Tapered roller bearing

Abstract

A tapered roller bearing includes inner and outer rings having tapered raceway surfaces. The inner ring also includes large-collar and small-collar surfaces respectively on large-diameter and small-diameter sides of its raceway surface. A plurality of tapered rollers are arrayed between the raceway surfaces. Each of the tapered rollers has a large end surface that contacts and is guided by the large-collar surface. A set curvature radius (R) of the large end surface of each of the tapered rollers and a base curvature radius (R.sub.BASE) from a vertex of a cone angle of each of the tapered rollers to the large-collar surface has a ratio R/R.sub.BASE in a range of 0.75 to 0.87, and when R.sub.ACTUAL represents an actual curvature radius of the large end surface, a ratio R.sub.ACTUAL/R is equal to or larger than 0.5.

Claims

1. A tapered roller bearing, comprising: an outer ring having a tapered raceway surface on an inner periphery thereof; an inner ring having a tapered raceway surface on an outer periphery thereof, and comprising a large-collar surface on a large-diameter side of the tapered raceway surface, and a small-collar surface on a small-diameter side of the tapered raceway surface; a plurality of tapered rollers arrayed between both of the tapered raceway surfaces so as to be freely rollable; and a cage configured to receive the tapered rollers, each of the tapered rollers having a large end surface to be held in contact with and guided by the large-collar surface of the inner ring during use of the bearing, wherein when R represents a set curvature radius of the large end surface of each of the tapered rollers, and R.sub.BASE represents a base curvature radius from a vertex of a cone angle of each of the tapered rollers to the large-collar surface of the inner ring, a ratio R/R.sub.BASE of the set curvature radius R to the base curvature radius R.sub.BASE is set within a range of from 0.75 to 0.87, and wherein when R.sub.ACTUAL represents an actual curvature radius of the large end surface of each of the tapered rollers, a ratio R.sub.ACTUAL/R of the actual curvature radius R.sub.ACTUAL to the set curvature radius R is set equal to or larger than 0.5.

2. The tapered roller bearing according to claim 1, wherein the large end surface of each of the tapered rollers and the large-collar surface of the inner ring are superfinished surfaces.

3. The tapered roller bearing according to claim 1, wherein the large-collar surface of the inner ring has a relief surface.

4. The tapered roller bearing according to claim 1, wherein the tapered raceway surface of the inner ring and the tapered raceway surface of the outer ring are each formed into a straight shape or a full-crowning shape having an arc, and wherein the tapered rollers each have a rolling surface formed into a logarithmic crowning shape.

5. The tapered roller bearing according to claim 1, wherein at least one of the inner ring, the outer ring, and the tapered rollers has a nitrogen-enriched layer, and the grain size number of austenite crystal grain in the nitrogen-enriched layer is larger than No. 10.

6. The tapered roller bearing according to claim 1, wherein a center of an abutment position between a rolling surface of each of the tapered rollers and the tapered raceway surface of the inner ring, and a center of an abutment position between the rolling surface of each of the tapered rollers and the tapered raceway surface of the outer ring are displaced from an axial center of each of the tapered rollers to the large-diameter side by a dimension that is larger than 0% of an effective rolling surface width of each of the tapered rollers and smaller than 20% of the effective rolling surface width.

7. The tapered roller bearing according to claim 1, wherein the tapered roller bearing is used for a transmission or a differential for an automobile.

8. A tapered roller bearing, comprising: an outer ring having a tapered raceway surface on an inner periphery thereof; an inner ring having a tapered raceway surface on an outer periphery thereof, and comprising a large-collar surface on a large-diameter side of the tapered raceway surface, and a small-collar surface on a small-diameter side of the tapered raceway surface; a plurality of tapered rollers arrayed between both of the tapered raceway surfaces so as to be freely rollable; and a cage configured to receive the tapered rollers, each of the tapered rollers having a large end surface to be held in contact with and guided by the large-collar surface of the inner ring during use of the bearing, wherein when R represents a set curvature radius of the large end surface of each of the tapered rollers, and R.sub.BASE represents a base curvature radius from a vertex of a cone angle of each of the tapered rollers to the large-collar surface of the inner ring, a ratio R/R.sub.BASE of the set curvature radius R to the base curvature radius R.sub.BASE is set within a range of from 0.75 to 0.87, and wherein when R.sub.ACTUAL represents an actual curvature radius of the large end surface of each of the tapered rollers, a ratio R.sub.ACTUAL/R of the actual curvature radius R.sub.ACTUAL to the set curvature radius R is set equal to or larger than 0.8.

9. The tapered roller bearing according to claim 8, wherein the large end surface of each of the tapered rollers and the large-collar surface of the inner ring are superfinished surfaces.

10. The tapered roller bearing according to claim 8, wherein the large-collar surface of the inner ring has a relief surface.

11. The tapered roller bearing according to claim 8, wherein the tapered raceway surface of the inner ring and the tapered raceway surface of the outer ring are each formed into a straight shape or a full-crowning shape having an arc, and wherein the tapered rollers each have a rolling surface formed into a logarithmic crowning shape.

12. The tapered roller bearing according to claim 8, wherein at least one of the inner ring, the outer ring, and the tapered rollers has a nitrogen-enriched layer, and the grain size number of austenite crystal grain in the nitrogen-enriched layer is larger than No. 10.

13. The tapered roller bearing according to claim 8, wherein a center of an abutment position between a rolling surface of each of the tapered rollers and the tapered raceway surface of the inner ring, and a center of an abutment position between the rolling surface of each of the tapered rollers and the tapered raceway surface of the outer ring are displaced from an axial center of each of the tapered rollers to the large-diameter side by a dimension that is larger than 0% of an effective rolling surface width of each of the tapered rollers and smaller than 20% of the effective rolling surface width.

14. The tapered roller bearing according to claim 8, wherein the tapered roller bearing is used for a transmission or a differential for an automobile.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1 is a vertical sectional view for illustrating a tapered roller bearing according to a first embodiment of the present invention.

(2) FIG. 2 is a vertical sectional view for illustrating design specifications of a large end surface of a tapered roller and a large-collar surface of an inner ring of FIG. 1.

(3) FIG. 3 is a graph for showing a relationship between a curvature radius of the large end surface of the tapered roller of FIG. 1 and an oil film thickness.

(4) FIG. 4a is a vertical sectional view of the tapered roller for illustrating a detailed shape of the large end surface of the tapered roller of FIG. 1.

(5) FIG. 4b is an enlarged vertical sectional view for illustrating a portion A of FIG. 4a.

(6) FIG. 4c is a schematic view of FIG. 4b.

(7) FIG. 5a is a vertical sectional view for illustrating an abutment state between a rolling surface of the tapered roller and a raceway surface of each of the inner ring and an outer ring of FIG. 1, and illustrating a case in which a vertex of crowning of the raceway surface of each of the inner and outer rings is displaced.

(8) FIG. 5b is a vertical sectional view for illustrating the abutment state between the rolling surface of the tapered roller and the raceway surface of each of the inner ring and the outer ring of FIG. 1, and illustrating a case in which an angle of the raceway surface of each of the inner and outer rings is changed.

(9) FIG. 6 is a vertical sectional view for illustrating a detailed shape of the tapered roller of FIG. 1.

(10) FIG. 7 is an enlarged view for illustrating a portion B of FIG. 6.

(11) FIG. 8a is a vertical sectional view for illustrating a detailed shape of the inner ring of FIG. 1.

(12) FIG. 8b is an enlarged view for illustrating a portion D of FIG. 8a.

(13) FIG. 9 is a schematic view for illustrating a shape of the raceway surface of the inner ring of FIG. 8a in a generating-line direction of the raceway surface.

(14) FIG. 10 is a view for illustrating a heat treatment method for the tapered roller bearing of FIG. 1.

(15) FIG. 11 is a view for illustrating a modification example of the heat treatment method of FIG. 10.

(16) FIG. 12a is a view for illustrating the microstructure of a bearing component subjected to the heat treatment of FIG. 10 or FIG. 11, in particular, austenite grain.

(17) FIG. 12b is a view for illustrating the microstructure and austenite grain of a related-art bearing component subjected to the heat treatment.

(18) FIG. 13a is an illustration of the austenite grain boundary of FIG. 12a.

(19) FIG. 13b is an illustration of the austenite grain boundary of FIG. 12b.

(20) FIG. 14 is a vertical sectional view for illustrating a transmission for an automobile to which the tapered roller bearing of FIG. 1 is applied.

(21) FIG. 15 is a vertical sectional view for illustrating a differential for an automobile to which the tapered roller bearing of FIG. 1 is applied.

EMBODIMENTS OF THE INVENTION

(22) A tapered roller bearing according to a first embodiment of the present invention is described with reference to FIG. 1 to FIG. 15. First, the outline of the tapered roller bearing according to this embodiment is described with reference to FIG. 1, FIG. 6, and FIG. 8. FIG. 1 is a vertical sectional view for illustrating an upper half of the tapered roller bearing according to this embodiment with respect to a center line of the tapered roller bearing. FIG. 6 is a vertical sectional view for illustrating a detailed shape of a tapered roller of FIG. 1. FIG. 8 are vertical sectional views for illustrating a detailed shape of an inner ring of FIG. 1.

(23) As illustrated in FIG. 1, a tapered roller bearing 1 comprises an inner ring 12, an outer ring 13, tapered rollers 14 incorporated between the inner ring 12 and the outer ring 13, and a cage 15 configured to retain the tapered rollers 14. An inner-ring-side raceway surface 12a (hereinafter, simply referred to as raceway surface 12a) having a tapered shape is formed on an outer periphery of the inner ring 12. A small-collar portion 12b is formed on a small-diameter side, and a large-collar portion 12c is formed on a large-diameter side. An outer-ring-side raceway surface 13a (hereinafter, simply referred to as raceway surface 13a) having a tapered shape is formed on an inner periphery of the outer ring 13. The plurality of tapered rollers 14 are incorporated between the raceway surface 12a of the inner ring 12 and the raceway surface 13a of the outer ring 13. The tapered rollers 14 are respectively received in pockets 15a of the cage 15, and are retained at equal intervals in a circumferential direction of the cage 15.

(24) A ground relief portion 12f is formed at a corner portion at which the raceway surface 12a of the inner ring 12 and a large-collar surface 12e of the large-collar portion 12c intersect each other, and a ground relief portion 12g is formed at a corner portion at which the raceway surface 12a and a small-collar surface 12d of the small-collar portion 12b intersect each other. As described above, the ground relief portions 12f and 12g are formed on the raceway surface 12a of the inner ring 12, and hence an effective raceway surface width LG (see FIG. 8a) of the raceway surface 12a is smaller than an effective rolling surface width LW (see FIG. 6) of a rolling surface 16 of each of the tapered rollers 14.

(25) The rolling surface 16 having a tapered shape is formed on an outer periphery of the tapered roller 14. A small end surface 14a is formed on a small-diameter side of the tapered roller 14, and a large end surface 14b is formed on a large-diameter side of the tapered roller 14. The large end surface 14b of the tapered roller 14 is received by the large-collar surface 12e of the inner ring 12. During use of the tapered roller bearing 1, the large end surface 14b is held in contact with and guided by the large-collar surface 12e of the inner ring 12. Here, the large end surface 14b is a ground surface. As illustrated in FIG. 6, the rolling surface 16 of the tapered roller 14 comprises a straight portion 16a and crowning portions 16b and 16c. The straight portion 16a is formed at a center portion of the rolling surface 16 in a generating-line direction thereof. The crowning portions 16b and 16c are formed at both end portions of the rolling surface 16 in the generating-line direction. Drop amounts of the crowning portions 16b and 16c are illustrated in FIG. 6 with emphasis. Details of the crowning portions 16b and 16c are described later. As illustrated in FIG. 1, the cage 15 comprises a small-diameter-side annular portion 15b, a large-diameter-side annular portion 15c, and a plurality of pillar portions 15d connecting the small-diameter-side annular portion 15b and the large-diameter-side annular portion 15c to each other in an axial direction of the tapered roller bearing 1.

(26) A gap S between the small end surface 14a of the tapered roller 14 and the small-collar surface 12d illustrated in FIG. 1 is set equal to or smaller than 0.3 mm. Accordingly, the effect of suppressing skew can be attained, and adapting rotation performed at the time of assembly of the tapered roller bearing 1 is reduced, thereby improving ease of assembly.

(27) The outline of the tapered roller bearing 1 according to this embodiment is described above. Next, characteristic configurations of the tapered roller bearing 1 according to this embodiment are described. First, with reference to FIG. 2 to FIG. 4, description is made of a ratio of an optimum curvature radius of the large end surface of the tapered roller to an actual curvature radius after processing, which is a first characteristic configuration. FIG. 2 is a vertical sectional view for illustrating design specifications of the large end surface of the tapered roller and the large-collar surface of the inner ring of FIG. 1. FIG. 3 is a graph for showing a relationship between the curvature radius of the large end surface of the tapered roller of FIG. 1 and an oil film thickness. FIG. 4 are views for illustrating a detailed shape of the large end surface of the tapered roller of FIG. 1. FIG. 4a is a vertical sectional view for illustrating the tapered roller. FIG. 4b is an enlarged vertical sectional view for illustrating a portion A of FIG. 4a. FIG. 4c is a schematic view of FIG. 4b. In FIG. 4b and FIG. 4c, hatching is omitted for simplification of the illustrations.

(28) As illustrated in FIG. 2, vertices of cone angles of the rolling surface 16 of the tapered roller 14, the raceway surface 12a of the inner ring 12, and the raceway surface 13a of the outer ring 13 match with each other at a point O on a center axis of the tapered roller bearing 1. A ratio R/R.sub.BASE of the optimum curvature radius R of the large end surface 14b of the tapered roller 14 to a distance R.sub.BASE from the vertex O to the large-collar surface 12e of the inner ring 12 is set within a range of from 0.75 to 0.87 in order to improve the oil film thickness at a contact portion between the large end surface 14b of the tapered roller 14 and the large-collar surface 12e of the inner ring 12.

(29) FIG. 3 is a graph for showing a ratio of the thickness of the oil film formed between the large end surface 14b of the tapered roller 14 and the large-collar surface 12e of the inner ring 12 with respect to the relationship of the ratio R/R.sub.BASE. The thickness of the oil film formed between the large end surface 14b of the tapered roller 14 and the large-collar surface 12e of the inner ring 12 is represented by t, and the vertical axis indicates a ratio t/t.sub.0 of the thickness t to an oil film thickness to given when the ratio R/R.sub.BASE is 0.76. As shown in FIG. 3, the oil film thickness t is maximum when the ratio R/R.sub.BASE is 0.76, and sharply decreases when the ratio R/R.sub.BASE exceeds 0.9.

(30) In terms of the optimum value of the oil film thickness, as described in Patent Document 1, the ratio R/R.sub.BASE is in a range of from 0.75 to 0.87. Thus, next, a relationship between a skew angle of the tapered roller 14 and the ratio R/R.sub.BASE is studied. The ratio R/R.sub.BAsE in this study is based on condition that the large end surface 14b of the tapered roller 14 is in a contact state while having a set ideal spherical surface (including no processing error). A relationship between the ratio R/R.sub.BASE and the skew angle of the tapered roller 14 is shown in Table 1.

(31) TABLE-US-00001 TABLE 1 Ratio R/R.sub.BAsE 1 0.95 0.9 0.85 0.8 0.75 Skew angle () 0 0.03 0.06 0.09 0.12 0.15

(32) As shown in Table 1, it was found that, as the ratio R/R.sub.BASE decreases, the skew angle increases. Meanwhile, the curvature radius R of the large end surface 14b of the tapered roller 14 shown in FIG. 3 corresponds to a dimension of the curvature radius R obtained when the large end surface 14b of the tapered roller 14 illustrated in FIG. 4a has the set ideal spherical surface. Specifically, as illustrated in FIG. 4b, when points P1, P2, P3, and P4, a midpoint P5 between the points P1 and P2, and a midpoint P6 between the points P3 and P4 are set at an end portion of the large end surface 14b of the tapered roller 14, a curvature radius R.sub.152 passing the points P1, P5, and P2, a curvature radius R.sub.364 passing the points P3, P6, and P4, and a curvature radius R.sub.1564 passing the points P1, P5, P6, and P4 form an ideal single arc curve satisfying a relation of R=R.sub.152=R.sub.364=R.sub.1564. In the above description, the points P1 and P4 are each a connection point between the large end surface 14b and an end surface chamfer 14d, and the points P2 and P3 are each a connection point between the large end surface 14b and a relief portion 14c. Here, the ideal single arc curve satisfying the relation of R=R.sub.152=R.sub.364=R.sub.1564 is referred to as set curvature radius R. The set curvature radius R described in Claims bears the above-mentioned meaning.

(33) However, in actuality, as illustrated in FIG. 4c, shear drops are formed at both ends of the large end surface 14b at the time of grinding. Consequently, the curvature radius R.sub.152 on one side is not equal to but smaller than the curvature radius R.sub.1564 of the entire large end surface 14b (the same holds true for the curvature radius R.sub.364 on another side). Here, the curvature radius R.sub.152 on the one side or the curvature radius R.sub.364 on the another side obtained after the large end surface 14b of the tapered roller 14 is processed is referred to as actual curvature radius R.sub.ACTUAL. The actual curvature radius R.sub.ACTUAL described in Claims bears the above-mentioned meaning.

(34) The set curvature radius R and the actual curvature radius R.sub.ACTUAL are obtained as follows. The curvature radius R.sub.1564 of the entire large end surface 14b of FIG. 4c is an approximate circle passing the four points P1, P5, P6, and P4 on the large end surface 14b illustrated in FIG. 4b. A measurement method for the curvature radii R.sub.152, R.sub.364, and R.sub.1564 is described. The curvature radii R.sub.152, R.sub.364, and R.sub.1564 were measured through use of the surface roughness measurement instrument Surftest (for example, model name: SV-3100) manufactured by Mitutoyo Corporation. In the measurement method, through use of the above-mentioned measurement instrument, a shape of the large end surface 14b of the tapered roller 14 in the generating-line direction was obtained, the points P1, P2, P3, and P4 were plotted, and then the midpoint P5 between the points P1 and P2 and the midpoint P6 between the points P3 and P4 were plotted. The curvature radius R.sub.152 on the one side was calculated as a radius of an arc curve passing the points P1, P5, and P2 (the same holds true for the curvature radius R.sub.364 on the another side). The curvature radius R.sub.1564 of the entire large end surface 14b was calculated as a radius of an approximate arc curve based on values obtained by plotting four points through use of a command of multiple input. The shape of the large end surface 14b in the generating-line direction was measured once in a diameter direction.

(35) Next, description is made of an influence due to a difference between the set curvature radius R and the actual curvature radius R.sub.ACTUAL. The large end surface 14b of the tapered roller 14 and the large-collar surface 12e of the inner ring 12 are brought into contact with each other only at a portion having the curvature radius R.sub.152 on the one side or the curvature radius R.sub.364 on the another side. Thus, in actuality, when the large end surface 14b and the large-collar surface 12e are brought into contact with each other with the actual curvature radius R.sub.ACTUAL (R.sub.152, R.sub.364) smaller than the set curvature radius R (R.sub.1564). Accordingly, contact surface pressure between the large end surface 14b and the large-collar surface 12e increases, and at the same time, the skew angle of the tapered roller 14 increases. The above-mentioned problem was found through verification of the actual grinding.

(36) When the skew angle increases and the contact surface pressure also increases under an environment in which an oil film is not sufficiently provided, contact between the large end surface 14b of the tapered roller 14 and the large-collar surface 12e is unstable, with the result that an oil film parameter decreases. When the oil film parameter is smaller than 1, boundary lubrication occurs, which leads to beginning of metal-to-metal contact, and hence a risk of occurrence of seizing may increase. Here, the oil film parameter is defined by a ratio A (=h/) of an oil film thickness h determined by the elastohydrodynamic lubrication theory to a composite roughness of a root mean square roughness of the large end surface 14b of the tapered roller 14 and a root mean square roughness of the large-collar surface 12e of the inner ring 12.

(37) Based on the result of study on the influence due to the difference between the set curvature radius R and the actual curvature radius R.sub.ACTUAL associated with the above-mentioned grinding, focus is made on a ratio of the actual curvature radius R.sub.ACTUAL to the set curvature radius R, and verification is made on a relationship among the contact surface pressure between the large end surface and the large-collar surface, the oil film thickness, the skew angle, and the oil film parameter. Moreover, through verification on a practicable range of the ratio of the actual curvature radius R.sub.ACTUAL to the set curvature radius R, it has been found that influence is exerted on a level of severity of a lubrication state at a peak of an operating temperature of a lubricating oil between the large-collar surface of the inner ring and the large end surface of the tapered roller that are held in slide contact with each other.

(38) Accordingly, the following study is made on a reference indicating the level of severity of the lubrication state at the peak of the operating temperature of the lubricating oil between the large-collar surface of the inner ring and the large end surface of the tapered roller.

(39) (1) Focus is made on the following. The large-collar surface is a tapered surface, and hence is linear and constant. Thus, the lubrication state between the large-collar surface of the inner ring and the large end surface of the tapered roller is determined by the curvature radius (actual curvature radius R.sub.ACTUAL) of the large end surface of the tapered roller and the operating temperature of the lubricating oil.
(2) Further, focus is made on the following. For applications to a transmission and a differential, the lubricating oil to be used is basically determined. Thus, viscosity of the lubricating oil is also determined.
(3) As a maximum condition at the peak of the operating temperature of the lubricating oil, an extremely severe temperature condition in which the peak is kept at a temperature of 120 C. for three minutes (one hundred and eighty seconds) is assumed. This temperature condition is the maximum condition at the peak, and bears the meaning that a steady state is returned after the elapse of about three minutes. In Description, this temperature condition is referred to as assumed peak temperature condition. It has been found that a threshold value can be obtained to set the ratio of the actual curvature radius R.sub.ACTUAL to the set curvature radius R, which does not cause sharp temperature rise under a lubrication state in which a viscosity characteristic of the lubricating oil is added to the assumed peak temperature condition.

(40) Based on the above-mentioned findings, the following was conceived. With reference to the lubrication state in which the viscosity of the lubricating oil is added to the assumed peak temperature condition, the reference indicating the level of severity of the lubrication state is obtained by the following relation. In Description, this reference is referred to as collar-portion lubrication coefficient.

(41) Collar-portion lubrication coefficient=viscosity at 120 C.(oil film thickness h).sup.2/180 seconds

(42) Here, the oil film thickness h is obtained by the following expression of Karna.
h=1.6410.sup.3(.sub.o).sup.0.74R.sub.x.sup.0.41W.sup.0.074[Expression 1]
R.sub.x: Equivalent curvature radius in a direction of motion
: Average speed
w: Load
.sub.o: Viscosity at normal pressure

(43) A turbine oil having ISO viscosity grade of VG32, which is a lubricating oil often used for a transmission, was used as a sample, and the collar-portion lubrication coefficient was calculated. The viscosity of VG32 at a temperature of 120 C. was 7.7 cSt (=7.7 mm.sup.2/s), and the oil film thickness h was obtained by Expression 1. As shown in Table 2, the oil film thickness h has the following values with respect to respective values of the ratio of the actual curvature radius R.sub.ACTUAL to the set curvature radius R.

(44) TABLE-US-00002 TABLE 2 Ratio R.sub.ACTUAL/R of actual curvature radius R.sub.ACTUAL to set curvature radius R 0.4 0.5 0.7 0.8 0.9 1.0 Oil film thickness h 3.343 3.782 4.332 4.527 4.624 4.632 (10.sup.4 mm)

(45) The viscosity of VG32 at the temperature of 120 C. is low, and the lubrication state in which the viscosity of the lubricating oil is added to the assumed peak temperature condition is extremely severe. In Description, this lubrication state is referred to as extremely severe lubrication state.

(46) In addition, a seizure resistance test using a rotary testing machine was carried out. A test condition for the seizure resistance test is as follows.

(47) <Test Condition>

(48) Bearing load: radial load of 4,000 N, axial load of 7,000 N

(49) Rpm: 7,000 min.sup.1

(50) Lubricating oil: turbine oil having ISO viscosity grade of VG32

(51) Sample bearing: tapered roller bearing (having an inner diameter of 35 mm, an outer diameter of 74 mm, and a width of 18 mm)

(52) For respective values of the ratio of the actual curvature radius R.sub.ACTUAL to the set curvature radius R, results of the contact surface pressure between the large end surface and the large-collar surface, the oil film thickness, the skew angle, the oil film parameter, and the collar-portion lubrication coefficient are shown in Table 3. In Table 3, the contact surface pressure, the oil film thickness, the skew angle, and the oil film parameter are shown as ratios. A denominator as a standard corresponds to a value obtained when processing can be performed so that the actual curvature radius R.sub.ACTUAL has the same dimension as that of the set curvature radius R, and a sign of 0 is added to each symbol representing the denominator.

(53) TABLE-US-00003 TABLE 3 Ratio R.sub.ACTUAL/R of actual curvature radius R.sub.ACTUAL to set curvature radius R 0.4 0.5 0.7 0.8 0.9 1.0 Contact surface pressure 2.7 2.2 1.6 1.4 1.2 1 ratio p/p0 between large end surface and large- collar surface Oil film thickness ratio 0.72 0.82 0.94 0.98 1.00 1.00 h/h0 Skew angle ratio /0 8 5 3 1.5 1.2 1 Oil film parameter ratio 0.72 0.82 0.94 0.98 1.00 1.00 /0 Collar-portion lubrication 4.78 6.12 8.03 8.77 9.14 9.18 coefficient (10.sup.9) Test result (1) x (2) (3) (4) (5) (6) Overall determination (1) x (2) x (3) (4) (5) (6)

(54) Details of test results (1) to (6) and overall determinations (1) to (6) in Table 3 are shown in Table 4.

(55) TABLE-US-00004 TABLE 4 Test result (2) Strong abutment was seen between (3) (5) (6) the large end The (4) The The surface of the same A significant same same (1) x roller and the result change point result result A large-collar as the was not as the as the temperature surface of the left particularly left left rose sharply. inner ring. column. seen. column. column. Overall (1) x (2) x (3) (4) (5) (6) deter- The The The The The The mina- collar-portion collar-portion collar-portion collar-portion same same tion lubrication lubrication lubrication lubrication deter- deter- coefficient coefficient coefficient coefficient mination mination was low, was low, was low, exceeded as the as the strong strong and strong 8 10.sup.9, a left left abutment abutment abutment sufficient oil column. column. occurred, and occurred, and occurred. film was the skew the skew However, the formed, and angle was angle was skew angle was the skew large. slightly large. substantially angle was Accordingly, Thus, there small, and small. Thus, it was was a fear in hence it was stable determined that a determined rotation was as x. behavior of that obtained, and the roller was development of there was no unstable sudden damage problem in during did not continuous rotation of the immediately use. bearing. occur. Accordingly, it Accordingly, it Accordingly, it was was was determined determined determined as . as x. as .

(56) A conclusion drawn from the results in Table 3 and Table 4 is that it is desired that the ratio R.sub.ACTUAL/R of the actual curvature radius R.sub.ACTUAL to the set curvature radius R be equal to or larger than 0.8 in the extremely severe lubrication state in which a low-viscosity oil of VG32 being a transmission oil is used. Therefore, in this embodiment, the ratio R.sub.ACTUAL/R of the actual curvature radius R.sub.ACTUAL to the set curvature radius R is set equal to or larger than 0.8.

(57) However, the tapered roller bearing according to this embodiment is not limited to the application to a transmission, and can also be applied to a differential or in another extremely severe lubrication state.

(58) From the results in Table 3 and Table 4, the following was found. It was confirmed that, through verification of the calculated collar-portion lubrication coefficient and results of the seizure resistance test, when the ratio R.sub.ACTUAL/R of the actual curvature radius R.sub.ACTUAL and the set curvature radius R was set so that the collar-portion lubrication coefficient exceeded 810.sup.9, and a practicable ratio was obtained. Thus, the collar-portion lubrication coefficient=810.sup.9 can be used as a threshold value for setting the practicable ratio R.sub.ACTUAL/R of the actual curvature radius R.sub.ACTUAL to the set curvature radius R.

(59) Further, the oil film parameter depends on the composite roughness of the large end surface 14b of the tapered roller 14 and the large-collar surface 12e of the inner ring 12. Thus, such a conclusion is drawn that it is desired that the large end surface 14b and the large-collar surface 12e be superfinished surfaces. Therefore, in this embodiment, the large end surface 14b and the large-collar surface 12e are the superfinished surfaces. Surface roughness of the large end surface 14b of the tapered roller 14 is equal to or smaller than 0.10 mRa, and surface roughness of the large-collar surface 12e of the inner ring 12 is equal to or smaller than 0.063 mRa. The superfinished surfaces described in Claims have the surface roughness described above.

(60) With reference to FIG. 5a and FIG. 5b, description is made of shapes of the raceway surfaces of the inner and outer rings for suppressing skew of the tapered roller, which are a second characteristic configuration of the tapered roller bearing according to this embodiment. FIG. 5a is a vertical sectional view for illustrating an abutment state between the rolling surface of the tapered roller and the raceway surfaces of the inner and outer rings, and illustrating a case in which a vertex of crowning of the raceway surface of each of the inner and outer rings is displaced. FIG. 5b is a vertical sectional view for illustrating a case in which an angle of the raceway surface of each of the inner and outer rings is changed. In FIG. 5a and FIG. 5b, for ease of understanding of the abutment state between the rolling surface of the tapered roller and the raceway surfaces of the inner and outer rings, crowning shapes of the raceway surfaces are illustrated with emphasis.

(61) The skew angle of the tapered roller 14 is significantly influenced by abutment positions of the rolling surface 16 of the tapered roller 14 with the raceway surface 12a of the inner ring 12 and the raceway surface 13a of the outer ring 13. When nominal design dimensions are obtained, a position of the vertex of the crowning corresponds to an axial center of the raceway surface 12a of the inner ring 12, an axial center of the raceway surface 13a of the outer ring 13, or an axial center of the rolling surface 16 of the tapered roller 14. Further, an angle of the raceway surface 12a of the inner ring 12 and an angle of the raceway surface 13a of the outer ring 13 match with each other at a cone center (vertex O of FIG. 2). When centers C of the abutment positions of the rolling surface 16 of the tapered roller 14 with the raceway surface 12a of the inner ring 12 and the raceway surface 13a of the outer ring 13 are offset by an amount , the abutment positions can be displaced to the large-diameter side or the small-diameter side. The following two methods can be carried out as the method therefor.

(62) FIG. 5a is an illustration of a method of displacing the vertex of the crowning. FIG. 5b is an illustration of a method of changing angles of a raceway surface 12a of an inner ring 12 and a raceway surface 13a of an outer ring 13. For example, in the case of FIG. 5a, with respect to an axial center N of the tapered roller 14, the position of the vertex of the crowning of each of the raceway surface 12a of the inner ring 12 and the raceway surface 13a of the outer ring 13 is offset to the large-diameter side by the amount , and thus the centers of the abutment positions are displaced to the line indicated by C.

(63) When abutment is performed on the large-diameter side in FIG. 5b, angles of the raceway surface 12a of the inner ring 12 and the raceway surface 13a of the outer ring 13 are inclined to the large-diameter side (inclined clockwise in a case of the outer ring, and inclined counterclockwise in a case of the inner ring), and the centers C of the abutment positions are offset by the amount with respect to the axial center N of the tapered roller 14. The two-dot chain lines of FIG. 5b indicate the angles of the raceway surfaces 12a and 13a when the axial center N of the tapered roller 14 matches with the centers C of the abutment positions. However, when the centers C of the abutment positions are displaced from the axial center N of the tapered roller 14, slippage occurs between the rolling surface 16 of the tapered roller 14 and the raceway surface 12a, 12a of the inner ring 12, 12 and between the rolling surface 16 of the tapered roller 14 and the raceway surface 13a, 13a of the outer ring 13, 13. As the displacement amount increases, a level of the slippage increases, which results in increase in rotation torque of the bearing.

(64) In order to suppress skew of the tapered roller 14, an analysis was carried out on a relationship among the displacement amount of the centers C of the abutment positions of the rolling surface 16 of the tapered roller 14 with the raceway surface 12a, 12a of the inner ring 12, 12 and the raceway surface 13a, 13a of the outer ring 13, 13, the skew angle, and the bearing torque, and a practicable range was verified. The results are shown in Table 5. In Table 5, the displacement amount is shown as a percentage with respect to the effective rolling surface width LW (see FIG. 6) of the rolling surface 16 of the tapered roller 14. A positive sign represents the abutment on the large-diameter side, and a negative sign represents the abutment on the small-diameter side. The skew angle 0 and the torque M0 have values obtained when the displacement amount is 0%.

(65) TABLE-US-00005 TABLE 5 Displacement amount (%) 10 5 0 +5 +10 +15 +20 Skew angle ratio /0 2 1.5 1 0.75 0.5 0.4 0.3 Rotation torque ratio M/M0 1.2 1.1 1 1.03 1.05 1.1 1.2 Determination x x x

(66) As shown in Table 5, it can be seen that the skew angle is smaller in the case of abutment on the large-diameter side than in a case in which the displacement amount is 0%. Further, as the displacement amount increases, the rotation torque M increases. A larger influence is exerted on the rotation torque M in the case of abutment on the small-diameter side than in the case of abutment on the large-diameter side. When the displacement amount is 5%, the skew angle becomes 1.5 times as large as the skew angle in the case in which the displacement amount is 0%. Thus, an influence on heat generation cannot be disregarded. Accordingly, it was determined as impracticable (). Further, when the displacement amount is equal to or larger than 20, slippage on the rolling surface 16 of the tapered roller 14 increases, which results in increase in rotation torque M and another trouble such as peeling. Accordingly, it was determined as impracticable ().

(67) From the above-mentioned results, it is desired that the displacement amount be equal to or larger than 0% and smaller than 20% in order to reduce the skew angle and the rotation torque M. In this embodiment, the displacement amount of the centers C of the abutment positions of the rolling surface 16 of the tapered roller 14 with the raceway surface 12a, 12a of the inner ring 12, 12 and the raceway surface 13a, 13a of the outer ring 13, 13 is set to a dimensional range that is equal to or larger than 0% and smaller than 20% of the effective rolling surface width LW of the tapered roller 14. Further, the centers C of the abutment positions are displaced to the large-diameter side from the axial center N of the tapered roller 14.

(68) In this embodiment, the raceway surface 12a, 12a of the inner ring 12, 12 and the raceway surface 13a, 13a of the outer ring 13, 13 each having the crowning shape are exemplified, but the present invention is not limited thereto. The raceway surface of the inner ring 12 and the raceway surface of the outer ring 13 may each have a straight shape. In this case, abutment widths of the rolling surface 16 of the tapered roller 14 with the raceway surface of the inner ring 12 and the raceway surface of the outer ring 13 are increased, but the centers C of the abutment positions are determined in accordance with the abutment widths. The centers of the abutment positions described in Description and Claims encompass the above-mentioned case.

(69) As a third characteristic configuration of the tapered roller bearing according to this embodiment, logarithmic crowning is formed on the rolling surface of the tapered roller, and the raceway surface of the inner ring and the raceway surface of the outer ring are each formed into a straight shape or a full-crowning shape having a gentle single arc.

(70) Detailed shapes of the tapered roller, the inner ring, and the outer ring are described with reference to FIG. 6 to FIG. 9. FIG. 6 is an enlarged front view for illustrating the tapered roller in FIG. 1. FIG. 7 is an enlarged view for illustrating a portion B in FIG. 6. FIG. 8 are enlarged vertical sectional views for illustrating the inner ring in FIG. 1. FIG. 9 is a schematic view for illustrating a shape of the raceway surface of the inner ring in FIG. 8 in the generating-line direction.

(71) As illustrated in FIG. 6, the rolling surface 16 of the tapered roller 14 comprises the straight portion 16a formed at the center portion of the rolling surface 16 in the generating-line direction, and the logarithmic crowning portions (hereinafter, simply referred to as crowning portions) 16b and 16c formed at the both end portions of the rolling surface 16 in the generating direction. The effective rolling surface width of the tapered roller 14 is represented by LW, and a width of the straight portion 16a is represented by LW1. A diameter of the tapered roller 14 on the large-diameter side is a roller diameter Dw.

(72) Here, the logarithmic crowning formed on the tapered roller 14 is described. A generating line of each of the crowning portions 16b and 16c is determined based on, for example, the logarithmic curve of the logarithmic crowning expressed by the following expression. This logarithmic crowning expression corresponds to a logarithmic crowning expression described in Japanese Patent No. 5037094 granted to the applicant of the present application.

(73) $\begin{array}{cc}z\left(y\right)=K_{1}A\ln \frac{1}{1-\left\{1-\exp \left(-\frac{z_m}{K_{1}A}\right)\right\}{\left(\frac{y-a}{K_{2}a}+1\right)}^2}& \left[\mathrm{Expression}2\right]\end{array}$
A: =2Q/IE
a: Length from an origin O to an end of an effective contact portion
E: Equivalent elastic modulus
K.sub.1: Parameter representing a degree of a curvature of crowning
K.sub.2: Parameter representing a ratio of crowning length with respect to a
I: Length of an effective contact portion in the generating line direction
Q: Load
y: Position of the contact portion in the generating-line direction
z(y): Drop amount at the axial position y
z.sub.m: Parameter representing an optimum value of a maximum drop amount of crowning at the end in the effective length of the roller

(74) The design parameters K.sub.1, K.sub.2, and z.sub.m in the logarithmic crowning expression described above are subjected to design. Description is made of a mathematical optimization method for the logarithmic crowning. Through determination of the design parameter K.sub.2 and appropriate selection of the parameters K.sub.1 and z.sub.m in the function expression expressing the logarithmic crowning, optimum logarithmic crowning can be designed. In general, the crowning is designed so as to reduce the surface pressure of the contact portion or a maximum value of stress. It is assumed that the rolling fatigue lifetime occurs in accordance with the von Mises yield criterion, and the parameters K.sub.1 and z.sub.m are selected so as to minimize a maximum value of the von Mises equivalent stress. The parameters K.sub.1 and z.sub.m can be selected with use of an appropriate mathematical optimization method. Various mathematical optimization methods have been proposed, and the direct search method as one example is capable of executing optimization without use of derivatives of function, and is effective for a case in which an objective function and variables cannot be directly expressed with use of expressions. In this case, the parameters K.sub.1 and z.sub.m are determined with use of the Rosenbrock method as one of direct search methods.

(75) The shape of each of the crowning portions 16b and 16c of the tapered roller 14 in this embodiment is the logarithmic curve crowning determined by Expression 2 described above. However, the expression for determination of the logarithmic curve crowning is not limited to the expression described above, the logarithmic curve may be determined with use of another logarithmic crowning expression.

(76) The crowning portions 16b and 16c of the tapered roller 14 illustrated in FIG. 6 each have crowning having a shape approximate to the logarithmic curve of the logarithmic crowning determined by the expression described above. With reference to FIG. 7, description is made of details of the logarithmic crowning portion 16b formed on the large end surface 14b side of the tapered roller 14. In FIG. 7, for ease of understanding of the drop amount of the crowning portion 16b, more emphasis is given as compared to the tapered roller 14 illustrated in FIG. 6. The crowning portion 16b has a complex arc shape formed by smoothly connecting three arcs having large curvature radii R1, R2, and R3 to the straight portion 16a. As the drop amounts of the crowning portion 16b, there are defined a drop amount Dr1 at a first gate, an intermediate drop amount Dr2 at a second gate, and a maximum drop amount Dr3 at a third gate so that the crowning shape approximate to the logarithmic curve is formed. The drop amount Dr3 corresponds to Dr of FIG. 6. Further, the drop amount Dr3 corresponds to z.sub.m in Expression 1 described above. With this, surface pressure distribution in the axial direction can be set even while avoiding the edge surface pressure. The drop amount varies depending on the size or the model number, but is about 50 m at maximum. The crowning portion 16c formed on the side of the small end surface 14a is similar to the crowning portion 16b, and hence description thereof is omitted. The straight portion of the rolling surface of the tapered roller described in Description also encompasses a portion having a straight shape and a portion having a substantially straight shape with crowning having a drop amount of about several micrometers.

(77) Next, with reference to FIG. 8 and FIG. 9, description is made of a shape of the raceway surface 12a of the inner ring 12 in the generating-line direction. FIG. 8a is a vertical sectional view for illustrating a detailed shape of the inner ring 12. FIG. 8b is an enlarged view for illustrating a portion D in FIG. 8a. FIG. 9 is a schematic view for illustrating a shape of the raceway surface 12a of the inner ring 12 of FIG. 8 in the generating-line direction. In FIG. 8a and FIG. 8b, a part of a contour on the large end surface 14b side of the tapered roller 14 is indicated by the two-dot chain lines.

(78) As illustrated in FIG. 8a and FIG. 9, the raceway surface 12a of the inner ring 12 is formed into a full-crowning shape having a gentle single arc, and is continuous with the ground relief portions 12f and 12g. A curvature radius Rc of the full-crowning having the gentle single arc is significantly large as to involve the drop amount of about 5 m at each end of the raceway surface 12a. As illustrated in FIG. 8a, the ground relief portions 12f and 12g are formed on the raceway surface 12a of the inner ring 12, and hence the raceway surface 12a has an effective raceway surface width LG.

(79) As illustrated in FIG. 8b, a relief surface 12h is formed on a radially outer side of the large-collar surface 12e so as to be smoothly continuous with the large-collar surface 12e. Owing to a wedge-shaped gap defined between the relief surface 12h and the large end surface 14b of the tapered roller 14, a drawing action for the lubricating oil is enhanced, thereby being capable of forming a sufficient oil film. As the shape of the raceway surface 12a of the inner ring 12 in the generating-line direction, the full-crowning shape having the gentle single arc is exemplified. However, the shape of the raceway surface 12a of the inner ring 12 in the generating-line direction is not limited thereto, and may be a straight shape.

(80) In the above, the shape of the raceway surface 12a of the inner ring 12 in the generating-line direction is described. A shape of the raceway surface 13a of the outer ring 13 in the generating-line direction is similar to the shape of the raceway surface 12a of the inner ring 12 in the generating-line direction, and hence description thereof is omitted.

(81) Now, description is made of verification results leading to a concept of this embodiment in which the rolling surface 16 of the tapered roller 14 is formed into the logarithmic crowning shape (having a straight shape at a center portion), and the raceway surface 12a of the inner ring 12 and the raceway surface 13a of the outer ring 13 are each formed into a straight shape or the full-crowning shape having a gentle single arc.

(82) With regard to a tapered roller bearing (having an inner diameter of 35 mm, an outer diameter of 62 mm, and a width of 18 mm) for a transmission of an automobile, under a low speed condition (first speed) with misalignment and a high speed condition (fourth speed) without misalignment, verification was made on the contact surface pressure on the raceway surface 13a of the outer ring 13 and on a ratio of a contact ellipse with respect to the effective rolling surface width LW (see FIG. 6) of the rolling surface 16 of the tapered roller 14. Samples used for the verification are shown in Table 6.

(83) TABLE-US-00006 TABLE 6 Sample 1 Sample 2 Sample is based on this embodiment. Tapered roller: full-crowning Tapered roller: logarithmic crowning shape (drop amount at each end (having a straight shape at a center of a rolling surface: small portion, drop amount at each end of a and having a size of about 3 m) rolling surface: large and having a size Inner ring: cut-crowning shape of from about 20 m to about 30 m) (having a straight shape at a center portion, Inner and outer rings: straight shape drop amount at each end of a or full-crowning shape (drop amount: rolling surface: large and small and having a size of about 5 m) having a size of about 15 m) Outer ring: full-crowning shape (drop amount at each end of a rolling surface: large and having a size of about 20 m)

(84) The verification results are shown in Table 7.

(85) TABLE-US-00007 TABLE 7 Contact ellipse Surface pressure on (major axis)/ raceway surface of roller effective Deter- Verification Sam- outer ring (MPa) rolling surface mina- condition ple P.sub.MAX P.sub.EDGE width LW tion Without Sam- 2,000 Undetected 75 misalignment ple 1 (high speed Sam- 1,500 Undetected 55 X condition) ple 2 With Sam- 3,000 Undetected 78 misalignment ple 1 (low speed Sam- 2,500 Detected 100 X condition) ple 2

(86) Under the high speed condition without misalignment, a load condition is relatively mild. Thus, as shown in Table 7, no edge surface pressure (P.sub.EDGE) is generated in both of Sample 1 and Sample 2. However, in Sample 2, the drop amount of the full-crowning of the outer ring is large, and the contact ellipse (major axis) is short. As a result, more variation is seen in the center C of the abutment position as compared to a case in which a contact region is long, which is liable to induce skew of the tapered roller. Accordingly, it was determined as impracticable ().

(87) In contrast, under the low speed condition with misalignment, load is high. Thus, in Sample 2, the ratio of the contact ellipse with respect to the roller effective rolling surface width LW is 100%, and an edge surface pressure is generated on the outer ring. Moreover, edge abutment occurs so that driving is performed under a contact state on the small end surface side of the tapered roller. As a result, large skew is induced. Accordingly, it was determined as impracticable ().

(88) From the above description, it was verified that formation of full-crowning having a large drop amount on the outer ring is not preferred for suppression of skew, and significance of Sample 1 was confirmed. Thus, this embodiment was achieved.

(89) The inner ring 12, the outer ring 13, and the tapered rollers 14 of the tapered roller bearing 1 according to this embodiment are each made of high-carbon chromium bearing steel (for example, SUJ2 steel), and at least one of bearing components among the inner ring 12, the outer ring 13, and the tapered rollers 14 is subjected to heat treatment for forming a nitrogen-enriched layer. This heat treatment method is described with reference to FIG. 10 and FIG. 11. FIG. 10 is a view for illustrating a heat treatment pattern of a method of performing primary quenching and secondary quenching. FIG. 11 is a view for illustrating a heat treatment pattern of a method of cooling a material to a temperature lower than a transformation point A.sub.1 midway through the quenching, performing heating again, and performing quenching finally. In FIG. 10 and FIG. 11, in a process T.sub.1, after penetration of carbon is performed sufficiently while carbon and nitrogen are dispersed in a steel blank, and then the blank is cooled to a temperature lower than the transformation point A.sub.1. Next, in a process T.sub.2 of FIG. 10 and FIG. 11, the blank is heated again to a temperature equal to or higher than the transformation point A.sub.1 and lower than the temperature in the process T.sub.1, and then oil quenching is performed.

(90) Through the above-mentioned heat treatment, as compared to a related-art case in which, subsequent to carbonitriding quenching, namely, carbonitriding treatment, quenching is performed once as it is, fracture resistance can be increased while a surface layer portion is subjected to carbonitriding, and a ratio of dimensional change over time can be reduced.

(91) The tapered roller bearing 1 manufactured through the heat treatment pattern of FIG. 10 or FIG. 11 has the microstructure in which a grain diameter of austenite crystal grain is equal to or smaller than a half of a grain diameter in the related art. Thus, lifetime is long against rolling fatigue, and fracture resistance is increased, thereby being capable of reducing the ratio of dimensional change over time. The heat treatment step of lowering a secondary quenching temperature is performed in order to micronize the crystal grain, and thus an amount of remaining austenite is reduced on the surface layer and inside the tapered roller bearing. As a result, excellent fracture resistance and excellent resistance against dimensional change over time can be obtained.

(92) FIG. 12 are views for illustrating the microstructure of the bearing component, in particular, austenite grain. FIG. 12a is a view for illustrating the bearing component in this embodiment. FIG. 12b is a view for illustrating a related-art bearing component manufactured by the heat treatment method. That is, FIG. 12a is an illustration of an austenite crystal grain size of a raceway ring (the inner ring or the outer ring) to which the heat treatment pattern illustrated in FIG. 10 is applied. Further, for comparison, FIG. 12b is an illustration of an austenite crystal grain size of the related-art bearing steel obtained through the heat treatment method. Further, FIG. 13a and FIG. 13b are illustrations of the austenite crystal grain sizes in FIG. 12a and FIG. 12b. Based on the structures having the austenite crystal grain sizes, a grain diameter of the related-art austenite has No. 10 in terms of the grain size number of JIS standard, and fine grain having No. 12 can be obtained through the heat treatment method illustrated in FIG. 10 or FIG. 11. Further, an average grain diameter in FIG. 12a was 5.6 m as a result of measurement by a section method.

(93) In addition to having the first to third characteristic configurations described above, the tapered roller bearing 1 according to this embodiment can have rolling fatigue lifetime that is significantly improved, and can obtain excellent fracture resistance and excellent resistance against dimensional change over time by forming the nitrogen-enriched layer on the bearing component, and then micronizing the grain in order to obtain an austenite grain diameter having No. 11 or more in terms of the grain size number.

(94) Description is made of the case in which the inner ring 12, the outer ring 13, and the tapered rollers 14 of the tapered roller bearing 1 according to this embodiment are each made of high-carbon chromium bearing steel (for example, SUJ2 material), and at least one of the bearing components among the inner ring 12, the outer ring 13, and the tapered rollers 14 is subjected to the heat treatment for forming the nitrogen-enriched layer, but the present invention is not limited thereto. The inner ring 12 and the outer ring 13 may be made of carburized steel such as chromium steel (for example, SCR435) or chromium-molybdenum steel (for example, SCM435). Carburizing, quenching, and tempering applied conventionally may be applied as the heat treatment.

(95) Next, a tapered roller bearing according to a second embodiment of the present invention is described. The tapered roller bearing according to this embodiment is different from the tapered roller bearing according to the first embodiment in that the tapered roller bearing according to the second embodiment is used at a slightly lower level of severity of the lubrication state in which the viscosity characteristic of the lubricating oil is added to the assumed peak temperature condition, and that there is enlarged a practicable range of the ratio of the actual curvature radius R.sub.ACTUAL to the set curvature radius R in the large end surface of the tapered roller. Other configurations and technical contents are the same as those of the first embodiment. Thus, all the contents including Table 1, Table 5 to Table 7, Expression 1 and Expression 2, and FIG. 1 to FIG. 15 are similarly applied, and only differences are described.

(96) In this embodiment, SAE 75W-90, which is a gear oil often used for a differential, was used as a sample, and the collar-portion lubrication coefficient was calculated. The viscosity of SAE 75W-90 at a temperature of 120 C. was 10.3 cSt (=10.3 mm.sup.2/s), and the oil film thickness h was obtained by Expression 1. As shown in Table 8, the oil film thickness h has the following values with respect to respective values of the ratio of the actual curvature radius R.sub.ACTUAL to the set curvature radius R.

(97) TABLE-US-00008 TABLE 8 Ratio R.sub.ACTUAL/R of actual curvature radius R.sub.ACTUAL to set curvature radius R 0.4 0.5 0.7 0.8 0.9 1.0 Oil film thickness h 4.419 4.999 5.725 5.983 6.137 6.122 (10.sup.4 mm)

(98) The viscosity of 75W-90 at the temperature of 120 C. is slightly higher than that of VG32, and the lubrication state in which the viscosity characteristic of the lubricating oil is added to the assumed peak temperature condition has a slightly alleviated condition as compared to the case of the first embodiment. In Description, this lubrication state is referred to as severe lubrication state.

(99) Similarly to the first embodiment, a seizure resistance test using a rotary testing machine was carried out. A test condition for the seizure resistance test is as follows.

(100) <Test Condition>

(101) Bearing load: radial load of 4,000 N, axial load of 7,000 N

(102) Rpm: 7,000 min.sup.1

(103) Lubricating oil: SAE 75W-90

(104) Sample bearing: tapered roller bearing (having an inner diameter of 35 mm, an outer diameter of 74 mm, and a width of 18 mm)

(105) For respective values of the ratio of the actual curvature radius R.sub.ACTUAL to the set curvature radius R, results of the contact surface pressure between the large end surface and the large-collar surface, the oil film thickness, the skew angle, the oil film parameter, and the collar-portion lubrication coefficient are shown in Table 9. In Table 9, the contact surface pressure, the oil film thickness, the skew angle, and the oil film parameter are shown as ratios. A denominator as a standard corresponds to a value obtained when processing can be performed so that the actual curvature radius R.sub.ACTUAL has the same dimension as that of the set curvature radius R, and a sign of 0 is added to each symbol representing the denominator.

(106) TABLE-US-00009 TABLE 9 Ratio R.sub.ACTUAL/R of actual curvature radius R.sub.ACTUAL to set curvature radius R 0.4 0.5 0.7 0.8 0.9 1.0 Contact surface pressure 2.7 2.2 1.6 1.4 1.2 1 ratio p/p0 between large end surface and large- collar surface Oil film thickness ratio 0.72 0.82 0.94 0.98 1.00 1.00 h/h0 Skew angle ratio /0 8 5 3 1.5 1.2 1 Oil film parameter ratio 0.72 0.82 0.94 0.98 1.00 1.00 /0 Collar-portion lubrication 12.2 14.4 18.8 20.5 21.6 21.4 coefficient (10.sup.9) Test result (1) (2) (3) (4) (5) (6) Overall determination (1) x (2) (3) (4) (5) (6)

(107) Details of test results (1) to (6) and overall determinations (1) to (6) of Table 9 are shown in Table 10.

(108) TABLE-US-00010 TABLE 10 Test result (1) A significant (2) (3) (4) (5) (6) change The same The same The same The same The same was not result as result as result as result as result as particularly the left the left the left the left the left seen. column. column. column. column. column. Overall (1) x (2) (3) (4) (5) (6) determi- The The skew The The same The same The same nation collar- angle was collar- determi- determi- determi- portion slightly portion nation as nation as nation as lubrication large. lubrication the left the left the left coefficient However, coefficient column. column. column. exceeded the largely 8 10.sup.9, collar- exceeded and a portion 8 10.sup.9, a sufficient lubrication sufficient oil film coefficient oil film was largely was formed. exceeded formed, However, 8 10.sup.9, and the the skew and a skew angle was sufficient angle was large, oil film small. and was Thus, hence formed. stable there was Thus, it rotation a fear in was was that a determined obtained, behavior that and there of the develop- was no roller was ment of problem unstable drastic in during damage contin- rotation did not uous use. of the occur. According- bearing. According- ly, it was According- ly, it was determined ly, it was determined as . determined as practicable as x. .

(109) A conclusion drawn from the results in Table 9 and Table 10 is that it is desired that the ratio R.sub.ACTUAL/R of the actual curvature radius R.sub.ACTUAL to the set curvature radius R be equal to or larger than 0.5 in the severe lubrication state in which the 75-90W being an oil for a differential is used. Therefore, in this embodiment, the ratio R.sub.ACTUAL/R of the actual curvature radius R.sub.ACTUAL to the set curvature radius R is set equal to or larger than 0.5. In particular, through introduction of a collar-portion lubrication coefficient as a reference indicating a level of severity of the lubrication state, a practicable range of the ratio of the actual curvature radius R.sub.ACTUAL to the set curvature radius R can be enlarged. Thus, depending on use conditions, proper bearing specifications can be selected.

(110) However, the tapered roller bearing according to this embodiment is not limited to the application to a differential, and can also be applied to a transmission or in another severe lubrication state.

(111) At the time of setting the practicable ratio of the actual curvature radius R.sub.ACTUAL to the set curvature radius R, only vicinities of the threshold value may be tested and confirmed. Thus, man-hours for design can be reduced. Under the severe lubrication state shown in Table 9, even when the ratio of the actual curvature radius R.sub.ACTUAL to the set curvature radius R is 0.4, the sufficient collar-portion lubrication coefficient can be obtained. However, under the severe lubrication state in which a lubricating oil having viscosity slightly lower than that shown in Table 9 is used, when the ratio of the actual curvature radius R.sub.ACTUAL to the set curvature radius R is 0.4, there may be a risk in that the collar-portion lubrication coefficient does not satisfy the threshold value of 810.sup.9 or more, and the skew angle is increased. Accordingly, it is proper that the ratio of the actual curvature radius R.sub.ACTUAL to the set curvature radius R be equal to or larger than 0.5.

(112) Finally, as suitable application of the tapered roller bearing according to the embodiments of the present invention, the outline of a transmission for an automobile and the outline of a differential for an automobile are described with reference to FIG. 14 and FIG. 15. FIG. 14 is a vertical sectional view for illustrating a main part of a transmission for an automobile. FIG. 15 is a vertical sectional view for illustrating a differential for an automobile.

(113) A transmission 30 illustrated in FIG. 14 is an example of a synchronous mesh-type transmission. An input shaft 32 is freely rotatably supported by a mission case 31 through intermediation of a tapered roller bearing 1.sub.1, and a main shaft 33 is arranged coaxially with the input shaft 32. The input shaft 32 and the main shaft 33 are supported by a tapered roller bearing 1.sub.2 of a pilot portion so as to be rotatable relative to each other. Although not shown, another part of the main shaft 33 is supported by a tapered roller bearing. A countershaft 34 arranged in parallel with the input shaft 32 and the main shaft 33 at a predetermined interval is supported by a tapered roller bearing 1.sub.3 and another tapered roller bearing (not shown). An input shaft gear 35 is provided integrally with the input shaft 32, and is always in mesh with a countershaft gear 36 of the countershaft 34.

(114) A main shaft gear (hereinafter simply referred to also as gear) 43 is freely rotatably mounted to the main shaft 33 through intermediation of a tapered roller bearing 1.sub.4 of an idler portion. The main shaft gear 43 is always in mesh with a gear 37 of the countershaft 34. The tapered roller bearing according to the embodiments of the present invention corresponds to each of the above-mentioned tapered roller bearings 1.sub.1 to 1.sub.4 and the another tapered roller bearing (not shown). Through operation of a selector (not shown), a synchro mechanism 39 is moved in the axial direction (right-and-left direction in FIG. 14), thereby performing gear changing operation.

(115) Next, a differential is described with reference to FIG. 15. FIG. 15 is a vertical sectional view for illustrating a differential for a general automobile. A drive pinion shaft 101 is accommodated on an input side of a differential case 100, and is freely rotatably supported by a pair of tapered roller bearings 1.sub.5 and 1.sub.6. A propeller shaft 102 is coupled to one end portion of the drive pinion shaft 101. A drive pinion gear (small speed reduction gear) 104, which meshes with a link gear (large speed reduction gear) 103, is provided integrally with another end portion of the drive pinion shaft 101.

(116) The link gear 103 is coupled to a differential gear case 105, and the differential gear case 105 is supported by a pair of tapered roller bearings 1.sub.7 and 1.sub.8 so as to be freely rotatable with respect to the differential case 100. Inside the differential gear case 105, a pair of pinion gears 106 and a pair of side gears 107, which mesh with the pair of pinion gears 106, are arranged. The pinion gears 106 are mounted to a pinion shaft 108, and the side gears 107 are mounted to the differential gear case 105. Right and left drive shafts (not shown) are coupled (for example, serration-coupled) to inner diameter portions of the side gears 107. The tapered roller bearing according to the embodiments of the present invention corresponds to each of the above-mentioned tapered roller bearings 1.sub.5 to 1.sub.8. Drive torque of the propeller shaft 102 is transmitted via the drive pinion gear 104, the link gear 103, the differential gear case 105, the pinion gears 106, the side gears 107, and the drive shafts in the stated order.

(117) The tapered roller bearing according to the embodiments of the present invention suppresses heat generation between the large end surface of the tapered roller and the large-collar surface of the inner ring, thereby improving seizure resistance and prolonging lifetime. Accordingly, the tapered roller bearing according to the embodiments of the present invention is suitably used for a transmission and a differential for an automobile.

(118) The present invention is not limited to the above-mentioned embodiments. As a matter of course, the present invention may be carried out in various modes without departing from the spirit of the present invention. The scope of the present invention is defined in claims, and encompasses equivalents described in claims and all changes within the scope of claims.

REFERENCE SIGNS LIST

(119) 1 tapered roller bearing 12 inner ring 12a raceway surface 12b small-collar portion 12c large-collar portion 12d small-collar surface 12e large-collar surface 12f ground relief portion 12g ground relief portion 12h relief surface 13 outer ring 13a raceway surface 14 tapered roller 14a small end surface 14b large end surface 15 cage 16 rolling surface 16a straight portion 16b logarithmic crowning portion 16c logarithmic crowning portion C center of abutment position Dr drop amount of logarithmic crowning end portion Dw roller diameter LG effective raceway surface width LW effective rolling surface width LW1 width of straight portion N axial center of tapered roller O vertex R set curvature radius R.sub.ACTUAL actual curvature radius R.sub.BASE base curvature radius S gap displacement amount