Rotating blade analysis

Abstract

Methods are provided for: (i) measuring the position of the blade stagger angle axis for one or more blades of a row of blades attached to a rotor, (ii) measuring the blade tip stagger angle for one or more such blades, and (iii) measuring the blade tip axial displacement for one or more such blades. The methods use forward and rearward blade tip timing datasets for successive rotations of the blades from two axially spaced blade tip timing probes. The forward probe is forward of the rearward probe along the axial direction of the rotor. The blade tip timing datasets allow the times of arrival of the blades at the respective probes to be measured. The methods also use a once per revolution dataset for the successive rotations of the blades. The once per revolution dataset allows the angular velocity of the blades to be measured.

Claims

1. A method of measuring the position of the blade stagger angle axis for one or more blades of a row of blades attached to a rotor, the method comprising the steps of: during rotation of the rotor, obtaining forward and rearward blade tip timing datasets for successive rotations of the blades from two axially spaced blade tip timing probes, a forward one of the blade tip timing probes being forward of a rearward one of the probes along the axial direction of the rotor, the forward and reward blade tip timing datasets allowing times of arrival of the blades at the respective probes to be measured; during rotation of the rotor, obtaining a once per revolution dataset for said successive rotations of the blades, the once per revolution dataset allowing angular velocity of the blades to be measured; determining, from the forward and rearward blade tip timing datasets, measured blade tip times of arrival at the forward and rearward probes of a blade for a reference revolution of the blades; determining, from the once per revolution dataset, predicted blade tip times of arrival at the forward and rearward probes of the blade for a further revolution of the blades assuming that there is no change in shape or relative position of the blade; determining, from the forward and rearward blade tip timing datasets, measured blade tip times of arrival at the forward and rearward probes of the blade for said further revolution of the blades; calculating the position of the blade stagger angle axis of the blade at said further revolution from the expression:
D.sub.FA=D.sub.FR(Δ.sub.F/(Δ.sub.F+Δ.sub.R)) or from the expression:
D.sub.RA=D.sub.FR(Δ.sub.R/(Δ.sub.F+Δ.sub.R)) where D.sub.FA is the distance along the axial direction of the rotor between the forward probe and the position of the blade stagger angle axis, D.sub.RA is the distance along the axial direction of the rotor between the rearward probe and the position of the blade stagger angle axis, D.sub.FR is the distance along the axial direction of the rotor between the forward probe and the rearward probe, Δ.sub.F is the difference between the measured blade tip time of arrival of the blade at the forward probe and the predicted blade tip time of arrival of the blade at the forward probe for said further revolution, and Δ.sub.R is the difference between the measured blade tip time of arrival of the blade at the rearward probe and the predicted blade tip time of arrival of the blade at the rearward probe for said further revolution; and performing a blade tip timing calibration based upon the calculated position of the blade stagger angle axis of the blade.

2. A method of measuring the blade tip stagger angle for one or more blades of a row of blades attached to a rotor, the method comprising the steps of: during rotation of the rotor, obtaining forward and rearward blade tip timing datasets for successive rotations of the blades from two axially spaced blade tip timing probes, a forward one of the blade tip timing probes being forward of a rearward one of the probes along the axial direction of the rotor, the forward and reward blade tip timing datasets allowing times of arrival of the blades at the respective probes to be measured; during rotation of the rotor, obtaining a once per revolution dataset for said successive rotations of the blades, the once per revolution dataset allowing angular velocity of the blades to be measured; determining, from the forward and rearward blade tip timing datasets, measured blade tip times of arrival at the forward and rearward probes of a blade for a revolution of the blades; calculating the blade tip stagger angle of the blade at said revolution from the expressions:
θ=a tan((R((α.sub.F−α.sub.R)−Δ.sub.α))/D.sub.FR)
and
Δ.sub.α=ω(T.sup.m.sub.F−T.sup.m.sub.R) where θ is the blade tip stagger angle of the blade at said revolution, D.sub.FR is the distance along the axial direction of the rotor between the forward probe and the rearward probe, R is the radial distance from the tip of the blades to the axis of the rotor, α.sub.F is the angular position of the forward probe, α.sub.R is the angular position of the rearward probe, ω is the measured angular velocity of the blades at said revolution, T.sup.m.sub.F is the measured blade tip time of arrival of the blade at the forward probe at said revolution, and T.sup.m.sub.R is the measured blade tip time of arrival of the blade at the rearward probe at said revolution; and performing a blade tip timing calibration based upon the calculated blade tip stagger angle of the blade.

3. A method of measuring the blade tip axial displacement for one or more blades of a row of blades attached to a rotor, the method comprising the steps of: during rotation of the rotor, obtaining forward and rearward blade tip timing datasets for successive rotations of the blades from two axially spaced blade tip timing probes, a forward one of the blade tip timing probes being forward of a rearward one of the probes along the axial direction of the rotor, the forward and reward blade tip timing datasets allowing times of arrival of the blades at the respective probes to be measured; during rotation of the rotor, obtaining a once per revolution dataset for said successive rotations of the blades, the once per revolution dataset allowing angular velocity of the blades to be measured; determining, from the forward and rearward blade tip timing datasets, measured blade tip times of arrival at the forward and rearward probes of a blade for a reference revolution of the blades; determining, from the once per revolution dataset, predicted blade tip times of arrival at the forward and rearward probes of the blade for a further revolution of the blades assuming that there is no change in shape or relative position of the blade; determining, from the forward and rearward blade tip timing datasets, measured blade tip times of arrival at the forward and rearward probes of the blade for said further revolution of the blades; calculating the position of the blade stagger angle axis of the blade at said further revolution from the expression:
D.sub.FA=D.sub.FR(Δ.sub.F/(Δ.sub.F+Δ.sub.R)) or from the expression:
D.sub.RA=D.sub.FR(Δ.sub.R/(Δ.sub.F+Δ.sub.R)) where D.sub.FA is the distance along the axial direction of the rotor between the forward probe and the position of the blade stagger angle axis, D.sub.RA is the distance along the axial direction of the rotor between the rearward probe and the position of the blade stagger angle axis, D.sub.FR is the distance along the axial direction of the rotor between the forward probe and the rearward probe, Δ.sub.F is the difference between the measured blade tip time of arrival of the blade at the forward probe and the predicted blade tip time of arrival of the blade at the forward probe for said further revolution, and Δ.sub.R is the difference between the measured blade tip time of arrival of the blade at the rearward probe and the predicted blade tip time of arrival of the blade at the rearward probe for said further revolution; calculating the blade tip stagger angle of the blade for each of a reference and further revolutions from the expressions:
θ=a tan((R((α.sub.F−α.sub.R)−Δ.sub.α))/D.sub.FR)
and
Δ.sub.α=ω(T.sup.m.sub.F−T.sup.m.sub.R) where θ is the blade tip stagger angle of the blade at each revolution, D.sub.FR is the distance along the axial direction of the rotor between the forward probe and the rearward probe, R is the radial distance from the tip of the blades to the axis of the rotor, α.sub.F is the angular position of the forward probe, α.sub.R is the angular position of the rearward probe, ω is the measured angular velocity of the blades at each revolution, T.sup.m.sub.F is the measured blade tip time of arrival of the blade at the forward probe at each revolution, and T.sup.m.sub.R is the measured blade tip time of arrival of the blade at the rearward probe at each revolution; determining updated predicted blade tip times of arrival at the forward and rearward probes of the blade for said further revolution from the expressions:
T.sup.P.sub.F,fur=T.sup.m.sub.F,refω.sub.ref/ω.sub.fur−D.sub.FA,fur(tan(θ.sub.fur)−tan(θ.sub.ref))/(Rω.sub.fur)
and
T.sup.P.sub.R,fur=T.sup.m.sub.R,refω.sub.ref/ω.sub.fur+D.sub.RA,fur(tan(θ.sub.fur)−tan(θ.sub.ref))/(Rω.sub.fur) where T.sup.p.sub.F, fur and T.sup.p.sub.R,fur are updated predicted blade tip times of arrival of the blade at respectively the forward and rearward probes at said further revolution and relative to the start of said further revolution, T.sup.m.sub.F,ref and T.sup.m.sub.R,ref are the measured blade tip times of arrival of the blade at respectively the forward and rearward probes at said reference revolution and relative to the start of said reference revolution, ω.sub.ref and ω.sub.fur are the measured angular velocities of the blades at respectively said reference revolution and said further revolution, D.sub.FA,fur and D.sub.RA,fur are the distances along the axial direction of the rotor between respectively the forward probe and the position of the blade stagger angle axis of the blade and the rearward probe and the position of the blade stagger angle axis of the blade at said further revolution, and θ.sub.ref and θ.sub.fur are the blade tip stagger angles of the blade at respectively said reference revolution and said further revolution; and determining the blade tip axial displacement at said further revolution relative to the blade tip axial position at said reference revolution from the expressions:
Δ.sub.ax=(2πRΔt.sub.cts)/(ω.sub.fur tan(θ.sub.fur))
and
Δt.sub.cts=(T.sup.m.sub.F,fur−T.sup.p.sub.F,fur)−(T.sup.m.sub.R,fur−T.sup.p.sub.R,fur) where Δ.sub.ax is the blade tip axial displacement at said further revolution relative to the blade tip axial position at said reference revolution, and T.sup.m.sub.F,fur and T.sup.m.sub.R,fur are the measured times of arrival of the blade at respectively the forward and rearward probes at said further revolution and relative to the start of said further revolution; and performing a blade tip timing calibration based upon the calculated blade tip axial displacement of the blade.

4. The method of claim 1 further including an initial step of generating the forward and rearward blade tip timing datasets and the once per revolution dataset.

5. The method of claim 2 further including an initial step of generating the forward and rearward blade tip timing datasets and the once per revolution dataset.

6. The method of claim 3 further including an initial step of generating the forward and rearward blade tip timing datasets and the once per revolution dataset.

7. The method of claim 1, wherein the blades are fan blades.

8. The method of claim 1, further comprising the step of locating the forward probe at a position which is swept by the leading edges of the blades.

9. The method of claim 1, further comprising the step of locating the rearward probe at a position which is swept by the trailing edges of the blades.

10. The method of claim 1, further comprising the steps of: implementing a computer model of the blades in motion; compiling computer modelled blade tip timing datasets for at least a first revolution of the blades; and validating the computer model of the blades by comparison of the computer modelled blade tip timing datasets to said forward and rearward blade tip timing datasets.

11. The method of claim 2, further comprising the steps of: implementing a computer model of the blades in motion; compiling computer modelled blade tip timing datasets for at least a first revolution of the blades; and validating the computer model of the blades by comparison of the computer modelled blade tip timing datasets to said forward and rearward blade tip timing datasets.

12. The method of claim 3, further comprising the steps of: implementing a computer model of the blades in motion; compiling computer modelled blade tip timing datasets for at least a first revolution of the blades; and validating the computer model of the blades by comparison of the computer modelled blade tip timing datasets to said forward and rearward blade tip timing datasets.

13. The method of claim 1, further comprising the steps of: implementing a computer model of the blades in motion; compiling computer modelled blade tip timing datasets for at least a first revolution of the blades; and calibrating the computer model of the blades by comparison of the computer modelled blade tip timing datasets to said forward and rearward blade tip timing datasets.

14. The method of claim 2, further comprising the steps of: implementing a computer model of the blades in motion; compiling computer modelled blade tip timing datasets for at least a first revolution of the blades; and calibrating the computer model of the blades by comparison of the computer modelled blade tip timing datasets to said forward and rearward blade tip timing datasets.

15. The method of claim 3, further comprising the steps of: implementing a computer model of the blades in motion; compiling computer modelled blade tip timing datasets for at least a first revolution of the blades; and calibrating the computer model of the blades by comparison of the computer modelled blade tip timing datasets to said forward and rearward blade tip timing datasets.

16. The method of claim 1 wherein said forward and reward blade tip timing datasets contain signals indicative of events selected from the group consisting of surge, stall and flutter.

17. The method of claim 2 wherein said forward and reward blade tip timing datasets contain signals indicative of events selected from the group consisting of surge, stall and flutter.

18. The method of claim 3 wherein said forward and reward blade tip timing datasets contain signals indicative of events selected from the group consisting of surge, stall and flutter.

19. A computer configured by a program to perform the method of claim 1.

20. A computer configured by a program to perform the method of claim 2.

21. A computer configured by a program to perform the method of claim 3.

22. A non-transitory computer readable storage medium encoded with a program for configuring a computer to perform the method of claim 1.

23. A non-transitory computer readable storage medium encoded with a program for configuring a computer to perform the method of claim 2.

24. A non-transitory computer readable storage medium encoded with a program for configuring a computer to perform the method of claim 3.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows schematically a BTT arrangement;

(2) FIG. 2 is a flow chart showing procedural steps in a method of measuring the blade tip axial displacement of a blade of a row of blades attached to a rotor;

(3) FIG. 3 shows schematically the measurement of the blade tip stagger angle if the blade at either a reference or a further rotation;

(4) FIG. 4 shows schematically the measurement of the stagger angle axis of the blade at the further rotation;

(5) FIG. 5 shows schematically rotation of the blade tip aerofoil section about the blade stagger angle axis;

(6) FIG. 6 shows schematically a circumferential time shift of the blade tip and the corresponding blade tip axial displacement; and

(7) FIG. 7 shows plots of measured blade tip axial displacement against rotor speed.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(8) FIG. 1 shows schematically a BTT arrangement. An OPR probe 1 monitors the position of rotor 2, while 1 to n BTT probes 3 provide timings for blades 4 mounted to the rotor.

(9) FIG. 2 is a flow chart showing procedural steps in a method of measuring the blade tip axial displacement of a blade of a row of blades attached to a rotor.

(10) In a first step 5, BTT datasets are generated for (i) a forward BTT probe positioned so that it is swept by the leading edges of a row of blades over successive rotations of the blades and (ii) a rearward BTT probe positioned so that it is swept by the trailing edges of the blades over the rotations. An OPR dataset is also generated for the successive rotations. The data in the datasets do not have to be filtered. In a next step 6, the datasets are used to measure the blade tip stagger angle for one of the blades and on a reference rotation (conveniently the first rotation) of the blades. At step 7, the datasets are used to measure the blade tip stagger angle for the blade on a further rotation of the blades. At step 8, the datasets are used to measure the position of the stagger angle axis of the blade at the further revolution. At step 9, the blade tip stagger angles and the position of the stagger angle axis are used to determine predicted blade tip times of arrival at the forward and rearward probes for the further revolution. Finally, at step 10, the predicted blade tip times of arrival are used to determine the blade tip axial displacement at the further revolution.

(11) Returning to steps 6 and 7, FIG. 3 shows schematically the measurement of the blade tip stagger angle at either the reference or further rotation. A blade tip 11 sweeps at an angular velocity ω passed the forward probe 12 at angular position α.sub.F and rearward probe 13 at angular position α.sub.R, the distance along the axial direction of the rotor between the forward and rearward probes being D.sub.FR. The angular shift Δ.sub.α of the leading or trailing edge of the blade between the arrivals at the forward and rearward probes is then:
Δ.sub.α=ω(T.sup.m.sub.F−T.sup.m.sub.R)

(12) where T.sup.m.sub.F is the measured time of arrival of the blade at the forward probe from the forward probe BTT dataset, and T.sup.m.sub.R is the measured time of arrival of the blade at the rearward probe from the rearward probe BTT dataset. The blade tip stagger angle θ, i.e. the angle between the chord C of the aerofoil section at the blade tip 11 and the axial direction X of the rotor, is then calculated for the particular revolution from the expression:
θ=a tan((R((α.sub.F−α.sub.R)−Δ.sub.α))/D.sub.FR)

(13) where R is the radial distance from the tip of the blades to the axis of the rotor.

(14) Turning then to step 8, FIG. 4 shows schematically the measurement of the blade stagger angle axis at the further rotation. On the assumption that there is no change in shape or relative position of the blade (i.e. there are no geometric or aerodynamic changes), predicted blade tip times of arrival at the forward and rearward probes of the blade for the further revolution are calculated from the angular velocity of the blades as measured by the OPR dataset. These predicted blade tip times of arrival are represented in FIG. 4 by a predicted chord position for the blade. The BTT datasets, however, provide the actual measured blade tip times of arrival at the forward and rearward probes of the blade for the further revolution. These measured blade tip times of arrival are represented in FIG. 4 by a measured chord position for the blade. Also shown in FIG. 4 are lines F, R respectively which are the paths swept by the positions on the blade tip corresponding to the forward 12 and rearward 13 probes, and the line S which is the path swept by the position on the blade tip through which the blade stagger angle axis passes

(15) The position of line S and hence the position of the blade stagger angle axis is calculated from the expression:
D.sub.FA=D.sub.FR(Δ.sub.F/(Δ.sub.F+Δ.sub.R))
or from the expression:
D.sub.RA=D.sub.FR(Δ.sub.R/(Δ.sub.F+Δ.sub.R))

(16) where D.sub.FA is the distance along the axial direction X of the rotor between the forward probe and the position of the blade stagger angle axis, D.sub.RA is the distance along the axial direction of the rotor between the rearward probe and the position of the blade stagger angle axis, D.sub.FR is the distance along the axial direction of the rotor between the forward probe and the rearward probe, Δ.sub.F is the difference between the measured time of arrival at the forward probe and the predicted time of arrival at the forward probe for said further revolution, and Δ.sub.R is the difference between the measured time of arrival at the rearward probe and the predicted time of arrival at the rearward probe for said further revolution.

(17) Turning next to step 9, the blade tip stagger angles at the reference and further rotations and the position of the stagger angle axis at the further rotation are used to establish updated predicted blade tip times of arrival at the forward and rearward probes for the further revolution. More particularly, by knowing the position of the stagger angle axis, the blade tip aerofoil section can be rotated about that axis by an amount corresponding to the change in stagger angle between the reference rotation and the further rotation, as shown schematically in FIG. 5. That is:
T.sup.p.sub.F,fur=T.sup.m.sub.F,refω.sub.ref/ω.sub.fur−D.sub.FA,fur(tan(θ.sub.fur)−tan(θ.sub.ref))/(Rω.sub.fur)
and
T.sup.p.sub.R,fur=T.sup.m.sub.R,refω.sub.ref/ω.sub.fur+D.sub.RA,fur(tan(θ.sub.fur)−tan(θ.sub.ref))/(Rω.sub.fur)

(18) where T.sup.p.sub.F,fur and T.sup.p.sub.R,fur are the updated predicted times of arrival of the blade at respectively the forward 12 and rearward 13 probes at the further revolution and relative to the start of the further revolution, T.sup.m.sub.F,ref and T.sup.m.sub.R,ref are the measured times of arrival of the blade at respectively the forward and rearward probes at the reference revolution and relative to the start of the reference revolution, ω.sub.ref and ω.sub.fur are the measured angular velocities of the blades at respectively the reference revolution and the further revolution, D.sub.FA,fur and D.sub.RA,fur are the distances along the axial direction of the rotor between respectively the forward probe and the position of the blade stagger angle axis and the rearward probe and the position of the blade stagger angle axis at said further revolution, and θ.sub.ref and θ.sub.fur are the blade tip stagger angles of the blade at respectively said reference revolution and said further revolution.

(19) At step 10, from T.sup.p.sub.F,fur and T.sup.p.sub.R,fur it is then possible to calculate a circumferential time shift of the blade tip, Δt.sub.cts, from the expression:
Δt.sub.cts(T.sup.m.sub.F,fur−T.sup.p.sub.F,fur)−(T.sup.m.sub.R,fur−T.sup.p.sub.R,fur)

(20) where T.sup.m.sub.F,fur and T.sup.m.sub.R,fur are the measured times of arrival of the blade at respectively the forward and rearward probes at said further revolution and relative to the start of said further revolution. The circumferential time shift is based on an assumption that the aero gas loading on each blade is constant from leading to trailing edge. In this case any difference between (T.sup.m.sub.F,fur−T.sup.p.sub.F, fur) and (T.sup.m.sub.R,fur−T.sup.P.sub.R,fur) corresponds to a circumferential time shift of the blade tip that is caused by a displacement, Δ.sub.ax, of the blade tip in the axial direction X, as shown schematically in FIG. 6. This displacement is calculated from the expression:
Δ.sub.ax=(2πRΔt.sub.cts)/(ω.sub.fur tan(θ.sub.fur))

(21) Thus from relatively nonintrusive and simple instrumentation, i.e. two BTT probes and an OPR probe, blade tip axial displacements can be measured.

(22) The method can be repeated for other revolutions so that the development of blade tip axial displacement can be followed or plotted. Likewise, the method can be repeated for other blades of the row of blades. The method is also suitable for obtaining measurements in real time.

(23) The method can be used for model validation (e.g. finite element model validation), BTT calibration, and also for characterisation of surge, stall and flutter events.

(24) FIG. 7 shows plots of blade tip axial displacement against rotor speed, the displacement being measured according to the above method for all blades of a row of blades. The upper plot shows the maximum displacement of the blades, the middle plot shows the mean displacement of the blades, and the bottom plot shows the minimum displacement of the blades.

(25) While the invention has been described in conjunction with the exemplary embodiments described above, many equivalent modifications and variations will be apparent to those skilled in the art when given this disclosure. Accordingly, the exemplary embodiments of the invention set forth above are considered to be illustrative and not limiting. Various changes to the described embodiments may be made without departing from the spirit and scope of the invention.