# Analysis and Compensation of Lorentz Force Magnetic Bearing Magnetic Flux Density Uniformity Error

## TL;DR

This paper proposes a method to improve the accuracy of measuring spacecraft angular rate by compensating for magnetic flux density errors in Lorentz force magnetic bearings.

## Contribution

A high precision method for angular rate measurement based on magnetic flux density uniformity error compensation in Lorentz force magnetic bearings is introduced.

## Key findings

- The proposed method achieves 96% accuracy in estimating induced current due to magnetic flux density errors.
- Error compensation improves the accuracy of MSCSG in measuring spacecraft angular rate by 12.5%.
- The relationship between rotor tilt angle, tilt angular rate, and magnetic flux density was established.

## Abstract

Aiming at the influence of the magnetic flux density uniformity error (MFDUE) of the Lorentz force magnetic bearing (LFMB) on the sensitivity accuracy of magnetically suspended control and sensing gyroscopes (MSCSGs) on the angular rate of a spacecraft, a high precision measurement method of the angular rate of a spacecraft based on the MFDUE compensation of LFMB is proposed. Firstly, the structure of MSCSG and the sensitivity principle of MSCSG to the spacecraft angular rate are introduced. The mechanism influencing the accuracy of MSCSG to spacecraft angular rate sensitivity is deduced based on the definition of magnetic flux density uniformity. Secondly, the 3D magnetic flux distribution of LFMB is analyzed using ANSYS. The relationship between the rotor tilt angle, tilt angular rate, and magnetic flux density is established. The induced current calculation model due to MFDUE is proposed, and the LFMB magnetic flux density error compensation is realized. Finally, the simulation results show that the estimation accuracy of the induced current by the proposed method can reach 96%, and the simulation and the experiment show that the error compensation method can improve the accuracy of MSCSG in measuring the spacecraft angular rate by 12.5%.