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Magnetic field analysis in electrical machines (e.g., motors, generators, transformers) is critical for optimizing performance, efficiency, and thermal management. Below is a structured approach to perform magnetic field analysis in MATLAB, leveraging its built-in PDE Toolbox and Finite Element Analysis (FEA) capabilities. 1. Problem Setup Key Equations For magnetostatic problems, Maxwell’s equations reduce to: ∇ ⋅ B = 0 and ∇ × H = J ∇⋅B=0and∇×H=J where: B = μ H B=μH (magnetic flux density), μ = μ 0 μ r μ=μ 0 ​ μ r ​ (permeability), J J is the current density. Typical Applications Motor/generator stator-rotor flux distribution. Inductance calculation. Core losses (hysteresis/eddy currents). Force/torque computation. 2. MATLAB Workflow Step 1: Define Geometry Use MATLAB’s PDE Toolbox to model the machine cross-section (2D analysis is common for simplicity). matlab Copy % Example: Create a simple motor geometry (stator + rotor + airgap) model = createpde(‘electromagnetic’,’magnetostatic’); % Define circles for stator, rotor, and airgap stator = [3,4,0,0,0.1,0.1]’; % Outer radius = 0.1 m rotor = [3,4,0,0,0.05,0.05]’; % Inner radius = 0.05 m airgap = [3,4,0,0,0.055,0.055]’; % Airgap radius = 0.055 m gd = [stator, rotor, airgap]; ns = char(‘stator’,’rotor’,’airgap’); g = decsg(gd, ‘stator – rotor – airgap’, ns’); geometryFromEdges(model, g); Step 2: Assign Material Properties Define μ r μ r ​ (relative permeability) for each region: matlab Copy % Stator/Rotor (Silicon Steel, μr = 2000) electromagneticProperties(model, ‘RelativePermeability’, 2000, ‘Region’, ‘stator’); electromagneticProperties(model, ‘RelativePermeability’, 2000, ‘Region’, ‘rotor’); % Airgap (μr = 1) electromagneticProperties(model, ‘RelativePermeability’, 1, ‘Region’, ‘airgap’); Step 3: Define Current Sources Assign current density J J to windings: matlab Copy % Define a coil with current density J = 1e6 A/m² electromagneticSource(model, ‘CurrentDensity’, 1e6, ‘Face’, [coil_faces]); Step 4: Boundary Conditions Dirichlet BC: Set magnetic potential A z = 0 A z ​ =0 at outer boundaries. Periodic BC: For symmetry in rotating machines. matlab Copy % Apply Dirichlet BC on outer stator boundary electromagneticBC(model, ‘Edge’, [outer_edges], ‘MagneticPotential’, 0); Step 5: Generate Mesh matlab Copy generateMesh(model, ‘Hmax’, 0.005); % Hmax controls mesh fineness pdeplot(model) Step 6: Solve Magnetostatic Problem matlab Copy result = solve(model); Step 7: Post-Processing Visualize magnetic flux density ( B B): matlab Copy Bx = result.MagneticFluxDensity.x; By = result.MagneticFluxDensity.y; B = sqrt(Bx.^2 + By.^2); pdeplot(model, ‘XYData’, B, ‘FlowData’, [Bx, By], ‘ColorMap’, ‘jet’); title(‘Magnetic Flux Density (B)’); 3. Torque Calculation For motors, compute torque using the Maxwell Stress Tensor: matlab Copy % Integrate B_tangential * B_normal over the rotor surface [theta, Br, Btheta] = calculateFluxTangential(result, rotor_boundary); mu0 = 4*pi*1e-7; torque = (1/mu0) * trapz(theta, Br .* Btheta) * rotor_radius^2; 4. Example: Permanent Magnet Motor matlab Copy % Define PM material (μr = 1.05, coercivity Hc = -1e6 A/m) electromagneticProperties(model, ‘RelativePermeability’, 1.05, … ‘Magnetization’, [0, -1e6], ‘Face’, pm_faces); 5. Advanced Features Transient Analysis: Use solvepde with time-stepping for eddy currents. Parameter Sweep: Optimize geometry/materials using parfor. Export to Simulink: Couple FEA results with system-level simulations. 6. MATLAB Tools & Functions PDE Toolbox: For 2D/3D FEA. FEMM Integration: Link to Finite Element Method Magnetics (via MATLAB scripting). Optimization Toolbox: For design refinement. 7. Limitations & Alternatives MATLAB’s PDE Toolbox is limited for complex 3D geometries. Consider: ANSYS Maxwell: Industry-standard for electrical machines. COMSOL: Multi-physics FEA. Open-Source Tools: FEMM (2D) or Elmer FEM. Sample Results Flux Density Plot: Flux Density Torque vs. Rotor Position: Torque Resources MATLAB PDE Toolbox Documentation FEMM-MATLAB Integration This workflow allows rapid prototyping of electrical machine designs in MATLAB, though complex industrial applications may require specialized FEA software.

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Magnetic field analysis in electrical machines (e.g., motors, generators, transformers) is critical for optimizing performance, efficiency, and thermal management. Below is a structured approach to…

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