Abstract:
An improved apparatus and method is disclosed for determining a torque imposed on the rotatable shaft based on its torsional displacement, said apparatus comprising a rotatable shaft with at least four paired probes positioned at each end of the shaft to detect and compensate for motion induced errors. Paired first and second horizontal probes are positioned 180 degrees apart and paired first and second vertical probes are also positioned 180 degrees apart, in parallel planes perpendicular to the long axis of the shaft. In addition, the paired first and second horizontal probes, are positioned 90 degrees apart from the paired first and second vertical probes. If the shaft moves horizontally, the time of arrival detected by the first horizontal first and second probes will be later than a nominal value and the time of arrival for the second horizontal first and second probes will be earlier than a nominal value with the same amount of error. Combining data from the first and second horizontal first and second probes will then automatically cancel out any error from horizontal motion. Similarly, combining data from first and second vertical first and second probes will eliminate the error due to vertical movement. Since any radial movement is a combination of horizontal and vertical movements, the use of at least four pairs of probes according to the present invention removes errors due to radial movement of the shaft in any direction.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention relates to an improved apparatus and method for measuring torque on a rotating shaft and particularly to an apparatus and method for measuring torque on a rotating load coupling shaft for driving a power generator.  
       BACKGROUND OF THE INVENTION  
       [0002]     Various machines, such as a gas turbine and/or a steam turbine, may be used to drive a load such as a power generator. In particular, a gas turbine and/or a steam turbine may be used to rotate a magnet within a stator to generate electric power. The power generator includes a shaft which is connected to the rotating magnet and which itself is connected to a large connecting shaft (also called a load coupling shaft) rotated by one or more turbines. The connecting shaft is typically large and stiff, thereby resulting in very small torsional displacements (strains) when a torque is imposed on the connecting shaft. A measurement of torque transmitted through the connecting shaft is often made to determine the power output of the machine(s) rotating the connecting shaft.  
         [0003]     The torque imposed on the connecting shaft has been measured in the past using strain gauges. However, the accuracy of torque measurements provided by strain gauges often does not meet engineering requirements because the uncertainty of such measurements is rather large as compared to the strains measured.  
         [0004]     A known digital light probe system, developed by GE Aircraft Engines, has been used for several applications in the past including measuring compressor rotating blade vibratory displacements.  
         [0005]     An existing high resolution torque measurement method employs a pair of high-powered laser probes, one probe at each end of the measured shaft. The probes are perpendicular to the shaft and their tips are positioned at roughly 0.050″ from the outer surface of the shaft. A pair of targets, one at each end, are placed between the probes and the shaft at corresponding locations and bonded to the surface of the shaft. As the targets pass by the probes in every revolution when the shaft is rotating, the timing measurement system records all the time of arrival data for the two probes. The software within the measurement system then processes the data by comparing the timing difference between the probes at two ends and convert the results into torsional displacement. Once the torsional displacement is known, the torque on the shaft is calculated using an analytical model or formula.  
         [0006]     The method described above works when the shaft remains stationary radially during rotation. However, the measured value may include errors produced from shaft movement when the shaft is subject to radial movement at either end and the torque value is subject to misinterpretation. Accordingly, there remains a need in the art for an improved apparatus and method to measure torque on a rotating shaft, such as a rotating load coupling shaft for driving a power generator, with a high degree of accuracy using multiple probes to remove errors produced from shaft movement so that the measured value represents the true torsional displacement of the shaft.  
       BRIEF DESCRIPTION OF THE INVENTION  
       [0007]     The present invention provides an improved apparatus and method for its use for measuring the torque on a rotatable shaft with an accuracy within +/−0.5%.  
         [0008]     In an exemplary embodiment of an improved apparatus and method according to the present invention, two sets of at least four probes are used at each end of a rotatable shaft to compensate for motion induced errors. Paired first and second horizontal probes are positioned 180 degrees apart and paired first and second vertical probes are also positioned 180 degrees apart, in parallel planes perpendicular to the long axis of the shaft. In addition, the paired first and second horizontal probes are positioned 90 degrees apart from the paired first and second vertical probes. If the shaft moves horizontally, the time of arrival for the first horizontal probe will be later than nominal value and the time of arrive for the second horizontal probe will be earlier than nominal value with the same amount of error. Combining the first and second horizontal probes will then automatically cancel out any error from horizontal motion. Similarly, combining first and second vertical probes will eliminate the error due to vertical movement. Since any radial movement is a combination of horizontal and vertical movements, the use of two sets of four or more probes according to the present invention removes errors due to radial movement of the shaft in any direction.  
         [0009]     In another exemplary embodiment according to the present invention, an apparatus is provided that incorporates a rotatable shaft; at least one first target coupled on the rotatable shaft so as to rotate therewith; at least one second target coupled on the rotatable shaft so as to rotate therewith, an axial location of the first target along the rotatable shaft being different than an axial location of the second target along the rotatable shaft; at least one first horizontal first probe for transmitting a first horizontal first transmission signal to the first target and receiving a first horizontal first response signal from the first target; at least one first horizontal second probe for transmitting a first horizontal second transmission signal to the first target and receiving a first horizontal second response signal from the first target; at least one second horizontal first probe for transmitting a second horizontal first transmission signal to the second target and receiving a second horizontal first response signal from the second target; at least one second horizontal second probe for transmitting a second horizontal second transmission signal to the second target and receiving a second horizontal second response signal from the second target; at least one first vertical first probe for transmitting a first vertical first transmission signal to the first target and receiving a first vertical first response signal from the first target; at least one first vertical second probe for transmitting a first vertical second transmission signal to the first target and receiving a first vertical second response signal from the first target; at least one second vertical first probe for transmitting a second vertical first transmission signal to the second target and receiving a second vertical first response signal from the second target; at least one second vertical second probe for transmitting a second vertical second transmission signal to the second target and receiving a second vertical second response signal from the second target; an axial location of the first horizontal and vertical first and second probes along the rotatable shaft being different than an axial location of the second horizontal and vertical first and second probes along the rotatable shaft; and a processor operatively coupled to each of the first and second horizontal and vertical first and second probes for determining a torsional displacement of the shaft based at least on the first and second horizontal and vertical first and second response signals received by the first and second horizontal and vertical first and second probes, respectively.  
         [0010]     In an alternate embodiment according to the present invention, an apparatus is provided that incorporates a rotatable shaft with a long axis; at least one first target coupled on the rotatable shaft so as to rotate therewith; at least one second target coupled on the rotatable shaft so as to rotate therewith at a location axially displaced from the first target; a first horizontal first probe for transmitting a first horizontal first transmission signal to the first target and receiving a first horizontal first response signal from the first target; at least one first horizontal second probe for transmitting a first horizontal second transmission signal to the first target and receiving a first horizontal second response signal from the first target; at least one second horizontal first probe for transmitting a second horizontal first transmission signal to the second target and receiving a second horizontal first response signal from the second target; at least one second horizontal second probe for transmitting a second horizontal second transmission signal to the second target and receiving a second horizontal second response signal from the second target; a first vertical first probe for transmitting a first vertical first transmission signal to the first target and receiving a first vertical first response signal from the first target; at least one first vertical second probe for transmitting a first vertical second transmission signal to the first target and receiving a first vertical second response signal from the first target; at least one second vertical first probe for transmitting a second vertical first transmission signal to the second target and receiving a second vertical first response signal from the second target; at least one second vertical second probe for transmitting a second vertical second transmission signal to the second target and receiving a second vertical second response signal from the second target; and a processor operatively coupled to each of the first and second vertical and horizontal first and second probes for determining a torsional displacement of the shaft based at least on the first and second vertical and horizontal first and second response signals received by the first and second vertical and horizontal first and second probes, respectively; wherein the first and second targets are coupled to the rotatable shaft on opposite axial ends thereof.  
         [0011]     Embodiments according to the present invention further include a method for determining a parameter of a rotatable shaft that includes:  
         [0012]     coupling at least one first target on the rotatable shaft so that the first target rotates therewith; coupling at least one second target on the rotatable shaft so that the second target rotates therewith; an axial location of the first target along the rotatable shaft being different than an axial location of the second target along the rotatable shaft; rotating the rotatable shaft; transmitting a first horizontal or first vertical first or second transmission signal to the first target from a first horizontal or first vertical first or second probe, respectively; receiving a first horizontal or first vertical first or second response signal from the first target from a first horizontal or first vertical first or second probe, respectively; transmitting a second horizontal or second vertical first or second transmission signal to the second target from a second horizontal or second vertical first or second probe, respectively; receiving a second horizontal or second vertical first or second response signal from the second target from a second horizontal or second vertical first or second probe, respectively; an axial location of the first horizontal and vertical first and second probes along the rotatable shaft being different than an axial location of the second horizontal and vertical first and second probes along the rotatable shaft; and determining a torsional displacement of the shaft based on at least the first vertical and horizontal first and second response signals and second vertical and horizontal first and second response signals received by the first and second vertical and horizontal first and second probes, respectively.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0013]      FIG. 1  is a diagram illustrating, inter alia, a cross sectional view of a rotating shaft in a simple cycle configuration whose torque is measured in accordance with an exemplary embodiment of the present invention.  
         [0014]      FIG. 2A  is a diagram illustrating signals received by at least two different laser light probes from a rotating shaft having no measurable torque imposed thereon.  
         [0015]      FIG. 2B  is a diagram illustrating signals received by at least two different laser light probes from a rotating shaft having a measurable torque imposed thereon.  
         [0016]      FIGS. 3A-3C  are diagrams illustrating an exemplary method for calculating torque of a rotating shaft based on its torsional displacement (circumferential twist).  
         [0017]      FIG. 4  is a diagram illustrating, inter alia, a cross sectional view of a rotating shaft in a combined cycle configuration whose torque is measured in accordance with an alternative exemplary embodiment of the present invention.  
         [0018]      FIG. 5  is a perspective view of the combined cycle configuration illustrated in  FIG. 4  (viewed from the reverse side of  FIG. 4 ).  
         [0019]      FIG. 6   a  is a cross sectional view of a rotating shaft according to the present invention taken from line  7 -- 7  in  FIG. 1  or  4 .  
         [0020]      FIG. 6   b  is a cross sectional view of a rotating shaft according to the present invention, showing target displacement by shaft movement. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0021]      FIG. 1  illustrates a shaft  20  that serves as a load coupling shaft in accordance with an exemplary embodiment of the invention. Shaft  20  is connected at a first axial end  24   a  to shaft  42  of gas turbine  40  and connected at a second axial end  24   b  to a rotatable shaft  62  of power generator  60 . Accordingly, shaft  20  forms a portion of a simple cycle configuration in the exemplary embodiment illustrated in  FIG. 1 .  
         [0022]     Shaft  20  is rotated by gas turbine machine  40 . In turn, the rotational force provided by gas turbine machine  40  is transmitted to rotatable shaft  62  of power generator  60 . Rotatable shaft  62  of power generator  60  is connected to a magnet  64  which rotates with rotatable shaft  62  (and hence with shaft  20 ) within a stator (not shown) of power generator  60  to generate electric power.  
         [0023]     Shaft  20  includes a hollow area  22  and one or more passageways  26  leading to hollow area  22 . Wires  38  extend through passageways  26  and hollow area  22  to carry signals to and/or from a RF telemetry system  36 . RF telemetry system  36  is capable of rotating along with shaft  20  and transmits/receives signals to/from, for example, power generator  60  through wires  38  or wirelessly through a transmitting antenna of the RF telemetry system  36 .  
         [0024]     A pair of targets  32  and  34  are bonded on an outer surface of shaft  20 . Targets  32  and  34  may be mounted on opposite axial ends of shaft  20 . For example, in the exemplary embodiment illustrated in  FIG. 1 , targets  32  and  34  are separated along the axial direction by approximately  80  inches. The respective radii of the outer surface on which targets  32  and  34  are bonded are approximately 11 and 22 inches, respectively. While  FIG. 1  illustrates targets  32  and  34  being bonded on the outer surface of shaft  20  at different radii, targets  32  and  34  could alternatively be mounted on an outer surface of shaft  20  at the same radii. Each of targets  32  and  34  may be formed by a pair of highly reflective tapes which are each capable of intensifying and reflecting a light signal which is incident on the tape. Each of the targets  32  and  34  may be aligned at the same circumferential position or be circumferentially offset from one another.  
         [0025]     Low power laser light first horizontal first probe  12  and second horizontal first probe  14  are positioned at an angle which is perpendicular to the long axis of shaft  20 . First horizontal probe  12  and second horizontal first probe  14  may be made of fiber optic cables for transmitting and receiving laser light signals. In an exemplary embodiment, the tips of first horizontal probe  12  and second horizontal first probe  14  which are closest to shaft  20  are approximately 0.05 inches from the outer surface of shaft  20 . First horizontal probe  12  and second horizontal first probe  14  are aligned in the same axial planes as targets  32  and  34 , respectively.  
         [0026]     In an exemplary embodiment according to the present invention, one or more first horizontal second probes  12   a  and one or more second horizontal second probes  14   a  are employed, and positioned in a circular arc around and perpendicular to the long axis of shaft  20  180 degrees from the positions of first horizontal first probe  12  and second horizontal first probe  14 , respectively. Similarly, as shown in  FIG. 1 , first vertical first probe  15  and second vertical first probe  17  are positioned in a circular arc around the shaft  20  at 180 degrees sepration from first vertical second probe  15   a  and second vertical second probe  17   a , respectively. In the exemplary embodiment as shown in  FIG. 1 , the first horizontal first and second probes  12  and  12   a  and the second horizontal first and second probes  14  and  14   a  are positioned with 90 degrees of separation in the same circular axial planes as the first vertical first and second probes  15  and  15   a  and second vertical first and second probes  17  and  17   a , respectively.  
         [0027]     Laser light probes  12 ,  12   a ,  14 ,  14   a ,  15 ,  15   a ,  17 , and  17   a  are each connected to processor  10 . Processor  10 , as will be discussed in more detail below, is capable of calculating a torsional displacement (circumferential twist) of rotating shaft  20  based upon measurements taken by laser light probes  12 ,  12   a ,  14 ,  14   a ,  15 ,  15   a ,  17 , and  17   a  and calculating a torque imposed on shaft  20  based on its torsional displacement. Processor  10 , may be implemented by, for example, General Electric Aircraft Engine (GEAE) digital light probe system.  
         [0028]     Revolutional target  33  is bonded on an outer surface of shaft  20  and may be formed by a metal. Like targets  32  and  34 , revolutional target  33  rotates along with shaft  20 . Revolutional target  33  rotates underneath revolutional probe  13  once per revolution of shaft  20 . Revolutional probe  13  may be, for example, an eddy current probe which detects the presence of (metal) revolutional target  33 . A signal from revolutional probe  13  is triggered and sent to processor  10  once during every revolution of shaft  20  as revolutional target  33  passes underneath and is detected by revolutional probe  13 . The trigger signal provided from revolutional probe  13  enables processor  10  to establish a reference zero timing for signals received by first laser probes  12  and revolutional probe  13  in every revolution of shaft  20 . Accordingly, a time measured from the reference zero time to the time first horizontal first probe  12  and first vertical first probe  15  receive a signal is started when revolutional probe  13  transmits a trigger signal to processor  10  in every revolution. In cooperation with revolutional target  33 , revolutional probe  13  thus forms a “one per revolution sensor.” The operation of revolutional probe  13  and revolutional target  33  also provide the necessary information to allow processor  10  to calculate the rotational speed of shaft  20 . Specifically, the rotational speed of shaft  20  may be determined by:
 
ω=2 n (1 /Δt ),
 
         [0029]     where Δt is the difference between two consecutive trigger signals sent from revolutional probe  13 ).  
         [0030]     In operation, gas turbine  40  will rotate shaft  20 , which will in turn rotate generator shaft  62  of power generator  60 . The rotation of generator shaft  62  enables magnet  64  to rotate within a stator of power generator  60  to generate electric power.  
         [0031]     As shaft  20  rotates, first target  32  will once pass underneath laser light probes  12 ,  12   a ,  15 , and  15   a  upon every revolution of shaft  20 . Similarly, as shaft  20  rotates, second target  34  will once pass underneath laser light probes  14 ,  14   a ,  17 , and  17   a  upon every revolution of shaft  20 . The laser light signals transmitted by laser light probes  12 ,  12   a ,  15 , or  15   a , and  14 ,  14   a ,  17 , or  17   a  will be incident on targets  32  and  34 , respectively, as those targets  32  and  34  pass underneath the respective probes as shaft  20  rotates. Targets  32  and  34  will intensify and reflect the transmitted laser light signals incident on targets  32  and  34 . The reflected laser light signals, which effectively form response laser light signals (i.e., laser light signals formed in response to the transmitted laser light signals incident on targets  32 , and  34 ) are received by laser light probes  12 ,  12   a ,  15 , or  15   a , and  14 ,  14   a ,  17 , or  17   a  which then send corresponding signals to processor  10 . Processor  10  determines and records the precise time at which the laser light signal reflected from target  32  is received by probes  12 ,  12   a ,  15 , or  15   a  and the precise time at which the laser light signal reflected from target  34  is received at probes  14 ,  14   a ,  17 , or  17   a . The difference between the respective reception times of the reflected laser light signals by probes  12 ,  12   a ,  15 , or 15 a , and  14 ,  14   a ,  17 , or  17   a  may then be detected. For example, a difference of time of as small as approximately 10 nanoseconds may be detected.  
         [0032]     The first horizontal first probe  12 , first horizontal second probe  12   a , first vertical first probe  15  and first vertical second probe  15   a  transmit first transmission first and second signals and receive first horizontal first and second responses to/from the first target  32 . The first vertical first probe  15 , first vertical second probe  15   a , second vertical first probe  17 , and second vertical second probe  17   a  transmit second vertical first and second transmissions and receive second vertical first and second responses to/from the second target  34 .  
         [0033]     The difference in time between the laser light signal receptions by probes  12 ,  12   a ,  14 ,  14   a ,  15 ,  15   a ,  17 , and  17   a  will change as different levels of torque is applied to rotating shaft  20 . After processor  10  has determined the difference in time, processor  10  can then determine an angular torsional displacement of shaft  20 . As an example, the torsional displacement measured in radians may be calculated, assuming the circumferential positions of targets  32  and  34  on shaft  20  are the same (i.e., targets  32  and  34  are circumferentially aligned), by multiplying Δ t times ω, where Δ t is the time difference between the receptions of laser light signals by probes ( 12 ,  12   a ,  15 , and  15   a  ) and probes ( 14 ,  14   a ,  17 , and  17   a ) and ω is the rotational speed of shaft  20 . The rotational speed ω of shaft  20  may be determined from the operation of revolutional probe  13  and revolutional target  33  as discussed above.  
         [0034]      FIGS. 2A and 2B  are diagrams illustrating the reception of laser light response signals received by laser light probes  12 ,  12   a ,  14 ,  14   a ,  15 ,  15   a ,  17 , and  17   a  resulting from laser light signals transmitted from laser light probes  12 ,  12   a ,  14 ,  14   a ,  15 ,  15   a ,  17 , and  17   a  being reflected by targets  32  and  34 , respectively, when two different levels of torque are imposed on rotating shaft  20  (again assuming that targets  32  and  34  have the same circumferential position). In particular,  FIG. 2A  is a diagram which illustrates laser light signals received by laser light probes  12 ,  12   a ,  14 ,  14   a ,  15 ,  15   a ,  17 , and  17   a  when no (measurable) torque is imposed on rotating shaft  20 . As can be seen from  FIG. 2A , the times at which the respective laser light signals are received by laser light probes ( 12 ,  12   a ,  15 , and  15   a  ) and laser light probes ( 14 ,  14   a ,  17 , and  17   a ) are simultaneous. Accordingly, there is no torsional displacement on shaft  20  (i.e., shaft  20  has not been twisted) as a result of the rotational force imposed on the shaft  20  since Δ t, the time difference between receptions of laser light signals by laser light probes ( 12 ,  12   a ,  15 , and  15   a  ) and laser light probes ( 14 ,  14   a ,  17 , and  17   a ) is 0 seconds. Of course, if targets  32  and  34  are bonded to shaft  20  at circumferentially offset positions, a time difference which depends at least on the rotational speed of shaft  20  would be expected when there is no torsional displacement of shaft  20 .  
         [0035]     In contrast to  FIG. 2A ,  FIG. 2B  is a diagram illustrating laser light signals received by laser light probes  12 ,  12   a ,  14 ,  14   a ,  15 ,  15   a ,  17 , and  17   a  when a measurable torque is imposed on shaft  20 . In particular, because of the torque imposed on shaft  20 , shaft  20  will have a torsional displacement (i.e., circumferential twist). Targets  32  and  34  which were previously circumferentially aligned therefore become circumferentially offset from one another so that the respective laser light signals reflected by targets  32  and  34  are received by laser light probes ( 12 ,  12   a ,  15 , and  15   a  ) and laser light probes ( 14 ,  14   a ,  17 , and  17   a ) at different times. This difference in time Δt may be multiplied by the rotational speed of the shaft (ω) to calculate the torsional displacement in radians.  
         [0036]     As illustrated generally in  FIGS. 3A-3C , processor  10  may then calculate the torque imposed on rotating shaft  20  based on its calculated torsional displacement in a highly accurate manner (e.g., with +0.5%). For example, the torque may be calculated from the torsional displacement using a finite element model analysis. Power generated by gas turbine  40  may be determined based on the calculated torque.  
         [0037]     In particular, torque on shaft  20  may be calculated from the torsional displacement as follows. If shaft  20  comprises a uniform material at a constant temperature and its cross-sectional area is uniform and constant over its entire length, then torque may be calculated using the closed form solution:  
       τ   =         (   θ   )     ⁢     (   G   )     ⁢     (   j   )         (   L   )           
 
         [0038]     where τ=torque on shaft, θ=torsional displacement in radians (angle change measured by probes ( 12 ,  12   a ,  15 , and  15   a  ) and probes ( 14 ,  14   a ,  17 , and  17   a ) and calculated by processor  10 ), G=shear modulus of the material of shaft  20  (available in engineering handbooks), j=polar moment of inertia and L=axial distance between probes  12 / 12   a  and  14 / 14   a . The polar moment of inertia (j) is the inherent stiffness of shaft  20  and can be calculated by:  
       j   =         (      )     ⁢     (     R   4     )       2         
 
         [0039]     for a solid circular cross section where R=radius of shaft  20 .  
         [0040]     The torque calculation becomes more complex to precisely determine if any one or more of the following occur:  
         [0041]     Shear modulus (G) changes along the length and/or radial direction (e.g., due to temperature changes of the shaft material or use of a different material).  
         [0042]     If the cross-sectional area of shaft  20  is not uniform (e.g., keyway notch)  
         [0043]     If the cross-sectional area is not constant along the length of shaft  20 .  
         [0044]     Items (2) and (3) affect the polar moment of inertia (j) calculation. While a combination of shaft design features (items (1) and (3) above) make it virtually impossible to accurately convert torsional displacement to torque using hand calculations (see  FIG. 3A ), Finite Element Analysis (FEA) can be utilized to accurately to make this calculation with great precision. Specifically, a Finite Element Model (FEM) is created that captures the shaft geometry, material properties, and boundary conditions. A necessary boundary condition is an arbitrary torque load applied parallel to the shaft centerline. The FEA is performed on the FEM and the result is a distribution of torsional displacement along shaft  20  as can be seen in  FIG. 3B . The amount of torsional displacement between the axially spaced probes  12 / 12   a  and  14 / 14   a  is readily available by FEA post processing. This is accomplished by taking the arbitrary torque value used in the FEM and dividing it by the calculated torsional displacement value determined from processor  10 . This is the constant that relates torsional displacement to torque as shown in  FIG. 3C . Thus, the torque carried by shaft  20  in operation can be calculated by taking the torsional displacement determined by processor  10  and multiplying by the FEA calculated constant.  
         [0045]     While shaft  20  illustrated in the exemplary embodiment of  FIG. 1  is rotated by a gas turbine  40 , those skilled in the art will appreciate that shaft  20  may alternatively be rotated by another machine such as a steam turbine, nuclear power generator or internal combustion engine. Moreover, although shaft  20  transmits the rotational force exerted on it from gas turbine  40  to rotate a magnet  64  in power generator  60 , those skilled in the art will appreciate that shaft  20  can be alternatively connected to drive other loads. For example, shaft  20 , once rotated by a machine such as turbine  40 , can be used to drive other loads such as rotating a propeller on a vehicle.  
         [0046]      FIGS. 4-5  illustrate another exemplary embodiment of the present invention. Reference numbers corresponding to parts previously described for previous embodiments will remain the same. Only the differences from previous embodiments will be discussed in detail. While  FIG. 1  illustrates shaft  20  as part of a simple cycle configuration,  FIGS. 4-5  illustrate shaft  20  as part of a combined cycle configuration. Specifically, shaft  20  illustrated in  FIGS. 4-5  is rotated by gas turbine  40  while steam turbine  50  imposes a rotational force on generator shaft  62  of power generator  60 . Axial end  24   a  of shaft  20  is connected to turbine shaft  42  of gas turbine  40  and axial end  24   b  of shaft  20  is connected to steam turbine shaft  52  of steam turbine  50 . Gas turbine  40  rotates turbine shaft  42  to rotate shaft  20  and, in turn, shaft  20  rotates steam turbine shaft  52  of steam turbine  50 . Thus, the torque imposed on shaft  20  by gas turbine  40  is transmitted to steam turbine shaft  52  which then imposes a torque on generator shaft  62 . Generator shaft  62  is thus subject to the combined rotational forces from steam turbine  50  and gas turbine  40 . Magnet  64  of power generator  60  thus rotates as a result of rotational forces provided by steam turbine  50  and gas turbine  40 .  
         [0047]     As discussed in the exemplary embodiment of the  FIG. 1 , as shaft  20  is rotated by gas turbine  40 , laser light signals transmitted from laser light probes  12 ,  12   a ,  15 , and  15   a  are reflected by targets  32  and  32   a  and probes  14 ,  14   a ,  17 , and  17   a  are reflected by targets  34  and  34   a , respectively, as they revolve and pass underneath probes  12 ,  12   a ,  14 ,  14   a ,  15 ,  15   a ,  17 , and  17   a . The laser light signals reflected from targets  32 ,  32   a ,  34  and  34   a  are received by laser light probes  12 ,  12   a ,  14 ,  14   a ,  15 ,  15   a ,  17 , and  17   a  and their respective times of arrival measured. Processor  10  then calculates the difference in the time at which laser light signals are received by laser light probes  12 ,  12   a ,  14 ,  14   a ,  15 ,  15   a ,  17 , and  17   a  to determine a torsional displacement and then determines a torque imposed on shaft  20  based upon its torsional displacement. Power generated by gas turbine  40  can be calculated from the determination of torque.  
         [0048]      FIGS. 6   a - b  further illustrate an embodiment according to the present invention with multiple targets passing underneath each of light probes  12 ,  12   a ,  14 ,  14   a ,  15 ,  15   a ,  17  and  17   a . Specifically, two (or more) targets  32 ,  32   a  pass underneath an array of light probes  12 ,  12   a ,  15 , and  15   a , and two (or more) targets  34 ,  34   a  pass underneath an array of light probes  14 ,  14   a ,  17 , and  17   a.    
         [0049]     As shaft  20  twists when it is loaded, targets  32  and  34  will be displaced from one another as discussed above. These targets  32  and  34  will also be displaced from one another if shaft  20  vibrates. The displacement from shaft vibration can be measured through the use of additional targets  32   a  and  34   a . By assessing the time of arrival of at least one of the sets of targets  32  and  32   a  (or  34  and  34   a ) within one revolution of shaft  20  and comparing it to the expected time of arrival based on the actual distance between the targets  32  and  32   a  and the rotational speed of shaft  20 , the displacement from vibration can be calculated. For example, if targets  32  and  32   a  are circumferentially offset from one another by 180 degrees. (see  FIG. 6   a ), the respective times of arrival of signals detected by probe  12  is expected to be one-half of the time required for one complete rotation. The time for a complete rotation may be determined through the operation of revolutional probe  13  and revolutional target  33  as discussed above. The displacement of shaft  20  due to its vibration may then be determined by the difference between the expected time difference and the actual time difference that respective response signals from targets  32  and  32   a  are detected by probes  12  and/or  12   a  and/or the difference between the expected time difference and the actual time difference that respective response signals from targets  34  and  34   a  are detected by laser light probe  14  and/or  14   a . The total torsional displacement may thus be determined by adding the displacement caused by the vibration and the load displacement (i.e., the torsional displacement caused by the rotational force imposed on shaft  20 ). Accordingly, by bonding additional targets  32   a  and/or  34   a  to shaft  20  and detecting response signals therefrom utilizing laser probes  12 ,  12   a ,  14 , and/or  14   a , a correctional value may be determined for the torsional displacement resulting from the rotational force imposed on shaft  20 . Accuracy in the torsional displacement measurement may therefore be enhanced.  
         [0050]     While  FIGS. 6   a - b  illustrate adding additional targets  32   a  and  34   a  onto shaft  20  as part of a simple cycle configuration, those skilled in the art will appreciate that targets  32   a  and  34   a  may also be added to a shaft  20  as part of a combined cycle configuration as illustrated in  FIGS. 4-5 .  
         [0051]     The terms “horizontal” and “vertical” are used herein to describe perpendicular planes relative to the long axis of the shaft  20 . It is to be understood that any two perpendicular planes relative to the long axis of the shaft  20  may be employed for probe locations in various embodiments according to the present invention, and such probe positions are not limited to any true horizontal or vertical planes relative to any given perspective.  
         [0052]     While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiments, it is to be understood that the invention is not to be limited to the disclosed embodiments, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.