Abstract:
An MHD sensor/actuator is provided for generating torque as well as sensing angular displacements around a sense/torque axis. A column of conductive liquid which rotates within a circumferential channel having an inner circumferential surface and outer circumferential surface provides an inertial proof mass, the relative motion of which within the channel generates a torque or represents a sensed displacement about the common axis of the circumferential channel. According to certain embodiments, a cylindrical column of magnets are located coaxially with the circumferential channel to produce a radially oriented magnetic field which is perpendicular to the common axis. According to other embodiments, a magnetic ring is provided coaxially with the circumferential channel to produce a magnetic field in the direction of the common axis.

Description:
GOVERNMENT RIGHTS 
   This invention was made with Government support under contract HQ0006-03-C-0066 awarded by the Missile Defense Agency. The Government has certain rights in the invention. 

   BACKGROUND OF THE INVENTION 
   The present invention relates to a magnetohydrodynamic device (MHD) which can be used as an actuator to enter a torque, or to sense relative rotational motion. 
   MHD devices have been developed and used to sense relative rotational motion of an inertial mass with respect to a case. According to prior U.S. patents by the inventor, including U.S. Pat. Nos. 4,718,276, 5,067,351 and 6,173,611, the motion of a sensor about a rotational axis may be detected as a voltage potential representing displacement, velocity, or acceleration about the axis. As set forth in these prior patents, a static magnetic field is arranged perpendicular to a liquid proof mass such as mercury, enclosed within a cylindrical channel. The cylindrical channel has an inside circumference, bearing one electrode, and an outside circumference bearing a second electrode. Due to rotation of the case about the axis of the liquid mass, a voltage is created across the electrodes which represents the displacement in radians of the mass in response to rotational movement of the cylindrical channel with respect to the liquid mass. By detecting the first differential of the voltage, and the second differential voltage, it is possible to obtain velocity and acceleration values of the imparted rotation. 
   MHD devices can also be operated as a torque producer. By applying a voltage across the channel, a force can be induced between the liquid mass and the channel which provides a torque to the channel vis-à-vis the liquid. 
   The present invention seeks to provide an MHD device which can both sense relative displacements between an internal liquid proof mass, and a channel containing the device, as well as impart a rotational torque between the liquid mass and dowel containing the liquid mass for applications requiring stabilization. This includes an application for providing active torque to cancel disturbances which are incident to a platform which is subject to vibrational forces or jitter. The MHD actuator has the capability of generating a reaction torque due to the heavy inertial fluid within the channel, and can transfer for angular momentum of the channel to a supporting surface to effectively cancel any disturbances to the platform. Applications in which the torque generation may be used for stabilization include inertial reference unit platforms, fast-steering mirrors line of sight controls, beam steering, scanning control, small satellite attitude control and active structural damping. 
   In the application of providing for stabilization, it is not only necessary to generate the required disturbance producing counter torque, but it is also required to sense the disturbances themselves, so that the torque of the appropriate magnitude can be applied to the platform to effectively cancel the sensed disturbances. 
   SUMMARY OF THE INVENTION 
   An MHD sensor/actuator is provided for generating torque as well as sensing angular displacements around a sensing/torque axis. A column of conductive liquid which rotates within a circumferential channel having an inner circumferential surface and outer circumferential surface provides an inertial proof mass, the relative motion of which within the channel represents a sensed displacement about the common axis of the circumferential channel. A cylindrical column of magnets are located coaxially with the circumferential channel to produce a radially oriented magnetic field which is perpendicular to the common axis. First and second contacts are connected to each end of the column of liquid, and the circumferential channel is sealed with first and second end caps. 
   The device can be connected to an electrical DC voltage to apply a current to the channel. The flow of current through one end of the channel to the other will produce a rotational torque between the liquid contained within the channel and the channel. The momentum generated from the torque can be transferred to a surface which supports the channel as a damping torque. 
   Alternatively, instead of applying voltage to the top and bottom ends of the circumferential channel, the voltage generated between the first and second contacts in response to relative motion of the liquid proof mass and circumferential channel may be used to indicate the relative angular velocity between the liquid proof mass and channel. 
   According to a second embodiment, an MHD actuator/sensor includes a conductive liquid which rotates within a sealed circumferential channel, and a magnet ring located coaxially with the circumferential channel to produce a magnetic field which is axially oriented in the direction of the common axis of the circumferential channel and the magnet structure. The circumferential channel and the magnet ring are enclosed within a case. The relative motion of which within the channel represents a sensed angular velocity about the common axis of the circumferential channel. First and second electrical contacts are connected to an inner circumferential member and an outer circumferential member, respectively, of the circumferential channel. 
   The device of the second embodiment can be connected to an electrical DC voltage to produce a current through the channel. The flow of current between the outer circumferential member and the inner circumferential member of the channel will produce a rotational torque between the liquid contained within the channel and the channel. The momentum generated from the torque can be transferred to a surface which supports the channel as a damping force. Alternatively, the device can also be used as a sensor, wherein the voltage generated between the first and second contacts in response to relative motion of the liquid proof mass and circumferential channel may be used to indicate the relative angular velocity between the liquid proof mass and channel. 
   Other features and advantages will become apparent from the following detailed description and drawings. 

   
     DESCRIPTION OF THE FIGURES 
       FIG. 1  illustrates a schematic top view of an MHD actuator/sensor including a liquid proof mass according to one. 
       FIG. 2  is a schematic side section view taken along section A—A of  FIG. 1 . 
       FIG. 3  is a section view of a practical embodiment of the invention. 
       FIG. 4  illustrates the predicted platform angle of a standard platform versus the current applied to the MHD actuator of  FIG. 3  versus frequency. 
       FIG. 5  is a simulation for the device of  FIG. 3 , representing the same test platform angular acceleration versus input current and frequency. 
       FIG. 6  illustrates the magnitude response versus frequency of the device of  FIG. 3  to sensing a rotational angular velocity. 
       FIG. 7  is a predicted angular rate phase response versus frequency of the MHD actuator sensor of  FIG. 3  in a sensor mode. 
       FIG. 8  is a schematic perspective view of an MHD actuator/sensor according to another embodiment. 
       FIG. 9  is a section view of an MHD actuator/sensor according to another embodiment of the invention which is an advancement of the embodiment of  FIG. 8 . 
       FIG. 10  is a section view of a portion of a single cell of a multiple channel MHD actuator/sensor. 
   

   DETAILED DESCRIPTION 
     FIGS. 1 and 2  are section schematic views of a MHD actuator sensor  10  in accordance with one embodiment. A cylindrical channel  12  having an inner circumferential wall  14  and an outer circumferential wall  16  supports a conductive liquid proof mass, such as liquid mercury  18 . The inside and outside of the walls  14 ,  16  are made of insulating material. Walls enclosing opposite ends of the channel  12  include or form electrodes  15 ,  17 . An annular magnet structure  19  surrounds the outer circumference of the cylindrical channel  12 . A casing (not shown) encloses the cylindrical channel  12  and the magnetic structure  19 . 
   The magnet structure  19  generates a DC magnetic field B r , which is radial to the common axis  11  of the channel  12  and magnet structure  19  and passes through the channel  12 . As will be explained, the application of a voltage V from a power source  13  to electrodes  15 ,  17  at each end of the channel  12  produces an axially-oriented current flow I z  through the liquid proof mass  18 . The result of the interaction of the magnetic field B r  and the current I z  is the generation of a torque τ fluid  between the proof mass  18  and the channel  12 . The torque τ fluid  is shown around the axis  11  of the cylindrical channel  12 . The general transmitted torque produced about the axis  11  on the channel  12  and the fluid angular acceleration which results in the torque are expressed as shown in the following equations 1 and 2, with reference to the legend presented in Table 1:
 
τ fluid   =−J   fluid {umlaut over (Θ)} fluid   (1)
 
   
     
       
         
           
             
               
                 
                   
                     Θ 
                     ¨ 
                   
                   fluid 
                 
                 = 
                 
                   
                     
                       υ 
                       
                         h 
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             Θ 
                             . 
                           
                           case 
                         
                         - 
                         
                           
                             Θ 
                             . 
                           
                           fluid 
                         
                       
                       ) 
                     
                   
                   + 
                   
                     
                       
                         - 
                         
                           B 
                           r 
                         
                       
                       ⁢ 
                       
                         I 
                         z 
                       
                     
                     
                       A 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       ρ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       r 
                     
                   
                 
               
             
             
               
                 ( 
                 2 
                 ) 
               
             
           
         
       
     
   
   
     
       
             
           
             
             
           
         
             
               TABLE 1 
             
           
           
             
                 
             
             
               Variables in Equations 1 and 2 
             
           
        
         
             
               Variable 
               Definition 
             
             
                 
             
             
               ν 
               kinematic viscosity (m 2 /s) 
             
             
               h 
               channel thickness (m) = (r o  + r i ) 
             
             
               r 
               rms channel radius (m) = ((r o   2  + r i   2 )/2) 1/2   
             
             
               B r   
               channel flux density (T) 
             
             
               A 
               channel mean cross-section area (m 2 ) = π (r o   2  − r i   2 ) 
             
             
               ρ 
               fluid density (kg/m 3 ) 
             
             
               {umlaut over (Θ)} fluid   
               fluid angular acceleration (rad/s 2 ) 
             
             
               {dot over (Θ)} fluid   
               fluid velocity (rad/s) 
             
             
               {dot over (Θ)} case   
               actuator case velocity (rad/s) 
             
             
               J fluid   
               fluid mass moment of inertia (kg-m 2 ) 
             
             
               τ fluid   
               transmitted torque (N-m) 
             
             
               I z   
               current (A) 
             
             
               L 
               channel length (m) 
             
             
                 
             
           
        
       
     
   
   The acceleration of the fluid in the channels is based on the generally known MHD equations which derives a cross-product of the electrical current I z  and the applied radially oriented magnetic field B r . The above equations quantify the generated torque about the axis on the channel with respect to the mercury proof mass. The angular momentum increase of the fluid induces a torque on the actuator case, and on any structure such as a platform to be stabilized in which the actuator is mounted. Thus, by selectively applying the voltage V to the actuator/sensor  10 , the actuator/sensor  10  can be used to counteract vibrations of a device to which the actuator/sensor  10  is mounted, such as the vibrations of a platform (represented by τ platform  in  FIG. 1 ). The device  10  also operates as a sensor of angular motion about the axis  11 . When the channel  12  rotates, the inertial proof mass  18  tends to stay at rest. In response to rotation of the channel  12  with respect to the liquid proof mass  18  about the axis  11 , the magnetic field B R  generates, via MHD effects, a voltage V across the electrodes  15  and  17 . With reference to Table 1, this voltage may be represented as:
 
 V=B   r   L ({dot over (Θ)} fluid −{dot over (Θ)} case ) r  
 
   The actuator represented by  FIGS. 1 and 2  is designed for applications such as stabilization of an Inertial Reference Unit (IRU) platform. The required torque for generating the required angular displacements of the platform is based on the moment of inertia of the IRU stable platform. Using assumed values of the moment of inertia for the rotation degrees of freedom of, say, 0.015 Kg M 2 , an angular acceleration profile can be generated that will allow the determination of the output torque versus input current frequency response of the actuator to be determined. 
     FIG. 3  shows a practical MHD actuator/sensor  100  based on the embodiment illustrated in  FIGS. 1 and 2 , wherein a radial magnetic field and an axial current are generated. The actuator/sensor  100  includes an insulated inner cylinder  102  having a cylindrical axis  110  located along a sensing/force generating axis of the device  100 . The inner cylinder  102  is made of first and second metal center bosses  104  that include threaded axial bore holes  105 . The outer cylindrical surfaces  108  of the bosses  104  may be covered with heat shrink insulation to insulate the bosses. The axial ends  109  of the bosses  104  are free of insulating material. The bosses  104  are axially attached to and insulated from each other with an insulating threaded member or ceramic screw  107  that is threaded into the bore hole  105  of each boss  104 . The bosses  104  are and are further insulated from one another by an insulating member  106 , such as a ceramic washer, which is disposed between the bosses  104  in contact with an inner axial end of each boss  104 . 
   The outer surface  108  of the inner cylinder  102  forms the inner circumferential surface of a cylindrical fluid channel  112  which contains a liquid proof mass  114 , such as liquid mercury. A cylindrical magnet structure  116  forms an outer circumference of the channel  112 . The magnet structure  116  may include first and second magnets  118 , a magnet holder  120  located between the magnet(s)  118  and the liquid proof mass  114 , and a magnet cover  122  surrounding the outer circumference of the magnet(s)  118 . Axial ends of the channel  112  are covered by first and second channel covers  124  having holes  126  that are aligned with through-holes  105  in the center bosses  104 . The channel covers  124  are made of an insulating material. Electrical contacts such as conductive washers  111  are fitted between the axial ends of the bosses  104  and the channel covers  124 , thereby providing small regions of electrical conductivity between the bosses  104  and the liquid proof mass  114 . 
   A pair of end caps  132  abut the channel covers  124 . The end caps  132  include holes  134 . A metallic case  128  surrounds the magnet structure, and includes first and second clearance holes  130  at axial ends thereof. A pair of electrodes such as threaded rods  136  extend through the clearance holes  130 , holes  134  and holes  126 , and are threaded into the bore holes  105  of the center bosses  104 . Fasteners such as nuts  138  are provided on the electrodes  136  to force the end caps  132  against the channel covers  124  and to thereby force the channel covers against the insulated cylinder  102  as the nuts  138  are turned down on the electrodes  136 . In this way, the fluid channel  112  is effectively sealed and the electrodes  136  can be maintained in secure electrical contact with the bosses  104 . 
   The device  100  is provided with circuitry for generating and sensing torque. The circuitry includes a power source  140  mounted to the case  128  and leads  142  extending from the power source  140  to the electrodes  136  within the case  128 . The power source may be, for example, a power op-amp. A cover  144  is provided to cover the power source  140 . 
   In actuator mode, a voltage applied by the power source/op-amp  140  causes the fluid  114  to rotate about the inner cylinder  102 , thereby generating a torque that acts on the case  128  and the device to which the actuator  100  is mounted. In sensor mode, rotation of the cylindrical channel  112  generates a voltage. The op-amp  140  amplifies the voltage signal produced by the contacts  136 , thereby providing an indication of the torque applied to the device to which the sensor  100  is mounted. 
   An experimental device based on the model of  FIG. 3  was constructed according to the design parameters listed in the following Table 3. 
                                 TABLE 3                   Design Parameters for MHD Actuator of FIG. 3            Parameter   Value   Units               Mercury Channel Length L   0.0274   meters       Mercury Channel Thickness h   0.002   meters       Radial Flux Density B r     0.22   Tesla       RMS Channel Radius, r RMS     0.0066   meters       Mercury Mass Moment of Inertia   1.056e-6   kg-m 2         (MOI)       Torque Scale Factor K t *   3.98e-5   Newton-meters/Amp       Max Torque for 15A max current   5.97e-4   Newton-meters       using the Apex PA13A Power       Amp       Power Dissipation @ Peak Torque   0.0765   Watt       Rotational Actuator Constant   0.0022   Newton-meters/(Watt) 1/2         (Torque) K RA                 *Torque Scale Factor = B r  L r rms  = (0.22 T) (0.0274 m) (0.0066 m) = 3.98e-5 Nm/Amp. A maximum torque of about 6e-4 Newton-meters can be produced using the maximum current of 15A for the Apex PA13A. Higher torques could also be produced by higher current.            
The experimental actuator/sensor vice was attached to an MHD Stable Reference Internal Reference Unit platform (MIRU, a controlled platform for providing an optical reference) to evaluate the performance of the actuator/sensor. An ARS-12A Angular Displacement Sensor (s/n F014, scale factor=100,000 V/rad) was also mounted to the platform to sense the angular displacement of the platform. The actuator/sensor was mounted with the torque axis aligned with the sense axis of the ARS-12A Angular Displacement Sensor.
 
   The torque produced by the actuator/sensor was then indirectly measured using the MIRU platform knowing the flexure torsional spring constant and damping, and the mass moment of inertia about the rotational axis and the angular motion produced as measured by the ARS-12A. The angular displacement output versus current input was measured for the EDM as plotted in  FIG. 4 . This can also be readily converted to the angular acceleration output versus current input to the actuator/sensor, plotted in  FIG. 5 , by simply multiplying every point in the displacement frequency response by (2pf) 2 . The EDM torque scale factor can be indirectly calculated by knowing the spring constant and the moment of inertia (MOI) of the platform about the axis of rotation. The response is based of the estimated mass moment of inertia about the rotational axes of the MIRU platform with the ARS-12A and EDM mounted of I x,y =0.0012 kgm 2  and a flexure rotational spring constant K θ  of 213 rad/Nm. The natural frequency f n  of the MIRU platform was measured at 67 Hz and is defined as f n =(K θ /I x,y ) 1/2 /(2p). The rotational damping coefficient of the MIRU was not needed to calculate the torque but was estimated at B θ= 0.015 (rad/s)/N−m. Based on the MIRU platform dynamics the torque constant was measured to be very close to the predicted torque of 3.95e−4 N−m/Amp. The second line overlaid on the graphs of  FIGS. 4 and 5  is the estimated MIRU platform response for an MHD actuator/sensor with a torque constant of 3.95e−4 N−m/A. 
   The actuator/sensor was also characterized for the rotational angular rate “sensing” function with regard to disturbances applied to the MIRU platform.  FIG. 6  illustrates the measured magnitude response versus the estimated, or modeled, response.  FIG. 7  illustrates the measured phase response compared to the modeled phase response for the actuator/sensor. The magnitude shown is the unamplified angular rate response. 
   As shown in  FIGS. 4–7 , by modeling and testing the torqueing and sensing functions of an MHD actuator/sensor, MHD sensors/actuators can be constructed with the parameters needed for successful operation in a given application 
     FIG. 8  is a schematic perspective view of a MHD actuator sensor  20  according to another embodiment. The actuator/sensor  20  includes a cylindrical channel  22  supporting a conductive liquid proof mass  28  (i.e., mercury). The channel  22  includes an inner cylindrical wall  24  which includes or forms a first electrode and an outer cylindrical electrode  26  which includes or is a second electrode. The channel  22  is closed at its ends by insulating walls  25  and  27 . A magnet ring  29  is arranged coaxial with the channel  22  along a common axis  21 . The channel  22  and magnet ring  29  are enclosed in a casing (not shown). Applying a voltage V from a power source  23  across electrodes  24  and  26  generates a radial current I r . The magnetic ring  29  generates an axial magnetic field B z , which interacts with the current I r  to cause the fluid  28  to rotate, thereby applying a torque τ fluid  to the actuator case (not shown). Thus, the actuator/sensor  20  may have the same practical applications as the actuator/sensor of the previous embodiment. 
   The general transmitted torque produced about the axis  21  on the channel  22  and the fluid angular acceleration which results in the torque are expressed as shown in the following equations 3 and 4, with reference to the legend presented in Table 3:
 
τ fluid   =−J   fluid {umlaut over (Θ)} fluid   (3)
 
   
     
       
         
           
             
               
                 
                   
                     Θ 
                     ¨ 
                   
                   fluid 
                 
                 = 
                 
                   
                     
                       υ 
                       
                         h 
                         2 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             Θ 
                             . 
                           
                           case 
                         
                         - 
                         
                           
                             Θ 
                             . 
                           
                           fluid 
                         
                       
                       ) 
                     
                   
                   + 
                   
                     
                       
                         B 
                         z 
                       
                       ⁢ 
                       
                         I 
                         r 
                       
                     
                     
                       A 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       ρ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       r 
                     
                   
                 
               
             
             
               
                 ( 
                 4 
                 ) 
               
             
           
         
       
     
   
   
     
       
             
           
             
             
           
         
             
               TABLE 3 
             
           
           
             
                 
             
             
               Variables in Equations 3 and 4 
             
           
        
         
             
               Variable 
               Definition 
             
             
                 
             
             
               ν 
               kinematic viscosity (m 2 /s) 
             
             
               h 
               channel thickness (m) = (r o  + r i ) 
             
             
               r 
               rms channel radius (m) = ((r o   2  + r i   2 )/2) 1/2   
             
             
               B z   
               channel flux density (T) 
             
             
               A 
               channel mean cross-section area (m 2 ) = π (r o   2  − r i   2 ) 
             
             
               ρ 
               fluid density (kg/m 3 ) 
             
             
               {umlaut over (Θ)} fluid   
               fluid angular acceleration (rad/s 2 ) 
             
             
               {dot over (Θ)} fluid   
               fluid velocity (rad/s) 
             
             
               {dot over (Θ)} case   
               actuator case velocity (rad/s) 
             
             
               J fluid   
               fluid mass moment of inertia (kg-m 2 ) 
             
             
               τ fluid   
               transmitted torque (N-m) 
             
             
               I r   
               current (A) 
             
             
               W 
               channel width (m) = (r o  − r i ) 
             
             
                 
             
           
        
       
     
   
   The device  20  also operates as a sensor of angular motion about the axis  21 . When the channel  22  rotates, the liquid mass  28  tends to stay at rest. The magnetic field B z  generates via MHD effects a voltage V across the electrodes  24  and  26 . In response to rotation of the channel  22  with respect to the liquid proof mass  28  about the axis  21 , the magnetic field B z  generates, via MHD effects, a voltage V across the electrodes  24  and  26 . Referring to Table 3, this voltage may be represented as:
 
 V=B   z   W ({dot over (Θ)} fluid −{dot over (Θ)} case ) r  
 
     FIG. 9  shows a more advanced, multiple-channel MHD actuator/sensor  200  derived from the embodiment of  FIG. 8 . As in the embodiment of  FIG. 8 , the actuator/sensor  200  has an axially-oriented magnetic field. As shown in  FIG. 9 , the sensor/actuator  200  includes a first MHD unit  210 , a second MHD unit  220 , a third MHD unit  210  identical to the first MHD unit, and a fourth MHD unit  230 . The units  210 ,  220  and  230  are stacked in a row and fastened together. 
   Each MHD unit  210 ,  220 ,  230  includes case  202  having an inner wall member  204  extending along the center axis  201  of the device and an outer circumferential wall member  206  that is spaced from and concentric with the inner wall member  204 . Three MHD channels, each including a magnet ring  242  and an annular fluid channel  244  positioned coaxial with magnet ring  242 , are located within the case  202  such that they are stacked in a row around the inner wall member  204  and inside the outer circumferential wall member  206 . As in previous embodiments, the annular fluid channel  244  contains a liquid proof mass  218 , such as liquid mercury. The case  202  also includes end caps  203  enclosing the axial ends of the MHD unit  210 ,  220 ,  230 . 
   MHD units  210 ,  220  and  230  are similar in structure, except that they employ the MHD channels with the magnet rings  242  in different polar orientations. More specifically, the magnet rings  242  in units  210  are arranged such that their polarities are opposite the polarities of the magnet rings  242  in init  220 . By arranging units  210  and unit  220  with opposite polarities, the overall magnetic dipole moment of the actuator/sensor  200  is reduced. Unit  230  includes magnetic rings  242  of varying polar orientation. 
   Within a given unit  210 ,  220 ,  230 , the MHD channels may be connected to each other in series and connected to circuitry including a power source, such as a power op-amp (not shown), by various arrangements of electrodes  252 ,  254 ,  256  contacting the inner circumferential walls  246  and the outer circumferential walls  248  of the annular fluid channels  244 . Electrodes  252  extend between the inner circumferential wall  246  of one fluid channel and the outer circumferential channel  248  of another, adjacent fluid channel  246 , thereby connecting adjacent MHD channels in series. The orientation and number of electrodes used will vary depending on the orientation of the magnet rings  242 , the number of magnet rings  242  desired to be coupled together and the and the desired response of the actuator/sensor  200 . 
   Insulating members  262 ,  264 ,  266  are provided to insulate the magnet rings  242 , fluid channels  244 , and electrodes  252 ,  254 ,  256  from each other, as needed. Additional insulating members may be provided to insulate the MHD unit from the case  202 . 
   The MHD units  210 ,  220  and  230  are electrically connected in series. The result is a single actuator/sensor with increased capabilities for generating torque and sensing disturbances. Circuitry (not shown) may be connected to read or apply a voltage across selected electrodes  252 ,  254 ,  256  in the device  200  and thereby operate the device as an actuator and/or sensor for applying a torque or sensing a torque about the axis  201 . 
   Estimated performance parameters for the twelve-channel MHD sensor/actuator embodiment are provided in Table 4 with the key parameters being the torque scale factor K t  of 2.12e−3 N−m/A, and the rotational actuator constant K RA  of 0.046 N−m/W 1/2 . The embodiment of  FIG. 9  exhibits a torque scale factor that is 53 times higher with a rotational actuator constant K RA  that is 21 times better than the model based on the embodiment of  FIG. 3 . This is predominantly due to the improved internal design of the embodiment of  FIG. 9 . 
   
     
       
             
           
             
             
             
           
         
             
               TABLE 4 
             
           
           
             
                 
             
             
               Enhanced MHD Actuator Design Parameters 
             
           
        
         
             
               Parameter 
               Value 
               Units 
             
             
                 
             
             
               Actuator Parameters 
                 
                 
             
             
               Mercury Channel Width; L = 12*(r o − 
               0.243 
               meters 
             
             
               r i ) 
             
             
               Mercury Channel Thickness; h 
               0.001 
               meters 
             
             
               Axial Flux Density Bz 
               0.50 
               Tesla 
             
             
               RMS Channel Radius, r RMS   
               0.0175 
               meters 
             
             
               Mercury Mass Moment of Inertia 
               4.47e-5 
               kg-m 2   
             
             
               (MOI) 
             
             
               Actuator Torque Parameters 
             
             
               Torque Scale Factor K t * 
               2.12e-3 
               Newton-meter/Amp 
             
             
               Current Required for 1.5 rad/s 2   
               35.9 
               Amperes 
             
             
               For AIRU (Ix,y = 0.0508 kg-m 2 ) 
             
             
               Channel Resistance 
               0.0021 
               Ohm 
             
             
               Rotational Actuator Constant K RA   
               0.26 
               Newton-meters/(Watt) 1/2   
             
             
               Rate Sensor Parameters 
             
             
               Angular Rate Scale Factor** 
               2.12e-3 
               Volts/(radian/sec) 
             
             
               Est. Noise Equivalent Angle (NEA, 
               200 
               Nanoradians RMS 
             
             
               1-1 kHz BW) 
             
             
                 
             
             
               *Torque Scale Factor = B z  W r RMS  = (0.50 T) (0.243 m) (0.0175 m) = 2.12e-3 N-m/Amp 
             
             
               **Angular Rate Scale Factor = B z  W r RMS  = (0.50 T) (0.243 m) (0.0175 m) = 2.12e-3 Volts/(radian/s) 
             
           
        
       
     
   
   The embodiment of  FIG. 9  shows only one possible configuration for a multiple-channel actuator/sensor. Many other configurations are possible, including actuators/sensors with any number of MHD channels. Additionally, each MHD unit could be configured to include less than three MHD channels or more than three MHD channels. 
     FIG. 10  shows a section view of one half of an MHD unit  340  according to another embodiment, wherein reference numerals shared with  FIG. 9  indicate similar components. Unit  340  shows a configuration that uses one MHD channel  340   a  as a sensor and two other MHD channels  340   b ,  340   c  connected in series as a torquer. The unit  340  could be employed in a device similar to the one shown in  FIG. 9 . 
   MHD channel  340   a  is electrically isolated from channels  340   b  and  340   c  and includes a pair of electrodes  352  and  354  in contact with the outer circumferential wall  248  and the inner circumferential wall  246 , respectively, of an annular fluid channel  244 . Electrodes  352  and  354  are provided with positive and negative leads  353  and  355 , respectively. As the MHD channel  340   a  is isolated from the MHD channels  340   b ,  340   c , it can be used as a sensor independently of channels  340   b  and  340   c.    
   MHD channels  340   b  and  340   c  are connected in series by an electrode  252 . The electrode  252  extends between the inner circumferential wall  246  of the annular fluid channel in MHD channel  340   b  and the outer circumferential wall  248  of the annular fluid channel in MHD channel  340   c . An electrode  254  in contact with the outer circumferential wall  248  of the annular fluid channel in MHD channel  340   b  is provided with a positive lead  255 . An electrode  256  in contact with the inner circumferential wall  246  of the annular fluid channel in MHD channel  340   c  is provided with a negative lead  257 . Thus, the MHD channels  340   b  and  340   c  may receive a voltage applied across the leads  255  and  257  and operate as a torque applying actuator while the MHD unit  340   a  acts as a sensor. 
   The foregoing description of the invention illustrates and describes the present invention. Additionally, the disclosure shows and describes only selected preferred embodiments of the invention, but it is to be understood that the invention is capable of use in various other combinations, modifications, and environments and is capable of changes or modifications within the scope of the inventive concept as expressed herein, commensurate with the above teachings, and/or within the skill or knowledge of the relevant art. 
   The embodiments described hereinabove are further intended to explain best modes known of practicing the invention and to enable others skilled in the art to utilize the invention in such, or other, embodiments and with the various modifications required by the particular applications or uses of the invention. Accordingly, the description is not intended to limit the invention to the form disclosed herein. Also, it is intended that the appended claims be construed to include alternative embodiments, not explicitly defined in the detailed description.