Reduced bearing temperature through sleeve improvements

Abstract

A novel sleeve as used in rolling mill rolls is disclosed in which a length l feature is introduced to the tapered end of the inner portion of the inner surface of the sleeve, the feature introduced allowing the sleeve to deflect as the load increases with a maximum radial deflection of δ. The feature introduced accommodates the temperature rise inside the sleeve by allowing the sleeve to deflect as the load increases.

Description

[Technical Field]

[0001] This invention generally relates to the field of rolling mill backup bearings, particularly oil film backup bearings. More specifically, the invention relates to improving the temperature profile within a bearing during operation. [Background technology]

[0002] Figures 1(A) and 1(B) show a known oil film bearing assembly as described in Patent Document 1. Industry standards include a cylindrical bushing (sometimes known as a bearing) and a cylindrical outer diameter / tapered inner diameter sleeve (sometimes known as a journal). The bushing has a cylindrical outer diameter that fits tightly inside the chock (bearing housing), and the sleeve has an inner taper angle that precisely matches the roll.

[0003] Patent Document 1 describes a typical rolling mill oil film bearing as follows: The roll 10 has a neck section 12. The neck section 12 may be conical as shown in Figure 1(A), or cylindrical in some alternative configurations. A sleeve 14 is received into and fixed to the neck section 12. The outside of the sleeve defines the journal face 16 of the roll neck. A bushing 18 has an internal bearing surface 20 that surrounds and rotatably supports the journal face 16. The bushing is housed in and fixed within a chock 22. The chock is closed at its outer end by an end plate 24 and a cover 26. A seal assembly 28 is provided between the roll and the inner end of the chock 22.

[0004] During the normal operation of the mill, when the rolls are rotating at a suitable speed for full hydrodynamic motion, a continuous flow of oil is supplied through one of the following: passage 29 in the chock, supply opening 30 in the bushing, and a set of ribores 32 in the bearing surface 20. From here, the oil enters the space between the bearing surface 20 and the rotating journal surface 16, forming the bearing load zone "Z" and the hydrodynamic length "L". HThe length of the bushing, which interacts with the sleeve and supports the oil film, forms a hydrodynamically maintained, somewhat wedge-shaped oil film 34. In Figure 1(A), a load is applied via the roll at "SF". The load is resisted by a force "F" applied to the chock. The load zone is located on the same side as the resisting force "F". The pressure profile in the load zone is schematically shown in Figure 1(A) at "P".

[0005] Conventional hydrostatic means are used to form the necessary oil film between the journal surface and the bearing surface when the roll is not rotating or is rotating at a speed slower than the speed required to form and maintain the hydrodynamic oil film 34.

[0006] Oil is continuously discharged from between the journal surface 16 and the bearing surface 20 at both the inner and outer ends of the load zone. Oil discharged from the inner end enters an inner sump 36 surrounded by the seal assembly 28 and the adjacent surfaces of the chock, bushing, and roll. Oil discharged from the outer end enters an outer sump 38 surrounded by the end plate 24 and the chock 22. The sumps 36 and 38 are interconnected by one or more passages 40 perforated through the chock, and the outer sump 38 is connected to a conventional lubrication system (not shown) that filters, cools, and recirculates the oil to the bearing for reintroduction between the bearing surface 16 and the journal surface 20.

[0007] A conventional sleeve used on the rolls of a rolling mill is shown by reference numeral 300 in Figure 3(A). The sleeve has an inner end 301 and an outer end 302, and the sleeve has (a) a hydrodynamic length L H A sleeve length L having a portion of the sleeve length that generates an oil film as shown. S (b) It comprises an outer surface 303 having a cylindrical shape with diameter OD, and an inner surface 304 having a cone-like shape with an inner diameter ID and a standard taper angle a at the inner end. In some alternative configurations, the inner surface 304 may also alternatively have a cylindrical shape. [Prior art documents]

Patent Document

[0008]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0009] Embodiments of the present invention are improvements over prior art systems and methods.

Means for Solving the Problems

[0010] In one embodiment, in FIG. 3(B) Option 1, the present invention provides a sleeve for use in the rolls of a rolling mill, the sleeve having an inner end and an outer end, the sleeve having (a) an outer surface shaped like a cylinder having a sleeve length L S , a hydrodynamic length L H , and an outer diameter OD, and (b) an inner surface having an inner diameter ID and a taper angle a at the inner end, the inner surface comprising (1) a first portion of length (L S -l), the conical first portion having a first inclined portion, the first portion, and (2) a second portion of length l, the second portion comprising (i) an undercut portion having an undercut radius r, the undercut portion being located adjacent to the end of the first portion proximate the inner end, the undercut portion, and (ii) a second inclined portion located adjacent to the undercut portion, the second inclined portion allowing the sleeve to flex as the load increases with a maximum radial deflection of δ. In one embodiment, δ is defined as (bearing load rating {F (metric ton)} / hydrodynamic length {L H (mm)})*a, where a is selected to be in the range of 0.02 ≦ a ≦ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is defined as b*hydrodynamic length {L H} and b is selected to be within the range of 20% ≦ b ≦ 35%, and b is preferably 25%. In the same embodiment, the length (L S-l) > length l. In the same embodiment, the undercut radius r is defined as c * length l, where c is chosen such that 2% ≤ c ≤ 10%, and c is preferably 5%.

[0011] In another embodiment, Option 2 shown in Figure 3(B), the present invention provides a sleeve for use in a rolling mill roll, the sleeve having an inner end and an outer end, and the sleeve having (a) sleeve length L S , hydrodynamic length L H (b) an outer surface having a cylindrical shape with an outer diameter OD, and an inner surface having an inner diameter ID and a taper angle a at the inner end, wherein the inner surface has (1) a length (L S -l) comprises a first part, the first part of which is conical and has a first inclined portion, and (2) a second part of length l, the second part including an undercut radius r, the total length l of the second part being undercut by a certain amount δ. In one embodiment, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L H (mm))*a is defined as, where a is chosen so as to be in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is b * hydrodynamic length {L H Defined as}, b is chosen such that it is in the range of 20% ≤ b ≤ 35%, and b is preferably 25%. In the same embodiment, length (L S -l) > length l. In the same embodiment, the undercut radius r is defined as c * length l, where c is chosen such that 2% ≤ c ≤ 10%, and c is preferably 5%.

[0012] In yet another embodiment, Option 1 shown in Figure 3(C), the present invention provides a sleeve for use in a rolling mill roll, the sleeve having an inner end and an outer end, and the sleeve having (a) sleeve length L S , hydrodynamic length L H (b) an outer surface having a cylindrical shape with an outer diameter OD, and an inner surface having an inner diameter ID and a taper angle a at the inner end, wherein the inner surface has (1) a length (LS (1) a first part of (1) a cone-shaped first part having a first inclined portion, and (2) a second part of length l, the second part including a second inclined portion located adjacent to the first inclined portion, the second inclined portion allowing the sleeve to flex as the load increases with a maximum radial deflection of δ. In one embodiment, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L H (mm))*a is defined as, where a is chosen so as to be in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is b * hydrodynamic length {L H Defined as}, b is chosen such that it is in the range of 20% ≤ b ≤ 35%, and b is preferably 25%. In the same embodiment, length (L S -l) > length l.

[0013] In another embodiment, Option 2 shown in Figure 3(C), the present invention provides a sleeve for use in a rolling mill roll, the sleeve having an inner end and an outer end, and the sleeve having (a) sleeve length L S , hydrodynamic length L H (b) an outer surface having a cylindrical shape with an outer diameter OD, and an inner surface having an inner diameter ID and a taper angle a at the inner end, wherein the inner surface has (1) a length (L S -l) comprises a first part, the first part of which is conical and has a first inclined portion, and (2) a second part of which is length l, the total length l of the second part is undercut by a certain amount δ. In one embodiment, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L H (mm))*a is defined as, where a is chosen so as to be in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is b * hydrodynamic length {L H Defined as}, b is chosen such that it is in the range of 20% ≤ b ≤ 35%, and b is preferably 25%. In the same embodiment, length (L S -l) > length l.

[0014] In yet another embodiment, Option 1 shown in Figure 3(B), the present invention provides a method for reducing the temperature rise inside a sleeve, the sleeve being used in a rolling mill roll, the sleeve having an inner end and an outer end, and the method is (a) sleeve length L S , outer diameter OD, and hydrodynamic length L H (b) providing an outer surface in the shape of a cylinder having (1) length (L S -l) a first part comprising (1) a cone-shaped first part having a first inclined portion, and (2) a second part of length l, the second part comprising (i) an undercut portion having an undercut radius r, the undercut portion being located adjacent to the end of the first part that is close to the inner end, and (ii) a second inclined portion located adjacent to the undercut portion, the second inclined portion allowing the sleeve to deflect as the load increases with a maximum radial deflection of δ. In one embodiment, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L H (mm))*a is defined as, where a is chosen so as to be in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is b * hydrodynamic length {L H Defined as}, b is chosen such that it is in the range of 20% ≤ b ≤ 35%, and b is preferably 25%. In the same embodiment, length (L S -l) > length l. In the same embodiment, the undercut radius r is defined as c * length l, where c is chosen such that 2% ≤ c ≤ 10%, and c is preferably 5%.

[0015] In another embodiment, Option 2 shown in Figure 3(B), the present invention provides a method for reducing the temperature rise inside a sleeve, the sleeve being used in a rolling mill roll, the sleeve having an inner end and an outer end, and the method is (a) sleeve length L S , hydrodynamic length L H(b) providing an outer surface in the shape of a cylinder having an outer diameter OD, and (b) providing an inner surface having an inner diameter ID and a taper angle a at the inner end, wherein the inner surface has (1) a length (L S -l) comprises a first part, the first part of which is conical and has a first inclined portion, and (2) a second part of length l, the second part including an undercut radius r, the total length l of the second part being undercut by a certain amount δ. In one embodiment, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L H (mm))*a is defined as, where a is chosen so as to be in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is b * hydrodynamic length {L H Defined as}, b is chosen such that it is in the range of 20% ≤ b ≤ 35%, and b is preferably 25%. In the same embodiment, length (L S -l) > length l. In the same embodiment, the undercut radius r is defined as c * length l, where c is chosen such that 2% ≤ c ≤ 10%, and c is preferably 5%.

[0016] In yet another embodiment, Figure 3(C) Option 1, the present invention provides a method for reducing the temperature rise inside a sleeve, the sleeve being used in a rolling mill roll, the sleeve having an inner end and an outer end, and the method is (a) sleeve length L S , hydrodynamic length L H (b) an outer surface having a cylindrical shape with an outer diameter OD, and an inner surface having an inner diameter ID and a taper angle a at the inner end, wherein the inner surface has (1) a length (L S (1) a first part of (1) a cone-shaped first part having a first inclined portion, and (2) a second part of length l, the second part including a second inclined portion located adjacent to the first inclined portion, the second inclined portion allowing the sleeve to flex as the load increases with a maximum radial deflection of δ. In one embodiment, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L H(mm))*a is defined as, where a is chosen so as to be in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is b * hydrodynamic length {L H Defined as}, b is chosen such that it is in the range of 20% ≤ b ≤ 35%, and b is preferably 25%. In the same embodiment, length (L S -l) > length l.

[0017] In another embodiment, Option 2 shown in Figure 3(C), the present invention provides a method for reducing the temperature rise inside a sleeve, the sleeve being used in a rolling mill roll, the sleeve having an inner end and an outer end, and the method is (a) sleeve length L S , hydrodynamic length L H (b) providing an outer surface in the shape of a cylinder having an outer diameter OD, and (b) providing an inner surface having an inner diameter ID and a taper angle a at the inner end, wherein the inner surface has (1) a length (L S -l) comprises a first part, the first part of which is conical and has a first inclined portion, and (2) a second part of which is length l, the total length l of the second part is undercut by a certain amount δ. In one embodiment, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L H (mm))*a is defined as, where a is chosen so as to be in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is b * hydrodynamic length {L H Defined as}, b is chosen such that it is in the range of 20% ≤ b ≤ 35%, and b is preferably 25%. In the same embodiment, length (L S -l) > length l.

[0018] This disclosure is described in detail with reference to the following figures, following one or more different examples. The figures are provided for illustrative purposes only and merely illustrate examples of this disclosure. These figures are provided to facilitate the reader's understanding of this disclosure and should not be considered to limit the width, scope, or applicability of this disclosure. Note that these figures are not necessarily made to scale for clarity and ease of explanation. [Brief explanation of the drawing]

[0019] [Figure 1(A)] This figure shows a known hydrodynamic bearing assembly. [Figure 1(B)] This is another diagram showing a known hydrodynamic bearing assembly. [Figure 2] Figures (A) to (C) show the temperature distribution on the sleeve and bushing for the given load / speed combinations. [Figure 3(A)] This figure shows one embodiment of the present invention, illustrating a standard sleeve and additional features added to the sleeve. [Figure 3(B)] This figure shows a standard sleeve and another embodiment of the present invention that illustrates additional features added to the sleeve. [Figure 3(C)] This figure shows a standard sleeve and yet another embodiment of the present invention, illustrating features added to the sleeve. [Modes for carrying out the invention]

[0020] While the present invention is illustrated and described in preferred embodiments, it can be manufactured in many different configurations. This disclosure should be considered illustrative of the principles of the present invention and the relevant functional specifications for its construction, and is not intended to limit the present invention to the illustrated embodiments. Preferred embodiments of the present invention are shown in the drawings and described in detail herein. Those skilled in the art will likely envision many other possible variations within the scope of the present invention.

[0021] It should be noted that in this specification, any reference to “an embodiment” or “an embodiment” means that the features referred to are included in at least one embodiment of the present invention. Furthermore, separate references to “an embodiment” in this specification do not necessarily refer to the same embodiment. However, such embodiments are not mutually exclusive, except as is readily apparent to those skilled in the art, unless otherwise stated. Accordingly, the present invention may include any various combinations and / or integrations of the embodiments described herein.

[0022] Testing bearings under various load and speed combinations shows that the oil film thickness on the inside of the bearing (the side closest to the roll surface) is thinner than that on the outer end. The difference is typically between 0.05 mm and 0.10 mm. Because the oil film is thinner at the inner end, the shear rate of the oil film is higher, and the bearing and sleeve temperatures also rise.

[0023] Figures 2(A) to 2(C) show graphs of the temperature distribution of the sleeve and bushing at the given load / speed combinations (i.e., 50 RPM & 730 tons, 220 RPM & 650 tons, and 290 RPM & 510 tons, respectively). This data was obtained by testing with a full-size 30-inch-75KL Morgoil hydrodynamic bearing. Thermocouples were installed on the bushing and sleeve. The sleeve has five thermocouples mounted axially, and as the sleeve rotates, the signals were output through the slip ring. The fixed bushing has four axial rows of thermocouples, two rows at + / -10 degrees from bottom dead center and two rows at + / -45 degrees. In the upper diagram of Figure 2(C), the bushing thermocouple positions are indicated by white stars, and the sleeve thermocouple positions are indicated by black circles.

[0024] Figures 2(A) to 2(C) show that the temperature inside the bushing and sleeve is higher for all load / speed combinations, especially in the load zone where the film is at its minimum thickness (+ / -10 degrees for the bushing).

[0025] Therefore, it is necessary to dynamically adjust the film thickness at the inner end of the bearing, which allows the temperature in that area to decrease as the load increases. This is important because it can reduce a major class of bearing failure called inboard edge wipe.

[0026] Conventional technology has many examples of attempting to modify the shape of a bearing (a stationary member) to conform to the deformed shape of a shaft or housing. The present invention differs in that the shape of the sleeve and bushing bearing surfaces does not change under no-load conditions, and in both cases, they are cylindrical. Instead, this new concept involves adding a manufactured feature to the sleeve to allow them to flex as the load increases, but also to control the overall deflection. For the purpose of explanation, the desired maximum radial deflection is given by (bearing load rating {F (metric tons)} / hydrodynamic length {L}. H It is calculated as (mm))*a, where a is chosen such that 0.02 ≤ a ≤ 0.04, and a is preferably 0.025.

[0027] The present invention provides a feature of length l on the tapered inner diameter (ID) of the inner end of a sleeve (e.g., a sleeve used in a rolling mill). It has a "hinge" mechanism that allows the inner end to flex inward, and its overall flex is (bearing load rating {F (metric tons)} / hydrodynamic length {L}. H The offset on the end is set by the offset calculated as (mm))*a, where a is selected so that it is in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025.

[0028] Figure 3(B) shows an embodiment of the present invention. In one embodiment, Figure 3(B) Option 1, the present invention discloses a sleeve 300 used on a roll of a rolling mill, the sleeve having an inner end 301 and an outer end 302, and the sleeve has (a) a sleeve length L S , diameter OD, hydrodynamic length L H(b) an outer surface 303 formed like a cylinder having an outer diameter OD, and an inner surface 304 having an inner diameter ID and a taper angle a at the inner end, wherein the inner surface 304 has (1) a length (L S -l) a first part, the first part being conical in shape having a first inclined portion 304 (which is part of the original taper, which is part of the inner surface 304); and (2) a second part of length l, the second part comprising (i) an undercut portion 312 located adjacent to the end of the first part near the inner end, the undercut radius r is preferably defined as 5% of l (310, the length of the second part), but can optionally be in the range of 2% to 10%; and (ii) a second inclined portion 308 located adjacent to the undercut portion, the second inclined portion 308 allowing the sleeve to flex when the load increases by a maximum radial deflection δ, where l is preferably 25%*L H It is defined as (hydrodynamic length), but may be in the range of 20% to 35% as needed. Also, the value of δ is preferably (bearing load rating {F (metric tons)} / hydrodynamic length {L} H It can be calculated as (mm))*a, where a is chosen so that it is in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. Alternatively, in Option 2 of Figure 3(B), instead of a taper from the hinge 312 to the inner end, the total length l is undercut by a certain amount δ calculated in the same way as in Option 1.

[0029] In another embodiment, Figure 3(C) Option 1, the present invention discloses a sleeve 300 used in a rolling mill roll, the sleeve having an inner end 301 and an outer end 302, and the sleeve having (a) length L S (b) an outer surface 303 having a cylindrical shape with an outer diameter OD, and an inner surface 304 having an inner diameter ID and a taper angle a at the inner end, wherein the inner surface has (1) a length (L S(1) a first part, the first part of which is cone-shaped and has a first inclined portion 304; and (2) a second part of length l, the second part including a second inclined portion 308 located adjacent to the first inclined portion 304, wherein the second inclined portion allows the sleeve to flex as the load increases with a maximum radial deflection of δ. Alternatively, in option 2 of Figure 3(C), instead of the taper of the second inclined portion 308, the total length l is undercut by a certain amount δ calculated in the same way as in option 1 above.

[0030] The bearing surface itself is cylindrical and deflects under load. This deflection can be controlled by manipulating the stiffness of the deflection characteristics. The length l is the hydrodynamic bearing length L. H It is a function of .

[0031] In one embodiment, as shown in Figure 3(B) Option 1, the present invention provides a sleeve for use in a rolling mill roll, the sleeve having an inner end and an outer end, and the sleeve having (a) sleeve length L S , hydrodynamic length L H (b) an outer surface having a cylindrical shape with an outer diameter OD, and an inner surface having an inner diameter ID and a taper angle a at the inner end, wherein the inner surface has (1) a length (L S -l) a first part comprising (1) a cone-shaped first part having a first inclined portion, and (2) a second part of length l, the second part comprising (i) an undercut portion having an undercut radius r, the undercut portion being located adjacent to the end of the first part that is close to the inner end, and (ii) a second inclined portion located adjacent to the undercut portion, the second inclined portion allowing the sleeve to deflect as the load increases with a maximum radial deflection of δ. In one embodiment, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L H (mm))*a is defined as, where a is chosen so as to be in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is b * hydrodynamic length {L HDefined as}, b is chosen such that it is in the range of 20% ≤ b ≤ 35%, and b is preferably 25%. In the same embodiment, length (L S -l) > length l. In the same embodiment, the undercut radius r is defined as c * length l, where c is chosen such that 2% ≤ c ≤ 10%, and c is preferably 5%.

[0032] In another embodiment, Option 2 in Figure 3B, the present invention provides a sleeve for use in a rolling mill roll, the sleeve having an inner end and an outer end, and the sleeve having (a) sleeve length L S , hydrodynamic length L H (b) an outer surface having a cylindrical shape with an outer diameter OD, and an inner surface having an inner diameter ID and a taper angle a at the inner end, wherein the inner surface has (1) a length (L S -l) comprises a first part, the first part of which is conical and has a first inclined portion, and (2) a second part of length l, the second part including an undercut radius r, the total length l of the second part being undercut by a certain amount δ. In one embodiment, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L H (mm))*a is defined as, where a is chosen so as to be in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is b * hydrodynamic length {L H Defined as}, b is chosen such that it is in the range of 20% ≤ b ≤ 35%, and b is preferably 25%. In the same embodiment, length (L S -l) > length l. In the same embodiment, the undercut radius r is defined as c * length l, where c is chosen such that 2% ≤ c ≤ 10%, and c is preferably 5%.

[0033] In yet another embodiment, Option 1 shown in Figure 3(C), the present invention provides a sleeve for use in a rolling mill roll, the sleeve having an inner end and an outer end, and the sleeve having (a) sleeve length L S , hydrodynamic length L H(b) an outer surface having a cylindrical shape with an outer diameter OD, and an inner surface having an inner diameter ID and a taper angle a at the inner end, wherein the inner surface has (1) a length (L S (1) a first part of (1) a cone-shaped first part having a first inclined portion, and (2) a second part of length l, the second part including a second inclined portion located adjacent to the first inclined portion, the second inclined portion allowing the sleeve to flex as the load increases with a maximum radial deflection of δ. In one embodiment, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L H (mm))*a is defined as, where a is chosen so as to be in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is b * hydrodynamic length {L H Defined as}, b is chosen such that it is in the range of 20% ≤ b ≤ 35%, and b is preferably 25%. In the same embodiment, length (L S -l) > length l.

[0034] In another embodiment, Option 2 shown in Figure 3(C), the present invention provides a sleeve for use in a rolling mill roll, the sleeve having an inner end and an outer end, and the sleeve having (a) sleeve length L S , hydrodynamic length L H (b) an outer surface having a cylindrical shape with an outer diameter OD, and an inner surface having an inner diameter ID and a taper angle a at the inner end, wherein the inner surface has (1) a length (L S -l) comprises a first part, the first part of which is conical and has a first inclined portion, and (2) a second part of which is length l, the total length l of the second part is undercut by a certain amount δ. In one embodiment, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L H (mm))*a is defined as, where a is chosen so as to be in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is b * hydrodynamic length {L H} is defined such that b is selected to be within the range of 20% ≦ b ≦ 35%, and b is preferably 25%. In the same embodiment, the length (L S -l) > the length l.

[0035] In yet another embodiment, in FIG. 3(B) Option 1, the present invention provides a method for reducing the temperature rise inside the sleeve, the sleeve is used for the roll of a rolling mill, the sleeve has an inner end and an outer end, and the method comprises: (a) the sleeve length L S , outer diameter OD, and hydrodynamic length L H providing an outer surface in the shape of a cylinder having; (b) providing an inner surface, the inner surface comprising: (1) a first portion of length (L S -l), the first conical portion having a first inclined portion, the first portion; and (2) a second portion of length l, the second portion comprising: (i) an undercut portion having an undercut radius r, the undercut portion being located adjacent to the end of the first portion close to the inner end, the undercut portion; and (ii) a second inclined portion located adjacent to the undercut portion, the second inclined portion allowing the sleeve to deflect as the load increases with a maximum radial deflection of δ. In one embodiment, δ is defined as (bearing load rating {F (metric ton)} / hydrodynamic length {L H (mm)})*a, where a is selected to be within the range of 0.02 ≦ a ≦ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is defined as b*hydrodynamic length {L H}, b is selected to be within the range of 20% ≦ b ≦ 35%, and b is preferably 25%. In the same embodiment, the length (L S -l) > the length l. In the same embodiment, the undercut radius r is defined as c*length l, where c is selected to be within the range of 2% ≦ c ≦ 10%, and c is preferably 5%.

[0036] In another embodiment, Option 2 of FIG. 3(B), the present invention provides a method for reducing the temperature rise inside the sleeve, the sleeve being used in the roll of a rolling mill, the sleeve having an inner end and an outer end, the method comprising: (a) the sleeve length L S , a hydrodynamic length L H , and providing an outer surface shaped like a cylinder having an outer diameter OD; and (b) providing an inner surface having an inner diameter ID and a taper angle a at the inner end, the inner surface comprising: (1) a first portion of length (L S -l), the conical first portion having a first inclined portion, the first portion; and (2) a second portion of length l, the second portion including an undercut radius r, the total length l of the second portion being undercut by a certain amount δ, the second portion. In one embodiment, δ is defined as (bearing load rating {F (metric ton)} / hydrodynamic length {L H (mm)})*a, where a is selected to be in the range of 0.02 ≦ a ≦ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is defined as b*hydrodynamic length {L H} and b is selected to be in the range of 20% ≦ b ≦ 35%, and b is preferably 25%. In the same embodiment, the length (L S -l) > the length l. In the same embodiment, the undercut radius r is defined as c*length l, where c is selected to be in the range of 2% ≦ c ≦ 10%, and c is preferably 5%.

[0037] In yet another embodiment, Option 1 of FIG. 3(C), the present invention provides a method for reducing the temperature rise inside the sleeve, the sleeve being used in the roll of a rolling mill, the sleeve having an inner end and an outer end, the method comprising: (a) the sleeve length L S , a hydrodynamic length L H , and an outer surface shaped like a cylinder having an outer diameter OD; and (b) an inner surface having an inner diameter ID and a taper angle a at the inner end, the inner surface comprising: (1) a length (L S(1) a first part of (1) a cone-shaped first part having a first inclined portion, and (2) a second part of length l, the second part including a second inclined portion located adjacent to the first inclined portion, the second inclined portion allowing the sleeve to flex as the load increases with a maximum radial deflection of δ. In one embodiment, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L H (mm))*a is defined as, where a is chosen so as to be in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is b * hydrodynamic length {L H Defined as}, b is chosen such that it is in the range of 20% ≤ b ≤ 35%, and b is preferably 25%. In the same embodiment, length (L S -l) > length l.

[0038] In another embodiment, Option 2 shown in Figure 3(C), the present invention provides a method for reducing the temperature rise inside a sleeve, the sleeve being used in a rolling mill roll, the sleeve having an inner end and an outer end, and the method is (a) sleeve length L S , hydrodynamic length L H (b) providing an outer surface in the shape of a cylinder having an outer diameter OD, and (b) providing an inner surface having an inner diameter ID and a taper angle a at the inner end, wherein the inner surface has (1) a length (L S -l) comprises a first part, the first part of which is conical and has a first inclined portion, and (2) a second part of which is length l, the total length l of the second part is undercut by a certain amount δ. In one embodiment, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L H (mm))*a is defined as, where a is chosen so as to be in the range of 0.02 ≤ a ≤ 0.04, and a is preferably 0.025. In the same embodiment, the value of l is b * hydrodynamic length {L H Defined as}, b is chosen such that it is in the range of 20% ≤ b ≤ 35%, and b is preferably 25%. In the same embodiment, length (L S-l) > length l.

[0039] conclusion Systems and methods for effectively reducing bearing temperature through sleeve improvements are shown in the embodiments described above. While various preferred embodiments have been shown and described, it will be understood that such disclosures are not intended to limit the invention, but rather to cover all modifications that fall within the spirit and scope of the invention, as defined in the appended claims. [Additional note 1] A sleeve for use in the roll of a rolling mill, wherein the sleeve has an inner end and an outer end, The aforementioned sleeve is (a) Sleeve length L S , hydrodynamic length L H , and the outer surface of a cylindrical shape having an outer diameter OD, (b) The inner surface having the inner diameter ID and taper angle a of the inner end Equipped with, The aforementioned inner surface is (1) Length (L S -l) the first part, wherein the first part which is cone-shaped has a first inclined portion, (2) The second part of length l and Equipped with, The second part above is, (i) an undercut portion having an undercut radius r, wherein the undercut portion is located adjacent to the end of the first portion that is close to the inner end, (ii) A second inclined portion located adjacent to the undercut portion, wherein the second inclined portion is tapered by a quantity δ. Equipped with, The second inclined portion of the sleeve allows the sleeve to flex as the load increases with a maximum radial deflection corresponding to the amount δ. [Additional note 2] δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L} H The sleeve as defined in Appendix 1, where (mm))*a, and a is selected such that a is in the range of 0.02 ≤ a ≤ 0.04. [Additional note 3] A sleeve as described in Appendix 2, where a is 0.025. [Additional note 4] The value of l is b * hydrodynamic length {L} H The sleeve as defined in Appendix 2, where b is chosen such that 20% ≤ b ≤ 35%. [Additional note 5] The sleeve described in Appendix 4, where b is 25%. [Additional note 6] The sleeve as described in Appendix 1, wherein the undercut radius r is defined as c * length l, and c is selected such that 2% ≤ c ≤ 10%. [Additional note 7] The sleeve described in Appendix 6, where c is 5%. [Additional note 8] Length (L S -l)>length l, as described in Appendix 1. [Additional note 9] The sleeve according to Appendix 1, wherein a bushing is positioned around the outer surface of the sleeve, and a gap exists between the bushing and the outer surface of the sleeve, the gap being configured to maintain a hydrodynamically maintained oil film. [Additional Note 10] The sleeve described in Appendix 9, in which the bushing is fixed inside the chock. [Additional Note 11] The sleeve according to Appendix 10, wherein the end plate and cover are provided at the outer end to seal the bushing and the sleeve. [Additional Note 12] A sleeve for use in the roll of a rolling mill, wherein the sleeve has an inner end and an outer end, The aforementioned sleeve is (a) Sleeve length L S , hydrodynamic length L H , and an outer surface having a cylindrical shape with an outer diameter OD, (b) The inner surface having the inner diameter ID and taper angle a of the inner end Equipped with, The aforementioned inner surface is (1) Length (L S -l) the first part, wherein the first part which is cone-shaped has a first inclined portion, (2) A second portion of length l, the second portion including an undercut radius r, the second portion being adjacent to the end of the first portion that is close to the inner end, and the entire length l of the second portion being undercut by a certain amount δ. A sleeve equipped with [a specific feature / feature]. [Additional Note 13] δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L} H The sleeve as defined in Appendix 12, where a is defined as (mm)})*a, and a is selected such that a is in the range of 0.02 ≤ a ≤ 0.04. [Additional Note 14] A sleeve as described in Appendix 13, where a is 0.025. [Additional Note 15] The value of l is b * hydrodynamic length {L} H The sleeve as defined in Appendix 13, where b is chosen such that 20% ≤ b ≤ 35%. [Additional Note 16] The sleeve described in Appendix 15, where b is 25%. [Additional Note 17] The sleeve according to Appendix 12, wherein the undercut radius r is defined as c * length l, and c is selected such that 2% ≤ c ≤ 10%. [Additional Note 18] The sleeve described in Appendix 17, where c is 5%. [Additional Note 19] Length (L S -l)>length l, as described in Appendix 12. [Additional Note 20] A sleeve for use in the roll of a rolling mill, wherein the sleeve has an inner end and an outer end, The aforementioned sleeve is (a) Sleeve length L S , hydrodynamic length L H , and an outer surface having a cylindrical shape with an outer diameter OD, (b) The inner surface having the inner diameter ID and taper angle a of the inner end Equipped with, The aforementioned inner surface is (1) Length (L S -l) the first part, wherein the first part which is cone-shaped has a first inclined portion, (2) A second portion of length l, the second portion including a second inclined portion located adjacent to the first inclined portion, the second inclined portion tapering by a quantity δ, and Equipped with, The second inclined portion allows the sleeve to flex as the load increases with a maximum radial deflection corresponding to the amount δ, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L} H The value of l is defined as (mm))*a, where a is chosen so that it is in the range of 0.02 ≤ a ≤ 0.04, and the value of l is b * hydrodynamic length {L H A sleeve defined as}, where b is chosen such that 20% ≤ b ≤ 35%. [Additional Note 21] A sleeve as described in Appendix 20, where a is 0.025. [Additional Note 22] The sleeve described in Appendix 21, where b is 25%. [Additional Note 23] Length (L S -l)>length l, as described in Appendix 20. [Additional note 24] A sleeve for use in the roll of a rolling mill, wherein the sleeve has an inner end and an outer end, The aforementioned sleeve is (a) Sleeve length L S , hydrodynamic length L H , and an outer surface having a cylindrical shape with an outer diameter OD, (b) The inner surface having the inner diameter ID and taper angle a of the inner end Equipped with, The aforementioned inner surface is (1) Length (L S -l) the first part, wherein the first part which is cone-shaped has a first inclined portion, (2) A second portion of length l, wherein the total length l of the second portion is undercut by a certain amount δ. Equipped with, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L} H The value of l is defined as (mm))*a, where a is chosen so that it is in the range of 0.02 ≤ a ≤ 0.04, and the value of l is b * hydrodynamic length {L H A sleeve defined as}, where b is chosen such that 20% ≤ b ≤ 35%. [Additional note 25] A sleeve as described in Appendix 24, where a is 0.025. [Additional note 26] The sleeve described in Appendix 24, where b is 25%. [Additional note 27] Length (L S -l)>length l, as described in Appendix 24. [Additional note 28] A method for reducing the temperature rise inside a sleeve, wherein the sleeve is for use in a rolling mill roll, and the sleeve has an inner end and an outer end. The aforementioned method, (a) Sleeve length L S , outer diameter OD, and hydrodynamic length L H The steps include providing an outer surface with a cylindrical shape having, (b) Steps to provide the inner self and Includes, The aforementioned inner surface is (1) Length (L S -l) the first part, wherein the first part which is cone-shaped has a first inclined portion, (2) The second part of length l and Equipped with, The second part above is, (i) an undercut portion having an undercut radius r, wherein the undercut portion is located adjacent to the end of the first portion that is close to the inner end, (ii) A second inclined portion located adjacent to the undercut portion, wherein the second inclined portion is tapered by a quantity δ. Equipped with, The method wherein the second inclined portion allows the sleeve to deflect as the load increases with a maximum radial deflection corresponding to the amount δ. [Additional note 29] δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L} H (mm)})*a is defined, where a is chosen so that it is within the range of 0.02 ≤ a ≤ 0.04, and the value of l is b * hydrodynamic length {L H The method described in Appendix 28, where b is defined as} and b is chosen such that 20% ≤ b ≤ 35%. [Additional note 30] Length (L S -l)>length l, as described in Appendix 28. [Additional note 31] The method described in Appendix 28, wherein a is 0.025. [Additional note 32] The method described in Appendix 28, wherein b is 25%. [Additional note 33] The method according to Appendix 28, wherein the undercut radius r is defined as c * length l, and c is selected such that 2% ≤ c ≤ 10%. [Additional note 34] The method described in Appendix 28, wherein c is 5%. [Additional note 35] A method for reducing the temperature rise inside a sleeve, wherein the sleeve is for use in a rolling mill roll, and the sleeve has an inner end and an outer end. The aforementioned method, (a) Sleeve length L S , hydrodynamic length L H , and the step of providing an outer surface in the shape of a cylinder having an outer diameter OD, (b) The step of providing an inner surface having an inner diameter ID and a taper angle a at the inner end. Includes, The aforementioned inner surface is (1) Length (L S -l) the first part, wherein the first part which is cone-shaped has a first inclined portion, (2) A second portion of length l, the second portion including an undercut radius r, the second portion being adjacent to the end of the first portion that is close to the inner end, and the entire length l of the second portion being undercut by a certain amount δ. A method that includes [a certain feature]. [Additional note 36] δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L} H (mm)})*a is defined, where a is chosen so that it is within the range of 0.02 ≤ a ≤ 0.04, and the value of l is b * hydrodynamic length {L H The method described in Appendix 35, defined as}, where b is chosen such that 20% ≤ b ≤ 35%. [Additional note 37] The method described in Appendix 36, wherein a is 0.025. [Additional note 38] The method described in Appendix 36, wherein b is 25%. [Additional note 39] The method according to Appendix 36, wherein the undercut radius r is defined as c * length l, and c is selected such that 2% ≤ c ≤ 10%. [Additional note 40] The method described in Appendix 39, wherein c is 5%. [Additional note 41] Length (L S -l)>length l, as described in Appendix 36. [Additional note 42] A method for reducing the temperature rise inside a sleeve, wherein the sleeve is for use in a rolling mill roll, and the sleeve has an inner end and an outer end. The aforementioned method, (a) Sleeve length L S , hydrodynamic length L H , and the step of providing an outer surface in the shape of a cylinder having an outer diameter OD, (b) The inner surface having an inner diameter ID and a taper angle a of the inner end, The aforementioned inner surface is (1) Length (L S -l) the first part, wherein the first part which is cone-shaped has a first inclined portion, (2) A second portion of length l, the second portion including a second inclined portion located adjacent to the first inclined portion, the second inclined portion tapering by a quantity δ, Equipped with, The method wherein the second inclined portion allows the sleeve to deflect as the load increases with a maximum radial deflection corresponding to the amount δ. [Additional note 43] δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L} H (mm)})*a is defined, where a is chosen so that it is within the range of 0.02 ≤ a ≤ 0.04, and the value of l is b * hydrodynamic length {L H The method described in Appendix 42, defined as}, where b is chosen such that 20% ≤ b ≤ 35%. [Additional note 44] The method described in Appendix 43, wherein a is 0.025. [Additional note 45] The method described in Appendix 43, wherein b is 25%. [Additional note 46] Length (L S -l)>length l, as described in Appendix 42. [Additional note 47] A method for reducing the temperature rise inside a sleeve, wherein the sleeve is for use in a rolling mill roll, and the sleeve has an inner end and an outer end. The aforementioned method, (a) Sleeve length L S , hydrodynamic length L H , and the step of providing an outer surface in the shape of a cylinder having an outer diameter OD, (b) The step of providing an inner surface having an inner diameter ID and a taper angle a at the inner end. Includes, The aforementioned inner surface is (1) Length (L S -l) the first part, wherein the first part which is cone-shaped has a first inclined portion, (2) A second portion of length l, wherein the total length l of the second portion is undercut by a certain amount δ. A method that includes [a certain feature]. [Additional note 48] δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L} H (mm)})*a is defined, where a is chosen so that it is within the range of 0.02 ≤ a ≤ 0.04, and the value of l is b * hydrodynamic length {L H The method described in Appendix 47, where b is defined as} and b is chosen such that 20% ≤ b ≤ 35%. [Additional note 49] The method described in Appendix 48, wherein a is 0.025. [Additional Note 50] The method described in Appendix 48, wherein b is 25%. [Additional note 51] Length (L S -l)>length l, as described in Appendix 47. [Explanation of Symbols]

[0040] 10 Roll, 12 Neck section, 14 Sleeve, 16 Bearing surface, Rotating journal surface, 18 Bushing, 20 Internal bearing surface, Journal surface, 22 Chock, 24 End plate, 26 Cover, 28 Seal assembly, 29 Passage, 30 Supply opening, 32 Rebore, 34 Hydrodynamic oil film, 36 Inner sump, 38 Outer sump, 40 Passage, 300 Sleeve, 301 Inner end, 302 Outer end, 303 Outer surface, 304 Inner surface, First inclined section, 308 Second inclined section, 310 Second length section, 312 Undercut section, Hinge

Claims

1. A sleeve for use in the roll of a rolling mill, wherein the sleeve has an inner end and an outer end, The aforementioned sleeve is (a) Sleeve length L Ｓ , hydrodynamic length L Ｈ , and the outer surface of a cylindrical shape having an outer diameter OD, (b) The inner surface having the inner diameter ID and taper angle α of the inner end Equipped with, The aforementioned inner surface is (1) Length (L Ｓ -l) The first part, wherein the first part is cone-shaped and has a first inclined portion, (2) The second part of length l and Equipped with, The second part mentioned above is, (i) An undercut portion having a recess radius r, wherein the undercut portion is located adjacent to the end of the first portion that is close to the inner end, (ii) A second inclined portion located adjacent to the undercut portion, wherein the second inclined portion is tapered by an amount δ. Equipped with, The second inclined portion allows the sleeve to flex as the load increases with a maximum radial deflection corresponding to the amount δ, A sleeve in which a bushing is positioned around the outer surface of the sleeve, and a gap exists between the bushing and the outer surface of the sleeve, the gap being configured to maintain a hydrodynamically maintained oil film.

2. A sleeve for use in the roll of a rolling mill, wherein the sleeve has an inner end and an outer end, The aforementioned sleeve is (a) Sleeve length L Ｓ , hydrodynamic length L Ｈ , and an outer surface having a cylindrical shape with an outer diameter OD, (b) The inner surface having the inner diameter ID and taper angle α of the inner end Equipped with, The aforementioned inner surface is (1) Length (L Ｓ -l) The first part, wherein the first part is cone-shaped and has a first inclined portion, (2) A second portion of length l, the second portion including a recess radius r, the second portion located adjacent to the end of the first portion that is close to the inner end, and the total length l of the second portion is undercut by a certain amount δ. Equipped with, A sleeve in which a bushing is positioned around the outer surface of the sleeve, and a gap exists between the bushing and the outer surface of the sleeve, the gap being configured to maintain a hydrodynamically maintained oil film.

3. A sleeve for use in the roll of a rolling mill, wherein the sleeve has an inner end and an outer end, The aforementioned sleeve is (a) Sleeve length L Ｓ , hydrodynamic length L Ｈ , and an outer surface having a cylindrical shape with an outer diameter OD, (b) The inner surface having the inner diameter ID and taper angle α of the inner end Equipped with, The aforementioned inner surface is (1) The first part with a length (L Ｓ - l), wherein the first part having a conical shape has a first inclined part, the first part, and (2) A second portion of length l, the second portion including a second inclined portion located adjacent to the first inclined portion, the second inclined portion tapering by a quantity δ, and Equipped with, The second inclined portion allows the sleeve to flex as the load increases with a maximum radial deflection corresponding to the amount δ, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L} Ｈ (mm)}) * a is defined as a, where a is chosen so that it is in the range of 0.02 ≤ a ≤ 0.04, and the value of l is b * hydrodynamic length { L Ｈ It is defined as}, and b is chosen such that it is within the range of 20% ≤ b ≤ 35%. A sleeve in which a bushing is positioned around the outer surface of the sleeve, and a gap exists between the bushing and the outer surface of the sleeve, the gap being configured to maintain a hydrodynamically maintained oil film.

4. A sleeve for use in the roll of a rolling mill, wherein the sleeve has an inner end and an outer end, The aforementioned sleeve is (a) Sleeve length L Ｓ , hydrodynamic length L Ｈ , and an outer surface having a cylindrical shape with an outer diameter OD, (b) The inner surface having the inner diameter ID and taper angle α of the inner end Equipped with, The aforementioned inner surface is (1) Length (L Ｓ -l) The first part, wherein the first part is cone-shaped and has a first inclined portion, (2) A second portion of length l, wherein the total length l of the second portion is undercut by a certain amount δ and Equipped with, δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L} Ｈ (mm)}) * a is defined as a, where a is chosen so that it is in the range of 0.02 ≤ a ≤ 0.04, and the value of l is b * hydrodynamic length { L Ｈ It is defined as}, and b is chosen such that it is within the range of 20% ≤ b ≤ 35%. A sleeve in which a bushing is positioned around the outer surface of the sleeve, and a gap exists between the bushing and the outer surface of the sleeve, the gap being configured to maintain a hydrodynamically maintained oil film.

5. A method for reducing the temperature rise inside a sleeve, wherein the sleeve is for use in a rolling mill roll, and the sleeve has an inner end and an outer end. The aforementioned method, (a) Sleeve length L Ｓ , outer diameter OD, and hydrodynamic length L Ｈ The steps include providing an outer surface with a cylindrical shape having, (b) Steps to provide inner experiences Includes, The aforementioned inner surface is (1) Length (L Ｓ -l) The first part, wherein the first part is cone-shaped and has a first inclined portion, (2) The second part of length l and Equipped with, The second part mentioned above is, (i) An undercut portion having a recess radius r, wherein the undercut portion is located adjacent to the end of the first portion that is close to the inner end, (ii) A second inclined portion located adjacent to the undercut portion, wherein the second inclined portion is tapered by an amount δ. Equipped with, The second inclined portion allows the sleeve to flex as the load increases with a maximum radial deflection corresponding to the amount δ, A method comprising: a bushing positioned around the outer surface of the sleeve, wherein a gap exists between the bushing and the outer surface of the sleeve, and the gap is configured to maintain a hydrodynamically maintained oil film.

6. A method for reducing the temperature rise inside a sleeve, wherein the sleeve is for use in a rolling mill roll, and the sleeve has an inner end and an outer end. The aforementioned method, (a) Sleeve length L Ｓ , hydrodynamic length L Ｈ , and the step of providing an outer surface that has the shape of a cylinder having an outer diameter OD, (b) The step of providing an inner surface having an inner diameter ID and a taper angle α at the inner end; Includes, The aforementioned inner surface is (1) Length (L Ｓ -l) The first part, wherein the first part is cone-shaped and has a first inclined portion, (2) A second portion of length l, the second portion including a recess radius r, the second portion located adjacent to the end of the first portion that is close to the inner end, and the total length l of the second portion is undercut by a certain amount δ. Equipped with, A method comprising: a bushing positioned around the outer surface of the sleeve, wherein a gap exists between the bushing and the outer surface of the sleeve, and the gap is configured to maintain a hydrodynamically maintained oil film.

7. δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L} Ｈ (mm)}) * a is defined as a, where a is chosen so as to be within the range of 0.02 ≤ a ≤ 0.04, and the value of l is b * hydrodynamic length {L Ｈ The method according to claim 6, wherein b is defined as} and b is selected such that 20% ≤ b ≤ 35%.

8. A method for reducing the temperature rise inside a sleeve, wherein the sleeve is for use in a rolling mill roll, and the sleeve has an inner end and an outer end. The aforementioned method, (a) Sleeve length L Ｓ , hydrodynamic length L Ｈ , and the step of providing an outer surface that has the shape of a cylinder having an outer diameter OD, (b) The inner surface having an inner diameter ID and a taper angle α at the inner end, The aforementioned inner surface is (1) Length (L Ｓ -l) The first part, wherein the first part is cone-shaped and has a first inclined portion, (2) A second portion of length l, the second portion including a second inclined portion located adjacent to the first inclined portion, the second inclined portion tapering by a quantity δ, Equipped with, The second inclined portion allows the sleeve to flex as the load increases with a maximum radial deflection corresponding to the amount δ, A bushing is positioned around the outer surface of the sleeve, and a gap exists between the bushing and the outer surface of the sleeve, and the gap is configured to maintain a hydrodynamically maintained oil film. A method in which δ is defined as (bearing load rating {F (metric tons)} / hydrodynamic length {L H (mm)}) * a, where a is selected within the range of 0.02 ≤ a ≤ 0.04, and the value of l is defined as b * hydrodynamic length {L H}, where b is selected within the range of 20% ≤ b ≤ 35%.

9. A method for reducing the temperature rise inside a sleeve, wherein the sleeve is for use in a rolling mill roll, and the sleeve has an inner end and an outer end. The aforementioned method, (a) Sleeve length L Ｓ , hydrodynamic length L Ｈ , and the step of providing an outer surface that has the shape of a cylinder having an outer diameter OD, (b) The step of providing an inner surface having an inner diameter ID and a taper angle α at the inner end; Includes, The aforementioned inner surface is (1) Length (L Ｓ -l) The first part, wherein the first part is cone-shaped and has a first inclined portion, (2) A second portion of length l, wherein the total length l of the second portion is undercut by a certain amount δ and Equipped with, A method comprising: a bushing positioned around the outer surface of the sleeve, wherein a gap exists between the bushing and the outer surface of the sleeve, and the gap is configured to maintain a hydrodynamically maintained oil film.

10. δ is (bearing load rating {F (metric tons)} / hydrodynamic length {L} Ｈ (mm)}) * a is defined as a, where a is chosen so as to be within the range of 0.02 ≤ a ≤ 0.04, and the value of l is b * hydrodynamic length {L Ｈ The method according to claim 9, wherein b is defined as} and b is selected such that 20% ≤ b ≤ 35%.

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