Model Order Reduction for Thermo-Elastic Assembly Group Models. SFB/Transregio 96. Dr. Jens Saak representing Project A06 SFB-TR/96

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1 September 19, 2012 Anif (Salzburg) Model Order Reduction for Thermo-Elastic Assembly Group Models Dr. Jens Saak Thermo-Energetische representing Gestaltung Project A06 SFB-TR/96 Chemnitz UT, Department of Mathematics, Mathematics in Industry and Technology : Thermo-energetic design of machine tools 1/19

2 Outline 1 Conflicting goals General approach Participating institutions Research fields and project groups Online / offline machine tool model 2 Challenges Thermo-Energetische 3 Preliminary Results Gestaltung MOR for parametric heat equations Time domain system identification : Thermo-energetic design of machine tools 2/19

3 : Conflicting goals DFG Transregio SFB 96: Thermo-energetic design of machine tools A systemic approach to solve the conflict between power efficiency, accuracy and productivity demonstrated at the example of machining production : Thermo-energetic design of machine tools 3/19

4 : Conflicting goals increase Productivity DFG Transregio SFB 96: Thermo-energetic design of machine tools A systemic approach to solve the conflict between power efficiency, accuracy and productivity demonstrated at the example of machining production : Thermo-energetic design of machine tools 3/19

5 : Conflicting goals increase Productivity increase product Quality DFG Transregio SFB 96: Thermo-energetic design of machine tools A systemic approach to solve the conflict between power efficiency, accuracy and productivity demonstrated at the example of machining production : Thermo-energetic design of machine tools 3/19

6 : Conflicting goals increase Productivity increase product Quality reduce Energy consumption DFG Transregio SFB 96: Thermo-energetic design of machine tools A systemic approach to solve the conflict between power efficiency, accuracy and productivity demonstrated at the example of machining production : Thermo-energetic design of machine tools 3/19

7 : General approach Systematic investigation of the possibilities for minimization of thermally driven manufacturing errors : Thermo-energetic design of machine tools 4/19

8 : General approach Systematic investigation of the possibilities for minimization of thermally driven manufacturing errors Compensation Correction ˆ physical manipulation of the thermoelastic causality chain via Thermo-Energetische machine components Gestaltung ˆ virtual ˆ material/design based Eine systemische ˆ low energy Lösung des Zielkonflikts ˆ model or measurement based computation of input corrections ˆ neutral in energy : Thermo-energetic design of machine tools 4/19

9 :Participating institutions ˆ Dresden TU Dresden (5 institutes) Fraunhofer IWU ˆ Aachen SFB/Transregio RWTH Aachen (4 institutes) 96 Fraunhofer IPT ˆ Chemnitz Thermo-Energetische Chemnitz UT (5+1 institutes) Gestaltung Fraunhofer IWU : Thermo-energetic design of machine tools 5/19

10 : Research fields and project groups A: online/offline machine tool model submodels system integration structure and parameter updates high fidelity and high resolution simulation B: parameters and correction parameter dependence identification of parameters development and evaluation of correction algorithms C: design and evaluation of machines and components development and evaluation of compensation approaches new measurement techniques basis for comparison : Thermo-energetic design of machine tools 6/19

11 : Research fields and project groups A: online/offline machine tool model submodels system integration structure and parameter updates high fidelity and high resolution simulation A06 B: parameters and correction parameter dependence identification of parameters development and evaluation of correction algorithms C: design and evaluation of machines and components development and evaluation of compensation approaches new measurement techniques basis for comparison : Thermo-energetic design of machine tools 6/19

12 : Online / offline machine tool model A01 tool deformation models A02 cutting energy models A03 grinding energy models A04 thermo-fluidic models A05 SFB/Transregio process network 96 model A06 high fidelity SIMULATION CORE Eine systemische simulation Lösung des Zielkonflikts A07 high precision simulation : Thermo-energetic design of machine tools 7/19

13 Challenges ˆ MOR for parametric heat equations Full observation Highly ruffled parameter dependence ˆ MOR for coupled thermo-elastic models Structure exploitation, Physically interpretable ROMs ˆ Interplay of MOR, parameter identification and sensitivity analysis ˆ Time domain system identification Transfer of frequency domain ideas (Loewner approach) Eine systemische Derivation Lösung of parametric des Zielkonflikts models : Thermo-energetic design of machine tools 8/19

14 MOR for parametric heat equations Sliding Carriage Support: ˆ ANSYS FEM model: dofs: n = inputs: m = 1 outputs: p = n ˆ sliding carriage movement input matrix depends on position Thermo-Energetische ˆ vertical position serves asgestaltung parameter : Thermo-energetic design of machine tools 9/19

15 MOR for parametric heat equations Sliding Carriage Support: ˆ ANSYS FEM model: dofs: n = inputs: m = 1 outputs: p = n SFB/Transregio (here: p = 1 ˆ= temperature mean) 96 ˆ sliding carriage movement input matrix depends on position Thermo-Energetische ˆ vertical position serves asgestaltung parameter ˆ here: [Baur/Benner 09] [Benner/Schneider 11] Balanced Truncation Model Order Reduction for LTI Systems with many Inputs or Outputs Eine systemische balanced Lösung truncation des + Zielkonflikts interpolation : Thermo-energetic design of machine tools 9/19

16 MOR for parametric heat equations Computations by N. Lang constant parameter mask Eine systemische absolute error Lösung G(jω, µ) des Ĝ(jω, Zielkonflikts µ) for k = 5 interpolation points. : Thermo-energetic design of machine tools 10/19

17 MOR for parametric heat equations Computations by N. Lang constant parameter mask Eine systemische absolute error Lösung G(jω, µ) des Ĝ(jω, Zielkonflikts µ) for k = 5 interpolation points. : Thermo-energetic design of machine tools 10/19

18 MOR for parametric heat equations Computations by N. Lang exponential parameter mask Eine systemische relative error Lösung G(jω, µ) des Ĝ(jω, Zielkonflikts µ) for k = 5 interpolation points. : Thermo-energetic design of machine tools 10/19

19 MOR for parametric heat equations Computations by N. Lang exponential parameter mask : Thermo-energetic design of machine tools 11/19

20 MOR for parametric heat equations Computations by N. Lang exponential parameter mask : Thermo-energetic design of machine tools 11/19

21 MOR for parametric heat equations balanced truncation + interpolation ˆ has difficulties with oscillations in parameter direction ˆ performs better when FEM discretization fine enough on contact surface (for academic test model) ˆ test with original model still due : Thermo-energetic design of machine tools 12/19

22 MOR for parametric heat equations balanced truncation + interpolation ˆ has difficulties with oscillations in parameter direction ˆ performs better when FEM discretization fine enough on contact surface (for academic test model) ˆ test with original model still due parametric H 2 -MOR ˆ seems to be more robust w.r.t. oscillations ˆ different strategy for model interpolation ˆ PMOR error FEM error for only 5 interpolation point in Eine systemische first tests Lösung des Zielkonflikts : Thermo-energetic design of machine tools 12/19

23 Time domain system identification spindle load dependent correction of tool displacements inputs: ˆ time domain measurement data for x, y, z, displacements ˆ 7 rotation speeds of the spindle ˆ 4 different load values each desired output: ˆ easy to use surrogate model for displacement simulations Thermo-Energetische ˆ preferably real time capable Gestaltung ˆ covering broad range of working conditions data courtesy of SP B06 (RWTH Aachen) : Thermo-energetic design of machine tools 13/19

24 Time domain system identification 20 Inputs u 1 = 1000 rpm, u 2 = 20 bar u 1 /100 u 2 deviation (µm) time (seconds) y 1 y 2 y 3 : Thermo-energetic design of machine tools 14/19 x 10 4

25 Time domain system identification 100 u 1 /100 u 2 deviation (µm) : Thermo-energetic design of machine tools 14/19 Y Z

26 Time domain system identification Perfect playground for Loewner? von Energieeinsatz, Genauigkeit Cooperation und with Produktivität Cosmin Ionita (Rice University) am SFB/Transregio Beispiel der 96: spanenden Thermo-energetic Fertigung design of machine tools 15/19

27 Time domain system identification Unfortunately not! von Energieeinsatz, Genauigkeit Cooperation und with Produktivität Cosmin Ionita (Rice University) am SFB/Transregio Beispiel der 96: spanenden Thermo-energetic Fertigung design of machine tools 15/19

28 Time domain system identification ˆ Loewner acts in frequency domain von Energieeinsatz, Genauigkeit Cooperation und with Produktivität Cosmin Ionita (Rice University) am SFB/Transregio Beispiel der 96: spanenden Thermo-energetic Fertigung design of machine tools 16/19

29 Time domain system identification ˆ Loewner acts in frequency domain ˆ transformation of time domain data required FFT/DFT von Energieeinsatz, Genauigkeit Cooperation und with Produktivität Cosmin Ionita (Rice University) am SFB/Transregio Beispiel der 96: spanenden Thermo-energetic Fertigung design of machine tools 16/19

30 Time domain system identification ˆ Loewner acts in frequency domain ˆ transformation of time domain data required FFT/DFT ˆ observation: Thermo-Energetische adds artificial peaks Gestaltung to the transfer function von Energieeinsatz, Genauigkeit Cooperation und with Produktivität Cosmin Ionita (Rice University) am SFB/Transregio Beispiel der 96: spanenden Thermo-energetic Fertigung design of machine tools 16/19

31 Time domain system identification Fallback: Subspace Identification (all data sets) deviation (µm) SFB/Transregio von Energieeinsatz, Genauigkeit Cooperation und with Produktivität Cosmin Ionita (Rice University) am SFB/Transregio Beispiel der 96: spanenden Thermo-energetic Fertigung design of machine tools 17/19

32 Time domain system identification Fallback: Subspace Identification (zoom on first and last sets (1k and 7k rpm)) deviation (µm) deviation (µm) von Energieeinsatz, Genauigkeit Cooperation und with Produktivität Cosmin Ionita (Rice University) am SFB/Transregio Beispiel der 96: spanenden Thermo-energetic Fertigung design of machine tools 17/19

33 Time domain system identification Fallback: Subspace Identification with additional I/O non-linearities) deviation (µm) deviation (µm) von Energieeinsatz, Genauigkeit Cooperation und with Produktivität Cosmin Ionita (Rice University) am SFB/Transregio Beispiel der 96: spanenden Thermo-energetic Fertigung design of machine tools 17/19

34 Time domain system identification Results ˆ Methods tried: Fourier+Loewner, partial realization, subspace identification (sid), sid+non-linearity ˆ sid performed best ˆ data sets with single rotation speed much better von Energieeinsatz, Genauigkeit Cooperation und with Produktivität Cosmin Ionita (Rice University) am SFB/Transregio Beispiel der 96: spanenden Thermo-energetic Fertigung design of machine tools 18/19

35 Time domain system identification Results ˆ Methods tried: Fourier+Loewner, partial realization, subspace identification (sid), sid+non-linearity ˆ sid performed best ˆ data sets with single rotation speed much better ToDo: parametric method ˆ use switching or interpolating model ˆ exploit better results for single rotation speed von Energieeinsatz, Genauigkeit Cooperation und with Produktivität Cosmin Ionita (Rice University) am SFB/Transregio Beispiel der 96: spanenden Thermo-energetic Fertigung design of machine tools 18/19

36 Questions? Comments? Suggestions? : Thermo-energetic design of machine tools 19/19