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4th International Conference on Electrical and Computer EngineeringICECE 2006, 19-21 December 2006, Dhaka, Bangladesh

OPTIMAL DESIGN OF VOICE COIL MOTOR FORAPPLICATIONIN ACTIVE VIBRATION ISOLATION

Rahul Banik, Dong-Yeon Lee and Dae-Gab Gweon

NOM Lab, Dept. of Mech. Engg., KAIST373-1 Guseong dong, Yuseong-gu, Daejeon 305-701, South Korea

E-mail: rahulbanikgkaist.ac.kr

ABSTRACTVibration isolators typically reduce the vibrationtransmitted to the nano-precision measuringinstrument providing managed stiffness anddamping. Active isolators use feedback to provide thenecessary control signal. In this paper we propose anoptimized design of a Voice coil motor that can beused to implement a suitable controller for activeisolation to attenuate the low frequency vibration.

1. INTRODUCTIONPrecision measuring instruments such as AtomicForce Microscopes with resolution in nano-meterrange are always affected by ground borne vibrationsthat have typical amplitude in sub micrometer region.A vibration isolation system reduces the effect ofsuch disturbance to transmit to the instrument usuallyby using a spring damper system with very low cutoff frequency which works as a low pass filter for thedisturbance. A passive system can be designed toprovide the necessary attenuation to this vibration. Toeffectively attenuate the low frequency groundvibration, a hybrid active passive system isnecessary([I], [3]).

The passive system attenuates high frequencydisturbance with reasonable attenuation rate and thenthe active system works to attenuate the lowfrequency vibration effect. The active systemimplements active control using sensors andactuators. The actuator of active vibration isolatorcan be of several types: mechanical mechanisms,piezoelectric actuators, pneumatic springs,electromagnetic motors and electrical linear motor.This research proposes implementation of

actuator, a Voice Coil Motor (VCM) on such anactive vibration isolator which works to control thevibration typically in range from 0.1 to 100 Hz. TheVCM was designed and optimized to providenecessary feedback force to nullify vibration effect.Necessary cost function was evaluated depending onpassive isolation effect and system dynamics. Forcegeneration was calculated using magnetic flux

reluctance method. Optimized result was thenevaluated comparing with the simulation result.

2. DESIGN OF THE SYSTEMThe isolation system is composed of four elastomermounts to support upper plate with the instrument tobe isolated(around 150Kg) along with three verticaland three horizontal VCMs mounted such that theycan control all six rigid body modes using feedbacksignal from the accelerometers connected to theupper plate as shown in figure 1. Accelerometersmeasure transmitted vibration from ground to upperplate and sends feedback signal to the actuators.

Fig. 1: Complete system with actuators and sensorsThe passive system can be realized as stiffness in

parallel with damper and actuators thus work as forcegenerators that work in parallel to the passive system.The actuators were designed as shown below

_ ~~~~~YOKE

_M AGNET_MMAGNET MANETr

Fig. 2: (a)Vertical actuator and (b)Horizontal actuator

3. OPTIMIZATION OF VERTICALVCMIn order to optimize these VCMs, a cost functionneeds to be defined along with design parameters thatcan be varied to arrive at the desired optimizationvalue. Force requirement depends on passive systemdynamics as the actuators work against stiffness and

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damping of the passive elastomers to providenecessary dynamic force to attenuate vibration.

The complete system model with two inputs(control signal input, Fu(s) and vibration input, b(s))contributing to output variable, p(s) is as follows:([M]s2 + [C]s + [K])p(s) = [C]sb(s) + [K]b(s) + FT (s)

tp(s) F~(s)+ ([C]s+[K]) b(s) (1)

([M]s2 + [C]s + [K]) ([M]s2 + [C]s + [K])M, C and K are mass, damping and stiffness

matrix respectively.To find the dynamic force required in vertical

direction, we use single degree of freedom modelwith K and C being the vertical directional stiffnessand damping respectively as:

K = 8.6*105 N/m and C = 1.42*103 Ns/m

Fig. 3: Single DOF system with actuation force Ft.From figure 3 we get force requirement for the

vertical actuator as follows[2]:Ms2P(s) + Cs(P(s) - B(s)) + K(P(s) - B(s)) = F]

3FVCM = 3nBgli = 3Kti> Ms T(s)XB + CSXB (T(s) -1) + KXB (T(s) -1) = 3FVCM

where T(s) Transmissibility of passive system

P(s) Cs+K

B(s) Ms2 +Cs+KWhere K, = Force constant = n*B9 *1n = No. of coil turns, Bg =Flux density at the air gap

and 1 = effective length of coil.Since control bandwidth is 0.1-100.OHz, to find

maximum force requirement, 100 Hz frequency was

considered since at that particular frequencymaximum acceleration and velocity is transferred tothe upper plate considering peak to peak groundvibration displacement B(s) = 100 micro meter.Transmissibility of passive system also varies withfrequency and it can be calculated from passivesystem dynamics as plotted in figure 4 and the valueis T(s) = 0.0143 = -36.9dB

Fig. 4: Transmissibility of passive system (verticaldirection)

Maximum force requirement is:3FVCM = S2XB+CSXB(T -1)+KVB(T -1) >FVCM =-29.33N

The VCM has to produce less than or equal to themaximum force requirement F = 30 N. So the costfunction is:minimc(|req|3|FV) =>(||fS2XB+CVB(T_1)+K2B(T= minimize (88 - 3FVCM )To choose the constraints we decide that the

designed actuator should have compact size alongwith maximum allowable temperature, saturated fluxdensity and maximum current through the coil as

constraints. The list is as follows:Table 1 : Cost function and constraints

COST(\

FUNCTION minimize (88-3FvcM)CONSTRAINTS

In order to optimize size of VCM, some geometricparameters are considered constant and the others are

varied at some defined range with the objective tominimize the cost function. Considering symmetrichalf part of the VCM, the geometric parameters are as

shown below:

Fig. 5: Symmetric half structure with geometricparameters.

Table 2: The fixed geometric parametersFixed constraints ValueLy (Magnet length) 40.0 mmTc (Coil thickness) 2.0mmWc (Coil width) 0.5*Wm

Way (Width of side air gap) 0.1*WmTcy (central yoke thickness) 2*TuyTch (Coil holder width) 2.00mmLc (Coil side length) 49.0mmLcc (Coil opposite side length) 14.00mmLce (Coil effective unit length) 2*((Lc-Tc)+(Lcc-Tc))

Table 3 shows the design variables with their range.

Table 3 : Design VariablesDesign Variables Design range

Tm (Magnet thickness) 2.0 - 5.0 mmWm (Magnet width) 10.0 - 25.0 mmTuy (Yoke thickness) 1.0- 5.0 mmi|Tg (Air gap thickness) 5.0 - 6.0 mmdc (coil diameter) 0.1- 1.0 mmIc (coil current) 0.3 - 1.0 Amp

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<70 (C)Temperature (T)VCM size <40(mm)X47(mm)(Height x Length x width) x 46(mm)

Generated force (N) < 30NSaturated Flux density < 1.8T(Bs)Coil Current (I) .< 1 .0 Amp.


Geometric constraints:Ly = 40 mm [combined length]

14 < Ty < 47 [combined thickness]

18 < Wy < 46 [combined width]Sog(1) =2IW +WL +2Wy < 46nin1>g(1) = 27 +1.22W <46n

and g(2) =2(W +T7m +I)+2IT <47> g(2) =4T,+2(7 +7Tg) <47nCurrent constraint:Current is considered to be less than or equal to1.OAmp to reduce the effect of electrical dynamics(i.e. effect of coil resistance and inductance)

Ic <1g(3):Ic -1.0<0

Heat dissipation constraint:Heat dissipation is selected on elastomer temperaturelimit. Since coil current is responsible for heatdissipation, heat flow circuit is as shown in figure 7.

..................,...,,...._.

-.............g.......................l._

.............................................

-qou|tqloutq20ut

q30ut q 2c4 u

Fig. 6: Coil assembly and its cross section along withheat flow direction

Fig. 7: Heat flow circuitHere h = Heat conductivity of air, k = Convectioncoefficient of coil holder material and As' arerespective cross sectionsFrom the figures we get the heat dissipation constraint

qout = qlout + 2q2out + q3out + 2q5out ' qs

g(4)= s -1.0<0 here qs =I2*R,qout

To optimize system parameters, reluctance methodwas used. The equivalent reluctance circuit for themagnetic flux can be represented as in figure 8.

Fig. 8: Equivalent reluctance circuit ofVCM

Relationship of different parameters in thereluctance circuit is as follows:

Fig. 9: Relationship of parametersImplementing all relations we performed the

optimization using Matlab toolbox with objective tominimize the cost function.

4. OPTIMIZATION RESULTOptimization was performed using the designvariables and minimizing the cost function whereg(1), g(2) and g(3) are linear inequality constraintsand g(4) is non linear inequality constraint.

To find the global converged value we iterate theoptimization process using many initial valuecombinations of the design parameters within thebound and then the cost function value was plottedas in figure below for all the iterations.

Fig. 10: Global MinimaFrom figure 10 the global minima was found and

the optimized design parameters were chosen withrespect to this global minima. Result of theoptimization process is as follows:

Fig. 11: Cost function convergence

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Figure 11 shows the cost function convergenceand the design variable convergence are shownbelow in figure 12

the result. The simulation model and result is asfollows:

Fig. 13: VCM model and flux distribution in thecross section.

Flux density distribution at the air gap is as follows:Flux densi at air gap

Fig. 14: Flux density distribution at air gapThe simulation result is shown in table 5Table 5:Comparison of Optimization and simulationParameter Value -Percent error from optimization resultN (No. of turns) 800 3.625Force 13.5 N -8.59Flux Density 10.47 T -4.25

From table 5 we see that simulation resultconforms to the optimization result.

The horizontal VCM can also be optimized in asimilar manner considering different parameters forthe horizontal isolation.

6. CONCLUSION

Fig. 12: Convergence of design variablesThe converged values are summarized in table 4.

Table 4: Optimization resultDesign Variables Design value after optimizationTm (Magnet thickness) 4.2617 mm = 4.25 mmWm (Magnet width) 24.5851 mm = 24.6 mmTuy (Yoke thickness) 4.9527 mm = 4.95mmTg (Air gap thickness) 5.1207 mm = 5.1 mmdc (coil diameter) 0.19 mmIc (Coil current') 0.9592 Amp. =0.96 Amp

Parameter ValueN (No. of turns) 770.84Force 14.6644 NFlux Density 0.49 T

Cost Function value 1.66e-10.

Force generated is FVCM = 2*Force = 29.12 N andFlux density is also within saturation limit (>1.8T).

5. SIMULATION

To verify the optimization result we perform FEMsimulation using Maxwell software and compared

The optimized design of a Voice Coil Motor wasperformed which can be used as an actuator for theActive Vibration Isolation system. The result of theoptimization was verified using FEM simulation.This optimized VCM can easily be implemented tocontrol the low frequency vibration typically withinthe range 0.1 to 100 Hz.

7. REFERENCE[1] Yi-De Chen, Chyun-Chau Fuh and Pi-Cheng Tung,

"Application of Voice Coil Motors in Active DynamicVibration Absorbers" , IEEE TRANSACTIONS ONM\AGNETICS, vol. 41, no. 3 pp. 1140-1154, March2005

[2] Duane C. Hanselman, "Brushless Permanent-MagnetMotor Design", McGraw-Hill, Inc. 1994

[3] Eric Flint, Patrick Flannery, Michael Evert and EricAnderson "Cryocooler Disturbance Reduction withSingle and Multiple Axis Active/Passive VibrationControl Systems" , Proceedings of the SPIEconference#3989, Paper#64, Newport Beach,CA, USA.

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