Realistic Motor Steady Thermal Sample

This showcase explains a steady-state motor thermal workflow using a mixed CHEXA/CPENTA BDF mesh, imported QVOL losses, JSON-defined additional losses, FEMH surface cooling, a thermal equivalent circuit, and stator/rotor gap coupling.

The purpose of this example is not to match a measured motor temperature. Instead, it demonstrates how to set up and audit the complete thermal path for an electric-machine design model:

• loss input from BDF QVOL
• coil copper loss from phase current and resistance
• permanent-magnet loss from a user-specified total heat value
• FEMH connection from selected FEM surfaces to thermal-network nodes
• stator/rotor air-gap thermal coupling
• surface assignment diagnostics to avoid double-counted boundary faces
• component heat balance, cooling path summary, and network-node temperatures

The public example is located under:

Examples/thermal/realistic_motor_steady/

The BDF used by the sample is included in that folder as:

Examples/thermal/realistic_motor_steady/QVOL_loss_mix.bdf

Model And Mesh

The motor thermal mesh is a BDF model with mixed solid elements. It contains two bulk sections that are treated as separate thermal components:

Component	Bulk section	Role
Stator	0	Stator core, slot coil regions, and stator-side losses.
Rotor	1	Rotor core, permanent magnet region, and rotor-side losses.

The figure below shows the motor mesh used in the showcase.

The mesh is used as a thermal conduction model. The BDF provides element geometry, property IDs, bulk sections, and QVOL heat sources. Additional engineering heat sources are added from JSON rather than overwriting the BDF QVOL data.

Loss Inputs

The total heat in the main realistic cases is:

Source	Input method	Heat
BDF QVOL	Imported from QVOL_loss_mix.bdf	1.091336675596593 W
Coil copper loss	thermal_volume_heat_sources, mode = "coil_copper_loss"	23.004 W
PM magnet loss	thermal_volume_heat_sources, mode = "total_heat"	1.25 W
Total	BDF QVOL + JSON volume heat	25.345336675596593 W

The BDF QVOL heat is the loss already exported by the upstream electromagnetic workflow. In this sample, the coil copper loss is added in JSON because the electromagnetic model uses external circuit resistance for the coil conductor.

The coil copper loss is computed from RMS phase current and phase resistance:

P_phase = I_rms^2 * R_phase
        = 3.0^2 * 0.852
        = 7.668 W

P_total = 3 * P_phase = 23.004 W

The phase target property IDs are:

Phase	Property IDs
U	10000, 10001
V	10004, 10005
W	10002, 10003

The PM loss is assigned to:

Region	Property ID	Heat input
Permanent magnet	50000	5.0 W * 0.25 = 1.25 W

The coil_fill_factor is used for diagnostic conductor-volume heat density. It does not rescale the I^2 R copper loss that is assembled into the FEM right hand side.

JSON Cases

The directory contains several JSON files. Each one is useful for a different stage of model checking.

JSON file	Purpose
input_realistic_motor_steady_import_summary.json	Check BDF import, PSOLID/MAT diagnostics, QVOL heat, coil loss, and PM loss.
input_realistic_motor_steady_all_external_balance.json	Connect all external faces by FEMH to verify closed heat balance. This is a verification boundary condition, not a physical cooling model.
input_realistic_motor_steady_physical_no_gap.json	Exclude gap faces from external FEMH cooling and run physical-style external cooling without stator/rotor gap coupling.
input_realistic_motor_steady_physical_gap_h20.json	Use physical-style external cooling plus air-gap coupling with direct h = 20 W/m2/K.
input_realistic_motor_steady_physical_gap_nu1.json	Use physical-style external cooling plus air-gap coupling with mode = "nu", Nu = 1, k_air = 0.026 W/m/K, and gap = 0.001 m.
input_realistic_motor_steady_physical_gap_h20_interface_resistance.json	Add shared-node interface thermal resistance for coil-to-stator and PM-to-rotor interfaces.
input_realistic_motor_steady_physical_gap_h20_interface_axial_endcool.json	Add axial end-face cooling paths through an end_space_air network node, representing first-order end-space and coil-end heat escape.
input_realistic_motor_steady_mount_shaft_network.json	Demonstrate a housing, mount, shaft, and bearing thermal equivalent circuit. Values are illustrative, not calibrated.

All realistic motor cases exclude the outer air property from the thermal FEM domain:

"bdf_import": {
  "exclude_property_ids": [50]
}

The BDF still contains the outer air region for electromagnetic meshing, but thermal conduction is solved only in the motor solids. This makes the stator outer surface available as the FEMH boundary connected to the housing or thermal equivalent circuit.

Boundary Conditions And FEMH Connections

FEMH connects selected FEM surface groups to thermal-network nodes. This lets the FEM model exchange heat with lumped thermal-circuit nodes such as housing, shaft, bearing, mount, and ambient.

In the physical boundary examples, the main surface groups are:

Surface group	Typical use
stator_external	All stator external faces. Used for diagnostics and set operations.
rotor_external	All rotor external faces. Used for diagnostics and set operations.
stator_gap_candidate_filtered	Stator-side air-gap candidate faces. Used for gap coupling only.
rotor_gap_candidate_filtered	Rotor-side air-gap candidate faces. Used for gap coupling only.
stator_external_cooling	Stator external cooling surface after excluding gap faces. Connected to housing by FEMH.
rotor_external_cooling	Rotor external cooling surface after excluding gap faces. Connected to shaft by FEMH.

The important modeling rule is:

Gap faces must not also be used as external FEMH cooling faces.

The model checks this with:

thermal_surface_assignment_summary.csv

For the physical gap cases, the intended result is:

femh_and_gap_overlap area = 0

If this value is not zero, the same face is carrying both external cooling and stator/rotor internal gap heat exchange, which double-counts the thermal path.

Gap Thermal Coupling

The stator and rotor meshes are separate thermal components. The air-gap heat path is represented by a surface-to-surface thermal coupling between paired gap faces.

The current implementation uses node_pair_lumped assembly:

1. Pair accepted stator and rotor gap faces.
2. Compute effective pair area.
3. Compute pair conductance from the chosen model.
4. Match source and target face nodes by nearest coordinates.
5. Stamp lumped two-node thermal conductances into the FEM matrix.

This showcase demonstrates two common input styles:

Mode	Formula	Example
h	G = h * A	h = 20 W/m2/K
nu	h_equiv = Nu * k_air / gap_thickness	Nu = 1, k_air = 0.026 W/m/K, gap = 0.001 m

For the Nu = 1 case:

h_equiv = 26.0 W/m2/K
gap total conductance = 6.800205753006171e-02 W/K

Thermal Equivalent Circuit

The thermal equivalent circuit represents cooling paths outside the FEM mesh. The updated concept diagram includes the radial housing/shaft paths, the stator/rotor gap path, and an axial end-space path used to approximate heat escape through the upper/lower motor end regions.

The main paths are:

Label	Meaning
FEMH-SR	FEMH connection from stator radial external surfaces to the housing node.
FEMH-RR	FEMH connection from rotor radial external surfaces to the shaft node.
G-gap	Surface-to-surface stator/rotor gap thermal coupling.
FEMH-SE	FEMH connection from stator end faces to end_space_air; in this one-layer extruded sample it also represents a first-order coil-end heat-escape path.
FEMH-RE	FEMH connection from rotor end faces to end_space_air.
R-EH	Thermal resistance from end_space_air to housing.
R-EA	Thermal resistance from end_space_air to ambient.
R-HA, R-SA	Representative housing/shaft paths to ambient.

FEMH ports form conductance paths between FEM surface temperatures and thermal-network nodes. RTH/GTH elements then move heat between network nodes. The gap surface is not also used as an external FEMH cooling surface; it is handled as an internal surface-to-surface heat-exchange path.

To inspect the thermal-network temperatures and heat flows, open:

thermal_network_nodes.csv
thermal_network_element_flows.csv
thermal_cooling_path_summary.csv
thermal_femh_ports.csv

The axial end-space case is:

input_realistic_motor_steady_physical_gap_h20_interface_axial_endcool.json

Representative values for that case are:

Quantity	Value
stator radial cooling average temperature	67.55 degC
stator end faces average temperature	72.67 degC
rotor radial cooling average temperature	44.38 degC
rotor end faces average temperature	44.71 degC
stator gap average temperature	67.92 degC
rotor gap average temperature	52.15 degC
gap heat source-to-target	0.824813796 W
global relative residual	3.782002356724577e-11

The coefficients are illustrative. For a compressor motor, tune FEMH coefficients and network resistances using measured case temperature, coolant/oil condition, end-space geometry, and 3D validation data.

Temperature Results

The figure below shows a representative steady-state temperature field for the physical boundary case with air-gap coupling.

The highest temperatures occur on the stator side in this illustrative setup because most of the added heat is coil copper loss. This does not mean the absolute values are calibrated to a real machine. The example is designed to show how heat sources and heat-flow paths can be audited.

The next figure focuses on the gap region.

Use this view together with thermal_gap_coupling_flow_summary.csv and thermal_gap_coupling_flows.csv to confirm that the sign and magnitude of gap heat flow are consistent with the stator and rotor gap-surface temperatures.

For the h = 20 W/m2/K gap case, representative values are:

Quantity	Value
Accepted gap face pairs	90
Gap total conductance	5.230927502312448e-02 W/K
Equivalent gap resistance	19.11706861847976 K/W
Gap heat source-to-target	2.181396948282994 W
Surface overlap area	0

For the Nu = 1 case:

Quantity	Value
Nu	1.0
h_equiv	26.0 W/m2/K
Gap total conductance	6.800205753006171e-02 W/K
Gap heat source-to-target	2.332210259864751 W

Heat Balance Checks

Start with the all-external balance case before interpreting physical boundary conditions. It checks that all heat sources enter the FEM right-hand side and leave through FEMH/network paths.

Representative balance:

FEM volume heat       = 25.34533667559660 W
FEM RHS heat          = 25.34533667559660 W
FEMH outflow          = 25.34533667548905 W
network TEMP outflow  = 25.34533667547321 W
global relative residual ~ 1e-11

For component-level checks, inspect:

thermal_component_heat_balance.csv

For the h = 20 W/m2/K physical gap case:

Component	QVOL and JSON heat	FEMH outflow	Net gap heat outflow	Average temperature
Stator	23.9886 W	21.8072 W	2.1814 W	187.839 C
Rotor	1.3567 W	3.5381 W	-2.1814 W	114.653 C

The positive stator gap heat outflow and negative rotor net gap heat outflow show that heat is flowing from the hotter stator-side gap surface to the rotor side in this illustrative case.

Output Files To Inspect

File	What to check
thermal_bdf_import_summary.csv	BDF import counts, QVOL counts, total BDF heat.
thermal_bdf_property_material_summary.csv	PSOLID/MAT diagnostics and analysis material source.
thermal_volume_heat_sources.csv	Coil copper loss, PM loss, assigned heat density, target volume.
thermal_fem_volume_heat.csv	BDF QVOL heat, JSON added heat, and total FEM volume heat.
thermal_global_heat_balance.csv	Total heat input, FEMH outflow, network outflow, residual.
thermal_surface_assignment_summary.csv	FEMH/gap overlap and unassigned external area.
thermal_surface_temperature_summary.csv	Area-weighted surface temperatures.
thermal_gap_pair_summary.csv	Gap face pairing count and quality.
thermal_gap_coupling_summary.csv	Assembled gap conductance and equivalent resistance.
thermal_gap_coupling_flow_summary.csv	Total heat transferred through the gap coupling.
thermal_cooling_path_summary.csv	FEMH and gap path conductance, temperatures, and heat flow.
thermal_network_nodes.csv	Thermal equivalent-circuit node temperatures.
thermal_network_element_flows.csv	Heat flow through thermal-network RTH/GTH elements.
mesh.vtk	Mesh geometry, property IDs, and element IDs.
thermal_result.vtk	Temperature field for ParaView.
boundary_faces.vtk	Surface-group and cooling-boundary visualization.

Modeling Notes

This sample intentionally uses illustrative coefficients. Before using a similar setup for design decisions, review:

• actual coil resistance and current conditions
• modeled axial-length fraction
• PM loss source and modeled fraction
• material thermal conductivities
• FEMH heat transfer coefficients
• housing, shaft, bearing, and mount thermal resistances
• gap heat-transfer model, such as measured h, k/gap, external Nu, or a user-defined preprocessing workflow
• surface assignment overlap
• mesh density in regions with steep thermal gradients

Temperature-dependent material properties, transient thermal analysis, radiation, automatic coil-end loss distribution, and calibrated rotating-gap correlations are outside the scope of this showcase.

Shared-node interface thermal resistance

The sample also includes an optional shared-node interface resistance case:

input_realistic_motor_steady_physical_gap_h20_interface_resistance.json

This case is intended for meshes where adjacent parts share nodes, such as coil-to-stator-core or PM-to-rotor-core interfaces. The input extracts matching internal faces from the specified property groups, duplicates the nodes on the selected side for the thermal solve, and stamps a lumped conductance between the original and duplicated thermal nodes.

Example input fragment:

"interface_thermal_resistances": [
  {
    "name": "coil_to_stator_slot_liner",
    "side_a": { "property_ids": [10] },
    "side_b": { "property_ids": [10000, 10001, 10002, 10003, 10004, 10005] },
    "split_side": "side_b",
    "mode": "thin_layer",
    "layer_thermal_conductivity": 0.2,
    "layer_thickness": 0.0002,
    "assembly": "shared_node_pair_lumped"
  },
  {
    "name": "pm_to_rotor_adhesive",
    "side_a": { "property_ids": [20] },
    "side_b": { "property_ids": [50000] },
    "split_side": "side_b",
    "mode": "thin_layer",
    "layer_thermal_conductivity": 0.2,
    "layer_thickness": 0.0002,
    "assembly": "shared_node_pair_lumped"
  }
]

Representative validation values for this sample are:

Interface	Faces	Area	h_equiv	Total conductance	Equivalent resistance
coil_to_stator_slot_liner	156	1.187038579243427e-02 m2	1000 W/m2/K	1.187038579243424e+01 W/K	8.424326028538720e-02 K/W
pm_to_rotor_adhesive	80	2.399721226189904e-03 m2	1000 W/m2/K	2.399721226189901e+00 W/K	4.167150705199728e-01 K/W

Check these CSV files when using interface resistance:

thermal_interface_resistance_summary.csv
thermal_interface_resistance_node_pairs.csv
thermal_interface_resistance_node_splits.csv
thermal_matrix_diagnostics.csv
thermal_global_heat_balance.csv

Axial End-Space Cooling And Coil-End Equivalent Path

input_realistic_motor_steady_physical_gap_h20_interface_axial_endcool.json adds axial heat-escape paths on top of the shared-node interface-resistance case. This is useful for a one-layer extruded 2D motor sample, where heat that would leave through the upper/lower end regions of a real 3D motor can otherwise be underrepresented.

The modeling approach is:

• Exclude the outer air property 50 from the thermal FEM domain.
• Connect stator_radial_external_cooling to the housing node through FEMH.
• Connect rotor_radial_external_cooling to the shaft node through FEMH.
• Extract stator_end_faces and rotor_end_faces with abs_normal_z_min = 0.9.
• Connect those end faces to an end_space_air node through FEMH.
• Connect end_space_air to housing and ambient through thermal resistances.

In this first-stage sample, the stator end-face FEMH path is also used as a practical equivalent path for slot coil and coil-end heat escape. A more detailed future model can split the coil end into its own thermal-network node or 3D region, then assign coil-end loss and cooling separately.

Representative result:

Quantity	Value
stator radial cooling average temperature	67.55 degC
stator end faces average temperature	72.67 degC
rotor radial cooling average temperature	44.38 degC
rotor end faces average temperature	44.71 degC
stator gap average temperature	67.92 degC
rotor gap average temperature	52.15 degC
gap heat source-to-target	0.824813796 W
global relative residual	-9.996386288e-12

The values are illustrative rather than calibrated. For a compressor motor, tune FEMH coefficients and network resistances using measured case temperature, coolant/oil condition, end-space geometry, and 3D validation data.