Space-mapping optimization applied to the design of a novel electromagnetic actuator for active suspension proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op woensdag 26 november 2008 om 16.00 uur door Laurent¸iu Encic˘a geboren te Boekarest, Roemeni¨e Dit proefschrift is goedgekeurd door de promotoren: prof.dr.ir. J.H. Blom en prof.dr. P.W. Hemker Copromotor: dr. E.A. Lomonova MSc prof.dr.ir. J.H. Blom vervult namens wijlen prof.dr.ir. A.J.A. Vandenput de rol van 1e promotor. This work is part of the IOP-EMVT program (Innovatiegerichte Onderzoekspro- gramma’s - Elektromagnetische Vermogenstechniek). This program is funded by SenterNovem, an agency of the Dutch Ministry of Economic Affairs. Copyright c 2008 by L. Encic˘a Printed by Eindhoven University Press A catalogue record is available from the Eindhoven University of Technology Library ISBN: 978-90-386-1464-9 Aceast˘alucrare este dedicat˘ap˘arint¸ilor mei ... Contents 1 Introduction 1 1.1 Goalofthethesis........................... 2 1.2 Vehicle stability and (semi-)active suspension systems ...... 2 1.2.1 Rollcontrol.......................... 3 1.2.2 Vibrationcontrol.. .. .. .. .. .. .. .. .. .. 5 1.2.3 Commercialsolutions . 7 1.3 Electromagneticactivesuspension . 10 1.3.1 Linearactuators .. .. .. .. .. .. .. .. .. .. 10 1.3.2 Proposedtopologies . 11 1.4 Designapproach: space-mapping . 12 1.5 Thesisobjectivesandorganization . 14 2 Design requirements for an electromagnetic active suspension 17 2.1 Quarter-carmechanicalmodel ofa vehicle . 17 2.2 Calculation of the cornering force and the anti-roll force envelope 23 2.3 Referencemeasurements . 30 2.3.1 Strutgeometry ........................ 32 2.3.2 Elasticproperties. 36 2.3.3 Dampercharacterization. 38 2.4 Designassumptions. .. .. .. .. .. .. .. .. .. .. .. 40 2.5 Designrequirements .. .. .. .. .. .. .. .. .. .. .. 41 2.6 Conclusionsandremarks. 42 3 Space-mapping optimization 45 3.1 Introduction.............................. 45 3.2 Optimization: short theoretical overview . ... 45 3.2.1 Problemstatement. 46 3.2.2 Solutionexistence . 46 3.2.3 Feasible region, feasible solution, optimal solution .... 47 v vi CONTENTS 3.2.4 Necessary and sufficient optimality conditions . 48 3.2.5 The Karush-Kuhn-Tucker optimality conditions . 50 3.2.6 Approaches for solving constrained optimization problems 51 3.2.7 Trust-region.......................... 53 3.3 Mainconceptofspace-mapping . 55 3.3.1 Inputmapping ........................ 56 3.3.2 Outputmapping ....................... 59 3.3.3 Parameterextraction. 61 3.4 SMandconstrainedoptimization . 62 3.5 ReviewofSMalgorithms . 64 3.5.1 OriginalSM.......................... 64 3.5.2 AggressiveSM ........................ 65 3.5.3 TrustregionASM ...................... 65 3.5.4 HybridASM ......................... 66 3.5.5 Surrogatemodel-basedSM . 67 3.5.6 ImplicitSM.......................... 67 3.5.7 OutputSMinterpolatingsurrogate . 68 3.5.8 Manifold-mapping . 68 3.6 ConvergenceofSMalgorithms . 69 3.7 Anewalgorithm: aggressiveoutputSM . 70 3.8 Numericalexamples .. .. .. .. .. .. .. .. .. .. .. 71 3.9 SM-baseddesignflow.. .. .. .. .. .. .. .. .. .. .. 72 3.10 Conclusionsandremarks. 76 4 Case I: Tubular linear actuator for active suspension 77 4.1 Introduction.............................. 77 4.2 Preliminarydesignconsiderations . 80 4.3 AOSM size optimization of the tubular actuator . 89 4.3.1 Design specifications and problem formulation . 89 4.3.2 Coarseandfinemodels . 92 4.3.3 Comparisonofobtainedresults . 95 4.4 Solutionpost-processing . 103 4.4.1 Forceresponse . .. .. .. .. .. .. .. .. .. .. 103 4.4.2 Translatorskewing . 111 4.4.3 Temperatureriseanddistribution . 117 4.5 Conclusionsandremarks. 121 5 Case II: Novel electromagnetic spring for active suspension 123 5.1 Introduction.............................. 123 CONTENTS vii 5.1.1 A pre-prototype: the α-ELMASP. 125 5.2 Design requirements: the output force envelope . 126 5.3 AOSM size optimization of the α-ELMASP . 128 5.3.1 Design specifications and problem formulation . 128 5.3.2 Coarseandfinemodels . 130 5.3.3 Results ............................ 132 5.4 NovelELMASPtopology . 132 5.5 Passive design: AOSM shape-optimization . 134 5.5.1 Design specifications and problem statement . 136 5.5.2 Coarseandfinemodels . 138 5.5.3 Results ............................ 139 5.5.4 Experimental setup and measurements . 148 5.5.5 Passiveeddy-currentdamping. 155 5.6 Activedesign ............................. 156 5.6.1 Novel design of commutated coils for active ELMASP re- sponse............................. 158 5.6.2 Demagnetizationverification . 162 5.7 Conclusionsandremarks. 162 6 Conclusions and recommendations 167 6.1 Space-mappingoptimization. 168 6.2 The tubular linear actuator solution . 169 6.3 Thenovelelectromagneticspring . 169 6.4 Thesiscontributions . 170 6.5 Recommendationsforfutureresearch. 171 6.5.1 Space-mappingandcoarsemodels . 171 6.5.2 Redesign ofthe electromagneticspring . 172 6.5.3 Thefutureelectriccar . 172 A List of symbols and abbreviations 173 A.1 Symbols ................................ 173 A.2 Abbreviations............................. 177 B Magnetic equivalent circuit models 179 B.1 MECmodelfromSection4.2 . 179 B.2 MECmodelfromSection4.3.2 . 180 B.3 MECmodelfromSection5.3.2 . 182 C NdFeB properties 185 viii CONTENTS Bibliography 195 Summary 197 Acknowledgments 199 Curriculum Vitae 201 1 Introduction A major consideration for the automotive industry is to provide passenger safety, through optimal road holding, and comfort, for a large variety of road conditions and vehicle manoeuvres. The passenger comfort and safety can be improved by providing an optimal road contact for the tires while minimizing the roll and heave of the vehicle body. The system responsible for this actions is the vehi- cle suspension, i.e., a complex system incorporating various arms, springs and dampers that separate the vehicle body, i.e., the sprung mass, from the tires and axles, i.e., the unsprung mass. Due their low cost and simple construction, many vehicles are equipped with fully passive suspension systems, incorporat- ing springs, dampers and anti-roll bars with fixed characteristics. Noting that optimal handling and passenger comfort are conflicting objectives, these pas- sive systems can only obtain a compromise between safety and comfort. How- ever, this compromise has been significantly reduced with the introduction of (semi-)active suspension systems. These systems incorporate adjustable ele- ments which provide spring stiffness and damping coefficients adaptable to the road conditions. The majority of the (semi-)active systems are pneumatic or hydraulic solutions which suffer from low efficiencies and response bandwidths, however they are characterized by high force and power densities. Commercial systems incorporating electromagnetic elements exploit the properties of the 1 2 Chapter 1. Introduction magneto-rheological fluids in damper technology or combine rotary actuators and mechanical elements in order to provide an adjustable spring stiffness. How- ever, given their form factor, high force densities and response bandwidth, linear electromagnetic actuators appear as a beneficial solution for a (semi-)active sus- pension system. Even though no commercial solutions are existing at this date, (semi-)active suspension systems with linear actuators have been proposed and demonstrated [1, 2]. Nevertheless, the same concept has been exploited, i.e., a suspension strut composed of a mechanical spring connected in parallel with a linear actuator. 1.1 Goal of the thesis An actuator topology that can provide both a zero-power spring character- istic and actuation forces necessary for vibration damping and vehicle body-roll control in a fully electromagnetic active suspension has not been investigated in the literature up to this moment. Therefore, this thesis introduces a novel topol- ogy of electromagnetic actuator aimed at replacing both spring and damper in a suspension strut. Furthermore, a design solution is obtained by means of a multi-level optimization approach, i.e., space-mapping, employing a new algo- rithm variant which is also derived in this thesis. The objectives of the thesis are further detailed in Section 1.5. The following sections present several essential aspects regarding the vehi- cle stability and suspension systems, the proposed novel solution and design approach. 1.2 Vehicle stability and (semi-)active suspension systems Typical vehicle behavior is pitching during braking and acceleration, and rolling in corners. Additionally, road irregularities cause vibrations in the vehi- cle and twisting forces. The body-roll during cornering is a demanding aspect of the vehicle attitude variation, which, apart from the reduced comfort, impairs the stability of the vehicle. The first impediment to passenger comfort is mo- tion sickness, which is a common by-product of exposure to optical depictions of inertial motion, especially when reading [3]. This phenomenon, called visually induced motion sickness (VIMS), has also been reported in a variety of vir- tual environments, such as fixed-base flight and automobile simulation [4]. The essential characteristics of stimuli that induce motion sickness is that they gen- 1.2. Vehicle stability and (semi-)active suspension systems 3 erate discordant information from the sensory systems that provide the brain with