Abstract:
A magnetostrictive force sensor universally usable in any environment with similar signals unaffected by the surrounding material. To this end, a sensor comprising a shaft of magnetostrictive material with an inductance coil wound around the shaft is provided with a magnetic shell enclosing the coil only or both the coil and the shaft. Upon application of the magnetic field, the resultant flow of magnetic flux is confined to a path through the shaft and the magnetic shell. By confining the magnetic flux path, the dependency of the sensor signal on the surrounding material and environment is essentially eliminated.

Description:
TECHNICAL FIELD 
   The present invention relates to a magnetostrictive (Villari effect) force sensor that provides same or similar signals without regard to the surrounding environment in which the sensor is placed. 
   BACKGROUND OF THE INVENTION 
   Various materials are known to exhibit the Villari effect, that is, their permeability μ varies with the stress (force) applied. The Villari effect can be thought of as the inverse of the magnetostrictive effect, which is a change in dimension of a material under applied magnetic field. These materials have been used in various configurations to make force sensors. A simple configuration for a force sensor  10 , that will serve here as exemplary, consists of a coil  12  wound around a shaft  14  made of the magnetostrictive material, as shown in  FIG. 1 . The magnitude of the voltage V coil  of the coil  12  is related to its inductance L as follows:
 
 |V   coil |=2π  f I L (μ)=2 π f I L ( F )  (1)
 
where f is the frequency in Hertz and I the magnitude of the sinusoidal current impressed on the coil  12 , and L is the coil inductance. Inductance L, as shown in Eq. 1, is a function of permeability μ or force F.
 
   The circuit shown in  FIG. 1A  can be used for the measurement of dynamic inductance, for instance as part of a magnetostrictive force sensing apparatus. Referring to the circuit in  FIG. 1A , L is the varying inductance, and R and R L  are fixed resistances. The voltage V is imposed at a frequency f chosen for best sensitivity. The measurement can be performed by measuring the change across a portion of the voltage divider (R) as V out . The inductance L is related to the magnitudes of the applied and measured voltages, |V| and |V out |, respectively, by the following formula: 
       L   =       R     2   ⁢   π   ⁢           ⁢   f       ⁢         1     k   2       -       [         R   L     R     +   1     ]     2               
 
where: 
       k   =            V   out               V              
 
The output voltage V out  can be processed by a microprocessor or other similar circuit to obtain a signal that is representative of the change in inductance L. Any non-linearity in the inductance-versus-force function can be also included in the algorithm to provide the desired force measurement output. Compensation factors for temperature variations, etc, may also be included. The resistance values, R and R L , may advantageously be chosen according to the average value of inductance L, frequency f and source V.
 
   The inductance L for a given number of coil turns N is generally a function of the permeability μ of the shaft  14 , and the length l and cross-section A of the magnetic flux path around coil  12 : 
             L   =       μ   ⁢           ⁢     N   2     ⁢   A     l             (   2   )             
 
   The magnetic field created by the coil  12  thus includes the shaft  14 , but also includes a return path as shown schematically by the magnetic flux lines  16  in  FIG. 2 . Eq. 2 must therefore be expressed as the sum of two terms, one for the shaft  14 , indicated by subscript “sh”, and one for the return path  16 , indicated by subscript “ret”: 
             L   =       N   2     ⁡     [           μ   sh     ⁢     A   sh         l   sh       +         μ   ret     ⁢     A   ret         l   ret         ]               (   3   )             
 
   From Eq. 3, it is clear that the sensor signal is a function of the surrounding material, that is, of the environment around the sensor  10 . The signal will differ when surrounded by a magnetic material versus a non-magnetic material or air. Therefore, sensors must currently be designed to take into account the environment in which the sensor is to be used. It would be desirable to devise a sensor in such a way as to remove the dependency on the properties of the surrounding material. 
   In addition, to obtain a large signal, a material with large magnetostrictive behavior must be chosen for the shaft  14 , i.e., a large μ variation (μ max −μ min ) for a given stress (force) change. However, the average value of μ sh  can also affect the signal. Also, since many magnetostrictive materials are conductive, eddy currents will be induced in the shaft  14 , which will restrict the magnetic field towards the outer surface  14   a  of the shaft  14 , thus reducing the effective cross section A sh  of the shaft  14 . In that sense, a high frequency f results in a larger signal (f is a multiplying factor in Eq. 1), but generates more eddy currents and further restricts the magnetic field to the shaft surface  14   a . Thus, design trade-offs are necessary. Therefore, it is further desirable to provide preferred combined values of operating frequency f average permeability μ sh  and resistivity ρ for the magnetostrictive material. 
   SUMMARY OF THE INVENTION 
   The present invention provides a magnetostrictive force sensor that can be used in any environment, and that provides similar signals unaffected by the surrounding magnetic material or the environment. To this end, a sensor comprising a shaft of magnetostrictive material with an inductance coil wound around the shaft is provided with a magnetic shell enclosing the coil only or both the coil and the shaft, whereby, upon application of the magnetic field, the resultant flow of magnetic flux is confined to a path through the shaft and the shell. By confining the magnetic flux path, the dependency of the sensor signal on the surrounding environment is essentially eliminated. In an exemplary embodiment, the shell comprises a high permeability, low resistivity material. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention will now be described, by way of example, with reference to the accompanying drawings, in which: 
       FIG. 1  is a general schematic of a force sensor of the prior art; 
       FIG. 1A  is a circuit for measuring a dynamically changing inductance; 
       FIG. 2  depicts a general configuration of the magnetic field in the prior art force sensor of  FIG. 1 ; 
       FIG. 3  schematically depicts a force sensor of the present invention, having a shell completely enclosing the magnetostrictive shaft and coil; 
       FIG. 4  is a graphical depiction of the inductance of the coil as a function of the permeability of the shaft material; 
       FIG. 5  schematically depicts a force sensor of the present invention, having a shell enclosing the coil with the magnetostrictive shaft protruding outside of the shell; 
       FIGS. 6 and 7  are graphical depictions of the inductance of the coil as a function of the permeability of the shaft in the presence of applied frequencies of 100 Hz and 10 kHz, respectively; 
       FIG. 8  is a graphical depiction of the impact of the resistivity and permeability of the magnetostrictive shaft on the inductance of the coil; 
       FIG. 9  is a schematic depiction of the force sensor of  FIG. 5 , having airgaps in the shell. 
       FIG. 10  is a depiction of a magnetostrictive shaft having a radial slit extending along the length of the shaft parallel to the shaft axis along a radius. 
   

   DETAILED DESCRIPTION 
   The present invention eliminates the dependency of the sensor signal on the surrounding magnetic material or the environment such that the sensor may be used within any environment. In other words, the sensor of the present invention provides similar signals irrespective of whether it is surrounded by air, conductive but non-magnetic materials (aluminum for instance), or steel. By virtue of this invention, it is possible to insert the sensor inside of a brake caliper without concern for the magnetic and electric properties of the steel used to make the caliper. It is further possible to use the same sensor for other applications, where the sensor might not be surrounded by steel, such as a brake pedal force sensor or seat occupant weight sensor. It could even be used as a laboratory instrument, meant to be transported from application to application, without a need for calibration to account for the sensor&#39;s surroundings. 
   Referring to  FIG. 2 , the return path of the magnetic flux around coil  12 , depicted by lines  16 , is in a position to be affected (interfered with) by the surrounding environment. Referring to Eq. 3 above, to eliminate dependency on the return path, the second term in the equation, namely: 
               L   ret     =       N   2     ⁡     [         μ   ret     ⁢     A   ret         l   ret       ]               (   4   )             
 
needs to have a constant value. To this end, a universal sensor  20  is provided by enclosing the sensor  10  in a magnetic shell  22 , as shown in  FIG. 3 . This shell  22  forces the magnetic return flux  16  to a specific path, thus forcing the terms μ ret , A ret , and l ret  to the characteristic and dimensions of the shell  22 .
 
   Various magnetic, conducting or non-conducting materials may be envisioned by a person having ordinary skill in the art for the surrounding shell  22 . An ideal material for shell  22  would be one with a low resistivity ρ and a high permeability μ. The low resistivity would generate sufficient eddy currents to restrict the field to within the shell  22 , thus making it possible to use a relatively thin shell. At the same time, the high permeability would result in large generated magnetic fields, and thus, strong signals. An exemplary shell material may have a permeability μ of at least about 200, and advantageously, at least about 500. A further exemplary shell material may have a resistivity less than about 40 μΩ-cm, and advantageously, less than about 20 μΩ-cm. Many steels would therefore constitute ideal shell materials. 
   Shell thickness can be determined by calculating the material skin depth δ, which is a function of frequency f, permeability μ, and resistivity ρ. The formula for skin depth in a planar structure is: 
       δ   =       ρ     π   ⁢           ⁢   f   ⁢           ⁢   μ             
 
The shell thickness should be at least equal to the skin depth, and advantageously at least several times the skin depth, in order to minimize the flux beyond the shell  22 . If it is equal to the skin depth, about 63% of the flux will be confined to the shell. If it is three times as thick as the skin depth, approximately 95% of the flux will be confined to the shell. Depending on frequency f, a shell thickness on the order of 0.5 mm (above 1 kHz), or about 1–2 mm (at lower frequency, such as 100 Hz to 1 kHz), would be sufficient. A larger thickness may be needed at yet lower frequencies, and would be acceptable in ensuring mechanical strength, ease of packaging, etc. because more flux would be carried by the shell  22 . Relating the shell thickness to the skin depth δ is thus a way to provide a desirable minimum dimension.
 
   Shell materials with a higher resistivity ρ could be also considered, and are within the scope of this invention. Their use would make it necessary to use a thicker shell, making for a bulkier sensor. However, size is not always a critical design element. Larger sizes may even be necessary in some designs to increase mechanical stiffness, for instance. At the same time, with a higher resistivity comes the possibility to use higher frequencies. 
     FIG. 4  shows the result of finite element analysis of an exemplary design for a universal sensor  20  of the present invention comprising a cylindrical shaft  14  surrounded by a coil  12  with 2,800 turns. The shaft  14  was 19 mm long, with a diameter of 10 mm. A shell  22  was modeled around the sensor  10  with a thickness of 0.5 mm, a permeability μ of 900 and a resistivity ρ of 13 μΩ-cm, which values are typical of common steels of the 1000 series. The inductance L of the coil  12  is calculated for various permeabilities of the shaft material, in three different scenarios. The curve with the caption “no shell, caliper μ=900 ″ corresponds to a sensor  10  placed inside a steel caliper environment of μ=900. This curve also corresponds to a sensor  20  of the present invention with a shell  22  of μ=900, and a surrounding steel caliper of also μ=900. The second curve, which is just above the first curve, corresponds to the same sensor  20  with shell  22 , surrounded by an aluminum alloy environment of μ=1. By virtue of shell  22 , it is seen that the signal varies by only about 7% as the surrounding material changes from a highly permeable material (steel) to one that is not permeable (aluminum). This difference in signal may be further reduced, either by increasing the frequency from the 100 Hz used in this example, or by increasing the thickness of the shell  22 . 
   Several variations are possible for the shell  22  in accordance with the present invention. First, the shape of shell  22  need not be rectangular as shown in the figures. Second, the shell  22  may be close to or touching the surrounding material, or may be at some distance from the surrounding material. Third, the thickness of shell  22  need not be uniform. Fourth, and perhaps most importantly, shell  22  may completely enclose the sensor  10  as shown in  FIG. 3 , or enclose only the coil  12  as shown in  FIG. 5 . In the latter embodiment, the sensor shaft  14  may protrude by any desired length outside of the shell  22 , and may protrude at one end or both ends of the shaft  14 . This protrusion would have the advantage of providing a direct physical contact between the sensing shaft  14  and the surface that is providing the force F being measured. Whether the shaft  14  is enclosed in the shell  22  or protruding through shell  22 , the shaft  14  and shell  22  are advantageously in physical contact, or as close to physical contact as practical, to facilitate restriction of the magnetic flux  16  to a path through the shaft  14  and shell  22 , as shown both in  FIGS. 3 and 5 . 
   It is also to be understood that magnetostrictive shaft  14  may be of any desirable shape, cylindrical or otherwise. It may be a separate piece, or an integral part of the structure through which the force to be measured is applied. Also, several materials may be used in combination to make shaft  14 , for instance to facilitate insertion of the sensor in the larger apparatus, or for any other practical reason. 
   There are various ways to make the shell  22  and to incorporate it with the sensor  10 , as may be appreciated by a person having ordinary skill in the art. One way consists of making a shell  22  as a separate piece and using it as a “housing” for the sensor  10 . In some cases, it may be desirable to manufacture the sensor  10  without a shell  22 , and then prepare the location where the sensor  10  will be placed with a specific material that is both conductive and permeable. In other words, shell  22  is then a part of the environment in which sensor  10  will later be placed. One way of preparing the sensor location consists of coating the cavity prior to inserting the sensor. Various coatings methods are known in the art. 
   It may be appreciated from  FIG. 4  that the inductance L of the coil  12  depends on the permeability μ of the magnetostrictive shaft  14 . In the presence of stress, this permeability will vary from some value μ max  to some value μ min . A large difference between the two is desirable, but the average value also has an impact on inductance L. This is because the overall inductance is very sensitive to permeability changes for low values of shaft insert permeability, but tends to reach a plateau or asymptot for higher values of shaft insert permeability, as seen in  FIG. 4 . Given, for instance, and in the case of  FIG. 4 , a difference (μ max −μ min ) of 50, the resulting inductance variation is approximately 600 mH if μ max  is 60, which is significantly larger than the variation of approximately 200 mH when μ max  is 200. The same effect is shown in  FIGS. 6 and 7 , for shaft permeabilities (abscissa axis) ranging from 1 to 900.  FIG. 6  corresponds to an applied frequency of 100 Hz, with a steel shell  22  and surrounding aluminum environment (top line), or all steel (bottom line).  FIG. 7  corresponds to an applied frequency of 10 kHz, with all steel. 
   The following design guidelines may be followed in forming a sensor  20  in accordance with the present invention. It is preferable to operate with a shaft material having a lower permeability μ sh , on the order of less than about 200, and preferably less than about 50. This is because the inductance change for a given Δμ is much larger at lower values of μ. Favorable exemplary materials are nickel and nickel alloys. Also, some stainless steels (series 300) are possible. They are considered “non-magnetic”; however, they exhibit a permeability on the order of 10 (small compared to most steels, which exhibit permeabilities of 1,000 or more). 
   As far as operating frequency is concerned, from lower to higher frequencies, the inductance L tends to drop, because, with eddy currents, the effective cross-section A of the magnetic flux path  16  is reduced. In the same exemplary study, a drop of a factor of about 10 was found between 100 Hz and 10 kHz, as can be seen by comparing  FIGS. 6 and 7 . However, the signal voltage V coil , according to Eq. 1, is proportional to frequency f, and therefore, from that point of view, there is an advantage to operating at higher frequencies. There is, therefore, an optimum range of operating frequencies balancing these two contradictory trends. 
   Since the optimum operating frequency and signal output is a function of eddy currents, it is a function of material resistivity.  FIG. 8  shows the impact of the resistivity ρ of the magnetostrictive shaft  14  on the inductance L. The calculations were performed at 10 kHz, with a surrounding material of μ=100. In one case (upper trace), the shaft resistivity ρ is infinite; in the other case (lower trace), the resistivity ρ is 10 μΩ-cm, corresponding approximately to some steels or nickel alloys. It can be concluded that higher resistivities are better because the flux penetrates more, thus expanding the effective flux cross-section A. However, the increase in inductance L is only 50% over a very large range of resistivities, making it therefore a factor of only a secondary nature. It can be further concluded that with higher resistivities, it is increasingly important to work with low-permeability shaft materials, as the knee of the curve is more pronounced, and located at increasingly lower values of μ. Higher resistivities can be achieved, for instance, by using powder metal as a base material for the shaft  14 . Higher resistivities can also be obtained by fabricating a composite material of magnetic and electrically insulating components. Also, a radial slit (or slits)  30  made in the shaft  14 , as depicted in  FIG. 10  can increase the resistance of the eddy current path. One slit may be sufficient to multiply the resistance by a factor of 4 or more. 
   In addition, it is desirable to minimize all airgaps  24  in the path  16  of the magnetic flux, as shown in  FIG. 9 . Airgaps  24  in the flux path  16  tend to dominate the inductance L, like a portion of high-resistivity wire would dominate the resistance of a long wire. Therefore, changes in inductance L of the shaft  14  as a response to varying stress would be drowned by the constant inductance of the airgap  24 . As stated previously, it is advantageous to have, as much as practical, physical contact between the shaft  14  and shell  22 , as shown in  FIGS. 3 and 5 , and thus, no air gaps. If it is necessary to have some airgap in-between, for instance to accommodate different coefficients of expansion, or to avoid physically restraining shaft  14 , then, the design should strive to minimize the airgap reluctance, by minimizing its length, and giving it a larger cross-section. 
   In use, a universal force sensor  20  of the present invention will exhibit similar signals without regard to the material or environment surrounding the sensor. The same universal force sensor  20  may thus be placed inside a steel brake caliper, a seat cushion or any other desired environment. 
   While the present invention has been illustrated by the description of embodiments thereof, and while the embodiments have been described in considerable detail, they are not intended to restrict or in any way limit the scope of the appended claims to such detail. Additional advantages and modifications will readily appear to those skilled in the art. For example, an outer shell  22  made of a conductive, permeable material, such as steel, has been described for a force sensor  20  consisting of a single coil  12  around a shaft  14 . However, shell  22  would apply equally well to multi-coil force sensors based on the measurement of the mutual inductance between two coils, etc. The invention in its broader aspects is therefore not limited to the specific details, representative apparatus and methods and illustrative examples shown and described. Accordingly, departures may be made from such details without departing from the scope or spirit of the general inventive concept.