Thrust foil bearing

Abstract

A thrust foil bearing (5) comprises: a base plate (10) orthogonal to a rotation center axis (8); a back foil (30) attached to the base plate (10) and including a plurality of back foil pieces (31) arranged in the circumferential direction of the rotation center axis (8) assumed in the base plate; and a top foil (20) including a plurality of top foil pieces (21) arranged in the circumferential direction and covering the plurality of back foil pieces (31). Each back foil piece (31) includes: a band section (32) that extends from the inner peripheral side to the outer peripheral side of the back foil (30); and a bump section (33) that extends from a proximal end section (33a), which is a fixed end connected to the band section (32), to a distal end section (33b) which is a free end, the bump section (33) including, between the proximal end section (33a) and the distal end section (33b), a curved section (35) protruding toward the top foil (20).

Description

Thrust foil bearing

[0001] The present disclosure relates to thrust foil bearings.

[0002] A thrust foil bearing is a type of fluid bearing that supports a rotating body without contact by forming a fluid film between the thrust foil bearing and the rotating body. The rotating body is mounted so that it can move axially and move finely due to vibration, impact, etc.

[0003] Regardless of such minute movements of the rotating body, thrust foil bearings must maintain the formation of a fluid film. To this end, thrust foil bearings include a thin metal plate inclined relative to the rotating body. The thin metal plate is axially flexible and, together with the rotating body, forms a fluid film and a wedge-shaped flow path for increasing internal pressure. Patent Document 1 discloses a thrust foil bearing including a plurality of top foil pieces as the above-mentioned thin metal plates and a plurality of bump foil pieces that elastically support the plurality of top foil pieces.

[0004] Japanese Patent Application Laid-Open No. 2020-037975

[0005] The bump foil piece in Patent Document 1 is composed of a corrugated sheet with a series of pairs of peaks and valleys. The corrugated sheet is formed by molding using a mold. On the other hand, the fluid film formed by a thrust foil bearing is very thin, at most a few micrometers thick. Therefore, high dimensional accuracy is required for the corrugated sheet during molding. Therefore, when forming the corrugated sheet by molding, pairs of peaks and valleys are formed one by one using a mold, thereby minimizing distortion of the corrugated sheet shape. Due to these processes, manufacturing the corrugated sheet takes time, which is a factor in increasing manufacturing costs.

[0006] The present disclosure has been made in consideration of the above-mentioned circumstances, and aims to provide a thrust foil bearing equipped with a back foil that can reduce the number of manufacturing processes while suppressing shape distortion.

[0007] A thrust foil bearing according to one aspect of the present disclosure comprises a base plate perpendicular to a central axis of rotation, a back foil placed on the base plate and including a plurality of back foil pieces arranged in a circumferential direction of the central axis of rotation, and a top foil including a plurality of top foil pieces arranged in the circumferential direction and covering the plurality of back foil pieces, each of the back foil pieces including a band portion extending from the inner side to the outer side of the back foil, and a bump portion extending from a base end serving as a fixed end connected to the band portion to a tip end serving as a free end, and including a curved portion that protrudes elastically deformably toward the top foil between the base end and the tip end.

[0008] The bump portion may be connected to only one of the edge portions on one side and the edge portion on the other side in the width direction of the band portion. The bump portion may be divided into a plurality of bump pieces arranged in the extension direction of the band portion. The back foil may include an annular first connecting portion located radially outward from the plurality of back foil pieces and connected to the band portion of each of the back foil pieces. The back foil may include an annular second connecting portion located radially inward from the plurality of back foil pieces and connected to the band portion of each of the back foil pieces.

[0009] According to the present disclosure, it is possible to provide a thrust foil bearing equipped with a back foil that can reduce the number of manufacturing processes while suppressing distortion of the shape.

[0010] FIG. 1 is a side view of an example of a turbomachine to which a thrust foil bearing according to an embodiment of the present disclosure is applied. FIG. 2 is a side view of the thrust foil bearing according to the embodiment. FIG. 3 is a front view of the thrust foil bearing according to the embodiment. FIG. 4A is a front view of a top foil according to the embodiment. FIG. 4B is a front view of a back foil according to the embodiment. FIG. 4C is a front view of a back foil piece according to the embodiment. FIG. 4D is a side view showing a state in which the top foil piece and the back foil piece are attached to a base plate. FIG. 5A is a diagram for explaining forming of a back foil piece in a comparative example. FIG. 5B is a diagram for explaining forming of a back foil piece according to the embodiment. FIG. 6A is a perspective view of a bump portion according to a modified example of the embodiment. FIG. 6B is a perspective view of a bump portion according to a modified example of the embodiment. FIG. 6C is a perspective view of a bump portion according to a modified example of the embodiment. FIG. 6D is a perspective view of a bump portion according to a modified example of the embodiment. FIG. 6E is a perspective view of a bump portion according to a modified example of the embodiment. FIG. 6F is a front view of a bump portion according to a modified example of the embodiment. Fig. 6G is a front view of a bump portion according to a modified example of the embodiment, and Fig. 7 is a front view of a back foil according to a modified example of the embodiment.

[0011] Hereinafter, several embodiments of the present disclosure will be described. Note that common parts in each drawing are assigned the same reference numerals, and duplicated explanations will be omitted. For convenience of explanation, the axial direction Z, the circumferential direction CD, the rotational direction TD, and the radial direction RD will be defined.

[0012] The axial direction Z is the extension direction of the central rotation axis 8 (see FIG. 1 ). The central rotation axis 8 is, for example, the central axis of the rotating body, the shaft 2 or the thrust collar 4, and is a reference axis for determining the position of each component in the thrust foil bearing 5 according to this embodiment. The circumferential direction CD is a circumferential direction centered on the central rotation axis 8. The rotation direction TD is the rotation direction of the shaft 2 and coincides with one direction of the circumferential direction CD. Furthermore, the radial direction RD is a direction that originates at the central rotation axis 8 and extends on a plane perpendicular to the central rotation axis 8.

[0013] First, an overview of the thrust foil bearing 5 according to this embodiment will be described. Fig. 1 is a side view of an example of a turbomachine 1 to which the thrust foil bearing 5 according to this embodiment is applied. As shown in Fig. 1, the turbomachine 1 includes a shaft 2, an impeller 3, a thrust collar 4, a pair of thrust foil bearings 5, a radial foil bearing 6, and a housing 7 that accommodates these.

[0014] The shaft 2 is rotatably supported by a radial foil bearing 6. The impeller 3 is attached to the end of the shaft 2. The impeller 3 is housed in the housing 7 with a tip clearance formed between the impeller 3 and the housing 7. The thrust collar 4 is a disk having a predetermined thickness in the axial direction Z, and is fixed to the shaft 2. The thrust collar 4 is sandwiched between a pair of thrust foil bearings 5. This limits the range of movement of the thrust collar 4 along the axial direction Z.

[0015] When the thrust collar 4 is stationary, it is placed in a state where it can come into contact with the top foil piece 21. When the thrust collar 4 begins to rotate, it rotates while rubbing intermittently or continuously against the top foil piece 21. At this time, the rotation of the thrust collar 4 causes fluid to flow into the wedge-shaped flow passage formed between the two, increasing the pressure within the flow passage. Then, as the rotational speed of the thrust collar 4 increases and the pressure further increases, the top foil 20 bends toward the back foil 30, and the thrust collar 4 moves away from the top foil 20. As a result, a film of fluid is formed between the thrust collar 4 and the top foil piece 21, and the thrust collar 4 begins to rotate without contacting the top foil piece 21.

[0016] The back foil piece 31 is provided between the top foil piece 21 and the base plate 10, and is configured as an elastic member that supports the top foil piece 21. When the pressure in the flow path fluctuates due to the thrust force of the thrust collar 4, the deflection of the top foil piece 21 changes according to the fluctuating pressure. The back foil piece 31 supports the top foil piece 21 to prevent the top foil piece 21 from deflecting excessively. This maintains an appropriate gap between the top foil piece 21 and the thrust collar 4, and enables the thrust collar 4 to be supported without contact.

[0017] Next, the configuration of the thrust foil bearing 5 will be described. Fig. 2 is a side view of the thrust foil bearing 5 according to this embodiment. Fig. 3 is a front view of the thrust foil bearing 5 according to this embodiment. Fig. 3 shows the top foil 20 with a portion thereof omitted. As shown in these figures, the thrust foil bearing 5 includes a base plate 10, a top foil 20, and a back foil 30.

[0018] The base plate 10 is a flat metal plate that is perpendicular to the central axis of rotation 8 and has a predetermined thickness (for example, several mm). The base plate 10 is fixed to, for example, the housing 7. The outer shape of the base plate 10 is not limited to the circular shape shown in FIG. 3 and may be, for example, rectangular. The base plate 10 has a flat surface 11 that faces the thrust collar 4. An insertion hole 12 is formed in the flat surface 11. The insertion hole 12 is formed centered on the central axis of rotation 8 and passes through the base plate 10. The shaft 2 is inserted into the insertion hole 12.

[0019] Depending on the application of the thrust foil bearing 5, the shaft may not pass through the thrust foil bearing 5. In this case, a thrust collar is fixed to the end of the shaft, but no insertion hole 12 is formed. Furthermore, the position of the rotational axis of the shaft is defined on the base plate 10, and the relative positions of the top foil 20 and the back foil 30 with respect to the base plate 10 are defined based on the position of this rotational axis.

[0020] 4A is a front view of the top foil 20. The top foil 20 is formed from a flexible metal sheet. The top foil 20 includes a plurality of top foil pieces 21 and an annular connecting portion 22, and is placed on the flat surface 11 of the base plate 10 or on the back foil 30 placed on the flat surface 11.

[0021] In this embodiment, the multiple top foil pieces 21 are arranged at equal angular intervals along the circumferential direction CD. For example, as shown in Fig. 4A , the multiple top foil pieces 21 are arranged at 60-degree intervals around the central rotation axis 8. Each top foil piece 21 has a generally fan-shaped shape with an arc-shaped notch at the apex, and covers the back foil piece 31 (at least the bump portion 33 described below) of the back foil 30 (see Fig. 3 ).

[0022] The top foil piece 21 of this embodiment has an edge portion 21a located on the rear side in the rotation direction TD and extending in the radial direction, and an edge portion 21b located on the front side in the rotation direction TD and extending in the radial direction. The edge portion 21a is provided as a fixed end of the top foil piece 21, while the edge portion 21b is provided as a free end of the top foil piece 21. In addition, the top foil piece 21 is inclined at a predetermined inclination angle from the edge portion 21a to the edge portion 21b so as to move away from the base plate 10.

[0023] The top foil 20 includes connecting portions 22 that are provided radially outward of the plurality of top foil pieces 21 and support the plurality of top foil pieces 21. The connecting portions 22 are formed in an annular shape and are connected to the edge portions 21 a of each of the top foil pieces 21. By fixing the connecting portions 22 to the base plate 10, the edge portions 21 a are stably positioned on the flat surface 11.

[0024] Each top foil piece 21 forms a wedge-shaped flow path 9 (see FIG. 2 ) with the thrust collar 4. When the rotating thrust collar 4 approaches the top foil 20, the pressure in the flow path 9 increases. This increase in pressure increases the pressing force of the top foil piece 21 against the bump portion 33 of the back foil piece 31. The bump portion 33 elastically deforms from its initial state due to this increase in pressing force, and as a result, the inclination angle of the top foil piece 21 decreases, and the gap between the thrust collar 4 and the top foil 20 is maintained.

[0025] Fig. 4B is a front view of the back foil 30. Fig. 4C is a front view of the back foil piece 31. Fig. 4D is a side view showing the top foil piece 21 and the back foil piece 31 attached to the base plate 10. Like the top foil 20, the back foil 30 is also formed from a flexible metal sheet. The back foil 30 includes a plurality of back foil pieces 31 arranged at intervals in the circumferential direction CD.

[0026] The multiple back foil pieces 31 are arranged at equal angular intervals along the circumferential direction CD. For example, as shown in FIG. 4B , the multiple back foil pieces 31 are arranged at 60-degree intervals around the central rotation axis 8. Each back foil piece 31 has a generally fan-shaped outer shape with an arc-shaped notch at its apex. As shown in FIG. 4C , the back foil piece 31 includes multiple band portions 32, at least one bump portion 33 connected to each band portion 32, and a connecting portion 34.

[0027] The connecting portion 34 is located radially outward of the plurality of band portions 32 and the plurality of bump portions 33, and connects the plurality of band portions 32. For example, as shown in Fig. 4C, the connecting portion 34 is formed in an arc shape having a predetermined width in the radial direction, and is connected to the end of each band portion 32.

[0028] The multiple band portions 32 are spaced apart in the circumferential direction CD and extend parallel to the flat surface 11 of the base plate 10. Each band portion 32 extends from the inner circumferential side to the outer circumferential side of the back foil 30. For example, as shown in FIG. 4C , the band portions 32 may extend in a direction parallel to one radial direction RD (i.e., at a specific azimuth angle). Alternatively, the band portions 32 may extend in multiple radial directions RD with different azimuth angles.

[0029] Each band portion 32 includes an end portion 32a connected to the connecting portion 34 and an end portion 32b located radially inward from end portion 32a. Each band portion 32 further includes an edge portion 32c on one side in the width direction of the band portion 32 and an edge portion 32d on the other side in the width direction of the band portion 32. The width direction here refers to a direction substantially perpendicular to the extension direction (longitudinal direction) of the band portion 32, such as the circumferential direction CD.

[0030] The bump portion 33 has a width shorter than the entire length of the band portion 32 along the radial direction RD. The bump portion 33 extends from a base end 33a, which serves as a fixed end connected to the band portion 32, to a tip end 33b, which serves as a free end. Furthermore, the bump portion 33 includes an elastically deformable curved portion 35 between the base end 33a and the tip end 33b. That is, the bump portion 33 is cantilevered by the band portion 32 and extends from the base end 33a in a predetermined direction (e.g., the circumferential direction CD) via the curved portion 35 to the tip end 33b.

[0031] As described above, the bump portion 33 is cantilevered by the band portion 32. Therefore, when only one bump portion 33 is provided for one band portion 32, the base end portion 33a of the bump portion 33 is connected to the edge portion 32c or the edge portion 32d of the band portion 32. When two bump portions 33 are provided for one band portion 32, the base end portion 33a of one of the two bump portions 33 is connected to the edge portion 32c of the band portion 32, and the base end portion 33a of the other of the two bump portions 33 is connected to the edge portion 32d of the band portion 32.

[0032] The curved portion 35 extends from the base end 33 a to the tip end 33 b so as to protrude toward the top foil piece 21. That is, the curved portion 35 is curved in an arch shape that protrudes toward the top foil piece 21. The arch shape allows the curved portion 35 to elastically deform, and the bump portion 33 can elastically deform in response to pressure via the top foil piece 21 while elastically supporting the top foil piece 21.

[0033] The height of the curved portions 35 along the axial direction Z is set according to the inclination angle set for the top foil piece 21. Specifically, as shown in Figures 4D and 6B , the curved portions 35 adjacent to each other in the circumferential direction CD are set so that the curved portions 35 located further forward in the rotational direction TD are higher. Note that the heights of the curved portions 35 adjacent to each other in the circumferential direction CD may be the same (see Figure 6B ). In this case, for example, as shown by the dotted line in Figure 4D , a recess 13 is formed in the flat surface 11. The bottom surface 13a of the recess 13 is inclined at the same inclination angle as the inclination angle of the top foil piece 21 after attachment, and the bump portion 33 is provided on the bottom surface 13a.

[0034] The tip 33b of the bump 33 is not connected to other members of the back foil 30, including the band 32, and is located in a position where it can come into contact with the base plate 10. When the bump 33 is pressed toward the base plate 10, the tip 33b slides on the base plate 10 in a direction away from the band 32. In other words, the tip 33b functions as a leg of the bump 33 that prevents excessive bending only in the vicinity of the base end 33a and promotes elastic deformation of the curved portion 35.

[0035] As described above, the back foil 30 is formed by molding a metal sheet using a mold 50. The bump portion 33 and the band portion 32 are formed as a single unit at one time by this molding process.

[0036] Fig. 5A is a diagram illustrating the forming process of the back foil piece 131 in a comparative example. Fig. 5B is a diagram illustrating the forming process of the back foil piece 31 according to the present embodiment. As shown in Fig. 5A, in the comparative example, it is assumed that three bump portions 133 are formed from a metal sheet 140 using a mold 150. For ease of explanation, the portion of the metal sheet 140 where the central bump portion 133 is formed is indicated by 140a, and the portions on both sides of that portion where the bump portions 133 are formed are indicated by 140b.

[0037] When the thin metal plate 140 is sandwiched between the upper mold 151 and the lower mold 152, the upper mold 151 and the lower mold 152 come into contact with the thin metal plate 140 at multiple points. If the friction at these contact points becomes excessively strong, the movement and extension of the thin metal plate 140 is restricted, and internal stress remains, making the shape prone to distortion. For example, as shown in FIG. 5A , when three bump portions 133 are formed at once, two portions 140b, 140b move in directions away from each other, and the portion 140a of the thin metal plate 140 between them is excessively stretched, making it prone to retaining internal stress that is prone to distortion.

[0038] On the other hand, the bump portions 33 according to this embodiment are formed on only one side or on both sides of one band portion 32. That is, the number of bump portions 33 provided on one band portion 32 is at most two.

[0039] Therefore, in a cross section including one band portion 32 and the bump portion 33 formed on one side thereof and perpendicular to the support surface on which the back foil piece 131 is disposed, only a single peak is formed as the bump portion 33 on one side of the band portion 32. Here, the peak is a structure including a bottom portion closest to the support surface and a peak provided between the bottom and the band portion 32. Here, the peak is not limited to a point as in this embodiment, and may have a width. In the peak, the bottom portion is capable of contacting the support surface, while the portion between the bottom and the band portion 32 is not configured to be capable of contacting the support surface.

[0040] In this embodiment, the bottom is a region with a width in cross section, but may also be a point in cross section. In this embodiment, the band portion 32 is also configured to be able to contact the support surface, but may also be configured with a gap between the band portion 32 and the support surface. In this embodiment, the tip portion 33b is included in the bottom. However, "only a single peak" also includes the case where the tip portion 33b is formed in the remaining portion that extends from the bottom toward the opposite side of the band portion 32 without forming a peak (i.e., the case where the tip portion 33b is separated from the support surface).

[0041] 5B , when the thin metal plate 40, which is the base material of the bump portion 33 and the band portion 32, is sandwiched between the upper mold 51 and the lower mold 52, the upper mold 51 and the lower mold 52 come into contact with the thin metal plate 40 at multiple points. As in the comparative example, the friction becomes locally strong at these contact points.

[0042] However, in this embodiment, the number of bumps 33 formed using the mold 50 for one band portion 32 is at most two, and the tip portion 33b of each bump 33 is formed as a free end. Therefore, when the metal sheet 40 is sandwiched between the upper mold 51 and the lower mold 52, the portion 40a of the metal sheet 40 that will become the bump 33 is allowed to slide and stretch to the left or right in FIG. 5 . In other words, this portion 40a avoids constraint due to excessive friction. As a result, the bumps 33 and band portion 32 can be formed into the desired shape without distortion. Furthermore, because residual stress is reduced, distortion of the bumps 33 and band portion 32 after formation can be suppressed.

[0043] In this embodiment, a single back foil piece 31 is provided with a plurality of band portions 32. That is, a single back foil piece 31 is provided with a plurality of bump portions 33. However, as shown in FIG. 5B , one end of each bump portion 33 is formed as a free end, which can suppress distortion. That is, a plurality of bump portions 33 can be formed in a single molding process, and the number of manufacturing steps can be reduced compared to when a corrugated plate having successive pairs of peaks and valleys is formed by repeatedly positioning and shaping the metal sheet 40.

[0044] Next, a modified example of this embodiment will be described. Figures 6A to 6G are diagrams illustrating a bump portion 33 according to a modified example of this embodiment. Figures 6A to 6E are perspective views of the bump portion 33 according to the modified example. Figures 6F and 6G are front views of the bump portion 33 according to the modified example. As shown in Figures 6A and 6B, the heights of the multiple bump portions 33 may be the same or different from each other. This is as described above.

[0045] Furthermore, the bump portions 33 may be connected to only one of the edge portions 32c on one side and the edge portion 32d on the other side in the width direction of the band portion 32. For example, as shown in FIG. 6C , the plurality of bump portions 33 may extend in a predetermined direction (e.g., the circumferential direction CD) only from the edge portion 32c of the band portion 32 corresponding to each bump portion 33. Alternatively, as shown in FIG. 6D , the plurality of bump portions 33 may extend in a predetermined direction (e.g., the circumferential direction CD) only from the edge portion 32d of the band portion 32 corresponding to each bump portion 33. By unifying the relative positions of the bump portions 33 with respect to each band portion 32, the distribution of the positions of the bump portions 33 can be made uniform, and the positional deviation of the contact points with the top foil piece 21 can be reduced.

[0046] Furthermore, the bump portion 33 may be divided by at least one slit 36 ​​into multiple bump pieces 37 aligned in the extension direction of the band portion 32. That is, as shown in FIG. 6E , the slit 36 ​​extends in a predetermined direction (e.g., the circumferential direction CD) within the bump portion 33. Therefore, the bump pieces 37 are aligned in the extension direction of the band portion 32. The slit 36 ​​can be applied to any of the above-mentioned configurations. As an example, FIG. 6F shows an example in which a slit 36 ​​is formed in the back foil piece 31 shown in FIG. 4C . Also, FIG. 6G shows an example in which the back foil piece 31 shown in FIG. 4C is modified from the configuration shown in FIG. 6C and further includes a slit 36. By dividing the bump portion 33, if a pressure distribution occurs in the wedge-shaped flow path, each bump portion 33 can move independently, ensuring tracking ability.

[0047] The dimensions of the multiple bump portions 33 (bump pieces 37) may be different from one another. The dimensions referred to here are, for example, the height, width, length from the base end 33a to the tip end 33b, the radius of curvature of the curved portion 35, and dimensions that define the outer shape as viewed from the axial direction Z. By individually changing the dimensions of the bump portions 33 (bump pieces 37), the positional distribution of the spring constant in the back foil piece 31 can be manipulated.

[0048] FIG. 7 is a front view of a back foil 30 according to a modified example of this embodiment. As shown in FIG. 7 , the back foil 30 may include a connecting portion (first connecting portion) 38. The connecting portion 38 is located radially outward of the multiple back foil pieces 31 and is formed in a ring shape to surround the multiple back foil pieces 31. The connecting portion 38 connects to the band portion 32 of each back foil piece 31 and supports them. The relative positions of the back foil pieces 31 are determined by the connection with the connecting portion 38. This facilitates positioning of the back foil pieces 31 relative to the base plate 10. Furthermore, through holes 38 a may be formed at multiple locations on the connecting portion 38. In this case, similar through holes (not shown) may also be formed in the top foil 20, and the back foil 30 and the top foil 20 may be fixed to the base plate 10 by screws or the like using these through holes 38 a. This allows the multiple back foil pieces 31 to be fixed together.

[0049] The back foil 30 may further include connecting portions (second connecting portions) 39 indicated by dotted lines in Fig. 7. The connecting portions 39 are located radially inward of the multiple back foil pieces 31. When insertion holes 12 are formed in the base plate 10, the connecting portions 39 are located radially inward of the multiple back foil pieces 31 and radially outward of the insertion holes 12. The connecting portions 39 connect to at least one band portion 32 of each back foil piece 31. The connecting portions 39 can suppress undesirable deformation of the inner peripheral portion of the top foil 20 (for example, warping approaching the thrust collar).

[0050] The present disclosure is not limited to the above-described embodiments, but is defined by the claims, and includes all modifications within the meaning and scope equivalent to the claims.

Claims

1. A thrust foil bearing comprising: a base plate perpendicular to a central axis of rotation; a back foil placed on the base plate and including a plurality of back foil pieces arranged in a circumferential direction of the central axis of rotation; and a top foil including a plurality of top foil pieces arranged in the circumferential direction and covering the plurality of back foil pieces, wherein each of the back foil pieces includes: a band portion extending from the inner circumferential side of the back foil toward the outer circumferential side; and a bump portion extending from a base end serving as a fixed end connected to the band portion to a tip end serving as a free end, and including a curved portion protruding elastically deformably toward the top foil between the base end and the tip end.

2. A thrust foil bearing according to claim 1, wherein the bump portion is connected to only one of the edge portions on one side and the edge portion on the other side in the width direction of the band portion.

3. A thrust foil bearing according to claim 1 or 2, wherein the bump portion is divided into a plurality of bump pieces aligned in the extension direction of the band portion.

4. A thrust foil bearing according to claim 1, wherein the back foil includes an annular first connecting portion located radially outward of the plurality of back foil pieces and connected to the band portion of each of the back foil pieces.

5. A thrust foil bearing according to claim 4, wherein the back foil includes a second annular connecting portion located radially inward of the plurality of back foil pieces and connected to the band portion of each of the back foil pieces.

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