Electric motor inner workings with glowing magnetic fields.

Unlock Efficiency: Fast Air-Gap Flux Density Calculation for Brushless Motors

Beau Callahan in Tech & Innovation December 2025 • 4 min read.

"Streamlining the Design Process for Electric Motors: A New Analytical Method"

Brushless motors are integral to numerous applications, from electric vehicles to industrial machinery. A key factor in their performance is the air-gap flux density, which directly influences torque and efficiency. Optimizing this parameter is crucial for designing high-performance motors.

Traditional methods for calculating air-gap flux density, such as Maxwell theory and Finite Element Analysis (FEA), are often complex and computationally intensive. These methods can be impractical for rapid prototyping and preliminary design stages where quick estimations are needed.

Recent research introduces a fast analytical method that offers a more efficient and practical approach to calculating air-gap flux density in permanent-magnet brushless motors (PMBMs). This method uses a lumped magnetic circuit model and demonstrates high accuracy compared to FEA results, making it a valuable tool for motor design.

The Fast Analytical Method: A Simplified Approach

Electric motor inner workings with glowing magnetic fields.

The core of this new approach lies in a simplified magnetic circuit model. Instead of complex numerical simulations, the method represents the motor's magnetic behavior using basic circuit elements, allowing for rapid calculation of the air-gap flux density.

Here's a breakdown of the key elements and steps involved:

Lumped Magnetic Circuit Model: Represents the motor's magnetic paths using components like reluctances for the magnet, air gap, stator, and rotor.
Simplified Calculations: Uses circuit analysis techniques to determine the flux distribution within the motor.
Analytical Equations: Derives equations to directly calculate the air-gap flux density based on motor geometry and material properties.
Comparison with FEA: Validates the analytical method by comparing its results with those obtained from Finite Element Analysis (FEA) software, demonstrating accuracy within a 5% error margin.

This analytical method simplifies the design process, especially in early stages. It allows engineers to quickly evaluate different motor configurations and optimize parameters without relying on time-consuming simulations. This approach also facilitates a better understanding of the factors influencing air-gap flux density.

Real-World Impact and Future Applications

The analytical method provides a fast and accurate way to predict the air-gap flux density, making it suitable for the pro-design phase of many engineering instruments. This is particularly useful when precise machine structure parameters are not yet known, allowing for rapid prototyping and optimization.

While the current method focuses on no-load situations, future research could extend the model to account for load conditions, armature reaction, and core saturation. This would further enhance its applicability and enable optimization of output torque under various operating conditions.

By providing a balance between accuracy and computational efficiency, this method empowers engineers and researchers to design better brushless motors for a wide range of applications, from electric vehicles and robotics to aerospace and industrial automation.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: 10.1051/matecconf/201818906008, Alternate LINK

Title: Fast Analytical Calculation Of The Air-Gap Flux Density In An Outer-Rotor Permanent-Magnet Brushless Motor

Subject: General Medicine

Journal: MATEC Web of Conferences

Publisher: EDP Sciences

Authors: Shuaichen Ye, Xiaoxian Yao

Published: 2018-01-01

Everything You Need To Know

Why is air-gap flux density important in brushless motors?

The air-gap flux density is a crucial parameter in permanent-magnet brushless motors (PMBMs) because it directly impacts the motor's torque and efficiency. Optimizing the air-gap flux density is essential for designing high-performance motors. By accurately calculating this parameter, engineers can ensure the motor delivers the desired performance characteristics, such as power output and operational efficiency.

What are the limitations of traditional methods for calculating air-gap flux density?

Traditional methods such as Maxwell theory and Finite Element Analysis (FEA) are complex and computationally intensive. These methods can be impractical for rapid prototyping and preliminary design stages where quick estimations are needed. The new analytical method offers a more efficient and practical approach to calculating air-gap flux density in permanent-magnet brushless motors (PMBMs). This method uses a lumped magnetic circuit model and demonstrates high accuracy compared to FEA results, making it a valuable tool for motor design.

How does the new analytical method work?

The Fast Analytical Method simplifies the calculation using a lumped magnetic circuit model. This model represents the motor's magnetic paths with basic circuit elements, like reluctances for the magnet, air gap, stator, and rotor. Circuit analysis techniques are then used to determine the flux distribution and derive equations for calculating the air-gap flux density based on motor geometry and material properties. The results are validated by comparing them to those obtained from Finite Element Analysis (FEA) software.

What are the advantages of using this new analytical method?

The primary benefit is streamlining the design process, especially in the early stages. It enables engineers to quickly evaluate different motor configurations and optimize parameters without relying on time-consuming simulations. This allows for rapid prototyping and faster iterations in the design process. It also facilitates a better understanding of the factors influencing air-gap flux density by providing a more direct and intuitive way to analyze motor behavior.

In what practical applications can this new method be utilized?

This method is particularly useful when precise machine structure parameters are not yet known, allowing for rapid prototyping and optimization. This is due to the method's ability to provide a fast and accurate way to predict the air-gap flux density, which is essential for the pro-design phase of many engineering instruments. The fast analytical method can be used in electric vehicles and industrial machinery.