力学与实践 ›› 2012, Vol. 34 ›› Issue (6): 50-54.DOI: 10.6052/1000-0879-12-196

• 应用研究 • 上一篇    下一篇

三线摆摆线质量对转动惯量精确测量的影响

葛宇宏, 葛志利   

  1. 南京化工职业技术学院, 南京210048
  • 收稿日期:2012-05-14 出版日期:2012-12-15 发布日期:2013-02-07
  • 通讯作者: 葛宇宏, 1959 年生, 男, 南京化工职业学院副教授, 主要研究方向为物理理论与实验教学. E-mail: yuhongge@hotmail.com

THE EFFECT OF MASS OF THREE-WIRE PENDULUM CYCLOID ON THE ACCURACY OF MEASURED MOMENT OF INERTIA

GE Yuhong, GE Zhili   

  1. School of Basic Studies, Nanjing College of Chemical Technology, Nanjing 210048, China
  • Received:2012-05-14 Online:2012-12-15 Published:2013-02-07

摘要: 三线摆法是测量转动惯量的常用方法, 理论上通常都是把摆线作理想处理(即摆线质量趋于0), 但在工程测量中, 被测工件往往较重, 摆线不再是轻质细线, 摆线质量势必会对空载悬盘的转动惯量测量产生影响. 本文应用哈密顿原理和变量替换, 导出三线摆摆线的变张力弦振动方程, 通过对摆线与悬盘连接点(x=0)的运动状态讨论, 推得摆线质量不能忽略情形下的对称式三线摆的转动惯量计算式, 并借助于MATLAB 软件快速便利地进行计算.

关键词: 转动惯量|三线摆|哈密顿原理|贝塞耳函数

Abstract: Using the three wire- pendulum to measure the moment of inertia is a common practice. The cycloid is usually assumed in an ideal state theoretically (i.e the mass of the cycloid approaches 0). But actually, if the workpiece measured is heavy, the mass of the cycloid can not be neglected, we have to consider the mass of the cycloid in the moment of inertia of the empty turning wheel. This paper uses the Halmiltonian theory and the variable substitution to derive the variable tension string vibration equation of the three wire-pendulum cycloid. And from the state of the point in the junction of the cycloid and the turning wheel (x=0), we obtain a computational formula for the moment of inertia by using the three wire-pendulum without neglecting the mass of the cycloid. In addition, we can make calculations by MATLAB.

Key words: moment of inertia|three wire-pendulum|Halmiltonian theory|Bessel function

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