High power epicyclic gearbox and operation thereof

Abstract

A gas turbine engine for an aircraft includes an engine core with a turbine, a compressor, and a core shaft connecting the turbine and compressor; a fan upstream of the engine core including a plurality of fan blades; and a gearbox that receives an input from a gearbox input shaft portion of the core shaft and outputs drive to a fan shaft so as to drive the fan at a lower rotational speed than the core shaft, the gearbox being an epicyclic gearbox including a sun gear, a plurality of planet gears, a ring gear, and a planet carrier arranged to have the plurality of planet gears mounted thereon, and wherein the sun gear receives input from the core shaft. At cruise conditions the torque on the core shaft is greater than 10,000 Nm and a ratio of core shaft stiffness to core shaft torque is within a specified range.

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 located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox that receives an input from a gearbox input shaft portion of the core shaft and drives the fan via a fan shaft at a lower rotational speed than the core shaft, the gearbox being an epicyclic gearbox comprising a sun gear that receives the input from the core shaft, a plurality of planet gears, a ring gear, and a planet carrier arranged to have the plurality of planet gears mounted thereon, wherein, at cruise conditions: torque on the core shaft is greater than 10,000 Nm; and a first sun input shaft ratio of: $\begin{array}{cc}\frac{\mathrm{tilt}\mathrm{stiffness}\mathrm{of}\mathrm{the}\mathrm{gearbox}\mathrm{input}\mathrm{shaft}}{\mathrm{the}\mathrm{torque}\mathrm{on}\mathrm{the}\mathrm{core}\mathrm{shaft}}& \end{array}$ is greater than or equal to 4 rad.sup.−1 and is less than or equal to 150 rad.sup.−1; wherein the tilt stiffness is determined (i) by treating the gearbox input shaft as being a free body at a forward point of the gearbox input shaft at which is applied a moment whose axis is perpendicular to an axis of the gas turbine engine and (ii) by considering a connection between a rearward end of the gearbox input shaft and a remainder of the core shaft to be rigid; and wherein the tilt stiffness is determined based on an angle measured between (i) a line parallel to the axis of the gas turbine engine and (ii) a local tangent to the gearbox input shaft at the forward point of the shaft at which the moment is applied.

2. The gas turbine engine of claim 1, wherein the first sun input shaft ratio is greater than or equal to 5 rad.sup.−1.

3. The gas turbine engine of claim 1, wherein: (i) the tilt stiffness of the gearbox input shaft is greater than or equal to 5×10.sup.4 Nm/radian and is less than or equal to 5×10.sup.6 Nm/radian; and/or (ii) radial bending stiffness of the gearbox input shaft is greater than or equal to 6×10.sup.5 N/m and is less than or equal to 3×10.sup.7 N/m; wherein the radial bending stiffness is determined (i) by treating the gearbox input shaft as being a free body at the forward point of the shaft at which is applied a force perpendicular to the axis of the gas turbine engine and (ii) by considering the connection between the rearward end of the gearbox input shaft and the remainder of the core shaft to be rigid; and wherein the radial bending stiffness is determined based on a displacement of the forward point that is measured perpendicular to the axis of the gas turbine engine along a line of action of the applied force.

4. The gas turbine engine of claim 1, wherein a second sun input shaft ratio of: $\frac{\mathrm{radial}\mathrm{bending}\mathrm{stiffness}\mathrm{of}\mathrm{the}\mathrm{gearbox}\mathrm{input}\mathrm{shaft}}{\mathrm{the}\mathrm{torque}\mathrm{on}\mathrm{the}\mathrm{core}\mathrm{shaft}}$ is greater than or equal to 7 m.sup.−2 and is less than or equal to 800 m.sup.−2, wherein the radial bending stiffness is determined (i) by treating the gearbox input shaft as being a free body at a forward point of the gearbox input shaft at which is applied a force perpendicular to the axis of the gas turbine engine and (ii) by considering a connection between a rearward end of the gearbox input shaft and a remainder of the core shaft to be rigid; and wherein the radial bending stiffness is determined based on a displacement of the forward point that is measured perpendicular to the axis of the gas turbine engine along a line of action of the applied force.

5. The gas turbine engine of claim 1, wherein a product of the tilt stiffness of the gearbox input shaft and the torque on the core shaft is equal to or greater than 5.5×10.sup.8 N.sup.2m.sup.2/radian and is less than 2.0×10.sup.11 N.sup.2m.sup.2rad.sup.−1.

6. 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 located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox that receives an input from a gearbox input shaft portion of the core shaft and drives the fan via a fan shaft at a lower rotational speed than the core shaft, the gearbox being an epicyclic gearbox comprising a sun gear that receives the input from the core shaft, a plurality of planet gears, a ring gear, and a planet carrier arranged to have the plurality of planet gears mounted thereon, wherein, at cruise conditions: torque on the core shaft is greater than 10,000 Nm; and a second sun input shaft ratio of: $\frac{\mathrm{radial}\mathrm{bending}\mathrm{stiffness}\mathrm{of}\mathrm{the}\mathrm{gearbox}\mathrm{input}\mathrm{shaft}}{\mathrm{torque}\mathrm{on}\mathrm{the}\mathrm{core}\mathrm{shaft}}$ is greater than or equal to 7 m.sup.−2 and is less than or equal to 800 m.sup.−2; wherein the radial bending stiffness is determined (i) by treating the gearbox input shaft as being a free body at a forward point of the gearbox input shaft at which is applied a force perpendicular to an axis of the gas turbine engine and (ii) by considering a connection between a rearward end of the gearbox input shaft and a remainder of the core shaft to be rigid; and wherein the radial bending stiffness is determined based on a displacement of the forward point that is measured perpendicular to the axis of the gas turbine engine along a line of action of the applied force.

7. The gas turbine engine of claim 6, wherein the second sun input shaft ratio is greater than or equal to 14 m.sup.−2.

8. The gas turbine engine of claim 6, wherein: (i) the radial bending stiffness of the gearbox input shaft is greater than or equal to 6×10.sup.5 N/m and is less than or equal to 3×10.sup.7 N/m; and/or (ii) tilt stiffness of the gearbox input shaft is greater than or equal to 5×10.sup.4 Nm/radian and is less than or equal to 5×10.sup.6 Nm/radian; wherein the tilt stiffness is determined (i) by treating the gearbox input shaft as being a free body at the forward point of the shaft at which is applied a moment whose axis is perpendicular to the axis of the gas turbine engine and (ii) by considering the connection between the rearward end of the gearbox input shaft and the remainder of the core shaft to be rigid; and wherein the tilt stiffness is determined based on an angle measured between (i) a line parallel to the axis of the gas turbine engine and (ii) a local tangent to the gearbox input shaft at the forward point of the shaft at which the moment is applied.

9. The gas turbine engine of claim 6, wherein a first sun input shaft ratio of: $\frac{\mathrm{tilt}\mathrm{stiffness}\mathrm{of}\mathrm{the}\mathrm{gearbox}\mathrm{input}\mathrm{shaft}}{\mathrm{the}\mathrm{torque}\mathrm{on}\mathrm{the}\mathrm{core}\mathrm{shaft}}$ is greater than or equal to 4 rad.sup.−1 and is less than or equal to 150 rad.sup.−1, wherein the tilt stiffness is determined (i) by treating the gearbox input shaft as being a free body at the forward point of the shaft at which is applied a moment whose axis is perpendicular to the axis of the gas turbine engine and (ii) by considering the connection between the rearward end of the gearbox input shaft and the remainder of the core shaft to be rigid; and wherein the tilt stiffness is determined based on an angle measured between (i) a line parallel to the axis of the gas turbine engine and (ii) a local tangent to the gearbox input shaft at the forward point of the shaft at which the moment is applied.

10. The gas turbine engine of claim 6, wherein a product of the radial bending stiffness of the gearbox input shaft and the torque on the core shaft is equal to or greater than 1.2×10.sup.9 N.sup.2 and is less than 8.0×10.sup.11 N.sup.2.

11. The gas turbine engine of claim 1, wherein: (i) a gear ratio of the gearbox is in a range from 3.2 to 4.5; and/or (ii) a specific thrust of the engine at cruise conditions is in a range from 70 to 90 NKg.sup.−1s; and/or (iii) a bypass ratio of the engine at the cruise conditions is in a range from 12.5 to 18.

12. The gas turbine engine according to claim 1, wherein: the turbine is a first turbine, the compressor is a first compressor, and the core shaft is a first core shaft; the engine core further comprises a second turbine, a second compressor, and a second core shaft connecting the second turbine to the second compressor; and the second turbine, second compressor, and second core shaft are arranged to rotate at a higher rotational speed than the first core shaft.

13. The gas turbine engine according to claim 1, wherein the gearbox input shaft provides a soft mounting for the sun gear such that some movement of the sun gear is facilitated, and wherein the core shaft comprises a more stiff section and a less stiff section, the less stiff section providing the gearbox input shaft and being arranged to lie between the more stiff section and the sun gear so as to provide, or to contribute to, the soft mounting for the sun gear.

14. The gas turbine engine according to claim 1, wherein the fan has a fan diameter greater than 240 cm and less than or equal to 380 cm.

15. A method of operating an aircraft, a gas turbine engine of the aircraft comprising: an engine core comprising a turbine, a compressor, and a core shaft connecting the turbine to the compressor; a fan located upstream of the engine core, the fan comprising a plurality of fan blades; and a gearbox that receives an input from a gearbox input shaft portion of the core shaft and drives the fan via a fan shaft at a lower rotational speed than the core shaft, the gearbox being an epicyclic gearbox comprising a sun gear that receives the input from the core shaft, a plurality of planet gears, a ring gear, and a planet carrier arranged to have the plurality of planet gears mounted thereon; and the method comprising controlling the aircraft such that torque on the core shaft under cruise conditions is greater than 10,000 Nm; and a first sun input shaft ratio of: $\frac{\mathrm{tilt}\mathrm{stiffness}\mathrm{of}\mathrm{the}\mathrm{gearbox}\mathrm{input}\mathrm{shaft}}{\mathrm{the}\mathrm{torque}\mathrm{on}\mathrm{the}\mathrm{core}\mathrm{shaft}\mathrm{under}\mathrm{cruise}\mathrm{conditions}}$ is greater than or equal to 4 rad.sup.−1 and is less than or equal to 150 rad.sup.−1; and/or a second sun input shaft ratio of: $\frac{\mathrm{radial}\mathrm{bending}\mathrm{stiffness}\mathrm{of}\mathrm{the}\mathrm{gearbox}\mathrm{input}\mathrm{shaft}}{\mathrm{the}\mathrm{torque}\mathrm{on}\mathrm{the}\mathrm{core}\mathrm{shaft}\mathrm{under}\mathrm{cruise}\mathrm{conditions}}$ is greater than or equal to 7 m.sup.−2 and is less than or equal to 800 m.sup.−2, wherein: the tilt stiffness is determined (i) by treating the gearbox input shaft as being a free body at a forward point of the gearbox input shaft at which is applied a moment whose axis is perpendicular to an axis of the gas turbine engine and (ii) by considering a connection between a rearward end of the gearbox input shaft and a remainder of the core shaft to be rigid; the tilt stiffness is determined based on an angle measured between (i) a line parallel to the axis of the gas turbine engine and (ii) a local tangent to the gearbox input shaft at the forward point of the shaft at which the moment is applied; the radial bending stiffness is determined (i) by treating the gearbox input shaft as being a free body at the forward point of the shaft at which is applied a force perpendicular to the axis of the gas turbine engine and (ii) by considering the connection between the rearward end of the gearbox input shaft and the remainder of the core shaft to be rigid; and the radial bending stiffness is determined based on a displacement of the forward point that is measured perpendicular to the axis of the gas turbine engine along a line of action of the applied force.

16. The method of claim 15, wherein the method comprises driving the gearbox with an input torque of: (i) greater than or equal to 11,000 Nm and less than 50,000 Nm at cruise; and/or (ii) greater than or equal to 28,000 Nm and less than 135,000 Nm at MTO.

17. A propulsor for an aircraft, the propulsor comprising: a fan comprising a plurality of fan blades; a gearbox; and a power unit for driving the fan via the gearbox, wherein: the gearbox is an epicyclic gearbox arranged to receive an input from a gearbox input shaft portion of a core shaft driven by the power unit and to drive the fan via a fan shaft at a lower rotational speed than the core shaft; the gearbox comprises a sun gear, a plurality of planet gears, a ring gear, and a planet carrier on which the planet gears are mounted; and at cruise conditions: torque on the core shaft is greater than 10,000 Nm; and a first sun input shaft ratio of: $\begin{array}{cc}\frac{\mathrm{tilt}\mathrm{stiffness}\mathrm{of}\mathrm{the}\mathrm{gearbox}\mathrm{input}\mathrm{shaft}}{\mathrm{the}\mathrm{torque}\mathrm{on}\mathrm{the}\mathrm{core}\mathrm{shaft}}& \end{array}$ is greater than or equal to 4 rad.sup.−1 and is less than or equal to 150 rad.sup.−1; and/or a second sun input shaft ratio of: $\frac{\mathrm{radial}\mathrm{bending}\mathrm{stiffness}\mathrm{of}\mathrm{the}\mathrm{gearbox}\mathrm{input}\mathrm{shaft}}{\mathrm{the}\mathrm{torque}\mathrm{on}\mathrm{the}\mathrm{core}\mathrm{shaft}}$ is greater than or equal to 7 m.sup.−2 and is less than or equal to 800 m.sup.−2, wherein: the tilt stiffness is determined (i) by treating the gearbox input shaft as being a free body at a forward point of the gearbox input shaft at which is applied a moment whose axis is perpendicular to an axis of the gas turbine engine and (ii) by considering a connection between a rearward end of the gearbox input shaft and a remainder of the core shaft to be rigid; the tilt stiffness is determined based on an angle measured between (i) a line parallel to the axis of the gas turbine engine and (ii) a local tangent to the gearbox input shaft at the forward point of the shaft at which the moment is applied; the radial bending stiffness is determined (i) by treating the gearbox input shaft as being a free body at the forward point of the shaft at which is applied a force perpendicular to the axis of the gas turbine engine and (ii) by considering the connection between the rearward end of the gearbox input shaft and the remainder of the core shaft to be rigid; and the radial bending stiffness is determined based on a displacement of the forward point that is measured perpendicular to the axis of the gas turbine engine along a line of action of the applied force.

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 schematic diagram illustrating radial bending stiffness of a cantilevered beam;

(6) FIG. 5 is a schematic diagram illustrating tilt stiffness of a cantilevered beam;

(7) FIG. 6 is a schematic diagram illustrating the application of a torque to a shaft;

(8) FIG. 7 is a sectional side view and close-up view illustrating the core shaft, and in particular the gearbox input shaft;

(9) FIG. 8 illustrates radial bending of the gearbox input shaft shown in FIG. 7;

(10) FIG. 9 illustrates tilt stiffness of the gearbox input shaft shown in FIG. 7;

(11) FIG. 10 illustrates tilt stiffness of the gearbox input shaft as shown in FIGS. 7 and 9;

(12) FIG. 11 illustrates torsional stiffness of the gearbox input shaft shown in FIG. 7;

(13) FIG. 12 is a sectional side view of the engine illustrating the application of a torque to the gearbox input shaft;

(14) FIG. 13 illustrates methods of various embodiments;

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

(16) FIG. 15 shows an aircraft with two engines as described herein.

DETAILED DESCRIPTION OF EMBODIMENTS

(17) 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.

(18) 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.

(19) 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 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.

(20) The linkages 36 may be referred to as a fan shaft 36, the fan shaft 36 optionally comprising two or more shaft portions 36a, 36b coupled together. For example, the fan shaft 36 may comprise a gearbox output shaft portion 36a extending from the gearbox 30 and a fan portion 36b extending between the gearbox output shaft portion and the fan 23. In the embodiment shown in FIGS. 1 and 2, the gearbox 30 is a planetary gearbox and the gearbox output shaft portion 36a may be integral with, or connected to, the planet carrier 34—it may therefore be referred to as a carrier output shaft 36a. In star gearboxes 30, the gearbox output shaft portion 36a may be integral with, or connected to, the ring gear 38—it may therefore be referred to as a ring output shaft 36a. In the embodiment shown in FIGS. 1 and 2, the fan portion 36b of the fan shaft 36 connects the gearbox output shaft portion 36a to the fan 23. The output of the gearbox 30 is therefore transferred to the fan 23, to rotate the fan, via the fan shaft 36. In alternative embodiments, the fan shaft 36 may comprise a single component, or more than two components. Unless otherwise indicated or apparent to the skilled person, anything described with respect to an engine 10 with a star gearbox 30 may equally be applied to an engine with a planetary gearbox 30, and vice versa.

(21) 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.

(22) 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.

(23) 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.

(24) 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.

(25) 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.

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

(27) 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. 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.

(28) 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.

(29) The following general definitions may be used herein:

(30) Radial Bending Stiffness

(31) A radial bending stiffness is a measure of deformation for a given force applied in any one selected radial direction (i.e. any direction perpendicular to and passing through the engine axis). The radial bending stiffness is defined with reference to FIG. 4 in terms of the deformation of a cantilevered beam 401. As illustrated in FIG. 4, a force, F, applied at the free end of the beam in a direction perpendicular to the longitudinal axis of the beam causes a linear perpendicular deformation, δ. The radial bending stiffness is the force applied for a given linear deformation i.e. F/δ. In the present application, the radial bending stiffness is taken relative to the rotational axis of the engine 9, and so relates to the resistance to linear deformation in a radial direction of the engine caused by a radial force. The beam, 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, along any radial direction, and the displacement, δ, is measured perpendicular to the axis of rotation 9, along the line of action of the force. The radial bending stiffness as defined herein has SI units of N/m. 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 displacement.

(32) When the force is applied perpendicular to the cantilevered beam, and at the free end of the beam, the resultant curvature is not constant but rather increases towards the fixed end of the beam.

(33) Tilt Stiffness

(34) A tilt stiffness is defined with reference to FIG. 5, which shows the resulting deformation of a cantilevered beam 401 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. 5, 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.

(35) Torsional Stiffness

(36) FIG. 6 illustrates the definition of the torsional stiffness of a shaft 401 or other body. A torque, τ, applied to the free end of the beam causes a rotational deformation, θ (e.g. twist) along the length of the beam. The torsional stiffness is the torque applied for a given angle of twist i.e. τ/θ. The torsional stiffness has SI units of Nm/rad.

(37) An effective linear torsional stiffness may be determined for a component having a given radius. The effective linear torsional stiffness is defined in terms of an equivalent tangential force applied at a point on that radius (with magnitude of torque divided by the radius) and the distance δ (with magnitude of the radius multiplied by θ) moved by a point corresponding to the rotational deformation θ of the component.

(38) Torque

(39) Torque, which may also be referred to as moment, is the rotational equivalent of linear force, and can be thought of as a twist to an object. FIG. 6 illustrates the application of a torque to a shaft. If the shaft is able to rotate freely, the torque will cause rotation of the shaft. If the shaft is held in place at one end, the shaft will wind up/twist, as shown in FIG. 6—one end of the shaft may rotate by an angle θ as compared to the other end. If the shaft can rotate against a load, a combination of wind-up and rotation may result from the application of the torque, with the torsional stiffness of the shaft affecting the amount of wind-up.

(40) The magnitude, τ, of torque, τ, of a body depends on three quantities: the force applied (F), the lever arm vector connecting the origin to the point of force application (r), and the angle (A) between the force and lever arm vectors:
τ=r×F
τ=|τ|=|r×F|=|r∥F|sin A where: τ is the torque vector and τ is the magnitude of the torque; r is the position vector or “lever arm” vector (a vector from the selected point on the body to the point where the force is applied); F is the force vector; × denotes the cross product; and A is the angle between the force vector and the lever arm vector (sin(A) is therefore one when the force vector is perpendicular to the position vector, such that τ=rF, i.e. magnitude of the force multiplied by distance between the selected point on the body and the point of application of the force).

(41) Torque has units of [force]×[distance] and may be expressed in units of Newton metres (N.Math.m). The net torque on a body determines the rate of change of the body's angular momentum.

(42) Gear Ratios

(43) For a pair of gears, the gear ratio is the ratio of the number of rotations of a driven gear to the number of rotations of a driver gear—the ratio of numbers of teeth of the driven gear and driver gear correspond to the number of rotations of one gear for one rotation of the other gear.

(44) More generally:

(45) $\mathrm{gear}\mathrm{ratio}=\frac{rot\mathrm{ation}\mathrm{speed}\mathrm{of}\mathrm{driven}\mathrm{gear}}{rot\mathrm{ation}\mathrm{speed}\mathrm{of}\mathrm{driver}\mathrm{gear}}$

(46) In the field of aerospace power gearboxes, the gearbox 30 is generally a reduction gearbox (i.e. the output rotational speed is lower than the input rotational speed). The gear ratio as defined above is therefore less than one, as the rotation speed of the driven gear is lower than that of the driver gear (e.g. a driven:driver ratio of 1:3 is a gear ratio of 1/3 for an example gearbox). In the field, the reduction ratio of the gearbox (the inverse of the gearbox ratio) is often referred to as the gearbox ratio for simplicity of numbers (so the example gearbox may be listed as having a gear ratio of 3 instead of 1/3); the skilled person would appreciate that a “gear ratio” greater than one would more accurately be referred to as a reduction ratio.

(47) In an epicyclic gearbox 30, such as that shown in FIG. 3, a sun gear 28 drives planet gears 32.

(48) 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 rotates, and is coupled to an output shaft via linkages 36, with the ring gear 38 fixed. The planet gears 32 therefore move around (“orbit”) the sun gear 28, carried by the planet carrier 34, as well as rotating about their own axes. In this example, the sun gear 28 is the input gear.

(49) For planetary gearboxes of this type, the gear ratio is:

(50) $i_{\mathrm{planetary}}=\frac{{\omega }_{\mathrm{carrier}}}{{\omega }_{sun}}=\frac{1}{1+\frac{Z_R}{Z_S}}$ where Z.sub.R is the number of teeth on the ring gear 38 and Z.sub.S is the number of teeth on the sun gear 28. This may also be written as a gear ratio of 1:

(51) $1+\frac{Z_R}{Z_S}.$

(52) In a planetary gearbox 30, the input and output shafts rotate in the same direction. For planetary gearboxes of various embodiments the gear ratio (reduction ratio) may be greater than or equal to 3.6 (1:3.6), and optionally may be greater than or equal to 4 (1:4).

(53) In other embodiments, the epicyclic gearbox 30 may have a star arrangement, in which the planet carrier 34 is held fixed, such that the planet gears 32 rotate in place but do not orbit the sun gear 28 with the ring (or annulus) gear 38 allowed to rotate. In such an arrangement the fan 23 is driven by the rotating ring gear 38. In this example, the ring gear 38 is the output (driven) gear and the sun gear 28 is again the input (driver) gear. In a star gearbox 30, the input and output shafts rotate in opposite directions.

(54) For star gearboxes, the gear ratio is:

(55) $i_{\mathrm{star}}=\frac{\mathrm{\#teeth}\mathrm{driven}}{\mathrm{\#teeth}\mathrm{driver}}=\frac{\mathrm{\#teeth}\mathrm{on}\mathrm{ring}\mathrm{gear}}{\mathrm{\#teeth}\mathrm{on}\mathrm{sun}\mathrm{gear}}=\frac{Z_R}{Z_S}$

(56) For star gearboxes of various embodiments the gear ratio (reduction ratio) may be less than or equal to 3.6 (1:3.6), and optionally may be greater than or equal to 3 (1:3). The gear ratio may be between 1:3 and 1:3.3 in various embodiments. The gear ratio of star gearboxes 30 may generally be lower than the gear ratio of planetary gearboxes 30.

(57) The gear ratio defines the ratio between the torque input to the gearbox 30 (via the sun input shaft, or core shaft, 26, in the embodiments being described) and the torque output from the gearbox 30 (via the fan shaft 36, extending from the carrier 34, in the embodiments being described):

(58) $\mathrm{Gear}\mathrm{ratio}=\frac{\mathrm{output}\mathrm{torque}}{\mathrm{input}\mathrm{torque}}$

(59) For a star gearbox:

(60) $\begin{array}{c}{i}_{\mathrm{star}}=-\frac{Z_R}{Z_S}=\frac{o\mathrm{utput}\mathrm{torque}}{\mathrm{input}\mathrm{torque}}\\ \mathrm{output}\mathrm{torque}=-\frac{Z_R}{Z_S}\mathrm{input}\mathrm{torque}\end{array}$

(61) The minus sign arises from the direction change of the torque. The change in torque across the gearbox is therefore by a factor of

(62) $1+\frac{Z_R}{Z_S}$
i.e. 1 plus the gear ratio), due to the reversal of direction. The change in torque across the gearbox is therefore by a factor of more than one, as

(63) $\frac{Z_R}{Z_S}$
is positive. The change in torque, Δτ, between the core shaft 26 and the fan shaft 36 for a star gearbox may therefore be shown as:
Δτ=(1+gearbox gear ratio)×torque on the fan shaft

(64) For a planetary gearbox:

(65) $\begin{array}{c}{i}_{\mathrm{planetary}}=\frac{1}{1+\frac{Z_R}{Z_S}}=\frac{o\mathrm{utput}\mathrm{torque}}{\mathrm{input}\mathrm{torque}}\\ \mathrm{output}\mathrm{torque}=\frac{1}{1+\frac{Z_R}{Z_S}}\mathrm{input}\mathrm{torque}\end{array}$

(66) The change in torque across the gearbox is therefore by a factor of

(67) 0$1-\frac{1}{1+\frac{Z_R}{Z_S}}$
(i.e. 1 minus the gear ratio). The change in torque across the gearbox is therefore by a positive factor of less than 1, as

(68) $\frac{Z_R}{Z_S}$
is positive, so

(69) $1+\frac{Z_R}{Z_S}>1.$

(70) The change in torque, Δτ, between the core shaft 26 and the fan shaft 36 for a planetary gearbox may therefore be shown as:
Δτ=(1−gearbox gear ratio)×torque on the fan shaft

(71) More specific definitions of stiffnesses and torques relating to embodiments described herein are provided below for ease of understanding.

(72) Gearbox Input Shaft Stiffnesses

(73) In the arrangement shown in FIGS. 1 and 2, the gearbox input shaft 26a (a portion of the core shaft 26) drives the sun gear 28. The gearbox input shaft 26a may therefore be referred to as a sun input shaft 26a. The gearbox input shaft 26a may be a sun input shaft 26a in star arrangements (as well as planetary). The gearbox input shaft 26a may also be referred to as a part of the core shaft 26—a forward portion 26a of the core shaft 26 which provides the input to the gearbox 30.

(74) The core shaft 26 therefore comprises a gearbox input shaft 26a, which rotates with the rest of the core shaft 26 but may have a different stiffness from the rest of the core shaft. In the arrangement being described with respect to FIGS. 1 and 2, the core shaft 26 extends between the turbine 19 and the gearbox 30, connecting the turbine 19 to the compressor 14, and the turbine and compressor to the gearbox 30. A rearward portion 26b of the core shaft 26 (the turbine shaft 26b) extends between the turbine 19 and the compressor 14, connecting the turbine to the compressor. A forward portion 26a of the core shaft 26 (the gearbox input shaft 26a) extends between the compressor 14 and the gearbox, connecting the turbine and compressor to the gearbox 30. As this forward portion 26a provides the torque to the gearbox 30, it is referred to as the gearbox input shaft 26a. In the described arrangement, a bearing 26c is present on the core shaft 26 at or near the axial position at which the rearward portion 26b meets the gearbox input shaft 26a.

(75) In some gearboxes 30, the planet carrier 34 may be driven by the gearbox input shaft 26a, for example—in such embodiments, the gearbox input shaft 26a may not be a sun input shaft 26a. However, this may make mounting of the sun gear 28 more difficult.

(76) In the arrangement being described, the core shaft 26 is divided into two sections as shown in FIG. 7; a first section 26a extending from the gearbox 30 and connected to the sun gear 28 (the gearbox input shaft 26a), and a second section 26b extending rearwardly from the first section and connected to the turbine 19 (the turbine shaft 26b).

(77) In the described arrangement, the first section 26a is designed to have a lower stiffness than the second section 26b—this may provide a soft mounting for the sun gear 28 whilst maintaining rigidity elsewhere in the engine 10. In such arrangements, the second section 26b is designed to be effectively rigid (as compared to the stiffness of the first section 26a). The second section 26b connecting the turbine and the compressor and the gearbox 30 may be referred to as the turbine shaft 26b. The turbine shaft 26b is arranged to transmit the torsional loads to drive the compressor and the gearbox 30, as well as the compressor and turbine axial loads.

(78) In alternative embodiments, the core shaft 26 may not be divided into sections of different stiffness, and may instead have a constant stiffness. In alternative or additional embodiments, the core shaft 26 may be divided into a larger number of sections.

(79) The core shaft 26 is mounted using a bearing 26c—the bearing 26c is the first bearing on the core shaft 26 axially downstream of the gearbox 30. In the embodiment being described, the bearing 26c is on the second section 26b of the core shaft 26—in other embodiments, it may be on a different, or on the only, shaft section.

(80) The stiffnesses of the gearbox input shaft 26a are measured holding the bearing 26c rigid, and taking the connection of the bearing 26c to the rest of the core shaft 26 as rigid, such that only the stiffnesses of the first portion 26a are considered (the remainder being treated as effectively rigid). For the purpose of determining torsional stiffness, the gearbox input shaft 26a is considered to be free at the end to which the applied torque τ is applied.

(81) Gearbox Input Shaft Radial Bending Stiffness

(82) As shown in FIGS. 1 and 2, the core shaft 26 extends between the driver gear (the sun gear 28) and the low pressure turbine 19. The low pressure turbine 19 drives rotation of the gearbox input shaft 26.

(83) In the arrangement being described with respect to these figures, the gearbox input shaft 26a is designed to have a relatively low radial bending stiffness to provide a “soft” mounting for the sun gear 28. The sun gear 28 may therefore move radially/perpendicularly to the engine axis 9 in response to forces on the sun gear 28, which may improve load distribution between the planet gears 32. In particular, flexibility in the mounting may improve load distribution as the contact regions between gears define constant force angles, and hence those contact regions with larger magnitude forces produce a net force away from their contact positions, which may in turn reduce the larger forces, making them nearer to the mean. Such a soft mounting of the sun gear 28 may be designed to accommodate movements to address one or more of carrier bearing location accuracy and clearance, planet and/or sun gear teeth spacing and thickness variation/manufacturing tolerances, and/or gearbox input shaft mainline bearing location accuracy and clearance, or the likes.

(84) The diagonally lined box 402 at the bearing 26c of the core shaft 26 is shown (in FIG. 8) to indicate the connection to the bearing 26c being treated as rigid (as for a cantilever beam mounting).

(85) In the embodiment being described, the gearbox input shaft radial bending stiffness is determined treating the portion 26a of the core shaft 26 forward of the bearing 26c (i.e. the gearbox input shaft 26a of the described arrangement) as a free-body fixedly mounted at the point of connection to the bearing 26c, with a force applied at the axial position of the axial centre point of the sun gear 28. This is illustrated in FIG. 8, with arrow F indicating the (radial) force on the gearbox input shaft 26a and δ illustrating the (radial) displacement of the end of the shaft 26a. The force, F, is shown acting along a line that passes through the engine axis 9—the skilled person would appreciate that a force towards the engine axis 9 on one side of the axis 9 is a force away from the engine axis on the other side of the axis 9, such that the stiffness takes into account bending both towards and away from the axis. The gearbox 30 is shown for reference, but the sun gear 28 is not shown as moving with the shaft 26a as the stiffness is calculated as a free body stiffness, as mentioned above.

(86) In various embodiments, the gearbox input shaft radial bending stiffness may be greater than or equal to 6×10.sup.5 N/m (i.e. 600 kN/m), and optionally greater than or equal to 8.0×10.sup.5 N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gearbox input shaft radial bending stiffness may be greater than or equal to 6.0×10.sup.5 N/m or 9.0×10.sup.5 N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the gearbox input shaft radial bending stiffness may be greater than or equal to 8.0×10.sup.5 N/m or 1.2×10.sup.6 N/m

(87) In various embodiments, the gearbox input shaft radial bending stiffness may be in the range from 6×10.sup.5 to 3×10.sup.7 N/m (i.e. 600 kN/m to 30,000 kN/m), and optionally in the range from 8.0×10.sup.5 to 1.8×10.sup.7 N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gearbox input shaft radial bending stiffness may be in the range from 6.0×10.sup.5 to 1.8×10.sup.7 N/m and optionally in the range from 8.5×10.sup.5 to 9.9×10.sup.5 N/m (and may be equal to 9.1×10.sup.5 N/m). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the gearbox input shaft radial bending stiffness may be in the range from 8.0×10.sup.5 to 3.0×10.sup.7 N/m, and optionally in the range from 9.5×10.sup.5 to 2.2×10.sup.6 N/m (and may be equal to 1.3×10.sup.6 N/m).

(88) The radial bending stiffness of the gearbox input shaft may be adjusted to lie within this range by selecting or modifying one or more of shaft materials, diameter, wall thickness, or the likes.

(89) Gearbox Input Shaft Tilt Stiffness

(90) Gearbox input shaft tilt stiffness is a measure of the resistance of the gearbox input shaft 26a to an applied moment, M, as illustrated in FIGS. 9 and 10. The axis of the moment is perpendicular to the engine axis 9. Two points of the input shaft 26 are selected for measuring tilt stiffness: a forward point at the axial position of the axial centre point of the sun gear 28 (where the moment is applied) and a rearward point at the axial position of the connection to the bearing 26c (treated as rigid).

(91) The skilled person would appreciate that FIGS. 8 and 9 are schematic only—the curvature of the shaft 26a would differ between the application of a force (FIG. 8) and the application of a moment (FIG. 9) as described above.

(92) In response to the applied moment, M, which is an anticlockwise moment in the example shown, but could be a clockwise moment in other examples, the gearbox input shaft 26a bends through an angle θ—the angle θ is constant at each point along its length for a shaft 26 having a constant section, but may vary with length for shafts 26 with non-constant sections, such as that shown in FIG. 9. For ease of depiction, FIG. 9 shows deformation occurring on the narrower part of the shaft 26 only. More generally, contributions to tilt stiffness from different portions of a shaft 26 of varying width may be combined to determine an overall stiffness.

(93) The curvature at the point of interest—the forward point at the axial position of the axial centre point of the sun gear 28—is selected for measurement of the angle θ. θ is measured between a line parallel to the engine axis 9 and the local tangent to the gearbox input shaft 26a at the forward point. This is shown in FIG. 10, noting that the tangent appears parallel to the length of the shaft 26 in this representation as the curvature is not shown. FIG. 5 illustrates the determination of the tangent and theta more clearly.

(94) In various embodiments, the gearbox input shaft tilt stiffness may be greater than or equal to 5×10.sup.4 Nm/radian, and optionally greater than or equal to 6.5×10.sup.4 Nm/radian. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gearbox input shaft tilt stiffness may be greater than or equal to 5×10.sup.4 Nm/radian or 8×10.sup.4 Nm/radian. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the gearbox input shaft tilt stiffness may be greater than or equal to 1.0×10.sup.5 Nm/radian or 2.4×10.sup.5 Nm/radian.

(95) In various embodiments, the gearbox input shaft tilt stiffness may be in the range 5×10.sup.4 to 5×10.sup.6 Nm/radian, and optionally in the range 6.5×10.sup.4 to 2.6×10.sup.6 Nm/radian. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the gearbox input shaft tilt stiffness may be in the range from 5×10.sup.4 to 8×10.sup.5 Nm/radian and optionally 8×10.sup.4 to 9×10.sup.4 Nm/radian (and may be equal to 8.6×10.sup.4 Nm/radian). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the gearbox input shaft tilt stiffness may be in the range from 1.0×10.sup.5 to 5.0×10.sup.6 Nm/radian, and optionally 2.2×10.sup.5 to 3.2×10.sup.5 Nm/radian (and may be equal to 2.6×10.sup.5 Nm/radian).

(96) The tilt stiffness of the gearbox input shaft 26a may be adjusted to lie within this range by selecting or modifying one or more of shaft materials, diameter, wall thickness, or the likes.

(97) Gearbox Input Shaft Torsional Stiffness

(98) Gearbox input shaft torsional stiffness is a measure of the resistance of the shaft 26a to an applied torque, τ, as illustrated in FIG. 11. It may be described as resistance to twisting, or winding, of the gearbox input shaft 26a. The axis of the moment is parallel to the engine axis 9. The diagonally lined box 402 at the location of the bearing 26c of the gearbox input shaft 26 is shown to indicate the connection to the bearing 26c being treated as rigid and non-rotating (as for a cantilever beam mounting). The gearbox input shaft 26a is otherwise treated as a free body (the sun gear-planet gear mesh stiffness is not included).

(99) A torque, τ, is applied to the gearbox input shaft 26a (at the forward position—the position of the axial mid-point of the sun gear 28) and causes a rotational deformation, θ (e.g. twist) along the length of the shaft 26a. θ is measured at the position of application of the torque. As described above, the core shaft 26 is held to be non-rotating at the location of the bearing 26c, such that the value of the twist increases from zero to θ along the length of the first shaft portion 26a (the gearbox input shaft 26a).

(100) The angle through which a point on the shaft circumference at the forward position moves is θ, where θ is the angle measured in radians. An effective linear torsional stiffness can therefore be defined for the gearbox input shaft 26a as described above, using the radius r of the gearbox input shaft 26a. In embodiments in which the gearbox input shaft 26a varies in radius, the radius of the gearbox input shaft 26a at the interface to the sun gear 28 may be used as the radius r (i.e. the radius at the forward end of the shaft for the embodiment shown). For the purpose of determining torsional stiffness, the gearbox input shaft 26a is considered to be free at the end to which the applied torque τ is applied.

(101) In the arrangement shown, the position of the axial mid-point of the sun gear 28 is also at or adjacent the forward end of the shaft 26a. In alternative embodiments, the gearbox input shaft 26a may extend further forward of the sun gear 28; the forward position used for the application of the torque, force or moment is still taken to be the position of the axial mid-point of the sun gear 28 in such embodiments.

(102) In various embodiments, the torsional stiffness of the gearbox input shaft 26a is greater than or equal to 1.4×10.sup.6 Nm/radian, and optionally greater than or equal to 1.6×10.sup.6 Nm/radian. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torsional stiffness of the gearbox input shaft may be greater than or equal to 1.4×10.sup.6 Nm/radian or 1.8×10.sup.6 Nm/radian. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torsional stiffness of the gearbox input shaft may be greater than or equal to 3×10.sup.6 Nm/radian or 5×10.sup.6 Nm/radian.

(103) In various embodiments, the torsional stiffness of the gearbox input shaft 26a is in the range from 1.4×10.sup.6 to 2.5×10.sup.8 Nm/radian, and optionally in the range from 1.6×10.sup.6 to 2.5×10.sup.7 Nm/radian. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torsional stiffness of the gearbox input shaft may be in the range from 1.4×10.sup.6 to 2.0×10.sup.7 Nm/radian, and optionally may be in the range from 1.8×10.sup.6 to 3×10.sup.6 Nm/radian (and optionally may be equal to 2.0×10.sup.6 Nm/radian). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torsional stiffness of the gearbox input shaft may be in the range from 3×10.sup.6 to 1×10.sup.8 Nm/radian and optionally may be in the range from 5×10.sup.6 to 6×10.sup.6 Nm/radian (and optionally may be equal to 5.7×10.sup.6 Nm/radian).

(104) In various embodiments, the effective linear torsional stiffness of the gearbox input shaft 26a is greater than or equal to 4.0×10.sup.8 N/m, and optionally greater than or equal to 4.3×10.sup.8 N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the effective linear torsional stiffness of the gearbox input shaft may be greater than or equal to 4.0×10.sup.8 N/m or 4.4×10.sup.8 N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, effective linear torsional stiffness of the gearbox input shaft may be greater than or equal to 4.3×10.sup.8 N/m or 6.8×10.sup.8 N/m.

(105) In various embodiments, the effective linear torsional stiffness of the gearbox input shaft is in the range 4.0×10.sup.8 to 3.0×10.sup.10 N/m, and optionally in the range from 4.3×10.sup.8 to 9.0×10.sup.9 N/m. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the effective linear torsional stiffness of the gearbox input shaft may be in the range from 4.0×10.sup.8 to 1.5×10.sup.10 N/m, and optionally may be in the range from 4.4×10.sup.8 to 5.4×10.sup.8 N/m (and optionally may be equal to 4.9×10.sup.8 N/m, and optionally 4.92×10.sup.8 N/m). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the effective linear torsional stiffness of the gearbox input shaft may be in the range from 4.3×10.sup.8 to 3.0×10.sup.10 N/m and optionally may be in the range from 5.0×10.sup.8 to 8.0×10.sup.8 N/m (and optionally may be equal to 6.8×10.sup.8 N/m, and optionally 6.84×10.sup.8 N/m).

(106) The torsional stiffness of the gearbox input shaft 26a may be adjusted to lie within this range by selecting or modifying one or more of shaft materials, diameter, wall thickness, or the likes.

(107) Torque on the Core Shaft

(108) At cruise conditions, a torque, τ, is applied to the core shaft 26 by the rotation of the turbine 19, as illustrated in FIG. 12. As torque does not vary with shaft radius for a rotating shaft, the torque is constant along the core shaft 26 even if the radius varies between the gearbox input shaft portion 26a and the turbine shaft portion 26b.

(109) The torque supplied by the turbine 19 to the core shaft (i.e. the torque on the core shaft) at cruise conditions may be greater than or equal to 10,000 Nm, and optionally greater than or equal to 11,000 Nm. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torque on the core shaft 26 at cruise conditions may be greater than or equal to 10,000 Nm or 11,000 Nm (and optionally may be equal to 12,750 Nm). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torque on the core shaft 26 at cruise conditions may be greater than or equal to 25,000 Nm, and optionally greater than or equal to 30,000 Nm (and optionally may be equal to 34,000 Nm).

(110) The torque on the core shaft at cruise conditions may be in the range from 10,000 to 50,000 Nm, and optionally from 11,000 to 45,000 Nm. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torque on the core shaft 26 at cruise conditions may be in the range from 10,000 to 15,000 Nm, and optionally from 11,000 to 14,000 Nm (and optionally may be equal to 12,750 Nm). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torque on the core shaft 26 at cruise conditions may be in the range from 25,000 Nm or 50,000 Nm, and optionally from 30,000 to 40,000 Nm (and optionally may be equal to 34,000 Nm).

(111) Under maximum take-off (MTO) conditions, the torque on the core shaft 26 may be greater than or equal to 28,000 Nm, and optionally greater than or equal to 30,000 Nm. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torque on the core shaft 26 under MTO conditions may be greater than or equal to 28,000 Nm, and optionally greater than or equal to 35,000 Nm (and optionally may be equal to 36,300 Nm). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torque on the core shaft 26 under MTO conditions may greater than or equal to 70,000 Nm, and optionally greater than or equal to 80,000 or 82,000 Nm (and optionally may be equal to 87,100 Nm).

(112) Under maximum take-off (MTO) conditions, the torque on the core shaft 26 may be in the range from 28,000 Nm to 135,000 Nm, and optionally in the range from 30,000 to 110,000 Nm. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the torque on the core shaft 26 under MTO conditions may be in the range from 28,000 to 50,000 Nm, and optionally from 35,000 to 38,000 Nm (and optionally may be equal to 36,000 Nm). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the torque on the core shaft 26 under MTO conditions may be in the range from 70,000 Nm or 135,000 Nm, and optionally from 80,000 to 90,000 Nm or 82,000 to 92,000 Nm (and optionally may be equal to 87,000 Nm).

(113) In the embodiments being described, the torque on the core shaft 26 is greater than or equal to 10,000 Nm under cruise conditions, and optionally below 50,000 Nm at cruise conditions.

(114) The inventor has discovered that particular ratios of the parameters defined above have significant impact on gearbox performance. In particular, one, some or all of the below conditions may apply to any embodiment:

(115) A first sun input shaft ratio can be defined (at cruise conditions), as:

(116) $\begin{array}{cc}\frac{\mathrm{the}\mathrm{tilt}\mathrm{stiffness}\mathrm{of}\mathrm{the}\mathrm{gearbox}\mathrm{input}\mathrm{shaft}\left(26\right)\left[\frac{\mathrm{Nm}}{rad}\right]}{\mathrm{the}\mathrm{torque}\mathrm{on}\mathrm{the}\mathrm{core}\mathrm{shaft}\left(26\right)\left[\mathrm{Nm}\right]}& \end{array}$

(117) In various embodiments, the first sun input shaft ratio may be greater than or equal to 4 rad.sup.−1, and optionally greater than or equal to 5.0 rad.sup.−1. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the first sun input shaft ratio may be greater than or equal to 4.0 rad.sup.−1, and optionally greater than or equal to 5 rad.sup.−1, further optionally greater than or equal to 6 rad.sup.−1 (and optionally may be equal to 6.7 rad.sup.−1). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, first sun input shaft ratio may be greater than or equal to 4.0 rad.sup.−1, and optionally greater than or equal to 6 rad.sup.−1 or 7 rad.sup.−1 (and optionally may be equal to 7.6 rad.sup.−1).

(118) In various embodiments, the first sun input shaft ratio may be in the range from 4 to 150 rad.sup.−1, and optionally in the range from 5.0 to 90 rad.sup.−1. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the first sun input shaft ratio may be in the range from 4.0 to 90 rad.sup.−1, and optionally from 5 to 50 rad.sup.−1, further optionally from 5 to 8 rad.sup.−1 (and optionally may be equal to 6.7 rad.sup.−1). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the first sun input shaft ratio may be in the range from 4.0 to 90 rad.sup.−1, and optionally from 6 to 50 rad.sup.−1 or 6 to 9 rad.sup.−1 (and optionally may be equal to 7.6 rad.sup.−1).

(119) In various embodiments, a product of the components of the first sun input shaft ratio, i.e. the tilt stiffness of the gearbox input shaft (26) multiplied by the torque on the core shaft (26), may also be calculated. The value of this product, in various embodiments, may be equal to or greater than 5.5×10.sup.8 N.sup.2 m.sup.2/radian, and optionally less than 2.0×10.sup.11 N.sup.2 m.sup.2/radian. Optionally, the product may be greater than or equal to 6.0×10.sup.8 N.sup.2m.sup.2rad.sup.−1, and further optionally may be less than 9.0×10.sup.10 N.sup.2m.sup.2rad.sup.−1. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the product value may be greater than or equal to 5.5×10.sup.8 N.sup.2m.sup.2rad.sup.−1, and optionally less than to 3.0×10.sup.10 N.sup.2m.sup.2rad.sup.−1. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the product value may be greater than or equal to 1.0×10.sup.9 N.sup.2m.sup.2rad.sup.−1, and optionally less than to 2.0×10.sup.11 N.sup.2m.sup.2rad.sup.−1.

(120) Alternatively or additionally, a second sun input shaft ratio can be defined (at cruise conditions), as:

(121) $\begin{array}{cc}\frac{\begin{array}{c}\mathrm{the}\mathrm{radial}\mathrm{bending}\mathrm{stiffness}\mathrm{of}\mathrm{the}\mathrm{gearbox}\\ \mathrm{input}\mathrm{shaft}\left(26\right)\left[N/m\right]\end{array}}{\mathrm{the}\mathrm{torque}\mathrm{on}\mathrm{the}\mathrm{core}\mathrm{shaft}\left(26\right)\left[\mathrm{Nm}\right]}& \end{array}$

(122) In various embodiments, the second sun input shaft ratio may be greater than or equal to 7 m.sup.−2, and optionally greater than or equal to 14 m.sup.−2, and further optionally greater than or equal to 35 m.sup.−2. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the second sun input shaft ratio may be greater than or equal to 7 m.sup.−2, or 14 m.sup.−2, and optionally greater than or equal to 50 m.sup.−2, further optionally greater than or equal to 65 m.sup.−2 (and optionally may be equal to 71 m.sup.−2). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the second sun input shaft ratio may be greater than or equal to 7 m.sup.−2, and optionally greater than or equal to 35 m.sup.−2 (and optionally may be equal to 38 m.sup.−2).

(123) In various embodiments, the second sun input shaft ratio may be in the range from 7 to 800 m.sup.−2, and optionally in the range from 14 to 400 m.sup.−2, and further optionally in the range from 14 to 100 m.sup.−2. In some embodiments, for example in embodiments in which the fan diameter is in the range from 240 to 280 cm, the second sun input shaft ratio may be in the range from 7 or 14 to 400 m.sup.−2, and optionally from 50 to 100 m.sup.−2, further optionally from 65 to 75 m.sup.−2 (and optionally may be equal to 71 m.sup.−2). In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the second sun input shaft ratio may be in the range from 7 to 400 m.sup.−2, optionally 7 to 70 m.sup.−2, and optionally from 35 to 45 m.sup.−2 (and optionally may be equal to 38 m.sup.−2).

(124) In various embodiments, a product of the components of the second sun input shaft ratio, i.e. the radial bending stiffness of the gearbox input shaft (26) multiplied by the torque on the core shaft (26), may also be calculated. The value of this product, in various embodiments, may be greater than or equal to 1.2×10.sup.9 N.sup.2, and optionally less than 8.0×10.sup.11 N.sup.2. In various embodiments, the value may be greater than or equal to 2.4×10.sup.9 N.sup.2, and optionally less than 4.0×10.sup.11 N.sup.2. Optionally, the product may be greater than or equal to 7.0×10.sup.9 N.sup.2, and optionally less than 2.0×10.sup.11 N.sup.2. In some embodiments, for example in embodiments in which the fan diameter is in the range from 330 to 380 cm, the product may be greater than or equal to 4.4×10.sup.9 N.sup.2, and optionally less than 8.0×10.sup.11 N.sup.2, or greater than or equal to 8.0×10.sup.9 N.sup.2, and optionally less than 8.0×10.sup.11 N.sup.2.

(125) The present disclosure also relates to methods 1300 of operating a gas turbine engine 10 on an aircraft 50. The methods 1300 are illustrated in FIG. 13. The method 1300 comprises starting up and operating 1302 the engine 10 (e.g taxiing on a runway, take-off, and climb of the aircraft 50, as suitable) to reach cruise conditions. Once cruise conditions have been reached, the method 1300 then comprises operating 1304 the gas turbine engine 10, which may be as described in one or more embodiments elsewhere herein, to provide propulsion under cruise conditions. The gas turbine engine 10 is operated such that any or all of the parameters or ratios defined herein are within the specified ranges. For example, the method comprises operating 1304 the gas turbine engine 10 such that any one or more of: (i) the torque on the core shaft (26) under cruise conditions is greater than 10,000 Nm, and optionally below 50,000 Nm; and/or (ii) the first sun input shaft ratio of:

(126) $\begin{array}{cc}\frac{\mathrm{the}\mathrm{tilt}\mathrm{stiffness}\mathrm{of}\mathrm{the}\mathrm{gearbox}\mathrm{input}\mathrm{shaft}\left(26\right)\left[\frac{\mathrm{Nm}}{rad}\right]}{\mathrm{the}\mathrm{torque}\mathrm{on}\mathrm{the}\mathrm{core}\mathrm{shaft}\left(26\right)\left[\mathrm{Nm}\right]}& \end{array}$ is greater than or equal to 4 rad.sup.−1, and optionally less than 150 rad.sup.−1, under cruise conditions (the first sun input shaft ratio may fall within any of the ranges as detailed above); and/or (iii) the second sun input shaft ratio of:

(127) $\begin{array}{cc}\frac{\begin{array}{c}\mathrm{the}\mathrm{radial}\mathrm{bending}\mathrm{stiffness}\mathrm{of}\mathrm{the}\mathrm{gearbox}\\ \mathrm{input}\mathrm{shaft}\left(26\right)\left[N/m\right]\end{array}}{\mathrm{the}\mathrm{torque}\mathrm{on}\mathrm{the}\mathrm{core}\mathrm{shaft}\left(26\right)\left[\mathrm{Nm}\right]}& \end{array}$ is greater than or equal to 7 m.sup.−2, and optionally less than 800 m.sup.−2, under cruise conditions (the second sun input shaft ratio may fall within any of the ranges as detailed above); and/or (iv) a first sun input shaft product of: the tilt stiffness of the gearbox input shaft×the torque on the core shaft is greater than or equal to 5.5×10.sup.8 N.sup.2m.sup.2rad.sup.−1, and optionally less than 2.0×10.sup.11 N.sup.2m.sup.2rad.sup.−1; and/or (v) a second sun input shaft product of: the radial bending stiffness of the gearbox input shaft×the torque on the core shaft is greater than or equal to 1.2×10.sup.9 N.sup.2, and optionally less than 8.0×10.sup.11 N.sup.2.

(128) FIG. 14 illustrates how the stiffnesses defined herein may be measured. FIG. 14 shows a plot of the displacement δ 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 δ in this description, the skilled person would appreciate that equivalent principles would apply to a linear or angular displacement.

(129) The stiffnesses defined herein, unless otherwise stated, are for the corresponding component(s) when the engine is off (i.e. at zero speed/on the bench). 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 attached (those cruise conditions being as defined elsewhere herein) may therefore be the same as for when the engine is not in use. 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 at room temperature and unmoving.

(130) 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.