Rotor blade arrangement

Abstract

The blades for a rotor of a gas turbine engine are all manufactured to the same design. However, manufacturing tolerances mean that in practice each individual blade is different to the others. It is proposed to arrange the blades around the circumference of the rotor in a manner that limits excessive stress being induced in the blades due to differences in the vibration response between a given blade and its two neighbouring blades.

Claims

1. A rotor for a gas turbine engine comprising a rotor hub and a plurality of rotor blades, each rotor blade being attached to the rotor hub at a rotor blade root, wherein: the plurality of rotor blades are arranged circumferentially around the rotor hub such that each rotor blade has two neighbouring rotor blades; the rotor blades have a critical mode shape that is excited at a frequency that corresponds to an excitation frequency in use, the natural frequency of a rotor blade for the critical mode shape being the critical natural frequency; the plurality of rotor blades define a median critical natural frequency; each rotor blade has a critical natural frequency that is either greater than, less than, or equal to the median critical natural frequency of all of the rotor blades; for a majority of rotor blades in a first set of rotor blades that have a critical natural frequency greater than the median, at least one of the neighbouring rotor blades also has a critical natural frequency greater than the median; for a majority of rotor blades in a second set of rotor blades that have a critical natural frequency less than the median, at least one of the neighbouring rotor blades also has a critical natural frequency less than the median; each rotor blade has a position in a list of the plurality of rotor blades ordered by ascending critical natural frequency; and a majority of the plurality of rotor blades have a position in the list of the plurality of rotor blades ordered by critical natural frequency that is within three places of the position in that the list of at least one of the neighbouring rotor blades of each of the majority of the plurality of rotor blades.

2. The rotor according to claim 1, wherein for all rotor blades of the plurality of rotor blades that do not define or exhibit the median critical natural frequency: rotor blades of the first set have at least one neighbouring rotor blade that also has a critical natural frequency greater than the median; and rotor blades of the second set have at least one neighbouring rotor blade that also has a critical natural frequency less than the median.

3. The rotor according to claim 1, wherein: the plurality of rotor blades form a third rotor blade set comprising a total number of n rotor blades, the standard deviation of the critical natural frequency of the rotor blades in the third rotor blade set being given by σ.sub.freq; and for the majority of the plurality of rotor blades, the difference between the critical natural frequency of the rotor blade and the critical natural frequency of at least one of its neighbouring rotor blades is less than the standard deviation of the critical natural frequency of the rotor blades in the third rotor blade set, σ.sub.freq.

4. The rotor according to claim 3, wherein the difference between the critical natural frequency of any given rotor blade in the third rotor blade set and the critical natural frequency of at least one of its neighbouring rotor blades is less than the standard deviation of the critical natural frequency of the rotor blades in the third rotor blade set, σ.sub.freq.

5. The rotor according to claim 1, wherein at least two adjacent blades from the plurality of rotor blades have a mean critical natural frequency that is closer to the critical natural frequency of the rotor blade with the highest critical natural frequency than to the median critical natural frequency.

6. The rotor according to claim 1, wherein at least two adjacent rotor blades have a mean critical natural frequency that is closer to the critical natural frequency of the rotor blade with the lowest critical natural frequency than to the median critical natural frequency.

7. The rotor according to claim 1, comprising: a subset R of p circumferentially adjacent rotor blades that all have a critical natural frequency that is greater than the median critical natural frequency, where p is given by:
p=max{g∈Z|g≤(n−1)/x} where: Z is the set of integers; n is the total number of rotor blades in the rotor; and x is an even number less than (n−1)/2.

8. The rotor according to claim 7, wherein x=2 or x=4.

9. The rotor according to claim 7, comprising at least two such subsets R of circumferentially adjacent rotor blades that all have a critical natural frequency that is greater than the median critical natural frequency, each subset R being circumferentially separated from another subset R by at least one rotor blade having a critical natural frequency that is less than the median critical natural frequency, wherein: the number of subsets R is equal to x/2.

10. The rotor according to claim 7, wherein within the subset R of circumferentially adjacent rotor blades, the critical natural frequency of each rotor blade is less than the critical natural frequency of the neighbouring rotor blade that is circumferentially closer to the rotor blade within the subset R that has the maximum critical natural frequency.

11. The rotor according to claim 10, wherein the rotor blade within the subset R that has the maximum critical natural frequency is positioned circumferentially centrally, such that the difference between the number of rotor blades in the subset R that are on the anticlockwise side of the rotor blade with the maximum critical natural frequency and the number of rotor blades in the subset R that are on the clockwise side of the rotor blade with the maximum critical natural frequency is either 0 or 1.

12. The rotor according to claim 1, comprising: a subset S of q circumferentially neighbouring rotor blades that all have a critical natural frequency that is less than the median critical natural frequency, where q is given by:
q=max{j∈Z|j≤(n−1)/y} where: Z is the set of integers; n is the total number of rotor blades in the rotor; and y is an even number less than (n−1)/2.

13. The rotor according to claim 12, wherein y=2 or y=4.

14. The rotor according to claim 12, comprising at least two such subsets S of circumferentially adjacent blades that all have a critical natural frequency that is less than the median critical natural frequency, each subset S being circumferentially separated from another subset S by at least one rotor blade having a critical natural frequency that is greater than the median critical natural frequency, wherein: the number of subsets S is equal to y/2.

15. The rotor according to claim 12, wherein within the subset S of circumferentially adjacent rotor blades, the critical natural frequency of each rotor blade is greater than the critical natural frequency of the neighbouring rotor blade that is circumferentially closer to the rotor blade within the subset S that has the minimum critical natural frequency.

16. The rotor according to claim 1, comprising a total of n rotor blades, wherein: if the rotor blades are arranged in critical natural frequency order from 1 to n, with blade 1 having the highest critical natural frequency and blade n having the lowest critical natural frequency, then rotor blade 1 and any one of rotor blades 2, 3 and 4 are neighbouring rotor blades, and wherein, optionally: rotor blade 2 and any one of rotor blades 3, 4 and 5 are neighbouring rotor blades that are different to and substantially circumferentially opposite to the rotor blade 1 and any one of 2, 3 and 4.

17. A rotor according to claim 1, wherein the excitation frequency is either the engine speed or a multiple of the engine speed of an engine in which the rotor is to be used.

18. A gas turbine engine comprising a rotor according to claim 1.

19. A method of assembling a rotor for a gas turbine engine, the rotor comprising a rotor hub and a plurality of rotor blades, each rotor blade having a critical natural frequency defined as the natural frequency of the rotor blade for a critical mode shape that is excited at a frequency that corresponds to an excitation frequency in use, wherein each rotor blade has a critical natural frequency that is either greater than, less than, or equal to the median rotor blade critical natural frequency of all of the plurality of rotor blades, the method comprising: attaching each rotor blade of the plurality of rotor blades to the rotor hub using a rotor blade root so as to arrange the rotor blades circumferentially around the rotor hub such that each rotor blade has two neighbouring rotor blades, wherein: the plurality of rotor blades define a median critical natural frequency; each rotor blade has a critical natural frequency that is either greater than, less than, or equal to the median critical natural frequency of all of the rotor blades; the method further comprises arranging the rotor blades such that: for the majority of rotor blades in a first set of rotor blades that have a critical natural frequency greater than the median critical natural frequency, at least one of the neighbouring rotor blades also has a critical natural frequency greater than the median; for the majority of rotor blades in a first set of rotor blades that have a critical natural frequency less than the median, at least one of the neighbouring rotor blades also has a critical natural frequency less than the median; each rotor blade has a position in a list of the plurality of rotor blades ordered by ascending critical natural frequency; and a majority of the plurality of rotor blades have a position in the list of the plurality of rotor blades ordered by critical natural frequency that is within three places of the position in the list of at least one of the neighbouring rotor blades of each of the majority of the plurality of rotor blades.

Description

DESCRIPTION OF THE DRAWINGS

(1) Embodiments will now be described by way of example only, with reference to the Figures, in which:

(2) FIG. 1 is a schematic of a rotor of a gas turbine engine;

(3) FIG. 2 is a graph showing the mass and position of rotor blades around the circumference of a rotor in a conventional arrangement;

(4) FIG. 3 is a sectional side view of a gas turbine engine;

(5) FIG. 4 is a close up sectional side view of an upstream portion of a gas turbine engine;

(6) FIG. 5 is a partially cut-away view of a gearbox for a gas turbine engine;

(7) FIG. 6 is a graph showing the critical natural frequency and position of rotor blades around the circumference of a rotor in accordance with an example of the present disclosure;

(8) FIG. 7 is a graph showing the critical natural frequency and position of rotor blades around the circumference of a rotor in accordance with an example of the present disclosure;

(9) FIG. 8 is a graph showing the critical natural frequency and position of rotor blades around the circumference of a rotor in accordance with an example of the present disclosure; and

(10) FIG. 9 is a graph showing the critical natural frequency and position of rotor blades around the circumference of a rotor in accordance with an example of the present disclosure.

DETAILED DESCRIPTION

(11) Aspects and embodiments of the present disclosure will now be discussed with reference to the accompanying figures. Further aspects and embodiments will be apparent to those skilled in the art.

(12) FIG. 3 illustrates a gas turbine engine 10 having a principal rotational axis 9. The engine 10 comprises an air intake 12 and a propulsive fan 23 that generates two airflows: a core airflow A and a bypass airflow B. The gas turbine engine 10 comprises a core 11 that receives the core airflow A. The engine core 11 comprises, in axial flow series, a low pressure compressor 14, a high-pressure compressor 15, combustion equipment 16, a high-pressure turbine 17, a low pressure turbine 19 and a core exhaust nozzle 20. A nacelle 21 surrounds the gas turbine engine 10 and defines a bypass duct 22 and a bypass exhaust nozzle 18. The bypass airflow B flows through the bypass duct 22. The fan 23 is attached to and driven by the low pressure turbine 19 via a shaft 26 and an epicyclic gearbox 30.

(13) In use, the core airflow A is accelerated and compressed by the low pressure compressor 14 and directed into the high pressure compressor 15 where further compression takes place. The compressed air exhausted from the high pressure compressor 15 is directed into the combustion equipment 16 where it is mixed with fuel and the mixture is combusted. The resultant hot combustion products then expand through, and thereby drive, the high pressure and low pressure turbines 17, 19 before being exhausted through the core exhaust nozzle 20 to provide some propulsive thrust. The high pressure turbine 17 drives the high pressure compressor 15 by a suitable interconnecting shaft 27. The fan 23 generally provides the majority of the propulsive thrust. The epicyclic gearbox 30 is a reduction gearbox.

(14) An exemplary arrangement for a geared fan gas turbine engine 10 is shown in FIG. 4. The low pressure turbine 19 (see FIG. 3) drives the shaft 26, which is coupled to a sun wheel, or sun gear, 28 of the epicyclic gear arrangement 30. Radially outwardly of the sun gear 28 and intermeshing therewith is a plurality of planet gears 32 that are coupled together by a planet carrier 34. The planet carrier 34 constrains the planet gears 32 to precess around the sun gear 28 in synchronicity whilst enabling each planet gear 32 to rotate about its own axis. The planet carrier 34 is coupled via linkages 36 to the fan 23 in order to drive its rotation about the engine axis 9. Radially outwardly of the planet gears 32 and intermeshing therewith is an annulus or ring gear 38 that is coupled, via linkages 40, to a stationary supporting structure 24.

(15) Note that the terms “low pressure turbine” and “low pressure compressor” as used herein may be taken to mean the lowest pressure turbine stages and lowest pressure compressor stages (i.e. not including the fan 23) respectively and/or the turbine and compressor stages that are connected together by the interconnecting shaft 26 with the lowest rotational speed in the engine (i.e. not including the gearbox output shaft that drives the fan 23). In some literature, the “low pressure turbine” and “low pressure compressor” referred to herein may alternatively be known as the “intermediate pressure turbine” and “intermediate pressure compressor”. Where such alternative nomenclature is used, the fan 23 may be referred to as a first, or lowest pressure, compression stage.

(16) The epicyclic gearbox 30 is shown by way of example in greater detail in FIG. 5. Each of the sun gear 28, planet gears 32 and ring gear 38 comprise teeth about their periphery to intermesh with the other gears. However, for clarity only exemplary portions of the teeth are illustrated in FIG. 5. There are four planet gears 32 illustrated, although it will be apparent to the skilled reader that more or fewer planet gears 32 may be provided within the scope of the claimed invention. Practical applications of a planetary epicyclic gearbox 30 generally comprise at least three planet gears 32.

(17) The epicyclic gearbox 30 illustrated by way of example in FIGS. 4 and 5 is of the planetary type, in that the planet carrier 34 is coupled to an output shaft via linkages 36, with the ring gear 38 fixed. However, any other suitable type of epicyclic gearbox 30 may be used. By way of further example, the epicyclic gearbox 30 may be a star arrangement, in which the planet carrier 34 is held fixed, with the ring (or annulus) gear 38 allowed to rotate. In such an arrangement the fan 23 is driven by the ring gear 38. By way of further alternative example, the gearbox 30 may be a differential gearbox in which the ring gear 38 and the planet carrier 34 are both allowed to rotate.

(18) It will be appreciated that the arrangement shown in FIGS. 4 and 5 is by way of example only, and various alternatives are within the scope of the present disclosure. Purely by way of example, any suitable arrangement may be used for locating the gearbox 30 in the engine 10 and/or for connecting the gearbox 30 to the engine 10. By way of further example, the connections (such as the linkages 36, 40 in the FIG. 4 example) between the gearbox 30 and other parts of the engine 10 (such as the input shaft 26, the output shaft and the fixed structure 24) may have any desired degree of stiffness or flexibility. By way of further example, any suitable arrangement of the bearings between rotating and stationary parts of the engine (for example between the input and output shafts from the gearbox and the fixed structures, such as the gearbox casing) may be used, and the disclosure is not limited to the exemplary arrangement of FIG. 4. For example, where the gearbox 30 has a star arrangement (described above), the skilled person would readily understand that the arrangement of output and support linkages and bearing locations would typically be different to that shown by way of example in FIG. 4.

(19) Accordingly, the present disclosure extends to a gas turbine engine having any arrangement of gearbox styles (for example star or planetary), support structures, input and output shaft arrangement, and bearing locations.

(20) Optionally, the gearbox may drive additional and/or alternative components (e.g. the intermediate pressure compressor and/or a booster compressor).

(21) Other gas turbine engines to which the present disclosure may be applied may have alternative configurations. For example, such engines may have an alternative number of compressors and/or turbines and/or an alternative number of interconnecting shafts. By way of further example, the gas turbine engine shown in FIG. 3 has a split flow nozzle 18, 20 meaning that the flow through the bypass duct 22 has its own nozzle 18 that is separate to and radially outside the core exhaust nozzle 20. However, this is not limiting, and any aspect of the present disclosure may also apply to engines in which the flow through the bypass duct 22 and the flow through the core 11 are mixed, or combined, before (or upstream of) a single nozzle, which may be referred to as a mixed flow nozzle. One or both nozzles (whether mixed or split flow) may have a fixed or variable area.

(22) Whilst the described example relates to a turbofan engine, the disclosure may apply, for example, to any type of gas turbine engine, such as an open rotor (in which the fan stage is not surrounded by a nacelle) or turboprop engine, for example. In some arrangements, the gas turbine engine 10 may not comprise a gearbox 30.

(23) The geometry of the gas turbine engine 10, and components thereof, is defined by a conventional axis system, comprising an axial direction (which is aligned with the rotational axis 9), a radial direction (in the bottom-to-top direction in FIG. 3), and a circumferential direction (perpendicular to the page in the FIG. 3 view). The axial, radial and circumferential directions are mutually perpendicular.

(24) FIG. 1 is a schematic showing a rotor 100 of the gas turbine engine 10. The rotor 100 may be a rotor in the engine 10, for example any rotor in the compressor sections 14, 15 or any rotor in the turbine sections 17, 19. The rotor 100 is arranged to rotate around the rotational axis 9 of the gas turbine engine 10.

(25) The rotor 100 comprises a rotor hub 110 and rotor blades 120. The rotor 100 shown by way of example in FIG. 1 comprises 36 rotor blades 120, but it will be appreciated that a rotor in accordance with the present disclosure may comprise any number (odd or even) of rotor blades 120.

(26) The rotor blades 120 are evenly spaced around the circumference of the hub. Accordingly, the angle between each and every pair of neighbouring blades 120 is the same as the angle between each and every other pair of neighbouring blades 120. The blades 120 may be provided to the hub 110 in any suitable manner. In the FIG. 1 example, each blade 120 comprises a blade root 125 that engages with a corresponding slot 115 in the hub 110. It will be appreciated that for clarity the blade root 125 and the slot 115 have only been shown at one blade location (AA) in FIG. 1, but all of the blades 120 are attached to the hub 110 in the same manner. Purely by way of example, the root 125 may be of a fir-tree design or a dovetail design.

(27) The circumferential positions at which each of the blades 120 is provided to the hub 110 (which correspond to the positions of the slots 115 in the FIG. 1 example) are labelled A-AJ in FIG. 1. Thus, it will be appreciated that each of the letters A-AJ represents the circumferential position on the rotor 100, rather than an individual blade. Accordingly, if the position of two blades were swapped, the labels would remain unmoved. As such, a blade at the circumferential position labelled with a particular letter (say, ‘E’) may be moved to a different circumferential position (say, ‘AB’) without changing the circumferential labels shown in FIG. 1. Each rotor blade 120 may be manufactured separately from the hub 110 and from the other rotor blades 120 using any suitable process, which may comprise, for example, casting and/or machining. Each rotor blade 120 is intended to be the same (for example in terms of mass and stiffness) as the other rotor blades 120, and thus to have the same critical natural frequency for a critical mode shape. However, due to manufacturing tolerances, the actual critical natural frequency of each blade 120 is not the same as all of the other blades. Indeed, typically, the critical natural frequency of each blade 120 is different to the critical natural frequency of each of the other blades 120.

(28) Accordingly, a given set of n blades 120, has a median critical natural frequency. Where the number n of blades 120 is odd, the median critical natural frequency is the critical natural frequency of the blade that has an equal number of blades with higher and lower critical natural frequencies in the set. Where the number n of blades 120 is odd, the median critical natural frequency is the mean critical natural frequency of the blade that has n/2 blades with a higher critical natural frequency and the blade that has (n−1)/2 blades with a higher critical natural frequency in the blade set. By way of example, the FIG. 1 rotor has 36 blades, such that the median critical natural frequency is calculated as the mean of the blades with the 18.sup.th and 19.sup.th highest critical natural frequencies in the blade set.

(29) Once the median critical natural frequency has been calculated, the critical natural frequency of every blade 120 in the blade set can be normalized by the median critical natural frequency.

(30) FIGS. 6 to 9 show different arrangements of the rotor blades 120 around the circumference of the rotor 100 in accordance with examples of the present disclosure. Specifically, the x-axis in FIGS. 6 to 9 shows the circumferential position A-AJ with reference to the FIG. 1 schematic, and the y-axis shows the critical natural frequency of the blade at each of the circumferential positions A-AJ, normalized (i.e. divided by) the median critical natural frequency of the blade set.

(31) It will be appreciated that the specific (and normalised) critical natural frequencies of the blades 120 in the blade set used for the examples of FIGS. 6 to 9 are by way of example only, and the actual absolute or normalised critical natural frequency of the blades 120 in the blade set may have any distribution. Purely by way of example, the critical natural frequency of the blade 120 with the highest critical natural frequency in the blade set (shown at position A in FIG. 6) is around 5.5% greater than the median critical natural frequency, and the critical natural frequency blade 120 with the lowest critical natural frequency in the blade set (shown at position C in FIG. 6) is just under 5% less than the median critical natural frequency.

(32) A set of n blades may be arranged in order of descending critical natural frequency, such that blade 1 is the blade with the highest critical natural frequency and blade n is the blade with the lowest critical natural frequency. Accordingly, the blades may be numbered 1 to n (i.e. 1, 2, 3 (n−2), (n−1), n), where the lower the critical natural frequency the blade, the higher the number.

(33) In each of FIGS. 6 to 9, the blades 120 are arranged in the positions A-AJ such that for the majority of rotor blades that have a critical natural frequency greater than the median (i.e. blades having a normalized critical natural frequency greater than 1), at least one of the neighbouring rotor blades also has a critical natural frequency greater than the median. Similarly, for the majority of rotor blades that have a critical natural frequency less than the median (i.e. blades having a normalized critical natural frequency less than 1), at least one of the neighbouring rotor blades also has a critical natural frequency less than the median.

(34) In the FIG. 6 arrangement, only the blades at positions Q and AI have a critical natural frequency greater than the median critical natural frequency but do not have at least one neighbouring rotor blade that has a critical natural frequency greater than the median. However, because the blades at positions Q and AI and their neighbouring blades are all close to the median critical natural frequency, they will not suffer from the significant increase in stress that may be induced in a blade that has a significantly different critical natural frequency to both of its neighbouring blades (such as the blade C in the conventional arrangement of FIG. 2). In the FIG. 7 arrangement, only the blade Q has a critical natural frequency greater than the median critical natural frequency but does not have at least one neighbouring rotor blade that has a critical natural frequency greater than the median, but again because the blade at position Q and its neighbouring blades are all close to the median critical natural frequency, they will not suffer from the significant increase in stress.

(35) FIGS. 8 and 9 show examples of arrangements in which for all of rotor blades that have a critical natural frequency greater than the median, at least one of the neighbouring rotor blades also has a critical natural frequency greater than the median. Similarly, FIGS. 8 and 9 are examples of arrangements in which for all of rotor blades that have a critical natural frequency less than the median, at least one of the neighbouring rotor blades also has a critical natural frequency less than the median.

(36) The critical natural frequency of the rotor blades in the set of rotor blades 120 has a standard deviation σ.sub.freq calculated in the conventional manner. Purely by way of example, the standard deviation of the normalized critical natural frequency of the rotor blades 120 in the rotor blade set (of 36 rotor blades) is 0.028 (i.e. 2.8%). The arrangements of FIGS. 6 to 9 are all examples of arrangements in which the difference between the critical natural frequency of any given rotor blade in the rotor blade set and the critical natural frequency of at least one of its neighbouring rotor blades is less than the standard deviation of the critical natural frequency of the rotor blades in the rotor blade set a σ.sub.freq.

(37) FIGS. 6 to 9 are all examples of arrangements that contain a subset R of at least p circumferentially neighbouring blades that all have a critical natural frequency that is greater than the median critical natural frequency, where p is given by:
p=max{g∈Z|g≤(n−1)/x}

(38) where:

(39) Z is the set of integers;

(40) n is the total number of rotor blades in the rotor; and

(41) x is an even number less than (n−1)/2.

(42) The arrangements of FIGS. 6 and 7 each contain 8 such subsets R, each containing 2 blades (p=2) with the value of x being 16 (i.e. the highest even number less than (n−1)/2, with n=36).

(43) The arrangement of FIG. 8 contains 1 such subset R containing 18 blades (p=17), with the value of x being 2.

(44) The arrangement of FIG. 9 contains 2 such subsets R each containing 9 blades (p=8), with the value of x being 4.

(45) FIGS. 6 to 9 are all examples of arrangements that contain a subset S of at least q circumferentially neighbouring blades that all have a critical natural frequency that is less than the median critical natural frequency, where q is given by:
q=max{j∈Z|j≤(n−1)/y}

(46) where:

(47) Z is the set of integers;

(48) n is the total number of rotor blades in the rotor; and

(49) y is an even number less than (n−1)/2.

(50) The arrangements of FIGS. 6 and 7 each contain 8 such subsets S, each containing 2 blades (q=2) with the value of y being 16 (i.e. the highest even number less than (n−1)/2, with n=36).

(51) The arrangement of FIG. 8 contains 1 such subset S containing 18 blades (q=17), with the value of y being 2.

(52) The arrangement of FIG. 9 contains 2 such subsets S each containing 9 blades (q=8), with the value of y being 4.

(53) Purely for completeness, and by way of non-limitative example, the table below shows the order of the rotor blades 120 provided around the circumference of the rotor 100 for each of the arrangements shown in FIGS. 6 to 9. The circumferential positions A-AJ relate to the schematic shown in FIG. 1. The blade number is the position of the blade in a list ordered by decreasing blade critical natural frequency, in which the blade with the highest critical natural frequency is blade ‘1’ and the blade with the lowest critical natural frequency is blade ‘n’, in this case blade ‘36’. In other words, a given blade has a lower critical natural frequency than all blades with a lower blade number, and higher critical natural frequency than all blades with a higher blade number.

(54) TABLE-US-00001 Circumferential Blade Number Position FIG. 6 FIG. 7 FIG. 8 FIG. 9 A 1 1 20 20 B 3 3 22 24 C 36 18 24 28 D 34 20 26 32 E 5 5 28 36 F 7 7 30 34 G 32 22 32 30 H 30 24 34 26 I 9 9 36 22 J 11 11 35 18 K 28 26 33 14 L 26 28 31 10 M 13 13 29 6 N 15 15 27 2 O 24 30 25 4 P 22 32 23 8 Q 17 17 21 12 R 19 19 19 16 S 2 34 17 19 T 4 36 15 23 U 35 2 13 27 V 33 4 11 31 W 6 21 9 35 X 8 23 7 33 Y 31 6 5 29 Z 29 8 3 25 AA 10 25 1 21 AB 12 27 2 17 AC 27 10 4 13 AD 25 12 6 9 AE 14 29 8 5 AF 16 31 10 1 AG 23 14 12 3 AH 21 16 14 7 AI 18 33 16 11 AJ 20 35 18 15

(55) Once again, it will be appreciated that a number of blade arrangements other than those shown by way of example in FIGS. 6 to 9 may be in accordance with, and enjoy the advantages associated with, the present disclosure.

(56) Once the blades have been arranged in the desired pattern (for example the pattern of any one of FIGS. 6 to 9), it may be necessary to balance the rotor 100. If required, this may be achieved by adding one or more balancing masses, such as the mass 130 shown by way of example in FIG. 1. However, some arrangements may not require further balancing, in which case the balancing mass 130 may be omitted.

(57) It will be understood that the invention is not limited to the embodiments above-described and various modifications and improvements can be made without departing from the concepts described herein. Except where mutually exclusive, any of the features may be employed separately or in combination with any other features and the disclosure extends to and includes all combinations and sub-combinations of one or more features described herein.