Finite-Element Analysis of a Constant-Force

8/13/2019 Finite-Element Analysis of a Constant-Force

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 24, NO. 4, JULYIAUGUST 198876

i nII

III

I

I

Fig. 3 . Flux patterns. a) Positio n 0 mm. b) Position 4 mm. c ) Position7 mrn.

iiii1 2 5

iFig. 4. Flux densities T ) . a) Position 0 mm; 700 At. b) Position 4 mm;500 At.and since flux densities throughout were calculated with actualmaterial reluctivities, it follows that the ca lculated forces takefull account of saturation.Through the proper definition of the surface S, one canobtain the magnetic force, either on the whole plunger or onany particular section of its surface. In that respect, and byselecting S small enough, the actual force distribution patternon the plunger can be determined. This was found to be apowerful tool for the solenoid analysis process.Flux patterns for various plunger positions 0, 4, and 7 mm)are shown in Fig. 3. All cases are computed with a currentexcitation of 500 At. Only the boundaries of the magneticcircuit shaded portions of Fig. 2 b) are shown in Fig. 3.Fig.4 shows flux densities around the core, in particular for theworst case, with the smallest displacement position 0 mm)and the largest ampere-turns 700 At). Except for local areasof saturation especially the pole), the device is mostlyunsaturated.

For the purpo se of mod el verification, the force characteris-tics as calculated from the finite-element analysis are com-pared with experimental data in Fig. 5. The force-versus-position curves are shown for three values of ampere-turnsfrom bottom to top: 300 At, 500 At, 700 At). A very goodagreement can be observed. The small discrepancies are wellwithin measurement imprecisions. The model was thereforeconsidered suitable for the analysis and design optimization ofthe solenoid.Ideally the force characteristics should be flat. Howev er, asFig. 5 shows, they peak at so me position which depends on thelevel of ampere-turns. The reasons for this will becomeapparent in the following sections.

111. SOLENOIDNALYSISA . Force Patterns

A better understanding of the working principle of thedevice can be ach ieved by analyzing the force distribution onthe plunger. Fig. 6shows the resulting pattern for 500 At andvarious positions ranging from 0 mm to 7 mm. The forcecharacteristics on the various plunger parts are shown in thefigure; they can be divided into three segments.At small displacements (0-1 mrn), the force on the taperedpart predominates. At medium displacements 2-4 mm) theforce on the flat part is the dominant one. This shift of forcefrom the tapered part to the flat part of the plunger is crucial in

bringing about the desired flat-force characteristics. When theairgap is small, the flux is large but goes mainly through thetapered surface. Because of the sharp angle of the taper only asmall portion of the large flux contributes to the axial usefulforce. When the airgap is larger, the flux is smaller, but alarger portion of it goes through the flat surface, where itcontributes in full to the useful force.The third segment of the force characteristics correspondsto displacemen ts beyond 5 mm. The bottom of the plunger isthen higher than the top of the pole. The force drops rapidlywith the distance x at an approximate rate of 1/x2 which istypical of conventional flat-face solenoids. This part of thecurve is undesirable. In fact, with the magnetic force actingagainst a spring see Fig. l , such a slope will provide poorlystable operating points. This suggests that, in general, oneshould avoid operating points where the plung er is higher thanthe pole.Finally, Fig. 6also shows the negative force pull back)applied to the plunger by the flux going through its uppersurface. This pull-back is relatively impo rtant at low displace-ments, where it severely reduces the useful force - 0.9 N atposition 0 mm for +3.8 N of useful force).B . Influence of Geometric Parameters

A parametric study was conducted by varying the geometricparameters, one at a time. Of particular importance is thegeometry of the two airgaps and the areas surrounding them.In the main airgap, these parameters are the sh ape of the poleits width); the angle of the taper; the shape of the plungerwidth of flat part and length of tapered portion); and finally,the respective lengths of plunger and pole. Th e geom etry wasstudied for a total stroke o f 7 mm.


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LEQUESNE: CONSTANT-FORCE SOLENOID FOR FLUID FLOW CONTROL 577

I I I I I I

heorettca l0 Exper imenta l

PLUNGERx i a l (U se fu l ) N e t Fo rce

0 0 Fo rce on Ta p e re d p a r tU........U Fo rce on f l a t p a r t

o r ce on u p p e r p a r t P a nU p p e r

Fig. 6. Force distribution on plunger.

I Pole Width: Fig. 7 a) shows the resulting force charac-teristic of a solenoid with a narrow pole while Fig. 7 b)corresponds to a wider pole. A narrow pole reduces the forceat higher displacements because it saturates. However, thissaturation is beneficial at smaller values of displacementbecause the fringing flux going through the flat part of theplunger also contributes to the force, and fringing flux isfavored by saturation. Still wider poles than the case of Fig.

7 b) were found to bring no difference because the iron in thepole is then completely unsaturated.In order for local saturation not to mask any change in forcepatterns, all subsequent curves are calculated with a widenedpole.2) Taper Angle: The influence of the taper angle is shownin Fig. 8.The largest angle value corresponds to almost no flatpart in the plunger. With such a taper, the airgap is rather large


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5 7 8 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 24, NO. 4, JULYIAUGUST 9 8 8

t

5 A t

t roke m m )

Fig. 7. Influence of pole width on force. a) Narrow. b) Wide.

;I.50 I851 3 5 7

St ro ke rnm)Fig. 8. Influence of taper angle on force

at large displacements. The consequence is a sharp drop inforce with increasing displacement.The smallest angle corresponds to no taper at all, that is, 0angle and a flat-face plunger. The force configuration is thenreversed, and the force is very small at small displacementswhen mo st of the flux is radial and does not con tribute to theforce. The force may even become neg ative if the pull-back onthe upper surface of the plunger is strong enough.These findings further support earlier remarks saying thatthe dominant force shifts from the flat part of the plunger to thetaper as the plunger moves downward. It also illustrates thesharp differences in force ch aracteristics that can be obtainedby varying the plunger geom etry. The d esired flat characteris-tic will be obtained with an angle balancing the two compo-nents of the plunger geometry, the flat and tapered parts.As can be observed in Fig. 5, the force peaks at someposition, and this peak shifts towards higher displacements asthe number of ampere-turns increases. It seems desirable tochoose a taper angle such that the peak of force corresponds tothe highest displacement with the highest level of current. T hiswill provide a positive slope of magnetic force versusdisplacement for most values of am pere-turns, helping stabil-ity when this force is opposed by the spring see Fig. 1).3) Shape of Plunger: Keeping the angle of the taper

constant (7.5 ) and varying the width of the n arrow flat part,the plunger length is accordingly long or short. As shown inFig. 9, a narrow flat part favors low displacements. Theseobservations are also in line with earlier remarks about thebalance of forces on the flat and tapered portions of theplunger.

4 Lengths of Plunger and Pole: Fig. 10 shows theinfluence of changing the height of the pole. Varying thelength of the plunger was found to have similar effect.The chan ge of length has an effect comparable to a shift inthe definition of the ze ro position of stroke. The peak shifts byapproximately as much as the pole is lengthened or shortened.With a short pole at the 7-mm position, the bottom surface ofthe plunger and the top surface of the pole are at the samelevel. There is already a significant drop in force because theairgap is rather large. With a long po le the force at position 1mm is very low because the tapered surfaces of the pole andplunger, which face each other, are very long and leave littlefringing flux to apply a force on the flat part. Again thesefindings concur with earlier remarks suggesting that the bestgeometry will be such that the top of the pole should beapproximately level with the bottom of the plunger at itslargest displacement.5) Secondary Airgap Design: While the secondary airgap


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LEQUESNE: CONSTANT-FORCE SOLENOID FOR FLUID FLOW CONTROL

6 -

4 --z?m

2 -

579

- WideNarrowz

g 4 -0

t 5 A II I L , L1 3 5 7

S t roke mm)*

Fig. 9. Influence of plunger shape on force. a) Narrow. (b) Medium. c)Wide.

Longer Po le ~ )_ _ _ _ M e d i u m P o ~ ~ t ~ o n ( - - - - - - )I Sh o r l e rPo l e -------)

500A t

5Stroke mm)

Fig. 10. Influence of plunger length on force.

upper airgap on Figs. 2 and 3) is necessary to allow theplunger motion, it is detrimental in two respects.It causes an MM F drop.Depend ing on its shape, some leakage flux will enter theplunger through its upper part, creating a pull-back on theplunger. This force can be critical at small displacementssee Fig. 6 .

The first problem can be corrected by reducing the airgapreluctance as much as possible. There are two means to this.

At the Smal lest D isp lacement.t he T w at the Plunger IS0 1 mm above Top of Pole0 -O Leve l w i th Top of Pole0 - 0 1 mm below Top of Pole

500 t

IStroke mm)

Pul l -Back Farce

Fig. 11. Influence of secondary pole position on force.

The airgap length should be as short as practically possible.Less reluctance can also be o btained by lengthening the pole,which reduces the flux density, and hence the MMF drop, inthe airgap. If the secondary pole is too long, however, therewill be leakage from one pole to the other.The second problem could be solved by either lengtheningthe plunger or lowering the pole. However, a long plungerincreases the overall solenoid volume, and a lower polereduces the area available for the coil. Th e final solution musttherefore be a compromise between minimum overall volumeand maximum coil area.Fig. 11 shows three curves where the top of plunger at thelowest displacement is either level, 1 mm above, or 1 mmbelow the top of the pole. The pull-back force, i.e., thenegative force exerted on the top surface of the plunger, is alsoshown. The best choice is when the plunge r is level or slightlyabove the pole at its lowest displacement. If the plunger goesfurther down, the drop in force becomes significant for verylittle gain in o verall volume.

IV. NEWDESIGNThe solenoid analysis presented in this paper was used toimprove the solenoid described in Fig. 2 , and a new designwas proposed Fig. 12).The main differences are

a new secondary pole design;the travel of the plunger with respect to the pole-at thelargest displacement the bottom of the plunger is aboutlevel with the top of the p ole, and at small displacementsthe plunger is lower in the new design;a smaller taper angle;


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580 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 24, NO. 4, JULYIAUGUST 1988

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iiiFig. 12. Solenoid optimization. a) Original design. b)New design

ew Design0 0 Orlg lna l D e a l o n

1 1 In 2 3 4 5 6 7

S t r o k e rnrnlFig. 13. Force level improvement.

a larger main pole;a larger main pole base.The travel of the plunger is such that plunger and polealways face each other. This provides for a full 7-mm trokewith a flat characteristic. The larger pole base avoids a fluxbottleneck. The larger pole in the portion of the pole facingthe plunger) is such as to get the maximum y et constant force.Both designs were built, and Fig. 13compares theirmeasured force characteristics. It show s improvements n tworespects. First, the force is larger for all positions of theplunger. Secondly, the force level is especially improved athigher displac eme nts, resulting in flatter characteristics. Thisis particularly important because it improves the linearity of

the relation ship between eq uilibrium positions of the plungerand amp ere-turns. Fig. 14 illustrates the latter point. If bothdesigns are fitted with the same spring a spring with the forcecharacte ristic show n in Fig. 13), one can ded uce the equilib-rium positions of the plunger for various levels of ampere-turns. Compared with an ideal straight line as in Fig. 14,experim entally determ ined equilibrium positions of the newdesign show much less dispersion than the ones of the formerdesign.V. CONCLUSION

This pape r has demo nstrated that soleno ids can be designedto provide a direct, linear, and co ntinuous control of a valve


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LEQUESNE: CONSTANT-FORCE SOLENOIDFOR FLUID FLOW CONTROL 5 8 1

0 New DesignO r i g i n a l D e s i g n

200 400 600 8 1000Ampere Turns

Fig. 14. Equilibrium positions versus ampere-turns

posit ion. The GM fini te-element package was shown to be apowerful design tool , capable of accurate performance predic-t ion. The analysis process showed the importance of thetruncated cone shape of the plunger; of balancing the forcesproduced by the tapered and flat port ions of the plungersurface; and of matching the respective posit ions of theplunger and of the facing pole.

A C K N O W L E D G ME N TThe author wishes to thank Paul Reinke and Will iam

Albertson of the GM Advanced Engineering Staff for theircontinued help and fo r providing test data.REFERENCES

[ I ] H C. Roters, Electromagnetic Devices, 3rd Ed. New York: JohnWiley, 1967.[2] J A. MacBain, A numerical analysis of time-dependent two-dimensional magnetic fields, IEEE Truns. Mug., vol. MAG-17, no.[3] J. A. MacBain, Magnetic field simulation from a voltage source, IEEE Truns. Mug., vol. MAG-19, no. 5, Sept. 1983.[4] T. W. Nehl, A. M. Pawlak, N. Mikhaeil-Boules, ANTIC85: Ageneral purpose finite element package for computer aided design and

6, pp. 3259-3261, NOV. 1981.

analysis of electromagnetic devices, IEEE Tran s. Mug., vol. MAG-24, no. 1, Jan. 1988.T. W. Nehl and A. M. Pawlak, Transient finite element modeling ofsolenoid actuators: The coupled power electronics, mechanical, andmagnetic field problem, IEEE Truns. Mug., vol. MAG-24 no. 1,Jan. 1988.[6] D. A. Lowther and P. P. Silvester, Computer Aided Design inMagnetics. New York: Springer-Verlag, 1986.[7] H. H. Woodson and J R. Melcher, Electromechunical Dynamics.John Wiley, 1968.

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Dr. Lequesne is a 1where he serves on the

Bruno P . L e q u e s n e (M85) graduated from theole Superieure dElectricite, France, in 1978,with the certified engineer degree, and received thePh.D. degree in electrical engineering from theUniversity of Missouri-Rolla, in 1984.He is currently a Staff Research Engineer withthe General Motors Research Laboratories in War-ren, MI, where his research interests are primarilyin the area of the design, analysis, and control ofelectromagnetic devices, and linear actuators inparticular.nember of the IEEE Industry Applications Society,Electric Machines Committee.

Finite-Element Analysis of a Constant-Force

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