张舒月　李青　伍继浩

摘   要：磁悬浮冷压缩机是大型超流氦制冷系统的关键部件. 针对某磁悬浮冷压缩机转子系统，通过构建基于铁木辛柯梁理论的转子有限元模型，以及将电控硬件的作用定义为等效刚度和等效阻尼，组建了闭环系统中磁悬浮转子的完整模型，并完成了临界转速和不平衡响应的仿真计算. 仿真和实验测得冷压缩机转子在相同PID控制器作用下的刚体临界转速分别为27 Hz和28 Hz，前两阶弯曲临界转速的百分比误差均不超过2%. 控制器的关键参数在一定范围内变化时，通过不平衡响应仿真计算和50 000 rpm范围内的升速实验这两种方法得到的转子动力学特性较为相符. 这验证了所提出的建模和动力学计算方法的可靠性和准确性，研究成果对冷压缩机转子的结构设计以及控制器调试具有重要参考意义.

关键词：有限元方法;主动式磁悬浮轴承;PID控制;不平衡响应;临界转速

中图分类号：TH452                              文献标志码：A

Dynamic Analysis and Experiments on Cold Compressor

Research of Magnetic Suspension Rotor

ZHANG Shuyue LI Qing WU Jihao

（1. State Key Laboratory of Technologies in Space Cryogenic Propellants，Technical Institute

of Physics and Chemistry，Chinese Academy of Sciences，Beijing 100190，China;

2. College of Energy and Power Engineering，Huazhong University of Science and Technology，Wuhan 430074，China）

Abstract：Magnetic suspension cold compressor is one of the crucial components of the large superfluid helium refrigeration system. For the rotor system of magnetic suspension cold compressor，by constructing a finite element rotor model based on Timoshenko beam theory and defining the role of electronic control hardware as equivalent stiffness and equivalent damping，this study builds a completed magnetic suspension rotor model in the closed-loop system and completes the simulation calculation of critical speed and unbalanced response. The rigid body modal frequencies of the cold compressor rotor with the same PID controller，obtained by simulation and experiment，are 27 Hz and 28 Hz，respectively;and the percentage error of the first two critical bending modal frequencies does not exceed 2%. The rotor dynamic characteristics obtained respectively through unbalanced response simulation and the speed-up experiment within the rated speed range of 50 000 rpm，respectively，are consistent. It shows the modeling and dynamic calculation methods proposed in this paper are reasonable and reliable，which have essential reference significance for the cold compressor rotors structural design and controller commissioning.

Key words：finite element method;active magnetic bearing;PID control;unbalanced response;critical speed

随着超流氦在高能物理、核聚變、超导电力等领域的广泛应用，大型超流氦低温制冷系统已成为不可或缺的基础支撑设施. 对于2 K温区的大型氦低温系统，目前国际上普遍通过采用串联多级离心式冷压缩机在低温负压下对过冷槽减压降温的方法来获得1.8 K ～ 2 K的超流氦[1].  冷压缩机作为超流氦系统核心部件，需要工作在负压低温环境下，工作转速达数万转每分钟. 苛刻的运行条件对转子的支撑设备提出了较高的要求. 常规的……