Presented at the COMSOL Conference 2010 Paris

Transcription

1 Presented at the COMSOL Conference 2010 Paris Fakultät Elektrotechnik und Informationstechnik Institut für Feinwerktechnik und Elektronik-Design Prof. Dr.-Ing. habil. Jens Lienig Robust and Reliability-Based Design Optimization of Electromagnetic Actuators Using Heterogeneous Modeling with COMSOL Multiphysics and Dynamic Network Models *,1, A. Kamusella 1 and Th.-Qu. Pham 2 1 Technische Universität Dresden, Institute of Electromechanical and Electronic Design, Germany, 2 OptiY e. K. Aschaffenburg, Germany * Corresponding author: D Dresden, Germany, holger.neubert@tu-dresden.de

2 Robust and Reliability-Based Design Optimization of Electromagnetic Actuators Using Heterogeneous Modeling with COMSOL Multiphysics and Dynamic Network Models Outline 1. Introduction 2. Electromagnetic Actuator Model 3. Optimization of the Actuator 4. Robustness Analysis and Optimization 5. Conclusions 2/31

3 1 Introduction Electromagnetic Actuators Fast actuation, medium forces and medium strokes compaired to other actuation principles High energy density, low cost Design varies in a very wide range Source: Magnet Schultz Ltd. Source: Deutsche Fotothek 3/31

4 Electromagnetic Actuators Minimum of elements: armature, yoke with a back iron, working air gap, parasitic guiding air gap and coil Bi-directional cause-effect relations between electric and magnetic field back iron coil return spring yoke working air gap armature guiding air gap 4/31

5 Braille Printer Needle which embosses the paper Paper as a nonlinear elasto-plastic counterforce load Dynamic forces of the masses Nonlinear magnetic material behavior needle paper sheet die yoke working air gap back iron coil return spring armature guiding air gap 5/31

6 Braille Printer Needle which embosses the paper Paper as a nonlinear elasto-plastic counterforce load Dynamic forces of the masses Nonlinear magnetic material behavior 6/31

7 Robust and Reliability-Based Design Optimization of Electromagnetic Actuators Using Heterogeneous Modeling with COMSOL Multiphysics and Dynamic Network Models 1. Introduction 2. Electromagnetic Actuator Model Static Magnetic Model Heterogeneous Dynamic Model 3. Optimization of the Actuator 4. Robustness Analysis and Optimization 5. Conclusions 7/31

8 2 Electromagnetic Actuator Model Static Magnetic Model FEA Model COMSOL Multiphysics 3.5a emqa application mode, axial symmetry Currents in the angular direction only MATLAB scripts Input design parameters and results handled with ASCII-files Non-linear ferromagnetic material in the form µ rel (B) Free meshing with normal mesh size 5,000 to 10,000 DoF, UMFPACK direct solver armature guiding air gap back iron surrounding air coil working air gap yoke 8/31

9 Static Magnetic Model Magnetic Material Non-linear ferromagnetic material in the form µ rel (B) as a look-up table stored in an ASCII file 3,6 2,7 B [T] 1,8 0,9 St3 0, H [A/m] 9/31

10 Static Magnetic Model Governing Equations Static behavior by Maxwell s equation using the magnetic vector potential A; j ext - external current density, σ conductivity, µ - permeability 1 A = j µ Magnetic force F on the armature by integration of the Maxwell s surface stress-tensor on an arbitrary surface S surrounding the armature ext 1 1 F = n S µ 0 2µ 0 2 ( B n) B B ds Flux linkage Ψ which is necessary to compute the dynamic behavior of the actuator-load system by the dynamic model Ψ = A Ψ B da Ψ 10/31

11 Static Magnetic Model Results 11/31

12 Static Magnetic Model Results Look-up tables F(x, i), Ψ(x, i) F(x, i) Ψ (x, i) i x i x 12/31

13 2 Electromagnetic Actuator Model Heterogeneous Dynamic Model Governing Equations ODE for the mechanical dynamics along the coordinate x; m moved mass of the needle and the armature, F load summarized reaction force of the paper and the return spring m&& x = F ( i x) F ( x) mag x load, x,, Kirchhoff s voltage law; u - terminal voltage, ir - Ohmic voltage drop, dψ/dt - induced back-emf (electromotive force) ( i x) u = i R + Ψ&, x 13/31

14 Heterogeneous Dynamic Model Network Generalized Kirchhoffian network model in SimulationX Involving look-up tables F(x, i), Ψ (x, i) from the static model Dynamic behavior F(t), x(t) Eddy currents and hysteresis are neglected Embossing sufficient or not (0...1), cycle time t cycle (to be minimized) u A i R + i -1 x Ψ(i,x) d/dt i x F(i,x) paper x m return spring bedstop 14/31

15 Heterogeneous Dynamic Model Simulation results Embossing sufficient or not x needle-max = mm Cycle time t cycle to be minimized 1.2 mm 15 V 25 A 50 N 0 mm 0 V 0 A 0 N -0.8 mm x needle Supply Coil voltage curr. Magn. force 0 ms 4 ms 15/31

16 Heterogeneous Dynamic Model SimulationX /31

17 Robust and Reliability-Based Design Optimization of Electromagnetic Actuators Using Heterogeneous Modeling with COMSOL Multiphysics and Dynamic Network Models 1. Introduction 2. Electromagnetic Actuator Model 3. Optimization of the Actuator Nominal Optimization Using the Static Magnetic Model Nominal Optimization Using the Heterogeneous Dynamic Model 4. Robustness Analysis and Optimization 5. Conclusions 17/31

18 3 Optimization of the Actuator Nominal Optimization Using the Static Magnetic Model 18/31

19 Nominal Optimization Using the Static Magnetic Model Constraints: magnetic force at maximum stroke F(x max ), power losses Objective: minimum overall volume Gradient-based optimization algorithm, 7 design variables 19/31

20 Nominal Optimization Using the Static Magnetic Model Preliminary design (a), optimized design (b) 20/31

21 Nominal Optimization Using the Heterogeneous Dynamic Model 21/31

22 Nominal Optimization Using the Heterogeneous Dynamic Model Slim preliminary design Compact design after static optimization x needle x needle Supply voltage Coil curr. Supply voltage Coil curr. Magn. force Magn. force 0 ms 4 ms Cycle time 0 ms 4 ms Cycle time 22/31

23 Nominal Optimization Using the Heterogeneous Dynamic Model Minimum cycle time 2,6 ms 0.6 mm 15 V 25 A 50 N 0 mm 0 V 0 A 0 N -0.8 mm x needle Supply Coil voltage curr. Magn. force 0 ms 3 ms Cycle time 23/31

24 Robust and Reliability-Based Design Optimization of Electromagnetic Actuators Using Heterogeneous Modeling with COMSOL Multiphysics and Dynamic Network Models 1. Introduction 2. Electromagnetic Actuator Model 3. Optimization of the Actuator 4. Robustness Analysis and Optimization Probabilistic Analysis Robust Design Optimization 5. Conclusions 24/31

25 4 Robustness Analysis and Optimization Principle of Robustness Analysis 25/31

26 Robustness Analysis of the Braille Printer d mag x 0needle Supply voltage d arm d mag d arm Supply voltage x 0needle 26/31

27 Probabilistic Analysis Latin-Hypercube sampling (LHS) around the nominal optimum with 200 samples Density functions of the system functionality (a) and of the cycle time (b) Failure probability of about 80 % at the nominal optimum (a) (b) 27/31

28 Probabilistic Analysis Sensitivity analysis System functionality d arm d mag x 0needle Supply voltage 28/31

29 Robust Design Optimization Find a design of higher reliability Optimiziation using response surfaces instead of the system model LHS with a large sample size (100,000) (a) (b) 29/31

30 5 Conclusions Design optimization was performed based on a heterogeneous dynamic model. This model consists of a dynamic network model that includes look-up tables computed from a static FEA model. The look-up tables were computed in each iteration step of the optimization according to the change in the design. Starting from a preliminary design we obtained an optimum design for a defined set of requirements. The failure probability of this design was significantly improved by a robustness analysis and optimization. The final design meets requirements regarding functionality as well as reliability. OptiY 4.0, SimulationX 3.3, COMSOL Multiphysics 3.5a Quad-core PC running Windows The presented methodology can be applied to many similar design optimization processes. 30/31

31 Robust and Reliability-Based Design Optimization of Electromagnetic Actuators Using Heterogeneous Modeling with COMSOL Multiphysics and Dynamic Network Models Thank you for your attention. 31/31