FEA Magnetic Simulation in Motor Design: How to Read a Flux Density Report

Before cutting a single piece of aerospace aluminum or ordering thousands of custom Neodymium blocks, a professional magnetic assembly OEM relies on Finite Element Analysis (FEA).

Using electromagnetic simulation software and measured material assumptions, engineers can estimate how a Halbach array or custom motor rotor will perform before tooling. However, for a buyer or a mechanical engineer reviewing an OEM's proposal, these colorful simulation reports can look like meaningless heat maps.

In this guide, we break down how to read an FEA magnetic simulation report, what the colors actually mean, and how to spot red flags before you approve a design for mass production.

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1. Understanding the Contour Plot (The "Heat Map")

The most common output of an FEA report is the magnetic flux density contour plot. This visual representation maps the concentration of magnetic flux (measured in Tesla or Gauss) across the 2D or 3D cross-section of your assembly.

• Red/Pink Zones (High Flux): These areas represent regions with the highest magnetic flux density, with values depending on magnet grade, air gap, geometry, and steel saturation. In a well-designed Halbach array, the intense red zones should concentrate in the air gap (the space between the rotor and the stator teeth).
• Blue/Green Zones (Low Flux): These areas represent regions with lower magnetic flux. In a Halbach array, the non-working face (the back side of the rotor) should show substantially reduced flux, indicating that the topology is reducing wasted leakage.

The Saturation Red Flag

When reviewing the contour plot, pay close attention to any ferromagnetic materials in the design (like a steel yoke or stator teeth). Electrical steel typically saturates around 1.8 to 2.1 Tesla. If the FEA report shows large patches of deep red or pink inside the steel components, the steel is magnetically saturated. It cannot carry any more flux, meaning your expensive magnets are being wasted, and the motor will suffer from severe inefficiencies and heat generation.

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2. Analyzing the Air Gap Waveform (The Line Graph)

While the contour plot is great for a quick visual check, the most critical data is found in the Air Gap Flux Density Waveform.

The FEA software will plot a line graph showing the strength of the magnetic field (By or Br) along a designated path through the center of the air gap.

• Traditional N-S-N-S Rotors: The waveform will look like a trapezoid or a square wave. It rises sharply, flattens out across the pole face, and drops sharply. This harsh transition is what causes cogging torque and motor vibration.
• Halbach Arrays: The waveform should approach a smooth sine wave when the magnetization pattern, segment count, and air gap are well matched.

Total Harmonic Distortion (THD)

A high-quality FEA report may run a Fourier transform on that waveform to calculate the Total Harmonic Distortion (THD). The goal of a Halbach array is to reduce THD to the level required by the application. A low THD supports smoother rotation, lower acoustic noise, and reduced torque ripple for precision robotics and medical scanners.

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3. Demagnetization Curves (The Operating Point)

Heat is the enemy of permanent magnets. A professional FEA report must include a thermal analysis showing the Permeance Coefficient (PC) or the operating point of the magnet on its B-H demagnetization curve at your target maximum temperature (e.g., 150°C).

If the operating point dips below the "knee" of the B-H curve at your peak temperature, the magnet will suffer irreversible demagnetization.

If you see this in a report, the OEM must revise the design. The solutions are:

1. Increase the magnet grade: Switch from N42SH (150°C) to N38UH (180°C).
2. Increase the magnet thickness: A thicker magnet in the direction of magnetization inherently resists demagnetization better (it increases the Permeance Coefficient).
3. Widen the air gap: Reduces the opposing field, though this sacrifices overall torque.

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4. Why You Shouldn't Rely on Free Online Calculators

Many engineers use free online magnetic calculators to estimate pull force or field strength. These calculators use simplified analytical equations (like the Biot-Savart law) that assume the magnet exists in an infinite vacuum.

They completely ignore:

• The non-linear saturation of surrounding steel.
• Flux leakage at the sharp corners of the magnets.
• The complex repelling interactions in a Halbach array.

For costly OEM programs, a 2D or 3D FEA model should be paired with prototype field mapping so the model assumptions can be checked against real material and assembly tolerances.

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OEM FEA Support from HalbachArray

At HalbachArray, our engineering review can include 2D/3D magnetic modeling, material-grade checks, and a prototype measurement plan before a custom Halbach array, BLDC rotor, or magnetic coupling enters the CNC and assembly queue.

When the project scope includes simulation, the deliverable can include documented model assumptions, field or force plots, thermal and demagnetization considerations, and inspection targets for prototype validation.

Send your preliminary CAD files to [email protected] to initiate a simulation review.