苗正 牛放 花少震

DOI：10.16661/j.cnki.1672-3791.2105-5042-6439

摘  要：为了提高等效法求非均质或者不规则几何体转动惯量的精度，该文以非均质发动机摇臂为研究对象，研究了拉格朗日插值法、牛顿插值法、抛物线插值法在根据等效原理求非均质发动机摇臂转动惯量的精度与截断误差。通过对比分析发现抛物线插值法的精度最低，拉格朗日插值法与牛顿插值法的截断误差较小。综合精度和误差分析可以得出，牛顿插值法在等效法求非均质发动机摇臂转动惯量上具有较高精度，该研究可以为等效法求非均质或者不规则几何体的转动惯量提供参考。

关键词：转动惯量   等效原理   插值方法   截断误差

中图分类号：O302                           文献标识码：A文章编号：1672-3791（2021）08（a）-0164-04

Study on Interpolation Method of Moment of Inertia Based on Equivalent Principle

MIAO Zheng   NIU Fang   HUA Shaozhen*

（School of Mechanical Engineering， Henan Institute of Technology， Xinxiang， Henan Province， 453003 China）

Abstract： In order to improve the accuracy of calculating the moment of inertia of heterogeneous or irregular geometry based on the equivalent method， heterogeneous engine rocker arm has been taken as the research object， then the Lagrange interpolation method， Newton interpolation method and parabola interpolation method were studied based on the equivalent principle to calculate the accuracy and truncation error of the moment of inertia of. Through comparative analysis， it is found that the accuracy of parabola interpolation method is the lowest， and the truncation error of Lagrange interpolation method and Newton interpolation method is smaller. Comprehensive accuracy and error analysis can be concluded that Newton interpolation method has high accuracy in the equivalent method to calculate the moment of inertia of heterogeneous engine rocker arm. This study can provide a reference for the equivalent method to calculate the moment of inertia of heterogeneous or irregular geometry.

Key Words： Moment of inertia; Equivalent principle; Interpolation method; Truncation error

转动惯量是刚体绕定轴转动时惯性的度量[1]，是航空航天、仪器仪表、汽车、电力等行业中重要的参量。由于转动惯量只和转轴的位置、刚体的质量分布以及港田的形状有关，所以对于一些非均质的几何体或者形状复杂的几何体，一般通过实验手段，基于等效原理，采用插值手段测定。吉丹霞等人[2]利用等效法研究了变速箱中不同轮系等效转动惯量的计算方法;仝哲旭等人[3]通过设计非接触平面涡卷弹簧，测量了正弦扭矩标准装置气浮轴系的转动惯量;赵亚燊等人[4]利用等效法计算了窄轮距拖拉机的转动惯量。周艳明等人[5]研究了三线摆实验中大摆角对转动惯量的影响，徐钱欣等人[6]、陈坤波等人[7]、陈庆东等人[8]利用改进的三线摆降低了实验误差。……