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A novel key performance analysis method for permanent magnet coupler using physics-informed neural networks

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Abstract

The non-contact transmission product permanent magnet coupler (PMC) has been widely used in industry due to its advantages such as low noise and vibration, high efficiency, high reliability, and overload protection. Owing to its complex electromagnetic behaviors, the accurate computation of key performances such as magnetic vector potential and torque is essential for optimizing its transmission efficiency. However, traditional calculation methods are based on analytical or simulation models, either imprecise or computationally intensive, hindering subsequent optimization design modeling. To address the above issue, this paper proposes a novel method based on physical-informed neural networks (PINN) to calculate the PMC performances with high accuracy and low computational cost. PINN integrates prior knowledge into the deep neural network’s loss functions to establish the model and accurately predict the PMC’s performance parameters. Experimental results demonstrate that PINN outperforms traditional calculation methods regarding feasibility, validity, and accuracy. Overall, PINN combines data-driven models with prior knowledge to achieve a data–knowledge dual driven, providing a new approach for optimizing PMC structure design.

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Data availability

The data used for this study is available on request to the authors.

Abbreviations

\(\,\,\varvec{A}\) :

Magnetic vector potential vector (Wb/m)

A :

Magnetic vector potential (Wb/m)

\(\,\,\varvec{B}\) :

Magnetic induction vector (T)

\(B_r\) :

Residual magnetic induction (T)

F :

Electromagnetic force (N)

g :

Thickness of air gap (m)

\(\,\,\varvec{H}\) :

Magnetic field intensity vector (A/m)

\(\,\,\varvec{J}\) :

Current density vector (\(A/m^2\))

k :

Correction factor

\(k_\textrm{th}\) :

The K-th hidden layer of the neural network

K :

The number of hidden layers in a neural network

\(\,\,\varvec{M}\) :

Magnetization vector (A/m)

\(\,\,\varvec{M}_r\) :

Remanence magnetization vector (A/m)

\(N_r,N_u\) :

The corresponding number of sampling points

n :

The number of harmonic order

\(n_1\) :

Input rotation speed of permanent magnet rotor (rpm/min)

\(n_2\) :

Output rotation speed of conductor rotor (rpm/min)

p :

Number of pole pairs

r :

True value of the governing equations

\({\hat{r}}\) :

Predicted value of the governing equations

\(r_1\) :

Thickness of PM yoke iron (m)

\(r_2\) :

Thickness of PM (m)

\(r_3\) :

Thickness of copper layer (m)

\(r_4\) :

Thickness of copper layer yoke iron (m)

\(r_m\) :

Average radius (m)

\(\gamma _m,\gamma _{cm}\) :

Dimensionless number

s :

Slip

t :

Time (s)

T :

Torque (N.m)

\(\tau _m\) :

Mean pole-arc length (m)

\(\tau _p\) :

Mean pole pitch (m)

u :

True value of the boundary conditions

\({\hat{u}}\) :

Predicted value of the boundary conditions

\(\mu _0\) :

Vacuum permeability (H/m)

\(\mu _x\) :

PM permeability (H/m)

\(\mu _{av}\) :

PM yoke iron permeability (H/m)

\(\mu _{eq}\) :

Copper layer yoke iron permeability (H/m)

\(\omega _1\) :

Angular velocity of the primary (rad/s)

\(\omega _c\) :

Width of copper layer (m)

\(\omega _m\) :

Width of PM (m)

x :

Two-dimensional model of PMC at x-direction distance (m)

y :

Two-dimensional model of PMC at y-direction distance (m)

\(y_1-y_6\) :

Six boundaries of PM two-dimensional model (m)

\(\sigma\) :

Conductivity (S/m)

\(\sigma _1\) :

Copper layer conductivity (S/m)

\(\sigma _2\) :

Copper layer yoke iron conductivity (S/m)

\({\tilde{M}}_n\) :

N-th harmonic order phasor form of magnetization (S/m)

\(\nabla \times \,\,\varvec{A}\) :

Curl of vector field

\(\partial\) :

Partial differential symbol

\(w^k\) :

Neural network weights of the \(k_\textrm{th}\) layer

\(b^k\) :

Neural network bias terms of the \(k_\textrm{th}\) layer

\(\lambda\) :

Unknown parameters of PDEs system

\(\,\,\varvec{x}\) :

The independent variable vector of PDEs system

\({\Phi }\) :

The independent variable vector of PDEs system

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Funding

This research work is supported by the National Natural Science Foundation of China (Grant No. 52105244), Fundamental Research Funds for the Central Universities (Grant No. 02090052020106).

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Authors and Affiliations

  1. College of Mechanical and Vehicle Engineering, Chongqing University, 174, Shazheng Street, Shapingba District, Chongqing City, 400044, China

    Huayan Pu, Bo Tan, Jin Yi & Jun Luo

  2. The State Key Laboratory of Mechanical Transmissions, Chongqing University, 174, Shazheng Street, Shapingba District, Chongqing City, 400044, China

    Shujin Yuan, Jinglei Zhao, Ruqing Bai & Jun Luo

  3. School of Mechatronics Engineering and Automation, Shanghai University, 99 ShangDa Road, BaoShan District, Shanghai City, 200444, China

    Huayan Pu

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Pu, H., Tan, B., Yi, J. et al. A novel key performance analysis method for permanent magnet coupler using physics-informed neural networks. Engineering with Computers 40, 2259–2277 (2024). https://doi.org/10.1007/s00366-023-01914-8

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