5.2 Microactuators
Electrostatic Actuation
The most widely utilized multicomponent microactuators are those based upon electrostatic transduc-tion. These actuators can also be regarded as a variable capacitance type, since they operate in an analogous mode to variable reluctance type electromagnetic actuators (e.g., variable reluctance stepper motors). Electrostatic actuators have been developed in both linear and rotary forms. The two most common configurations of the linear type of electrostatic actuators are the normal-drive and tangential or comb-drive types, which are illustrated in Figs. 5.1 and 5.2, respectively. Note that both actuators are suspended by flexures, and thus the output force is equal to the electrostatic actuation force minus the elastic force required to deflect the flexure suspension. The normal-drive type of electrostatic microac-tuator operates in a similar fashion to a condenser microphone. In this type of drive configuration, the actuation force is given by
where A is the total area of the parallel plates, ε is the permittivity of air, v is the voltage across the plates, and x is the plate separation. The actuation force of the comb-drive configuration is given by
where w is the width of the plates, ε is the permittivity of air, v is the voltage across the plates, and d is the plate separation. Dimensional examination of both relations indicates that force is independent of geometric and kinematic scaling, that is, for an electrostatic actuator that is geometrically and kinemat-ically reduced by a factor of N, the force produced by that actuator will be the same. Since forces associated with most other physical phenomena are significantly reduced at small scales, micro-scale electrostatic forces become significant relative to other forces. Such an observation is clearly demonstrated by the fact that all intermolecular forces are electrostatic in origin, and thus the strength of all materials is a result of electrostatic forces [6].
The maximum achievable stroke for normal configuration actuators is limited by the elastic region of the flexure suspension and additionally by the dependence of actuation force on plate separation, as given by the above stated equations. According to Fearing, a typical stroke for a surface micromachined normal config-uration actuator is on the order of a couple of microns. The achievable displacement can be increased by forming a stack of normal-configuration electrostatic actuators in series, as proposed by Bobbio et al. [8,9].
The typical stroke of a surface micromachined comb actuator is on the order of a few microns, though sometimes less. The maximum achievable stroke in a comb drive is limited primarily by the mechanics of the flexure suspension. The suspension should be compliant along the direction of actuation to enable increased displacement, but must be stiff orthogonal to this direction to avoid parallel plate contact due to misalignment. These modes of behavior are unfortunately coupled, so that increased compliance along the direction of motion entails a corresponding increase in the orthogonal direction. The net effect is that increased displacement requires increased plate separation, which results in decreased overall force.
The most common configurations of rotary electrostatic actuators are the variable capacitance motor and the wobble or harmonic drive motor, which are illustrated in Figs. 5.3 and 5.4, respectively. Both motors operate in a similar manner to the comb-drive linear actuator. The variable capacitance motor is characterized by high-speed low-torque operation. Useful levels of torque for most applications there-fore require some form of significant micromechanical transmission, which do not presently exist. The rotor of the wobble motor operates by rolling along the stator, which provides an inherent harmonic-drive-type transmission and thus a significant transmission ratio (on the order of several hundred times). Note that the rotor must be well insulated to roll along the stator without electrical contact. The drawback to this approach is that the rotor motion is not concentric with respect to the stator, which makes the already difficult problem of coupling a load to a micro-shaft even more difficult.
Examples of normal type linear electrostatic actuators are those by Bobbio et al. [8,9] and Yamaguchi et al. [10]. Examples of comb-drive electrostatic actuators are those by Kim et al. [11] and Matsubara et al. [12], and a larger-scale variation by Niino et al. [13]. Examples of variable capacitance rotary elec-trostatic motors are those by Huang et al. [14], Mehragany et al. [15], and Trimmer and Gabriel [16].
Examples of harmonic-drive motors are those by Mehragany et al. [17,18], Price et al. [19], Trimmer and Jebens [20,21], and Furuhata et al. [22]. Electrostatic microactuators remain a subject of research interest and development, and as such are not yet available on the general commercial market.
Electromagnetic Actuation
Electromagnetic actuation is not as omnipresent at the micro-scale as at the conventional-scale. This probably is due in part to early skepticism regarding the scaling of magnetic forces, and in part to the fabrication difficulty in replicating conventional-scale designs. Most electromagnetic transduction is based upon a current carrying conductor in a magnetic field, which is described by the Lorentz equation:
dF = Idl xB
where F is the force on the conductor, I is the current in the conductor, l is the length of the conductor, and B is the magnetic flux density. In this relation, the magnetic flux density is an intensive variable and thus (for a given material) does not change with scale. Scaling of current, however, is not as simple. The resistance of wire is given by
where ρ is the resistivity of the wire (an intensive variable), l is the length, and A the cross-sectional area. If a wire is geometrically decreased in size by a factor of N, its resistance will increase by a factor of N. Since the power dissipated in the wire is I2R, assuming the current remains constant implies that the power dissipated in the geometrically smaller wire will increase by a factor of N. Assuming the maximum power dissipation for a given wire is determined by the surface area of the wire, a wire that is smaller by a factor of N will be able to dissipate a factor of N2 less power. Constant current is therefore a poor assumption. A better assumption is that maximum current is limited by maximum power dissipation, which is assumed to depend upon surface area of the wire. Since a wire smaller by a factor of N can dissipate a factor of N2 less power, the current in the smaller conductor would have to be reduced by a factor of N3/2. Incorporating this into the scaling of the Lorentz equation, an electromagnetic actuator that is geometrically smaller by a factor of N would exert a force that is smaller by a factor of N5/2. Trimmer and Jebens have conducted a similar analysis, and demonstrated that electromagnetic forces scale as N2 when assuming constant temperature rise in the wire, N5/2 when assuming constant heat (power) flow (as previously described), and N3 when assuming constant current density [23,24]. In any of these cases, the scaling of electromagnetic forces is not nearly as favorable as the scaling of electrostatic forces. Despite this, electromagnetic actuation still offers utility in microactuation, and most likely scales more favorably than does inertial or gravitational forces.
Lorentz-type approaches to microactuation utilize surface micromachined micro-coils, such as the one illustrated in Fig. 5.5. One configuration of this approach is represented by the actuator of Inoue et al. [25],
FIGURE 5.6 Microcoil array for planar positioning of a permanent micromagnet, as described by Inoue et al. [25]. Each coil produces a field, which can either attract or repel the permanent magnet, as determined by the direction of current. The magnet does not levitate, but rather slides on the insulated surface.
which utilizes current control in an array of microcoils to position a permanent micro-magnet in a plane, as illustrated in Fig. 5.6. Another Lorentz-type approach is illustrated by the actuator of Liu et al. [26], which utilizes current control of a cantilevered microcoil flap in a fixed external magnetic field to effect deflection of the flap, as shown in Fig. 5.7. Liu reported deflections up to 500 µm and a bandwidth of approximately 1000 Hz [26]. Other examples of Lorentz-type nonrotary actuators are those by Shinozawa et al. [27], Wagner and Benecke [28], and Yanagisawa et al. [29]. A purely magnetic approach (i.e., not fundamentally electromagnetic) is the work of Judy et al. [30], which in essence manipulates a flexure-suspended permanent micromagnet by controlling an external magnetic field.
Ahn et al. [31] and Guckel et al. [32] have both demonstrated planar rotary variable-reluctance type electromagnetic micromotors. A variable reluctance approach is advantageous because the rotor does not require commutation and need not be magnetic. The motor of Ahn et al. incorporates a 12-pole stator and 10-pole rotor, while the motor of Guckel et al. utilizes a 6-pole stator and 4-pole rotor. Both incorporate rotors of approximately 500 µm diameter. Guckel reports (no load) rotor speeds above 30,000 rev/min, and Ahn estimates maximum stall torque at 1.2 µN m. As with electrostatic microactuators, microfabricated electromagnetic actuators likewise remain a subject of research interest and development and as such are not yet available on the general commercial market.