Suppression of Thrust Fluctuation of a New Ironless Tubular Permanent Magnet Synchronous Linear Motor Based on the Halbach Array

S Bastien Besset,Jun-an Zhang,Hao Dong,Bo Li,Zhiping Shi,Xiaolong Zhao

doi:10.1155/2021/3196773

Abstract

The air gap magnetic field (AGMF) is the key factor in determining the ironless tubular permanent magnet synchronous linear motor (ITPMSLM). The distortion of its waveform causes thrust fluctuation during the operation of the motor, resulting in poor machining accuracy of the machine tool. To solve this problem, this paper proposes a new chamfered permanent magnet structure (CPMS) to improve its performance. First, the equivalent magnetic charge method is used to analyze the AGMF, and the analytical expressions of the no-load back EMF and thrust of the new motor are obtained. Second, the AGMF of six kinds of CPMS is analyzed by the Fourier coefficient. Taking the minimum harmonic distortion rate as the optimization objective, the CPMS that makes the AGMF waveform reach the best sinusoidal property is obtained and the no-load back EMF and thrust of the new motor are analyzed. Then, the new motor is compared with the ITPMSLM of rectangle permanent magnet structures (RPMS). Finally, according to the CPMS, the test prototype is built and tested under different working conditions. The research results show that when the outer circumference is 45o chamfered, the ratio of permanent magnet thickness h2 to the chamfered thickness h1 is 0.8; the sinusoidal property of AGMF is the best, and this structure can effectively reduce the motor thrust fluctuation rates to less than 0.01%, which verifies the effectiveness of the CPMS in improving the sinusoidal property in the AGMF and restraining the thrust fluctuation of the ITPMLSM.

Highlights

Studies used the equivalent magnetization method to solve the electromagnetic field of the motor, which deduces the analytical property of magnetic density, back EMF, and inductance and proposes an improved TPMSLM [14,15,16]
Other studies analyzed the magnetic field of axially magnetized TPMSLM with an analytical method but did not analyze the influence of structural parameters on air gap magnetic field (AGMF), especially thrust fluctuation [20, 21]. e magnetic pole offset method was used to weaken the cogging force of TPMSLM and give the calculation of the magnetic pole offset, but it is difficult to use this method for the axial magnetization structure of TPMSLM [22, 23]
Most of the methods to weaken the thrust fluctuation of a TPMSLM are for a TPMSLM with an iron core, and there are few studies on restraining the thrust fluctuation of an ironless tubular permanent magnet synchronous linear motor (ITPMSLM). e AGMF is the key problem in determining the thrust performance of the ITPMSLM, and its waveform distortion is the key factor in producing thrust fluctuation during the operation of an ITPMSLM. erefore, with a chamfered permanent magnet structure (CPMS), the minimum harmonic distortion rate of the AGMF waveform as the optimization objective is proposed to suppress the thrust fluctuation of an ITPMSLM

Summary

Model Establishment of the New Motor

The AGMF of the ITPMLSM is a variable vector with size and direction; according to the motor structure, it is divided into the radial component and the axial component, and the AGMF density of the radial component is the main source of motor thrust. erefore, this section first calculates the analytical model of radial AGMF density [34] and calculates the analytical model of the no-load back EMF and thrust of the ITPMSLM with CPMS of the Halbach array (hereinafter referred to as the new motor). Because the motor stator is composed of n permanent magnets, using the superposition principle, the magnetic density of the AGMF of the motor can be obtained as follows: B(ρ, z) 􏽘 􏼐Bxn+ + Bxn− + Byn+ + Byn+􏼑. If the position of the axis of a group of coils is Z, the average magnetic density of the radial AGMF in the coil area of the group is the following: z+tw/2 Rs. e no-load back EMF of this group of coils at this position is the following: EA NBavLavv πNBav(z) Rs + Rs1􏼁v. It is considered that the coils are concentrated at the average magnetic density, and the thrust of a group of coils can be obtained as follows: F(z) NBavLavI πNBav(z) Rs + Rs1􏼁I(z). E thrust fluctuation rate can reflect the stability of thrust during motor operation. e smaller the thrust fluctuation rate, the more stable the motor operation (i.e., the smaller the thrust fluctuation)

Model Calculation and Analysis of the New Motor

Finite Element Verification

Findings

Thrust Performance Test