Injection Molding Quality

{ "metadata": { "name": "Injection Molding Quality", "description": "Central composite design for 4-response multi-objective injection molding optimization with custom bounds on all responses" }, "factors": [ { "name": "melt_temp", "levels": [ "200", "280" ], "type": "continuous", "unit": "C" }, { "name": "injection_pressure", "levels": [ "50", "120" ], "type": "continuous", "unit": "MPa" }, { "name": "cooling_time", "levels": [ "10", "30" ], "type": "continuous", "unit": "s" } ], "fixed_factors": { "mold_material": "P20_steel", "part_weight": "45g" }, "responses": [ { "name": "surface_finish", "optimize": "maximize", "unit": "Ra_um" }, { "name": "dimensional_accuracy", "optimize": "maximize", "unit": "%" }, { "name": "cycle_time", "optimize": "minimize", "unit": "s" }, { "name": "warpage", "optimize": "minimize", "unit": "mm" } ], "settings": { "operation": "central_composite", "test_script": "use_cases/306_injection_molding/sim.sh" } }

============================================================ MULTI-OBJECTIVE OPTIMIZATION Method: Derringer-Suich Desirability Function ============================================================ Overall desirability: D = 0.6615 Response Weight Desirability Predicted Direction --------------------------------------------------------------------- surface_finish 1.5 0.8474 1.71 Ra_um ↑ dimensional_accuracy 2.0 0.9240 99.62 % ↑ cycle_time 1.0 0.1578 52.90 s ↓ warpage 1.5 0.8600 0.21 mm ↓ Recommended settings: melt_temp = 240 C injection_pressure = 85 MPa cooling_time = 20 s (from observed run #17) Trade-off summary: surface_finish: 1.71 (best observed: 1.86, sacrifice: +0.15) dimensional_accuracy: 99.62 (best observed: 99.62, sacrifice: +0.00) cycle_time: 52.90 (best observed: 17.80, sacrifice: +35.10) warpage: 0.21 (best observed: 0.12, sacrifice: +0.09) Model quality: surface_finish: R² = 0.6617 (quadratic) dimensional_accuracy: R² = 0.1482 (linear) cycle_time: R² = 0.2237 (linear) warpage: R² = 0.2377 (linear) Top 3 observed runs by overall desirability: 1. Run #17 (D=0.6615): melt_temp=240, injection_pressure=85, cooling_time=20 2. Run #18 (D=0.6356): melt_temp=240, injection_pressure=85, cooling_time=20 3. Run #22 (D=0.6307): melt_temp=200, injection_pressure=50, cooling_time=10

=== Main Effects: surface_finish === Factor Effect Std Error % Contribution -------------------------------------------------------------- injection_pressure 1.1820 0.0764 68.6% cooling_time 0.2967 0.0764 17.2% melt_temp 0.2450 0.0764 14.2% === ANOVA Table: surface_finish === Source DF SS MS F p-value ----------------------------------------------------------------------------- melt_temp 4 0.0977 0.0244 0.296 0.8734 injection_pressure 4 1.0303 0.2576 3.121 0.0720 cooling_time 4 0.1142 0.0285 0.346 0.8405 Lack of Fit 2 0.8790 0.4395 5.326 0.0393 Pure Error 7 0.5776 0.0825 Error 9 1.4566 0.0825 Total 21 2.6987 0.1285 === Summary Statistics: surface_finish === melt_temp: Level N Mean Std Min Max ------------------------------------------------------------ 166.97 1 1.4800 0.0000 1.4800 1.4800 200 4 1.2833 0.5905 0.4100 1.7100 240 12 1.3832 0.3493 0.6740 1.8560 280 4 1.2508 0.2663 0.8970 1.5360 313.03 1 1.2350 0.0000 1.2350 1.2350 injection_pressure: Level N Mean Std Min Max ------------------------------------------------------------ 120 4 1.4390 0.2050 1.2410 1.7100 148.901 1 1.8560 0.0000 1.8560 1.8560 21.099 1 0.6740 0.0000 0.6740 0.6740 50 4 1.0950 0.5472 0.4100 1.5370 85 12 1.3986 0.2420 0.8320 1.6570 cooling_time: Level N Mean Std Min Max ------------------------------------------------------------ 1.74258 1 1.5430 0.0000 1.5430 1.5430 10 4 1.2463 0.5788 0.4100 1.7100 20 12 1.3563 0.3473 0.6740 1.8560 30 4 1.2877 0.2901 0.8970 1.5370 38.2574 1 1.4940 0.0000 1.4940 1.4940 === Main Effects: dimensional_accuracy === Factor Effect Std Error % Contribution -------------------------------------------------------------- injection_pressure 2.8400 0.2304 43.6% melt_temp 2.8000 0.2304 43.0% cooling_time 0.8775 0.2304 13.5% === ANOVA Table: dimensional_accuracy === Source DF SS MS F p-value ----------------------------------------------------------------------------- melt_temp 4 6.5785 1.6446 2.127 0.1596 injection_pressure 4 6.9055 1.7264 2.232 0.1458 cooling_time 4 2.7909 0.6977 0.902 0.5018 Lack of Fit 2 2.8380 1.4190 1.835 0.2287 Pure Error 7 5.4136 0.7734 Error 9 8.2516 0.7734 Total 21 24.5265 1.1679 === Summary Statistics: dimensional_accuracy === melt_temp: Level N Mean Std Min Max ------------------------------------------------------------ 166.97 1 98.1200 0.0000 98.1200 98.1200 200 4 98.0375 1.3876 96.2400 99.6200 240 12 97.3200 0.9730 95.8500 98.8500 280 4 97.5150 0.7653 96.5800 98.2700 313.03 1 95.3200 0.0000 95.3200 95.3200 injection_pressure: Level N Mean Std Min Max ------------------------------------------------------------ 120 4 98.1775 1.2444 96.5800 99.6200 148.901 1 98.8500 0.0000 98.8500 98.8500 21.099 1 96.0100 0.0000 96.0100 96.0100 50 4 97.3750 0.8458 96.2400 98.0500 85 12 97.2017 0.9922 95.3200 98.1900 cooling_time: Level N Mean Std Min Max ------------------------------------------------------------ 1.74258 1 98.0000 0.0000 98.0000 98.0000 10 4 97.6075 1.5408 96.2400 99.6200 20 12 97.1225 1.1235 95.3200 98.8500 30 4 97.9450 0.4931 97.2200 98.2700 38.2574 1 97.8100 0.0000 97.8100 97.8100 === Main Effects: cycle_time === Factor Effect Std Error % Contribution -------------------------------------------------------------- melt_temp 23.6000 1.9786 52.9% injection_pressure 11.7000 1.9786 26.2% cooling_time 9.3167 1.9786 20.9% === ANOVA Table: cycle_time === Source DF SS MS F p-value ----------------------------------------------------------------------------- melt_temp 4 511.4092 127.8523 3.367 0.0603 injection_pressure 4 356.7192 89.1798 2.348 0.1322 cooling_time 4 324.0417 81.0104 2.133 0.1587 Lack of Fit 2 350.6357 175.3178 4.617 0.0527 Pure Error 7 265.8200 37.9743 Error 9 616.4557 37.9743 Total 21 1808.6259 86.1250 === Summary Statistics: cycle_time === melt_temp: Level N Mean Std Min Max ------------------------------------------------------------ 166.97 1 35.3000 0.0000 35.3000 35.3000 200 4 41.4000 9.4998 33.6000 52.9000 240 12 33.3417 6.1364 20.0000 42.3000 280 4 37.1750 14.2860 18.1000 49.1000 313.03 1 17.8000 0.0000 17.8000 17.8000 injection_pressure: Level N Mean Std Min Max ------------------------------------------------------------ 120 4 38.4250 15.9151 18.1000 52.9000 148.901 1 42.3000 0.0000 42.3000 42.3000 21.099 1 30.6000 0.0000 30.6000 30.6000 50 4 40.1500 7.1389 33.6000 47.1000 85 12 31.6917 7.0010 17.8000 38.9000 cooling_time: Level N Mean Std Min Max ------------------------------------------------------------ 1.74258 1 38.4000 0.0000 38.4000 38.4000 10 4 37.7250 15.1319 18.1000 52.9000 20 12 31.5333 7.2951 17.8000 42.3000 30 4 40.8500 8.4113 33.6000 49.1000 38.2574 1 36.4000 0.0000 36.4000 36.4000 === Main Effects: warpage === Factor Effect Std Error % Contribution -------------------------------------------------------------- melt_temp 0.9278 0.0742 52.7% cooling_time 0.4520 0.0742 25.7% injection_pressure 0.3805 0.0742 21.6% === ANOVA Table: warpage === Source DF SS MS F p-value ----------------------------------------------------------------------------- melt_temp 4 0.9057 0.2264 2.201 0.1497 injection_pressure 4 0.5534 0.1383 1.345 0.3258 cooling_time 4 0.7769 0.1942 1.888 0.1968 Lack of Fit 2 0.0000 0.0000 0.000 1.0000 Pure Error 7 0.7200 0.1029 Error 9 0.3065 0.1029 Total 21 2.5425 0.1211 === Summary Statistics: warpage === melt_temp: Level N Mean Std Min Max ------------------------------------------------------------ 166.97 1 0.7250 0.0000 0.7250 0.7250 200 4 0.5052 0.2187 0.2100 0.6760 240 12 0.8472 0.2821 0.5180 1.5000 280 4 0.6012 0.4539 0.1200 1.1940 313.03 1 1.4330 0.0000 1.4330 1.4330 injection_pressure: Level N Mean Std Min Max ------------------------------------------------------------ 120 4 0.5475 0.4928 0.1200 1.1940 148.901 1 0.8010 0.0000 0.8010 0.8010 21.099 1 0.9280 0.0000 0.9280 0.9280 50 4 0.5590 0.1306 0.4250 0.6760 85 12 0.8829 0.3316 0.5180 1.5000 cooling_time: Level N Mean Std Min Max ------------------------------------------------------------ 1.74258 1 0.5180 0.0000 0.5180 0.5180 10 4 0.6348 0.4170 0.2100 1.1940 20 12 0.9238 0.3073 0.6350 1.5000 30 4 0.4718 0.2616 0.1200 0.6760 38.2574 1 0.7210 0.0000 0.7210 0.7210

=== Optimization: surface_finish === Direction: maximize Best observed run: #18 melt_temp = 200 injection_pressure = 120 cooling_time = 30 Value: 1.856 RSM Model (linear, R² = 0.0307, Adj R² = -0.1308): Coefficients: intercept +1.3386 melt_temp -0.0271 injection_pressure +0.0434 cooling_time -0.0551 RSM Model (quadratic, R² = 0.2831, Adj R² = -0.2546): Coefficients: intercept +1.3282 melt_temp -0.0271 injection_pressure +0.0434 cooling_time -0.0551 melt_temp*injection_pressure -0.2756 melt_temp*cooling_time -0.0226 injection_pressure*cooling_time -0.0181 melt_temp^2 -0.0389 injection_pressure^2 +0.0302 cooling_time^2 +0.0242 Curvature analysis: melt_temp coef=-0.0389 negligible curvature injection_pressure coef=+0.0302 negligible curvature cooling_time coef=+0.0242 negligible curvature Predicted optimum (from linear model, at observed points): melt_temp = 200 injection_pressure = 120 cooling_time = 10 Predicted value: 1.4642 Surface optimum (via L-BFGS-B, linear model): melt_temp = 200 injection_pressure = 120 cooling_time = 10 Predicted value: 1.4642 Model quality: Weak fit — consider adding center points or using a different design. Factor importance: 1. melt_temp (effect: 0.5, contribution: 38.0%) 2. injection_pressure (effect: 0.4, contribution: 34.4%) 3. cooling_time (effect: 0.4, contribution: 27.6%) === Optimization: dimensional_accuracy === Direction: maximize Best observed run: #17 melt_temp = 240 injection_pressure = 148.901 cooling_time = 20 Value: 99.62 RSM Model (linear, R² = 0.0437, Adj R² = -0.1157): Coefficients: intercept +97.4314 melt_temp -0.0559 injection_pressure +0.2598 cooling_time -0.0487 RSM Model (quadratic, R² = 0.4725, Adj R² = 0.0769): Coefficients: intercept +97.2024 melt_temp -0.0559 injection_pressure +0.2598 cooling_time -0.0487 melt_temp*injection_pressure -0.9575 melt_temp*cooling_time +0.1900 injection_pressure*cooling_time +0.4725 melt_temp^2 +0.0005 injection_pressure^2 +0.1880 cooling_time^2 +0.1550 Curvature analysis: injection_pressure coef=+0.1880 convex (has a minimum) cooling_time coef=+0.1550 convex (has a minimum) melt_temp coef=+0.0005 negligible curvature Notable interactions: melt_temp*injection_pressure coef=-0.9575 (antagonistic) injection_pressure*cooling_time coef=+0.4725 (synergistic) Predicted optimum (from quadratic model, at observed points): melt_temp = 200 injection_pressure = 120 cooling_time = 30 Predicted value: 99.0528 Surface optimum (via L-BFGS-B, quadratic model): melt_temp = 200 injection_pressure = 120 cooling_time = 30 Predicted value: 99.0528 Model quality: Weak fit — consider adding center points or using a different design. Factor importance: 1. injection_pressure (effect: 3.0, contribution: 60.6%) 2. melt_temp (effect: 1.1, contribution: 22.9%) 3. cooling_time (effect: 0.8, contribution: 16.5%) === Optimization: cycle_time === Direction: minimize Best observed run: #16 melt_temp = 280 injection_pressure = 120 cooling_time = 10 Value: 17.8 RSM Model (linear, R² = 0.1291, Adj R² = -0.0160): Coefficients: intercept +34.8864 melt_temp +0.0643 injection_pressure +3.9024 cooling_time +0.8303 RSM Model (quadratic, R² = 0.4390, Adj R² = 0.0183): Coefficients: intercept +33.1798 melt_temp +0.0643 injection_pressure +3.9024 cooling_time +0.8303 melt_temp*injection_pressure -4.2625 melt_temp*cooling_time +1.8875 injection_pressure*cooling_time +6.5375 melt_temp^2 +0.3683 injection_pressure^2 +1.0733 cooling_time^2 +1.1183 Curvature analysis: cooling_time coef=+1.1183 convex (has a minimum) injection_pressure coef=+1.0733 convex (has a minimum) melt_temp coef=+0.3683 convex (has a minimum) Notable interactions: injection_pressure*cooling_time coef=+6.5375 (synergistic) melt_temp*injection_pressure coef=-4.2625 (antagonistic) melt_temp*cooling_time coef=+1.8875 (synergistic) Predicted optimum (from quadratic model, at observed points): melt_temp = 200 injection_pressure = 120 cooling_time = 30 Predicted value: 49.3206 Surface optimum (via L-BFGS-B, quadratic model): melt_temp = 200 injection_pressure = 50 cooling_time = 30 Predicted value: 19.9157 Model quality: Weak fit — consider adding center points or using a different design. Factor importance: 1. injection_pressure (effect: 34.8, contribution: 79.8%) 2. cooling_time (effect: 4.7, contribution: 10.7%) 3. melt_temp (effect: 4.2, contribution: 9.6%) === Optimization: warpage === Direction: minimize Best observed run: #21 melt_temp = 280 injection_pressure = 50 cooling_time = 10 Value: 0.12 RSM Model (linear, R² = 0.0236, Adj R² = -0.1391): Coefficients: intercept +0.7614 melt_temp -0.0084 injection_pressure -0.0633 cooling_time -0.0040 RSM Model (quadratic, R² = 0.3091, Adj R² = -0.2091): Coefficients: intercept +0.8792 melt_temp -0.0084 injection_pressure -0.0633 cooling_time -0.0040 melt_temp*injection_pressure +0.1705 melt_temp*cooling_time -0.1032 injection_pressure*cooling_time -0.1690 melt_temp^2 -0.0692 injection_pressure^2 -0.0552 cooling_time^2 -0.0524 Curvature analysis: melt_temp coef=-0.0692 negligible curvature injection_pressure coef=-0.0552 negligible curvature cooling_time coef=-0.0524 negligible curvature Predicted optimum (from linear model, at observed points): melt_temp = 240 injection_pressure = 21.099 cooling_time = 20 Predicted value: 0.8769 Surface optimum (via L-BFGS-B, linear model): melt_temp = 280 injection_pressure = 120 cooling_time = 30 Predicted value: 0.6856 Model quality: Weak fit — consider adding center points or using a different design. Factor importance: 1. injection_pressure (effect: 1.0, contribution: 76.4%) 2. melt_temp (effect: 0.2, contribution: 14.5%) 3. cooling_time (effect: 0.1, contribution: 9.1%)