Heated platen
Thermal FEA of heater placement, interface contact, surface losses and controlled warm-up.
Completed commissioning study
Three heaters with nominal 1000 W/(m 2 K) contact, bottom U 2 W/(m 2 K), 60 W maximum power, independent 125 C heater/105 C surface cutoff with 2 s response. Six 22/35 C ambient x 5/10/20 W/(m 2 K) convection cases reach 88-92 C across the working area for a 300 s hold.
Executed synthetic/theoretical results, rejected cases and acceptance matrix. Source: complete_validation.py.
Model
- 200 x 120 x 8 mm plate; central 160 x 80 mm working area; 22 C ambient; target band 88-92 C.
- Linear triangular plate elements with consistent heat capacity; three lumped heater nodes; finite surface contact conductance.
- Equal-power comparison: 23.266 W total. Controlled cases: 60 W maximum power, identical center-sensor PI law.
- Implicit Euler: M (T[n+1]-T[n])/dt + K T[n+1] = f[n]. All temperatures are rises above ambient internally.
Steady results
| layout | poor_contact | top_h_W_m2K | minimum_working_C | maximum_working_C | maximum_heater_C | in_band |
|---|---|---|---|---|---|---|
| even | False | 5 | 124.913 | 125.96 | 130.489 | False |
| even | False | 10 | 89.043 | 90.0 | 94.581 | True |
| even | False | 20 | 61.442 | 62.328 | 66.95 | False |
| even | True | 5 | 124.522 | 125.591 | 171.736 | False |
| even | True | 10 | 88.779 | 89.758 | 136.39 | True |
| even | True | 20 | 61.278 | 62.185 | 109.194 | False |
| edge | False | 5 | 124.993 | 125.743 | 130.271 | False |
| edge | False | 10 | 89.08 | 89.856 | 94.437 | True |
| edge | False | 20 | 61.447 | 62.241 | 66.862 | False |
| edge | True | 5 | 124.613 | 125.387 | 171.767 | False |
| edge | True | 10 | 88.828 | 89.627 | 136.456 | True |
| edge | True | 20 | 61.294 | 62.11 | 109.286 | False |
| central | False | 5 | 124.52 | 126.507 | 131.007 | False |
| central | False | 10 | 88.637 | 90.539 | 95.092 | True |
| central | False | 20 | 61.029 | 62.858 | 67.452 | False |
| central | True | 5 | 124.135 | 126.137 | 172.072 | False |
| central | True | 10 | 88.38 | 90.296 | 136.697 | True |
| central | True | 20 | 60.871 | 62.715 | 109.476 | False |
Warm-up
| case | settled_in_band_s | final_min_C | final_max_C | peak_heater_C | peak_working_C |
|---|---|---|---|---|---|
| nominal-h5 | 2006 | 89.121 | 89.817 | 102.946 | 99.22 |
| nominal-h10 | 2018 | 88.859 | 89.822 | 102.056 | 96.757 |
| nominal-h20 | 1890 | 88.43 | 89.922 | 101.06 | 92.834 |
| poor-h5 | 2000 | 89.128 | 89.842 | 178.462 | 99.345 |
| poor-h10 | 2012 | 88.844 | 89.832 | 181.977 | 96.835 |
| poor-h20 | 1892 | 88.387 | 89.921 | 190.901 | 92.852 |
- Settled time is the first sample after which all working-area nodes stay in band for the remainder of the 3600 s simulation.
- Fixed power does not hold the target throughout the loss sweep. Feedback compensates in the examined cases, with startup overshoot.
- Poor contact is a heater-temperature risk. A plate sensor alone cannot protect the interface.
Verification
- 29 convergence, analytical-limit and energy-balance checks pass.
- Analytical limit: as conductivity becomes large, plate rise approaches P divided by total plate loss conductance, with heater backing loss disabled.
| dt_s | settled_in_band_s | final_min_C | peak_working_C |
|---|---|---|---|
| 4 | 2020 | 88.8593027511462 | 96.77046970444238 |
| 2 | 2018 | 88.85946390244314 | 96.75667182826378 |
| 1 | 2017 | 88.85945696211712 | 96.726739829556 |
Bench plan
- Attach thermocouples at the nine supplied coordinates; document attachment and calibration uncertainty.
- Log all surface points, heater temperatures, ambient and electrical power from cold start.
- Repeat with actual insulation and a controlled degraded-contact coupon, stopping below component limits.
- Measure a grid across the full working area before claiming physical uniformity.
Limits
- A 2D thin-plate approximation assumes temperature uniform through 8 mm thickness; this is not 3D contact FEA.
- Heater construction, interface materials and mounting require selection and physical measurement.
- Heat-loss and contact coefficients are sensitivity assumptions. Radiation is not separate; measured effective losses should replace these inputs.
- Poor contact produces high heater temperatures even when the plate reaches its band. Component limits and independent overtemperature protection are not qualified.
- No physical temperature or curing-performance tests were performed. The PI controller is a numerical reference, not production firmware.
- CAD includes nominal envelopes, plate drawing and sensor coordinates. Wiring, fasteners, insulation grade and heater procurement remain application-specific.
Numerical library reference
scikit-fem heat equation example. The supplied model adds finite heater contact, distributed losses and lumped heater capacities.
Reference design by CJ Ackley. Numerical and geometry checks are not a physical qualification.