﻿ MSCSG转子不平衡振动原理分析与建模<sup>*</sup>
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MSCSG转子不平衡振动原理分析与建模

1. 航天工程大学 研究生院, 北京 101416;
2. 航天工程大学 宇航科学与技术系, 北京 101416;
3. 北京控制工程研究所, 北京 100190

Principle analysis and modeling of rotor imbalance vibration in magnetically suspended control and sensing gyroscope
XIA Changfeng1, CAI Yuanwen1, REN Yuan2, WANG Weijie2, FAN Yahong3, YIN Zengyuan1
1. Company of Postgraduate Management, Space Engineering University, Beijing 101416, China;
2. Department of Aerospace Science and Technology, Space Engineering University, Beijing 101416, China;
3. Beijing Institute of Control Engineering, Beijing 100190, China
Received: 2018-01-18; Accepted: 2018-03-02; Published online: 2018-05-04 08:28
Foundation item: National Natural Science Foundation of China (51475472, 61403396, 51605489)
Corresponding author. REN Yuan, E-mail:renyuan_823@aliyun.com
Abstract: Magnetically suspended control and sensing gyroscope (MSCSG) is a kind of new-concept gyro, which takes Lorentz force magnetic bearing as torquer to drive the rotor to tilt in radial direction. As there is dynamic unbalance in the magnetically suspended rotor system because of the uneven mass distribution, the generation principle of imbalance vibration is analyzed and the analytic model of it is established. First, the working principle of MSCSG is introduced. Then, the geometric analytic relation between geometric and inertial axis of rotor is determined on condition that rotor is unbalanced; the mathematic model of unba-lance vibration torque is established and the observability of imbalance disturbance is demonstrated. The model of bearing-rotor control system containing vibration source is constructed and the vibration generation mechanism in closed-loop system is analyzed. The dynamic response characteristics of unbalance vibration with different rotate speeds are simulated and the simulation result indicates the correctness of the proposed model. Finally, the requirement for suppression of unbalance vibration is put forward according to its vibration characteristics, which lays the theoretical foundation for realizing MSCSG rotor imbalance vibration control.
Keywords: magnetically suspended control and sensing gyroscope (MSCSG)     Lorentz force magnetic bearing     rotor imbalance     observability     vibration modeling

1 MSCSG工作原理

MSCSG结构如图 1所示，主要由陀螺房、陀螺转子、轴向磁轴承、力矩器、径向磁轴承、旋转电机、位移传感器构成。其中，旋转电机驱动转子绕轴向高速旋转，力矩器驱动转子绕径向偏转，径向磁轴承驱动转子沿径向平动，轴向磁轴承驱动转子沿轴向平动。

 图 1 MSCSG结构示意图 Fig. 1 Structure diagram of MSCSG

MSCSG采用LFMB为力矩器驱动转子偏转，LFMB产生的电磁力依据安培力定律，即磁感应强度为B的磁场中沿与磁场垂直方向放置长度为L的线圈，当流经线圈中电流为I时，线圈将受到大小为BIL的安培力作用。LFMB组件结构如图 2所示。转子外沿一周的狭长内壁上放置着上、下2层磁钢，2层磁钢的内、外磁钢间充磁方向相反，因此形成了如图 2中虚线所示的闭合磁场。LFMB的定子部分由4组匝数相同的线圈构成，位于内、外磁钢间的狭缝中，沿LFMB周向均匀分布，4组线圈成对使用，正对的2组线圈为一对，用于实现转子的二自由度偏转控制。

 图 2 LFMB工作原理 Fig. 2 Working principle of LFMB

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2 MSCSG转子不平衡问题几何分析

MSCSG转子除轴向旋转自由度由电机驱动控制，其余5个由磁轴承悬浮的自由度均需通过传感器来获得转子位置信息。该位置信息既提供给闭环控制器进行反馈控制，也作为转子悬浮工作状态的判定依据。转子偏转自由度为LFMB控制的自由度，需要位移传感器测量转子的位置信息来实现偏转通道的偏转角信息反馈。MSCSG偏转通道4个位移传感器安装在上陀螺房的传感器支架上，配置方式如图 3(a)所示，4个传感器在同一平面上，过定子坐标系原点O对检测面投影，如图 3(b)中黑色虚线所示。

 图 3 传感器探头配置及检测面示意图 Fig. 3 Schematic diagram of sensor probe configuration and detection surface

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 图 4 偏转角检测原理 Fig. 4 Testing principle of deflection angle

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 图 5 转子惯性轴与几何轴位置关系 Fig. 5 Position relation between inertial axis and geometric axis of rotor

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3 磁轴承-转子控制系统不平衡振动建模 3.1 不平衡扰动项能观性分析

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u=[iα  iβ]T，可得到式(8)对应的状态方程表达式为

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3.2 含振动源的磁轴承-转子控制系统动力学建模

 图 6 转子不平衡条件下MSCSG转子偏转控制系统闭环结构 Fig. 6 Closed-loop structure of rotor tilt control system in MSCSG considering rotor imbalance

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 图 7 磁轴承-转子控制系统框图 Fig. 7 Block diagram of magnetic bearing-rotor control system
4 仿真分析

 参数 数值 Jz/(kg·m2) 0.016 6 Jy/(kg·m2) 0.009 7 ki 0.001 ωD 240 kh 0.001 5 n 200 l/m 0.115 8 a2l 2 200 000 a2h 92 100 ls/m 0.078 ka/(V·A-1) 0.22 ωf/Hz 310 Jx/(kg·m2) 0.009 7 kp 15.1 kd 3.2 kl 0.001 5 B/T 0.4 lm/m 0.059 a1l 2 400 a1h 370 ks/(V·m-1) 10 300 δ/(°) 0.009 ωa/Hz 240 φ/(°) 10

 图 8 不平衡振动响应仿真结果 Fig. 8 Simulation results of unbalance vibration response
5 结论

1) MSCSG转子质量分布不平衡条件下，转子惯性主轴与几何主轴不一致，导致转子系统产生不平衡振动力矩。

2) MSCSG转子转速不为零的条件下，转子质量分布不平衡产生的振动力矩可观测。

3) MSCSG转子不平衡量经过磁轴承-转子控制系统产生电流刚度力矩，引起的振动与转子转速同频，为实现对转子的主动振动控制，必须对转速同频扰动量进行抑制。

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#### 文章信息

XIA Changfeng, CAI Yuanwen, REN Yuan, WANG Weijie, FAN Yahong, YIN Zengyuan
MSCSG转子不平衡振动原理分析与建模
Principle analysis and modeling of rotor imbalance vibration in magnetically suspended control and sensing gyroscope

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(11): 2321-2328
http://dx.doi.org/10.13700/j.bh.1001-5965.2018.0044