• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2016, Vol. 52 ›› Issue (7): 54-59.doi: 10.3901/JME.2016.07.054

• 机械动力学 • 上一篇    下一篇

永磁轴承承载能力分子电流模型的积分定义求解方法

张海波, 邱玉江, 蒋书运   

  1. 东南大学机械工程学院 南京 211189
  • 出版日期:2016-04-05 发布日期:2016-04-05
  • 作者简介:张海波,男,1987 年出生。主要研究方向为永磁轴承。E-mail:zhhaibo87@163.com;邱玉江,男,1978年出生,博士研究生。主要研究方向飞轮储能技术、转子动力学。E-mail:nylgjdxqyj@163.com;蒋书运(通信作者),男,1966 年出生,博士,教授,博士研究生导师。主要研究方向为飞轮储能技术、高速加工机床、机械动力学和摩擦学等。E-mail:jiangshy@seu.edu.cn
  • 基金资助:
    国家自然科学基金(11172065, 11472078)和江苏省产学研前瞻性合作(BY2015070-26)资助项目

Analysis of the Equivalent Surface Current Model for the Permanent Magnet Bearing by Using the Integral Definition

ZHANG Haibo, QIU Yujiang, JIANG Shuyun   

  1. School of Mechanical Engineering, Southeast University, Nanjing 211189
  • Online:2016-04-05 Published:2016-04-05

摘要: 分子电流理论是一种计算永磁轴承力学特性的经典理论,利用此理论分析计算永磁轴承承载力时一般采用蒙特卡罗法或椭圆积分法等求解四重积分,蒙特卡罗法数值稳定性差,椭圆积分法求解析解过程中,有时会出现奇异值。为了简化计算,提出了永磁轴承承载力方程的积分定义求解方法,该方法将被积函数的积分域分割成有限个微域,对于每个微域,以被积函数的微域中心值与微域体积的乘积作为被积函数的积分值,将所有微域的积分和值近似作为函数积分值;基于双丝杠导轨副与3维力传感器,研制了永磁轴承力学性能的测试装置,完成永磁轴承承载力的试验验证;较为系统地对比分析了积分定义法与蒙特卡罗法、有限元法数值解的计算结果。研究结果表明:积分定义法计算过程简单,易于编写计算程序,相对误差 较小。

关键词: 承载力, 分子电流法, 积分定义法, 永磁轴承

Abstract: The equivalent surface current is a typical method for calculating the mechanical property of permanent magnet bearing. However, Monte Carlo method or elliptic integral method are usually used to solve a quadruple integral for the equivalent surface current. However, the numerical stability is poor for the Monte Carlo method, and singular values sometimes appear for the elliptic integral method. In order to simplify the calculation, the integral definition method is proposed to solve the equations of the load capacity for the permanent magnet bearing, in details, the integral domain of integrand is divided into a infinite number of small domains, the integral value of each small domain is approximatively equal to the production of the center value of integrand and the volume of small domain, the integral value of integrand is approximatively equal to the sum of total integral value of small domains. The testing device is developed by using double layers ball screw drive systems and a 3-DOF force sensor to test the mechanical property for the permanent magnet bearing, and the results show the theoretical value of the integral definition method agrees well with the tested one. A comparative study confirms that the integral definition method is superior to the Monte Carlo method and finite element method in either the simplification of calculation process and program development or the calculation error.

Key words: equivalent surface currents, integral definition method, load capacity, permanent magnet bearings

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