistance moment are given in details,then the motion differential equation is deduced in consideration of the effect of the friction resistance moment.Then the influences of the friction resistance moment on the pendulum period,the pendulum count and the static equilibrium position are analyzed.By presenting the numerical solution of the motion differential equation,the qualitative analysis of trend of the measurement period is conducted when the photoelectric sensor is located at different positions between the two static equilibrium positions,andthe installation location of the photoelectric sensor is optimized.The calculation result of example shows that the effect of the friction resistance moment on the measurement accuracy of the polar moment of inertia of projectiles by the torsion pendulum method can not be ignored,and its measurement error decreases by one order magnitude when using the method in this paper.
In view of the effect of the friction resistance moment on the measurement accuracy of polar moment of inertia of projectiles by the torsion pendulum method,the measurement method is modified.The calculation method and the approximate constant processing of the friction resistance moment are given in details,then the motion differential equation is deduced in consideration of the effect of the friction resistance moment.Then the influences of the friction resistance moment on the pendulum period,the pendulum count and the static equilibrium position are analyzed.By presenting the numerical solution of the motion differential equation,the qualitative analysis of trend of the measurement period is conducted when the photoelectric sensor is located at different positions between the two static equilibrium positions,andthe installation location of the photoelectric sensor is optimized.The calculation result of example shows that the effect of the friction resistance moment on the measurement accuracy of the polar moment of inertia of projectiles by the torsion pendulum method can not be ignored,and its measurement error decreases by one order magnitude when using the method in this paper.
引文
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[2]侯文.大型弹箭及航天器转动惯量测量方法研究[J].中北大学学报,2008,29(6):505-509.Hou Wen.Research on measurement method for moment of inertia of large-scale projectiles and spacecrafts[J].Journal of North University of China,2008,29(6):505-509.
[3]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 Wenyan,Li Huipeng,Zhang Chunfu.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.
[4]Richard S Boynton,Daniel Otlowski.A new high speed mass properties instrument[J].SAWE Paper3341,2004.
[5]张心明,郑英杰,迟占铎.质偏对卧式扭摆法测量弹体转动惯量精度的影响[J].兵工学报,2013,34(6):797-800.Zhang Xinming,Zheng Yingjie,Chi Zhanduo.Effect of centroidal deviation on measurement of rotational inertia of projectile body by torsion pendulum method[J].Acta Armamentarii,2013,34(6):797-800.
[6]李慧鹏,唐文彦,张春富,等.基于阻尼比实时算法的转动惯量测量研究[J].南京理工大学学报,2008,32(4):472-475.Li Huipeng,Tang Wenyan,Zhang Chunfu,et al.Measurement of moment of inertia based on real-time computing damping ratio[J].Journal of Nanjing Uni-versity of Science and Technology,2008,32(4):472-475.
[7]成大先.机械设计手册(第5版)[M].北京:化学工业出版社,2010.
[8]Singiresu S Rao.机械振动(第4版)[M].李欣业,张明路,译.北京:清华大学出版社,2014.
[9]邹红玉,郑红平.扭摆法测量转动惯量实验中光电门摆放位置的探究[J].物理实验,2009,29(6):29-31.Zou Hongyu,Zheng Hongping.Discussion on position of optical gate in rotational inertia experiment[J].Physics Experimentation,2009,29(6):29-31.