Low Space Order Analysis of Radial Pressure in SPMSM With Analytical and Convolution Approaches

Abstract

This paper presents an analysis of low the space order of the air-gap radial Maxwell pressures in Surface Permanent Magnet Synchronous Machines (SPMSM) with fractional slot concentrated windings. The air-gap Maxwell pressures result from the multiplication of the flux density harmonics due to magnetomotive forces and permeance linked to the magnet, the armature, and the stator slots and their interactions. One low space order is selected and different approaches are compared to determine the origin of this pressure. First, an analytical prediction tool ACHFO (Analytical Calculation of Harmonic Force Orders) is issues to calculate the space and time orders of these magnetic pressure harmonics while identifying their origin in terms of interactions between magnet, armature and teeth effects. Additionally, the analytical prediction of ACHFO is compared with the flux density convolution and finite element approaches. The main advantage of our tool is the speed of computation. Finally, an experimental Operational Deflection Shape measurement (ODS) is performed to show the deflection shape of the low space order selected.

An Improved 2-D Subdomain Model of Squirrel-Cage Induction Machine Including Winding and Slotting Harmonics at Steady State

“…Torque ripple harmonics are in fact pulsating harmonics of tangential force whose orders are ( > 0, = 0). Using the convolution product theorem, each harmonic of force can be decomposed into a product of two flux density harmonics [17]. In this particular case, the first torque ripple harmonic (600 , 0) comes from the combination of two flux density harmonics ℎ 1 and ℎ 2 due to rotor slotting and mmf at:…”

Inverse approach for concentrated winding surface permanent magnet synchronous machines noiseless design

“…It also tracks the origin of the lowest space orders, i.e. combined interactions between the armature (winding), magnets and slotting effects (permeance), and its own interactions too [13]. The relation created from (4) is given in (7) where r,f ; υ, fs; µp, fs; are respectively space and frequency order airgap radial pressure, armature effect (winding) and magnet effect.…”

“…The main harmonic [−10, 2] of radial pressure has the highest magnitude as it is linked to the number of poles. The spatial order 2 to 2f, which is a characteristic of this winding type, is observed linked to the Greatest Common Divider GCD (Zs, 2p) [13,15]. The spatial order 0 (0f -6f and 12f) exits and corresponds to the breathing mode for the electrical machines [15,16].…”

“…Moreever the FE simulation validates our analytical model. For double-layer concentrated winding the spatial and frequency harmonic content is quite rich [13,14]. The main harmonic [−10, 2] of radial pressure has the highest magnitude as it is linked to the number of poles.…”