Abstract:
An element that moves resonantly has its resonant frequency dynamically tuned to a desired frequency by two components that cooperate via magnetic fields, one component being mounted for motion with the moving element.

Description:
BACKGROUND OF THE INVENTION 
     This invention relates to devices having a moving element characterized by resonant motion. Typically, such a device has a characteristic resonant frequency based on a spring constant and on the inertia of the moving element. 
     It is known to tune the resonant frequency of such a device by, e.g., adding mass or adjusting the spring constant of the spring element. 
     SUMMARY OF THE INVENTION 
     The invention is a device having an element characterized by resonant motion wherein the frequency of the resonant motion is tunable dynamically while the device is in motion. 
     As a result, the frequency of motion can be tuned to correspond to the frequency of motion of another resonant device, thereby keeping them synchronized. 
     Other features and advantages will become apparent from the following description of the preferred embodiment, and from the claims. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     We first briefly describe the drawings. 
     DRAWINGS 
     FIG. 1 is an isometric schematic view of a tunable resonant device. 
     FIG. 2 is an isometric view, exploded, of the tunable element of the device of FIG. 1. 
     FIGS. 3, 4 are diagrammatic end views of the tunable element of the device of FIG. 1, in two different angular positions, respectively. 
     FIG. 5 is an isometric view of the rotor and stator of the tunable portion of the resonant device. 
     FIG. 6 shows an alternative embodiment of FIG. 2. 
     FIG. 7 shows a set of magnetization curves for neodymium iron boron. 
     FIG. 7A shows a set of magnetization curves for samarium-cobalt. 
     FIG. 8 is a diagrammatic view of the tunable device of FIG. 1 connected to a controller and another scanner. 
    
    
     STRUCTURE AND OPERATION 
     Referring to FIG. 1, a tunable resonant scanner 10 includes a rotatable mechanical suspension 12 (e.g., a flexural suspension of the kind available under the name Flexure Bearings from Bendix Corp.) which holds an optical element (not shown) for scanning a beam 14. The axis of rotation of suspension 12 is colinear with a shaft 16 that is driven by a conventional rotating actuator 18 (e.g., such as is disclosed in U.S. Pat. No. 4,090,112 and U.S. Pat. No. 4,076,998, incorporated herein by reference). Actuator 18 includes angular position or velocity sensors (not shown) that enable operation of suspension 12 and actuator 18 as either a directly driven, or a feedback controlled resonant system 20. System 20, like all resonant systems, has a characteristic resonant frequency of operation based on the inertia (I) of its moving elements and the spring constant (K) of the suspension 12. 
     In order to maintain or track a selected operating resonant frequency, scanner 10 is provided with a resonance tuner 22. The tuner establishes a selectable degree of shift in the spring rate of the system, thus enabling continuous, dynamic tuning of the resonant frequency. Tuner 22 is tied to suspension 12 by a rotating shaft 24, colinear with shaft 16. 
     Referring to FIG. 2, within tuner 22, shaft 24 is attached to a co-axially located cylindrical permanent magnet 26 having its magnetization oriented along a diameter perpendicular to the axis of rotation 28. Magnet 26 is made from a strongly anisotropic material with high coercive force, e.g., a rare earth. 
     A hollow, low carbon steel cylindrical shell 30 concentrically surrounds magnet 26 and is held in a fixed rotational position relative to suspension 12. (In FIG. 2, shell 30 is shown pulled away from the magnet.) One of its functions is to enhance the magnetic field in the coil region. 
     Two coils 32, 34 respectively lie entirely within the North (N) and South (S) magnetic fields of magnet 26. 
     Referring to FIG. 3, when magnet 26 is in its central rotational position (corresponding to the central rotational position of suspension 12), the two segments of coil 32 evenly straddle the N pole, and the two segments of coil 34 evenly straddle the S pole, with angles a all being approximately 45° . Coils 32, 34 are both attached to the inner wall of shell 30. 
     The magnetic field (B) in the air gap 40 between magnet 26 and shell 30 at the location of a segment 44 of coil 32 has a value 
     
         B=K B.sub.r cos θ                                    (1) 
    
     that depends on the angle 0 between the axis of the magnet and the diameter on which segment 44 lies (i.e. 45° ) B 4  is a constant residual inductance of magnet 26, and K is a non-dimensional constant (typically between 0.5 and 1) that depends on the geometry and particular magnetic material chosen, as well as the conditions of shell 30. 
     Referring to FIGS. 5, 7, the derivation of equation (1) is as follows: 
     The magnetic properties of anisotropic magnet 26 at a typical operating range can be approximated by 
     
         B.sub.m =-H.sub.m B.sub.r /H.sub.c +B.sub.r                (2) 
    
     where B m  is the induction, H m  is the field intensity, B r  is the residual inductance, and H c  is the coercive force. 
     Applying Ampere&#39;s Law, ∫H.dl=NI along path q-r-s-t of FIG. 5, assuming no currents are present, yields: 
     
         H.sub.a 2.g.F+H.sub.m.d·cos θ=0             (3) 
    
     where H a  is the magnetic field intensity in the air gap 40, d is the diameter of magnet 26, and F is an experimental constant with a value of, e.g., 1.3. 
     Gauss&#39;s law ∫B.dA=0 can be applied to the elemental axial surface of the volume defined by the points a, a&#39;, p, p&#39;, n, n&#39;, e, e&#39; where the material is sufficiently anisotropic that the field crosses only the boundaries of the surface a a&#39; p p&#39; and the surface e e. n n&#39;. This yields: 
     
         B.sub.m.dA.sub.m =B.sub.a.dA.sub.a                         (4) 
    
     where subscript &#34;a&#34; refers at section nn&#39;, pp&#39; to the air gap and subscript &#34;m&#34; refers to the magnet material. Because dA m  =dA a .cos θ, equation (4) becomes 
     
         B.sub.m.cos θ=B.sub.a.                               (5) 
    
     In the air gap, 
     
         B.sub.a =μH.sub.a,                                      (6) 
    
     where μ is the permeability of air. 
     Equations (2) and (5) combine to yield: 
     
         B.sub.a /cos θ=B.sub.r (1-H.sub.m /H.sub.c),         (7) 
    
     and equations (3) and (6) combine to yield 
     
         2gF B.sub.a /μ+H.sub.m.dcos θ=0                   (8) 
    
     Equations (7) and (8) simplify to 
     
         B.sub.a =B.sub.r.cosθ/(1+B.sub.r /μH.sub.c.2 gF/d) (9) 
    
     Most rare earth magnets have B r  ≃H c  and if g/d is small, typically less than 0.3, equation (9) simplifies to 
     
         B.sub.a =K.B.sub.r.cos θ,                            (10) 
    
     where 0.5&lt;K&lt;1 
     the same as equation (1). 
     Referring to FIG. 4, if magnet 26 rotates by an angle γ relative to coils 32 and 34, the field (B u ) at segment μ of coil 32 is derived from equation (1) where θ=45° +γ. 
     This simplifies to: 
     
         B.sub.u =0.707 K B.sub.r (cos γ-sin γ)         (11) 
    
     and similarly the field B v  at segment v is: 
     
         B.sub.v =0.707 K B.sub.r (cos γ=sin γ)         (12) 
    
     The resulting torque (T) on coil 32 having N turns of wire, from a current I, is derived from Lorenz forces. Noting that forces at segments u and v are in opposition because the current flows in opposite directions in the two halves of coil 32, we find that 
     
         T=0.707 K B.sub.r L N I d (sin γ)                    (13) 
    
     where L is the length of the segment and d is twice the radius where the coil segment is located, and approximately the diameter of the magnet. For small angles, equation (13) yields approximately: 
     
         T=0.707 K B.sub.r L N I d γ                          (14) 
    
     As coil 32 is attached to the shell 30, T is also the torque acting upon the frame of scanner 10, which is normally held fixed. Consequently an equal torque of opposite sign is exerted on magnet 26 and hence on shaft 24. 
     Equation 14 is the expression of a spring where the value of the spring constant is controlled by the current (I) in coil 32. The equivalent torque constant for the two coil device (including coil 34) is: 
     
         T/γ=1.414 K B.sub.r L N I d                          (15) 
    
     For example, in a specific scanner with a 200 Hz resonant frequency, an armature with total inertia of 2.5 gm-cm 2 , and a suspension with a spring constant of 3,790,000 dy-cm/rad, the tuner could have the following parameters: 
     
         d=0 .9 cm 
    
     
         g=0 .4 cm 
    
     
         N=175 turns/coil 
    
     
         L=1 cm 
    
     
         B.sub.r =1.1 tesla 
    
     
         K=0.5, approximately 
    
     The calculated value of the magnetic spring with a current of 0.5 ampere is 61.10 -4  N-m/rad or 61,000 dy-cm/rad or 1.6% of the suspension&#39;s spring constant. This should result in a tunable resonant frequency range of approximately 0.8% of the reference frequency or 1.6 Hz. As the sign of the control spring is dependent on the current polarity, it can add or subtract to the mechanical spring. Therefore within the confines of a±0.5 amp. control current, the total tunable frequency range is doubled, 1.6% or 3.2 Hz. This prediction comes very close to the measured value of 3.43 Hz. 
     Other embodiments are within the following claims. For example, because torque is strongly dependent upon the nonuniformity of the magnetic field in the area where the coils straight segments are located, a gap region with a magnetic field which is a stronger function of angular position may be created. This may be especially useful when the total angle of rotation is limited, and can be achieved in various ways, e.g., by shaping the inner wall of sleeve 30 to be noncylindrical, for example, oval shaped or an elongated circular shape. Alternatively, the magnet could have a non-circular shape or non-uniform magnetic properties. A combination of both is also possible. 
     Referring to FIG. 6, in another embodiment driver and/or velocity sensor coils 50, 52 are within air gap 40. As electrical signals produced by the driver and/or velocity sensor coils 50, 52 alternate at the resonant frequency they can easily be distinguished from the tuning current which follows only the variations of this resonant frequency, at a much lower rate. (Suitable driver and velocity sensors are, e.g., disclosed in Montagu, U.S. Pat. No. 4,076,298, and Silverstone, U.S. Pat. No. 4,090,112.) 
     Referring again to FIG. 1, in another embodiment, element 18 contains both driver and tuning capabilities and element 22 contains tachometer and tuning capabilities, therefore doubling the tuning range of the system by essentially doubling the heat dissipation capability of the scanner 10. 
     Referring to FIG. 8, in another embodiment, tuner 22 is connected to a controller 60 which is in turn connected to another scanner 62. Controller 60 is arranged to dynamically control tuner 22 to cause system 20 to be tuned to the frequency of scanner 62.