Aircraft gas turbine engine with improved response to rotor unbalance

Abstract

An aircraft gas turbine engine includes a fan system having a reverse traveling wave first flap mode, Fan RTW, and including a fan upstream of the engine core; a fan shaft; and a front engine structure to support the shaft and having a front engine structure nodding mode FSN including two modes at similar, but unequal, natural frequencies in orthogonal directions; and a gearbox. The engine includes a gearbox, and a gearbox output shaft to couple output of the gearbox to the fan shaft. An LP rotor system including the fan system and the gearbox output shaft has a first reverse whirl rotor dynamic mode, Rotor RW. A frequency margin of: $\frac{\mathrm{the}\mathrm{frequency}\mathrm{difference}\mathrm{between}\mathrm{mode}\mathrm{FSN}\mathrm{and}\mathrm{the}\mathrm{highest}\mathrm{frequency}\mathrm{of}\mathrm{either}\mathrm{synchronous}\mathrm{Fan}\mathrm{RTW}\mathrm{or}\mathrm{synchronous}\mathrm{Rotor}\mathrm{RW}}{\mathrm{the}\mathrm{lowest}\mathrm{natural}\mathrm{frequency}\mathrm{of}\mathrm{the}\mathrm{front}\mathrm{structure}\mathrm{nodding}\mathrm{pair}\mathrm{of}\mathrm{modes}}$
is in the range from 5 to 50%.

Claims

1. A gas turbine engine for an aircraft, the gas turbine engine comprising: an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor; a fan system having a reverse travelling wave first flap mode, Fan RTW, and comprising: a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a fan shaft; a front engine structure arranged to support the fan shaft, the front engine structure having a front engine structure nodding mode, FSN, comprising a pair of modes at similar, but not equal, natural frequencies in orthogonal directions; and a gearbox and a gearbox output shaft arranged to couple an output of the gearbox to the fan shaft, wherein the gearbox receives an input from the core shaft and outputs drive to the fan via the gearbox output shaft so as to drive the fan at a lower rotational speed than the core shaft; wherein the fan system and the gearbox output shaft together form an LP rotor system having a first reverse whirl rotor dynamic mode, Rotor RW; and wherein a front engine structure frequency margin of: $\frac{\begin{array}{c}\mathrm{the}\mathrm{frequency}\mathrm{difference}\mathrm{between}\mathrm{mode}\mathrm{FSN}\\ \mathrm{and}\mathrm{the}\mathrm{highest}\mathrm{frequency}\mathrm{of}\mathrm{either}\\ \mathrm{synchronous}\mathrm{Fan}\mathrm{RTW}\mathrm{or}\mathrm{synchronous}\mathrm{Rotor}\mathrm{RW}\end{array}}{\begin{array}{c}\mathrm{the}\mathrm{lowest}\mathrm{natural}\mathrm{frequency}\mathrm{of}\mathrm{the}\mathrm{front}\\ \mathrm{structure}\mathrm{nodding}\mathrm{pair}\mathrm{of}\mathrm{modes}\end{array}}$ is in the range from 5 to 50%.

2. The gas turbine engine of claim 1, wherein the front engine structure frequency margin is greater than 10%.

3. The gas turbine engine of claim 1, wherein the front engine structure frequency margin is less than 45%.

4. The gas turbine engine of claim 1, wherein the frequency difference between mode FSN and the highest frequency of either synchronous Fan RTW or synchronous Rotor RW is in the range from 2 Hz to 15 Hz.

5. The gas turbine engine of claim 1, wherein the lowest natural frequency of the front structure nodding pair of modes is in the range from 14 Hz to 26 Hz.

6. The gas turbine engine of claim 1, wherein the gas turbine engine has a maximum take-off (MTO) speed; and the LP rotor system has a first forward whirl rotor dynamic mode, 1FW, and a forward whirl frequency margin of: $\frac{\begin{array}{c}\mathrm{the}\mathrm{frequency}\mathrm{difference}\mathrm{between}\mathrm{synchronous}1\mathrm{FW}\\ \mathrm{and}\mathrm{the}\mathrm{first}\mathrm{engine}\mathrm{order}\mathrm{line}\mathrm{at}\mathrm{MTO}\mathrm{speed}\end{array}}{\mathrm{the}\mathrm{MTO}\mathrm{speed}}$ is in the range from 10 to 100%.

7. The gas turbine engine of claim 6, wherein the MTO speed is in the range from 25 Hz to 45 Hz.

8. The gas turbine engine of claim 7, wherein the MTO speed is in the range from 25 Hz to 30 Hz.

9. The gas turbine engine of claim 8, wherein the fan has a fan diameter greater than 216 cm.

10. The gas turbine engine of claim 7, wherein the MTO speed is in the range from 35 Hz to 45 Hz.

11. The gas turbine engine of claim 10, wherein the fan has a fan diameter less than 216 cm.

12. The gas turbine engine of claim 1, wherein the gas turbine engine has a maximum take-off (MTO) speed; and a mutual frequency margin of: $\frac{\begin{array}{c}\mathrm{the}\mathrm{frequency}\mathrm{difference}\mathrm{between}\mathrm{mode}\mathrm{Fan}\mathrm{RTW}\\ \mathrm{and}\mathrm{mode}\mathrm{Rotor}\mathrm{RW}\mathrm{at}\mathrm{the}\mathrm{MTO}\mathrm{speed}\end{array}}{\left(\begin{array}{c}\mathrm{the}\mathrm{lowest}\mathrm{frequency}\mathrm{of}\mathrm{either}\mathrm{mode}\mathrm{Fan}\mathrm{RTW}\mathrm{or}\\ \mathrm{Rotor}\mathrm{RW}\mathrm{at}\mathrm{the}\mathrm{MTO}\mathrm{speed}+\mathrm{the}\mathrm{MTO}\mathrm{speed}\end{array}\right)}$ is in the range from 5 to 50%.

13. The gas turbine engine of claim 12, wherein the frequency difference between mode Fan RTW and mode Rotor RW at the MTO speed is in the range from 2 Hz to 15 Hz.

14. The gas turbine engine of claim 12, wherein the lowest frequency of either mode Fan RTW or Rotor RW at the MTO speed is in the range from 4 Hz to 22 Hz.

15. The gas turbine engine of claim 1, wherein the gas turbine engine has a maximum take-off (MTO) speed; and a backward whirl frequency margin of: $\frac{\begin{array}{c}\mathrm{the}\mathrm{lowest}\mathrm{frequency}\mathrm{of}\mathrm{either}\mathrm{mode}\mathrm{Fan}\mathrm{RTW}\mathrm{or}\\ \mathrm{Rotor}\mathrm{RW}\mathrm{at}\mathrm{the}\mathrm{MTO}\mathrm{speed}\end{array}}{\mathrm{the}\mathrm{MTO}\mathrm{speed}}$ is in the range from 15 to 50%.

16. The gas turbine engine of claim 15, wherein the lowest frequency of either mode Fan RTW or Rotor RW at the MTO speed is in the range from 4 Hz to 22 Hz.

17. A method of operation of a gas turbine engine for an aircraft, the gas turbine engine having a maximum take-off (MTO) speed, and comprising: an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor; a fan system having a reverse travelling wave first flap mode, Fan RTW, and comprising a fan located upstream of the engine core, the fan comprising a plurality of fan blades and a fan shaft; a front engine structure arranged to support the fan shaft, the front engine structure having a front engine structure nodding mode, FSN, comprising a pair of modes at similar, but not equal, natural frequencies in orthogonal directions; and a gearbox and a gearbox output shaft arranged to couple an output of the gearbox to the fan shaft, wherein the gearbox receives an input from the core shaft and outputs drive to the fan via the gearbox output shaft so as to drive the fan at a lower rotational speed than the core shaft; wherein the fan system and the gearbox output shaft together form an LP rotor system having a first reverse whirl rotor dynamic mode, Rotor RW, the method comprising: operating the gas turbine engine such that a front engine structure frequency margin of: $\frac{\begin{array}{c}\mathrm{the}\mathrm{frequency}\mathrm{difference}\mathrm{between}\mathrm{mode}\mathrm{FSN}\\ \mathrm{and}\mathrm{the}\mathrm{highest}\mathrm{frequency}\mathrm{of}\mathrm{either}\\ \mathrm{synchronous}\mathrm{Fan}\mathrm{RTW}\mathrm{or}\mathrm{synchronous}\mathrm{Rotor}\mathrm{RW}\end{array}}{\begin{array}{c}\mathrm{the}\mathrm{lowest}\mathrm{natural}\mathrm{frequency}\mathrm{of}\mathrm{the}\mathrm{front}\\ \mathrm{engine}\mathrm{structure}\mathrm{nodding}\mathrm{pair}\mathrm{of}\mathrm{modes}\end{array}}$ is in the range from 5 to 50%.

18. The method of claim 17, comprising operating the gas turbine engine such that the frequency difference between mode FSN and the highest frequency of either synchronous Fan RTW or synchronous Rotor RW is in the range from 2 Hz to 15 Hz.

19. The method of claim 17, wherein the fan system and the gearbox output shaft together form an LP rotor system having a first forward whirl rotor dynamic mode, 1FW; the method comprising: operating the gas turbine engine such that a forward whirl frequency margin of: $\frac{\begin{array}{c}\mathrm{the}\mathrm{frequency}\mathrm{difference}\mathrm{between}\mathrm{synchronous}1\mathrm{FW}\\ \mathrm{and}\mathrm{the}\mathrm{first}\mathrm{engine}\mathrm{order}\mathrm{line}\mathrm{at}\mathrm{MTO}\mathrm{speed}\end{array}}{\mathrm{the}\mathrm{MTO}\mathrm{speed}}$ is in the range from 10 to 100%.

20. The method of claim 19, comprising operating the gas turbine engine such that the frequency difference between synchronous 1FW and the first engine order line at the MTO speed is in the range from 8 Hz to 45 Hz.

Description

BRIEF 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 sectional side view of a gas turbine engine;

(3) FIG. 2 is a close up sectional side view of an upstream portion of a gas turbine engine;

(4) FIG. 3 is a partially cut-away view of a gearbox for a gas turbine engine;

(5) FIG. 4 is a sectional side view of a forward portion of a gas turbine engine;

(6) FIG. 5 is a sectional side view of a forward portion of a gas turbine engine different from that shown in FIG. 4;

(7) FIG. 6 is a Campbell diagram in the inertial reference frame, illustrating various vibrational modes;

(8) FIG. 7 is the Campbell diagram of FIG. 6 with parameters A, B and C marked;

(9) FIG. 8 is the Campbell diagram of FIG. 6 with parameters D, E and F marked;

(10) FIG. 9 is a schematic diagram illustrating radial bending stiffness of a shaft;

(11) FIG. 10 is a sectional side view of a forward portion of a gas turbine engine as shown in FIG. 4, illustrating how radial bending stiffness of the front engine structure is determined;

(12) FIG. 11 is a schematic diagram illustrating tilt stiffness of a shaft;

(13) FIG. 12 is a sectional side view of a forward portion of a gas turbine engine as shown in FIG. 4, illustrating how tilt stiffness of the fan shaft is determined;

(14) FIG. 13 is a graph of displacement against load, illustrating an elastic region within which stiffnesses of components may be determined;

(15) FIG. 14 is a sectional side view of a gas turbine engine similar to that shown in FIG. 1, but with a different fan shaft arrangement;

(16) FIG. 15 illustrates various methods;

(17) FIG. 16 schematically illustrates whirl modes of the fan and fan shaft (Rotor RW, 1FW, Fan FTW, Rotor FW);

(18) FIG. 17 schematically illustrates the first nodding (bending) mode of a front engine structure (FSN); and

(19) FIG. 18 schematically illustrates the reverse traveling wave (RTW) first flap mode of a fan system (Fan RTW).

DETAILED DESCRIPTION OF THE DISCLOSURE

(20) FIG. 1 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.

(21) 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 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.

(22) An exemplary arrangement for a geared fan gas turbine engine 10 is shown in FIG. 2. The low pressure turbine 19 (see FIG. 1) 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 process 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.

(23) 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.

(24) The epicyclic gearbox 30 is shown by way of example in greater detail in FIG. 3. 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. 3. 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.

(25) The epicyclic gearbox 30 illustrated by way of example in FIGS. 2 and 3 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.

(26) It will be appreciated that the arrangement shown in FIGS. 2 and 3 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. 2 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. 2. 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. 2.

(27) 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.

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

(29) 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. 1 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 engine 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.

(30) 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. 1), and a circumferential direction (perpendicular to the page in the FIG. 1 view). The axial, radial and circumferential directions are mutually perpendicular.

(31) The engine 10 is arranged to be mounted on a wing of an aircraft for use, by means of one or more mounts 41. In the arrangements being described, the engine 10 is surrounded by a nacelle 21, which surrounds the fan 23. In the example shown in FIG. 4 (in which figure the nacelle 21 is not visible), the front engine mount 41 (i.e. the forwardmost mount connecting the engine 10 to the wing, however many mounts there may be) may be described as a front core mount 41, as it connects the core 11 directly to the wing. In the alternative example shown in FIG. 5, the front mount 41 is a fan case front mount, instead of a core front mount, as it connects the fan case 45 to the wing of the aircraft (the fan case 45 generally being positioned immediately within the nacelle 21, around the axial location of the fan blade tips). The below description may apply equally to engines 10 with core mounts 41 and/or fan case mounts 41; the example with a core mount shown in FIG. 4 is chosen for discussion below by way of example only; the disclosure is not limited to such an arrangement.

(32) The engine comprises a fan shaft 36 extending, in a geared engine 10, between a fan input position and a gearbox output position. In the arrangement shown in FIG. 14, the fan shaft 36 additionally extends rearward of the gearbox output position, with the additional fan shaft length providing options for fan shaft mounting rearward of the gearbox 30. The fan shaft 36 transmits drive from the gearbox 30 to the fan 23. The fan shaft 36 may be defined as the torque transfer component that couples the output of the gearbox 30 to the fan input. For the purposes of defining the stiffness of the fan shaft 36, it is considered to extend between a fan input position (i.e. the axial position of the connection of the fan 23 to the fan shaft 36) and a rear bearing b on the fan shaft 36 as described below.

(33) In various arrangements, the fan shaft 36 is supported by two bearings—a first/forward bearing, a, located nearest the fan 23, and a second/rearward bearing, b, located rearward of the first bearing, a. The bearings a, b, limit radial movement of the shaft 36, so enforcing node positions for whirl modes of the fan shaft 36. In alternative arrangements, such as that shown in FIG. 14, the fan shaft 36 may be supported by more than two bearings—for example by three bearings. The bearings a, b are both (or all) located rearward of the fan input position; the rotor system comprising the fan 23 and fan shaft 36 may therefore be described as a cantilevered rotor system, as the fan 23 is only supported by a fan shaft 36 which is supported rearward of the axial location at which the fan 23 is connected to the fan shaft 36.

(34) For the arrangements described in detail below, the fan shaft 36 extends rearwardly through the gearbox 30, as shown in FIG. 14. The additional length of the fan shaft 36 may serve to improve or facilitate axial location of the fan shaft 36. In the arrangement shown in FIG. 14, the gearbox 30 is a planetary gearbox, and the fan shaft 36 is therefore driven by a gearbox output shaft 35 connected to the planet carrier 34. The fan shaft 36 is therefore driven by the rotation of the planet carrier 34, and does not otherwise interact with the gearbox 30, despite passing through it. In an engine 10 with a star gearbox 30, the fan shaft 36 would instead be driven by the ring gear 38.

(35) The forward bearing, a, on the fan shaft 36 of this arrangement is located near the fan 23, forward of the gearbox 30, and more specifically near (and rearward of) the fan input position, i.e. the connection between the fan shaft 36 and the fan 23. The forward bearing, a, is a roller bearing mounted to a static structure of the engine 10 (and more specifically in the example shown, generally rigidly connected to the static structure 24, including the fan outlet guide vane/engine stator). The rearward bearing, b, on the fan shaft 36 of this arrangement is located rearward of the gearbox 30. The rearward bearing, b, is a location bearing, serving to axially locate the fan shaft 36. Bearing b is an inter-shaft bearing in the arrangement shown; axially locating the fan shaft 36 with respect to the core shaft 26. An additional bearing axially locates the core shaft 26 within the engine 10.

(36) In the arrangement shown in FIG. 14, a third bearing, c, is provided on the fan shaft 36, between bearings a and b. This bearing c is a catcher bearing provided for safety. In alternative arrangements, this bearing c may not be present. In various embodiments with more than two bearings on the fan shaft 36, the forwardmost bearing, nearest the fan 23, may be taken as bearing a and the rearmost bearing, furthest from the fan, as bearing b.

(37) The engine 10 further comprises a front engine structure 42 and a power gearbox rear panel (PGB rear panel) 43.

(38) The front engine structure 42 is substantially conical in shape in the arrangement shown in FIGS. 1 and 14, extending rearwardly and outwardly from the forward bearing, a, towards the engine section stator 24. It is rigidly mounted on the engine stationary structure 24 (in the arrangement shown, the engine section stator 24 is structural and forms a part of the engine stationary structure—in other arrangements, the engine stationary structure 24 may not include the engine section stator), and provides a mounting for the forward bearing a, and, where present, the intermediate bearing c. In the arrangement shown, the front engine structure 42 extends from an axial position forward of the gearbox 30 to an axial position along the length of the gearbox 30. The front engine structure 42 therefore provides some support to the fan 23, and also provides sealing and containment for the power gear box chamber 30, which generally contains an air/oil mist in operation. The forward bearing, a, is mounted on (or an integral part of) the front engine structure 42.

(39) The PGB rear panel 43 may play a role in sealing and locating the gear box 30; it may additionally provide a rotor dynamic function to the intermediate pressure compressor 14. The PGB rear panel 43 is substantially conical in shape in the arrangement shown in FIGS. 1 and 14, extending rearwardly and inwardly from a position near the engine section stator 24 towards the rearward bearing, b. The PGB rear panel is rigidly mounted on the engine stationary structure 24 (in the arrangement shown, the engine section stator 24 is structural and forms a part of the engine stationary structure—in other arrangements, the engine stationary structure 24 may not include the engine section stator). In the arrangement shown, the PGB rear panel 43 extends from an axial position along the length of the gearbox 30 to an axial position rearward of the gearbox 30.

(40) The PGB rear panel 43 therefore provides some support to the fan shaft 36, via the core shaft 26, and also provides sealing and containment on the rearward side of the power gear box chamber 30, which generally contains an air/oil mist in operation.

(41) The front engine structure 42 and the PGB rear panel 43 together form an enclosure around the gearbox chamber 30a, shielding the rest of the engine 10 from the air/oil mist generally generated by the gearbox 30 in operation. The front engine structure 42 and the PGB rear panel 43 are arranged not to rotate with the fan shaft 36, and may therefore be referred to as parts of the static structure of the engine 10.

(42) For ease of discussion herein: a “fan system” is defined as comprising the fan 23 (fan blades and hub) and the fan shaft 36; and a “low pressure rotor system” (LP rotor system) is defined as comprising all components 23, 36 of the fan system, and additionally the gearbox output shaft 35 that drives the fan shaft 36 (in the arrangement shown in FIG. 14, the gearbox output shaft 35 is the carrier output shaft, as it is a planetary gearbox 30).

(43) Engine Vibrational Modes

(44) FIGS. 4 and 5 each illustrate a forward portion of a geared turbine engine 10, with a relatively large-diameter fan 23, for example having a fan diameter greater than or equal to 215 cm, and optionally greater than or equal to 250 cm. The fan 23 is located forward of the front engine mount 41 in a cantilevered mounting arrangement (i.e. the fan shaft 36 is supported on only one side of the mounting position of the fan 23, namely rearward of the axial position at which the fan 23 is connected to the fan shaft 36, such that the fan shaft 36 may be treated as a cantilevered beam).

(45) An engine 10 of this type may generally have three natural frequencies (modes) of interest that may be coincident or near-coincident in frequency. These modes are: 1) The first nodding (bending) mode of the front engine structure 42 (FSN); 2) The reverse traveling wave (RTW) first flap mode of the fan 23 system (Fan RTW); and 3) The first reverse whirl (RW) rotor dynamic mode of the LP rotor system (Rotor RW).

(46) FIG. 6 provides a Campbell diagram in the inertial reference frame, showing various vibrational modes.

(47) As discussed herein, rotational frequency values are not directional—frequencies are all given as absolute (positive) values, irrespective of rotation direction. Similarly, all frequency differences are provided as positive values, with whichever frequency of the pair to be compared has the lowest absolute value subtracted from whichever frequency has the highest absolute value. All of the vibrational modes described are the lowest order vibrations of their respective type (the fundamental)—higher frequency harmonics may also be present, but in various aircraft designs including those of the examples being described the fundamentals are of particular interest as several of these first order modes are near-coincident with each other and/or close to forcing frequencies (unbalance or aerodynamic) likely to be present in use. The near-coincidence and/or forcing can amplify the vibrational responses. In addition, the skilled person would appreciate that, whilst higher order vibrations of the same type have smaller amplitudes than the lower order vibrations and are therefore often less important from the perspective of their effect on the engine 10, they could present a hazard if forced and/or if near-coincident.

(48) The first nodding (bending) mode of the front engine structure 42 may be called the Front engine Structure Nodding mode, and referred to as FSN. The FSN line is shown as a dashed line in FIGS. 6 to 8.

(49) The first nodding mode of the front engine structure 42 (FSN) is illustrated schematically in FIG. 17. The whole of the front engine structure 42 bends, or “nods”, forward of the position of the rear bearing, b, and the front mount 41. It will be appreciated that FIG. 17 (and correspondingly also FIGS. 16 and 18) are intended to demonstrate the mode-shape of the relevant mode, but that the displacement is exaggerated for clarity of demonstration.

(50) The reverse traveling wave first flap mode of the fan 23 is an example of a Backward Whirl mode of the fan, and may be referred to as Fan RTW. The skilled person would appreciate that the fan 23 inherently has some flexibility, as required to exhibit Fan RTW vibrations, and may therefore be referred to as a flexible fan 23. The Fan RTW line is shown as a solid dark grey line in FIGS. 6 to 8. The Fan RTW mode is mostly composed of movement of the fan blades, with only a small contribution from the fan shaft 36. FIG. 18 schematically illustrates the reverse traveling wave (RTW) first flap mode of a fan system 23, 36 (Fan RTW). As illustrated by the figure, the movement of the fan shaft 36 is smaller than that of the fan blades 23, and indeed is often negligible.

(51) The first reverse whirl rotor dynamic mode of the fan shaft 36 is another example of a Backward Whirl mode, and may be referred to as Rotor RW. The Rotor RW line is shown as a dot-dashed black line in FIGS. 6 to 8. The Rotor RW mode is mostly composed of bending of the fan shaft 36, with some contribution from fan blade flex.

(52) The two vibration modes described above, Fan RTW and Rotor RW, are therefore both “backward whirl” (or “reverse whirl”) modes; i.e. the direction of the whirl is opposite to the direction of rotation of the rotor system 23, 36. In the example shown in FIG. 6, the lowest frequency reverse whirl mode is the reverse traveling wave first flap mode (Fan RTW) of the flexible fan 23. The second lowest frequency reverse whirl mode is the first reverse whirl rotor dynamic mode (Rotor RW) of the fan shaft 36. However the opposite may occur in other arrangements (i.e. Rotor RW may have a lower frequency than Fan RTW).

(53) The Campbell Diagram (FIG. 6) also shows the synchronous line, 1EO, which may also be referred to as the first engine order line. Line 1EO represents the fan shaft speed operating line, and is shown as a solid black line in FIGS. 6 to 8. FIG. 6 therefore illustrates coincidence between natural frequencies, ω.sub.n, of the modes FSN, Fan RTW and Rotor RW, and the engine fan shaft speed (forcing frequency) Ω.sub.fan, at the intersections of the mode lines with line 1EO.

(54) If the rotor first reverse whirl mode (Rotor RW) and/or the reverse traveling wave first fan blade flap mode (Fan RTW) have an insufficient frequency margin above the maximum fan shaft rotation speed (i.e. if the mode frequencies are too similar to the maximum fan shaft rotation frequency/if there is not enough of a difference in frequency between them), either or both of these modes can be excited by a forcing load that is static in the inertial reference frame (as viewed by an outside observer viewing the engine 10). Examples of such forcing include aerodynamic loads on the fan blades 23, and fan blade tip rubs.

(55) If the frequency margin were zero (i.e. if the mode frequency were equal to maximum fan shaft rotation frequency), the reverse traveling wave of the fan 23 and/or the rotor response would be stationary in the inertial reference frame, and hence a stationary aerodynamic load or fan blade tip rub could rapidly increase the response amplitude to damaging/hazardous levels.

(56) A frequency margin, referred to as the backward whirl frequency margin, may therefore be tuned appropriately to avoid this response amplification.

(57) The maximum fan speed (i.e. MTO fan speed) is considered for establishing this frequency margin because at lower rotor speeds the first reverse whirl mode (Rotor RW) and reverse traveling wave first fan blade flap mode (Fan RTW) have higher frequencies in the inertial reference frame, while the rotor speed is lower. The maximum rotor speed condition is therefore always the condition in which the lowest backward whirl frequency margin occurs in engines 10 as described.

(58) A first parameter, A, is defined as the lowest frequency of either mode Fan RTW or Rotor RW at the Maximum Take-Off (MTO) speed. In the example shown in FIG. 6, a line corresponding to the MTO speed (vertical dotted line) has been added to the Campbell Diagram for ease of determining this parameter. For the example shown, Fan RTW is lower than Rotor RW, and the value for the Fan RTW mode line where it intersects the MTO line is therefore taken as the value for parameter A, as shown in FIG. 7.

(59) A second parameter, B, is defined as being equal to the MTO speed. The MTO speed is a rotational speed of the fan 23 and shaft 36, and is therefore defined in terms of a frequency—i.e. as a frequency of rotation—for ease of comparison with the other frequencies described herein.

(60) The backward whirl frequency margin is expressed as A/B. The backward whirl frequency margin A/B may be maintained within the range from 15% to 50%, and preferably greater than 25%, in various arrangements.

(61) If the rotor first reverse whirl mode (Rotor RW) and reverse traveling wave first fan blade flap mode (Fan RTW) have an insufficient mutual frequency margin (i.e. if they are too close to each other in frequency), these modes can interact such that any forcing as described above may excite both of these modes instead of just one. This may again lead to deleterious increased amplitudes of vibrational responses.

(62) A parameter, D, may be defined as the frequency difference between the modes Fan RTW and Rotor RW at MTO, as marked on FIG. 8. This is measured as the difference in frequency between the intersection of the line for Fan RTW and MTO, and the intersection of the line Rotor RW and MTO.

(63) The mutual frequency margin may then be expressed as D/(A+B). The frequency margin D/(A+B) may be maintained within the range from 5% to 50% and preferably greater than 10%, in various arrangements.

(64) The front engine structure nodding mode (FSN) is a mode of a portion of the static structure, the static structure being the part of the engine 10 arranged not to rotate relative to an aircraft or other structure on which the engine is mounted in use (i.e. not to rotate with any of the shafts 26, 36, fan 23 or turbines 19 in use).

(65) The FSN mode can be directly excited by rotor unbalance such as unbalance of the fan 23 and/or fan shaft 36. The response to unbalance may be amplified if the rotor unbalance at the forcing frequency (fan rotational speed, for example measured as a rotation frequency) is coincident with the natural frequency of the FSN mode. The amplification may remain small provided that mode FSN does not have a frequency coincident, or near coincident, with the frequency of Fan RTW or Rotor RW. However, the vibration amplitude may be deleteriously increased if the FSN mode frequency is close to the frequency of Fan RTW or Rotor RW.

(66) The frequency of the FSN mode depends on the stiffness of various structures 42, 24 which directly and/or indirectly support the fan shaft 36, and in particular on the stiffness of the front engine structure 42. In various embodiments, the main stiffness path to the front mount plane (a) from the fan 23 may be up through the front engine structure 42, including the engine section stator 24.

(67) In general, the stiffness of the front engine structure 42 may not be radially symmetrical—for example not being equal in orthogonal directions due to a non-axisymmetric engine mount arrangement. As a result the front engine structure nodding (FSN) mode is generally composed of a pair of modes at similar, but not equal (for example being separated by 0-10% only, e.g. by 2 Hz), natural frequencies in orthogonal directions in such examples. This combination of orthogonal modes may cause the front engine structure vibration response to rotor unbalance to be elliptical in orbit, and therefore the rotor (fan 23 and fan shaft 36) housed in the front engine structure 42 may be forced by an elliptical orbit at its bearing supports a, b. The elliptical orbit may comprise both forward and reverse traveling wave components; a mechanism is therefore presented to excite reverse whirl modes Fan RTW or Rotor RW if they are coincident or near-coincident with the FSN frequency. This combined effect could rapidly increase the vibration response amplitude to nuisance levels, or in extreme cases to potentially damaging/hazardous levels. A front engine structure frequency margin may therefore be tailored to avoid this amplification mechanism.

(68) A parameter, E, is defined as the frequency difference between mode FSN and the highest frequency mode of Fan RTW and Rotor RW at their respective synchronous natural frequencies, as shown in FIG. 8. In the example shown in FIG. 8, Rotor RW is higher than Fan RTW, so the frequency difference between the Rotor RW line where it crosses 1EO and the FSN line is used. If Fan RTW were higher than Rotor RW, the frequency difference between the Fan RTW line where it crosses 1EO and the FSN line would be used.

(69) A parameter, F, is defined as the lowest natural frequency of the front engine structure nodding pair of modes (FSN), as shown in FIG. 8. On the Campbell Diagram, the FSN line shown is for the lowest natural frequency of the front engine structure nodding pair of modes.

(70) The front engine structure frequency margin is expressed as E/F. The front engine structure frequency margin E/F may be maintained within the range from 5% to 50%, and preferably greater than 10%, in various arrangements.

(71) In axisymmetric engine mount arrangements, the FSN mode may be composed of only a single mode, reducing or avoiding this excitation pathway; consideration of the front engine structure frequency margin may be less important, or even unnecessary, in such arrangements.

(72) The FSN mode may tend to move, and potentially bend, a nacelle 21 within which the engine is mounted. A mass of the nacelle 21 may therefore be considered in tuning the front engine structure frequency margin, E/F. For example, the nacelle mass may be selected to be within the range of 1000 kg to 3000 kg, and optionally 1500 kg to 2500 kg. In general, the frequency of the FSN mode may reduce in proportion to the ratio of the nacelle 21 modal mass to the engine 10 modal mass, where the modal mass is calculated as the mass that participates by way of kinetic energy contribution to the total energy in the FSN mode. For example, a geared turbine engine 10 with a relatively large fan diameter and no nacelle may exhibit a FSN mode at 26 Hz. The same engine 10 mounted within a nacelle with a mass of 1500 kg, may exhibit a FSN mode at 20 Hz. The same engine 10 mounted within a nacelle with a mass of 2500 kg, may exhibit a FSN mode at 16 Hz. It will be appreciated that these values are provided by way of illustrative example only, and are not intended to be limiting.

(73) A geared turbine engine 10 of the type with a relatively large fan diameter and a rotor that is cantilevered forward of the front engine mount 41, as shown in FIGS. 4 and 5, may additionally have a natural frequency (mode) of interest at a higher frequency. This mode may be formed by a combination of two forward whirl (FW) modes: 1) The forward traveling wave first flap mode of the (flexible) fan 23 system (Fan FTW); and 2) The first forward whirl rotor dynamic mode of the LP rotor system (Rotor FW).

(74) The two vibration modes described above, Fan FTW and Rotor FW, are both “forward whirl” modes; i.e. the direction of the whirl is the same as the direction of rotation of the fan and LP rotor system 23, 36.

(75) On the Campbell Diagram in the inertial reference frame (FIG. 6), a forward whirl mode is identified as 1FW (1st Forward Whirl), and marked with a dot-dot-dashed line. 1FW may be described as a combined shape mode in that it has attributes of both the forward traveling wave first fan flap mode (Fan FTW) shape as well as the first forward whirl rotor dynamic mode shape of the fan shaft (Rotor FW).

(76) FIG. 16 schematically illustrates the whirl modes of the fan 23 and fan shaft 36 (Rotor RW, 1FW, Fan FTW, Rotor FW). it will be appreciated that the mode shape is generally the same for forward and reverse whirl modes, with the difference being the rotation direction of the whirl—forward whirl modes rotate in the same direction as the shaft 36 whereas reverse whirl modes rotate in the opposite direction to the shaft 36.

(77) If the rotor first forward whirl mode (1FW) has insufficient frequency margin above the maximum fan speed (MTO speed), this mode can be excited by unbalance on the rotor 23, 36, for example by unbalance of the fan 23. A high balance quality and/or control of the rotor dynamic response may be provided by the introduction of damping to prevent a high vibration response. The consequence of failing to prevent a high vibration response would be that vibrations of the rotor 23, 36 may cause nuisance, impose component life limitations, and/or require frequent fan trim balance operations. In some cases the response amplitude could increase to damaging or hazardous levels.

(78) A frequency margin, referred to as the forward whirl frequency margin, may therefore be tuned appropriately.

(79) A parameter, C, is defined as the frequency difference between the intersection of 1FW with the synchronous (first engine order) line 1EO, and the intersection of MTO with 1EO, as shown on FIG. 7.

(80) The forward whirl frequency margin is expressed as C/B, where B is the maximum take-off speed (MTO speed), which is defined in terms of the frequency of rotation, as described above. The forward whirl frequency margin C/B may be maintained within the range from 10% to 100%, and preferably greater than 30%, in various arrangements.

(81) To summarise, four frequency margins are defined herein:

(82) TABLE-US-00001 TABLE 1 Frequency Margins Name Definition Range Backward whirl frequency A/B 15% to 50%, optionally margin greater than 20%, 25%, 30%, or 35%, and optionally less than 45%, or 40% Forward whirl frequency C/B 10% to 100%, optionally greater margin than 20%, 30%, 40%, or 50%, and optionally less than 90%, 80%, 70%, or 60% Mutual frequency D/(A + B) 5% to 50%, optionally greater margin than 10%, 15%, 20%, or 25%, and optionally less than 45%, 40%, or 35% Front engine structure E/F 5% to 50%, optionally greater frequency margin than 10%, 15%, 20%, or 25%, and optionally less than 45%, 40%, or 35%

(83) In various arrangements, AB≥25%, C/B≥30%, D/(A+B)≥10%, and E/F≥10%.

(84) The following six parameters, easily obtainable from a Campbell Diagram as illustrated in FIGS. 6 to 8, are used to calculate the frequency margins:

(85) TABLE-US-00002 TABLE 2 parameters Name Definition Range A the lowest frequency of either 4 Hz to 22 Hz, optionally mode Fan RTW or Rotor RW 5 Hz to 15 Hz, and at Maximum Take-Off Speed further optionally 6 Hz to 10 Hz B Maximum Take-Off (MTO) 25 Hz to 45 Hz, optionally speed 25 Hz to 30 Hz, e.g. for an engine with a large fan diameter (greater than 216 cm - 85 inches), or optionally 35 Hz to 45 Hz, e.g. for an engine with a smaller fan diameter C the frequency difference 8 Hz to 45 Hz, optionally between the intersection 20 Hz to 40 Hz, and of 1FW with 1EO and the further optionally 25 Hz intersection of MTO to 35 Hz with 1EO D the frequency difference 2 Hz to 15 Hz, optionally between mode Fan RTW 5 Hz to 15 Hz, and further and mode Rotor RW optionally 5 Hz to 8 Hz at MTO E the frequency difference 2 Hz to 15 Hz, optionally between mode FSN and 2 Hz to 10 Hz, and further the highest frequency mode optionally 3 Hz to 5 Hz of Fan RTW and Rotor RW at their respective synchronous natural frequencies F the lowest natural frequency 14 Hz to 26 Hz, optionally of the front engine 15 Hz to 25 Hz, and structure nodding pair further optionally 18 Hz of modes (FSN) to 22 Hz

(86) All of these parameters have the units of frequency—Hz—and all the frequency margins are therefore dimensionless.

(87) In various arrangements, one, some, or all of the four frequency margins described may be maintained within the specified ranges. Various engine properties may be controlled so as to adjust vibrational properties, including the following. The skilled person would appreciate that the engine 10 may be tuned so as to allow the frequency margin(s) to lie within the specified ranges in a variety of different ways, as multiple parameters affect engine vibrational properties. The below examples of engine properties are therefore provided by way of example only.

(88) In particular, the inventors appreciated that tuning of the fan 23 stiffness, fan shaft 36 stiffness, and/or the engine front engine structure 42 stiffness may allow or facilitate the avoidance of frequency coincidence between natural frequencies and their potential excitation sources.

(89) The fan diameter may be greater than or equal to 215 cm (85″) or 250 cm (100″), and optionally may be selected to be in the range from 215 cm to 420 cm or from 250 cm to 370 cm (100″ to 145″). The same fan size may be used for both composite and metallic fan blades 23.

(90) The fan mass (the mass of the fan 23, including the hub) may be in the range from 300 to 1000 kg.

(91) The fan moment of inertia (the moment of inertia of the fan 23, including the hub) about the longitudinal engine axis may be in the range from 100 to 600 kg.Math.m.sup.2.

(92) The fan shaft length, L, defined between the forward bearing a and the rearward bearing b as shown in FIGS. 4 and 5, may be in the range from 900 mm to 1800 mm. The fan shaft length, L, may be defined between the axial centre-points of the bearings a, b. In arrangements with more than two bearings on the fan shaft 36, L may be defined between the fan shaft bearing closest to the fan 23 and the fan shaft bearing furthest from the fan 23.

(93) The front engine structure cantilever distance, D.sub.c, defined as the distance between the radial plane of the front mount 41 (the front mount plane) to the forward bearing, a, as shown in FIG. 4 may be in the range from 800 mm to 1700 mm. The front engine structure cantilever distance, D.sub.c, may be defined between the axial centrepoint of the forward bearing a, and the axial centrepoint of the front mount 41 (i.e. the front mount plane is located at the axial centre point of the front mount 41).

(94) Radial Bending Stiffness

(95) A radial bending stiffness is defined with reference to FIG. 9 in terms of the deformation of a cantilevered beam 900, which moves between a first position 900a and a second position 900b on the application of a force. As illustrated in FIG. 9, a force, F, applied at the free end of the beam 900a in a direction perpendicular to the longitudinal axis of the beam causes a linear perpendicular deformation, δ, seen in the second position 900b. The radial bending stiffness is the force applied for a given linear deformation i.e. F/δ. In the present application, the radial direction is relative to the rotational axis 9 of the engine 10, and so relates to the resistance to linear deformation in a radial direction of the engine caused by a radial force. The beam 900, or equivalent cantilevered component, extends along the axis of rotation of the engine, the force, F, is applied perpendicular to the axis of rotation of the engine 10, along any radial direction, and the displacement, δ, is measured perpendicular to the axis of rotation, along the line of action of the force, F. The radial bending stiffness as defined herein has SI units of N/m, and may be scaled to alternative units such as kN/mm. In the present application, unless otherwise stated, the radial bending stiffness is taken to be a free-body stiffness i.e. stiffness measured for a component in isolation in a cantilever configuration, without other components present which may affect its stiffness.

(96) The determination of the radial bending stiffness of the front engine structure 42 is described with respect to FIG. 10. The front engine structure 42 is considered in isolation (i.e. without the fan shaft 36 and other components), and the deflection in response to a radial shear force, F, applied to the front engine structure 42 at the axial centrepoint of the forward bearing, a, is determined, with the engine static structures earthed (i.e. treated as rigid/not moving) at the radial plane of the front mount 41.

(97) The deflection, δ, is measured in line with the applied force, F, at the centerline of the forward bearing, a. Diagonal lines are used to indicate that the structure is held to be rigid in a radial plane aligned with the front engine mount 41—the bending of the structure forward of this connection is measured.

(98) In engines 10 with a non-axisymmetric engine mount 41 arrangement, the radial bending stiffness of the front engine structure 42 may not be equal in orthogonal directions. Measurements may therefore be taken at, or calculations performed for, multiple positions, e.g. two orthogonal positions, and the lowest value may be provided for the radial bending stiffness of the front engine structure 42. In the example being described, a mounting of the front engine structure 42 may provide an obvious asymmetry and measurements may therefore be taken in line with the mount and perpendicular to the mount, for example. The lowest stiffness may generally correspond to the lowest FSN frequency, which may be of interest for the minimum frequency separation to Fan RTW or Rotor RW mode.

(99) The front engine structure radial bending stiffness may be in the range from 80 to 180 kN/mm.

(100) Tilt Stiffness

(101) A tilt stiffness is defined with reference to FIG. 11, which shows the resulting deformation of a cantilevered beam 900 from a first position 900a to a second position 900b under a moment M applied at its free end. The tilt stiffness is a measure of the resistance to rotation of a point on the component at which a moment is applied. As can be seen in FIG. 11, an applied moment at the free end of the cantilevered beam causes a constant curvature along the length of the beam between its free and fixed ends. The applied moment M causes a rotation θ of the point at which it is applied. The tilt stiffness as defined herein therefore has SI units of Nm/rad., and may be scaled to alternative units such as N.Math.mm/rad.

(102) The determination of the tilt stiffness of the fan shaft 36 is described with respect to FIG. 12. Diagonal lines are used to indicate that the fan shaft 36 is held to be pinned at the bearings a and b—the bearings a, b, are treated as rigid. The shaft 36 is treated as being pinned at the bearings a,b, as this is representative of the boundary conditions when installed in the engine 10. In arrangements with more than two bearings on the fan shaft 36, the fan shaft 36 may be held to be pinned at all such bearings.

(103) The moment, M, is applied around a rotation axis oriented along a radius of the engine 10 and at the axial position of the centre of gravity (CoG) of the fan assembly (i.e. the CoG of the fan 23, and not including the fan shaft 36). The rotation axis of the tilt moment, M, extends into the page as drawn in FIG. 12. The fan assembly CoG axial position on the fan shaft 36 is generally at least approximately in line with, and often slightly forward of, the forward bearing, a, although the precise position may vary between different engine arrangements.

(104) The change in angle, θ, is measured between the engine axis 9 and the tangent to the fan shaft 36 at the axial position of the CoG of the fan assembly (the point of application of the moment). The angular deflection is measured in response to a point radial moment applied to the fan shaft 36 in isolation (i.e. without the front engine structure 42 or other components) at the fan centre of gravity, with bearing centres pinned at “a” and “b”.

(105) The fan shaft tilt stiffness may be in the range from 5×10.sup.9 to 12×10.sup.9 N mm/rad.

(106) FIG. 13 illustrates how the stiffnesses defined herein may be measured. FIG. 13 shows a plot of the displacement 6 resulting from the application of a load L (e.g. a force, moment or torque) applied to a component for which the stiffness is being measured. At levels of load from zero to L.sub.p there is a non-linear region in which displacement is caused by motion of the component (or relative motion of separate parts of the component) as it is loaded, rather than deformation of the component; for example moving within clearance between parts. At levels of load above L.sub.Q the elastic limit of the component has been exceeded and the applied load no longer causes elastic deformation—plastic deformation or failure of the component may occur instead. Between points P and Q the applied load and resulting displacement have a linear relationship. The stiffnesses defined herein may be determined by measuring the gradient of the linear region between points P and Q (with the stiffness being the inverse of that gradient). The gradient may be found for as large a region of the linear region as possible to increase the accuracy of the measurement by providing a larger displacement to measure. For example, the gradient may be found by applying a load equal to or just greater than L.sub.P and equal to or just less than L.sub.Q. Values for L.sub.P and L.sub.Q may be estimated prior to testing based on materials characteristics so as to apply suitable loads. Although the displacement is referred to as 6 in this description, the skilled person would appreciate that equivalent principles may apply to a linear or angular displacement.

(107) The stiffnesses defined herein, unless otherwise stated, are for the corresponding component(s) when the engine is under cruise conditions. The stiffnesses generally do not vary significantly over the operating range of the engine; the stiffness at cruise conditions of the aircraft to which the engine is used (those cruise conditions being as defined elsewhere herein), or at MTO conditions, may therefore be the same as for when the engine is not in use (i.e. off—at zero speed/on the bench). However, where the stiffness varies over the operating range of the engine, the stiffnesses defined herein are to be understood as being values for when the engine is operating at cruise conditions.

(108) FIG. 15 illustrates a method 1000 which may be performed, optionally using an engine 10 as described above. The method 1000 comprises starting up 1002 an engine 10 of an aircraft and reaching operating conditions, and operating 1004 the aircraft. During operation 1004, the aircraft may operate at MTO speed for one or more time periods. One or more of the following may apply:

(109) (i) a backward whirl frequency margin (AB) of:

(110) $\frac{\begin{array}{c}\mathrm{the}\mathrm{lowest}\mathrm{frequency}\mathrm{of}\mathrm{either}\mathrm{mode}\mathrm{Fan}\mathrm{RTW}\mathrm{or}\\ \mathrm{Rotor}\mathrm{RW}\mathrm{at}\mathrm{the}\mathrm{MTO}\mathrm{speed}\end{array}}{\mathrm{the}\mathrm{MTO}\mathrm{speed}}$
may be in the range from 15 to 50%;

(111) (ii) a forward whirl frequency margin (CB) of:

(112) $\frac{\begin{array}{c}\mathrm{the}\mathrm{frequency}\mathrm{difference}\mathrm{between}\mathrm{synchronous}1\mathrm{FW}\\ \mathrm{and}\mathrm{the}\mathrm{first}\mathrm{engine}\mathrm{order}\mathrm{line}\mathrm{at}\mathrm{MTO}\mathrm{speed}\end{array}}{\mathrm{the}\mathrm{MTO}\mathrm{speed}}$
may be in the range from 10 to 100%;

(113) (iii) a mutual frequency margin (D/(A+B)) of:

(114) $\frac{\begin{array}{c}\mathrm{the}\mathrm{frequency}\mathrm{difference}\mathrm{between}\mathrm{mode}\mathrm{Fan}\mathrm{RTW}\\ \mathrm{and}\mathrm{mode}\mathrm{Rotor}\mathrm{RW}\mathrm{at}\mathrm{the}\mathrm{MTO}\mathrm{speed}\end{array}}{\left(\begin{array}{c}\mathrm{the}\mathrm{lowest}\mathrm{frequency}\mathrm{of}\mathrm{either}\mathrm{mode}\mathrm{Fan}\mathrm{RTW}\mathrm{or}\\ \mathrm{Rotor}\mathrm{RW}\mathrm{at}\mathrm{the}\mathrm{MTO}\mathrm{speed}+\mathrm{the}\mathrm{MTO}\mathrm{speed}\end{array}\right)}$
may be in the range from 5 to 50%; and/or

(115) (iv) a front engine structure frequency margin (E/F) of:

(116) $\frac{\begin{array}{c}\mathrm{the}\mathrm{frequency}\mathrm{difference}\mathrm{between}\mathrm{mode}\mathrm{FSN}\\ \mathrm{and}\mathrm{the}\mathrm{highest}\mathrm{frequency}\mathrm{of}\mathrm{either}\\ \mathrm{synchronous}\mathrm{Fan}\mathrm{RTW}\mathrm{or}\mathrm{synchronous}\mathrm{Rotor}\mathrm{RW}\end{array}}{\begin{array}{c}\mathrm{the}\mathrm{lowest}\mathrm{natural}\mathrm{frequency}\mathrm{of}\mathrm{the}\mathrm{front}\\ \mathrm{structure}\mathrm{nodding}\mathrm{pair}\mathrm{of}\mathrm{modes}\end{array}}$
may be in the range from 5 to 50%.

(117) The features as described above for the engine 10 may apply equivalently in the described methods 1000.

(118) It will be understood that the invention is not limited to the embodiments above-described and that 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.