The present invention relates to an apparatus for measuring
torsional displacement of a rotating shaft.
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.
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.
Accordingly, there remains a need in the art 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. The present invention satisfies
this need. For example, the present invention is capable of measuring torque of
a rotating shaft within a +/- 0.5% accuracy.
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.
Known systems for determining the torque being transmitted
through a rotating shaft are described in
. A known apparatus for measuring the vibrations in a rotating shaft is
US 4, 148,222
describes an apparatus and method for measuring torsional vibration.
According to the present invention, there is provided an
apparatus as defined in appended claim 1.
The processor may determine a torque imposed on the rotatable
shaft based upon its torsional displacement. The processor may determine the torsional
displacement based on the difference in time between when the first response signal
is received by the first probe and when the second response signal is received by
the second probe.
The first and second probes may be formed by laser probes
and the first and second targets may include a reflective material so that the first
transmission signal is a laser light signal and the first response signal is a laser
light signal formed from a reflection of the first transmission signal by the first
target and the second transmission signal is a laser light signal and the second
response signal is a laser light signal formed from a reflection of the second transmission
signal by the second target. The first and second targets may be coupled to the
rotatable shaft on opposite axial ends thereof. Explanatory examples and embodiment
of the invention will now be described, by way of example, with reference to the
accompanying drawings, in which:
- FIGURE 1 is a diagram illustrating, inter alia, a cross sectional view of a
rotating shaft in a simple cycle configuration whose torque is measured.
- FIGURE 2A is a diagram illustrating signals received by two different laser
light probes from a rotating shaft having no measurable torque imposed thereon.
- FIGURE 2B is a diagram illustrating signals received by two different laser
light probes from a rotating shaft having a measurable torque imposed thereon.
- FIGURES 3A-3C are diagrams illustrating an exemplary method for calculating
torque of a rotating shaft based on its torsional displacement (circumferential
- FIGURE 4 is a diagram illustrating, inter alia, a cross sectional view of a
rotating shaft in a combined cycle configuration whose torque is measured.
- FIGURE 5 is a perspective view of the combined cycle configuration illustrated
in Figure 4 (viewed from the reverse side of Figure 4).
- FIGURE 6 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.
- FIGURE 7 is a cross sectional view taken from line 7-7 in Figure 6.
Figure 1 illustrates a shaft 20 that serves as a load coupling
shaft. Shaft 20 is connected at one axial end 24a to shaft 42 of gas turbine 40
and connected at the other axial end 24b to a rotatable shaft 62 of power generator
60. Accordingly, shaft 20 forms a portion of a simple cycle configuration exemplary
embodiment illustrated in Figure 1.
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.
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.
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, as illustrated in Figure 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 Figure 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.
A pair of low power laser light probes 12 and 14 are positioned
at an angle which is perpendicular to shaft 20. Laser light probes 12 and 14 may
be made of fiber optic cables for transmitting and receiving laser light signals.
The tips of laser light probes 12 and 14 which are closest to shaft 20 are approximately
0.05 inches from the outer surface of shaft 20. Laser light probes 12 and 14 are
aligned in the same axial planes as targets 32 and 34, respectively.
Laser light probes 12 and 14 are 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 and 14 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.
Target 33 is bonded on an outer surface of shaft 20 and
may be formed by a metal. Like targets 32 and 34, target 33 rotates along with shaft
20. Target 33 rotates underneath probe 13 once per revolution of shaft 20. Probe
13 may be, for example, an eddy current probe which detects the presence of (metal)
target 33. A signal from probe 13 is triggered and sent to processor 10 once during
every revolution of shaft 20 as target 33 passes underneath and is detected by probe
13. The trigger signal provided from probe 13 enables processor 10 to establish
a reference zero timing for signals received by laser probes 12 and 13 in every
revolution of shaft 20. Accordingly, a time measured from the reference zero time
to the time laser probe 12 or 14 receives a signal is started when probe 13 transmits
a trigger signal to processor 10 in every revolution. In cooperation with target
33, probe 13 thus forms a "one per revolution sensor." The operation of probe 13
and 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 &ohgr; = 2 x &pgr; x (1/time difference between two consecutive
trigger signals sent from probe 13).
In operation, gas turbine 40 will rotate shaft 20, which
will in turn rotate shaft 62 of power generator 60. The rotation of shaft 62 enables
magnet 64 to rotate within a stator of power generator 60 to generate electric power.
As shaft 20 rotates, targets 32 and 34 will once pass underneath
laser light probes 12 and 14 upon every revolution of shaft 20. The laser light
signals transmitted by laser light probes 12 and 14 will be incident on targets
32 and 34, respectively, as those targets 32 and 34 pass underneath probes 12 and
14. 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, 34) are received
by laser light probes 12 and 14 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 probe 12 and the precise time at
which the laser light signal reflected from target 34 is received at probe 14. The
difference between the respective reception times of the reflected laser light signals
by probes 12 and 14 may then be detected. For example, a difference of time of as
small as approximately 10 nanoseconds may be detected.
The difference in time between the laser light signal receptions
by probes 12 and 14 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 (&Dgr;t x &ohgr;) where &Dgr;t
is the time difference between the receptions of laser light signals by probes 12
and 14 and &ohgr; is the rotational speed of shaft 20. The rotational speed &ohgr;
of shaft 20 may be determined from the operation of probe 13 and target 33 as discussed
Figures 2A and 2B are diagrams illustrating the reception
of laser light response signals received by laser light probes 12 and 14 resulting
from laser light signals transmitted from laser light probes 12 and 14 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, Figure 2A is a diagram which illustrates laser light signals
received by laser light probes 12 and 14 when no (measurable) torque is imposed
on rotating shaft 2. As can be seen from Figure 2A, the times at which the respective
laser light signals are received by laser light probes 12 and 14 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
&Dgr;t, the time difference between receptions of laser light signals by laser
light probes 12 and 14, 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.
In contrast to Figure 2A, Figure 2B is a diagram illustrating
laser light signals received by laser light probes 12 and 14 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 and 14 at different times.
This difference in time &Dgr;t may be multiplied by the rotational speed of the
shaft w to calculate the torsional displacement in radians.
As illustrated generally in Figures 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.
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:
where T = torque on shaft, &thgr; = torsional displacement in radians (angle change
measured by probes 12, 14 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 and 14. The polar moment of
inertia (j) is the inherent stiffness of shaft 20 and can be calculated by
for a solid circular cross section where R = radius of shaft 20.
The torque calculation becomes more complex to precisely
determine if any one or more of the following occur:
- (1)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).
- (2)If the cross-sectional area of shaft 20 is not uniform (e.g., keyway notch)
- (3)If the cross-sectional area is not constant along the length of shaft 20.
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 Figure 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 Figure 3B. The amount of torsional displacement between the two axially spaced
probes 12 and 14 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 Figure 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.
While shaft 20 illustrated in the example of Figure 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.
Figures 4-5 illustrate another example. Reference numbers
corresponding to parts previously described will remain the same. Only the differences
from previous examples (will be discussed in detail. While Figure 1 illustrates
shaft 20 as part of a simple cycle configuration, Figures 4-5 illustrate shaft 20
as part of a combined cycle configuration. Specifically, shaft 20 illustrated in
Figures 4-5 is rotated by gas turbine 40 while steam turbine 50 imposes a rotational
force on shaft 62 of power generator 60. Axial end 24a of shaft 20 is connected
to shaft 42 of gas turbine 40 and axial end 24b of shaft 20 is connected to shaft
52 of steam turbine 50. Gas turbine 40 rotates shaft 42 to rotate shaft 20 and,
in turn, shaft 20 rotates shaft 52 of steam turbine 50. Thus, the torque imposed
on shaft 20 by gas turbine 40 is transmitted to shaft 52 which then imposes a torque
on shaft 62. 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.
As discussed in the example of the Figure 1, as shaft 20
is rotated by gas turbine 40, laser light signals transmitted from laser light probes
12 and 14 are reflected by targets 32 and 34, respectively, as they revolve and
pass underneath probes 12 and 14. The laser light signals reflected from targets
32 and 34 are received by laser light probes 12 and 14 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 and 14 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.
Figures 6-7 illustrate an embodiment of the present invention.
Again, reference numbers corresponding to parts previously described will remain
the same. Only the differences will be discussed in detail. Figures 6-7 illustrate
multiple targets passing underneath each of light probes 12, 14. Specifically, two
(or more) targets 32, 32a pass underneath light probe 12 and two (or more) targets
34, 34a pass underneath light probe 14 upon rotation of shaft 20.
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 32a and 34b. By
assessing the time of arrival of at least one of the sets of targets 32 and 32a
(or 34 and 34a) 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 32a and
the rotational speed of shaft 20, the displacement from vibration can be calculated.
For example, if targets 32 and 32a are circumferentially offset from one another
by 180° (see Fig. 7), 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 probe
13 and 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
32a are detected by probe 12 and/or the difference between the expected time difference
and the actual time difference that respective response signals from targets 34
and 34a are detected by laser light probe 14. 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 32a and/or 34a to shaft
20 and detecting response signals therefrom utilizing laser probes 12 and/or 14,
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.
While Figs. 6-7 illustrate adding additional targets 32a,
34a onto shaft 20 as part of a simple cycle configuration, those skilled in the
art will appreciate that targets 32a, 34a may also be added to a shaft 20 as part
of a combined cycle configuration as illustrated in Figs. 4-5.