双线圈磁流变阀仿真评估及性能分析

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Sep．2013机 床 与 液 压Hydromechatronics Engineering Vo1．41 No．18DOI：10．3969／j．issn．1001-3881．2013．18．003Simulation Evaluation and Performance Analysis ofa Double Coil M agnetorheological ValveHU Guoliang ，YU Lifan，LI Haiyan，HUANG Min，LONG MingSchool of Mechanical&Electronical Engineering，East China Jiaotong University，Nanchang 330013，China1．IntroductionAbstract：In this paper，a double coil magnetorheoIogicaI(MR)valve with outer annular resist-ance gap was developed according to the rheological properties of magnet0rheOIOgical fluids.

Meanwhile．the magnetic circuit of the double coil MR valve was also calculated．The finite ele.

ment modeling and analysis of double coil MR valve were carried out using ANSYS，the efects ofbobbin diameter，active core length and thickness of resistance gap on the magnetic flux densitywere investigated too，and the optimal magnetic field distribution and magnetic flux density of thedouble coil MR valve were achieved．The mathematical model of the pressure drop of the doublecoil MR valve was established，and the influences of the structure parameters of the double coilMR valve on the pressure drop were obtained．The new valve design can improve the eficiencyof double coil MR valve significantly.

Key words：MR valve，double coil，structure design，finite element analysis，pressure dropA hydraulic system is widely used in industrialapplications where large inertia and torque loads haveto be handled．Various types of valves have been a—dopted as the key parts of the hydraulic system．A—mong them，an electro-hydraulic servo valve is fre—quently employed to achieve accurate and fast controlresponses in modern hydraulic control systems，suchas precise position and speed control applications[1]，However，the electro—hydraulic serve valve sys.

tern is complex，expensive and limited in time re-sponse．Therefore，alternative actuating mechanismshave been studied to replace the conventional one.

Recently，one of the efective methods is to usea magnetorheological (MR)fluid which is suspen—sions of microsized particles dispersed in nonmagneticcarrying fluids[2]．Such fluid exhibits unusual char.

Received：2012—12—25Supported by the National Natural Science Foundation ofChina(51165005)HU Guoliang，Doctor，Professor．E—mail：glhu2006### 163．conacteristics in that their rheological properties can becontinuously and reversibly changed within millisec—ends by solely applying or removing a magneticfields．This interesting property has inspired the de—sign of a large variety of MR devices in various engi—neefing applications such as MR valves[3—10]，shock absorbers and dampers[1 1—12]，enginemounts and clutch systems[13—14]，etc.

MR valve is one of the devices generally used tocontrol the speed of hydraulic actuator of MR fluid.

Using MR valve in hydraulic systems accrues manyadvantages，including：no moving parts in valves，e-liminating the complexity and durability issues inconventional mechanical valves，providing a directtransduction from an electrical control signal to achange in mechanical properties[15—17].

In recent years，the researches of MR valves areconcentrated on getting large pressure drop or fast re-sponse by designing a novel structure or optimizing anexisting structure．Such as，Roseraqeld and Wereley[1 8]proposed an analytical optimization designmethod for MR valves and dampers based on the as—sumption of constant magnetic flux density throughoutHydromechatronics Engineeringthe magnetic circuit to ensure that one region of themagnetic circuit does not saturate prematurely andcause a bottleneck effect． Nguyen and Choi『19 —2 1]presented the geometric optimal design of MRvalves constrained in a specifc volume using the fi—nite element method to improve valve performancesuch as pressure drop．Li et a1．[22]optimized thedesign of a high—efficiency MR valve using finite ele—ment analysis． The simulation result indicates thatthe maximum block pressure could be over 1900kPa．Saloom et a1．[23]developed a new type ofMR valve．and the valve coil was outside of the effec.

tive area of the MR fluid． The simulation resultsshowe that the emciency of the MR valve is superiorto that of common MR valve with one coil annular flu.

id flow resistance channels． Salloom 『24．25] alsoproposed a MR proportional directional control valve(4／3 MR valve)。and the experiment was conductedto show the principle work of the valve functionally.

Yoo et a1．『26—28] designed the miniature MRvalve with the maximum performance of the MR effectin fluid mechanics．and he also constructed a hy—draulic actuation system using four MR valves con.

figured as a Wheatstone bridge．Hu et a1．[29—33]designed an energy absorber using a MR bypass valvefilled with ferromagnetic beads．and the experimentalresults show that it can provide high controllabledamping force and a wide force range． Wang et a1.

[34-36]developed a large—scale modular MRF by—pass damper with a two—stage disk type bypass MRvalve，which can provide a pressure drop over 9．0MPa．Wang also compared the response times of theMR valve with the annular flow and radial flow geom.

etries．Wang and Ai[37—38]designed an MR valvewith annular flow and radial flow resistance gaps.

The results show that the radial fluid flow gaps ifl theMR valve can reach a higher eficiency and largercontrolable range than those by annular fluid flowgaps to some extent.

However，the above—mentioned MR valves haveonly one exciting coil．In order to increase the fluidflow blocking force of MR valves．it is usual to in.

crease the volume size and energy consumption of MRvalves．which wil make the miniaturization 0f MRvalves dificult ahhough the optimization of the mag—netic flux and structure may be able to increase theefficiency of MR valves.

In this paper，a double exciting coil was used inthe new designed MR valve，and the finite elementmodeling of the new proposal double coil MR valvewas developed．The main objective of this paper is toevaluate the double coil MR valve using ANSYS，andthe perform ance of the valve is also investigated indetail.

2．Structure and working principle of adouble coil M R valveAs shown in Fig．1．the double coil MR valvewith outer annular resistance gap mainly consists ofvalve body，valve spool and two exciting coils．Theexciting coils wound on the valve spool，and it is leadout through the hole of the end cover．The end coverhas a threaded hole which connects with the pipeioint of the hydraulic circuit．The located blocks areprovided between the spool ends and the end coversas a precision positioning device，and the diversionholes are distributed in the located block．There is atransition fit between the located block and the valvebody．and the located block and the valve spool isconnected by located pin．So the resistance gap be—tween the valve spool and the valve body is uniforil1.

and the intensity of the magnetic field on the MR flu.

id is improved.

1．end cover，2．1ocated block，3．guide pad，4．1ocated pin5．valve spool，6．exciting coil，7．valve bodyFig．1 Schematic of the double coil MR valveI l I① ② ⑧l lController IFig．2 Principle of pressure regulating of the MR valveThe principle of pressure regulating of the doub—le coil MR valve is shown in Fig．2．When the cur—HU Guoliang，et al：Simulation Evaluation and Performance Analysis ofa Double Coil Magnetorheological Valverent Il and，2 was input to the two exciting coils，theclosed loop of the magnetic circuits would be formedamong the valve spool，the valve body and the resist—ance gap，and the magnetic field will be generated inthe three resistance gaps．The intensity of the mag—netic fields can be adjusted by controling the currentl and I2．At the same time，the pressure drop be—tween the resistance gaps can be controlled too.

3．M agnetic circuit of the double coilM R valveWhen the current directions of the two excitingcoils are reverse，the pressure drop is bigger than thepressure drop when the curent directions are thesame and the magnetic circuit of the double col MRvalve is shown in Fig．3．Because the structure of thedouble coll MR valve are distributed symmetrically.

and L3 equals 2Ll，the effects of the two exciting coilsare only considered as one coil．As the iron permea.

bility is higher than the air，the flux leakage can beignored． The magnetic resistances of each segmentare as follows.

1 l l I× >< fi I I>i< >< 4 ll l l l f￡ ￡：Fig．3 Magnetic circuit of the double coil MR valveR ：77r1the magnetic resistance of flank is defined asR2 rthe magnetic resistance of resistance gap isR。= i(1)(2)(3)and the magnetic resistance ot valve body is1 + l 、，r 3 r2 j／Xo
(4)7r L — 十凡where the constant o is the vacuum permeability，and is the permeability of the material of the valvespool and the valve body.

The total magnetic resistance is given byR =2Ro+R1+2R2+R3 (5)According to the Ohm ’s law for magnetic cir-cult，the magnetomotive force is represented asⅣ，=B0S0R (6)where B0 is the magnetic flux density of resistancegap，and S0 is the flux area of resistance gap.

4．Simulation analysisMethod(FEM)using Finite ElementFig．4 shows the axisymmetric two．dimensionalfinite element model of the double coil MR valve。

The maten‘als of the valve spool and valve body areboth 10 stee1．its perm eability is defined by the B．Hcurve of 10 steel；the material of exciting coil is cop-per，its relative perm eability is 1；the resistance gapis fu11 of MR fluid．its perm eability is defined by theB．H curve of MRF一132DG．The value of the currentdensity in two exciting coils is equal，and is set as 8A／mm .

Vavle bodyExciting coilValve spoolResistance gapFig．4 Two—dimensional finite element modelThe electromagnetic simulation result is shownin Fig．5 and Fig．6． From the simulation result，when the curent directions of the two exciting coilsare reverse，the resistance gap is divided into threeeffective parts by magnetic field，and the magneticflux density of three effective parts is approximatelyequa1．If the two exciting coils have the same curentdirection，the magnetic flux density in the middlepart will be zero.

Fig．5 Magnetic flux of the double coil MR valveX a
aneOenang a mne m
g eHydromechatronics Engineering(a)Current oftile sanle direction (b)Current ofreverse directionsFig．6 Magnetic density contour of the double coil MR valveFig．7 and Fig．8 show the magnetic flux densityin different value and direction of the current of twoexciting coils．When the value and direction of cur.

rent are different，the magnetic flux density of middlepart is approximately the average of the both ends，and the magnetic flux density of the side that close tothe high—curent coil is the bigger． If the value ofcurrent is diferent and the direction is same．the dis.

tribution of magnetic flux density in middle part isUneven .

O·8O·7O·60．5喜O_40．30．20．10O 90 80 7O．60 5O 40．30．20．1OO 10 20 30 40 50 60 70s{mm(a)11=o 1A，12=0 3A0 lO 20 3O 4O 50 60 7OslInm(b)』．=O 4A，I2=0 2AFig．7 Magnetic flux density under the reverse directioninput current with different input values In or—der to improve the quality of magnetic circuit of MR valve
． theinfluences of bobbin diameter．active core length and resist—ance gap thickness on magnetic flux density were considered，as shown in Fig．9．Fig．10 and Fig．1】．respectively．Fig．9shows the magnetic flux density of resistance gap in diferentbobbin diameter ．While the bobbin diameter is less than acertain value，the magnetic flux density of the resistance gapincreases with the increase of the bobbin diameter．However
.

when the bobbin diameter is greater than a certain value
． themagnetic flux density is decreased with the increase 0f the bob—bin diameter．The reason is that the magnetic flux density ofthe central axis segment becomes saturated when the bobbindiameter is lesser．and it is the main factor to limit the mag.

netic flux density．While bobbin diameter is greater than acertain value，it becomes the main factors to influence themagnetic flux density due to the reduction of the coil turnscausing magneto motive force to reduce.

0．90．80．70．6G 0 5∞ O 40．3O 20．1O0 10 20 30 40 50 60 70m m Fig．8 Magnetic flux density under the same directioninput current with diferent input values1．6l 2S 0．8∞0．4OO l0 l 5 20，．／m m Fig．9 Magnetic flux density of resistance gapin diferent bobbin diameterFig．1 0 shows the magnetic flux density of theresistance gap in different active core length L1．Themagnetic resistance of the gap becomes larger withthe increase of the active core length．At the sametime，the reduction of the turns of the exciting coilsmakes the magneto motive force decrease，and it willmake the magnetic flux density in resistance gap de．-|lrease .

1．61·2S o．8硷 0 4O4 8 12{／ramFig．10 Magnetic flux density of resistanceactive core lengthl 6gap in diferentHU Guoliang，et al：Simulation Evaluation and Performance Analysis ofa Double Coil Magnetorheological ValveFig．1 1 shows the influence of resistance gapthickness h1 on magnetic flux density． With the in—crease of the thickness of the resistance gap， themagnetic resistance of the gap increases，and themagnetic flux density decreases.

G∞ 1 11．00．90．80 5 l O 1．5 2．0Fig．1 1 Magnetic flux density of resistance gapin different resistance gap thickness5．M odeling and performance analysis ofthe pressure drop of the double coil M Rvalve5．1．Mathematic modelingIn the absence of magnetic field，MR fluid be。

haves like Newtonian fluids．Hence，in the presenceof magnetic，the MR fluid folows Bingham’s plasticof flow，having variable yield strength．In this mod—el，the constitutive relation of MR fluid is：『 = (B)sgn( )+叼 f丁l>l r (B)l【 =0 l丁l

Fig．12(a)depicts the annular fluid flow resist—alice channel between the inner face of the valve bodyand the outer annular face of the valve spool with aradius of R．In general，the annular fluid flow resist—ance channel of the valve containing the MR fluid ismodeled as an approximate flat parallel plate modelcontaining the MR fluid．As shown in Fig．12(b)，the width of the equivalent rectangular duct is 2订 .

and R equals 2+0．5 h；the length L of the equiva—lent rectangular duct equals 2L1+2L2+L3；and thethickness h of the equivalent rectangular duct is thethickness of the annular flow resistance gap.

(a)annular modelfb1 flat parallel plate modelFig．12 Modeling of the MR fluid flow in an annularflow resistance channelAccording to the constitutive equation of MR flu—id，the pressure drop of the valve is calculated by△P =△P +△P (8)where A P and A P are the field-dependent and theviscous pressure drop of the double coils MR valve，respectively.

The viscous pressure drop △P"can be calculat—ed as shown in Fig． 1 3，which depicted the forcecondition of infinitesimal element in resistance gap.

i 州Fig．13 The force condition of infinitesimal elementin resistance gapThe force balance equation of infinitesimal ele—ment ispdy+( +d )dy=(P+(1p)d +rdy (9)The kinematic viscosity of the fluid isdu (10)where“is the fluid velocity.

From Eq．9 and Eq．10，one obtains that the flu—id velocity u satisfiesM ： z+cly+c2 z
Hydromechatronics Engineeringwhere dp／dx is the constant pressure gradient alongthe flow direction，and its value is the same as the△p ／L；。1 and c2 are depended on the boundary con。

ditions．Thus the boundary conditions for the fiat par-alel plate flow region are．9u(0)=M(h)=0 (12)So thatU = y + yThe flow rate is computed asg =rM ：J(h 2wRdy(13)(14)From Eq．13 and Eq．14，one obtains that theviscous pressure drop A P satisfies△p = (15)In the other hand，下田s ‘sA6—6e,rreu6evr isgiven by卸 =2c L1r + cL3 (16)where r l and丁 2 are the yield stresses of the MR flu-id in the end ducts and the middle duct．respective-ly：c is a coefficient which depends on the flow veloc-ity profile and has a value ranging from a minimumvalue of 2．0 to a maximum value of 3．0.

From Eq．8，Eq．15 and Eq．16，the pressuredrop of the valve is expressed as△p= +2c +c L3
丁 (17)While the pressure drop is the biggest，the cur—rent directions of the two exciting coils are reverseand the current values are the maximum allowed val—He．In the condition of above， 1 and丁v2 are approx—imately equal and the pressure drop of the valve canbe deftRed as~rRh
+4c h丁y．t j 。 (18)To evaluate the valve performance，an amplif-ying factor is introduced and defined as the ratio ofthe field—dependent pressure drop to viscous pressuredrop：卢 = PT=In order to improve the amplifying factor ，ac—cording to Eq．19，the value of L1，h and R shouldbe as large as possible．However，with the increaseof the L1，h and R，the magnetic flux density of re—sistance gap decreases，the yield stresses of the MRfluid reduces and the valve performance degrade.

Therefore，the value of L1，h and R should be appro—priate to guarantee the valve performance.

5．2．Simulation resultsThe relationship between the pressure drop andthe flow rate is shown in Fig．14．Th e pressure dropincreases linearly with the increase of the flow ratewhen the resistance gap thickness is 0．5 mm.

4．03 83．63．43 23．OO 1 2 3 4q／(L·min )Fig．14 The pressure drop in different flow rateWhen analyzing the relationship between thepressure drop and the resistance gap thickness，it isassumed that the magnetic flux density of the resist—ance gap does not vary with the change of the resist—ance gap thickness． Fig． 15 shows the relationshipbetween the pressure drop and the resistance gapthickness when the flow rate is 4 L／min．The pres—sure drop decrease with the increase of the resistancegap thickness.

茎司o 5 o．6 o 7 o．8 o 9 1．oh／mmFig．15 The pressure drop in diferent resistancegap thickness． When analyzing the relationship between thepressure droD and the average radius of the resistancegap，it is assumed that the magnetic flux density ofthe resistance gap does not vary with the change ofthe average radius of the resistance gap． Fig． 16shows the relationship between the pressure drop andthe average radius of the resistance gap when the flowrate is 4 L／min，and the resistance gap thickness is0．5 mm．Observing Fig． 1 6，the pressure drop de。

对 ＼5 4 3 2 l 0 HU Guoliang，et al：Simulation Evaluation and Performance Analysis ofa Double Coil Magnetorheological Valve 17creases with the increase of the average radius of theresistance gap.

矗司 ，．／m m Fig．16 The pressure drop in diferent averageradius of the resistance gap6．ConclusionsIn this work，the new proposed double coil MRvalve provided a better performance through the finiteelement analysis and numerical simulations．The re—lationships of the bobbin diameter，active core lengthand thickness of resistance gap on the magnetic fluxdensity were obtained．At the same time．the influ-ences of the structure parameters of the double coilMR valve on the pressure drop were also reached.

The new valve design has improved the eficiency ofdouble coil MR valve significantly.

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摘要：利用磁流变液体的可控特性，设计了一种外侧圆环阻尼间隙双线 圈磁流变阀，同时计算了双线圈磁流变阀的磁路。采用ANSYS有限元仿真软件对双线圈磁流变阀进行 了建模仿真分析 ，比较了绕线筒直径、有效阻尼长度及阻尼间隙对磁场特性的影响，得出了最佳磁力线分布和磁感应强度大小。建立了双线圈磁流变阀的压差数学模型，分析了磁流变阀结构参数对压降特性的影响。相关结论的应用可有效地提高阀的工作效率。

关键词：磁流变阀；双线圈；结构设计；有限元分析；压降中图分类号：TH137．5