Abstract:
Presented herein is a non-contact torque sensing apparatus and method for measuring the instantaneous torque, or torsional stress/strain, transmitted through an elongated power transmission member such as a rotatable shaft. Polarized light is directed along a measurement light path in a cavity of a shaft where it intercepts a polarizing filter. The polarizing filter is operable to alter the polarization angle of the light according to torsional twisting of the shaft. A measurement device measures the change in the polarization angle of the light to obtain the shaft twist angle. Shaft torque is then calculated from the twist angle.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of U.S. Provisional Patent Application No. 60/883,244, filed Jan. 3, 2007 entitled “LASER TORQUE SENSOR FOR TRANSMISSIONS” and which is hereby incorporated by reference in its entirety. 
     
    
     TECHNICAL FIELD 
       [0002]    The present invention is directed to a sensor or apparatus for the non-contact measurement of torsional stress in a power transmitting rotating shaft, one such example being the input or output shaft of a transmission, by measuring changes in at least one property of light transmitted along the shaft to determine the torque transmitted by the shaft. 
       BACKGROUND OF THE INVENTION 
       [0003]    When torque is applied to a shaft, stress is applied along helical lines of compression and tension along the surface of the shaft. Various methods are known for measurement of the torque in a shaft. One method is to bond strain gauges to the exterior surface of the shaft with the strain gauges positioned in a cross configuration. The strain gauges function as elements of a resistive bridge circuit measuring compression and tension in the shaft surface along their length as the shaft torsionally twists. Torque measurement in a rotating shaft can be a challenge to implement when using strain gauges as the sensing elements as the strain gauges necessarily need to interface electrically with other off-shaft electronics. The off-shaft electronics are necessary to perform the resistance bridge measurements so as to detect and quantify tension and compression resulting from torsional twisting of the shaft as indicative of transmitted shaft torque. 
         [0004]    Transmitted torque in a shaft may also be determined by measurement of the angular displacement between two gears mounted to the shaft in a distally spaced relationship along the axis of rotation of the shaft. Using this method, the angular displacement between spaced gears is indicative of the twist angle over the length of the shaft between the gears, the twist angle being indicative of torque transmitted along the shaft. 
       SUMMARY OF THE INVENTION 
       [0005]    The present invention is directed to a non-contact sensor or apparatus for measuring the instantaneous torque, or torsional stress/strain, transmitted through an elongated power transmission member such as a rotatable shaft, such as (for example) a shaft driveably coupling an engine to a vehicle transmission, or within the transmission, or elsewhere within a vehicle drivetrain. In accordance with the disclosed invention, a rotatable shaft is provided with a cavity in a portion of a length of the shaft between a first portion of the shaft and a second portion of the shaft. A light source is provided emitting polarized light along a measurement light path in the cavity from the first portion of the shaft to the second portion of the shaft. A polarizing filter is provided and secured in the cavity in the second portion of the shaft. The polarizing filter is operable to change the angular polarization of light in the polarized light beam. A measurement device is provided to detect the change in the polarization angle in the light path as introduced by the polarizing filter. When torque is transmitted by the shaft, the transmitted torque causes elastic twisting in the shaft about the axis of rotation of the shaft. The torsional twisting of the shaft results in an angular rotation of the polarizing filter relative to the polarization direction of the polarized light beam and thereby results in a change in polarization angle of the light passing through the polarizing filter. This change in polarization angle is detected and is indicative of transmitted torque in the shaft, providing the basis by which the transmitted torque in the shaft may be calculated, as will be discussed more fully in later sections herein. 
         [0006]    According to one aspect of the invention, the light source is a laser light source, the light source includes a light-polarizing filter to provide a coherent single wavelength polarized light beam to transmit along the measurement light path. 
         [0007]    According to another aspect of the invention, the torque sensor apparatus includes a beam splitter configured to split the light beam from the light source into two light beams, one following the measurement light path and one following a reference light path. The beam splitter provides a reference light path having an angular polarization determined by angular polarization of light from the light source. In this aspect of the invention the measurement device detects the change in polarization angle as a detected difference in the angular polarization of the reference light path and angular polarization of the light after the polarizing filter. The detected difference in angular polarization is indicative of the torsional twisting in the shaft and therefore the torque transmitted by the shaft. 
         [0008]    According to another aspect of the invention, the light source in the torque sensor apparatus is a laser light source that includes a second light-polarizing filter to polarize light emitted by the light source. The light source is positioned external to the shaft rather than within the cavity of the shaft. Polarized light from the second polarizing filter is directed to enter the shaft cavity through an entrance aperture in the first portion of the shaft. The entrance aperture extends through the wall of the shaft between the cavity and the outside surface of the shaft. The torque sensor apparatus further includes a first reflectance element secured within the first portion of the shaft cavity and configured to redirect the polarized light from the entrance aperture in a direction so as to intercept the polarization filter provided in the cavity in the second portion of the shaft cavity. A second reflectance element is also secured within the shaft cavity and configured to redirect polarized light leaving the polarization filter in the cavity to exit the shaft through an exit aperture in the shaft. The measurement device is positioned outside the shaft and is aligned to detect polarized light emitted through the exit aperture. The entrance aperture and the exit aperture are aligned on the shaft to permit light from the light source mounted external to the shaft to redirect through the cavity and reach the measurement device when the shaft is in at least one angular position of shaft rotation. 
         [0009]    According to another aspect of the invention, the first reflectance element includes a first metallic tube into which the first reflectance element is mounted. Similarly, the second reflectance element includes a second metallic tube into which the second reflectance element is mounted. The first and second metallic tubes are sized and fitted to secure to the shaft within the cavity of the shaft. 
         [0010]    According to another aspect of the invention, the shaft cavity is a portion of an axial bore through one end of the shaft, the axial bore providing access to the cavity for installation of the first reflectance element and the second reflectance element through the end bore of the shaft. 
         [0011]    According to another aspect of the invention, the first reflectance element includes a first reflective surface configured to redirect the polarized light from the entrance aperture by reflection along a length of the shaft cavity to the polarization filter in the shaft cavity. The second reflectance element includes a second reflective surface configured to redirect the polarized light from the polarization filter in the cavity to exit the shaft cavity through an exit aperture in the shaft by reflection. 
         [0012]    According to another aspect of the invention, the reflective surfaces of the first and second reflectance elements are substantially planar reflective surfaces. 
         [0013]    According to another aspect of the invention, the reflective surfaces of both the first and second reflectance elements are each a conical reflective surface. 
         [0014]    According to another aspect of the invention, a half wave plate is provided and positioned after the light source and the second polarizing filter and before the beam splitter. The effect of the half wave plate yields a doubling in the sensitivity of the measurement device in detecting shaft torque, as will be explained more fully later. 
         [0015]    According to another aspect of the invention, the change in polarization angle of light leaving the polarization filter located in the shaft cavity results in a change in the intensity of light exiting the exit aperture of the shaft and reaching the measurement device. In this aspect of the invention, the measurement device is configured and adapted to detect and utilize this change in light intensity to determine the change in polarization angle of light reaching the measurement device from the shaft exit aperture. Additionally, the measurement device is configured to detect changes in the intensity of light in the reference light path and correct the measured intensity of light from the shaft exit aperture according to measured changes in reference light path intensity to cancel out variations in the intensity of light emitted by the light source. 
         [0016]    Additionally, a method is disclosed for the measurement of torque transmitted by a shaft in accordance with the foregoing apparatus of the invention, as will be explained more fully later herein. 
         [0017]    The above features and advantages and other features and advantages of the present invention are readily apparent from the following detailed description of the best modes for carrying out the invention when taken in connection with the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]    The drawings show a form of the invention that is presently preferred; however, the invention is not limited to the precise arrangement shown in the drawings. 
           [0019]      FIG. 1  illustrates a schematic side perspective view of one embodiment of a laser torque sensor applied to measure transmitted torque in a shaft, depicting reflectance elements secured into a bore as well as other components of the laser torque sensor, consistent with the present invention; 
           [0020]      FIG. 2  illustrates a schematic sectional view of another embodiment of the laser torque sensor applied to measure transmitted torque in a shaft, consistent with the present invention; 
           [0021]      FIG. 3  illustrates a schematic sectional view of yet another embodiment of a laser torque sensor applied to measure transmitted torque in a shaft in which the reflectance elements are adapted to permit the use of a plurality of entrance and exit apertures in the shaft, consistent with the present invention; 
           [0022]      FIG. 4  illustrates a schematic view of the laser torque sensor of  FIG. 2  further including a half wave plate to effectively double the sensitivity of the torque sensor, consistent with the present invention; 
           [0023]      FIG. 5  illustrates a schematic section view cut through the shaft of  FIG. 3  (without the reflectance elements) depicting one arrangement of the light entrance holes or light exit holes consistent with the present invention; 
           [0024]      FIG. 6  is a graph depicting the general relationship between normalized intensity of light received at the light detector/sensor and shaft twist angle due to the attenuation of the intensity of polarized light in the measurement path as it passed through the polarizing filter in the shaft cavity, consistent with at least one embodiment of the present invention; 
           [0025]      FIG. 7   a  is a schematic illustration of a shaft equipped with features of the present invention for torque measurement, depicted herein to support the discussion of the mathematical relationship between shaft twist angle and transmitted torque; 
           [0026]      FIG. 7   b  is a schematic illustration of the cross section along B-B of the shaft in  FIG. 7A  in which only the shaft wall is illustrated to clearly label parameters used in the calculation of the moment of inertia of the cylindrical shaft section for relating twist angle to transmitted torque; and 
           [0027]      FIG. 8  depicts a method of non-contact measurement of torque transmitted in a shaft consistent with the present invention. 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0028]      FIG. 1  illustrates a schematic side perspective view of one embodiment of a laser torque sensor  10  applied to measure instantaneous torque, or torsional stress/strain transmitted by a rotatable shaft  12 . In accordance with the disclosed invention, the rotatable shaft  12  is provided with a cavity  14  in a portion of a length of the shaft between a first portion  20  of the shaft  12  and a second portion  22  of the shaft  12 . In the illustrated embodiment, the cavity  14  is a portion of the axial bore  62  in the shaft  12 . The laser torque sensor  10  further includes a first reflectance element  38  and second reflectance element  42  each secured into the cavity  14  in the shaft  12 . The reflectance elements  38 ,  42  are installable into the cavity  14  of the shaft  12  through the opening of the bore  62  provided on a first end  66  of the shaft  12 . The first reflectance element  38  is secured in the cavity  14  at a first portion  20  of the shaft  12  while the second reflectance element  42  is secured in the cavity  14  in a second portion  22  of the shaft  12  where the second portion  22  is spaced apart from the first portion  20  by some defined distance. The shaft  12  includes a light entrance aperture  16  in the first portion  20  of the shaft  12  and a light exit aperture  18  in the second portion  22  of the shaft  12 . Each aperture  16 ,  18  extends from an outside surface  70  of the shaft  12  into the cavity  14  of the shaft  12 . In the embodiment illustrated in  FIG. 1 , the first reflectance element  38  and second reflectance element  42  each have a generally ‘C’ shaped housing. The use of a ‘C’ shaped housing is specific to exemplary embodiment of  FIG. 1  and is not limiting. The reflectance elements  38 ,  42  may include any shape of housing or alternately no housing at all as long as the reflectance elements  38 ,  42  are securable to the shaft  12  within the cavity  14 . The ‘C’ shaped housing of the first reflectance element  38  is secured into the cavity  14  with the opening  68  of the ‘C’ aligned with the light entrance aperture  16  of shaft  12 . Similarly, the ‘C’ shaped housing of the second reflectance element  42  is secured into the cavity  14  with the opening  72  of the ‘C’ aligned with the light exit aperture  18 . 
         [0029]    The laser torque sensor  10  includes a light source  24  emitting light along a first light path  30 . In  FIG. 1 , the light source  24  is secured proximate to and separate from the shaft  12  such that the shaft  12  is free to rotate about an axis of rotation  48  independent of light source  24 . The laser torque sensor includes a polarizing filter  26  positioned proximate to the light source  24 . In certain embodiments of the light source  24 , the polarizing filter  26  may be included as part of the light source  24 . The polarizing filter  26  is positioned to intercept the first light path  30  emitted by light source  24  and to polarize the light leaving the polarizing filter  26  along the polarized portion  74  of the first light path  30  in an angular direction of a first axis of polarization  28 . The laser torque sensor  10  further includes a beam splitter  32 , such as (for one non-limiting example) a light-transparent planar plate with a partially reflective mirror-like coating. The beam splitter  32  is adapted to transmit a defined percentage of the light incident upon the beam splitter  32  into a first measurement light path  34  and to reflect substantially the remaining percentage of incident light along a reference light path  36 . The first measurement light path  34  is positioned and directed towards the shaft  12  so as to be alignable with the entrance aperture  16  by rotation of the shaft  12  about the axis of rotation  48 , wherein the first measurement light path  34  enters the cavity  14  through the light entrance aperture  16 . In the first portion  20  of the shaft  12 , the first reflectance element  38  includes a first reflective surface  40  configured to reflect polarized light in the first measurement light path  34  to a second measurement light path  46  directed along a length of the cavity  14  in a direction substantially parallel to the axis of rotation  48  of the shaft  12  so as to impinge upon the second reflective surface  44  of second reflectance element  42  secured in the second portion  22  of the shaft  12 . The laser torque sensor  10  additionally includes a polarizing filter  52  positioned in the second portion  22  of the shaft  12  and secured to the ‘C’ shaped housing of the second reflectance element  42 . Again, the ‘C’ shape of the housing is specific to the exemplary embodiment illustrated in  FIG. 1  and is not limiting, as discussed earlier. The polarizing filter  52  is positioned to intercept polarized light in the second measurement light path  46  before it reaches the second reflective surface  44 . As the polarizing filter  52  is secured to the second reflectance element  42  which is then secured within the second portion  42  of the shaft  12 , the polarizing filter  52  is thereby constrained to rotate in unison with the second portion  22  of shaft  12 . The polarizing filter  52  has a second axis of polarization  54  by which it polarizes light in the second measurement light path  46  passing through the polarizing filter  52 . The second reflectance surface  44  is configured to reflect light polarized by the polarization filter  52  along a third measurement light path  50  which exits the shaft  12  through the light exit aperture  18 . The exit aperture  18  is positioned and configured to align the third measurement light path  50  with a measurement light-sensing portion  76  of a measurement device  56  by rotation of the shaft  12  about the axis of rotation  48 . The exit aperture  18  and entrance aperture  16  are cooperatively aligned such that when the entrance aperture  16  is rotatably aligned to permit light in the first measurement light path  34  to enter the entrance aperture  16 , then also the exit aperture  18  is aligned to permit light in the third measurement light path  50  to reach the measurement light sensing portion  76  of the measurement device  56  so that light can complete the measurement circuit from the light source  24  through the shaft cavity  14  to the measurement device  56 . Similarly, light from the reference light path  36  impinges upon the reference light-sensing portion  78  of the measurement device  56 . The measurement device  56  is positioned to receive light from the third measurement light path  50  and to detect a difference in polarization angle of the light between the third measurement path  50  and the reference light path  36 . Torque transmitted by the shaft  12  results in angular twisting of the shaft  12 , which results in a change in the polarization angle of light in the third measurement path  50  induced by to the angular alignment of the axis of polarization  54  of the second polarizing filter  52 . Torsional twisting in the shaft  12  is detected as a difference in polarization angle between the reference light path  36  and the third measurement light path  50  by the measurement device  56 . This change in polarization angle is directly related to the torque transmitted by the shaft  12 , as will be discussed in detail in a later portion of this application. The measured torque, determined from the measured difference in polarization angle, is output as an electronic measurement signal  80 . The electronic measurement signal  80  may be any of: a digital electronic signal representing torque, an analog voltage signal representing torque, an analog current signal representing torque, as well as other signal output types as would be known to one skilled in the art. The torque signal may be presented in a human readable form by, for example, an analog or digital torque indicator  82 , or provided as an input to an on-board vehicle engine management or transmission management computer, as well as provided as an input to other devices or for other uses as would be known to one skilled in the art. The light source  24  is preferably a laser light source. 
         [0030]    It is to be understood that the cavity  14  may occupy only a portion of the length of the shaft  12 , the cavity  14  providing space within the shaft  12  to hold reflectance elements  38 ,  42 . Additionally, the presence in the shaft  12  of the cavity  14  in the illustrated embodiment as well as in other embodiments necessarily reduces the material cross section of the shaft  12  around the cavity  14 , making the cavity portion of the shaft  14  more susceptible to torsional twisting and thereby improving the accuracy and sensitivity of shaft torque measurements. 
         [0031]      FIG. 2  illustrates a schematic view of the components of the laser torque sensor of  FIG. 1  applied to a tubular shaft wherein the cavity  114  extends completely through the length of the shaft  112 . As in  FIG. 1 , the laser torque sensor  110  includes the light source  24 , polarizing filter  26 , beam splitter  32 , light entrance aperture  116 , light exit aperture  118 , first reflectance element  38  secured within the first portion  120  of the shaft  112 , second reflectance element  42  secured within the second portion  122  of the shaft  112 , polarizing filter  52 , and measurement device  56  configured to provide a measured torque signal  80  as an output.  FIG. 2  provides a better illustration of the preferred mounting of the second polarizing filter  52  secured immediately in front of the reflective surface  44  of the second reflectance element  42  within the second portion  122  of the shaft. The measurement device  56  is configured to measure torsional twisting of the shaft  112  substantially over the length L between the first portion  120  and the second portion  122  of the shaft. This measured angular twist is converted to a shaft torque measurement, as will be discussed later in this application. Other than noted above, the operation of laser torque sensor  110  is identical to previous laser torque sensor discussions presented with  FIG. 1 . 
         [0032]      FIG. 3  illustrates a schematic sectional view of yet another embodiment of a laser torque sensor  210  applied to measure transmitted torque in a shaft  212  in which the reflectance elements  238 ,  242  have light reflective surfaces  84 ,  86  respectively. The reflectance elements  238 ,  242  may be made of a plastic or metallic material. In one embodiment, the light reflective surfaces  84 ,  86  are cone shaped surfaces machined, formed or otherwise disposed onto reflectance elements  238 ,  242 . In another embodiment the reflective surfaces  84 ,  86  each consist of two angled planar surfaces having a triangular profile when viewed from a side as depicted in  FIG. 3 . In yet another embodiment, the reflective surfaces  84 ,  86  each consist of four angled planar surfaces forming a pyramid shape and having a side profile as shown in  FIG. 3 . In all cases, the reflective surfaces  84 ,  86  are angled substantially at 45 degrees relative to the axis of rotation  248  of the shaft  212  such that the angle θ 1  between the first measurement light path  234  and the reflected second measurement light path  246  is substantially 90 degrees. The same angular relationship also existing between the second measurement light path  246  and the third measurement light path  250 . As discussed earlier with  FIG. 2 , the measured angular twist of the shaft  212  occurs over the length L between the first portion  220  and second portion  222  of the shaft  212 . As discussed with  FIGS. 1 and 2 , laser torque sensor  210  includes light source  24 , polarizing filter  26 , beam splitter  32 , light entrance apertures  216 ,  217 , light exit apertures  218 ,  219 , polarizing filter  252  and measurement device  56  configured and adapted to provide a measured torque signal  80  as an output. The use of reflective surfaces  84 ,  86  having a triangular profile is particularly useful when the shaft  212  is provided with one pair of light entrance/exit apertures  216 ,  218  respectively, or with two opposing pairs of light entrance/exit apertures ( 216 ,  217 ) and ( 218 ,  219 ) respectively. Similarly, the use of reflective surfaces  84  having a pyramid shape with four angled planar surfaces each is particularly useful when the shaft  212  is provided with up to four pairs of light entrance/exit apertures (not shown) in which neighboring aperture pairs are provided at positions located 90 degrees apart radially about the circumference of the shaft  212 . When the reflective surfaces  84 ,  86  are cone shaped, they are suitable for use in shafts having any number of entrance apertures (not shown) and exit apertures (not shown). 
         [0033]      FIG. 4  illustrates a schematic view of the laser torque sensor  110  of  FIG. 2  further including a half wave plate  64  positioned between the polarizing filter  26  and the beam splitter  32 . The half wave plate  64  effectively doubles the sensitivity of the measurement device  56  to the detection of angular twisting in the shaft  112  over the length L. This can be illustrated as follows. In the laser torque sensor  110  of  FIG. 2 , a torsional angular twist in the shaft over the length L of θ T  degrees (see  FIG. 7A ) results in a difference in polarization angle between the reference light path  336  and the third measurement light path  350  of θ T  degrees. Providing a the half wave plate  64  between the polarization filter  26  and the beam splitter  32  has the effect that a torsional angular twist in the shaft  112  over the length L of θ T  degrees now results in a difference in polarization angle between the reference light path  336  and the third measurement light path  350  of 2 θ T  degrees, exactly twice the actual angular twist of the shaft. The half wave plate  64  may be included as discussed above in any laser torque sensor embodiment of the present invention to improve torque measurement sensitivity. Other than noted above, the operation of laser torque sensor  110  of  FIG. 4  is identical to the previous laser torque sensor discussions presented with  FIG. 1 . 
         [0034]    While  FIG. 3  depicts only two entrance apertures  216 ,  217  and two exit apertures  218 ,  219 , it is to be understood that it is intended and in certain cases advantageous to have multiple entrance and exit apertures positioned in a band about the circumference of the shaft  212 . For example,  FIG. 5  illustrates a schematic section view cut through the shaft  212  of  FIG. 3  depicting one exemplary arrangement having four apertures  88  distributed about the circumference of the shaft  212 , where the illustrated aperture  88  positions radially about the shaft  212  are indicative of the angular positions of light entrance and light exit apertures. As noted above, the use of multiple pairs of light entrance and exit apertures are considered to be advantageous. For example, the use of four pairs of apertures permits light to be conducted through the shaft  212  when the shaft  212  is at any one of four positions of shaft rotation, thereby permitting four measurements of shaft twist angle to be performed in each complete rotation of the shaft  212 . 
         [0035]      FIG. 6  is a graph illustrating the general relationship between the twist angle θ T  (see  FIG. 7A ) and the normalized intensity of the light passing through the polarizing filter  52  (see  FIG. 1 ). It is assumed in  FIG. 6  that when the twist angle θ T  is 0 degrees, then the polarization of light in measurement light paths  34 ,  46  (see  FIG. 1 ) match the axis of polarization  54  (see  FIG. 1 ) of the polarizing filter  52  (see  FIG. 1 ).  FIG. 7   a  illustrates a twist angle range of −90 to 0 degrees, although it is to be understood that the sign of the twist angle indicates the direction of the torque, which can be positive or negative. The magnitude of the twist angle is indicative of the unsigned magnitude of the applied torque according to the equations provided above. It is to be understood that for positive twist angles, the twist angle vs. normalized intensity curve is the same general curve as illustrated in  FIG. 6  mirrored about the twist angle=0 axis. 
         [0036]      FIGS. 7A and 7B  serve to further illustrate the twist angle induced into the shaft  412  by an applied torque T, and the relationship between the twist angle θ T  and the applied torque T. An understanding of this relationship is important in converting the measured shaft twist angle so as to arrive at the torque applied to the shaft. The shaft  412  in  FIGS. 7A and 7B  is provided with at least two spaced apertures  88  such as light entrance and exit apertures discussed in various embodiments earlier. In  FIG. 7A  either aperture  88  is operable as either a light entrance or light exit aperture. To facilitate discussion of the concepts, one end of the shaft  412  is depicted as connected to ground  90  so as to resist rotation while a torque T is applied to the opposing end of the shaft  412 . The torque T produces a torsional twisting in the shaft  412  in the cylindrical section of the shaft between the spaced apertures  88 . Each aperture  88  has an axis depicted as  92 ,  94  extending through the center of the aperture  88  and intersecting the axis of rotation  448  of the shaft  412 . In  FIG. 7A  the axis  94  is also translated or copied to the aperture  88  near the applied torque T as axis  194  for easy angular comparison with the axis  94 . In the embodiment illustrated in  FIG. 7A , when no torque is applied to the shaft  412 , the twist angle between axes  194  and  94  is zero. As torque T is applied to the shaft  412  in increasing magnitude, the twist angle θ T  increases in proportion to the applied torque. 
         [0037]    The observed twist angle θ T  (shown as θ in equation 1 below) is related to the rigidity modulus G, the distance L between the light entrance/exit holes, the moment of inertia J of the cylindrical shaft section and the applied torque T by the following equation. 
         [0000]    
       
         
           
             
               
                 
                   θ 
                   = 
                   
                     
                       
                         ( 
                         T 
                         ) 
                       
                        
                       
                         ( 
                         L 
                         ) 
                       
                     
                     
                       
                         ( 
                         J 
                         ) 
                       
                        
                       
                         ( 
                         G 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0038]    For a cylindrical shaft section, the moment of inertia is given by: 
         [0000]    
       
         
           
             
               
                 
                   J 
                   = 
                   
                     
                       π 
                        
                       
                         ( 
                         
                           
                             r 
                             e 
                             4 
                           
                           - 
                           
                             r 
                             i 
                             4 
                           
                         
                         ) 
                       
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where r e  and r i  are defined in  FIG. 7B , r i  being the inside radius of the bore or cavity  414 , and r e  being the outside radius of the shaft  412  measured from the outside surface  470  of the shaft to the center of the shaft. 
         [0039]    Then the torque is related to the shaft twist angle θ T  by the following equation: 
         [0000]    
       
         
           
             
               
                 
                   G 
                   = 
                   
                     
                       2 
                        
                       
                         ( 
                         T 
                         ) 
                       
                        
                       L 
                     
                     
                       
                         π 
                          
                         
                           ( 
                           
                             
                               r 
                               e 
                               4 
                             
                             - 
                             
                               r 
                               i 
                               4 
                             
                           
                           ) 
                         
                       
                        
                       
                         θ 
                         T 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0040]    Referring again to  FIGS. 1 and 7   a . The polarization of light paths  34 ,  46 ,  50  and  36  are all the same when no torque is applied to the shaft (torque as discussed and illustrated with  FIG. 7   a ). After a torque is applied to the shaft  12  in  FIG. 1 , the torque induces angular twisting in the shaft  12  over the length L (shown in  FIG. 7A ) inducing a change in polarization angle in the third measurement light path  50 . This change in angular polarization is either θ T  in the torque measurement sensor configuration of  FIG. 1  or is equal to 2θ T  when the half wave plate  64  is present as shown in  FIG. 4 . 
         [0041]    This information together with the chart of  FIG. 6  enables an alternate method of indirectly detecting the change in angular polarization between the third measurement light path  50  and the reference light path  36  illustrated in  FIG. 1 .  FIG. 6  illustrates that the normalized intensity of the light passing through the polarizing filter  52  decreases as the twist angle increases in absolute magnitude. In  FIG. 1 , the twist angle is exactly equivalent to the change in angular polarization between the third measurement light path  50  and the reference light path  36 , as discussed earlier above. The graph of  FIG. 6  provides a relationship that indicates how the intensity of the light reaching the measurement device  56  decreases as the shaft twist angle increases in absolute magnitude. Using this knowledge, the measurement device  56  may alternately be configured to indirectly rather than directly measure the shaft twist angle or change in polarization angle by measuring changes in the intensity of the light reaching the detector along the third measurement light path  50 . In this configuration, the measurement device  56  monitors the intensity of light in the reference light path  36  and compensates the detected intensity of light in the third measurement light path  50  according to changes in intensity in the reference light path  36  so as to cancel out variations in the emitted light intensity of the light source  24 . 
         [0042]      FIG. 8  depicts a method of non-contact measurement of torque transmitted in a shaft consistent with the present invention. The method begins at block  802  by providing a light source emitting a polarized light beam. The polarized light source is preferably a laser light source. The method continues at block  804  with splitting a reference light beam from the polarized light beam emitted by the light source. At block  806  the polarized light beam is directed along a length of the shaft. At block  808  the angular polarization of the light transmitted along the shaft is changed according to torsional twisting of the shaft. At block  810  the angular change in polarization due to torsional twisting of the shaft is measured relative to the reference light beam. At block  812  the torque is then determined from the measured change in polarization. 
         [0043]    While the best modes for carrying out the invention have been described in detail, those familiar with the art to which this invention relates will recognize various alternative designs and embodiments for practicing the invention within the scope of the appended claims.