A Performance Improvement Strategy for Solenoid Electromagnetic Actuator in Servo Proportional Valve

applied sciences

Article A Performance Improvement Strategy for Solenoid Electromagnetic Actuator in Servo Proportional Valve

Shijie Wang 1, Zhidan Weng 2 and Bo Jin 1,3,*

1 State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hang Zhou 310027, China; [email protected] 2 Ningbo HOYEA Machinery Manufacture Co.Ltd., Ningbo 315131, China; [email protected] 3 Ningbo Research Institute, Zhejiang University, Ningbo 315100, China * Correspondence: [email protected]

Received: 31 May 2020; Accepted: 23 June 2020; Published: 25 June 2020

Abstract: This study presents a simulation model, optimization strategy and the experimental validation of a solenoid electromagnetic actuator that is widely used in industry components, especially in pneumatic/hydraulic valves. In the preliminary design, a two-dimensional magnetostatic finite element analysis (FEA) model is proposed and verified by static push-force comparisons between the two-dimensional FEA model, the three-dimensional FEA model and the experimental results. Then, a static and dynamic performance improvement strategy is proposed. To optimize the static push-force of the actuator, a static multi-objective optimization strategy for actuator structure parameters was developed based on a genetic algorithm. An experimental analysis of dynamic performance was carried out to improve the dynamic response of the actuator. By using a high-precision measuring device in the static-push-force test and dynamic direct current-input-signal tests, the comparisons results between the manufactured conventional actuator and the manufactured optimal actuators showed that the proposed optimization strategy was feasible. Through the static optimization strategy, the average static push-force in the working stroke was improved by 21.8%. Moreover, through the dynamic optimization strategy, the cutoff frequency of the push force response was improved by 129.1%, 79.6% and 74.3%, respectively, at three key positions in the working stroke.

Keywords: servo proportional valve; solenoid electromagnetic actuator; ﬁnite element analysis; multi-objective optimization; genetic algorithm

1. Introduction Nowadays, electromagnetic actuators as force generation components are widely used in vehicle clutch and fuel injection systems, inverter compressors and many other pneumatic/hydraulic valves. Linear proportional solenoids (LPS) is generally employed in proportional control valves (PCV) and servo proportional valves (SPV) due to their simple structure, high reliability, low cost and long stroke. However, diﬀerent from the low performance requirement of PCV, the LPS need a high static push-force and a high frequency force response in SPV. This means the study of electromagnetic actuators is necessary for the improvement of electro–hydraulic control performance. In last decades, many studies for electromagnetic actuators have shown that the static and dynamic performance are closely related to design parameters [1–3]. The optimization methods of electromagnetic actuators include parametric analysis [4–6] and global optimization algorithms [7–10]. Moreover, many researchers have used the parametric methods to optimize the shape of electromagnetic devices in their study [11,12]. For example, Huang, N.B. et al. [13] studied the improvement of solenoid static electromagnetic forces and the reduction of open- and closed-response times of fuel injectors by optimizing the coil cross-sectional shape and the relative position of the coil and the armature. However,

Appl. Sci. 2020, 10, 4352; doi:10.3390/app10124352 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 4352 2 of 19 the obvious disadvantages of parametric analysis methods could be found in previous studies, such as the heavy workload of multi-objective and the limited number of optimization parameters. In addition, it usually obtains a locally optimum result that has a lower performance than the results of global optimization algorithms. Therefore, a global optimization algorithm still needs to be used in the study of electromagnetic actuators. To optimize structure parameters, a numerical calculation model of electromagnetic actuator must first be established. The numerical magnetic field calculation methods of electromagnetic actuator include equivalent magnetic circuit (EMC) method [14] and finite element analysis (FEA) method [15]. Cai, B. et al. [16] studied the influences of five main the shape parameters (thickness of the coil, thickness of the magnetic ring, thickness of plunger sleeve, thickness of upper plunger sleeve and the gap between the plunger and the plunger sleeve) on the magnetostatic force. A magnetostatic force comparison between EMC model, FEA model and the experimental result has shown that the two-dimensional FEA model has a good agreement to measured result with a large amount of computation. However, with the improvement of computer computing power, the calculation time-cost of the two-dimensional FEA model is greatly reduced. Z.-Y. Sun et al. [17] studied the effects of driving current and solenoid valve structure parameters (iron-core length, magnetic pole cross-sectional area, coil turn, coil position, armature thickness, damping hole position, damping hole size and width of the working air–gap) on the static electromagnetic force and the other characteristics by a three-dimensional FEA model in ANSYS MAXWELL software. Since the three-dimensional model will cost a large numerical calculation time in FEA, it is only used to analyze the influence of different parameters and values. Thus, in order to reduce the time cost for parameter optimization, the need of the two-dimensional FEA is obvious. In addition, some other researchers investigated the dynamic response characteristics of electromagnetic actuator by analyzing the influence of mechanical system parameters [18] and power drive system parameters [19]. For example, [20] Lee, S.H. et al. reduced the moving time of solenoid actuator by the natural frequency of mechanical system as optimization goal. However, only validate the optimization result by simulation model, is unsuitable for experimental work [21]. Wu, S. et al. optimized the performances of the response time, size and thermal performance by a theoretical model of solenoid actuator, which employed EMC method. Moreover, it is inaccurate to only consider the static EMC models without dynamic phenomenon, such as the hysteresis and the eddy current in the magnetic materials. Thus, experimental analysis strategy is also essential for the dynamic performance of the LPSs. This study aims to improve the static and dynamic performances of the LPS, which is used in SPV [22]. In order to improve the static performance, a multi-objective optimization strategy is presented in this study. The optimization objectives of the static performance include maximum average push force in the working stroke, minimum standard deviation of the push force in the working stroke and the maximum average push force to moving mass ratio. Since these objectives are mixed with each other, a genetic algorithm (GA) optimization algorithm was used to optimize the shape of the LPS by a high accuracy magnetostatic FEA model. In order to improve the dynamic performance, an experimental analysis of the coil parameters and the LPS component material of was employed in this study. A comparison result between the manufactured conventional actuator and the manufactured optimal actuator could be found through using a high-precision measuring device in the static-push-force test and dynamic direct current-input-signal test. By the static optimization strategy, the average static push-force in the working stroke was improved by 21.8%. Moreover, by the dynamic optimization strategy, the cutoff frequency of the push force response was improved by 74%, 79.6% and 74.3%, respectively, at start, middle and end position in the working stroke. In summary, this study is organized as following chapters: In Section2, the magnetostatic 3D FEA model of the LPS is introduced and developed. Meanwhile, the static-force optimization process of the LPS is also described. Then, in Section3, the dynamic performance improvement strategy of the LPS’s coil parameters and materials is presented and verified by the high precision test device. Finally, Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 21 Appl. Sci. 2020, 10, 4352 3 of 19 Finally, the proposed performance optimization strategy is validated with the test data of the themanufactured proposed performance optimal LPS. optimization The overall strategy descriptio is validatedn of this withperformance the test data optimization of the manufactured strategy is optimalshown in LPS. Figure The 1. overall description of this performance optimization strategy is shown in Figure1.

Figure 1.1. Overall description of this performanceperformance optimization strategy.

2.2. Static Performance Optimization ofof SolenoidSolenoid ElectromagneticElectromagnetic ActuatorActuator

2.1.2.1. Structure and SimulationSimulation ModelModel TheThe structurestructure parametersparameters areare thethe mainmain factorsfactors ofof thethe staticstatic performanceperformance optimization.optimization. InIn orderorder toto simplifysimplify thethe complexitycomplexity ofof optimization,optimization, thisthis studystudy onlyonly optimizesoptimizes thethe parametersparameters ofof thethe corecore componentscomponents suchsuch asas armature,armature, stator,stator, coil,coil, yokeyoke andand non-magneticnon-magnetic ring. ring. Moreover,Moreover, aa seriesseries ofof magnetostaticmagnetostatic modelsmodels areare neededneeded toto describedescribe thethe force versus displacement curve of the LPS static performance. These models are distinguished by different air gap, symbol A in curve of the LPS static performance. These models are distinguished by different air gap, symbol1 A1 Figurein Figure2, between 2, between armature armature and and the stator.the stator. Moreover, Moreover, the air the gap air ofgap each of each model model is expressed is expressed in 0.2-mm in 0.2- intervals.mm intervals. Therefore, Therefore, at least at 14least calculation 14 calculation models models are required are required for entire for entire working working stroke stroke (from 1-mm(from air1-mm gap air to gap 3.6-mm to 3.6-mm air gap). air gap). The The holes holes in the in the armature armature include include shaft shaft hole hole and and the the two two oil oil throughthrough holes.holes. Oil-through-holeOil-through-hole isis usually usually used used to to introduce introduce oil oil and and reduce reduce moving moving mass mass of theof the LPS. LPS. In the In 3Dthe models,3D models, the influencethe influence of these of these two two holes holes is considered is consider ined Figure in Figure3 and 3 and the resultthe result is shown is shown in Figure in Figure4b. Considering4b. Considering the calculationthe calculation time oftime the 3Dof the model 3D andmodel the numberand the ofnumber calculation of calculation models, a simplifiedmodels, a two-dimensionalsimplified two-dimensio (2D) modelnal was(2D) used model for structurewas used parameter for structure optimization. parameter The optimization. description of thisThe cylindricaldescription axisymmetric of this cylindrical 2D model axisymmetric (about axis 2D Z) mode is shownl (about in Figureaxis Z)2 isa. shown Moreover, in Figure the mesh 2a. Moreover, of the 2D FEAthe mesh model of isthe shown 2D FEA in Figure model2 b.is shown in Figure 2b. Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 21 Appl. Sci. 2020, 10, 4352 4 of 19 Appl.Appl. Sci. Sci. 2020 2020, 10,, 10x FOR, x FOR PEER PEER REVIEW REVIEW Z 4 of4 21of 21 a A1 1 a a3 Z f 2 a Z 3 y3 y 4 y4 5 a y6 A1 a 1 a a3 A1 1 a 2 a3 f f3 y 2 a4 4 f3 yy 3 y f6 a4 f 2 3 y4 y 5 y6 f1 5 y4 5 c y6 c 2 f f4 1 f6 y1 4 fy y2 f6 f1 f 5 2 c2 f1 5 c2 c cf1 t y y1 1 2 X 1 t f2 t f2 X X

(a) (a) (a)

(b) (b)( b)

Figure 2. 2. Simplified 2D finite element analysis (FEA) model of linear proportional solenoid (LPS). (a) FigureFigure 2.Simpliﬁed Simplified2. Simplified 2D2D 2D finite ﬁnite finite element element element analysis analysis analysis (FEA) (FEA)(FEA) mo modelmodeldel of linearof of linear linear proportional proportional proportional solenoid solenoid solenoid (LPS). (LPS). (LPS).(a) (a) geometry structure and the design parameters; (b) the mesh of the 2D FEA model. (a)geometry geometrygeometry structure structure structure and and and th theeth designe designdesign parameters; parameters;parameters; (b) ( (thebb)) the themesh mesh mesh of theof of the 2D the 2D FEA 2D FEA FEA model. model. model.

Non-magnetic ring Yoke Non-magneticNon-magnetic ring ring YokeYoke CoilCoilCoil StatorStatorStator ShaftShaftShaft

ArmatureArmatureArmature

FigureFigureFigure 3. 3. Geometry Geometry Geometry3. Geometry structure structure structure definitiondefinition deﬁnition definition of of theof the the LPS. LPS. LPS.

160 160160 140 140140 120 120120 100100 100 80 80 80 60 60 Push Force(N) Push

Push Force(N) Push 60 Measurement result in rated current Push Force(N) Push 40 40 Measurement result in rated current 40 Measurement Three-dimensional result in FEA rated model current result in rated current 20 Three-dimensional FEA model result in rated current 20 Three-dimensional Two-dimensional FEA FEA model model result result in in rated rated currentcurrent 20 Two-dimensional FEA model result in rated current 0 0 Two-dimensional FEA model result in rated current 0 0.20.2 0.6 0.6 1.0 1.0 1.4 1.4 1.8 1.8 2.2 2.2 2.6 2.6 3.0 3.0 3.4 3.4 3.8 3.8 4.2 4.2 0.2 0.6 1.0Displacement 1.4 1.8 in 2.2 working 2.6 stroke(mm) 3.0 3.4 3.8 4.2 Displacement in working stroke(mm) Displacement in working stroke(mm) (a) (a) Figure(a 4.) Cont. Appl. Sci. 2020, 10, 4352 5 of 19

Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 21

Position 1 Position 2

(b)

Position 1 Position 2

(c)

FigureFigure 4. 4.Verification Verification of of simplified simplified 2D2D FEAFEA model:model: ( (aa)) push push force force comparison; comparison; (b ()b flux) flux density density field field resultresult of of the the 3D 3D FEA FEA model; model; ( c()c) flux flux density density fieldfield resultresult of the the 2D 2D FEA FEA model. model.

TheThe definition definition of theof the LPS LPS shape shape parameters parameters are shownare shown in Figure in Figure2a. All 2a. parameters All parameters can be can divided be intodivided four parameter into four arrays.parameter Parameter arrays. Parameter array Parmature array{a1, Parmature a2, a3,{a1, a4} a2, represents a3, a4} represents the design the parameters design ofparameters the armature, of the which armature, includes which the lengthincludes and the radius length of and the radius armature of the and armature the length and of the return length spring of holereturn and spring the thickness hole and of the the thickness spring sleeve. of the spring Parameter sleeve. array ParameterPyoke{y1, array y2, P y3,yoke{y1, y4, y5,y2, y6}y3, y4, includes y5, y6} the designincludes parameters the design of theparameters stator design of the parameter stator design y1, theparameter non-magnetic y1, the ringnon-magnetic design parameters ring design from y2parameters to y5 and thefrom yoke y2 to parameter y5 and the y6—thickness yoke paramete ofr they6—thickness armature sleeve.of the armature Parameter sleeve. array ParameterPcoil{c1, c2} representsarray Pcoil the{c1, length c2} represents and thickness the length of the and coil winding.thickness Otherof the fixedcoil winding. shape parameters Other fixed (radius shape and theparameters length of the(radius 2D model, and the height length of of the the stator 2D model, and the height three thicknessof the stator parameters and the ofthree the thickness bobbin) are parameters of the bobbin) are contained in array Pfixed{f1, f2, f3, f4, f5, f6}. The conventional values of contained in array Pfixed{f1, f2, f3, f4, f5, f6}. The conventional values of the shape design parameters the shape design parameters array are Parmature{31.4 mm, 9.02 mm, 16.9 mm, 4.5 mm}, Pyoke{5.5 mm, 3.7 array are Parmature{31.4 mm, 9.02 mm, 16.9 mm, 4.5 mm}, Pyoke{5.5 mm, 3.7 mm, 3 mm, 3.9 mm, 1 mm, mm, 3 mm, 3.9 mm, 1 mm, 2 mm}, Pcoil{8.2 mm, 41.5 mm} and Pfixed{26.8 mm, 67.5 mm, 23 mm, 1.4 2 mm}, Pcoil{8.2 mm, 41.5 mm} and Pfixed{26.8 mm, 67.5 mm, 23 mm, 1.4 mm, 1.1 mm, 1.2 mm}. mm, 1.1 mm, 1.2 mm}. The theoretical Equations of this simplified 2D model are shown as below. The theoretical Equations of this simplified 2D model are shown as below. The magnetic field strength H is obtained by the Ampere’s law: The magnetic field strength H is obtained by the Ampere’s law:   →iN →H =i N (1) H = c (1) c1 1 Appl. Sci. 2020, 10, 4352 6 of 19

where i represents coil excitation direct current, N is the number of turns of the coil, c1 represents the length of flux path in the cross-sectional area of the yoke. The numerical relationship between H and the magnetic flux density B and the magnetic flux Φ in the cross-sectional area of the yoke are obtained as follows:

→B = µH→ (2)

→ φ = BSe (3) 2 2 Se = π(f1) π(f1 t) (4) − − where µ is the magnetic permeability of the material, Se is the equal cross-sectional area of the yoke in the 2D model and t is the equal thickness of the yoke in the 2D model. Meanwhile, the cross-sectional area Se is equal to the area of the yoke in the 3D model (45-mm width and 50-mm height rectangle with a hole of 21-mm radius). All components of the LPS in the 2D model are cylindrical axisymmetric structures, but the yoke of the LPS in the 3D model is a cube structure. A simplified 2D model is established, which has equal yoke cross-sectional area with the 3D model. From the basic theoretical Equations (1)–(3), it can be obtained that H in the yoke of these two models are equal in the same simulation condition. Moreover, B in the yokes are also equal by the same material parameter µ. Thus, when the cross-sectional area S of the two models are equal, the magnetic flux Φ in the yoke of the two models will equal and the simplified 2D model will be considered suitable. The 2D-magnetostatic field simulator solver computes are derived from Ampere’s law and Maxwell’s differential equation: H→ = →J (5) ∇ × →B = 0 (6) ∇ · →B = →A (7) ∇ × 1 ( →A) = →J (8) ∇ × µ∇ × where J is the current density of the direct current excitation of the coil. A is the magnetic vector potential. To calculate the magnetostatic field result of the 2D model and the 3D model, ANSYS MAXWELL (ANSYS, Inc., Canonsburg, PA, USA, 2019, version: ANSYS Electronics suite 2019R2) software is employed in this study. These simulation model are calculated by a workstation with two CPU (Intel E5-2650v2) and 32 GB DDR3 memory. The 2D FEA model with 3.6-mm air gap (A1) has 45,732 elements and the calculation time cost is 1 min and 30 s and the workstation can calculate 30 tasks at same time. While, the 3D FEA model with 3.6-mm air gap (A1) has 746,669 elements, and the calculation time cost is 31 min and 49 s, and the workstation only calculate one task. Therefore, replacing 3D FEA model with 2D FEA model can reduce the time cost by more than 99.8%. The boundaries of the 2D FEA model is balloon boundary and the boundaries of the 3D FEA model is zero tangential H field boundary. The current density of the coil excitation is 5.56 106 A/m2. This study calculated a × series of FEA model with different air gap (A1), which are distinguished by the interval of the 0.2-mm air gap. The FEA model use the conventional values of each components and pure iron as the soft magnetic material to calculate the static electromagnetic force of the armature. The property of pure iron are shown in Figure5. The absolute values of the static electromagnetic force of the armature are shown in Figure4a. Appl. Sci. 2020, 10, 4352 7 of 19 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 21

2.5

2.0

1.5

1.0 Flux Density(T) Flux

0.5 pure iron

0.0 0 20000 40000 60000 80000 100000 120000 140000 Magnetic Field Strength(A/m) Figure 5. MagneticMagnetic property property of pure iron.

In Figure Figure 44a,a, thethe staticstatic forceforce versusversus displacementdisplacement curvescurves ofof thethe experimentalexperimental result,result, thethe 3D3D modelmodel simulation result and the 2D model simulation result of conventional LPS are illustrated. The push force of the the 2D 2D FEA FEA model model in in Figure Figure 44aa isis the armaturearmature static electromagnetic forceforce alongalong thethe negativenegative direction of the Z coordinate axis in FiguresFigure 2 and 44c.c. Moreover,Moreover, pushpush forceforce ofof thethe 3D 3D FEA FEA model model in in Figure4 4aa is is the the armature armature static static electromagnetic electromagnetic force force along along the the negative negative direction direction of Y of coordinate Y coordinate axis axisin Figure in Figure4b. By4b. the By comparisonthe comparison of theseof these curves, curves, the the 2D 2D model model has has same same accuracy accuracy as as the the 3D 3D model. model. It alsoalso can can be be confirmed confirmed that that both 2Dboth and 2D the and 3D modelthe 3D can model guarantee can equalguarantee accuracy equal on magnetostaticaccuracy on magnetostaticforce calculation. force In Figurecalculation.4b,c, the In fluxFigure density 4b,c, fieldthe flux of the density 3D model field and of the flux3D model density and field the of flux the density2D model field are of illustrated, the 2D model respectively. are illustrated, The air respectively. gap A1 of the The two air modelsgap A1 of are the 3.6 two mm models and the are other 3.6 mmcalculation and the conditions other calculation are the sameconditions as well. are the same as well. By the the comparison comparison of of the the flux flux de densitynsity field field results results at position at position 1, the 1, thecross cross section section of the of 3D the FEA 3D resultFEA result indicates indicates that thatthe circle the circle flux flux density density field field in inPosition Position 1 1is issimilar similar with with the the 2D 2D cylindrical axisymmetric FEA model result. Moreover, Moreover, based on the calculation results in Figure 44a,a, andand thethe fluxflux density field field of Position 2 in Figure4 4b,c,b,c, thethe holesholes inin axialaxial symmetrysymmetry 2D 2D model model are are feasible. feasible. Therefore, the validity of the equal yoke cross- cross-sectionalsectional area simplified simplified method can be indicated inin Figure 44.. The maximum deviation occurs at at the end positi positionon of the working stroke (3-mm position at working stroke). The reason of calculation error ca cann be considered by the saturation phenomenon of the magnetic materials.materials. TheThe maximummaximum 4 4 T T flux flux density densit fieldy field of of the the armature armature at positionat position 2 in 2 Figure in Figure4b,c 4b,ccan explaincan explain why why the numericalthe numerical calculation calculation is not is consistentnot consistent with with the reality. the reality.

2.2. Multi-Objective Multi-Objective Genetic Genetic Algorithm Algorithm Optimi Optimizationzation for Structure Parameters of the LPS LPS isis usedused to to generate generate the the push push force force to SPV,to SPV, its performance its performance directly directly influences influences the valve the control valve controlquality. quality. The static The push-force static push-force magnitude, magnitude, output effi outputciency andefficiency constant and performance constant performance at different airat differentgap are theair gap main are factors the main of the factors LPS. of Thus, the LPS. static Thus, performance static performance optimization optimization design objects designinclude objects includeaverage average push force, push the force, standard the st deviationandard deviation of the push of the force push in theforce working in the working stroke and stroke the averageand the averagepush force push to movingforce to mass moving ratio. mass To solve ratio. this To optimizationsolve this optimization issue, genetic issue, algorithm genetic is employedalgorithm tois employedobtain the to optimal obtain shape the optimal parameters. shape Theparameters. presented The 2D presented model is used2D model to calculate is used the to pushcalculate force the at pusheach 0.2-mmforce at intervaleach 0.2-mm air gap interval in the workingair gap in stroke the working (from 1-mm stroke air (from gap to1-mm 3.6-mm air gap air gap).to 3.6-mm It means air gap).that there It means fourteen that there 2D models fourteen with 2D dimodelsfferent with air gap different A1 in air one gap group A1 in of one the group LPS design of the parameters.LPS design parameters.All these work All arethese accomplished work are accomplished by ANSYS MAXWELLby ANSYS MAXWELL (ANSYS, Inc., (ANSYS, Canonsburg, Inc., Canonsburg, PA, USA, 2019, PA, USA,version: 2019, ANSYS version: Electronics ANSYS Electronics suite 2019R2). suite 2019R2). The following Equation (9) shows the optimization fitnessfitness function:

FAVG Fex FAVG Dex D Kex | Fm | f itness = −−| | + − + K −− AVG (9) F FexF DDex− D exKex (9) fitness =++ex AVG ex m FDex ex K ex Appl. Sci. 2020, 10, 4352 8 of 19 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 21

Equation (9)(9) includesincludes three three normalized normalized objects objects and and each each factor: factor: average average electromagnetic electromagnetic forceforce-FAVG, standard deviation of the absolute value of the static electromagnetic force-D and the average FAVG, standard deviation of the absolute value of the static electromagnetic force-D and the average electromagnetic force to mass ratio of the moving parts in SPV-F /m. In this study, F is calculated electromagnetic force to mass ratio of the moving parts in SPV-FAVGAVG/m. In this study, FAVGAVG is calculated by thethe averageaverage push push forces forces of of each each sampling sampling air gapair ingap the in working the working stroke stroke and the and expectation the expectation average force-F is set as 170 N. It is used to evaluate the excitation force performance in the coil rated current averageex force-Fex is set as 170 N. It is used to evaluate the excitation force performance in the coil rated(direct current current). (direct The LPScurrent). generates The LPS electromagnetic generates electromagnetic force to overcome force the to springovercome force the and spring flow force andof SPV flow and force provides of SPV acceleration and provides for acceleration the spool of for SPV. the The spool maximum of SPV. flow The forcemaximum of SPV flow is 25-N force and of SPVthe maximum is 25-N and spring the maximum force is 50 spring N. The force armature is 50 N. of theThe LPSarmature pushes of the the spool LPS pushes from the the end spool position from the(3.6-mm end position air gap) (3.6-mm to the start air positiongap) to the (1-mm start air posi gap)tion in (1-mm the LPS air working gap) in the stroke. LPS Theworking spring stroke. is used The to springstore energy is used and to thestore push energy the spooland the and push the armaturethe spool backand the to the armature end position back to of the end working position stroke. of Thus, the magnitude of F is the key performance of the LPS for static requirement (overcome flow the working stroke. Thus,AVG the magnitude of FAVG is the key performance of the LPS for static requirementforce) and dynamic (overcome requirement flow force) (large and force dynamic generation). requirement By the consideration (large force ofgeneration). deviation betweenBy the consideration2D simulation resultof deviation and the between measurement 2D simulation result, this result study and chose the 170N measurement as the value result, of FAVG thisto ensurestudy that F is twice as much as the sum of the spring force and flow force. D is used to evaluate the chose AVG170N as the value of FAVG to ensure that FAVG is twice as much as the sum of the spring force and standard deviation of the push force at each sampling position and the expectation standard deviation flow force. D is used to evaluate the standard deviation of the push force at each sampling position of the push force—D —is set as 10 N. It means that the difference between maximum push force and and the expectation exstandard deviation of the push force—Dex—is set as 10 N. It means that the differenceminimum between push force maximum is 65-N inpush the force working and range,minimum at worst push situation.force is 65-N In thein the Equation working (9), range,FAVG /atm worstrepresents situation. the push In the force Equation output e(9),fficiency FAVG/m and represents the expectation the push force force to massoutput ratio—K efficiencyex—is and set the as 1.8expectation N/g. force to mass ratio—Kex—is set as 1.8 N/g. A genetic algorithm—100 population size and 49 generations—was employed to solve this optimization problem and the optimal shape design parameters was obtained. The GA optimization details andand flowflow chart chart were were shown shown in Figure in Figure6. In this6. In study, this westudy, set the we individual set the individual crossover probability crossover probabilityas 0.5 and variable as 0.5 and crossover variable probability crossover asprobability 0.2 and variable as 0.2 and exchange variable probability exchange as probability 0.1 to guarantee as 0.1 tothat guarantee enough new that individuals enough new were individuals produced. Wewere also produced. set the uniform We also mutation set the probability uniform asmutation 0.3 and probabilityindividual mutationas 0.3 and probability individual as mutation 0.2 and variableprobability mutation as 0.2 and probability variable as mutation 0.1 to escape probability local optimal as 0.1 toresult escape by thelocal large optimal mutation result probability. by the large mutation probability.

Start Rolette selection of parents (selection pressure: 4)

Crossover to produce Generate initial children population (Simulated Binary (based on conventional Crossover) values)

Mutation of children Calculate fitness of (Polynomial Mutation) individuals

Calculate fitness of children Satisfy stop criterion End (maximum number of generations :49) Pareto Front (Number of Survivors: 20)

Next generation

Figure 6. TheThe flow ﬂow chart chart of the genetic al algorithmgorithm (GA) optimization steps.

The iteration resultresult isis shownshown inin Figure Figure7 and7 and the the shape shape design design parameter parameter array array can can be deﬁnedbe defined by byPtotal Ptotal{a1,{a1, a2, a2, a3, a3, a4, a4, y1, y1, y2, y2, y3, y3, y4, y4, y5, y5, y6, y6, c1, c1, c2}. c2}. All All values values ofof thethe keykey designdesign parametersparameters are shown in Table 1 1.. Appl. Sci. 2020, 10, 4352 9 of 19 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 21

0.3

0.2

Fitness 0.1

0.0 0 1020304050 Iterations Figure 7. TheThe multi-objective multi-objective GA GA optimization optimization iteration result of the LPS shape parameters.

Table 1. The values and the design ranges of key design parameters and the key characteristics of the design results.

Key Parameter and Key Range of the Design Conventional Electrical Steel Optimal Type LPS Characteristic Parameter (mm) Type LPS Optimal Type LPS length of the armature—a1 25 mm–34.4 mm 31.4 mm 32.3 mm 33.2 mm radius of the armature—a2 correlated to c2 and y6 9.02 mm 9.65 mm 10.15 mm depth of the spring 4 mm–20 mm 16.9 mm 4.7 mm 8 mm hole—a3 thickness of the spring 3 mm–8 mm 4.5 mm 5.2 mm 4.5 mm hole sleeve—a4 thickness of the stator—y1 4 mm–8 mm 5.5 mm 5.5 mm 4.9 mm non-magnetic ring—y2 3.5 mm–3.9 mm 3.7 mm 3.6 mm 3.7 mm non-magnetic ring—y3 1.5 mm–5 mm 3 mm 2.5 mm 3.3 mm non-magnetic ring—y4 3 mm–6 mm 3.9 mm 3.4 mm 3.3 mm non-magnetic ring—y5 1 mm–3 mm 1 mm 2.6 mm 2.2 mm thickness of the armature 1.5 mm–3 mm 2 mm 2.3 mm 1.9 mm sleeve—y6 length of the coil—c1 correlated to c1 8.2 mm 7.7 mm 7.6 mm thickness of the coil—c2 6 mm–8.5 mm 41.5 mm 43.8 mm 44.6 mm moving mass 85.8 g 99.1 g 112.1 g rated average force 123.4 N 149.6 N 131.3 N force response frequency 32.7 Hz 52.8 Hz 57.0 Hz

2.3. Simulation and the Measurement Results All simulation resulted in this study were calculated by ANSYS MAXWELL (ANSYS, Inc., Canonsburg, PA, USA, 2019, version: ANSYS Electronics suite 2019R2). To ensure the accuracy of the measurement results, ZLDS100 (ZSY GROUP LTD) laser displacement sensor and U9C (HBM) force transducer were employed in the performance test device. The structural details of the test device are shown in Figure8a; the experimental setup is shown in Figure8b. For static performance test, a series of the static push-force versus displacement curves are depicted in Figure9. By the comparison of the manufactured optimal LPS and conventional LPS in different coil excitation current, it can be seen that the static performance of the optimal LPS showed a high force generation and a well constant performance in low coil current. When the coil current was rated current (1980 ampere-turn), the numerical calculation error will increase with the influence of the magnetic saturation phenomenon in the soft magnetic material of the LPS. The comparison of the design objectives is shown in Figure 10. The average force shown in Figure 10a was calculated by the measured values in Figure9. The results indicate that the optimal-type LPS can generate more push force than the conventional type. Moreover, the standard deviation of the force versus displacement curves is shown in Figure 10b. In high magnetomotive force condition (1980 and 1587 ampere-turn), the push force of the conventional-type LPS showed a better constant performance. However, in low magnetomotive force condition (1188, 792 and 396 ampere-turn), the optimal-type LPS showed a better constant performance. Moreover, considering the same push force output, the optimal-type LPS was more stable. As shown in Figure 10c, it can be seen that the optimal-type LPS showed a better force output efficiency. Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 21

Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 21 2.3. Simulation and the Measurement Results 2.3. Simulation and the Measurement Results All simulation resulted in this study were calculated by ANSYS MAXWELL (ANSYS, Inc., Canonsburg,All simulation PA, USA, resulted 2019, version: in this ANSYSstudy were Electronics calculated suite by 2019R2). ANSYS ToMAXWELL ensure the (ANSYS, accuracy Inc., of the measurementCanonsburg, results, PA, USA, ZLDS100 2019, version: (ZSY GROUP ANSYS Electronics LTD) laser suite displacement 2019R2). To sensor ensure and the U9C accuracy (HBM) of the force transducermeasurement were results, employed ZLDS100 in the (ZSY performance GROUP LTD) test de laservice. displacement The structural sensor details and of U9C the (HBM)test device force are showntransducer in Figure were 8a; employed the experimental in the performance setup is shown test de invice. Figure The structural8b. For static details performance of the test devicetest, a seriesare of shownthe static in Figurepush-force 8a; the versus experimental displacement setup is curves shown are in Figuredepicted 8b. in For Figure static 9.performance By the comparison test, a series of the manufacturedof the static push-force optimal LPS versus and displacement conventional curves LPS arein different depicted incoil Figure excitation 9. By the current, comparison it can ofbe the seen thatmanufactured the static performance optimal LPS of and the conven optimaltional LPS LPS showed in different a high coil force excitation generation current, and ita canwell be constant seen performancethat the static in performancelow coil current. of the When optimal the LPS coil showed current a washigh ratedforce generationcurrent (1980 and ampere-turn), a well constant the performance in low coil current. When the coil current was rated current (1980 ampere-turn), the numerical calculation error will increase with the influence of the magnetic saturation phenomenon numerical calculation error will increase with the influence of the magnetic saturation phenomenon inAppl. the Sci. soft2020 magnetic, 10, 4352 material of the LPS. 10 of 19 in the soft magnetic material of the LPS.

LPS Controler Interface Interface Shaft Force Sansor Laser Displacement Sensor LPS Controler Shaft Force Sansor Laser Displacement Sensor

PowerPower Supply Supply

BallBall Screw Screw CouplingCoupling MovingMoving Platform Platform StepStep MotorMotor LPSLPS TestTest Device Device I/O I /BoardO Board (a(a) ) (b()b )

FigureFigure 8. 8. SchematicSchematic Schematic of ofof performance performanceperformance test: ( (aa))) testtest test device;device; device; ( b( (bb) )test) test test and and and acquisition acquisition acquisition system. system. system.

200 200 180 180 160 160 140 2D FEA result of Optimal Type LPS in 1980 Ampere-turn 140 2D FEAOptimal result Type of OptimalLPS in 1980 Type Ampere-turn LPS in 1980 Ampere-turn 120 Conventional Optimal Type Type LPS LPS in 1980in 1980 Ampere-turn Ampere-turn 120 100 Conventional Optimal Type Type LPS LPS in 1584 in 1980 Ampere-turn Ampere-turn 100 Conventional Optimal Type Type LPS LPS in 1584in 1584 Ampere-turn Ampere-turn 80 Conventional Optimal Type Type LPS LPS in 1188 in 1584 Ampere-turn Ampere-turn 80Push Force(N) 60 Conventional Optimal Type Type LPS LPS in 1188in 1188 Ampere-turn Ampere-turn Push Force(N) Conventional Optimal Type Type LPS LPS in in792 1188 Ampere-turn Ampere-turn 60 40 Conventional Optimal Type Type LPS LPS in 792in 792 Ampere-turn Ampere-turn 40 20 Conventional Optimal Type Type LPS LPS in 396 in 792Ampere-turn Ampere-turn Conventional Type LPS in 396 Ampere-turn 20 0 Optimal Type LPS in 396 Ampere-turn 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 Conventional Type LPS in 396 Ampere-turn 0 0.4 0.8 1.2Displacement 1.6 2.0 in working 2.4 storke(mm) 2.8 3.2 3.6 4.0 Displacement in working storke(mm) FigureFigure 9. 9.Experimental Experimental testtest resultsresults of the static force force versus versus displacement displacement in indifferent diﬀerent magnetomotive magnetomotive FigureforceAppl.force Sci. condition. 9. condition.2020 Experimental, 10, x FOR PEER test REVIEW results of the static force versus displacement in different magnetomotive12 of 21 force condition. The comparison200 of the design objectives is shown in Figure8 10. The average force shown in Figure 10aThe was comparison calculated by of thethe measureddesign objectives values in is Figure shown 9. in The Figure results 10. indicate The average that the force optimal-type shown in FigureLPS 150 6 10acan was generate calculated more by push the force measured than the values conventional in Figure type. 9. The Moreover, results the indicate standard that deviation the optimal-type of the force LPS canversus generate displacement more100 push curves force isthan shown the conventionalin Figure 10b. type.In high Moreover, 4magnetomotive the standard force condition deviation (1980 of the and force versus1587 ampere-turn),displacement50 thecurves push is force shown of the in conventional-typeFigure 10b. In high LPS2 magnetomotive showed a better force constant condition performance. (1980 and

However, inAverage Force(N) low magnetomotive force condition (1188, 792 and 396 ampere-turn), the optimal-type LPS 1587 ampere-turn),0 the push force of the conventional-type LPS0 showed a better constant performance.

showed a better constant performance. Moreover, consideringStandard Deviation(N) the same push force output, the optimal- However, in low magnetomotive1980 1584 1188 force 792 condition 396 (1188, 792 and 396 ampere-turn), the optimal-type LPS type LPS was more stable. As shown in Figure 10c, it can be seen1980 that the 1584 optimal-type 1188 792 LPS 396 showed a showed a better constantMagnetomotive performance. Force(ampere-turn) Moreover, consideringMagnetomotive the same push Force(ampere-turn) force output, the optimal- better force output efficiency. type LPS was more stable. As shown in Figure 10c, it can be seen that the optimal-type LPS showed a (a) (b) better force output efficiency. 2

1.5 The Conventional Type 1

0.5 The Optimal Type 0 Force to Mass Ratio(N/g) Mass Force to 1980 1584 1188 792 396 Magnetomotive Force(ampere-turn)

(c)

FigureFigure 10. Comparison10. Comparison of of optimization optimization objectivesobjectives values values based based on on measured measured force force in the in working the working stroke:stroke: (a) average (a)average force; force; (b ()b standard)standard deviation of of the the force; force; (c)force (c) force to mass to mass ratio. ratio.

Although the push force constant performance is worse than conventional-type LPS in high magnetomotive force condition, the constant performance of the optimal-type LPS has no disadvantage in large force requirement condition, based on the large force output ability and good constant performance in low magnetomotive force condition. Thus, the presented static performance optimization strategy of the LPS is valuable.

3. Dynamic Performance Improvement of Solenoid Electromagnetic Actuator In previous chapter, we already discussed the static performance improvement strategy of the LPS. The optimization object-force to mass ratio of the strategy has already take the dynamic performance of mechanical system into account. Moreover, the dynamic performance of the LPS coil current subsystem and the push force generation subsystem also make great influence to the mechanical system of the LPS. Therefore, it is necessary to discuss the influence and improvement strategy of these two subsystem. For the dynamic performance improvement strategy of the coil current subsystem, we will analysis and verify the influence of the coil rated current by theoretical method and the experimental method. For the dynamic performance improvement strategy of the push force generation subsystem, we will also analysis and verify the influence of the magnetic materials of the LPS armature by theoretical method and the experimental method.

3.1. The Analysis of the Coil Winding Parameters Obviously, the resistance and the inductance of the coil winding will directly affect the coil current response and finally affect the push force response property. Thus, the analysis of different rated excitation current is employed to improve the dynamic performance of the LPS. The theoretical principle is shown as below. According to the Hopkinson’s formula, the magnetomotive force-F can be described as: Appl. Sci. 2020, 10, 4352 11 of 19

3. Dynamic Performance Improvement of Solenoid Electromagnetic Actuator In previous chapter, we already discussed the static performance improvement strategy of the LPS. The optimization object-force to mass ratio of the strategy has already take the dynamic performance of mechanical system into account. Moreover, the dynamic performance of the LPS coil current subsystem and the push force generation subsystem also make great influence to the mechanical system of the LPS. Therefore, it is necessary to discuss the influence and improvement strategy of these two subsystem. For the dynamic performance improvement strategy of the coil current subsystem, we will analysis and verify the influence of the coil rated current by theoretical method and the experimental method. For the dynamic performance improvement strategy of the push force generation subsystem, we will also analysis and verify the influence of the magnetic materials of the LPS armature by theoretical method and the experimental method.

3.1. The Analysis of the Coil Winding Parameters Obviously, the resistance and the inductance of the coil winding will directly affect the coil current response and finally affect the push force response property. Thus, the analysis of different rated excitation current is employed to improve the dynamic performance of the LPS. The theoretical principle is shown as below. According to the Hopkinson’s formula, the magnetomotive force-F can be described as:

F = φRm (10) where Rm is the magnetic reluctance. The deﬁnition of Rm is expressed as:

δ Rm = (11) µS

Moreover, according to the deﬁnition of the magnetic ﬂux density B and Ampere’s law, F is expressed as: F = Ni (12)

The deﬁnition of the inductance L is expressed as follow:

Nφ L = (13) i Combining the Equations (12) and (13), the inductance of the coil-L can be expressed as:

N2 L = (14) Rm

The simpliﬁed equivalent circuit of the coil drive control system of the LPS is shown in Figure 11: Since the pulse-width modulation (PWM) signal of the controller is assumed to be 100% duty cycle with ignoring the voltage drop of the other components of the controller, the controller can be simpliﬁed as 24 V DC power supply. Thus, it can be clearly obtained from Figure 11 that the LPS drive circuit is a resistor–inductor circuit, and the current response is determined by the Equation:

Lt/R V(1 e− ) i(t) = − (15) R Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 21

= φ F Rm (10)

where Rm is the magnetic reluctance. The definition of Rm is expressed as: δ R = (11) m μS

Moreover, according to the definition of the magnetic flux density B and Ampere’s law, F is Appl. Sci. 2020, 10, 4352 12 of 19 expressed as: F = Ni (12) where i(t) representsThe definition the of time-dependent the inductance L is coil expressed excitation as follow: current, V is the drive voltage of the coil (24 V DC), R represents the resistance of the coil. Since the LPS is a direct current (DC) electromagnetic Nφ actuator with 24 V DC power supply, the drive voltage-VL = is constant. Thus, the current response(13) time i related with R and L. Theoretically, according to the value of V and R, the coil current can rise to the maximum value.Combining But the it isEquation obvious (12) that and the(13), power the inductance consumption of the coil- ofL the cancoil be expressed and the as: controller are too high under maximum current. Thus, a rated powerN loss2 of the coil is limited in this study. The rated L = (14) power loss Prated can be expressed as: R 2m Prated = IratedR (16) The simplified equivalent circuit of the coil drive control system of the LPS is shown in Figure where I11:rated is the rated current of the coil.

R inductance ofcoil

Resistance of coil 24V DC L

FigureFigure 11. 11.Simpliﬁed Simplified equivalentequivalent circuit circuit of the of theLPS LPScoil. coil.

AccordingSince tothe thepulse-width Equations modulation (12),(14)–(16), (PWM) signal the response of the controller time ofis assumed the rated to current-be 100% dutytrated can be describedcycle as with follow ignoring Equation: the voltage drop of the other components of the controller, the controller can be simplified as 24 V DC power supply. Thus, it can be clearly obtained from Figure 11 that the LPS drive circuit is a resistor–inductor circuit, and2 the current response is determined! by the Equation: Frated VIrated trated = ln −Lt/ R (17) RmPratedV(1−VeIrated ) Prated it()= − (15) R trated represents the time cost of the coil current from 0 to Irated. In this study, the rated magnetomotivewhere it()force-F representsrated theis time-dependent 1980 ampere-turn, coil excitation the drive current, voltage V is the of drive the LPS-Vvoltage of is the 24 coil V DC and the power(24 V loss DC), ofR represents the coil-P therated resistanceis 32 W, of the these coil. ratedSince th parameterse LPS is a direct are current constant (DC) electromagnetic in the coil parameter actuator with 24 V DC power supply, the drive voltage-V is constant. Thus, the current response time analysis. Moreover, Rm is correlated with structure parameters of the LPS and it is unchanged with coil related with R and L. Theoretically, according to the value of V and R, the coil current can rise to the winding parameters. Thus, the response time of the rated current-t is only related to coil rated maximum value. But it is obvious that the power consumption of the coilrated and the controller are too current-highIrated under. maximum current. Thus, a rated power loss of the coil is limited in this study. The rated Withpower the loss increasing Prated can be of expressed excessive as: excitation current, the power consumptions of drive components in the controller and the coil winding of the LPS are increased rapidly. For the requirement of actually P = IR2 (16) use, the rated current increased from 3A to 5Arated in this study.rated Correlatively, the turns number of the coil windingwhere is reduced Irated is the from rated 660current to 396of the and coil. the resistance of the coil winding is reduced from 3.5 Ω to 1.3 Ω. The resistanceAccording to of the the Equations coil is measured (12),(14)–(16), by multimeter the response (FLUKE). time of the Thus, rated the current- coppertrated losscan ofbe the LPS and thedescribed rated magnetomotive as follow Equation: force can stay constantly. By the magnetic circuit calculation Equations 6 1 in reference [21], the Rm calculation result of the conventional-type LPS is 2.08145 10 H at end × − position (3.6-mm air gap) of the working stroke. According to the Equation (14), the time constant T of the 3A-coil is 59.8 ms and the time constant T of the 5A-coil is 58 ms. The theoretical correlation between rated current and the rated current step response time is calculated and shown in Figure 12 according Equation (17). The response times in different rated current indicate that the current response performance can be improved effectively by the increasing of the rated current and with the increasing of the rated current, the reduction of the response time is decreasing. The rated current response time of 3A-coil LPS is 34.4 ms and the rated current response time of the 5A-coil LPS is 18.2 ms, it can be seen that 5A is an appropriate rated current. In order to verify this dynamic performance improvement strategy, the shape of the optimal-type LPS was optimized by static optimization strategy and the coil winding was also designed by dynamic performance improvement strategy. The dynamic performance test mainly measured the response of the coil current and the push force at fixed position in the working stroke. The start position (1-mm air gap), middle position (2.3-mm air gap) and end position (3.6-mm air gap) were set as the key Appl. Sci. 2020, 10, x FOR PEER REVIEW 14 of 21

2 Frated VI t = ln rated rated − (17) RImratedPVPrated rated

trated represents the time cost of the coil current from 0 to Irated. In this study, the rated magnetomotive force-Frated is 1980 ampere-turn, the drive voltage of the LPS-V is 24 V DC and the power loss of the coil-Prated is 32 W, these rated parameters are constant in the coil parameter analysis. Moreover, Rm is correlated with structure parameters of the LPS and it is unchanged with coil winding parameters. Thus, the response time of the rated current-trated is only related to coil rated current-Irated. Appl. Sci. 2020With, 10 ,the 4352 increasing of excessive excitation current, the power consumptions of drive 13 of 19 components in the controller and the coil winding of the LPS are increased rapidly. For the requirement of actually use, the rated current increased from 3A to 5A in this study. Correlatively, positionsthe turns of the number working of thestroke. coil winding Moreover, is reduced the from input 660 signal to 396 and of dynamic the resistance test of was the coil rated winding current (direct current),is reduced which from was 3.5 3A Ω andto 1.3 5A Ω. forThe the resistance conventional-type of the coil is measured LPS and by the multimeter optimal-type (FLUKE). LPS, Thus, respectively. Sincethe 50 Hzcopper was loss close of the to theLPS cuto and ffthefrequency rated magnetomot of the optimal-typeive force can stay LPS, constantly. we choose By 50 the Hz magnetic as the frequency circuit calculation Equations in reference [21], the Rm calculation result of the conventional-type LPS of the input signal to clearly verify this improvement strategy. The test resulted of the manufactured is 2.08145 × 106 H−1 at end position (3.6-mm air gap) of the working stroke. According to the Equation conventional-type(14), the time constant LPS and T of thethe 3A-coil manufactured is 59.8 ms optimal-typeand the time constant LPS were T of the shown 5A-coil in is Figure 58 ms. The13. From the comparisontheoretical of correlation the coil current between responserated current in and Figure the rated13a, current it could step be response confirmed time thatis calculated the coil current responseand shown performance in Figure was 12 according improved Equation effectively (17). by the optimized coil winding parameters. With the improvementThe response of the times current in different response rated performance, current indicate the that push the current force response performance performance can could be improvedbe improved immediately. effectively All by thesethe increasing conclusions of the rated could current also beand proved with the from increasing Figure of the13 b,c.rated Moreover, current, the reduction of the response time is decreasing. The rated current response time of 3A-coil the detailsLPS is 34.4 of the ms Bodeand the plot rated of current frequency response response time of arethe 5A-coil shown LPS in Figureis 18.2 ms, 14 .it Therefore,can be seen that the dynamic improvement5A is an appropriate strategy ofrated changing current. coil winding parameters was valuable.

100

Response time of different rated current coil 80

Appl. Sci. 2020, 10, x FOR PEER REVIEW 15 of 21 40

resulted of the manufacturedResponse time(ms) conventional-type LPS and the manufactured optimal-type LPS were shown in Figure 13.20 From the comparison of the coil current response in Figure 13a, it could be confirmed that the coil current response performance was improved effectively by the optimized coil winding parameters.0 With the improvement of the current response performance, the push force response performance 2345678910could be improved immediately. All these conclusions could also be proved from Figure 13b,c. Moreover, the details of theRated Bode current(A) plot of frequency response are shown in Figure 14. Therefore, the dynamic improvement strategy of changing coil winding parameters was valuable. FigureFigure 12. 12.Theoretical Theoretical response response time time of of the the rated rated curre currentnt at end at position end position of the working of the workingstroke. stroke.

In order to verify this dynamic performance improvement strategy, the shape of the optimal- 140 140 type LPS1.0 was optimized by static optimization strategy and1.0 the coil winding was also designed by 120 120 dynamic0.8 performance improvement strategy. The dynamic0.8 performance test mainly measured the response of the coil current and the push force100 at fixed position in the working stroke. The start100 0.6 0.6 position (1-mm air gap), middle position (2.3-mm80 air gap) and end position (3.6-mm air gap) were80

set as the0.4 key positions of the working stroke. More60 over,0.4 the input signal of dynamic test was rated60

current (direct current), which was 3A and 5A for thePush Force(N) conventional-type LPS and the optimal-type 40 40 Push Force(N) 0.2 0.2 LPS, respectively. Since 50 Hz was close to the 20cutoff frequency of the optimal-type LPS, we choose20 Current to Rated Current Ratio 50 Hz 0.0as the frequency of the input signal to clearlyCurrent to Rated Current Ratio verify0.0 this improvement strategy. The test 0 0

-0.2 -20 -0.2 -20 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Time(ms) Time(ms) (a) (b)

1.0 140 120 0.8 100 Coil current input signal 0.6 80 Current-the Conventional Type LPS Current-the Optimal Type LPS 0.4 60

Force(N) Force-the Conventional Type LPS 40 Force-the Optimal Type LPS 0.2 20

Current to Rated Current Ratio Rated Current to Current 0.0 0

-0.2 -20 0 5 10 15 20 25 30 35 40 Time(ms) (c)

FigureFigure 13. The 13. 50-Hz The 50-Hz current current input input signal signal response response comparison comparison of of the the three three types types LPS: LPS: (a(a))start start position of the workingposition of stroke; the working (b) middle stroke; position (b) middle of the position working of the stroke; working (c) endstroke; position (c) end ofposition the working of the stroke. working stroke. Appl. Sci. 2020, 10, 4352 14 of 19 Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 21

0.1 1 10 100 0.1 1 10 100 0 0

-1 -30

-2

-60 -3 -90 -4 Stroke End Position Stroke End Position -5 -120 0 0

-1 -30 -2

-60 -3 Phase/° -90 -4 Stroke Middle Position Stroke Middle Position Amplitude/dB -5 -120 0 0

-1 -30

-2 conventional-typeConventional Type LPS conventional-typeConventional Type LPS

optimal-typeCoil Optimization LPS only -60 optimal-typeCoil Optimization LPS only electrical steel Optimal LPS -3 electricalCoil and Material steel Op Optimazationtimal LPS Coil and Material Optimazation -4 -90 Stroke Start Position Stroke Start Position -5 -120 0.1 1 10 100 0.1 1 10 100 Frequency/Hz Frequency/Hz FigureFigure 14.14. FrequencyFrequency response of of the the push push force force at at fixed ﬁxed air air gap. gap.

3.2.3.2. The The Analysis Analysis of of the the Magnetic Magnetic MaterialsMaterials ExceptExcept the the coil coil winding winding parameters,parameters, the soft magnetic magnetic material material of of the the LPS LPS is isanother another important important factorfactor on on the the static static and and dynamic dynamic performanceperformance of of th thee LPS. LPS. Due Due to to the the high high saturation saturation magnetization, magnetization, purepure iron iron is is usually usually used used in in thethe LPSLPS toto generategenerate largelarge static push-force. push-force. However, However, the the dynamic dynamic performanceperformance of of the the LPS LPS requires requires lowlow remanenceremanence and and low low coercivity coercivity characterizes characterizes of ofsoft soft magnetic magnetic materialmaterial to to generate generate less less power power loss. loss. Thus, Thus, selecting selecting the the appropriate appropriate soft soft magnetic magnetic material material of of each each part ofpart the LPSof the is anLPS improvement is an improvement method method for dynamic for dynamic performance. performance. The theoreticalThe theoretical principle principle is shown is asshown below. as below. AccordingAccording to to the the empiricalempirical BertottiBertotti Equation for for the the core core loss loss calculation, calculation, the the total total power power is is presented as: presented as: P = P=++++ P + P + P (18) totalPPtotalmechanical mechanicalcoreloss P coreloss Pcopperloss copperloss P solidlosssolidloss (18) 2 2 1.5 Pcoreloss = Ph + Pc + Pe = kh f B m + kc( f Bm) + ke( f Bm) (19) 221.5 PPPPkfBkfBkfB=++=Z +() + () (19) coreloss h c e h mJ 2dVol c m e m P = e (20) solidloss σ 2 Vol JdVol P = e (20) solidloss  2σ PcopperlossVol= i R (21) where Ptotal represents the total power consumption, Pmechanical represents the mechanical power, Pcoreloss = 2 represents the power loss generated by timePiR varyingcopperloss magnetic field, Pcopperloss represents the power(21) loss generated by coil of the LPS and Psolidloss represents the resistive loss in the conductor volume of where Ptotal represents the total power consumption, Pmechanical represents the mechanical power, Pcoreloss the LPS [23]. kh, kc and ke represent the coefficients related to hysteresis loss, eddy current loss and represents the power loss generated by time varying magnetic field, Pcopperloss represents the power loss excessive loss, respectively. kh, kc and ke are determined by the measurement of specific magnetic generated by coil of the LPS and Psolidloss represents the resistive loss in the conductor volume of the material. f represents the frequency of the magnetic field, Bm represents the maximum amplitude of LPS [23]. kh, kc and ke represent the coefficients related to hysteresis loss, eddy current loss and Appl. Sci. 2020, 10, 4352 15 of 19

the magnetic flux density. Je represents the eddy current density, σ represents the conductivity of the magnetic materials and Vol represents the volume of the magnetic materials of the LPS. By the coil winding parameters improvement strategy, the Pcopperloss of conventional-type LPS and the optimal-type LPS are equal. Therefore, the mechanical power P is correlated with Appl. Sci. 2020, 10, x FOR PEER REVIEW mechanical 17 of 21 Ptotal, Pcoreloss and Psolidloss. According to the expression of Pcoreloss and Psolidloss, when Ptotal is constant, excessivePmechanical isloss, related respectively. to materials kh, ofkc theand LPS. ke are determined by the measurement of specific magnetic material.Taking f represents the armature the intofrequency account—the of the magnetic only moving field, part Bm represents of the LPS—electrical the maximum steel amplitude is employed of theas the magnetic soft magnetic flux density. materials Je represents of the armature the eddy in current this study. density, The σ electrical represents steel the armature conductivity is made of the by magneticcold-drawn materials non-oriented and Vol silicon represents steel rod, the which volume meet of IECthe 60404-8-6magnetic classmaterials c1 standard. of the LPS. The comparisons of theBy magnetic the coil winding hysteresis parameters loops of pureimprovement iron and electricalstrategy, the steel Pcopperloss are shown of conventional-type in Figure 15 and LPS the and test themagnetic optimal-type fields include LPS are the equal. DC magnetic Therefore, field the and mechanical 20-Hz-, 50-Hz- power and 100-Hz-ACPmechanical is correlated magnetic field.with ItP cantotal, Pbecoreloss seen and that Psolidloss the pure. According iron has to large the maximumexpression relative of Pcoreloss permeability, and Psolidloss,low when remanence Ptotal is constant, and low P coercivitymechanical is relatedin DC magnetic to materials field, of butthe whenLPS. the frequency of the AC magnetic field increased, the electrical steel showsTaking a better the dynamicarmature performance into account—the than pureonly moving iron. As part a specific of the electromagneticLPS—electrical steel actuator is employed used in asSPV, the LPS soft is magnetic required materials both high of dynamic the armature performance in this study. and high The static electrical performance. steel armature Therefore, is made based by cold-drawnon the high dynamicnon-oriented performance silicon requirement,steel rod, which electrical meet steel IEC is more60404-8-6 suitable class as c1 the standard. metrical of The the comparisonsarmature. Moreover, of the magnetic for large hysteres push-forceis loops requirements, of pure iron pure and iron electr isical employed steel are as shown the material in Figure ofthe 15 andother the non-moving test magnetic components. fields include the DC magnetic field and 20-Hz-, 50-Hz- and 100-Hz-AC magneticIn order field. to It verify can be the seen improvement that the pure of electrical iron has steel, large an maximum electrical steelrelative optimal-type permeability, LPS waslow remanenceredesigned and and low the manufactured.coercivity in DC Considering magnetic field, the di butfferences when the ofMagnetic frequency Hysteresis of the AC Loopsmagnetic between field increased,electrical steelthe electrical and pure steel iron, shows the static a better optimization dynamic strategyperformance in present than pure study iron. was As employed a specific to electromagneticredesign the structure actuator of electricalused in SP steelV, LPS optimal-type is required LPS. both Moreover, high dynamic the rated performance current of and electrical high static steel performance.optimal-type LPSTherefore, increased based from on 3the A high to 5 A;dynamic the other performance coil winding requirement, parameters electrical were the steel same is asmore the suitableoptimal-type as the LPS. metrical Thus, of only the the armature. material Moreover of the armature, for large was push-force the variable requirements, between the optimal-typepure iron is employedLPS and the as electricalthe material steel of optimal-type the other non-moving LPS. components.

2.0 2.0

1.5 1.5

1.0 1.0

0.5 0.5

0.0 0.0

-0.5 -0.5

-1.0 DC -1.0 AC20Hz pure iron -1.5 -1.5 pure iron electrical steel electrical steel -2.0 -2.0 -6000 -4000 -2000 0 2000 4000 6000 -6000 -4000 -2000 0 2000 4000 6000 2.0 2.0

1.5 1.5 Flux Density(T) 1.0 1.0

0.5 0.5

0.0 0.0

-0.5 -0.5

-1.0 AC50Hz -1.0 AC100Hz -1.5 pure iron -1.5 pure iron electrical steel electrical steel -2.0 -2.0 -6000 -4000 -2000 0 2000 4000 6000 -6000 -4000 -2000 0 2000 4000 6000 Magnetic Field Strength(A/m) Figure 15. 15. MagneticMagnetic Hysteresis Hysteresis Loops Loops of ofpure pure iron iron and and electrical electrical steel steel in DC-magnetic in DC-magnetic field ﬁeldand AC- and magneticAC-magnetic field ﬁeld of 20 of Hz,50 20 Hz,50 Hz and Hz and100 Hz. 100 Hz.

InThe order test objectsto verify include the improvement the conventional-type of electrical LPS, steel, theoptimized-type an electrical steel LPS optimal-type and the electrical LPS steelwas redesignedoptimal-type and LPS. the The manufactured. amplitude of sine Considering wave input th signale differences was rated of current Magnetic (direct Hysteresis current) andLoops the betweentest frequencies electrical were steel 1 and Hz, pure 20 Hz, iron, 50 Hzthe andstatic 70 optimization Hz. All LPS strategy were tested in present at middle study position was employed (2.3-mm to redesign the structure of electrical steel optimal-type LPS. Moreover, the rated current of electrical steel optimal-type LPS increased from 3 A to 5 A; the other coil winding parameters were the same as the optimal-type LPS. Thus, only the material of the armature was the variable between the optimal-type LPS and the electrical steel optimal-type LPS. The test objects include the conventional-type LPS, the optimized-type LPS and the electrical steel optimal-type LPS. The amplitude of sine wave input signal was rated current (direct current) and the test frequencies were 1 Hz, 20 Hz, 50 Hz and 70 Hz. All LPS were tested at middle position Appl. Sci. 2020, 10, 4352 16 of 19 air gap) of the working stroke. The measured push force response curves are shown in Figure 16. As represented in Figure 16, the electrical steel optimal-type LPS showed a lower amplitude attenuation than other two types LPS. These comparison results indicate that replacing the armature material with electrical steel could also improve the dynamic performance of the LPS. Although the material replacing improvement strategy had great advantage to improve the dynamic performance, it also had a disadvantage of the push force decreasing. But by the contribution of the static performance strategy, the electrical steel optimal-type LPS had same magnitude of the push force at low frequency.

3.3. Dynamic Performance Test The force frequency response magnitude plots and phase plots at the start position (1-mm air gap), the middle position (2.3-mm air gap) and the end position (3.6-mm air gap) of the working Appl.stroke Sci. are2020 illustrated, 10, x FOR PEER inFigure REVIEW 14 . Moreover, the amplitude of the input signal was rated current18 of 21 (direct current). As seen from Figure 14, the cutoﬀ frequency of the magnitude plots is lower than the (2.3-mm air gap) of the working stroke. The measured push force response curves are shown in phase plots. Therefore, it can be concluded that the dynamic performance of the LPS was determined Figure 16. As represented in Figure 16, the electrical steel optimal-type LPS showed a lower by the amplitude–frequency characteristics. From the amplitude plot, both the optimal-type LPS and amplitude attenuation than other two types LPS. These comparison results indicate that replacing the electrical steel optimal-type LPS showed better dynamic performance than the conventional-type the armature material with electrical steel could also improve the dynamic performance of the LPS. LPS. The improvement of the coil parameter optimization strategy and the armature optimization Although the material replacing improvement strategy had great advantage to improve the dynamic strategy could be illustrated by Figure 14. In addition, from Figure 14, it also could be conﬁrmed that performance, it also had a disadvantage of the push force decreasing. But by the contribution of the the amplitude attenuation of the electrical steel optimal-type LPS was less than the optimal-type LPS. static performance strategy, the electrical steel optimal-type LPS had same magnitude of the push Thus, the electrical steel optimal-type LPS was more suitable than the optimized-type LPS for high force at low frequency. dynamic performance requirement situation.

180 1.0 160 1.0 140 150 0.8 0.8 120 120 0.6 100 0.6 90 80 0.4 60 0.4 60 0.2 40 0.2 30

20 Push Force(N)

Push Force(N) Push 0.0 0.0 0 0 Coil current input signal Coil current input signal -0.2 Force-the Conventional Type LPS -20 -0.2 Force-the Conventional Type LPS -30 Current to Rated Ratio Current Current to RatedCurrentRatio Force-the Optimal Type LPS -40 Force-the Optimal Type LPS -0.4 -60 Force-the Electrical Steel Optimal Type LPS -0.4 Force-the Electrical Steel Otpimal Type LPS -60 0 102030405060708090100 0 500 1000 1500 2000 Time(ms) Time(ms) (a) (b) 1.0 140 1.0 140 120 120 0.8 0.8 100 100 0.6 0.6 80 80 0.4 60 0.4 60

0.2 40 0.2 40 Push Force(N) 20 Force(N) Push 20 0.0 0.0 Coil current input signal 0 Coil current input signal 0 -0.2 -0.2 Force-the Conventional Type LPS

Force-the Conventional Type LPS Current to Rated Current Ratio Current to Rated Current Ratio Current Rated to Current -20 -20 Force-the Optimal Type LPS Force-the Optimal Type LPS -0.4 -0.4 Force-the Electrical Steel Optimal Type LPS -40 Force-the Electrical Steel Optimal Type LPS -40

0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Time(ms) Time(ms) (c) (d)

Figure 16. Force–responseForce–response comparison comparison of of the the three three types LPS. LPS. ( (aa)) 1-Hz-current 1-Hz-current input input signal; signal; ( (b)) 20 20 Hz Hz currentcurrent input signal; ( c) 50-Hz-current input signal; (d) 70-Hz-current inputinput signal.signal.

3.3. Dynamic Performance Test The force frequency response magnitude plots and phase plots at the start position (1-mm air gap), the middle position (2.3-mm air gap) and the end position (3.6-mm air gap) of the working stroke are illustrated in Figure 14. Moreover, the amplitude of the input signal was rated current (direct current). As seen from Figure 14, the cutoff frequency of the magnitude plots is lower than the phase plots. Therefore, it can be concluded that the dynamic performance of the LPS was determined by the amplitude–frequency characteristics. From the amplitude plot, both the optimal-type LPS and the electrical steel optimal-type LPS showed better dynamic performance than the conventional-type LPS. The improvement of the coil parameter optimization strategy and the armature optimization strategy could be illustrated by Figure 14. In addition, from Figure 14, it also could be confirmed that the amplitude attenuation of the electrical steel optimal-type LPS was less than the optimal-type LPS. Thus, the electrical steel optimal-type LPS was more suitable than the optimized-type LPS for high dynamic performance requirement situation. Table 2 illustrates the cutoff frequency of the conventional-type LPS, the optimal-type LPS and the electrical steel optimal-type LPS at start, middle and end position in the working range. The Appl. Sci. 2020, 10, 4352 17 of 19

Appl. Sci. 2020, 10, x FOR PEER REVIEW 19 of 21 Table2 illustrates the cuto ff frequency of the conventional-type LPS, the optimal-type LPS optimal-typeand the electrical LPS increased steel optimal-type by 73.4%, LPS 52.2% at start,and 57.5%, middle respectively and end position. Moreover, in the the working electrical range. steel optimalThe optimal-type type increased LPS increased by 129.1%, by 79.6% 73.4%, and 52.2% 74.3%, and 57.5%,respectively. respectively. Moreover, the electrical steel optimal type increased by 129.1%, 79.6% and 74.3%, respectively. Table 2. Cutoff frequency of the three types of the LPS at different position in the working stroke. Table 2. Cutoff frequency of the three types of the LPS at different position in the working stroke. Conventional Optimal Electrical Steel Position Position Conventional Type LPSType Optimal LPS Type LPSType ElectricalLPS SteelOptimal Optimal Type Type LPS LPS start positionstart position 31.6 Hz 31.6 Hz 54.8 Hz 54.8 Hz 72.4 72.4 Hz Hz middle positionmiddle position 34.7 Hz 34.7 Hz 52.8 Hz 52.8 Hz 62.3 62.3 Hz Hz end position 32.7 Hz 51.5 Hz 57.0 Hz end position 32.7 Hz 51.5 Hz 57.0 Hz

In summary, we can clearly obtain a conclusion from Figure 14 and Table2 2 that that increasingincreasing thethe coil rated current strategy and the replacing materialmaterial strategy signiﬁcantlysignificantly improved the dynamic performance of the LPS. These two types types of of the the LPS LPS were were used used in in different diﬀerent requirements requirements of of the the LPS; LPS; which one is more suitable depends on what kind of occasion it is usedused for.for. The optimal-type LPS showed high static push-force generation and the electrical steel optimal-type LPS showed high push-force frequency response. The manufactured LPS is shown in Figure 1717..

Figure 17. TheThe three three types of manufactured LPSs. 4. Conclusions 4. Conclusions This study presented a performance optimization strategy for LPS used in SPV. The strategy This study presented a performance optimization strategy for LPS used in SPV. The strategy mainly includes a multi-objective static performance optimization strategy and a dynamic performance mainly includes a multi-objective static performance optimization strategy and a dynamic experimental improvement strategy. By this optimization strategy, the optimized types of the LPS performance experimental improvement strategy. By this optimization strategy, the optimized types were manufactured and tested. The main conclusions are listed in the following: of the LPS were manufactured and tested. The main conclusions are listed in the following: (1) An equal yoke cross-sectional area simplified method was proposed in this study to reduce (1) An equal yoke cross-sectional area simplified method was proposed in this study to reduce the the time cost of the 3D FEA model of the LPS. The simplified 2D FEA model was verified by time cost of the 3D FEA model of the LPS. The simplified 2D FEA model was verified by the the comparison of the static push-force versus displacement curves. The simulation result and comparison of the static push-force versus displacement curves. The simulation result and the the measurement result indicated that the simplified 2D FEA model showed equal calculation measurement result indicated that the simplified 2D FEA model showed equal calculation accuracy with 3D FEA model and the time cost of the 2D FEA model was reduced more than accuracy with 3D FEA model and the time cost of the 2D FEA model was reduced more than 99.8% 99.8% by comparison with 3D FEA model. by comparison with 3D FEA model. (2) A multi-objective GA static performance optimization strategy was presented in this study to (2) A multi-objective GA static performance optimization strategy was presented in this study to optimize the shape parameters of the LPS. An optimization fitness was proposed to obtain large optimize the shape parameters of the LPS. An optimization fitness was proposed to obtain large push force and guarantee the deviation of the push force in the working stroke and improve the push force and guarantee the deviation of the push force in the working stroke and improve the output efficiency (push force to mass ratio). The global optimization result was obtained and the output efficiency (push force to mass ratio). The global optimization result was obtained and the manufactured. According to the comparison results of the manufactured optimal-type LPS and manufactured. According to the comparison results of the manufactured optimal-type LPS and conventional-type LPS, the push force of the optimal-type LPS was increased by 21.8% in the Appl. Sci. 2020, 10, 4352 18 of 19

conventional-type LPS, the push force of the optimal-type LPS was increased by 21.8% in the rated current (total 1980 Ampere-turn magnetomotive force). Moreover, in low force requirement states, the optimal-type LPS also illustrated a good static performance. (3) A dynamic performance improvement strategy of increasing coil rated current was proposed. To certify the performance inﬂuence of the coil rated current, a theoretical analysis and an experimental test were employed. Both the theoretical results and test results could validate the advantage of increasing rated current. According to the comparison result of the manufactured optimal-type LPS and conventional-type LPS, the force response frequency of the optimal-type LPS were increased by 73.4%, 52.2% and 57.5%, respectively at start, middle and end position in the working stroke. (4) In addition, a dynamic performance improvement strategy of replacing magnetic material of the armature was proposed. To verify the inﬂuence of the magnetic materials, a theoretical analysis and an experimental test were also employed. Both the theoretical analysis and the experimental tests also validated the advantage of electric steel. According to the comparison results of the manufactured electrical steel optimal-type LPS and conventional-type LPS, the force response frequency of the electrical steel optimal type increased by 129.1%, 79.6% and 74.3%, respectively at start, middle and end position in the working stroke.

From what have been discussed above, the improvement of the static optimization strategy and dynamic improvement strategy can be veriﬁed by the test results of the high accuracy device. However, some gaps also can be found in this study. For example, the deviation between simpliﬁed 2D FEA model and the measurement result can be reduced by considering the magnetic saturation phenomenon in the LPS. Moreover, an optimization algorithm and a multi-objective goal, which includes power loss and the current response time could be used to optimize coil winding parameters in further study.

Author Contributions: Conceptualization, S.W.; methodology, S.W.; software, S.W.; validation, S.W. and Z.W.; formal analysis, S.W.; investigation, S.W.; resources, Z.W.; data curation, S.W.; writing—original draft preparation, S.W.; writing—review and editing, S.W. and B.J.; visualization, S.W.; supervision, B.J.; project administration, B.J.; funding acquisition, Z.W. and B.J. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Ningbo Municipal Bureau of Science and Technology, Grant Number 2019B10052. Acknowledgments: The authors would like to thank Ya Hui Guan for her contribution in review work. Conﬂicts of Interest: The authors declare no conﬂicts of interest.

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