SHAFT COMPONENT AND METHOD FOR PRODUCING A SHAFT COMPONENT

Abstract

A shaft component, which in particular can be connected or is connected to the input or output side of a gear box in a gas turbine engine, in particular an aircraft engine, wherein the shaft component has at least two regions comprising fiber reinforced plastic, with fibers in the at least two regions differing in their composition, their geometric properties, their density, their radial position, their axial position and/or in their fiber orientation in the shaft component.

Claims

1-22. (canceled)

23. A shaft component, which in particular can be connected or is connected to the input or output side of a gear box in a gas turbine engine, wherein the shaft component has at least two regions comprising fiber reinforced plastic, with fibers and/or their matrix in the at least two regions differing in their composition, their geometric properties, their density, their radial position, their axial position and/or in their fiber orientation in the shaft component.

24. The shaft component of claim 23, wherein in at least one of the regions, the fibers are arranged in an angular range of +/-40° to 50° in relation to the main axis of rotation of the shaft component.

25. The shaft component of claim 23, wherein in at least one of the regions the fibers are arranged in an orientation range of about 0° in relation to the main axis of rotation of the shaft component.

26. The shaft component of claim 23, wherein, in at least one of the regions the fibers are arranged in an angular range 60 to 90° in relation to the main axis of rotation of the shaft component.

27. The shaft component of claim 23, wherein a region which is adjacent to another region with a different fiber orientation, is a transitional zone while the fiber changes angle, in particular the transitional zone is configured in such a way that more than 90% of the fiber angle change is contained within an axial extant no greater than 10% of the shorter of the two adjacent regions.

28. The shaft component of claim 23, wherein the shaft component has a non-constant or non-uniform diameter along the axis of rotation.

29. The shaft component of claim 28, wherein shaft component comprises undulations.

30. The shaft component of claim 23, wherein the ratios between resin and fibers are different in the at least two different regions.

31. The shaft component of claim 23, wherein fiber bundle counts and fiber diameters are different in the at least two different regions.

32. The shaft component of claim 23, wherein the angle of the fiber arrangement varies radially in the at least two different regions.

33. The shaft component of claim 23, wherein at least one woven material is used in least one of the two different regions.

34. The shaft component of claim 23, wherein the ratio between the largest diameter and the smallest diameter of the shaft component is less than 1.1.

35. The shaft component of claim 23, wherein at least one first region comprising fibers with orientations going from 40° to 50° to 65° to 90° and at least one second region with fibers with orientations going from 0° to 50° and the at least one first region being adjacent to the at least one second region.

36. The shaft component of claim 23, wherein the fiber-reinforced plastic comprises carbon fibers, metal filaments, synthetic fibers or a mixture thereof.

37. The shaft component of claim 23, wherein the fiber-reinforced plastic comprises aramid fibers, ceramic fibers or a mixture of aramid fibers and ceramic fibers.

38. A method for producing a shaft component, which can be connected or is connected to the input or output side of a gear box in a gas turbine engine, wherein fibers are incorporated in a matrix, the fibers and/or their matrix being incorporated in the shaft component so that in at least two regions differ in their composition, their geometric properties, their density, their radial position, their axial position and/or in their fiber orientation in the shaft component.

39. The method of claim 38, wherein a winding method, a braiding method, a Tailored Fiber Placement method or a combination of those methods is used for incorporating the fibers in the matrix or in the shaft component.

40. The method of claim 38, wherein the fiber-reinforced plastic comprises carbon fibers, metal filaments, synthetic fibers or a mixture thereof.

41. The method of claim 40, wherein the fiber-reinforced plastic comprises aramid fibers, ceramic fibers or a mixture of aramid fibers and ceramic fibers.

42. 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, which is positioned upstream of the engine core, wherein the fan comprises a plurality of fan blades; and a gear box, which can be driven by the core shaft, wherein the fan can be driven by means of the gear box at a lower rotational speed than the core shaft, wherein a shaft component of claim 23 is connected to the gear box as part of a drive shaft for the fan.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The present disclosure will be explained in more detail on the basis of exemplary embodiments with reference to the accompanying drawings in which:

[0058] FIG. 1 shows a sectional lateral view of a gas turbine engine;

[0059] FIG. 2 shows a close-up sectional lateral view of an upstream portion of a gas turbine engine;

[0060] FIG. 3 shows a partially cut-away view of a gear box for a gas turbine engine;

[0061] FIG. 4 shows a schematic view an embodiment of a shaft component with two regions of different fiber properties;

[0062] FIG. 5 shows a radial section through the wall of a shaft component;

[0063] FIG. 5A shows a variation of the embodiment in FIG. 5 with two different regions in radial positions;

[0064] FIG. 6 shows a schematic view of a further embodiment with two regions of different angular fiber arrangements;

[0065] FIG. 7 shows a schematic view of a further embodiment with three regions having different fiber properties;

[0066] FIG. 8 shows sectional view of a shaft arrangement with a gear box;

[0067] FIG. 9A shows a schematic representation of a shaft known in the prior art;

[0068] FIG. 9B shows a schematic representation of a shaft component with two regions which fiber angle orientations differ from a third region;

[0069] FIG. 9C shows the center line of the embodiment of FIG. 9B for a different load case.

[0070] The following table lists the reference numerals used in the drawings with the features to which they refer:

TABLE-US-00001 Ref no. Feature A Core airflow B Bypass airflow P Parallel offset 9 Main axis of rotation 10 Gas turbine engine 11 Enine core 12 Air inlet 14 Low-pressure compressor 15 High-pressure compressor 16 Combustion device/equipment 17 High-pressure turbine 18 Bypass thrust nozzle 19 Low pressure turbine 20 Core thrust nozzle 21 Engine nacelle 22 Bypass duct 23 Fan 24 Stationary supporting structure 26 Shaft

TABLE-US-00002 Ref no. Feature 27 Connecting shaft 28 Sun gear 30 Gear box 32 Planet gears 34 Planet carrier 36 Linkage 38 Ring gear 40 Linkage 50 Shaft component 51 First region comprising fiber reinforced plastic 52 Second region comprising fiber reinforced plastic 53 Third region comprising fiber reinforced plastic 54 Undulation/bellow 60 Fiber 71 First undulant section 72 Second undulant section 73 Third undulant section

DETAILED DESCRIPTION OF THE DISCLOSURE

[0071] Aspects and embodiments of the present disclosure will now be discussed with reference to the accompanying figures. Further aspects and embodiments will be apparent to those skilled in the art.

[0072] FIG. 1 illustrates a gas turbine engine 10 having a main axis of rotation 9. The gas turbine engine 10 comprises an air inlet 12 and a fan 23 that generates two air flows: a core air flow A and a bypass air flow B. The gas turbine engine 10 comprises a core 11 that receives the core air flow A. When viewed in the order corresponding to the axial direction of flow, the engine core 11 comprises a low-pressure compressor 14, a high-pressure compressor 15, a combustion device 16, a high-pressure turbine 17, a low-pressure turbine 19, and a core thrust nozzle 20. An engine nacelle 21 surrounds the gas turbine engine 10 and defines a bypass duct 22 and a bypass thrust nozzle 18. The bypass air flow 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 planetary gear box 30.

[0073] During operation, the core air flow 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 device 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 expelled through the core thrust nozzle 20 to provide some thrust force. The high-pressure turbine 17 drives the high-pressure compressor 15 by means of a suitable connection shaft 27. The fan 23 generally provides the major part of the propulsive thrust. The epicyclic planetary gear box 30 is a reduction gear box.

[0074] 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 gear 28 of the epicyclic planetary gear box 30. Radially to the outside of the sun gear 28 and meshing therewith are a plurality of planet gears 32 that are coupled to one another by a planet carrier 34. The planet carrier 34 guides the planet gears 32 in such a way that they circulate synchronously around the sun gear 28 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 to the outside of the planet gears 32 and meshing therewith is an annulus or ring gear 38 that is coupled, via linkages 40 to a stationary supporting structure 24.

[0075] Note that the terms “low-pressure turbine” and “low-pressure compressor” as used herein may be taken to mean the lowest-pressure turbine stage and lowest-pressure compressor stage (i.e. not including the fan 23) respectively and/or the turbine and compressor stages that are connected together by the connecting shaft 26 with the lowest rotational speed in the engine (i.e. not including the gear-box 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 can be referred to as a first, or lowest-pressure, compression stage.

[0076] The epicyclic planetary gear box 30 is shown by way of example in greater detail in FIG. 3. The sun gear 28, planet gears 32 and ring gear 38 in each case comprise teeth on their periphery to allow intermeshing with the other gearwheels. However, for clarity, only exemplary portions of the teeth are illustrated in FIG. 3. Although four planet gears 32 are illustrated, it will be apparent to a person skilled in the art that more or fewer planet gears 32 can be provided. Practical applications of an epicyclic planetary gear box 30 generally comprise at least three planet gears 32.

[0077] The epicyclic planetary gear box 30 illustrated by way of example in FIGS. 2 and 3 is a planetary gear box in which the planet carrier 34 is coupled to an output shaft via linkages 36 with the ring gear 38 being fixed. However, any other suitable type of planetary gear box 30 may be used. As a further example, the planetary gear box 30 may be a star arrangement, in which the planet carrier 34 is held fixed, with the ring gear (or annulus) 38 allowed to rotate. In such an arrangement, the fan 23 is driven by the ring gear 38. As a further alternative example, the gear box 30 can be a differential gear box in which the ring gear 38 and the planet carrier 34 are both allowed to rotate.

[0078] It is self-evident that the arrangement shown in FIGS. 2 and 3 is merely an example, and various alternatives fall within the scope of protection of the present disclosure. Purely by way of example, any suitable arrangement may be used for locating the gear box 30 in the gas turbine engine 10 and/or for connecting the gear box 30 to the gas turbine engine 10. As a further example, the connections (e.g. the linkages 36, 40 in the example of FIG. 2) between the gear box 30 and other parts of the gas turbine engine 10 (such as e.g. the input shaft 26. the output shaft and the fixed structure 24) may have a certain degree of stiffness or flexibility. As a further example, any suitable arrangement of the bearings between rotating and stationary parts of the gas turbine engine 10 (for example between the input and output shafts of the gear box and the fixed structures, such as the gear-box casing) may be used, and the present disclosure is not limited to the exemplary arrangement of FIG. 2. For example, where the gear box 30 has a star arrangement (described above), a person skilled in the art would readily understand that the arrangement of output and supporting linkages and bearing positions would usually be different than that shown by way of example in FIG. 2.

[0079] Accordingly, the present disclosure extends to a gas turbine engine having any arrangement of types of gear box (for example star or epicyclic-planetary), supporting structures, input and output shaft arrangement, and bearing locations.

[0080] Optionally, the gear box may drive additional and/or alternative components (e.g. the intermediate-pressure compressor and/or a booster compressor).

[0081] Other gas turbine engines to which the present disclosure can be applied may have alternative configurations. For example, engines of this type may have an alternative number of compressors and/or turbines and/or an alternative number of connecting shafts. As a further example, the gas turbine engine shown in FIG. 1 has a split flow nozzle 20, 22 meaning that the flow through the bypass duct 22 has its own nozzle that is separate from and radially outside the core thrust 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 example described relates to a turbofan engine, the disclosure may be applied, for example, to any type of gas turbine engine, such as e.g. an open-rotor engine (in which the fan stage is not surrounded by an engine nacelle) or a turboprop engine. In some arrangements, the gas turbine engine 10 may not comprise a gear box 30.

[0082] The geometry of the gas turbine engine 10 and components thereof, is/are defined by a conventional axis system, comprising an axial direction (which is aligned with the axis of rotation 9), a radial direction (in the bottom-to-top direction in FIG. 1), and a circumferential direction (perpendicular to the view in FIG. 1). The axial, radial and circumferential directions run so as to be mutually perpendicular.

[0083] In the following, several embodiments of shaft components 50 to be used in connection with the input and/or output side of the gear box 30 are described in an exemplary way.

[0084] The figurative representations in FIGS. 4 to 7 are considered schematic to show that the shaft components 50 can have at least two regions 51, 52, 53 comprising fiber reinforced plastic, the fibers 60 and/or their matrix in the at least two regions 51, 52, 53 differ in their composition, their geometric properties, their density, their radial position, their axial position and/or in their fiber orientation arrangement in the shaft component 50. This can for example mean that the ratio between the resin and the fibers is different in at least two regions 51, 52.

[0085] For the sake of simplicity, all shaft components 50 in FIGS. 4 to 7 are shown as straight tubes, i.e. devices having constant inner and outer diameters. The embodiments are not limited to such tubular devices, as is shown in context of FIG. 8. Therefore, all features discussed in the context of shaft components 50 with constant diameters can also be applied to shaft components 50 having e.g. undulant walls (i.e. having bellows 54) as shown in FIG. 8.

[0086] The shaft component 50 can also comprise e.g. conical parts or flanges. At the ends of the shaft components 50 (not shown here), metallic end fittings can be positioned. The attachment of the end fittings can effected by adhesive and/or mechanical means. The shaft coupling can be e.g. a spline or a curvic coupling.

[0087] By deliberately varying the properties of the fibers e.g. in their axial position along the shaft component 50, at least two regions 51, 52, 53 are created in the shaft component 50 having different mechanical properties. This is a deliberate introduction of an anisotropy along the axial direction of the shaft component 50 that can be tailored to achieve specific design objectives.

[0088] As shown in FIG. 4, a first region 51 can have a fiber arrangement or fiber material deliberately softening this region 51 against torsional loads. Whereas a different second region 52 can be stiffer against torsional loads. In FIG. 4 the regions 51, 52 are adjacent to each other, which does not always have to be the case.

[0089] It is possible that e.g. the shaft component 50 has uniform fiber properties but for two regions 51, 52 distributed along the axis. As shown in the context of FIG. 6, more than two regions 51, 52, 53 are also possible, giving a wide range of design choices for optimizations.

[0090] The regions 51, 52, 53 can differ e.g. in the orientation of the fibers 60 resulting in differences in the behavior. In addition or alternatively, different fibers 60 could be used. Different geometric properties (e.g. fiber diameters, fiber lengths) have an effect on the mechanical properties of the shaft component 50.

[0091] Also, the ratio of resin and fibers 60 can be different in different regions 51, 52, 53 of the shaft component 50.

[0092] In FIG. 5 it is shown that radial variation in the fibers 60 can be used as well. In the embodiment shown, the first region 51 comprises three layers of fibers 60, the second layer 52 comprises two layers of fibers. As in the embodiment of FIG. 4, the regions 51, 52 are axially adjacent.

[0093] In FIG. 5A it is shown that the regions 51, 52 can also be positioned radially. The radially outer region 51 has fibers 60 oriented axially; the radially inner region 52 has fibers 60 in circumferential orientation. Obviously, there could be more than two regions 51, 52 arranged radially.

[0094] It is not mandatory, that different regions 51, 52, 53 have to have the same axial lengths, as shown in FIG. 5A. In other embodiments, the regions 51, 52, 53 might have different axial lengths.

[0095] In FIG. 6 an embodiment of a shaft component 50 with two adjacent regions 51, 52 is shown, each region having different orientations of the fibers 60. In the first region 51, the fibers 60 are wound under 45°/-45°, in the second region 52 the fibers 60 are wound under 90° to the rotational axis 9 of the shaft component 50.

[0096] In FIG. 7 an embodiment of a shaft component 50 with three regions 51, 52, 53 is shown. The first and the second region 51, 52 are axially adjacent. The third region 53 is set axially apart.

[0097] In FIG. 8 two shaft components 50', 50"are shown, both being undulant shafts, i.e. shafts having some convolutions or bellows. The first shaft component 50' is on the output side of the gear box 50. This first shaft component 50' comprises two bellows 54. The second shaft component 50" is on the input side of the gear box 30. The second shaft component 50" comprises three bellows 54. The bellows 54 can introduce a certain lateral flexibility and torsional stiffness. Both shaft components 50', 50" comprise two different regions 51, 52 with different properties related to the fibers 60.

[0098] Since the mechanical properties of the shaft components 50 can be mechanically tailored by using regions 51, 52, 53 with different properties, the sizing of the bellows 54 (also responsible for mechanical properties of the shaft component) can be reduced or even substituted by the regions 51, 52, 53 having different properties each.

[0099] In following, some of the different properties, to be used in different regions 51, 52, 53 are listed in an exemplary way. [0100] Regions 51, 52, 53 having different fiber directions in different layers - parallel and perpendicular to shaft axis 9, resulting in different stiffness. [0101] Regions 51, 52, 53 having different fiber directions in different layers - at different angles and hand of twist relative to the shaft axis 9, resulting in different stiffness. [0102] Regions 51, 52, 53 having different fiber packing densities in different layers resulting in different density/stiffness. [0103] Regions 51, 52, 53 having different fiber materials in different layers different resulting in different strength/stiffness. [0104] Regions 51, 52, 53, having different fiber diameters or cross sections in different layers resulting in different stiffness/second moment of inertia. [0105] Regions 51, 52, 53 having a combination of woven fiber ribbon and individual fibers in different layers resulting in a combination of multidirectional and unidirectional properties. [0106] Regions 51, 52, 53 having a combination of fiber or ribbon wound into a shaft form while ‘dry’, then impregnated with the resin matrix. [0107] Regions 51, 52, 53 having a fiber or ribbon wound into a shaft form when preimpregnated with resin, then cured using heat.

[0108] Even though the embodiments of the shaft component 50 have been exemplary shown in the context of a geared turbo engine 10, the shaft components 50 can also be used in other contexts. Similar concepts may be of use on other components/engine designs where tailored stiffness is required, for example flexible couplings or shafts in the accessory drive train, e.g. to drive the accessory gearbox, oil pumps, fuel pumps, generators. These may be positioned on the engine main line, or off the engine mainline (e.g. on the intercase or fan case).

[0109] In the following some embodiments are described in which certain regions 51, 52, 53 have a certain fiber orientation.

[0110] The following table shows assignments of different composite shaft sections (Type A to E) with certain fiber orientations (i.e. ranges of angles).

TABLE-US-00003 Section type Fiber Orientation (from shaft central axis projected into composite section) Axial Stiffness and Strength Property Bending Stiffness and Strength Property Torsional Stiffness and Strength Property A 0° to 25° especially 0° Very High Very High Very Low B 25° to 40° High High Medium C 40° to 50° especially 45° Medium Medium Very High D 50° to 65° Low Low Medium E 65° to 90° especially 90° Very Low Very Low Very Low

[0111] Each of the different fiber orientations reacts differently to axial, bending and torsional loads, as indicated in above table.

[0112] The axial and bending stiffness are highest with relatively small fiber orientation angles and decreases with increasing fiber orientation angles.

[0113] The torsional stiffness is highest around a fiber orientation angle of 45° and falls off towards smaller and higher fiber orientation angles.

[0114] When describing fiber orientations, only one of the matched pair of orientations is listed. The region will be made of fibers at both the quoted angle and its matched pair with a negative sign.

[0115] So a region of e.g. section type C with 45° refers to a shaft region with an equal amount of fiber in the +45° and the -45° directions.

[0116] These pair of angles can be considered as right handed helix and left handed helix angles. The equal amount of fiber is important as it produces a composite with a symmetric

[0117] The fiber orientations of 0° and 90° are exceptions to this as for these two angles, the negative value is the same as the positive. Hence 0° is with all the fibers axially aligned and 90° is with all the fibers circumferentially aligned to the shaft.

[0118] Note that although both the stiffness and strength of the various section types listed in the table above follow the trend as tabulated, the proportions of the stiffness and strength changes will differ in magnitude.

[0119] Each region 51, 52, 53 does not have to be exclusively composed of fibers in one pair of orientations, so a composite can be made with a mixture of different angles in different layers to give some merged combination of the stiffness and strength properties.

[0120] It is possible that a composite shaft component 50 can been designed with just one region 51 (e.g. designated A-C or B-C) formed from a mixture of section type A or B to give adequate bending stiffness to increase the modal frequency and avoid whirling vibrations, combined with a section type C to give adequate torsional strength. The total composite thickness and the mixture proportions of a given design would be determined to meet the specific requirements of the shaft.

[0121] In the upper half of FIG. 9A a generally known shaft design is shown schematically. The left end of the shaft component 50 is linked to the sun gear 26, the right end of the shaft component is linked to a driving part, such as a turbine section (not shown here). The shaft component 50 comprises three undulant sections 71, 72, 73 with the aim of deliberately altering the stiffness of the shaft component 50.

[0122] In the lower half of FIG. 9A a representation of the center line of the shaft component 50 is shown under a load causing a parallel offset P.

[0123] Starting from left, the centerline is relatively straight till the first undulant section 71 as the shaft component is relatively stiff. The first and second undulant sections 71, 72 reduce the stiffness locally, so that the center line comprises two slightly curved sections in the respective undulant sections. Towards the right, the third undulant section 73 introduces a further localized reduction of the stiffness, causing a further curved section in the center line.

[0124] Embodiments considered here, differ by utilizing different regions 51, 52, 53 composed of different section types within the shaft component 50.

[0125] This is shown for example in FIG. 9B and FIG. 9C. FIG. 9B shows an embodiment of a shaft component 50 approaching a similar behavior than the one shown by the shaft component 50 in FIG. 9B but using different regions with different fiber properties. In FIG. 9B the load case with a parallel offset of the center line is shown as in FIG. 9A. In FIG. 9C a center line for the same shaft component 50 as in FIG. 9B is shown under constrained bending load.

[0126] Here the shaft component comprises two regions 51, 52 (designated C-E) at either end of a region 53 (designated A-C or B-C) creating a shaft component 50 design which retains adequate torsional strength and stiffness to avoid whirling vibrations, but with a tailored bending stiffness to isolate the gearbox from damaging mis-alignments and bending moments. This has the same or similar effect as the design of the shaft component 50 in FIG. 9A. The regions 51, 52, 53 are adjacent to each other. This also means that in all regions three regions 51, 52, 53 fibers with an angular fiber orientation between 40° and 50° (section type C) are present.

[0127] While the regions designated C-E have low or very low axial stiffness properties, they only contribute to the overall stiffness of the shaft in proportion to their length, allowing the design to meet the overall target axial stiffness.

[0128] Similarly, the central region 53 designated A-C or B-C maintains the natural frequency at a high value and avoids any damaging whirling vibrations. The two regions 51, 52 designated C-E both deform in a pivoting style motion to allow any mis-mismatch between the ends of the shaft component 50 while isolating the gearbox from damaging bending moments.

[0129] By designing composite shafts with the methods described above, the axial and torsional stiffness’ can be maintained while producing significant reductions in the bending moment shaft stiffness, without the need to include reductions in stiffness with large geometric features as shown in regions 51, 52. The composite shaft can actually have a plain cross-section without any significant disturbance.

[0130] It should be understood that the above description is intended for illustrative purposes only, and is not intended to limit the scope of the present disclosure in any way. Also, those skilled in the art will appreciate that other aspects of the disclosure can be obtained from a study of the drawings, the disclosure and the appended claims. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. Various features of the various embodiments disclosed herein can be combined in different combinations to create new embodiments within the scope of the present disclosure. In particular, the disclosure extends to and includes all combinations and sub-combinations of one or more features described herein. Any ranges given herein include any and all specific values within the range and any and all sub-ranges within the given range.