The nature of the application under consideration dictates the information required to properly select a voice coil actuator (VCA), whether the application requires a linear or a rotary VCA. For example, operating at a fixed force will have a different demand than operation under servo conditions, where the duty cycle (duration on versus duration off) may be required. In general, four parameters will determine the actuator selection:

(1) Peak force/torque requirement (Fƿ)

(2) RMS force/torque requirement (F RMS)

(3) Linear or rotary velocity (v), and

(4) Total stroke or move distance (D)**Note: The environmental requirements will also affect actuator selection **

Peak force, Fƿ, is the sum of the force due to load, FL, FF, and the acceleration of mass, Fm:

Fƿ = FL + FF + Fm * **( Equation 1 )**

Looking at the separate components above in Equation (1), the force due to the load is the force acting directly against the actuator at all times. For example, a vertically oriented actuator supporting a mass against gravity will always have the force of gravity as a load component (if not supported mechanically). The force due to friction is determined by the mechanical configuration of the complete motion assembly and includes such factors as bearings, grease, linkages, surface-to-surface contracts, etc. Finally, the force due to the acceleration of mass is the product of load (including actuator coil) mass, mLTC, and load acceleration, α, as shown in Equation (2).**( Equation 2 )**

Root-Mean-Square or RMS force/torque is used to approximate the average continuous force requirement of an application. It is described by the following equation:

**( Equation 3 )**

Where t1 is the acceleration time, t2 is the run time, t3 is the deceleration time, and t4 is the dwell time in a move profile.

Velocity, v, is also dictated by the configuration of the mechanical system coupled to the actuator coil and by the type of move that is to be effected. For example, a constant force application would require an actuator with low velocity rating. A point-to-point positioning application would require an actuator with rated velocity higher than the average move velocity. The rated velocity would account for acceleration, deceleration, and run times of the motion profile. Figure 1 relates rated velocity to average velocity for point-to-point positioning move profiles.

**( Figure 1 )**

*Other factors may contribute to the overall force requirement. The values of these factors are typically more difficult to assess. They are taken into consideration by employing a “rule-of-thumb” safety margin: 20% of the calculated force value.

Stroke may be specified as the total displacement from one end of travel to the other end, or as a plus/minus (±) displacement from a mid-stroke reference point. Typical voice coil strokes range from microns to about 4 inches of total travel. The mass or volume of a voice coil increases as stroke increases. This condition results from the added magnet materials needed in long stroke applications, as well as the additional back-iron needed to carry the flux of the added magnets. Force and stroke usually have an inverse relationship – i.e., high-force/short-stroke, or low-force/long-stroke.

**( Figure 2 )**

**Do I need any other information if my application requires a Rotary Actuator?**

The four parameters required for proper sizing of linear actuators have rotary equivalents: (1) peak torque requirement, Tƿ, (2) RMS torque requirement, TRMS, (3) angular velocity, v, and (4) angular displacement or stroke. (Again, environmental conditions also affect selection).

The rotary equivalent to the acceleration force equation is shown in Equation (4) below:

**( Equation 4 )**

This section presents conversions factors and physical characteristics of motion utilized in the sizing and selection of linear and rotary voice coil actuators. This provides a technical basis for the calculations shown later in this document, under the selection entitled “Application Types”.

Rotary system torque requirements are a bit more difficult to determine due to inertia considerations. The inertia of the moving coil (including the support arm that attaches the coil to its pivot point) and the load inertia can significantly increase the level of torque required during angular acceleration and deceleration of loads. A few facts from rotational dynamics can help provide a reasonable estimate of system inertias. Figure 2, above, illustrates four objects rotated about an axis and equations describing the corresponding rotational inertias. In all cases, m is the mass of the object. Four objects of known weight, W, substitute W/g (g= acceleration of gravity) for m:

**( Equation 5 )****B. Solid Cylinder (about Cylinder Axis) **

**( Equation 6 )****C. Solid Cylinder (about Central Diameter)**

**( Equation 7 )****D. Solid Cylinder (about Axis through End) **

**( Equation 8 )**

Finally, there is a useful relationship between the inertia, Jd, of a body about any axis and its rotational inertia J (described above), about an axis through its center of mass, parallel to the first axis. The relation is shown in Equation (9):

**( Equation 9 )**

Where m is the mass of the body and d is the distance between the two parallel axes.

APPLYING VOICE COIL ACTUATORS – THEORY

Within certain limits defined by the magnetic circuit geometry, the force produced by a permanent magnet, linear voice actuator is linearly proportional to the current through its coil, as shown in Equation (1). The ratio of the force to current is called the force constant, KF, of a voice coil actuator:

**( Equation 10 )****( Figure 3 )**

Figure 3 depicts the equivalent circuit of a voice coil actuator. When a voltage, V, is applied across the terminals, a current, I, circulated through windings of resistance, R. At the same time, the actuator generates a back electromotive force (EMF), VB.

This back EMF is proportional to the speed of the moving coil by a constant, KB:**( Equation 11 )**

And directly opposes the applied voltage. In addition, the actuator coil has an inductive voltage drop (Note: This value is usually small, often negligible):

**( Equation 12 )**

Letting Vc represent the IR drop across the coil, and after applying Kirchoff’s Voltage Law we get the equation that describes the Voice Coil Actuator:**( Equation 13 )**

It is now possible to derive all of the parameters needed in sizing and applying voice coil actuators. Please refer to the glossary section of this guide for a listing of the definitions and units pertaining to the variables employed in the following equations.

Peak current requirement: **( Equation 14 )**

Hot copper coil resistance at maximum operating temperature:**( Equation 15 )**

Resistive peak voltage drop across the coil:**( Equation 16 )**

Maximum back EMF generated by the coil:

**( Equation 17 )**

Where VMAX is the maximum speed attainable, under no-load conditions.

**( Equation 18 )**

Substituting Equations (11), (15) and (16) into Equation (12) provides a value for the peak drive voltage requirement, in terms of known parameters:**Force Control Operation**

Voice coil actuators have linear force vs. travel characteristics, low electrical and mechanical time constants, and a high electrical-to-mechanical energy conversion rate. They are cog-free, and have no preferred coil position.

These attributes result in a level of smoothness and controllability that make voice coils ideal services for use in all types of servo modes, including positioning, velocity regulation, force/torque blocks, hybrid servos, and volume restricted applications, such as optical scanners and linear compressions.

**( Figure 4 )**

In its simplest servo form, the voice coil will be used as a force generator, where velocity and position are not critical considerations. In this mode, an operational amplifier is used to adjust the current level applied to an actuator, based on the signal generated from some feedback element that senses force, directly or indirectly. Figure 9 illustrates the force mode diagram.

**Position Control Operation **

In a position control mode, additional feedback elements are added to the system. Feedback devices are needed to sense the velocity and position because the system has to operate in more than one mode. Consider, for example, a point-to-point move that is accomplished with a trapezoidal velocity profile, such as the one described in Figure 1. This means that the coil will be accelerating during the first one-third period of the move profile, moving at a constant speed during the second third, and decelerating during the last one-third period of the move, coming to rest at a specific location. In this case, it is best to compensate the system separately for each mode of operation and switch between modes at the appropriate time.

A block diagram corresponding to the dual-control mode, point-to-point move is illustrated in Figure 5. *

In the trapezoid move profile, the actuator would be in the velocity mode during the acceleration and constant velocity portions of the move. The mode selector switch would be sensing velocity through sensor P. During deceleration, the selector switch would be in the position control mode, sensing coil position through sensor P.

(** Figure 5 )**

INSTALLATION CONSIDERATIONS

The standard voice coil actuator is a part-set consisting of a coil assembly. For proper operation, the two parts must be supported and aligned to allow relative movement. The coil must be centered within the magnet/core air gap throughout the entire stroke. It is not necessary to center the coil from precisely; however care must be taken to prevent the coil winding from rubbing against the core or the magnets. Actuator data sheets list the clearances between the coil and the magnet assemblies pertaining to each model.

Like a motor parts-set, bearings or brushings can be used to provide support and alignment.* The limited motion characteristics of voice coils also make it possible to use other support devices such as flexures. A flexure is a component that allows limited motion in the desired axis, yet minimizes off-axis motion. Typically, the flexure is tailored by the user or OEM for the application, although some are available commercially.

Another mechanical consideration in integrating parts-sets into a system is the heat dissipation requirements. Actuator force or torque ratings shown in our specification sheets and throughout the website are maximums obtained with the device sitting on a bench top, under free convection cooling conditions. Substantial increases in the force or torque outputs may be obtained by mounting the coil assembly onto a heat sink surface, or providing a forced airflow across the coil. .

Voice coils are usually provided with two flying leads or with two terminal posts. They can be provided with high-flexibility “Cooner” lead wire to reduce the work hardening effects encountered in high frequency actuation applications.

Linear and rotary potentiometers (pots) are used most often to sense position in servo systems utilizing voice coil technology. Other devices are used when special considerations such as high resolution or space limitations preclude the use of pots. Rotary feedback devices include capacitive sensors, optical encoders, resolvers, inductosyns, or RVDT’s (rotary variable differential transformers). Linear feedback devices include optical encoders, inductosyns, magnetoresistive sensors (contactless pots), and LVDT’s (linear variable differential transformers).

Optical encoders and potentiometers are available from BEI Sensors, a brand of CST.

APPLICATION EXAMPLES

A linear voice coil actuator with greater than normal clearance on each side of the coil can be used to execute small mirror tilt angles in beam steering mirror systems. Typically, the actuators are used in opposing pairs of one or more sets around the periphery of the mirror or its mounting plate. The mirror is supported and aligned by a bearing, usually a flexure spring, while the moving members of the actuator are connected to the mirror. The stationary members are connected to a common structure or a reaction member, depending on performance requirements. The voice coil actuators are used in push-pull pairs, and extra coil clearance is provided to accommodate on-axis and off-axis rotation. Figure 6 depicts a fast-steering mirror application in which four actuators were used to position a mirror across two axes at MIT Lincoln Laboratories.**( Figure 6 )**

Because the magnetic gap of the actuator is increased to accommodate the overall deflections of the coils, performance is compromised. To minimize this effect, a flux-focus magnetic circuit is often used. This type of circuit yields higher gap flux densities.

Volume restricted applications that call for mounting of the mirror directly on the actuator sometimes pose a special problem. The heat generated by the actuator coil winding may not be tolerable due to its effect on the properties of the mirror. In these cases, the mirror can be mounted directly to the magnet assemblies and the coil assemblies mounted to the structural or reaction member, which is usually a more massive heat sink.

Beam steering mirrors are used in optical scanning, pointing, aiming, tracking, and stabilization applications. The inherent features of a voice coil actuator (high force-to-mass ration, linear constants and cog-free motion) are ideal for the design of high performance electro-optical assemblies.

*In some cases the actuator moving member is simply mounted to the load’s bearing assembly.

Linear voice coil actuators are increasingly employed in the precision control of various types of valves. The infinite position sensitivity (limited only by the resolution of the servo control system), the exceptionally fast response times and frequency response characteristics, and the absence of hysteresis and friction make the voice coil actuator an ideal valve control device. In fact, voice coils are finding significant industry acceptance in applications that use traditional technologies such as hydraulics, pneumatics, solenoids, and even rotary-to-linear motor conversion mechanics.**( Figure 7 )**

Example: Figure 7 shows a pilot valve assembly concept drawing, in which an engineer has allocated a footprint for an actuator to drive a valve. In this example, the engineer has specified the parameters shown below:**( Figure 8 )**

**Step 1 - Determination of speed and acceleration: :** Assuming a triangular velocity profile, Figure 1B may be used to calculate the speed of the move.

**( Equation 19 )**

But in a triangular move profile, acceleration, α, occurs in the first half of the move - or, in this case, in 4 mSec.

**( Equation 20 )**

**Step 2 - Determination of acceleration and RMS force:**From the physical property, Fα = mα, where Fα is the force of a mass, m, accelerating at a rate, α.

**( Equation 21 )**

Disregarding the coil assembly mass for the time being, the RMS force may be calculated by use of Equations (1) and (3), which state that the force due to load (1lb) and friction (0lb) must be added to the acceleration force (to obtain peak force, Fα) and subtracted from the deceleration force. (Note that t2 is zero in triangular velocity profile)

**( Equation 22 )**

Table 4 can now be used to identify an appropriate actuator candidate. In this example, the LA14-15-020A appears to be an appropriate model or unit since it meets the total peak force requirement of 1.9 lb (including safety margin); the total RMS force requirement of 1.3 lb (including safety margin); the total stroke requirement of ±0.75 inches; and the envelope requirement of 1.5 in. O.D. max., 1.6.in. L. max.

**Step 3 - Effect of actuator coil mass on selection criteria: :**The mass of the actuator coil affects only the acceleration force requirement. The selected actuator has a coil mass of .63 oz., which is significant, compared to the load mass. The adjusted acceleration force is:

**( Equation 23 )**

The adjusted RMS force is 1.5 lbs. including the 20% safety margin, this translates to 3.1 lbs. peak and 1.8 Lbs. RMS, respectively. The LA14-15-020A is still the appropriate choice.

**Step 4 - Winding verifications:**It was stated earlier that the back EMF voltage generated by the actuator during operation subtracts directly from the available voltage supply. It is, therefore, imperative to allow enough voltage headroom to pull the current that will generate the desired force at the speed of the operation.

**( Equation 24 )**

**(Table 4 )**

**4.2:**Calculation of force-producing voltage: (Assuming L [di/dt] is nearly negligible or approx. 1V)

**( Equation 25 )**

**4.3:**Calculation of force-producing current: (Rcold =4.2ohms)

**( Equation 26 )****4.4:**Calculation of maximum available force at 3.13 ft/sec operation and 28V DC power supply:**( Equation 27 )**

Enough to handle the peak and continuous force requirements, at the necessary speed of operation.**Conclusion:** The model LA14-15-020A VCA with the catalog winding meets the speed and force requirement of this valve application.**A. Gimbal Assemblies **

Rotary voice coil actuators are well suited for use in gimbal assemblies. The low inertia, high torque output of the coils helps attain the fast response, high power operation requirements typical of gimbal controlled hardware. The sector motor design configuration of BEI Kimco’s rotary voice coils offers a significant reduction in payload. Since these rotary devices provide torque output over a limited angle of operation instead of torque over a full 360 degrees, like conventional motors, their design allows maximum efficiency for minimum volume and weight.

**Step 1-** Inner axis acceleration torque requirement: Equation (4) can be used to determine the torque needed to accelerate the mirror during the 40 degree excursion. Load (mirror) inertia, actuator coil inertia, and acceleration rate are the parameters required to solve the equation. In the example, the load inertia is given; however, coil inertia and acceleration rate are not provided. The acceleration rate may be determined from the angular displacement requirement and the triangular velocity move profile presented in Figure 1B, as follows:

**( Equation 28 )**

But in a triangular move profile, acceleration occurs during the first half of the move, or, in this case, in 16 mSec-**( Equation 29 )**

Ignoring coil inertia for the time being, the torque required to accelerate the mirror is:**( Equation 30 )**

The torque must be available for deceleration, as well. In addition, the continuous duty operation calls for selection of an actuator with a continuous rating of at least the 18 required oz-in of acceleration torque.

Referring to Table 4, one of the six rotary actuators shown does not meet the 18 oz-in continuous torque requirement. Furthermore, only one of the remaining units meets the ±20° (total of 40°) angular displacement call-out. These conditions facilitate selection. It appears that model RA60-10-002A is the appropriate choice; however, it is now important to go back and check the effect of the RA60-10-002A coil inertia on the overall torque requirement.

The selected actuator has a coil inertia of approx. 8.5 x 〖10〗^(-5) oz 〖Sec〗^2 (not shown in Table 4), about an axis perpendicular to the plane of motion, through the center of the mass in the coil. In this application, the coil will not rotate about its own center of mass. Instead, it will be levered for rotation about an axis parallel to its own axis, two inches away from its axis. Equation (9) may be used to determine the inertia of the coil, relative to the axis of the rotation (i.e., the rotation axis of the mirror):

**( Equation 31 )**

A value considerably higher than initially calculated. The total peak torque, Tα requirement is there for 34 oz-in, including load and friction torque. (The low load & friction torque magnitude is not a significant RMS factor in this continuous peak torque requirement application, as verified by utilizing the RMS torque version of Equation (3).) Using the recommended 20% safety margin, proper actuator selection calls for an actuator with a peak and continuous torque rating of-** **** ( Equation 32 )**

A quick check of Table 4 still indicated proper selection.**Step 2- **Inner axis winding verification:

2.1 Calculation of generated back:**( Equation 33 )**

2.2 Calculation of torque-producing voltage: (Again, assuming VL is about 1 V)**( Equation 34 )**

2.3 Calculation of torque-producing current: (RCOLD = 1.1 ohms)**( Equation 35 )**

2.4 Calculation of maximum available torque at 44 Rad/Sec operation and 12V DC power supply:

**( Equation 36 )**

Conclusion #1: The RA60-10-002A VCA with the catalog winding meets the speed and both peak and continuous torque requirements of the inner axis assembly.**Step 3 - **Outer axis (complete assembly) acceleration torque requirement: As before, it is necessary to estimate the inertia of the load (including the inner axis support structure, the RA60-10-002A actuator, and the mirror) about its center axis. Equation (9) may then be used to estimate the inertia of the load about the outer axis, which is located 1-7/8” away from the center axis of the load. In this example, the engineer estimated the total load inertia, relative to its center axis, at 0.4 oz-in Sec². It should be noted that the weight of the load is 35 oz (17 oz support weight, plus 3.4 oz mirror weight, plus 15 oz RA60-10-002A actuator weight). The inertia about the axis of rotation is:**( Equation 37 )**

The operating speed, using the triangular velocity profile:**( Equation 38 )**

Acceleration rate = (5.0 Rad/Sec)/70 mSec=71 Rad/Sec² Assuming for the moment that the inertia contributed by the outer axis actuator coil is not significant, the total acceleration torque due to inertia is thus:**( Equation 39 )**

Application of the 20% safety margin brings the required torque rating to 1.2 X 50 oz-in = 60 oz-in. It appears that the RA68-12-001A is a likely candidate. Again, we need to check the effect of the coil inertia on the overall torque requirement.

The RA68-12-001A coil has an inertia of approximately 6.5 X 10-4 oz-in Sec2 (not shown in Table 4) about an axis perpendicular to the plane of motion, through the center of mass of the coil. The axis of rotation is at the fulcrum of the coil base, parallel and two inches away from the axis of the coil. The revised coil inertia for the assembly is:**( Equation 40 )**

The revised total acceleration torque is:**( Equation 41 )**

The total peak torque requirement is 60 oz-in. (Again, the low load and friction torque magnitude is not a significant RMS factor in this continuous peak torque requirement application.) Application of the 20% safety margin leads to a selection of an actuator with a peak and continuous torque rating of 72 oz-in and 61 oz-in, respectively.*

*The application described above has been presented in a simplified fashion. Utilization of two inner axis gimbals, located symmetrically about the outer axis gimbal, mitigates any reaction torque and servo effect of operating the inner and outer axis gimbals at the same time.

**Step 4-**Outer axis winding verification:**( Equation 42 )**

Conclusion #2: The RA68-12-001A VCA with the catalog winding meets the speed and torque requirements of the outer axis gimbal assembly.

The data, specifications, and electrical parameters presented in this guide illustrate typical applications, are for reference only and are subject to change without notice. Although efforts have been made to insure the accuracy of the information given, nothing herein is intended or should be construed as a warranty of the performance or design of BEI Kimco. Product and data warranties are described solely in BEI Kimco contractual documents.