Cogging Torque Harmonics Research Articles

Research on Synergistic Reduction of Cogging Torque and Ripple Torque of Interior Permanent Magnet Synchronous Motor Based on Magnetic Field Harmonic Offset Method

This paper presents a method for reducing the cogging torque and ripple torque of interior permanent magnet synchronous motor (IPMSM) based on the magnetic field harmonic offset method. This method establishes the internal correlation between cogging torque harmonics and ripple torque harmonics. The suppression or cancellation of magnetic field harmonics in the rotor pole is utilized as transmission link to simultaneously weaken or eliminate lower order harmonics of cogging torque and ripple torque, which can improve operating quality of the IPMSM and obtain an acceptable total average torque. A mathematical and physical model of harmonic offset method for cogging torque is established, the distribution characteristics of permeability harmonics and field harmonics that affect cogging torque are analyzed, the analytical expression for the electromagnetic torque of the IPMSM including reluctance torque is derived, and the collaborative suppression mechanism of cogging torque and ripple torque, as well as common solutions, are studied. Finally, the suppression law of cogging torque and operating ripple torque is verified by the finite element simulation, and the compromise selection principle of permanent magnetic pole is summarized. Due to the absence of the average torque of motor in the offset method, the effects of effective pole arc of the combined rotor on the torque ripple and torque-speed characteristic curve of the IPMSM are compared and evaluated.

Analysis and Reduction of Cogging Torque for Flux-Switching Permanent Magnet Machines

In this article, a new modeling approach is proposed to investigate cogging torque and the corresponding reduction techniques of flux-switching permanent magnet (FSPM) machines. First, based on the superposition of each single rotor tooth, an analytical expression of cogging torque in FSPM machines is derived and confirmed by the finite-element analysis (FEA). Then, three feasible techniques, i.e., successively shifting rotor teeth, alternately shifting rotor teeth, and stepped skewing rotor blocks, are proposed for cogging torque minimization of FSPM machines. Correspondingly, generally analytical expressions of these three methods are deduced, through which the analytically optimal shifting angles can be determined. Besides, the cogging torque harmonics are analyzed by both analytical expressions and FEA, and then, the multidimensional techniques, namely three rotor-based reduction methods combined with the optimal stator tooth width, are introduced and studied to further suppress cogging torque. Finally, prototyped machines are manufactured and tested, and the corresponding experiments verify the effectiveness of the reduction methods.

Statistical Analysis of the Effect of Magnet Placement on Cogging Torque in Fractional Pitch Permanent Magnet Motors

Theoretically, the layout of fractional pitch permanent magnet motors should ensure the cancellation of most cogging torque harmonics. In reality, manufacturing errors lead to incomplete cancellation and higher than expected cogging torque. One potential manufacturing error is the variation in angle between neighboring magnets. This paper uses the superposition technique to analytically determine the expected magnitude of each cogging torque harmonic based on a Gaussian distribution of angular magnet placement variation. A simple expression is presented for the expected value of each harmonic's magnitude based upon the harmonic number, the number of magnets, and the standard deviation of the Gaussian placement distribution. The derived expression is validated using Monte Carlo simulations and experimental implementation.

Synthesis of cogging-torque waveform from analysis of a single stator slot

A simple analytical technique is proposed to synthesize the cogging-torque waveform of a permanent-magnet brushless machine from the cogging torque, which is associated with a single stator slot. An analytical expression is derived, which reveals the relationship between the two. It is then applied to two motors, which have a fractional number of slots per pole. It is shown that the resultant cogging-torque waveform can be synthesized to a high accuracy, as confirmed by both finite-element analysis and measurements. It is also shown that not all the cogging-torque harmonics that exist in the cogging-torque waveform due to a single slot will be present in the resultant cogging torque, and that the most significant components can be identified analytically.

2D harmonic analysis of the cogging torque in synchronous permanent magnet machines

Presents an approach to determine sources of cogging torque harmonics in permanent magnet electrical machines on the basis of variations of air‐gap magnetic flux density with time and space. The magnetic flux density is determined from the two‐dimensional (2D) finite element model and decomposed into the double Fourier series through the 2D fast Fourier transform (FFT). The real trigonometric form of the Fourier series is used for the purpose to identify those space and time harmonics of magnetic flux density whose involvement in the cogging torque is the greatest relative contribution. Carries out calculations for a symmetric permanent magnet brushless machine for several rotor eccentricities and imbalances.