全部

力学与实践 ›› 2010, Vol. 32 ›› Issue (5): 72-75.doi: 10.6052/1000-0879-lxysj2010-072

• 应用研究 • 上一篇    下一篇

实时测算阻尼比研究转动惯量

葛宇宏   

  1. 南京化工职业技术学院 江苏 南京 210048
  • 收稿日期:2010-03-02 修回日期:2010-03-16 出版日期:2010-10-08 发布日期:2010-09-26

REAL-TIME COMPUTATION OF MOMENT OF INERTIA AND DAMPING RATIO

  • Received:2010-03-02 Revised:2010-03-16 Online:2010-10-08 Published:2010-09-26

摘要: 以``长摆线三线摆''为物理动力学模型, 采用拉格朗日第二类方程研究阻尼对工件 转动惯量测量的影响, 针对``振幅测量法''中很难测准摆幅幅值等实际问题,提出 一种``等弧--时间比法'', 即通过计算悬盘在不同周期内、在相同位 置摆过相等圆弧所用时间比来计算系统阻尼比$\zeta$的方法, 提高外形尺寸较大 工件的转动惯量测量精度.

关键词: 长摆线三线摆;转动惯量;阻尼比;拉格朗日第二类方程

Abstract: In this paper, taking the prolate cycloid-three-wire as a model of physical dynamics, we consider the damping's influence on computation of workpiece's moment of inertia by using the second kind Lagrange's equation. It is difficult to calculate the value of amplitude of swing accurately by the amplitude measuring method. So, an equal arc length- time ratio method is proposed to improve the precision for a workpiece of large size. The damping ratio $\zeta $ is obtained by calculating the time ratio of hanging dish which swings beyond the equal arc length in the same location with different periods.

Key words: Prolate cycloid -three-wire, moment of inertia, damping ratio, the second kind Lagrange's equation