Theory & Practice of Electromagnetic Design of DC Motors & Actuators

George P. Gogue & Joseph J. Stupak, Jr.

G2 Consulting, Beaverton, OR 97007



A number of different types of magnetic device are commonly called actuators. It might be reasonable to group them into four categories:

(1) Voice-coil actuators and swing-arm actuators

(2) Solenoids and related devices

(3) Linear multiphase motors

(4) Other types

11.1 Voice coil and swing-arm actuators:

11.1.1 Introduction:

Voice-coil actuators are a special form of electric motor, capable of moving an inertial load at extremely high accelerations (more than 20 times the rate of acceleration of gravity "g" at the Earth's surface) and relocating it to an accuracy of millionths of an inch over a limited range of travel. Motion may be in a straight line (linear actuators) or in an arc (rotary, or swing-arm actuators). After completing a motion (called a "seek" in the computer peripheral memory industry) the moving parts must stop vibrating very quickly. This period, called the settling time, may be a few milliseconds or less.

Most voice-coil actuators are used in high-performance computer peripheral memories ("Winchester" drives) but they are also found in shaker tables, medical equipment, high-speed lens focusing applications, laser tools, servo valves, instruments, and elsewhere.

The first voice-coil actuators resembled scaled-up loudspeaker mechanisms in construction, from which they were named. These early designs (as shown in Figure 11.1) had a very short gap with high field strength (perhaps 12 kG) and a long coil. They were replaced in the early 70's with motors in which the magnetic fields were much longer and at lower intensity (typically 2-6 kG), an example of which is shown in Figure 11.2. The coils of this design are much shorter and remain entirely within the gap region. The moving mass is less and is capable of higher acceleration with less settling time. Coil resistance is lower and linearity is improved.

A flat motor configuration, shown in Figure 11.3, has increased moving mass and electrical resistance but is easy and inexpensive to build. Both flux direction and current direction are reversed on opposite sides of the coil, resulting in forces which sum in the same direction. The same idea is often used in swing-arm actuators, using either flat (Figure 11.4a) or curved (Figure 11.4b) coils. It is also possible in a rotary mechanism to use a coil or coils which have axes pointing in the direction of travel, like the linear actuator of Figure 11.2.

Magnets may be placed next to the coil, as in Figure 11.2. They may also be located remotely, with flux carried to the coil through steel pole pieces. The latter permits higher flux density, increasing the output force or permitting a smaller and lighter coil, at the cost of increased volume, complexity, cost and flux-leakage. An example is shown in Figure 11.5.

11.1.2 Basic principles:

When electric current flows in a conducting wire which is in a magnetic field, as shown in Figure 11.6, a force is produced on the conductor which is at right angles to both the direction of current and magnetic field,

If the conductor (wire) is at right angles to the direction of travel and magnetic field then the force in the travel direction, in usual US engineering units, is:

The design of voice-coil motors for accurate performance is far more challenging than it appears at first. The very simple linear relationship above is complicated in practice by variations in the static magnetic field, flux-leakage, nonlinearities in the B-H curve of the pole steel, field variations caused by DC coil current, other effects caused by the rate of change of flux, effects on the drive electronics caused by coil motion, changing resistance due to heating, changing inductance and other problems.

The ratio of force produced to coil current is usually called the "force constant" but it would be more accurate to refer to it as the force-current ratio because it is significantly affected by many factors.

When a conductor moves with speed v in a magnetic field of strength B, an electromotive force (voltage) is induced across the conductor in a direction to oppose motion (if current is able to flow). This back EMF, as it is called, is for orthogonal directions of B, F and v:

If a fixed supply voltage is applied across the coil of a VCM (voice-coil motor) it will accelerate until the back EMF just equals the supply voltage (if the allowed travel is long enough). The speed at which the two voltages are equal is called the terminal velocity . The coil cannot exceed this speed without a higher applied voltage. In practice the coil is usually limited to a lower speed, called the cutoff velocity , by the controls. If the controls should fail,

however, the coil may approach this speed as it accelerates into the "soft" end stop. A limit on may be imposed by the space available for deceleration, by the maximum allowed deceleration rate to avoid damage (e.g. to the recording heads) and by the stop force/distance characteristics.

The same voltage is imposed across any other conductor which might be moving in the gap. Eddy currents thus caused may severely limit actuator motion. Such unintentional conductors might include part of the coil support tube, or fins to help cool the coil, etc. For such parts in a uniform magnetic field, a circular path around the bobbin can be prevented by using an insulator-filled axial cut (such as an epoxy joint). However, in a fringing field, such as at the end of the magnets, circular paths for eddy currents may exist locally in spite of axial cuts.

11.1.3 Shorted turn:

When voltage is suddenly applied to the coil of a voice-coil actuator, the resulting mmf (amps x turns) either increases or decreases the overall magnetic field. The magnitude of the mmf is, in engineering units:

A delay is experienced in the buildup of the stored energy, represented above by the current i. The effect may be described as circuit inductance although it is somewhat non-linear. If a sleeve of conductive material (copper) is added concentric to the coil but fixed to the magnet/pole structure, eddy currents are induced in it by changes in coil current. These currents cause magnetic fields which oppose the original changes of field and thus to a large extent cancel the apparent inductance. The result is a much faster, more linear response. The penalty, on the other hand, is increased gap width which in turn decreases B and the force-current ratio. In addition, the coil appears to have an increased resistance (reflected from the shorted turn). Heating is increased, although the extra heat is generated in the shorted turn, rather than in the coil. The shorted turn is usually placed inside the coil, on the center pole, and running its full length. It is possible, in some designs, to place it outside and surrounding the coil instead. The thickness of the shorted turn can be analytically determined, by methods too lengthy to be considered here. If placed inside the coil, it may be less than 70% as thick as the coil, as a rough rule-of-thumb.

11.1.4 Equivalent circuit:

The shorted turn acts like a shorted one-turn secondary of a transformer, as shown in Figure 11.2. The circuit is equivalent to that shown in Figure 11.7, with symbol meanings as follows:

The equivalent circuit of Figure 11.7 has an impedance of:

The amplitude of the frequency response of the circuit is shown in Figure 11.8. The shorted turn resistance , decreases at lower frequencies due to electrical conduction in the iron behind the turn and increases at high frequencies due to skin effects.

11.1.5 Static magnetic circuit:

Magnetic lines of flux must close on themselves so that any flux entering a closed surface must also leave it. The flux is equal to the flux-density or magnetic induction B integrated over an area A:

If the flux-density (measured in Gauss) is uniform over areas () and (), where (m) refers to the magnet at its neutral magnetic plane and (g) refers to the gap (at the coil), and using (l) to denote flux "leakage", i.e. flux which takes paths other than the useful ones through the coil, then:

Where kl = a leakage factor, equal to or greater than 1

Along any closed path, the line integral of mmf (magnetomotive force) must equal the current flowing through the enclosed area. If there is no current (i.e. a static magnetic circuit) the integral must equal zero:

This integral can be thought of as occurring in several parts, with one through the magnet, one through the gap (which includes all non-magnetic regions including the coil and shorted turn as well as any open volume) and one or more in the pole pieces:

Assuming that the permeability of the pole material is essentially constant (although not necessarily from place to place), H is constant within the magnet and in the gap. If the field strength in the pole pieces is proportional to them, then:

In the gap, is related to by the permeability of free space, which is very nearly the same for air, copper, aluminum, plastics, etc. In engineering units, of course, the definitions of Gauss (the measure of B) and Oersted (the unit of H) have been adjusted so that the permeability of space is one Gauss per Oersted:

In the magnet, B is related to H by the B-H curve which is supplied by the manufacturer. The B-H curve of one magnet material is shown in Figure 11.9.

These equations, which are now restated, are sometimes referred to as the magnetic design equations:

The above relationships are well-known and widely used in magnetics design. It is reasonable to use them for first-order calculations in the steel pole regions of a linear motor.

However, they are somewhat too simplified to use in determining the magnetic operating point, or the flux-density (B) at the coil (and thus the flux/current ratio) by direct application in a single calculation.

By assuming that the flux is purely radial (no leakage) and that the B-H curve is a straight line in the region of interest (a good assumption, for "square loop" materials like ferrites, samarium-cobalt and neodymium-iron) and that the magnetic reluctance may be modeled as a constant , an analytic solution may be found.

Figure 11.11 (a) B-H Curve

Figure 11.11 (b) Shorted-turn Motor Cross Section

From the B-H curve, it can be seen that, on the upper slanted part of the curve:

Another method is to apply the design formulas (Equations 11.15-11.18) to the magnet and gap to get an approximate value. The flux paths are then divided up into segments, using this initial guess as a starting point. For each segment, H and B.A is found and summed.

Repeated adjustments are then made iteratively to B and H to drive the error sums toward zero. This latter approach may appear crude but it permits inclusion iteratively of the nonlinear effects of the pole steel, flux-leakage paths, effects of coil current, etc. Since the material properties are probably not known to an accuracy of better than a few percent, convergence to an error of 1% or less is probably sufficient. The B-H curve of mild steel is shown in Figure (11.10).

A B-H curve for a fairly strong ceramic material (3.6x10 Gauss-Oersted maximum energy product) was shown in Figure 11.9. Ceramic magnets are popular for use in linear actuators because of low cost, reliable supply, good resistance to demagnetization and reasonable magnetic strength. If higher resistance to demagnetization is required, then a ceramic of the "grade 7" variety might be considered. Although the material is less powerful than the type shown (which is sometimes referred to as "Grade 8", a designation which varies from one manufacturer to another), the grade 7 material has a "knee" (the downward bend in the B-H curve) which occurs below the H axis. It is much less likely to be accidentally partially demagnetized by coil current, temperature effects and outside fields. Ceramic (ferrite) magnet material up to a maximum energy product of 4.4 x 10 G-Oe is offered for sale at present. If a higher energy material is required, then samarium-cobalt or neodymium-iron must be considered. These materials are both available in bonded form (combined with plastics) which have prices and characteristics somewhere between those of the solid sintered very high-energy materials and ceramics.

11.1.6 Coil construction:

The coil is the most critical element of the design, and all the other components are scaled from it. A small decrease in coil size may permit a considerable reduction in cost, size and overall weight. For these reasons it is best that the motor design not be limited to standard AWG (American Wire Gage) sizes of wire. It is entirely possible to have special wire made to any dimensions required at a cost which is not prohibitive for either design or production. Heat is the ultimate limiter of VCM performance, so the wire should be in a fully annealed state. Cold-worked wire may have as much as 10% or more greater electrical resistance than annealed wire of the same size. The cross-section should be rectangular, with rounded edges. Rectangular wire is somewhat more difficult to handle but has a much better "packing factor" (the ratio of copper to total coil volume).

It is sometimes asserted that the division of number of turns, width and thickness of wire in the coil is unimportant and may be left until late in the design. It can be shown, in fact, that many important motor parameters depend only on total coil volume, provided that packing factor and input power are constant. As wire size decreases, however, the minimum thickness of insulation which can be applied and still result in even, reliable coverage of the wire does not decrease as fast. At small sizes the insulation occupies a significantly larger share of cross-sectional area than it does for larger ones.

The designer is usually faced with the choice between using aluminum or copper for the coil wire. Aluminum has about half the conductivity of copper but only weighs about a third as much. Its increased volume may be an advantage since it would produce a longer coil with increased surface area for better cooling. On the other hand increased coil length may raise the settling time because the longer coil will have a lower first frequency of vibration. Motor length will be increased and there are other structural design consequences. Aluminum wire is harder to terminate and has greater thermal expansion. The only method known to the authors to determine which is best for a particular set of design specifications is to do a preliminary design on paper for each and compare them.

The coil must be carefully considered from a structural point of view or it may come apart in service. It is subjected to high forces, great accelerations, elevated temperatures and rapid thermal cycling.

Space permits only a brief outline of some of the thermal considerations in coil design. Since heating will be the ultimate limiter of the motor's performance, the coil's ability to reject heat is of considerable importance. Although some heat will be conducted away through the bobbin, the major path of heat rejection is from the coil surface into the surrounding air. The coil internal thermal resistance will probably be found to be insignificant compared with the thermal resistance of the boundary layer of air at the surface of the coil.

Calculation of heat transfer through the boundary layer can be done with the use of three dimensionless parameters, the Nusselt number, Reynolds number and Prandtl number. They are as follows:

If the coil is in forced convection with laminar flow [N(Re)<400,000] and if N(Pr)>0.6 (valid for air) then:

From the Nusselt number N(Nu) the heat transfer coefficient h may be calculated. If the flow is fully turbulent or is in transition, other relationships using these same three numbers must be used.

11.1.7 Improving linearity:

Even under conditions of no current flowing in the coil, flux across the gap of a voice-coil motor of the simple shape shown in Figure 11.2 is not uniform for a number of reasons. Near the ends of the magnet gaps the field is diminished because the flux spreads out into the space beyond the magnets. Near the front (outer end) the open face of the center pole provides a leakage path from the outer shell around the magnets. The field is retarded less (because of the leakage) near the front than it is further in. The steel in the center pole carries very little flux near the front and has little reluctance. The flux-density and the reluctance per unit length build up deeper in toward the back of the motor.

When a steady DC current is passed through the coil, a magnetic field is set up which adds to or reduces the static field (depending on the directions of current and field) increasing or decreasing the degree of saturation of the center pole steel. The paths followed by coil-generated flux are not the same as for the static field. Significant leakage across the gap occurs and it is different for various positions, current level and direction.

It is possible to greatly alleviate these problems by careful magnetics design. If the center pole is "hollowed out" from the face, flux-leakage across it can be greatly reduced. If the hole has a shape such that the cross-sectional area of the remaining steel increases linearly with distance inward (a parabola) then the pole steel will all be at about the same permeability. If the gap thickness is varied, becoming wider near the back of the motor, the static flux-paths can be adjusted to have equal reluctances. The coil should complete its stroke entirely within the gap region with small flux guard regions of magnet overlapping at each end.

In order to understand the consequences of pole dimensional changes to correct nonlinearities, a means of calculating the path permeances is needed. The static problem of magnetic permeance is described by Laplace's equation:

Direct, analytic solutions of this equation are possible for certain shapes but actual configurations are nearly always too complicated to solve. Instead, Roter's method (an approximate, non-iterative calculation, Ref. 12) is often used for preliminary work. Computer methods (by finite element) are becoming readily available at moderate cost for the personal computer owner but are at present only two-dimensional.

Considerable engineering judgment is therefore still required. Three-dimensional programs of sufficient capacity are offered by a number of sources for mainframe computer use. Another numerical method, finite difference, is also applicable to this problem but is not in wide use. This method is simple enough to be used by almost anyone either by hand or with the aid of a personal computer. Mathematical modeling using a personal computer is also a widely used approach which has had good results (Ref. 39).

Older methods include flux-mapping by graphical means and analog models using resistance paper (two-dimensional) or electrical resistance in a water tank (three-dimensional) and capacitive measurements on foil covered plastic-foam models. The graphical mapping technique is occasionally useful in special circumstances. The physical modeling methods are much slower and less cost effective than computer techniques and are rarely if ever used today.

11.1.8 Actuator dynamics:

An actuator designer would like to have, as a starting point for his design, information such as the required current, duty cycle, maximum forces and accelerations, stroke etc. Instead, he is often given an average access time, carriage mass, distances allowed for deceleration in a soft crash and other system performance information, from which the parameters of actuator performance must be derived. The required mathematics to do this transformation may be quite lengthy and difficult.

Provided that the intended control scheme meets certain conditions, an approximate method exists (Ref. 35) which gives surprisingly good agreement with much more complete calculations and with measured performance. It is useful for approximate, first estimates of performance, for reviewing specifications for consistency and as a check for calculations.

The procedure is known as the Third-Stroke method. The effects of damping, friction and even of back EMF are ignored. For the last simplification to be reasonable, the cutoff speed should be limited to less than about 65% or so of the terminal velocity. Acceleration and deceleration are assumed to be constant and equal (except for direction, of course). The cutoff speed is set so that when the VCM coil starts at one extreme end of its travel, accelerating toward the other end, cutoff speed is reached when 1/6 of the total travel is reached. If, at that point, current is reversed and deceleration is begun, the coil will stop after traveling a total of 1/3 of the total stroke (in acceleration plus deceleration). It can be shown that the time for this seek (motion) is equal to the average access time. The time required to make the longest seek, from one extreme end to the other, is just twice this time. For this longest seek, it accelerates over the first 1/6th of the distance, coasts for 2/3 of the distance at the cutoff speed and then decelerates for the final 1/6 distance (this is shown in Figure 11.12). Any seek which is less than 1/3 of the total distance is made by accelerating, then decelerating, with no coasting period, because the coil never reaches the cutoff speed. A seek longer than 1/3 of the total distance coasts for a period dependent on distance.



"Average" access time in this case means the time (not including settling times) required to make a large number of seeks of every length, divided by the number of seeks. It is assumed that for each seek, any starting point or ending point on the length of possible travel is equally likely.

References 38 & 39 provide a further look into actuator design and performance as well as into innovative designs.

11.2 Solenoids:

11.2.1 Introduction:

The word solenoid is a Greek derivative meaning "tube-like", and refers originally to the coil only. As generally applied today, it means a coil of wire with an outer flux return path of permeable material (usually steel), with one end open and the other usually closed, and a magnetically permeable plunger which is pulled into the center of the coil when electric current is passed through the winding. Some typical constructions are shown in Figure 11.13.

If electric current is passed through a coil, a magnetic field is set up around it, outside the coil as well as inside. Although a theoretically infinite coil would have no field outside it, that is definitely not the case for a real coil of finite length. The field inside the coil, however, is much larger than it is outside, and considerable magnetic energy is stored in the interior. If a bar of permeable material, such as steel, is brought near one end of the solenoid, it will be drawn into it as the majority of the stored magnetic energy is transformed to mechanical work. This is independent of the direction of current in the coil. The pull of the solenoid may be greatly increased by adding an outer flux return path of low magnetic resistance, usually including a closed end. Most solenoids include a fixed center pin extending part way (less than half) into the center bore, which improves performance. The coil itself is usually wound on a bobbin of non-magnetic and usually electrically non-conductive material. The bobbin often also serves as a guide for the plunger. A solenoid of this construction operates in one direction only and the plunger is returned, when the current is cut off by some auxiliary means, such as a spring. Occasionally a double-acting solenoid is made, with two separate coils pulling in opposite directions. Other means also exist to return the plunger but a spring is the usual choice.

11.2.2 First order force calculations:

The first-order behavior of a solenoid (Figure 11.14) may be derived by using the idealized assumptions that, first: the only resistance to magnetic flux flow (i.e. reluctance) occurs in the gap and, hence, no mmf loss occurs in the steel pole structures or across the pole-sidewall interface. Second: that the field is uniform in the gap and zero elsewhere (no leakage flux around the gap). Third: that the permeable pole material does not saturate.

The magnetomotive force set up by the coil is:

Assuming uniformity of field and a constant gap length,

The energy stored in a volume of space occupied by a magnetic field is:

The mechanical energy produced against the magnetic force is:


Furthermore, the mechanical work must be equal to the electrical energy given up, and so:

11.2.3 Idealized model:

A better characterization may be obtained by using somewhat less ideal assumptions. MMF drop is allowed in the pole material and in the gap from the plunger to the wall. Uniformity of field in the gap and also at the plunger-wall interface is assumed and the permeability of the pole material is made constant. Pole saturation is still ignored.

The total reluctance is the sum of reluctance in the gap, plunger-wall and iron (permeable material) in series,

These reluctances are, under the simplifying assumptions,

In the above, the calculation for is rather more approximate than the others, since the relative permeability is certainly not independent of B, nor is it constant throughout the pole structures at a given value of B in the working gap. The value of is just what is required to fit the relationship, and is only approximately related to a real geometric area. However, the assumptions are justified, because is usually small compared to the other reluctances and so the corresponding error is probably not significant, as long as parts of the structure are not magnetically saturated. Substituting equations (11.45) to (11.47) into equation (11.44) and rearranging:

Solving for from equation (11.43) and proceeding as before, the solution for force is:

That is, the solution looks just like the first order calculation (e.g. 11.41) with a fixed additional length added to the gap, equal to

as shown in Figure 11.15. The equivalent length l' is not necessarily the same as the actual pole-wall gap, and may be reduced by increasing the area for flux crossing to the plunger. With increasing field strength in the gap as the gap distance closes, however, a point is reached at which some part of the flux path in the pole material starts to saturate and the curve levels out to a maximum force. This maximum force will not be exceeded, even if the current i is increased.

The inverse-squared dependence of the solenoid force with distance is not what one would wish in an actuator. At the beginning of the stroke, when the load is to be accelerated, very little force is available. On the other hand, at the end of the stroke, when the load should be decelerating to a stop, the force increases dramatically, slamming the plunger home with authority, causing noise and shock. A number of methods to give a better shape to the force-position curve will be discussed in following text.

11.2.4 Bobbin and winding:

The solenoid coil is often made on a bobbin, which provides a firm base for the winding and wire connections. The bobbin adds some cost and, in addition, takes up very valuable space which could be used for more wire to reduce heating and to improve performance. The use of a bobbin is usually amply justified, however, by the reduced cost of winding. It also may serve as a guide for the plunger. If it is made of plastic such as nylon or acetal (Delrin), it provides a low coefficient of friction for the plunger and will not conduct electrical eddy currents which might otherwise slow down the pull-in time while wasting energy. On the other hand, a plastic bobbin may expand if overheated, seizing the plunger. A metal bobbin may be more expensive but requires less volume. If speed of response is important, the metal bobbin may be split on a line parallel to the center axis with a non-conductive joint, in order to prevent eddy currents from following at the circumference of the bobbin (opposed to current in the winding), which slows down the rate of change of magnetic field.

11.2.5 Packing factor:

The relative fraction of wire to total volume of the coil space is called the packing factor. When this term is used, one must be careful to determine whether only the bare wire is included, or wire plus insulation. There is very little difference for large wire, especially with a single "build" (a single thin coat of insulating varnish), but in small wire or for thicker builds, the fraction occupied by insulation may be significant. In this section, packing factor will always refer to wire including insulation, unless stated otherwise. A coil wound by hand with little care may have a packing factor of as little as 25%. A typical layer-wound coil, wound with round wire by machine or hand may have a packing factor of about 60% and cannot exceed 78.5% because of voids between the wires, even when touching. If square or rectangular wire is used, however, the packing factor may exceed 90%. Rectangular wire is easier to wind than square wire, because it tends to lie flat rather than cocking on edge as it is wound. In practice, a ratio of width to thickness of about 1.5 to 2.5 seems to work out best.

Wire is available with a thin coat of bonding agent, which is hard when wound but bonds to the other wires in the coil when heated in an oven, or when dipped in alcohol. The bonding layer adds to the wire thickness, however (decreasing the packing factor). Very tight, strong coils may be wound "wet" with epoxy painted onto the wire as it is coiled. Coils may also be impregnated under vacuum with thin epoxy (often heated to reduce viscosity) after winding. A simpler but somewhat less effective method which is widely used, is to drip winding varnish onto the coil after it is wound, which has a tendency to pull into the voids. A void-filling bonding agent strengthens the coil and also aids in heat transfer.

After winding, terminating the wires and varnishing or potting, the outside of the coils is often wrapped with tape to add some protection against abrasion and wire motion on the surface.

11.2.6 Gap location:

At first consideration, it might appear that the location of the working gap would be unimportant and that any of the positions shown in Figure 11.16 would be about equivalent. That is not the case, however; the best result is usually obtained when the gap is approximately centered in the coil. In a theoretical, thin-walled solenoid of infinite length, no flux crosses the coil but in a real, thick-walled coil of finite length, it certainly may, causing reduced force. If the plunger is near one of the ends of the solenoid, flux may spread out from it to the ends, also reducing the force (Figure 11.16a, b). The direction of flux may also change considerably with changes in gap, with unexpected results. A central gap position minimizes these problems.

11.2.7 Plunger face shape:

The force-distance characteristics of a solenoid may be altered somewhat by shaping the gap, i.e. the ends of both the plunger and fixed center pin. In Figure 11.17 the plunger tip has the shape of a truncated cone. When the gap is large, there is relatively little difference in flux paths from that of a square-ended plunger and the resulting forces are similar. When the gap is small, however, the surface area of the conical tip is larger than that of a square-cut end. If the amount of magnetic flux is the same in both, the flux-density at the surface is reduced for the cone. The force per unit area is reduced by the square of the ratio of area, and the total force (due to increased area of the cone) is reduced proportionally to the area ratio. This force is directed at an angle, rather than parallel to the axis and the radial components cancel. The overall result is a smaller increase in force near the end of the stroke for the cone-tipped plunger than for the flat-ended cone. The flat at the end of the cone is added to prevent problems with a sharp point (they are easily damaged, or might even cause injury) and are often used to provide a stop to prevent complete closure and sticking or for a pad to absorb shock and reduce noise.

11.2.8 Remanence and sticking:

If a magnetic circuit is permitted to close completely, with no gap at all in the circuit, then when the current in the coil is interrupted, it is often found that the solenoid "sticks". The plunger may be held in place with considerable force which the return spring is unable to overcome. Slowly over seconds or minutes, the magnetic field fades and then the solenoid opens. If immediately closed by hand, however, the magnetic field which caused it to stick is found to have disappeared. If the solenoid is forced open immediately after the coil has been energized and then immediately closed by non-electrical means, it is found that there is no remaining magnetization. Apparently the domains of even relatively "soft" steel maintain themselves in alignment, resulting in a high magnetic field, for some period of time if there is little resistance to flux in the form of a gap, until they are gradually disordered by thermal agitation of the individual atoms. As soon as a gap appears, the magnetic order ceases. The "fix" for this problem is to provide for a very thin spacer to prevent complete closure. A typical solenoid spacer might be on the order of .005 inches thick and a high-speed valve might have a spacer as thin as .0005 inches.

11.2.9 The plunger-wall flux crossing region:

Flux in the outer shell must cross a sliding joint to get into the plunger. The gap here reduces plunger force and so should be as small as possible. The effective gap length l' may be reduced by making the flux-crossing zone longer in the axial direction. The plunger will not be perfectly centered in this gap and so it will be pulled toward one side more strongly than the other, which will in turn tend to move it even further off center. The unbalanced side load caused in this manner may result in an unexpectedly large frictional load on the plunger, reducing the useful force considerably. Increasing the area crossed by the flux would reduce the side force. Good centering by the plunger guide in the center hole is very helpful (see Reference 36).

11.2.10 Solenoid drive circuit considerations:

The solenoid load looks to its power source like a constant resistance (the winding resistance) and a variable inductance, which is relatively small when the plunger is out and becomes large when the plunger is in. Because of the fixed resistance, the current is approximately constant during the stroke. In order to speed up the stroke, solenoids are often boosted with a high initial voltage, which is reduced after it has pulled in. The initial boost may be provided by discharge of a capacitor, for example. Sometimes an additional resistor is switched into the circuit after pull-in to reduce heating when the force is higher than required for holding the plunger in place.

Solenoids may have considerable stored magnetic energy when energized. A very large voltage across the switch and coil windings may result when current is off and even lead to component failure. If required, a "freewheeling" diode may be placed across the winding, as shown in Figure 11.18a. The diode does not carry current during normal operation of the coil but allows the current to continue to flow in a loop after the power supply is cut off, until the stored energy is dissipated in the coil resistance.

11.2.11 Solenoids operating against springs:

A frequently attempted experiment is to locate a load with variable position, by using a solenoid against a spring and by adjusting the voltage. Unfortunately, it won't work! The solenoid either does not move or, as soon as the force gets high enough to overcome the spring, it moves all the way to the inside stop. occasionally the solenoid will assume an intermediate point but the restraining force is very weak and it is discovered that there are two, or perhaps even three semi-stable points, rather than one. Which point the system will assume may depend on inertia, friction, small disturbances, how fast the current is changed, etc. The explanation for this behavior is that almost all springs obey Hooke's law, i.e. force is proportional to the extension distance (possibly with offset where the spring is under some tension at the inner stop). The solenoid force which the spring is attempting to balance, however, is inversely proportional to the square of the distance. A solenoid force curve is shown against some possible spring curves in Figure 11.19. Spring curves a, b and c start from an initial force such that the return force is equal to the remaining stroke force against the spring, at the right end of the stroke diagram. Curve a results in only two possibilities, full-in or full-out. Curve b results in a single point of balanced forces, but it is unstable. The slightest disturbance will cause the system to move all the way to the right, or left, of the curve. Curve c has three very marginally stable points: a very unsatisfactory arrangement.

Linear extension-type springs used to return rotating elements driven by solenoids may pivot at their ends, as well as stretch. It would seem that the spring hooks at each end would simply rock easily on their supports but it is found, in practice, that the frictional forces there may first torque the spring, then suddenly release with sound and large force alternations. A correction for this problem is to insert discs of a bearing material such as acetal (Delrin) or brass into the spring eyelets. The outer diameter of the discs must be grooved to receive the hook wire, and provided with a center bore. The discs are then mounted on close-fitting pivot shafts. For fast motions, the resonance of the spring may become a problem. The frequencies of resonance are:

11.2.12 Constant force and variable position solenoids:

There are at least two solenoid-like devices which are capable of constant force, or near-constant force, over the stroke distance. By varying this force, a servo-positioner may be made.

The device shown in Figure 11.20 is sometimes called a constant-force solenoid. Rather than being pulled from the end, with flux lines parallel to the direction of motion, this arrangement operates from changes in the magnetic field around the sides of the plunger, in a manner often referred to as variable-reluctance. As the plunger pulls into a surrounding tube of permeable material, a region of high magnetic flux is set up with a fixed gap distance. The gap region increases linearly with change of plunger position. Since the energy stored in the gap is proportional to volume, and force is proportional to the rate of change of energy with distance, the resulting force on the plunger is, therefore, approximately constant.

The actuator shown in Figure 11.21 is known as the "controlled-field actuator" (CFA, see Reference 37). This modified solenoid is capable of producing constant force, independent of position and can be controlled from an outside signal. The force is independent of supply voltage, provided it is high enough to allow the required current. The extra energy is not wasted but is simply not used, so that the CFA is far more efficient than a normal solenoid for some purposes.

In addition, the device produces a signal proportional to its position, so that it is also a position sensor. Position accuracy is on the order of a few percent, which is sufficient for some purposes, although not for others. The CFA works by providing another small fixed gap in the magnetic path, into which a Hall-effect magnetic field sensor is placed. When the field builds up to a preset trigger point, the Hall sensor turns off the current from the source, and the coil inductance continues to drive current around a loop through a flyback diode. As the field decays, a lower limit is reached at which the source is reconnected and the cycle repeats. The constant average flux produces a constant force. The average current flowing in the solenoid is proportional to position, for a fixed force. The average current divided by the Hall sensor output voltage is proportional to position, regardless of the commanded force.

11.2.13 Solenoid actuation speed:

Solenoids are somewhat slower than other types of linear actuator, for several reasons. Considerable magnetic energy must be built up in the gap before significant motion occurs. The energy to do this must come from the power source, which takes time, if the current is limited by the coil resistance. The high levels of magnetic flux required in the pole parts cause hysteresis and eddy current losses, which must in turn be made up by the power source, again requiring time. If a spring is used for the return, the energy to extend it must come from the solenoid stroke. This leaves less force available to accelerate the plunger, increasing the stroke time. The initial storage of energy may be speeded up by using an initial high-voltage pulse, followed by reduced current once the plunger starts to move. The hysteresis problem may be alleviated by the use of low-hysteresis material such as very low carbon iron. Eddy currents may be suppressed by constructing the solenoid of lamination stacks. The laminations may be held together by narrow welded strips (beads), by snapping them together with the aid of formed depressions, by rivets (a common choice) or screws. They may also be bonded between laminations, which also helps reduce noise. Another possibility is to use high electrical resistance material such as silicon-iron for the plunger, etc. Slotting the plunger and shell along the axis helps.

11.2.14 Some other solenoid types:

If a hole of smaller diameter than the plunger is made through the normally closed end of a solenoid, and the plunger is provided with a nonpermeable push rod extending from the plunger face through the hole, the solenoid action becomes a push instead of a pull.

The outer shell or flux return path may be made of stamped or formed metal of rectangular shape, rather than as a tube. Two (or rarely, three) sides are usually left open with this construction, called "open frame". The extended sides of the frame provide some protection from mechanical damage for the coil, although less than with a tubular shell, and the open sides allow much better air flow for coil cooling. In Figure 11.22, three possible constructions of a formed box frame are shown. The shape shown in Figure 11.22a is the least expensive to manufacture but is infrequently used because it is weak and easily deformed. The type shown in Figure 11.22b and c is symmetrical, which pleases mechanical designers and is easy to assemble. The joint between the end part and the "U" body, however, is found to have a variable added reluctance (especially if the parts are plated before assembly) which may increase the differences in force between solenoids in production.

Large industrial solenoids made of lamination stacks to reduce eddy currents are usually made with rectangular cross-section, for reasons of cost and ease of manufacture. Open-frame construction is used to aid cooling. The molded bobbins used in them have rectangular cross-sections too, which increases slightly the difficulty of winding and decreases the packing factor of the coil.

If very large conductor cross-sectional area (per turn) is required, it may be advantageous to use copper or aluminum strip instead of wire. Large diameter wire is hard to coil because of the force required, and increased AC resistance due to "skin effect" may limit the rate of current change for round wire. A single strip the width of the coil is much easier to wind, has less skin effect AC resistance and may have better packing factor. Since each conductor reaches the edge of the coil, heat transfer out of the coil may be better as well.

Such strip is sometimes left uninsulated and is electrically isolated from the next turn by winding it interleaved with a thin strip of "fish paper", nomex or plastic. The insulation is cut slightly wider than the conductor strip, to prevent shorting at the edges. AC solenoids:

A solenoid made for DC use will operate on AC but is likely to shake and "chatter" excessively. In addition, the impedance imposed by the variation of inductance of the coil with plunger position may limit performance. In order to provide a steadier pull, solenoids made to operate on AC current have parts of the plunger and/or fixed center pin divided into two separate flux paths. One of these paths has a loop of conductor (usually copper) around it, forming a "shaded pole". Due to the conductivity of the secondary winding around this flux path, the flux through it is delayed in phase. As the coil current drops through zero on each half cycle, the flux in the non-shaded path stops and no force is generated momentarily across it. At the same time, however, the flux in the shaded path remains high, with force still being generated across it, until current again builds up in the other circuit. The force across the shaded path then goes to zero and the plunger is held in by the force across the unshaded path. The force ripple, i.e. the variation of force with time, may be considerable with this type of solenoid but is often acceptable. Rotary solenoids:

There are several types of solenoid which produce rotary action (with a small axial deflection too, in some cases). One type has a mushroom-like cap which is pulled down by an attached plunger. Between the cap and solenoid body are several ball bearings, riding in grooves which slant downward in the cap and body. As the cap moves down a short distance, it must also rotate. The groove depth may be shaped to improve the linearity of torque versus rotation angle.

A different type of rotary solenoid uses two internal spirals, one fixed on the center pin, the other rotating on the output shaft corresponding to the plunger. Rotary action narrows the small gap between them and travel of about 40° is achieved without axial motion.

11.2.15 Testing of solenoids:

In order to get a true indication of the force versus displacement of a solenoid, it is necessary to mount the plunger relative to the solenoid body so that it does not touch the side walls, creating variable and unrepeatable friction. One way to achieve this is to mount the plunger upright on a strain-gage-type transducer and mount it in turn to the bed of a milling machine. A tabletop miniature mill of the "drill-mill" variety is a relatively inexpensive machine which serves well. The table may then be moved in two orthogonal directions horizontally to locate the plunger. The spindle is locked in rotation and the solenoid body is mounted to it. The mill-head quill may then be raised and lowered accurately to provide for the distance variable. In order to measure this distance accurately, a dial indicator may be mounted on the mill frame. It must be kept in mind that the strain-gage, although very stiff, will nonetheless have some compliance and will add or subtract a small amount to the distance indicated, dependent on the amount of force generated. A correction should therefore be applied. This deflection may be calculated from the gage vendor's data and may be on the order of a few thousandths of an inch. For volume production, a stepper motor may be added to the mill to raise and lower the body and the data may be fed to a computer which automatically corrects the reading, controls the applied current and plots out the results. Because of changes of resistance of the coil as it heats up, current, instead of voltage, should be controlled in solenoid tests.

11.3 Linear multiphase motors:

These actuator types resemble electric motors which have been slit along one side and spread out flat. They take many of the same forms as rotary motors. A small carriage with attached magnets may be used with a multipole wound stator for rapid and accurate servo positioning of a load. Linear actuators of this type are used in machine tools. Induction-type linear motors have coils wound on a moving pole structure, which induces eddy currents in a fixed rail. The eddy currents cause a magnetic field opposing and repelling the original field, causing thrust. Motors of this type have been used to power magnetically levitated trains. Reference 29 contains design information on these types of actuators.

Figure 11.23 Polyphase linear motor

A production type of multiphase actuator is shown in Figure 11.23. A steel rod with a copper sheath is pushed through a wound stator assembly (without contacting the stator), by magnetic fields set up by three-phase AC current and induced currents in the copper sheath. The force is reversible by connecting the wires in a different order. A typical unit can exert up to 90 lb. force on a 1 inch diameter rod, which may be of any length, at a maximum speed of 2 ft/sec. The duty cycle of this device is limited, however: on-to-total time is only about 3% without an auxiliary cooling fan.

11.4 Other actuators:

A few less common magnetic actuators exist which do not fall into any of the categories previously discussed. One such device is an impact printer head, used on high-speed printers for computers. A small, powerful magnet attached to a spring-loaded arm hammer is held against a magnetically permeable platen by its own field. When the platen is magnetized by current in a surrounding coil, the head is driven forward by repulsion with great speed and force, printing a character on the paper. It then bounces back, to be recaptured again by the now de-energized platen.

Figure 11.24 Servo valve control

In one type of servo valve, pilot chambers push a spool which controls the main flow (Figure 11.24). Two holes, close together, lead to the pilot chambers. A jet of fluid is aimed at the two holes by a magnetic tilt mechanism, so that a small rotation of the jet assembly directs the jet to one or other of the holes, or somewhere in between. The jet is rotated by a permeable bar between two sets of biasing magnets. With no current, the fields are just balanced at the center rest position but current through the coil causes the stable position to shift in one direction or the other, rotating the nozzle. Deflection versus current is linear over a small range.