Analytical Study of Stator Tooth Modulation on Electromagnetic Radial Force in Permanent Magnet Synchronous Machines

Abstract

The electromagnetic radial force acting on the stator inner periphery will induce radial vibration and acoustic noise in permanent magnet synchronous machines. The radial force components are transmitted through the stator teeth to the yoke to introduce deformations. The influence of the stator tooth structure can be considered as an equivalent mechanical modulation effect on these electromagnetic radial force components. As a result, high-order electromagnetic radial force components can be modulated and potentially result in eminent stator low-mode vibration. In this paper, an analytical model is developed to offer an intuitive knowledge of stator tooth modulation effect on electromagnetic radial force. The validity of the proposed analytical method has been underpinned by both finite element analysis and experimental results. Such an effective yet simple analytical model can be of significant benefit for the stator radial vibration analysis. It can be employed to not only promptly investigate the stator radial vibration characteristics but also perform effective optimization on stator radial vibration reduction in permanent magnet synchronous machines.

Investigation of Noise Sources in Fractional-Slot Concentrated Winding Motors Considering High-Order Radial/Tangential Electromagnetic Force Combination and Modulation

“…The sampling length is 2𝜋 , corresponding to the period of the spatial harmonic force of the electromagnetic force. Its spatial order is denoted by 𝑛, as shown in ( 16) and (17). Through discrete sampling by teeth, ( 16) and ( 17) can be derived, where the positive and negative signs of spatial order (𝑛 − 𝑘𝑍 1 ) When the spatial order of the distributed electromagnetic force in the air gap does not satisfy the sampling theorem, the ECF harmonic will contain the Nyquist frequency.…”

“…This conclusion is reached by disregarding the influence of high-order force waves. According to ( 16)-( 17), under the modulation effect of stator teeth on high-order force waves, the impact of high-order force waves on the stator is comparable to that of low-order force waves, potentially leading to low-order modal vibration [14]- [17], [19]. Concurrently, the tangential AEFD exhibits the same spatial and temporal distribution as the radial AEFD, sharing similar characteristics in causing motor vibration.…”

“…The findings indicated that larger modulation forces are more detrimental to vibration, and tangential force effects also play a significant role in affecting vibration. Liang et al [17] proposed a model to examine the electromagnetic force modulation effect by equivalently applying the AEFD to the stator yoke. The study showed that high-order force waves, under the influence of teeth, generate low-order modulation vibrations, and the amplitude of modulation vibrations is solely related to the stator slot opening.…”

Design of multi‐phase permanent magnet synchronous motor with fractional‐slot windings for electromagnetic vibration reduction considering stator teeth modulation

“…With the development of electromagnetic force theory of PMSM, the effect of stator teeth modulation on electromagnetic force is revealed [16]. It points out that high order electromagnetic force can be modulated into low order ones by the slotting structure of the stator.…”

The Analysis of Permanent Magnet Vernier Synchronous Machine Vibration and Noise

“…By analyzing the model and electromechanical pulse response, the relationship between stator current and stator acceleration is established [10]. The shape of the stator teeth can influence the distribution of the radial electromagnetic force higher-order harmonics, causing the machine to enter low-mode vibration, thereby optimizing the vibration reduction in the PMSM [11]. For machines with built-in permanent magnets, the geometric shape of the magnetic isolation bridge affects the distribution of the magnetic field and has an impact on the spatial-temporal distribution of radial electromagnetic force.…”