Greg Heins

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 harmonics 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.

Accurate Torque Ripple Measurement for PMSM

Torque ripple in permanent-magnet synchronous motors is generally undesirable. Significant work has been done to minimize this torque, either by modifying the mechanical motor design or by careful controller design. Surprisingly, however, little work has been published on the accuracy of torque ripple measurement. A successful measurement requires a mechanical design with readily modeled dynamics, sensors with suitable bandwidth and resolution, a method of applying a smooth load to the motor, and a method for calibrating the measurement. This paper presents a thorough approach to the accurate measurement of torque ripple. The proposed system has been validated by finite-element modeling, analytical calculations, and experimental analysis.

Decoupling manufacturing sources of cogging torque in fractional pitch PMSM

Fractional pitch is commonly used to significantly reduce cogging torque in PMSM, however, maximum benefit is dependent on accurate stator and rotor manufacturing. This paper presents a method of decoupling the stator and rotor contributions to total cogging torque. Rotor causes are further decoupled into magnet placement and strength variation. Decoupling is possible due to stator and rotor affected harmonics being independent of one another. Magnet strength and position decoupling is based on the analysis of the cogging torque waveform generated by the rotor interaction with a single slot stator and utilizes the zero torque produced when a single magnet is directly over a slot. Superposition and least squares minimization is then used to determine strength variation and simulate cogging torque with and without placement and strength variation. Analysis of ten production stators and rotors is presented and discussed, with the overall findings confirming that for the motors tested, the largest contributors to manufacturing induced cogging torque were the stator, magnet placement inaccuracy and magnet strength variation. Eliminating stator variation would improve cogging torque by 45%, perfect magnet placement would result in a 29% reduction in cogging torque and eliminating magnet strength variations would achieve a 7% reduction.

Adaptive feedforward control to compensate cogging torque and current measurement errors for PMSMs

Torque ripple minimisation is achieved by an adaptive feedforward control method to reduce cogging torque and current measurement errors. Experiments have been conducted to show that torque ripples are highly sensitive to changes in current offset and cogging torque. An easy way to adapt to cogging torque changes (due to temperature) is proposed and implemented after an initial estimation of the cogging torque is done. This initial estimation is necessary for manufacturing inaccuracies and ongoing adaptation is to cope with operating conditions changes. Higher harmonics of the cogging torque can also be compensated through this way. Current offset which contributes to a large proportion of the torque ripple is also compensated through an adaptive method. The advantages of the proposed scheme combine the benefits of preprogrammed waveform methods which are easy to implement and a simple adaptive system to effectively reduce RMS torque ripple factor from 11.30% to 1.7%.

Identifying manufacturing induced rotor and stator misalignment in brushless permanent magnet motors

Cogging torque in fractional pitch PMSM is minimized when manufacturing induced errors are also minimized. This paper investigates additional cogging torque harmonics resulting from misalignment of the rotor and stator caused by assembly and manufacturing tolerances in an axial flux, fractional pitch PMSM. A hybrid analytical / FEA method utilizing superposition of a pole transition over a single stator slot is developed to predict the effect on cogging torque of angular misalignment in combination with pole and slot placement inaccuracies. This work extends on that previously published by inducing varying degrees of assembly misalignment of the stator and rotor to determine the effect on cogging torque waveforms. Experimental data is presented supporting the analytical data indicating that static angular misalignment produces sidebands about the rotor affected harmonics and dynamic angular misalignment creates sidebands around the stator affected harmonic. There is good agreement between the analytical method, FEA and measured experimental data.

Winding factors and magnetic fields in permanent magnet brushless machines with concentrated windings and modular stator cores

Removing some sections of the stator yoke in a permanent magnet brushless machine can be beneficial for reducing punching waste and simplifying motor manufacture. However in some cases, restricting the possible flux paths in this way will have a detrimental impact on the torque and air-gap harmonics. This paper discusses the potential implications of modular stator core arrangements and presents the air-gap flux density harmonics and winding factors for potential slot/pole combinations. FEA simulations are presented to support the analytical calculations. The analysis suggests that the performance reduction from using a modular stator is minimal when the number of slots and poles are similar but drops off substantially when this is not the case. A modular core stator will increase the MMF sub-harmonics due to the magnet field but can reduce the sub-harmonics due to the armature if a single layer winding is used. The effect of slotting is very similar for a modular and conventional core machine and FEA results match previously published analytical analyses.

Computationally Efficient Method for Identifying Manufacturing Induced Rotor and Stator Misalignment in Permanent Magnet Brushless Machines

A computationally efficient method is presented to investigate additional cogging torque harmonics resulting from misalignment of the rotor and stator caused by assembly and manufacturing tolerances in an axial flux fractional pitch permanent magnet synchronous machine (PMSM). The superposition method creates a complete cogging torque profile by using a library of pole transitions over a single stator slot. The method extends previously published work, and is used to predict the effect of eccentricity misalignment in combination with pole and slot placement inaccuracies on cogging torque. Experimental data are presented supporting the superposition data indicating that static and dynamic eccentricity produce first- and second-order sidebands about the rotor and stator affected harmonics, respectively. There is good agreement between the hybrid superposition method, FEA, and measured experimental data.

Winding Factors and Magnetic Fields in Permanent-Magnet Brushless Machines With Concentrated Windings and Modular Stator Cores

Removing some sections of the stator yoke in a permanent magnet brushless machine can be beneficial for reducing punching waste and simplifying motor manufacture. However in some cases, restricting the possible flux paths in this way will have a detrimental impact on the torque and air-gap harmonics. This paper discusses the potential implications of modular stator core arrangements and presents the air-gap flux density harmonics and winding factors for potential slot/pole combinations. FEA simulations are presented to support the analytical calculations. The analysis suggests that the performance reduction from using a modular stator is minimal when the number of slots and poles are similar but drops off substantially when this is not the case. A modular core stator will increase the MMF sub-harmonics due to the magnet field but can reduce the sub-harmonics due to the armature if a single layer winding is used. The effect of slotting is very similar for a modular and conventional core machine and FEA results match previously published analytical analyses.

Increase in operating range and efficiency for variable gap axial flux motors

For applications requiring a constant power source such as traction, efficient power electronic utilization requires an electric machine capable of flux weakening. Usually flux weakening is achieved by using an interior permanent magnet machine (IPM) and by applying current in the d-axis. Other recent work has used two inverters or pulses of current to demagnetize and magnetize the magnets depending on the operating point. This paper presents an axial flux machine with mechanical flux weakening capability. Experimental data shows that the torque constant can be reduced to five times its maximum value and the efficiency in the rated operating range can be increased by up to 15% points. To demonstrate the impact of the mechanical flux weakening mechanism on the efficiency of the system, the motor data was used to model the performance of an electric motorcycle over a World Harmonized Light Vehicles Test Procedures (WLTC)[1] drive cycle. If a self locking automated actuation mechanism is used, the peak power required by the actuation mechanism is 4% of the traction motor power rating and the energy used over the drive cycle is 0.05% of the traction motor energy use, suggesting negligible impact on the overall efficiency. If a non locking mechanism is used, the actuating power and energy will be substantially lower.

Cogging torque prediction for mass-produced axial flux PMSM stators

Stator manufacturing processes for axial flux permanent magnet synchronous motors (AFPMSM) are susceptible to variation leading to cogging torque. To date, there are no methods which synthesize cogging torque based on stator manufacturing errors. This paper presents a superposition method based on stator geometry to predict critical cogging harmonics for AFPMSM stators. Geometry is obtained using image processing techniques on a scanned image of the stator. The proposed method has been validated by comparison with experimental cogging torque data. A correlation of 0.82 linear regression was found using the method proposed in this paper. Process capability was tested by measuring slot widths and checking deviation.