Design and Finite Element Analysis of Surface and Interior Permanent Magnet Motors for High-Efficiency Applications

Abstract

This paper presents a comprehensive design methodology and performance analysis of permanent magnet motor topologies using finite element analysis (FEA). Starting from defined customer specifications—including torque, speed, and thermal constraints—we investigate the impact of rotor-stator geometries and magnet configurations on electromagnetic torque, cogging torque, back-EMF waveform quality, and efficiency. Three architectures—Surface Permanent Magnet (SPM), Interior Permanent Magnet (IPM) with radial and V-type configurations, and spoke-type designs—are evaluated for torque density, field weakening capability, flux density saturation, and losses. MotorSolve simulation software enabled detailed insights into air gap flux distribution, stator and rotor saturation, harmonic effects, and power dissipation. This study highlights the design trade-offs in meeting high torque-speed demands while optimizing for compactness and thermal stability in motor systems for e-mobility and industrial automation.

1. Introduction

Electric motors have become foundational to modern electrified systems, particularly electric vehicles (EVs), robotics, and high-efficiency industrial drives. In such applications, achieving a balance between compact form factor, torque production, efficiency, and thermal manageability is a key engineering challenge. Permanent magnet machines, especially Surface-mounted Permanent Magnet (SPM) and Interior Permanent Magnet (IPM) types, offer a high torque-to-volume ratio, low losses, and superior performance in variable-speed regimes. However, their design intricacies require a combination of analytical modeling, optimization, and electromagnetic simulation.

This study is motivated by a practical design case for a compact high-speed motor to deliver a nominal torque of 2 Nm at a base speed of 2750 rpm and peak torque up to 5.7 Nm. The design envelope is constrained to an outer diameter of 90 mm and a length of 110 mm. The paper uses this requirement as a benchmark to evaluate different rotor and stator configurations through analytical formulas and FEA-driven simulations using MotorSolve. The goal is to determine an architecture that satisfies performance requirements while minimizing losses, cogging torque, and thermal hotspots.

2. Specification-Driven Design Process

The motor specification includes:

Nominal Torque: 2 Nm
Peak Torque: 5.7 Nm
Base Speed: 2750 rpm
Extended Speed: up to 4000 rpm with field weakening
Peak Current: 40 A for 15 s
Voltage: 24 V nominal
Outer Diameter: 90 mm
Stator Length: 110 mm (maximum stack length 70 mm)

From this, we derive key mechanical and electrical limits, including stator bore diameter (~80 mm), rotor diameter range (33 mm to 49 mm), and air gap length (typically 0.5–1 mm). Torque per unit volume is calculated to assess the feasibility of different magnetic configurations.

Using the electromagnetic torque approximation:

T=(3/2)DLBβN_sIcos⁡(δ)

Where:

D = Air gap diameter
L = Stack length
B = Average flux density (1 T assumed)
β = Magnet arc angle (90 degrees assumed)
Ns = Turns per phase
I = Peak phase current
δ = Control angle (90 degrees below base speed)

Initial estimates indicate achievable torques between 4–6 Nm, depending on rotor diameter and magnet configuration.

3. Rotor Topology Comparison

Three rotor configurations were chosen for evaluation:

Design A: Surface-mounted Permanent Magnet (SPM)
Design B: Interior PM with radial spoke-type magnets
Design C: Interior PM with V-type buried magnets

All designs use 8-pole, 9-slot stator configurations. Rotor diameters were set at 42 mm, 43 mm, and 46 mm, respectively, with stator teeth widths varying from 6 mm to 11.6 mm. Magnetic materials include NdFeB 40/23 and M19 laminated steel.

FEA was used to simulate:

Torque vs. Rotor Position
Cogging Torque Profile
Air Gap Flux Distribution
Flux Linkages (Ld, Lq)
Harmonic Distortion in Back-EMF
Torque-Speed Curves under Field Weakening

4. FEA-Based Electromagnetic Insights

Initial SPM simulations showed:

Peak torque of 5.3 Nm
Cogging torque of 0.015 Nm
Back-EMF waveform slightly distorted at 56 A
Efficiency ~90.2%

Design B (Spoke-type IPM):

Better flux path control and sinusoidal waveform
Torque: 5.75 Nm
Improved efficiency at 91.5%
Reduced cogging torque

Design C (V-type IPM):

Highest torque: ~6.0 Nm
Better high-speed performance under field weakening
Peak flux density: ~2.1 T

All designs maintained air gap flux uniformity but showed harmonic distortion at higher currents. Tooth saturation and stator back iron stress were more pronounced in SPM due to surface leakage.

5. Flux Behavior and Saturation Analysis

Detailed plots of:

Air Gap Flux Density: sinusoidal for IPM, distorted under current loading for SPM
Stator Back Iron Flux: up to 1 T with visible saturation pockets
Tooth Flux Density: peaks reaching 2 T, indicating material stress
Rotor Back Iron Flux: more uniform in IPM; SPM suffered from leakage saturation

Magnet flux patterns in spoke and V-type designs were significantly more efficient, with better alignment between north-south poles and reduced skew.

6. Torque-Speed and Field Weakening Behavior

All motors were evaluated for constant torque up to base speed, then transitioning into a field weakening zone using phase advance.

Design B achieved:

2 Nm at 2750 rpm
Extended to 3500 rpm with reduced torque
Higher efficiency zone maintained up to 85% rated speed

Torque-speed curves showed clear non-linear drops beyond base speed, as expected with field weakening.

7. Efficiency and Loss Distribution

MotorSolve allowed decomposition of total losses:

Winding Losses: ~80 W
Core Losses: ~20 W
Rotor Losses: ~5 W
Total Losses: ~113 W

The predicted temperature rise within the 90 mm x 110 mm housing was consistent with natural convection estimates. The estimated motor efficiency is 90.2% under 2.7 Nm, 4000 rpm operation.

8. Conclusion

This paper demonstrates a systematic design and simulation approach to achieving high-efficiency motor designs within strict dimensional and performance constraints. Analytical torque estimation and FEA-driven refinement enable engineers to evaluate complex trade-offs between rotor architectures, magnet placement, and thermal behavior.

Speaking-type IPM motors offered the best compromise between torque performance, efficiency, and field weakening capacity among the three designs. SPMs, while simpler, suffered from higher cogging and lower back-EMF quality.

Future work may involve optimization of winding layout, skewing angles, and three-phase drive simulation under dynamic loading for embedded controller validation.

Check out the Video below.