Piston induction electro-thermo-mechanical coupling

Induction electro-thermo-mechanical field MLP

A 40 kHz alternating current in copper coils induces eddy currents and losses in an aluminum piston. Heating drives thermal expansion, while quarter-model symmetry and axial restraint produce displacement and stress fields.

Adjust coil current from 90 to 110 A to predict surface magnetic flux density, eddy current density, electromagnetic loss density, temperature, displacement and von Mises stress. The 97 A validation, 93 A development holdout and frozen 107 A final blind comparison passed.

Geometry

Quarter piston with ring grooves, internal cavity and curved skirt

Geometry scope

same_geometry_only

Fixed conditions

frequency_hz: 40000; geometry: registered quarter-piston

Adjustable inputs

Output fields

• Piston surface: Magnetic flux density X real, Magnetic flux density Y real, Magnetic flux density Z real, Magnetic flux density X imag, Magnetic flux density Y imag, Magnetic flux density Z imag, Eddy current density X real, Eddy current density Y real, Eddy current density Z real, Eddy current density X imag, Eddy current density Y imag, Eddy current density Z imag, Electromagnetic loss density, Temperature, Displacement X, Displacement Y, Displacement Z, Displacement magnitude, von Mises stress

Registered verification

registered_status

passed

registered_parameters

coil_current_a: 107

registered_reference

Independent native COMSOL 107 A electro-thermo-mechanical surface solution

holdout_metrics

bx_real: rmse: 0.0001637382348454086; relative_l2: 0.021249349910999173; correlation: 0.9997687933528515; max_abs_error: 0.0019517744516509075; reference_min: -0.03864575109955467; reference_max: 0.030265631629656717; prediction_min: -0.0382828028539; prediction_max: 0.0285048066779; status: PASS; by_real: rmse: 0.00016581923897380103; relative_l2: 0.02164312772504123; correlation: 0.9997608090521579; max_abs_error: 0.0015424827146946454; reference_min: -0.03819394677939314; reference_max: 0.02360053914331651; prediction_min: -0.0383176488138; prediction_max: 0.0235321994184; status: PASS; bz_real: rmse: 0.0002752671224121746; relative_l2: 0.013154216274058607; correlation: 0.9998709053655513; max_abs_error: 0.0038231938811499203; reference_min: -0.004185499558617602; reference_max: 0.07430730976556628; prediction_min: -0.00426712954546; prediction_max: 0.0733167271184; status: PASS; bx_imag: rmse: 3.847722384917882e-05; relative_l2: 0.04003414999621503; correlation: 0.9991979367862802; max_abs_error: 0.0003491039603296659; reference_min: -0.005016870980646236; reference_max: 0.004996253825896712; prediction_min: -0.00491704401952; prediction_max: 0.00494958158886; status: PASS; by_imag: rmse: 3.956105842146761e-05; relative_l2: 0.04148738205497442; correlation: 0.999138673728228; max_abs_error: 0.00030127321352611456; reference_min: -0.004838957049195116; reference_max: 0.0069168667800253375; prediction_min: -0.00478835838414; prediction_max: 0.0069265129886; status: PASS; bz_imag: rmse: 5.543888798887775e-05; relative_l2: 0.031314163353720975; correlation: 0.9994195786430977; max_abs_error: 0.0007567735757656944; reference_min: -0.0055033979272864735; reference_max: 0.022021085836819904; prediction_min: -0.00554316379272; prediction_max: 0.0215656296498; status: PASS; jx_real: rmse: 365830.3127397484; relative_l2: 0.011149983206055728; correlation: 0.9999024038914655; max_abs_error: 6672172.438439694; reference_min: -16676816.98968655; reference_max: 102060790.26567982; prediction_min: -12746313.3347; prediction_max: 102286717.236; status: PASS; jy_real: rmse: 349175.4402049273; relative_l2: 0.01055503245454613; correlation: 0.9999120480057229; max_abs_error: 2630814.1418559784; reference_min: -102276741.52031241; reference_max: 1875747.4566516343; prediction_min: -102824394.592; prediction_max: 2415867.02547; status: PASS; jz_real: rmse: 57116.67897707068; relative_l2: 0.045996567511499664; correlation: 0.998942916781577; max_abs_error: 513171.9053572635; reference_min: -24180626.312343862; reference_max: 29956067.13814959; prediction_min: -23906908.834; prediction_max: 29991778.7787; status: PASS; jx_imag: rmse: 407207.83242837625; relative_l2: 0.012468245431140916; correlation: 0.9998838789439438; max_abs_error: 10213130.147074893; reference_min: -62529978.23547489; reference_max: 106804241.52117492; prediction_min: -52316848.0884; prediction_max: 107637029.392; status: PASS; jy_imag: rmse: 381637.537881782; relative_l2: 0.011582377684317337; correlation: 0.9998989715416459; max_abs_error: 5673637.902577803; reference_min: -107457370.80053748; reference_max: 2902019.3660406065; prediction_min: -106838808.377; prediction_max: 4302059.08919; status: PASS; jz_imag: rmse: 66335.09435493902; relative_l2: 0.047136316646821524; correlation: 0.9988882195277159; max_abs_error: 1139058.3228004829; reference_min: -29205407.89225255; reference_max: 37488598.72177329; prediction_min: -29183752.8987; prediction_max: 37335190.1666; status: PASS; displacement_x: rmse: 1.6030423140148272e-06; relative_l2: 0.007246124813772409; correlation: 0.9998854622591149; max_abs_error: 1.2280667129974186e-05; reference_min: -3.3342979632014198e-15; reference_max: 0.00035477810841360685; prediction_min: -5.64597116699e-06; prediction_max: 0.00036019486239; status: PASS; displacement_y: rmse: 1.5912249984280455e-06; relative_l2: 0.007115448068736831; correlation: 0.9998868455700884; max_abs_error: 1.139275186850306e-05; reference_min: -7.699069434807458e-14; reference_max: 0.000355135332218019; prediction_min: -6.66199892843e-06; prediction_max: 0.000360254364223; status: PASS; displacement_z: rmse: 2.364058418734371e-06; relative_l2: 0.004272469793071477; correlation: 0.9998960012643566; max_abs_error: 2.257559063654753e-05; reference_min: -5.083535728617497e-18; reference_max: 0.0007137479331621937; prediction_min: -1.91601616769e-05; prediction_max: 0.000719871965973; status: PASS; loss_density_w_m3: rmse: 1248931.8580226065; relative_l2: 0.012705906580040872; correlation: 0.9998775641695958; max_abs_error: 29951672.759013653; reference_min: 0.0004981715055409101; reference_max: 367016081.13501364; prediction_min: 0.00159004753051; prediction_max: 337064408.376; status: PASS; temperature: rmse: 0.3481271538575333; relative_l2: 0.000622082264665095; correlation: 0.9944313802426317; max_abs_error: 2.1501855407652783; reference_min: 549.5692119350156; reference_max: 563.1213712853732; prediction_min: 547.933357732; prediction_max: 564.021046561; temperature_rise_relative_l2: 0.0013064084164874548; status: PASS; displacement_magnitude: rmse: 2.1198086432047153e-06; relative_l2: 0.0033304692822573308; correlation: 0.9998897657818614; max_abs_error: 1.6439314005719792e-05; reference_min: 0.00014287304290084307; reference_max: 0.0007922741912825495; prediction_min: 0.000152128128347; prediction_max: 0.000797722863241; status: PASS; von_mises_stress_pa: rmse: 29356.884152164363; relative_l2: 0.01543084963405731; correlation: 0.9994975484773637; max_abs_error: 502853.06252316386; reference_min: 74052.17913366485; reference_max: 14026607.338023163; prediction_min: 66832.9242337; prediction_max: 13523754.2755; status: PASS

thresholds

per_em_phasor_component_relative_l2_max: 0.05; loss_density_relative_l2_max: 0.05; temperature_rmse_k_max: 1.0; temperature_rise_relative_l2_max: 0.05; per_displacement_component_rmse_m_max: 5e-06; per_displacement_component_relative_l2_max: 0.05; displacement_magnitude_rmse_m_max: 5e-06; displacement_magnitude_relative_l2_max: 0.03; von_mises_stress_rmse_pa_max: 500000.0; von_mises_stress_relative_l2_max: 0.08; per_nonconstant_em_thermal_displacement_correlation_min: 0.98; von_mises_stress_correlation_min: 0.95; loss_density_min_w_m3: 0.0; temperature_min_k: 293.15; displacement_magnitude_min_m: 0.0; von_mises_stress_min_pa: 0.0

summary

97 A validation, 93 A development holdout and frozen 107 A final blind comparison passed for the registered surface.