Abstract:
A system for determining magnetic permeability of a material. Two electrical inductors formed as primary and secondary concentric coils share a common magnetic core space. A first AC voltage applied to the primary coil creates a magnetic flux in the core proportional to the magnetic permeability of the material. The magnetic flux induces an AC voltage in the secondary coil indicative of the apparent magnetic permeability of the sample. The apparent permeability is corrected for conductivity by imposing a second AC voltage and resistor in series across first and second electrodes disposed in the material. When the material is a magnetorheological fluid, the magnetic permeability is proportional to the concentration of magnetic particles in the sample and can be back-calculated from the amplitude of the secondary voltage signal.

Description:
RELATIONSHIP TO OTHER APPLICATIONS AND PATENTS 
       [0001]    The present application is a Continuation-In-Part of a pending U.S. patent application Ser. No. 11/681,258, filed Mar. 2, 2007. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of The Invention 
         [0003]    The present invention relates to methods and apparatus for inferential measurement; more particularly, to methods and apparatus for determining the magnetic permeability of a material; and most particularly, to a method and apparatus for using such measurement to control the concentration of a magnetic material in a magnetorheological (MR) fluid. 
         [0004]    2. Discussion of the Related Art 
         [0005]    MR fluids are well known and may be defined practically as fluid materials whose apparent viscosities are reversibly increased by exposure of the fluid to a magnetic field. The increase in viscosity is anisotropic, being greatest in the direction of the magnetic field due to formation of fibrils of magnetized particles. This property, known in the art as “stiffenening”, has been employed to great success in the field of extremely high resolution shaping, finishing, and polishing of surfaces, especially optical elements, wherein very small amounts of material may be removed in a highly precise and controlled manner. This field is known generally in the art as magnetorheological finishing (MRF). See, for example, U.S. Pat. Nos. 5,971,835; 6,746,310; and 6,893,322, the relevant disclosures of which are incorporated herein by reference. 
         [0006]    A problem in the art of MRF is maintaining a constant magnetic particle concentration in the MR fluid entering the magnetic work zone. MR fluid is supplied to the work zone by a delivery system that draws MR fluid from a mixing sump into which used MR fluid passes from the work zone for mixing and reuse. The used MR fluid typically is depleted in carrier (water) by evaporation and also is heated, both of which alterations must be corrected before the MR fluid may be reused. Without replenishment of water lost to evaporation, the bulk supply of MR fluid in the sump will gradually increase in particle concentration during an MRF operation. This is an undesirable operating condition because particle concentration is an important factor governing the rate of removal of material from a substrate being finished. Thus, it is important to know what the particle concentration is in the MR fluid being supplied from the sump at any given time and to provide a proper water replenishment rate to the sump to replace the water lost to evaporation in use, thereby dynamically keeping the concentration constant at an aim value. 
         [0007]    U.S. Pat. No. 5,554,932 discloses a system for measuring magnetic saturation flux density of a sample material. First and second sample holders are disposed symmetrically on either side of a cylindrical permanent magnet. Coils are placed around the sample holders and the permanent magnet is rotated. The signals induced in the coils in the absence of a magnetic material in one of the sample holders are applied to an amplifier/meter in such a manner as to provide a null signal. When a sample is placed in one of the sample holders, the magnetic saturation flux density can be measured. A shortcoming of the disclosed system is that the mechanical device is relatively cumbersome and has a critical moving part (the permanent magnet). 
         [0008]    U.S. Pat. No. 6,650,108 discloses a system for inferring concentration of magnetic particles in a flowing MR fluid. The system is based on inductance measurement that converges in an impedance measurement with relatively complex technique involving high sensitivity electric bridge circuits. A shortcoming of the disclosed system is that resolution is relatively low. 
         [0009]    U.S. patent application Ser. No. 11/681,258, filed Mar. 2, 2007, discloses a simple, high-resolution means for continuously measuring and monitoring the concentration of magnetic particles in the mixed sump MR fluid to permit controlled real-time dilution thereof before the sump MR fluid is reused for finishing. A shortcoming of the disclosed system is that the apparent concentration (magnetic permeability) is also a function of the electrical conductivity of the MR fluid. 
         [0010]    What is needed in the art is a simple, high-resolution means for continuous compensation of output signal for changes in fluid conductivity in the mixed sump MR fluid to permit controlled real-time dilution thereof before the sump MR fluid is reused for finishing. 
         [0011]    It is a principal object of the present invention to include consideration of fluid conductivity in determining, particle concentration in an MR fluid. 
       SUMMARY OF THE INVENTION 
       [0012]    Briefly described, in a method and apparatus of the present invention, two electrical inductors share the same magnetic core. Preferably, the inductors are formed as primary and secondary concentric coils. When an AC voltage is applied to the primary coil, an axially-directed magnetic flux is created in the core which is proportional in intensity to the magnetic permeability of the core. In turn, due to the effect of mutual inductance, the magnetic flux induces an AC voltage in the secondary coil which is in phase with the source voltage. The magnetic permeability of the core depends upon the concentration of magnetic particles in the sample (when the “core” is a sample of MR fluid), and thus the concentration of magnetic particles can be back-calculated from the amplitude of the secondary voltage signal. 
         [0013]    Sensitivity of measurements and system resolution can be increased by using a differential approach using two identical sets or pairs of coils wherein a reference material forms a magnetic core for one coil set and the MR fluid forms a magnetic core for the other coil set. 
         [0014]    Because magnetically-induced circulating eddy currents in the liquid conductive core generate magnetic field that is opposite to the external magnetic field, the apparatus output signal may be affected. The strength of such eddy currents is a function of conductivity of the MR fluid, which can change over time due to chemical processes such as oxidation occurring during the working life of the MR fluid. Therefore a conductivity term must be included when calculating the voltage output of the apparatus, and conductivity of the MR fluid must be measured continuously during use. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    The foregoing and other objects, features, and advantages of the invention, as well as presently preferred embodiments thereof, will become more apparent from a reading of the following description in connection with the accompanying drawings in which: 
           [0016]      FIG. 1  is a schematic drawing of an exemplary embodiment of a system in accordance with the invention for measuring magnetic permeability, including means for continuously measuring conductivity; and 
           [0017]      FIG. 2  is a schematic drawing showing application of the exemplary embodiment in an MR fluid finishing machine. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0018]    Referring to  FIG. 1 , in a system  10  in accordance with the invention suitable for measuring the magnetic permeability of the material of a magnetic core  12 , two inductors (primary coil  14  and secondary coil  16 ) share magnetic core  12 , which is a sample of a magnetic material to be tested, such as an MR fluid in the sump of an MR finishing machine. When an AC voltage V p  is applied to primary coil  14 , an axially-directed magnetic flux  18  is created in core  12  in accordance with Equation 1: 
         [0000]    
       
         
           
             
               
                 
                   B 
                   = 
                   
                     μ 
                      
                     
                       N 
                       l 
                     
                      
                     
                       
                         I 
                         p 
                       
                       
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     1 
                   
                   ) 
                 
               
             
           
         
       
     
         [0019]    where μ is the magnetic permeability of the core, N is the number of primary coil turns, l is the coil&#39;s length, I p , is the current amplitude, and I p /√{square root over ( 2 )} is the root mean square current. 
         [0020]    In turn, due to the effect of mutual inductance, magnetic flux  18  induces an AC voltage V s  in secondary coil  16  in phase with the source voltage in accordance with Equation 2: 
         [0000]      V s =2πfNAB  (Eq. 2) 
         [0021]    where f is current frequency and A is the cross-sectional area of core  12 . From Equation 1 and Equation 2, it follows that the root mean square voltage V s  generated in secondary coil  16  is given by Equation 3: 
         [0000]    
       
         
           
             
               
                 
                   
                     V 
                     S 
                   
                   = 
                   
                     4.44 
                      
                     
                         
                     
                      
                     μ 
                      
                     
                         
                     
                      
                     f 
                      
                     
                         
                     
                      
                     
                       
                         
                           N 
                           2 
                         
                          
                         A 
                       
                       l 
                     
                      
                     
                       I 
                       p 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Eq 
                     . 
                     
                         
                     
                      
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
         [0022]    Primary coil  14  behaves as a load with respect to the AC voltage source V p , and secondary coil  16  behaves as a source with respect to resistor R 2 . At the same time, the magnetic permeability μ depends on magnetic properties of core  12 . In turn, these properties are dependent on concentration φ of the magnetic particles in the sample, as given by Equation 4: 
         [0000]      μ= f (φ)  (Eq. 4) 
         [0023]    When all parameters of system  10 , including the AC voltage applied to the primary coil, are held constant, any variation in concentration of magnetic particles concentration in magnetic core  12  will result, as it follows from Equation 3, in the proportional change of AC voltage V s  in secondary coil  16 . In doing so, the system output signal follows variations in the sample magnetic particles concentration. In the general case, it can be defined as shown in Equation 5: 
         [0000]        V   s   =f (φ, k   1   ,k   2  . . . )  (Eq. 5) 
         [0024]    where k 1 , k 2  . . . are some constant parameters which depend on system geometry and system electrical parameters. The magnitude of output signal can be manipulated by (pre)setting different system parameters such as number of turns and geometries of the coils, frequency and voltage of the oscillator, impedance of the components, and the like. System  10  further may contain a temperature sensor (not shown), such as a thermistor, means to compensate for thermal variation in circuit impedance and change in output signal due to variations of temperature, and an electronic controller for processing data from system  10 , calculating the magnetic permeability, and controlling replenishment of the MR fluid in the sump as shown in  FIG. 2  and described below. 
         [0025]    At the same time, MR fluid is a water-based suspension of micron-size iron and abrasive particles. To retard particles sedimentation and corrosion, the fluid contains some chemical additives which result in relatively high fluid pH and conductivity. When such conductive fluid is placed in an AC magnetic field, eddy-currents are induced within the conductive material in closed circular paths which are perpendicular to the inducing external magnetic field. Such induced eddy-currents oppose changes in the inducing external magnetic field and as a result, an AC magnetic field produced by the circulating eddy-currents may reduce the larger external AC magnetic field and therefore reduce the apparatus output signal. 
         [0026]    Further, fluid conductivity may vary in time due to chemical processes (oxidation) occurring during fluid life in an MRF machine, resulting in instability of the output signal and consequent errors in fluid monitoring and material removal rate. 
         [0027]    What is more, an additional source of error is dependence of fluid conductivity on concentration of iron particles, which is the primary function to be measured by the present method. 
         [0028]    What is needed is a simple, high-resolution means for continuous compensation of output signal for changes in fluid conductivity in the mixed sump MR fluid to permit controlled real-time dilution thereof before the sump MR fluid is reused for finishing. 
         [0029]    For this purpose, the fluid conductivity is continuously measured. System  10  includes two electrodes  20 , 22  disposed in the MR fluid core  12  at opposite ends of primary and secondary coils  14 , 16  and connected to a voltage source V c  (AC, 10,000 Hz to avoid polarization of electrodes) through resistor R 3 . A voltage from resistor R 3  is proportional to conductivity of MR fluid core  12 , and may be used in the controller to compute and compensate for conductivity variation in circuit impedance and change in output signal due to variations of conductivity. 
         [0030]    In this case, a conductivity-adjusted output signal V s1  can be defined as a variation on Equation 5 wherein a conductivity term is added: 
         [0000]        V   s1   =f (φ, k   1   ,k   2  . . . )+ψ( G )  (Eq. 6) 
         [0031]    where G is fluid conductivity 
         [0032]    A proper quantitative relationship between the concentration and the voltage V s1  in the secondary coil is determined by calibration with samples of known magnetic particles concentration, which calibration gives the following general expression for concentration: 
         [0000]      φ= aV   s1   +b   (Eq. 7) 
         [0033]    where a and b are constants defined by calibration. 
         [0034]    Referring to  FIG. 2 , an exemplary application is shown for a system  210  in accordance with the present invention in assisting in maintaining a constant concentration of magnetic particles in MR fluid in an MR finishing apparatus  200 . 
         [0035]    As is known in the prior art for an MR finishing apparatus  200  and described more fully in the incorporated references, a carrier wheel  230  has a surface  232 , preferably spherical, for receiving a ribbon  234  of MR fluid in a non-stiffened state from nozzle  236 . Surface  232  carries ribbon  234  into a work zone  238  between surface  232  and an off-spaced work piece  240  to be finished. Shaped magnetic pole pieces (not shown) create an oriented magnetic field within work zone  238  that causes the MR fluid therein to become stiffened to a consistency approximating putty. The stiffened MR fluid, which may also contain non-magnetic particles of abrasives such as cerium oxide, ablates the surface of work piece  240  in controlled fashion as it is drawn through work zone  238 . Carrier surface  232  continuously supplies and removes MR fluid to and from work zone  238 . A scraper  242  removes used MR fluid, no longer stiffened, from carrier surface  232  and returns it via a suction pump  244  to a mixing sump  246 , wherein the used MR fluid is mixed with a bulk supply of MR fluid  220  and from whence mixed MR fluid  220  is drawn by delivery pump  248  and supplied again to nozzle  236  via non-magnetic tube  250 . 
         [0036]    A mutual inductance sensor  219  supplied with means for MR fluid conductivity measurements in accordance with the present invention and controllably driven by an AC power supply  252  as described above is placed concentrically outside non-magnetic tube  250  filled with flowing MR fluid  220 . Output signals  254  and  255  from sensor  219  are directed to a programmable controller  256 , programmed with algorithms and look-up tables in accordance with Equations 1 through 7 and having a set point corresponding to an aim concentration, which controls a pump  258  to dispense replenishment water  260  into sump  246  at a controlled flow rate to compensate for water evaporated from the MR fluid ribbon  234  when exposed on carrier wheel  230  during use thereof. Replenishment water  260  is mixed with the bulk supply MR fluid within sump  246  to dilute the bulk concentration to aim. Thus, the concentration of magnetic particles in MR fluid  220  as drawn from sump  246  for supply to work zone  238  is maintained at the aim concentration, providing a stable and predictable rate of material removal from work piece  240 . 
         [0037]    While the invention has been described by reference to various specific embodiments, it should be understood that numerous changes may be made within the spirit and scope of the inventive concepts described. Accordingly, it is intended that the invention not be limited to the described embodiments, but will have full scope defined by the language of the following claims.