Device for centring and guiding a shaft of a turbine engine of an aircraft
By designing some columnar members in the flexible cage of the aircraft turbine engine bearing to be joined with gaps and others to be joined without gaps, the problem of uniform rigidity in the flexible cage in the prior art is solved, thereby improving the stability and performance of the engine and reducing manufacturing costs.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SAFRAN AIRCRAFT ENGINES SAS
- Filing Date
- 2022-03-09
- Publication Date
- 2026-07-21
Smart Images

Figure CN116981831B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a device for centering and guiding the shaft of an aircraft turbine engine. Background Technology
[0002] Aircraft turbine engines include shafts, such as low-pressure shafts and high-pressure shafts, which are centered and guided to rotate by bearings, which are typically rolling bearings, such as roller bearings or ball bearings.
[0003] A rolling bearing consists of an outer ring and an inner ring, with rollers or balls arranged between them. The inner ring is fixed to the shaft to be guided, and the outer ring is attached to a bearing support, which is a rigid part of the turbine engine stator.
[0004] Turbine engine shafts can reach very high speeds, typically between 2,000 rpm and 30,000 rpm. These speeds excite the shaft's intrinsic modes, and if the modes respond strongly, this can have a detrimental effect on the motor.
[0005] To control the position of the modes, bearings are typically combined with flexible cages, which allow for relaxation of the shaft's boundary conditions and reduction of the frequency of the intrinsic modes. This can bring the modes down below the operating range.
[0006] In this application, "flexible cage" refers to a component or assembly that provides a flexible connection between the outer ring of a bearing and the bearing's support. The flexibility of the cage is typically ensured by its elastic deformation capacity (e.g., in terms of torsion and / or bending). To provide this capacity, the cage includes at least one series of columnar members distributed around and extending substantially parallel to the axis of the bearing.
[0007] There are currently two flexible cage technologies used for bearings.
[0008] The first technology described in documents FR-A1-3 009 843 and FR-A1-3 078 370 is an integral flexible cage. This type of cage typically comprises an inner cylindrical wall and an outer cylindrical wall or attachment flange, with the outer ring of the bearing attached or integrated into the inner cylindrical wall, and the outer cylindrical wall or attachment flange used for attachment to the bearing support. The wall is connected by a series of generally C-shaped columnar members or two series of columnar members extending around and connected to each other. Thus, the columnar members and the wall are formed as a single piece.
[0009] The second technique described in document FR-A1-3 009 843 relates to a cage obtained by assembling individual columnar members with supports and rings. Each columnar member includes an elongated body and is attached to a support at a first longitudinal attachment end for attachment and to a ring at a second longitudinal attachment end for attachment.
[0010] In the prior art, the main body has a circular cross-sectional shape, i.e., an axisymmetric shape (the cross-sectional shape of the main body of the column is symmetrical about the longitudinal axis of the main body). The flexible cage equipped with these columnar members also has an axisymmetric shape, and the rigidity of the flexible cage is the same regardless of the lateral direction of the load force on the cage.
[0011] The prior art also includes the techniques described by FR-A1-3 091 902, FR-A1-2 519 101, GB-A-2 3100 258, US-A1-2016 / 177765, GB-A-2 111 137 or CN-B-103 244 276.
[0012] The present invention proposes an improvement to this second technology, which in particular enables the rigidity of the flexible cage to be adjusted according to the direction of the load. Summary of the Invention
[0013] This invention proposes a device for centering and guiding the shaft of an aircraft turbine engine, the device comprising:
[0014] - The outer ring of a rolling bearing, the ring extending about an axis and including an aperture arranged about the axis and oriented parallel to the axis;
[0015] - A ring bearing support extending about the axis and at least partially about the ring, the support including an aperture arranged about the axis and oriented parallel to the axis; and
[0016] A series of columnar members, which connect the ring to the support, are distributed around an axis and extend generally parallel to that axis. Each of these columnar members includes a first longitudinal end and a second longitudinal end, the first longitudinal end engaging in an orifice in the ring, and the second longitudinal end engaging in an orifice in the support.
[0017] The feature is that some of the columnar members, referred to as the first columnar member, have ends that engage in the orifice without gaps, while other columnar members, referred to as the second columnar member, have ends that engage in the orifice of the ring and / or support with gaps, the gaps being configured such that the device has different rigidities in at least two directions perpendicular to the axis.
[0018] Regardless of the position of the columnar member around its respective axis, a device equipped with a columnar member comprising an axisymmetric body, using the prior art, has the same rigidity in all lateral directions (perpendicular to the axis). This means that the rigidity of the device in a first direction perpendicular to the axis (e.g., in a horizontal plane) is the same as the rigidity of the device in a second direction perpendicular to the axis (e.g., in a vertical plane).
[0019] In contrast, this invention allows for different stiffnesses to be imparted to the device depending on the lateral direction of the load. In effect, the gap is oriented in a given direction, resulting in lower stiffness when a load is applied to the device in that given direction. Advantageously, the device comprises two different stiffnesses in the lateral direction. Providing different stiffnesses in two mutually perpendicular lateral directions is particularly useful for stabilizing the shaft, as this reduces the speed at which instability occurs in the shaft guided by the device. The invention is advantageous because it forms the flexible cage by assembling columnar members, allowing for a variety of possible configurations while limiting the cost of the device. In the case of a monolithic flexible cage, for example, changes in features would require the manufacture of new components. This would mean additional costs and delays during the development phase, especially in the event of errors in the dimensional design of prototype components. The time required to manufacture new components is non-compressible.
[0020] It should also be understood that the present invention covers all combinations of the shape of the cross-section of the end of the columnar member and the shape of the corresponding orifice of the ring and support member. These shapes may be selected from circular or non-circular shapes, such as oblong, elliptical, rectangular or trapezoidal.
[0021] The apparatus according to the invention may include one or more of the following features, which may be employed individually or in combination with each other:
[0022] When the device is loaded in a first direction perpendicular to the axis, the second column moves in the gap while the first column remains stationary. When the device is loaded in a second direction perpendicular to the axis, which is different from the first direction, the first and second columns remain stationary in their respective orifices.
[0023] These directions are perpendicular to each other;
[0024] -The first columnar member and the second columnar member alternate around the axis;
[0025] - The cross-sections of the first and second ends of the columnar member are circular;
[0026] - The openings of the ring and the support include a first opening and a second opening. The cross-section of the first opening is circular, and the cross-section of the second opening is oblong or elliptical.
[0027] - The second orifice is oriented such that the second orifice has an elongated shape in the same direction;
[0028] - The orifice is formed in the annular flange of the ring and the support;
[0029] - The outer ring includes an outer cylindrical surface, which together with the inner cylindrical surface of the support defines an annular space for forming a damping oil film.
[0030] The present invention also relates to an aircraft turbine engine comprising at least one device as described above. Attached Figure Description
[0031] Other features and advantages of the invention will become apparent from the following detailed description, and with reference to the accompanying drawings, in order to understand it:
[0032] [ Figure 1 ] Figure 1 It is a schematic perspective view of an axial cross-section of a device for guiding and centering the bearings of an aircraft turbine engine, based on existing technology;
[0033] [ Figure 2 ] Figure 2 This is a schematic diagram of the axial cross-section of another device for guiding and centering the bearings of an aircraft turbine engine, based on existing technology.
[0034] [ Figure 3 ] Figure 3 This is a very schematic cross-sectional view of a device for guiding and centering a turbine engine bearing of an aircraft according to an embodiment of the present invention;
[0035] [ Figure 4 ] Figure 4 yes Figure 3 A schematic axial section view of the device along section axis II;
[0036] [ Figure 5 ] Figure 5 yes Figure 3 A schematic axial section view of the device along section axis II-II; and
[0037] [ Figure 6 ] Figure 6 yes Figure 3 A schematic axial section view of the device along section axis III-III. Detailed Implementation
[0038] First refer to Figure 1 , Figure 1The first integral flexible cage 10 technology according to the prior art is shown.
[0039] The flexible cage 10 ensures the connection between the outer ring 12 of the rolling bearing 14 and the annular support 16 of the bearing 14.
[0040] In addition to the outer ring 12, the bearing 14 includes an inner ring 18, which is fixed to the shaft of the turbine engine (not shown). In the example shown, rings 12 and 18 define roller raceways.
[0041] The outer ring 12 is integrated into the inner cylindrical wall 10a of the cage frame 10, which includes a radially outer annular flange 10b for attachment to the support member 16 via a screw and nut type device (not shown).
[0042] The cage 10 includes two series of columnar members 20 and 22, which are radially inner columnar members and radially outer columnar members respectively relative to the axis X of the bearing 14 and the shaft guided by the bearing.
[0043] Columnar members 20 and 22 are distributed around axis X and extend parallel to the axis. Columnar member 20 extends around columnar member 22. A first longitudinal end of columnar member 20 is connected to flange 10b, and a second longitudinal end of columnar member 20 is connected to another columnar member 22 via an annular segment 24 of cage 10 having a C-shaped cross-section. Columnar member 22 extends linearly from wall 10a to segment 24.
[0044] The support member 16 forms part of the stator of the turbine engine and has a generally truncated conical shape. At the inner periphery of the support member, the support member includes an inner cylindrical surface 16a for contractile engagement with an annular member 26, which extends around the cage wall 10a and, together with the cage wall, defines an annular space 28. This annular space is supplied with oil to form an oil film to dampen vibrations transmitted by the bearing 14 during operation.
[0045] Figure 2 The second flexible cage 30 technology with independent columnar members 32 is shown according to the prior art.
[0046] The flexible cage 30 also ensures the connection between the outer ring 12 of the rolling bearing 14 and the annular support 16 of the bearing 14.
[0047] In addition to the outer ring 12, the bearing 14 includes an inner ring 18, which is fixed to the shaft A of the turbine engine. In the example shown, rings 12 and 18 define roller raceways.
[0048] The outer ring 12 includes a radially outer annular flange 12a which includes an aperture through which the end 32a of the columnar member 32 passes. These ends 32a have threads and receive nuts 34 which are fastened against the flange 12a.
[0049] The opposite end 32b of the columnar member 32 is attached in a hole of the support member 16.
[0050] The cage 30 includes a series of columnar members 32 which are distributed around an axis X and extend parallel to this axis. Each columnar member 32 includes a body 32c the cross-section of which is circular and which is thus symmetric about an axis Y of the body. These columnar members 32 are also symmetric with respect to each other about the axis X.
[0051] Thus, the flexible cage 30 is "axisymmetric" and the stiffness of the cage 10 and the bearing 14 is thus the same in all transverse directions (perpendicular to the axis X).
[0052] However, from a dynamic point of view, it may be interesting to have different stiffnesses in two orthogonal directions: this provides a stabilizing effect for the device by delaying the speed at which instability appears due to the internal damping of the shaft.
[0053] In fact, unlike the single mode in the axisymmetric case, by forming different flexibilities in at least two directions, at least two modes will appear.
[0054] In the case where the initial radial stiffness K of the axisymmetric cage is such that K1 < K < K2 (where K1 and K2 are the stiffnesses of the asymmetric flexible cage in different directions 1 and 2 transverse to the axis X respectively), then the frequencies of the modes formed will lie within the frequency of the initial single mode.
[0055] In this case, the frequency at which instability can occur is increased, thereby making it possible to limit the potentially damaging instability risk of the engine.
[0056] Controlling the azimuthal movement of the shaft can also be used to improve the performance of the engine. Under mechanical or thermal loads, the motor housing deforms and these distortions produce different gap openings and gap closings depending on the azimuth. This means a deterioration in the performance of the motor, which can be limited if the dynamic displacement is optimized to compensate for some of the distortions (for example by making the flexible cage stiffer in the direction of gap closing and softer in the direction of gap opening).
[0057] The present invention makes it possible to meet this need with the following axisymmetric columnar members, some of which are joined in a non-gapped manner while other axisymmetric columnar members are mounted in the outer ring 12 and the support member 16 in a gapped manner.
[0058] Figures 3 to 6 An embodiment of a device for centering and guiding the shaft of an aircraft turbine engine is shown.
[0059] The device includes:
[0060] - The outer ring 12 of the rolling bearing 14 extends about an axis X and includes orifices 42a, 42b arranged about the axis X and oriented parallel to the axis X;
[0061] - Annular bearing support 16, extending about axis X and at least partially about ring 12, the support 16 including orifices 44a, 44b arranged about and oriented parallel to axis X; and
[0062] - A series of columnar members 40, 41, which connect the ring 12 to the support member 16.
[0063] The columnar members 40 and 41 are distributed around and extend generally parallel to axis X. Each of these columnar members 40 and 41 includes an elongated body 40c or 41c extending between a first longitudinal end 40a or 41a and a second longitudinal end 40b or 41b. Each of the first ends 40a or 41a engages in one of the orifices 42a or 42b of the ring 12, and each of the second ends 40b or 41b engages in one of the orifices 44a or 44b of the support member 16.
[0064] The first columnar member 40 and the second columnar member 41 are distinguishable from the columnar members 40 and 41. The ends 40a and 40b of the first columnar member 40 engage with the orifices 42a and 44a in the ring 12 and the support member 16 in a gapless manner. The ends 41a and 41b of the second columnar member 41 engage with the orifices 42b and 44b in the ring 12 and / or the support member 16 in a gapless manner. It should be understood that the first end 41a of the columnar member 41 may engage with the orifice 42b of the ring 12 in a gapless manner, and the second end 41b may engage with the orifice 44b of the support member 16 in a gapless manner. It should also be understood that the first end 41a of the columnar member 41 may engage with the orifice 42b of the ring 12 in a gapless manner, and the second end 41b may engage with the orifice 44b of the support member 16 in a gapless manner. It should also be understood that the first end 41a of the column 41 may engage in the orifice 42b of the ring 12 with a gap, and the second end 41b may engage in the orifice 44b of the support 16 with a gap. The gaps are configured such that the device has different rigidities in at least two different directions perpendicular to the axis X.
[0065] The two directions perpendicular to the axis X are preferably perpendicular to each other.
[0066] In the following text, we are interested in the situation where the two ends 41a, 41b of the second column 41 are engaged in the orifices 42b, 44b of the ring 12 and the support 16 with a gap.
[0067] exist Figure 3 In the example of the illustrated embodiment, first columnar members 40 and second columnar members 41 alternate around axis X. It should be understood that at least one first columnar member 40 may be located between two second columnar members 41 around axis X, and at least one second columnar member 41 may be located between two first columnar members 40 around axis X. In other words, the number of first columnar members 40 located between two second columnar members 41 may be more than one. The number of second columnar members 41 located between two first columnar members may also be more than one.
[0068] Advantageously, the first ends 40a, 41a of the columnar members 40, 41 have a generally circular cross-section. Advantageously, the second ends 40b, 41b also have a generally circular cross-section. In another embodiment not described, the first ends 40a, 41a and the second ends 40b, 41b may have a generally non-circular (e.g., oblong or elliptical) cross-sectional shape.
[0069] The axial cross-section of the ring 12 is generally L-shaped and includes a cylindrical portion 12b, one axial end of which is connected to a radially outer annular flange 12a for attaching the columnar members 40, 41.
[0070] The cylindrical portion 12b of the ring 12 includes an annular groove 12c at its inner periphery for rolling the balls of the bearing 14, and the cylindrical portion of the ring includes an outer cylindrical surface 12d at its outer periphery, which, together with the support 16, defines an annular space for forming a damping oil film.
[0071] Support member 16 is partially shown in the accompanying drawings.
[0072] The support 16 includes a first cylindrical wall 16b that extends around the cylindrical portion 12b of the ring 12 and includes an inner cylindrical surface 16a that, together with the surface 12d, defines the aforementioned damping oil film formation space.
[0073] The support member 16 includes a second cylindrical wall 16c extending around a first cylindrical wall 16b or even around a flange 12a of the ring 12. The first cylindrical wall 16b and the second cylindrical wall 16c are joined together by a generally radial annular wall 16d, which includes an opening 46 through which the bodies 40c, 41c of the columnar members 40, 41 pass with a gap. Advantageously, the opening 46 has a generally circular cross-section.
[0074] In the example shown, it can be seen that columnar members 40 and 41 pass through the annular space formed between walls 16b and 16c. Wall 16d is located at one axial end of this space.
[0075] The support member 16 also includes an annular flange 16e.
[0076] The orifices 42a and 42b in the ring 12 and the orifices 44a and 44b in the support 16 may include first orifices 42a and 44a and second orifices 42b and 44b. Advantageously, the first orifices 42a and 44a have a generally circular cross-section. Optionally (not shown), the first orifices 42a and 44a may have a non-circular overall cross-sectional shape, such as an oblong or elliptical shape. In this way, the corresponding ends 40a and 40b of the first columnar member 40 can be joined in the ring 12 and the support 16 in a gapless manner, such as... Figure 4 As shown, where Figure 4 It shows Figure 3 The device is shown in a cross-sectional view along section axis II. It should be understood that, by engaging the ring 12 and support 16 in a gapless manner, the ends 40a and 40b of the first columnar member 40 have circular cross-sections when the first orifices 42a and 44a have generally circular cross-sectional shapes, or alternatively, the ends 40a and 40b of the first columnar member 40 have non-circular cross-sectional shapes when the first orifices 42a and 44a have generally non-circular cross-sectional shapes. It should also be understood that the dimension of each of the ends 40a and 40b is approximately equal to the dimension of each of the first orifices 42a and 44a.
[0077] Advantageously, the cross-sections of the second orifices 42b and 44b are generally oblong or elliptical. Alternatively (not shown), the cross-sections of the second orifices 42a and 44a can be generally circular. In this way, the corresponding ends 41a and 41b of the second columnar member 41 can be engaged in the ring 12 and the support member 16 with a gap. Figure 5 As shown in the example, Figure 5 It shows Figure 3In the cross-sectional view of the device along cross-sectional axis II-II, the second orifices 42b and 44b may preferably have an elongated shape in the same direction. It should be understood that the elongated shape of the orifices 42b and 44b means that the first longitudinal dimension of the orifice is greater than a second dimension of the orifice that is substantially perpendicular to the first longitudinal dimension. It should also be understood that the first longitudinal dimension is greater than the diameter of the ends 41a and 41b of the columnar member 41, and the second dimension is substantially equal to the diameter of the ends 41a and 41b. In other words, a gap exists only in the longitudinal direction with respect to the columnar member 41. In another embodiment, not shown, a gap may exist between the circularly cross-sectional ends 41a and 41b of the second columnar member 41 and the substantially circularly cross-sectional second orifices 42b and 44b. In this embodiment, the diameter of the second orifices 42b and 44b is greater than the diameter of the ends 41a and 41b, and the gap is consistently positive in all directions. In another embodiment, not shown, gaps may exist between the ends 41a, 41b of the second columnar member 41, whose cross-section is non-circular (e.g., oblong or elliptical), and the second openings 42b, 44b, whose cross-sections are generally circular. It should be understood that in this embodiment, the cross-sections of the ends 41a, 41b may preferably have an elongated shape in the same direction. The elongated shape of the ends 41a, 41b means that the first longitudinal dimension of the end is larger than a second dimension of the end that is generally perpendicular to the first longitudinal dimension. Therefore, it should be understood that gaps exist when the diameters of the second openings 42b, 44b are approximately equal to the first longitudinal dimension of the cross-section of the ends 41a, 41b. In other words, gaps exist only with the columnar member 41 in the direction perpendicular to the first longitudinal dimension.
[0078] Orifices 42a and 42b may be formed in flange 12a. Orifice 42a passes through end 40a of column 40, and orifice 42b passes through end 41a of column 41; these ends 40a and 41a may be threaded and receive nuts 43 fastened against flange 12a.
[0079] Orifices 44a and 44b may be formed in flange 16e. Orifice 44a passes through end 40b of column 40, and orifice 42b passes through end 41b of column 41; these ends 40b and 41b may be threaded and receive nuts 45 fastened against flange 16e.
[0080] The bodies 40c and 41c of each columnar member 40 and 41 can be connected to each of the ends 40a, 40b, 41a, and 41b via annular sleeves 40d and 41d. The sleeves 40d and 41d may include flat regions that can be supported on the flange 16e of the support member 16 and the flange 12a of the ring 12, respectively, thereby preventing the columnar members 40 and 41 from rotating about the longitudinal axis of the columnar member.
[0081] exist Figure 3 In the example shown, the cage 10 is not axisymmetric with respect to axis X, and the rigidity of the cage is also not axisymmetric. The rigidity of the cage 10 in the transverse direction parallel to plane P (arrow F2) is greater than the rigidity of the cage 10 in the direction perpendicular to these planes P (arrow F1). In fact, when the cage 10 is loaded in the direction parallel to plane P (arrow F2), only the first column 40 works to produce a certain rigidity. The second column 41 engages in the orifices 42b, 44b in the ring 12 and the support 16 with a gap, and the second column can move in the direction of load F2 in the gap in the orifices 42b, 44b. In this way, a portion of the load F2 can be absorbed. When the cage 10 is loaded in the direction perpendicular to plane P (arrow F1), all the columns 40, 41 are loaded, and the rigidity of the cage 10 is greater. This is because the second column 41 cannot move in that direction in the orifices 42b, 44b, as Figure 6 As shown, Figure 6 It shows Figure 3 The device is shown in a cross-sectional view along cross-sectional axis III-III, parallel to the load F1. In other words, when the cage 10 is loaded in a given direction and the gaps of the orifices 42b and 44b are oriented in that same given direction (e.g., a direction parallel to plane P (arrow F2)), the stiffness in that given direction is low. It should be understood that when the device is loaded in a first direction perpendicular to axis X (arrow F2), the second column 41 moves in the gap while the first column 40 remains stationary, and when the device is loaded in a second direction perpendicular to axis X (arrow F1), different from the first direction, the first column 40 and the second column 41 remain stationary in their respective orifices 42a, 42b, 44a, 44b. Therefore, different stiffnesses can be obtained depending on the direction of the load.
[0082] The present invention also relates to an aircraft turbine engine comprising at least one device as described above.
[0083] Therefore, the advantage of the device and flexible cage according to the invention is that the rigidity of the cage varies depending on the angular position of the force transmitted to the cage in the direction transverse to the main axis of the cage.
Claims
1. A device for centering and guiding the shaft of an aircraft turbine engine, the device comprising: - The outer ring (12) of the rolling bearing (14) extends about an axis (X) and includes orifices (42a, 42b) arranged about the axis and oriented parallel to the axis. - A ring bearing support (16) extending about the axis (X) and at least partially about the outer ring (12), the ring bearing support (16) including orifices (44a, 44b) arranged about the axis and oriented parallel to the axis; and - A series of columnar members (40, 41) connecting the outer ring to the annular bearing support, the columnar members being distributed around and extending parallel to the axis (X), each of the columnar members including a first longitudinal end (40a, 41a) and a second longitudinal end (40b, 41b), the first longitudinal end engaging in one of the orifices (42a, 42b) of the outer ring, and the second longitudinal end engaging in one of the orifices (44a, 44b) of the annular bearing support. The characteristic feature is that some of the columnar members (40, 41), referred to as the first columnar member (40), have ends (40a, 40b) that engage in the orifices (42a, 44a) of the outer ring and the annular bearing support in a gapless manner, and the other columnar members (41), referred to as the second columnar member (41), have ends that engage in the orifices (42b, 44b) of the outer ring (12) and / or the annular bearing support (16) in a gapless manner, the gap being configured such that the device has different rigidities in at least two directions perpendicular to the axis.
2. The apparatus according to claim 1, wherein, At least two directions perpendicular to the axis are perpendicular to each other.
3. The apparatus according to claim 1 or 2, wherein, The first columnar member (40) and the second columnar member (41) alternate around the axis.
4. The apparatus according to claim 1 or 2, wherein, The cross-sections of the first and second longitudinal ends of the series of columnar members (40, 41) are circular.
5. The apparatus according to claim 4, wherein, The openings of the outer ring (12) and the annular bearing support (16) include a first opening (42a, 44a) and a second opening (42b, 44b), the first opening having a circular cross-sectional shape and the second opening having an oblong cross-sectional shape or an elliptical cross-sectional shape.
6. The apparatus according to claim 5, wherein, The second orifice (42b, 44b) is oriented such that the second orifice has an elongated shape in the same direction.
7. The apparatus according to claim 1 or 2, wherein, The orifice of the outer ring is formed in the annular flange (12a) of the outer ring, and the orifice of the annular bearing support is formed in the annular flange (16e) of the annular bearing support (16).
8. The apparatus according to claim 1 or 2, wherein, The outer ring (12) includes an outer cylindrical surface (12d), which together with the inner cylindrical surface (16d) of the annular bearing support (16) defines an annular space for forming a damping oil film.
9. An aircraft turbine engine comprising at least one device according to any one of claims 1 to 8.