Dynamic Simulation of Electromagnets. European COMSOL Conference. 5 November 2008
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1 Pesented at the COMSOL Confeence 28 Hannove Dynamic Simulation of Electomagnets Euopean COMSOL Confeence 5 Novembe 28 1 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
2 Contents 1. Electonic bake systems by Continental Automotive Systems ABS ESC 2. COMSOL fo electomagnetic actuatos Magnetic foce Amatue movement by mesh defomation Fast calculation of system dynamics 3. Conclusion 2 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
3 Contents 1. Electonic bake systems by Continental Automotive Systems ABS ESC 2. COMSOL fo electomagnetic actuatos Magnetic foce Amatue movement by mesh defomation Fast calculation of system dynamics 3. Conclusion 3 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
4 Anti-lock bake system (ABS) contol slip between wheel and oad stick fiction > slip fiction maximie foce between wheel and oad maintain lateal guiding foce tagets: vehicle emains stable vehicle can be steeed shote stopping distance in most situations 1 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
5 ABS components 11 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
6 ABS hydaulic layout bake pedal, booste, maste cylinde outlet valve inlet valve wheel bake 12 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
7 ABS active contol constant pessue phase pessue decease phase inlet valve closed outlet valve open 13 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
8 Antilock Bake System ABS µ-split Baking with ABS 14 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
9 Antilock Bake System ABS µ-split Baking without ABS 15 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
10 Electonic Stability Contol ESC Active Yaw Contol 18 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
11 Electonic Stability Contol ESC ABS: Anti-lock Bake System + EBD: Electonic Bake foce Distibution + TCS: Taction Contol System + AYC: Active Yaw Contol = ESC: Electonic Stability Contol 19 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
12 Contents 1. Electonic bake systems by Continental Automotive Systems ABS ESC 2. COMSOL fo electomagnetic actuatos Magnetic foce Amatue movement by mesh defomation Fast calculation of system dynamics 3. Conclusion 2 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
13 Electonic Stability Contol ESC Exploded View MK6 ESC 21 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
14 Electomagnetic inlet valve 22 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
15 Magnetiation of steel magnetic field H = µ 1 µ B magnetic flux density 2 COMSOL > Physics > Subdomain Settings flux density [T] magnetic field [ka/m] COMSOL > Physics > Equation System > Subdomain Settings nomb_qa = sqt( eps + abs(b_qa)^2 + abs(b_qa)^2 ) 23 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
16 Mateials, mesh, solution satuation! foce : 23.1 N 24 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
17 Contents 1. Electonic bake systems by Continental Automotive Systems ABS ESC 2. COMSOL fo electomagnetic actuatos Magnetic foce Amatue movement by mesh defomation Fast calculation of system dynamics 3. Conclusion 25 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
18 Geomety and defomation domain simplified geomety amatue with defomation domain amatue with igid hull yoke coe amatue winding 26 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
19 27 / D. Haald Bille / pinted 21 Octobe 28 Continental AG Idea of ALE ( abitay Lagangian-Euleian ) mesh defomation physical equation fo u(, ) patial diff l equation (PDE) fo U(R,): R R efeence coodinates space coodinates ), ( ), ( R R = = (, ) U u ), ( ), ( def u R U = R u R u R U + = u u U + = chain ule R R = with = R U R U u 1 + = R U R U u 1 solve system of equations inset into PDE fo u
20 Detemine the functions (R, ) and (R, ) 1. pescibed a) physical defomation (e.g. stuctual mechanics) b) explicit fomula ecommended hee (puely axial motion of igid pats) 2. fom bounday conditions a) Laplace smoothing: 2 2 R = b) Winslow smoothing: 2 R = 28 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
21 Explicit defomation () ? / D. Haald Bille / pinted 21 Octobe 28 Continental AG
22 Continuous / diffeentiable defomations () / D. Haald Bille / pinted 21 Octobe 28 Continental AG
23 Continuous / diffeentiable defomations () / D. Haald Bille / pinted 21 Octobe 28 Continental AG
24 Continuous / diffeentiable defomations () / D. Haald Bille / pinted 21 Octobe 28 Continental AG
25 Continuous / diffeentiable defomations () / D. Haald Bille / pinted 21 Octobe 28 Continental AG
26 Continuous / diffeentiable defomations () / D. Haald Bille / pinted 21 Octobe 28 Continental AG
27 Continuous / diffeentiable defomations () / D. Haald Bille / pinted 21 Octobe 28 Continental AG
28 Continuous / diffeentiable defomations () / D. Haald Bille / pinted 21 Octobe 28 Continental AG
29 Continuous / diffeentiable defomations () / D. Haald Bille / pinted 21 Octobe 28 Continental AG
30 Continuous / diffeentiable defomations () / D. Haald Bille / pinted 21 Octobe 28 Continental AG
31 Continuous / diffeentiable defomations () / D. Haald Bille / pinted 21 Octobe 28 Continental AG
32 Continuous / diffeentiable defomations () / D. Haald Bille / pinted 21 Octobe 28 Continental AG
33 Continuous / diffeentiable defomations () 1.25 ecommended hee: linea defomation / D. Haald Bille / pinted 21 Octobe 28 Continental AG
34 Geomety and defomation domain simplified geomety amatue with defomation domain amatue with igid hull yoke coe amatue winding 42 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
35 Voltage step esponse mesh defomation and magnetic field 43 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
36 Voltage step esponse eddy cuents 44 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
37 Voltage step esponse amatue motion solenoid cuent [A] with eddy cuents without eddy cuents magnetic foce [N] eddy cuent powe [W] amatue coe yoke total time [ms] 45 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
38 Voltage step esponse amatue motion gap [mm].5 with eddy cuents without eddy cuents velocity [m / s] time [ms] 46 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
39 Compaison to expeiment 16 Inlet valve - foce vesus gap fo 25 ampee tuns 14 COMSOL test bench 12 foce [N] gap [mm] 47 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
40 Contents 1. Electonic bake systems by Continental Automotive Systems ABS ESC 2. COMSOL fo electomagnetic actuatos Magnetic foce Amatue movement by mesh defomation Fast calculation of system dynamics 3. Conclusion 48 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
41 49 / D. Haald Bille / pinted 21 Octobe 28 Continental AG Static dependence of field on solenoid cuent (up to eddy cuents) coil ext ot S e I n B e v H E ϕ σ σ = + A ot = (neglect eddy cuents fom field change) t A E = J H = ot coil ext ot ot 1 ot S e I n A e v A t A ϕ σ µ µ σ = + ),, ( x v I A A ext = coil ext ) ( S e I n B e v E ϕ σ + + = ext ) ( J B v E + + = σ B H = µ µ
42 Dynamics of solenoid cuent: integal paamete magnetic flux 1 I ext = ( Uext + U R ind ) 1 n = U + ext 2 π R S coil Scoil E d d 1 d n = U ext 2 π A d d R dt S coil S coil Ψ I 1 = U R d Ψ, dt = Ψ(A ext ext ) Ψ = Ψ( A( I, v, x) ) ext 5 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
43 System dynamics I 1 = U R d Ψ, dt Ψ = Ψ ext ext ( I ext, v, x) I ext = I ext COMSOL solves fo I ext ( Ψ, v, x) Ψ( I = Ψ ext ) look-up table / intepolation pesc Ψ [mvs] m/s 2 2 m/s m/s 1-2 m/s -4 m/s I [A] ext d Ψ dt = U ext R I ext ( Ψ, v, x) + amatue equation of motion + simple effective eddy cuent model 51 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
44 Effective eddy cuent model I stat ( Ψ) effective eddy cuent inductance L eddy extenal voltage U ext (t) i eddy effective eddy cuent esistance R eddy solenoid esistance R Ψ' ( t) = U ext ( t) R ( I ( Ψ( t) + ψ (t) ) + i eddy ( t) ) stat L eddy i eddy '( t) = L Ψ'( t) Reddy ieddy( t) eddy 1 ms Reddy τ1 ψ '( t) = τ 2 Ψ'( t) ψ ( t) ( τ 1.2 ms) detemine L eddy, R eddy, τ 1,τ 2 fom least squaes fit to Comsol esult 52 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
45 Geneation of small systems of odinay diffeential equations look-up table y & = f ( u, y) paamete fit u u y 1/s y y f(u, y) Integato educed linea model dynamic system (e.g. Simulink) fast solution field poblem (e.g. COMSOL) paamete vaiation integation into compehensive model 53 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
46 Conclusion simulation in industial development 1. efficiency fewe pototypes bette expeiments 2. poduct pefomance moe vaiants automatic optimiation functional insight obseve new quantities isolate paamete influence 3. obust poducts ceate limit configuations study toleances statistically 54 / D. Haald Bille / pinted 21 Octobe 28 Continental AG
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