Lorentz-Force Load Extraction & Mapping to Structural FEA

The Transfer Is a Model in Its Own Right

When electromagnetic and structural meshes differ, load mapping is not a clerical operation. It is a numerical model that converts one discretised field into another and can introduce smoothing, extrapolation, imbalance or artificial concentration. The analyst should therefore define mapping requirements before exporting data: which bodies receive load, which force representation is being transferred, whether the structural model uses solids, shells or beams, and which global resultants must be conserved. A high-fidelity electromagnetic solution can be undermined by a low-quality transfer.

Choose the Appropriate Source Quantity

Field solvers may provide volumetric force density, elemental force, nodal force, surface traction, torque density or integrated component forces. Volumetric force density is suitable when the structural model resolves the same conducting volume. Surface traction can be natural for air-gap pressure or interface loading. Integrated resultants may be preferable for simplified supports or rigid substructures. The source quantity should be chosen to preserve the physical load path, not merely because it is easiest to export.

Coordinate Systems and Signs Must Be Explicit

Electromagnetic models frequently use local cylindrical, rotating or device-specific coordinates, while structural models may use a global Cartesian frame. Transform vector quantities before comparison and document the transformation. For rotating machines, distinguish stationary and rotating frames and define the angular reference for spatial harmonics. For repeated sectors, confirm whether the exported force represents one sector, the full circumference or a Fourier coefficient. A sign error or frame mismatch can produce a structurally plausible but physically inverted result.

Conservation of Force and Moment

The primary mapping verification is equilibrium. Sum the mapped structural loads and compare them with the integrated electromagnetic force. Compute moments about the same origin. If the transfer changes the resultant materially, the interpolation, body selection or coordinate transformation is wrong. For self-equilibrating load patterns with near-zero net force, moment alone may also be near zero; in those cases compare physically meaningful subassembly resultants and spatial harmonic coefficients rather than relying only on the whole-model total.

Mapping checks:
F_EM = ∫_V f_EM dV   ≈   Σ F_struct

M_EM,O = ∫_V r × f_EM dV   ≈   Σ r_i × F_struct,i

Preserve Local Gradients Only Where They Matter

Electromagnetic meshes may resolve skin depth, tooth tips, conductor edges and small gaps much more finely than the structural mesh. Mapping every local peak is neither always possible nor always meaningful. If local traction drives a real stress concentration or contact response, the structural mesh must resolve the loaded region. If the structural decision is global support load, a conservative smoothing or resultant reduction may be appropriate. The transfer should be no more detailed than the receiving structural idealisation can physically support.

Mapping to Shell and Beam Models Requires Deliberate Reduction

A three-dimensional body-force distribution cannot be copied directly to a line or midsurface without deciding how eccentricity is retained. For shells, integrate through-thickness force to membrane load and retain any moment generated by off-midsurface loading. For beams, reduce the three-dimensional field to force and moment per unit length about the beam reference line. Neglecting eccentricity can remove torsion or bending that is important to supports and joints. The reduced loads should reconstruct the original force and moment over each transfer region.

Transient and Harmonic Loads Need Time and Phase Control

For time-domain current events, force may scale nonlinearly with current and can contain strong peaks or sign changes. Transfer the force history at a timestep that resolves the structural bandwidth or reconstruct it from a verified reduced representation. In harmonic analysis, establish whether the field solver exports complex peak amplitude, RMS amplitude or instantaneous values. Preserve phase between force components and between spatial locations. Independent magnitude-only envelopes can create combinations that never occur physically and can destroy cancellation that is real.

Interpolation Beyond the Source Mesh Is a Warning

Extrapolated loads are often less trustworthy than interpolated loads. If structural geometry extends beyond the electromagnetic domain or has changed revision, a mapper may silently project values outside the solved field. Use geometric overlap checks and visualise mapped coverage, but do not rely on visual inspection alone. A useful QA table reports source and target body names, total source force, total target force, moment, unmapped fraction and any extrapolated region.

Verification Model Before Production Model

Before transferring a complex production field, test the mapping process with a simple synthetic load for which force and moment are known. Apply uniform body force, a linear traction gradient or another controlled field and confirm exact or near-exact recovery on the structural mesh. This separates mapper defects from electromagnetic-model uncertainty. Re-run the mapping test after major mesh, geometry or automation changes.

Body Selection and Reaction-Path Completeness

A transfer can conserve the force on the selected conductor and still miss the mechanical system load if equal-and-opposite electromagnetic reactions act on omitted bodies. Decide whether the structural scope needs only the loaded component or the complete reaction pair. For example, a coil and magnetic yoke can exchange large internal force while the external support sees a different resultant. Use free-body diagrams to define which electromagnetic bodies belong inside each structural boundary, and compare subassembly resultants accordingly. This is especially important when different teams own the conductor, magnetic circuit and supporting structure.

Engineering Outcome

A mapped Lorentz-force field is defensible when another engineer can trace it from the electromagnetic solution to the structural load deck, reproduce the transformation, and show that equilibrium, coordinate systems, temporal convention and spatial content are preserved. The transfer process should be version-controlled and reviewed with the same care as the source and receiving analyses.

Treat field-to-structure mapping as a controlled numerical transformation. A colourful transferred contour is not evidence that equilibrium or phase has been preserved.

Key takeaways

• Select the source force representation to match the structural idealisation.
• Verify mapped force and moment in consistent coordinates.
• For dynamic loads, preserve amplitude convention, phase and spatial harmonic content.