JP4429841B2 - Roller bearing - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a roller bearing optimum for use in an misalignment condition. <P>SOLUTION: In this roller bearing forming crowning on a raceway surface of a bearing bearing ring or a rolling face of a roller, a profile line of negative side crowning 13b formed toward a negative side in the direction of generating line is a curve expressed by an expression (I), and a profile line of positive side crowning formed toward a positive side in the direction of generating line is a curve expressed by an expression (II). When optimizing design parameters K1n, K2n, zmn and K1p, K2p, zmp in the expressions (I) and (II) by taking misalignment into account, at least one of K1n&ne;K1p, K2nan&ne;K2pap, and zmn&ne;zmp is satisfied. <P>COPYRIGHT: (C)2006,JPO&amp;NCIPI

Description

  The present invention relates to a roller bearing in which a crowning is formed on at least one of an inner ring raceway surface, an outer ring raceway surface and a roller rolling surface.

  In a roller bearing in which a plurality of rollers are interposed between the raceway surfaces of a pair of bearing raceways consisting of an inner ring and an outer ring, such as a cylindrical roller bearing and a tapered roller bearing, The rolling contact is in line contact. If the rolling contact surface of the bearing race is a simple cylindrical surface or conical surface, an edge load occurs and the fatigue life of the roller bearing decreases. Therefore, in order to extend the fatigue life, the roller bearing is required to set the contact state of the bearing raceway so that the distribution of the contact surface pressure becomes substantially uniform.

  For this reason, conventionally, at least one of the inner ring raceway surface, the outer ring raceway surface, and the roller rolling surface is formed with a crowning so that the contact surface pressure distribution is substantially uniform (for example, Patent Documents). 1). Crowning means that the inner ring raceway surface, the outer ring raceway surface or the roller rolling surface has a slight curvature. Crowning includes full crowning formed over the entire region of the inner ring raceway surface, outer ring raceway surface or roller rolling surface in the generatrix direction, and cut crowning partially formed at one end portion or both end portions in the generatrix direction.

  As the contour shape of the crowning in the axial section of the roller bearing, Johns, PM and Gohar, R. described in the following formula (TRIBOLOGY international June 1981 pp.131-136) in "Roller bearings under radial and eccentric loads" (TRIBOLOGY international June 1981 pp.131-136) The optimal rolling element curve expressed in 1) (hereinafter referred to as the Johns-Gohar curve) is proposed.

As shown in FIG. 8, the Johns-Gohar curve of the equation (1) is a yz coordinate system in which the roller generatrix is the y-axis and the origin O is at the center of the effective contact portion of the bearing raceway. This represents a z-axis symmetric curve that passes through the origin O and has an asymptotic line of y = ± L / 2 (1−0.3033b / a) ^−1/2 . The effective contact portion is a contact region when assuming a two-dimensional contact at the bearing race and has a substantially uniform width in the circumferential direction of the roller. z (y) is a crowning drop amount (displacement in the direction perpendicular to the bus line from the roller bus bar to the rolling surface of the roller) at the position y in the roller bus bar direction. Q is the load, E 'is the equivalent elastic modulus, L is the length of the effective contact portion of the bearing race, b is the Hertz contact half width (the half width in the circumferential direction of the effective contact portion), and a is effective from the origin O. This is the length in the bus direction to the end of the contact portion (usually, a = L / 2). In addition, the contact half width b of Hertz is calculated | required by following formula (2).

In the formula (2), R is an equivalent radius, and the radius of the bearing race (inner ring outer diameter or outer ring inner diameter) in the effective contact portion is R _1, and the roller radius in the effective contact portion is R _2. (3).

Further, assuming that the elastic modulus of the bearing race and the roller is E ₁ and E ₂ and the Poisson's ratio of the bearing race and the roller is ν ₁ and ν ₂ , the equivalent elastic modulus E ′ is obtained by the following equation (4). .

  By the way, as a result of analyzing the contact surface pressure of the crowning represented by the Johns-Gohar curve in the formula (1), the present inventors have confirmed that the contact surface pressure is slightly increased at the end of the crowning. . This is also pointed out in Patent Document 2. Patent Document 2 proposes a crowning curve obtained by improving the Johns-Gohar curve of Formula (1) so that the maximum value of equivalent stress is not distributed in the generatrix direction of the effective contact portion (see Formula (5) below). .

In Expression (5), K is a safety factor and is determined in the range of 0.8 to 5. The coefficients k ₁ and k ₂ are determined as shown in the following formulas (6) and (7) by the effective contact length L and the contact half width b of Hertz.

Utility Model Registration No. 2554882 JP 2000-346078 A (see formula (16) and formula (19))

  Similar to the Johns-Gohar curve of Equation (1), the crowning curve of Equation (5) is related to the z-axis with the origin O serving as the apex in the yz coordinate system having the origin O at the center of the effective contact portion. It represents the contour of a full crowning that is symmetrical with positive and negative lines. However, in a misalignment state where the rolling contact surface of the bearing race is relatively inclined, there is a difference in contact surface pressure at both ends of the effective contact portion, and an edge load is generated at one end of the effective contact portion. It tends to occur. For the roller bearings used in such a misaligned state, when the crowning shape is set using the formula (5), it is possible to form the optimum crowning in the region on the one side in the busbar direction from the center of the effective contact portion. Even if possible, an excessive or excessive crowning is formed in the region on the other side in the busbar direction.

  That is, a roller bearing used in a misaligned state has a difference in contact surface pressure at both end portions of the effective contact portion, and thus it is necessary to form a positive / negative non-symmetrical crowning. However, Expression (5) represents a positive / negative line-symmetric full crowning in which the vertex of the crowning is in the center of the effective contact portion, and is positive / negative non-linear symmetry in which the crowning vertex is shifted from the center of the effective contact portion. It does not represent the full crowning or the cut crowning with positive and negative asymmetrical symmetry. For this reason, the crowning curve represented by the above formula (5) does not have an optimum shape for the roller bearing used in a misaligned state.

  Misalignment may occur due to the structural characteristics of the bearing itself, such as the tapered roller bearing, in which the raceway surface of the bearing race and the rolling surface of the tapered roller are inclined with respect to the bearing axial direction. For example, in a shaft system in which both ends are supported by two roller bearings, the center of the roller bearings at both ends is mounted so as to be displaced in a direction perpendicular to the shaft center. In some cases. In the latter case, misalignment occurs not only in the tapered roller bearing but also in other roller bearings such as a cylindrical roller bearing.

  The present invention has been made in view of such circumstances, and an object thereof is to provide a roller bearing that is optimal for use in a misaligned state.

In order to solve the above problems, a roller bearing according to the present invention is a roller bearing in which a crowning is formed on at least one of an inner ring raceway surface, an outer ring raceway surface, or a roller rolling surface, and the inner ring raceway surface, the outer ring raceway surface, or the roller rolling surface. The contour line shape in the cross section in the axial direction of the negative crowning formed toward the negative side of the generatrix is taken as the curve represented by the formula (8), and the origin is on the generatrix of the moving surface. a contour line shape in axial section of the positive crowning formed towards the curve represented by the formula _{(9), K 1n ≠ K} 1p, K 2n a n ≠ K 2p a p, the z _mn ≠ z _mp The design parameters K _1n , K _2n , and z _mn in the equation (8) and the design parameters K _1p , K _2p , and z _mp in the equation (9) are set so as to satisfy at least one of them.

In equations (8) and (9), z (y) is the amount of crowning drop (displacement in the direction perpendicular to the bus) at the y-axis position y of the inner ring raceway surface, outer ring raceway surface or roller rolling surface, and Q is the load. , L is inner or outer ring at the effective contact portions of the length, E 'is the equivalent elastic modulus, a _n is the generatrix direction length to the negative end of the effective contact portion from the origin, a _p is the effective contact portion from the origin Is the length in the direction of the bus line up to the positive side end.

When the Johns-Gohar curve represented by the formula (1) in the conventional example is applied to the crowning, the contact surface pressure is slightly increased at the end of the crowning. Therefore, the present inventors have added a coefficient K ₁ to the formula (1). , K ₂ ′ and the constant term is parameterized to obtain the following equation (10).

Expression (10) has the same form as Expression (5) in the conventional example, assuming that K ₁ = Kk ₂ and (1−0.3033K ₂ ′ b / a) = k ₁ ² . It should be noted that the coefficients K ₁ and K ₂ ′ in the equation (10) can be set regardless of the Hertz contact half width b and the effective contact portion length L, and have the meanings Kk ₂ and k ₁ in the equation (5). Make it different.

The crowning represented by Expression (10) represents a positive and negative line-symmetrical full crowning with the origin at the center of the effective contact portion and the vertex as the origin. When considering roller bearings used in a misaligned state, it is necessary to set the coefficients K ₁ and K ₂ ′ in each case by dividing equation (10) when y <0 and y> 0. is there. Therefore, assuming that the coefficients K ₁ and K ₂ ′ when y <0 are K _1n and K _2n ′, and the coefficients K ₁ and K ₂ ′ when y> 0 are K _1p and K _2p ′, ) Can be rewritten as shown in equations (11) and (12).

  Equation (11) represents the negative crowning formed from the origin to the negative in the direction of the bus, and Equation (12) represents the positive crowning formed from the origin to the positive in the direction of the bus. Yes.

On the other hand, positive and negative axisymmetric crowning includes not only full crowning but also cut crowning. In full crowning, the start point of the negative crowning coincides with the start point of the positive crowning, whereas in the cut crowning, the start point of the negative crowning does not coincide with the start point of the positive crowning. A straight part is formed between them. Therefore, the present inventors have made it possible to express the cut crowning by translating the curves represented by the equations (11) and (12) in the direction of the generatrix, so that the start point coordinates (s ₁ , 0) and (s ₂ , 0) are introduced into the equations (11) and (12). Incidentally, the start point coordinates (s _1, 0) of the negative crowning, the generatrix direction length to the negative end of the effective contact portion from the origin and a _n, a bus length of the negative crowning When y _{mn , (s 1, 0) =} - can be represented as _{(a n + y mn, 0} ). Similarly, the starting point coordinates (s ₂ , 0) of the positive side crowning are _defined as a _p in the bus direction length from the origin to the positive side end of the effective contact portion, and y _mp in the bus direction length of the positive side crowning. Then, it can be expressed as (s ₂ , 0) = (a _p −y _mp , 0). Thereby, Formula (11) and Formula (12) are expressed like the following Formula (13) and Formula (14).

In addition, each crowning curve represented by Formula (13) and Formula (14) is obtained by translating each Crowning curve represented by Formula (11) and Formula (12). Therefore, the crowning curve represented by Expression (13) has a length in the busbar direction y _mn and a drop amount at the negative side end of the effective contact portion, that is, the maximum drop amount z _mn of the negative side crowning is expressed by Expression (11). ) Is the same as the crowning curve. Similarly, the crowning curve represented by Expression (14) has the same length y _{mp in the} generatrix direction and the maximum drop amount z _mp of the positive side crowning as the crowning curve represented by Expression (12). Accordingly, the lengths y _mn and y _mp in the generatrix direction of the crowning curves represented by the equations (13) and (14) are based on the equations (11) and (12), and the equations (15) and (16) It can be expressed as

As in the equations (15) and (16), the negative-side crowning bus-direction length y _mn and the positive-side crowning bus-direction length y _mp are respectively K _1n , K _2n ′, z _mn and K _1p , It cannot be obtained unless K _2p ', z _mp is given. In addition, since the coefficients K _1n and K _1p in the equations (13) and (14) are multiplied by the load Q, they can be interpreted as the magnification of the load Q as a physical meaning, and the coefficients K _2n ′, If the coefficients K _1n and K _1p are changed by determining K _2p ′ and the lengths y _mn and y _mp in the busbar direction, the curvature of each crowning curve changes, so geometrically, the curvature of the crowning curve is determined. It can be interpreted as a parameter. On the other hand, the coefficients K _2n ′ and K _2p ′ in the equations (13) and (14) have unclear physical meanings, which hinder the evaluation of the crowning curve. For this reason, it is necessary to eliminate the coefficients K _2n ′ and K _2p ′ from the equations (13) and (14) and introduce parameters having physical significance.

Therefore, when the coefficients K _2n ′ and K _2p ′ obtained from the equations (15) and (16) are substituted into the equations (13) and (14), respectively, the following equations (17) and (18) are obtained. It is done.

Here, the proportion of generatrix direction length y _mn of negative crowning for generatrix direction length a _n to the negative end of the effective contact portion from the origin is defined as _{K 2n (K 2n = y mn} / a n) When the y _mn = K _2n a _n into equation (17), the above equation (8) is obtained. Similarly, the proportion of generatrix direction length a generatrix direction of the positive crowning for _p length y _mp up positive end of the effective contact portion from the origin is defined as _{K 2p (K 2p = y mp} / a p) , Y _mp = K _{2p ap} is substituted into equation (18), the above equation (9) is obtained.

Equations (8) and (9) are obtained by changing the curvature of each crowning curve, the length in the direction of the bus, if K _1n , K _2n , z _mn and K _1p , K _2p , z _mp are changed as design parameters, respectively. The maximum drop amount can be changed. Then, by optimizing the design parameters K _1n , K _2n , and z _mn in the equation (8) and the design parameters K _1p , K _2p , and z _mp in the equation (9), the crowning that does not cause edge loading is performed. The contour line shape can be obtained. In the case of a roller bearing used in a misaligned state, the crowning curves represented by the equations (8) and (9) are positive and negative non-linearly symmetric, so the curvatures K _1n and K _{1p of the} negative and positive crowning are negative. , the generatrix direction length of the negative and positive side crowned _{K 2n a n, K 2p a} p, the maximum drop amount z _mn of the negative side and the positive side crowning, all z _mp will never match. Therefore, to meet the K _1n ≠ K _1p, at least any one of the relationship among the _{K 2n a n ≠ K 2p a} p, z mn ≠ z mp.

The design parameters K _1n , K _2n , z _mn in equation (8) and the design parameters K _1p , K _2p , z _mp in equation (9) can be optimized by a numerical optimization method. . Numerical optimization methods include mathematical methods represented by feasible direction method and Rosenbrock method, and exploratory methods such as annealing method and genetic algorithm. As the objective function for optimization, the maximum surface pressure applied to the raceway surface or the roller rolling surface of the bearing race or the rolling fatigue life can be used.

According to the present invention, the contour line of the negative crowning formed on the generatrix on the inner ring raceway surface, outer ring raceway surface or roller rolling contact surface toward the negative side in the generatrix direction is expressed by the above equation (8). and curve represented, and the contour line of the positive crowning formed toward the generatrix direction positive side and the curve represented by the above formula _{(9), K 1n ≠ K} 1p, K 2n a n ≠ K Design parameters K _1n , K _2n , z _{mn in} equation (8) and design parameters K _1p , K _2p in equation (9) so as to satisfy at least one of the relations of _2p a _p , z _mn ≠ z _mp , Z _mp can be provided to provide a roller bearing that is optimal for use in a misaligned state.

  The best mode for carrying out the present invention will be described below with reference to the accompanying drawings.

  FIG. 1 shows an example in which the roller bearing according to the present invention is applied to a cylindrical roller bearing. As shown in FIG. 1, the cylindrical roller bearing includes an inner ring 11, an outer ring 12, and a plurality of cylindrical rollers 13, 13,... That are rotatably interposed between the inner ring raceway surface 11a and the outer ring raceway surface 12a. The retainer 14 that holds the cylindrical rollers 13, 13,... At a predetermined interval in the circumferential direction of the bearing is a main component. In this embodiment, the negative side crowning 13b whose contour line is expressed by the equation (19) on the rolling surfaces 13a, 13a,... Of each cylindrical roller 13, 13,. A positive-side crowning 13c is provided. The raceway surface 11a of the inner ring 11 and the raceway surface 12a of the outer ring 12 are each formed in a cylindrical surface shape.

  FIG. 2 shows a yz coordinate system in which the y-axis is taken in the generatrix direction of the cylindrical roller 13, the origin O is taken at an arbitrary position on the generatrix of the cylindrical roller 13, and the z-axis is taken in the direction perpendicular to the generatrix. The example of a crowning curve represented by Formula (19) and Formula (20) is shown. In FIG. 2, the origin O is set at a position offset from the center C of the effective contact portion to the negative side. The effective contact portion is a contact portion between the inner ring 11 or the outer ring 12 and the cylindrical roller 13 when no crowning is formed on the cylindrical roller 13.

In the equations (19) and (20), the z-direction displacement z (y) is the amount of crowning drop at the y-axis position y of the cylindrical roller 13, Q is the load, L is the length of the effective contact portion in the generatrix direction, E 'equivalent modulus, a _n is the generatrix direction length to the negative end F ₁ of the effective contact portion from the origin O, a _p is the generatrix direction length to the positive end F ₂ of the effective contact portion from the origin O That's it. Load Q, the generatrix direction length of the effective contact portion L, and the equivalent elastic modulus E 'is given as a design condition, the generatrix direction length a _n to the end F _1, F ₂ of the effective contact portion from the origin O, a _p is a value determined by the position of the origin O.

K _1n , K _2n , z _mn in the equation (19) and K _1p , K _2p , z _mp in the equation (20) are design parameters of the negative side crowning 13b and the positive side crowning 13c, respectively. Design parameters K _1n and K _1p in the equations (19) and (20) mean the magnification of the load Q, geometrically, the curvature of the negative crowning 13b and the positive crowning 13c. Design parameters K _2n in equation (19) means the ratio of the generatrix direction length y _mn of negative crowning 13b for generating line direction length a _n from the origin O to the negative end of the effective contact portions (K _2n = Y _mn / a _n ), the design parameter K _2p in equation (20) is the bus-direction length y _{mp of the} positive crowning 13c with respect to the bus-direction length a _p from the origin O to the positive end of the effective contact portion. (K _2n = y _mn / a _n ). The design parameters z _mn and z _mp in the equations (19) and (20) are the drop amounts at the end portions F ₁ and F ₂ of the effective contact portion, that is, the maximum drop amount of the negative crowning 13b and the maximum of the positive crowning 13c. It means drop amount.

FIG. 3 shows a change in curvature of the positive crowning 13c when the design parameters K _2p and z _mp are set to predetermined values and the design parameter K _1p is changed within a range of 10 to 200. According to FIG. 3, when the value of the design parameter K _1p increases, the radius of curvature of the positive side crowning 13c increases, and when the value of the design parameter K _1p decreases, the radius of curvature of the positive side crowning 13c decreases. Similarly, the radius of curvature of the negative side crowning 13b also changes depending on the value of the design parameter K _1n .

On the other hand, design parameters K _2n, the use of K _2p, the generatrix direction length y _mn of negative crowning 13b is represented as y _mn = K _2n a _n, the generatrix direction length y _mp of positive crowning 13c is y _mp = K _{2p ap} (see FIG. 2). The coordinates of the starting point O ₁ of the negative crowning 13b, using _{a n, K 2n, (-} a n + K 2n a n, 0) and is expressed, in the coordinate origin O ₂ of the positive crowning 13c is, a _p , K _2p , it is expressed as (a _p −K _2p a _p , 0).

When the design parameter K _2n in Equation (19) is reduced, the starting point O ₁ of the negative crowning 13b moves toward the negative side in the busbar direction and approaches the negative end of the effective contact portion. Conversely, when the design parameter K _2n is increased, the starting point O ₁ of the negative crowning 13b moves to the positive side in the bus direction. Therefore, when the design parameter K _2n in the equation (19) is changed, the length y _{mn of the} negative crowning 13b in the bus direction is changed. When the range of the design parameter K _2n is 0 <K _2n <1, the starting point O ₁ of the negative crowning 13b is located on the negative side of the origin O as shown in FIG. When K _2n = 1, the starting point O ₁ of the negative crowning 13b coincides with the origin O, and when 1 <K _2n , the starting point O ₁ of the negative crowning 13b is positioned on the positive side with respect to the origin O. To do.

Similarly, when the design parameter K _2p is changed, the starting point O ₂ of the positive-side crowning 13c is displaced in the bus-line direction, and the length y _{mp of the} positive-side crowning 13c is changed. When the range of the design parameter K _2p is 0 <K _2p <1, the starting point O ₂ of the positive crowning 13c is located on the positive side with respect to the origin O as shown in FIG. When K _2p = 1, the starting point O ₂ of the positive crowning 13c coincides with the origin O, and when 1 <K _2p , the starting point O ₂ of the positive crowning 13c is positioned on the negative side with respect to the origin O. To do. However, the starting point O ₂ of the positive side crowning 13c is assumed to be at the same position as the starting point O ₁ of the negative side crowning 13b or at a positive side position relative to the starting point O ₁ .

As described above, when the design parameters K _2n and K _2p are changed, the starting points O ₁ and O ₂ of the negative side crowning 13b and the positive side crowning 13c can be taken at the central portion C of the effective contact portion, or the effective contact. It can also take the position offset from the center part C of the part to either the busbar direction negative side or the positive side. Furthermore, the starting points O ₁ and O ₂ of the negative side crowning 13b and the positive side crowning 13c can be at the same position or at different positions. When satisfying _{K 2n a n + K 2p a} p = L, starting O _1, O ₂ is consistent, crowning of the formula (19) and (20) becomes full crowning. When the _{K 2n a n + K 2p a} p <L, the position of the starting point O _1, O ₂ are different, the crowning of the formula (19) and (20) is cut crowning. The region between the start point _{O 1, O 2 {- (} a n -K 2n a n) ≦ y ≦ (a p -K 2p a p)} represents a straight portion of the crowning is not formed.

On the other hand, since the design parameters z _mn and z _mp are drop amounts at the negative side end F ₁ or the positive side end F ₂ of the effective contact portion, when these values are changed, the equations (19) and ( The outer ends of the negative side crowning 13b and the positive side crowning 13c represented by 20) are displaced in the direction perpendicular to the bus.

From the above, equation (19) is a crowning curve formed of a logarithmic curve such as a Johns-Gohar curve, and is predetermined from the origin O taken at an arbitrary position on the bus bar of the cylindrical roller 13 to the negative side in the bus bar direction. distance (a _n -K _2n a _n) are formed toward the generatrix direction negative side as a position starting O ₁ a that across the curvature K _1n, the generatrix direction length K _2n a _n, and the maximum drop amount z _mn It represents the contour line of the negative crowning 13b to be determined, and by changing the design parameters K _1n , K _2n , and z _mn , the contour lines of various negative crowning 13b having different curvatures, generatrix lengths and maximum drop amounts can be obtained. Can be represented. Similarly, the equation (20) is a crowning curve formed of a logarithmic curve such as a Johns-Gohar curve, and a position separated from the origin O by a predetermined distance (a _p −K _2p a _p ) on the positive side in the bus line direction. Designed as a starting point O ₂ , which represents the contour of the positive crowning 13c formed by the curvature K _1p , the bus direction length K _{2p ap} , and the maximum drop amount z _mp . _1p, K _2p, by changing the z _mp, may represent a curvature, the contour line of the generatrix direction length and the maximum drop amount differs various positive crowning 13c.

When the design parameters K _1n , K _2n , and z _mn in the equation (19) and the design parameters K _1p , K _2p , and z _mp in the equation (20) are optimized, the crowning shape that does not cause an edge load is generated. Is obtained. Such optimization can be performed by a numerical optimization technique. Numerical optimization methods include mathematical methods represented by feasible direction method and Rosenbrock method, and exploratory methods such as annealing method and genetic algorithm. As the objective function for optimization, the maximum contact surface pressure applied to the raceway surface or roller rolling surface of the bearing race or the rolling fatigue life can be used.

Note that the optimization of the design parameters K _1n , K _2n , and z _mn in Expression (19) and the optimization of the design parameters K _1p , K _2p , and z _mp in Expression (20) may be performed independently. However, they may be performed simultaneously in a mutually dependent manner.

In the case of a cylindrical roller bearing used in a misaligned state, a difference in contact surface pressure is likely to occur at both ends of the effective contact portion, so that the crowning formed on the cylindrical roller bearing is a positive / negative non-linear symmetry. The positive / negative axisymmetric crowning is different in at least one of the curvature, the length in the busbar direction, and the maximum drop amount of the negative side crowning 13b and the positive side crowning 13c. Therefore, in the case of a cylindrical roller bearing used in a misaligned state, the optimum design parameters K _1n , K _2n , and z _mn in equation (19) and the design parameters K _1p , K _2p , and z _mp in equation (20) are used. Doing reduction, it will satisfy _{K 1n ≠ K 1p, K 2n} a n ≠ K 2p a p, at least any one of z _mn ≠ z _mp.

In Figure 2, a crowning of the positive and negative _{non-axisymmetric, K 1n ≠ K 1p, K} 2n a n ≠ K 2p a p, while indicating shall meet all z _mn ≠ z _mp, crowning of positive and negative non-axisymmetric In addition to what is shown in FIG. 2, there are also those shown in FIGS. 4 to 7, for the sake of convenience, positive and negative axisymmetric crowning is shown using the same yz coordinate system as in FIG. 2 in which the origin O is offset from the center C of the effective contact portion to the negative side.

4 shows a positive and negative axisymmetric full crowning in which the starting point O ₁ of the negative side crowning 13b and the starting point O ₂ of the positive side crowning 13c are located at the center C of the effective contact portion, and FIG. 5 shows the starting point O of the negative side crowning 13b. It illustrates ₁ and positive crowning 13c negative and cut crowning of positive and negative non-axisymmetric and equidistant offset to the positive side of the start point O ₂ from the center C of the effective contact portion of.

In FIG. 4 and FIG. 5, the generatrix direction length y _mp generatrix direction length y _mn and the positive crowning 13c of negative crowning 13b is equal, it will satisfy the _{K 2n a n = K 2p a} p. In this case, in order to make the crowning curves represented by the equations (19) and (20) positive and negative non-symmetrical, the curvatures K _1n and K _1p are made positive and negative, or the maximum drop amount z is positive and negative. _mn and z _mp are made different. In other words, when z _mn = z _mp is satisfied as shown by the solid line in each figure, positive and negative non-symmetrical crowning is obtained by setting K _1n ≠ K _1p . Further, as in the curves shown by broken lines in each figure, by setting z _mn ≠ z _mp , positive and negative axisymmetric crowning can be obtained. In the case of the curve shown by the broken line in each figure, K _1n = K _1p or K _1n ≠ K _1p may be satisfied.

FIG. 6 shows positive and negative axisymmetric full crowning in which the starting point O ₁ of the negative crowning 13b and the starting point O ₂ of the positive crowning 13c are offset from the central part C of the effective contact portion to one side in the generatrix direction, and FIG. An example of positive and negative asymmetric cut crowning in which the start point O _{1 of the} crowning 13 b and the start point O ₂ of the positive side crowning 13 c are offset from the central part C of the effective contact portion to one side in the generatrix direction is illustrated. In FIG. 6, the starting points O ₁ and O ₂ are set at the origin O, and the starting point O ₂ is set at the origin O in FIG.

In FIG. 6 and FIG. 7, the generatrix direction length y _mp generatrix direction length y _mn and the positive crowning 13c of negative crowning 13b is different, to meet the _{K 2n a n ≠ K 2p a} p become. Therefore, in the case of FIG. 6 and FIG. 7, the positive and negative axisymmetric crowning is obtained whether or not K _1n ≠ K _1p and / or z _mn ≠ z _mp is satisfied. In the case of FIG. 6, since taking the starting point O _1, O ₂ to the origin _{O, K 2n = K 2p =} 1 , and the since taken a position offset from the center C of the effective contact portions origin O, a _n ≠ a _p .

  The optimum crowning shape for a cylindrical roller bearing used in a misaligned state varies depending on the design conditions of the cylindrical roller bearing, particularly the degree of misalignment. According to the equations (19) and (20), as shown in FIG. 2 and FIGS. 4 to 7, many types can be represented as positive and negative axisymmetric crowning, so that the optimum according to the design conditions Can be obtained. Therefore, the roller bearing according to the present invention is optimal for use in a misaligned state.

  As described above, the embodiment of the present invention has been described. However, the present invention is not limited to the above embodiment, and various modifications are possible. For example, in the above embodiment, the case where the crowning is formed on the cylindrical roller 13 is given. However, the present invention is also applicable to the case where the crowning is formed on the inner ring raceway surface 11a and the outer ring raceway surface 12a. In the above embodiment, the cylindrical roller bearing is described. However, the present invention can be applied to other roller bearings such as a tapered roller bearing.

It is sectional drawing which shows an example at the time of applying the roller bearing which concerns on this invention to a cylindrical roller bearing. It is a yz coordinate diagram which shows an example of the crowning shape of the roller bearing which concerns on this invention. It is a yz coordinate diagram which shows an example of the curvature change of the positive side crowning when the design parameter _K1p is changed. It is a yz coordinate diagram which shows the other example of the crowning shape of the roller bearing which concerns on this invention. It is a yz coordinate diagram which shows the other example of the crowning shape of the roller bearing which concerns on this invention. It is a yz coordinate diagram which shows the other example of the crowning shape of the roller bearing which concerns on this invention. It is a yz coordinate diagram which shows the other example of the crowning shape of the roller bearing which concerns on this invention. It is a yz coordinate diagram which shows an example of the conventional crowning shape.

Explanation of symbols

11 Inner ring 11a Inner ring raceway surface 12 Outer ring 12a Outer ring raceway surface 13 Roller 13a Roller rolling surface 13b Negative side crowning 13c Positive side crowning 14 Cage

Claims (1)

In roller bearings with a crowning formed on at least one of the inner ring raceway surface, outer ring raceway surface or roller rolling surface, the origin is set on the generatrix of the inner ring raceway surface, outer ring raceway surface or roller rolling surface, and the negative direction in the busbar direction The contour shape in the axial section of the negative crowning formed toward the curve is represented by the formula (I), and the contour line in the axial section of the positive crowning formed toward the positive in the busbar direction the shape and the curve represented by the formula _{(II), K 1n ≠ K} 1p, K 2n a n ≠ K 2p a p, so as to satisfy at least one of z _mn ≠ z _mp, design parameters in formula (I) Roller bearings characterized by setting K _1n , K _2n , z _mn and design parameters K _1p , K _2p , z _mp in the formula (II);
Where z (y) is the amount of crowning drop at the position y in the generatrix direction of the inner ring raceway surface, outer ring raceway surface or roller rolling surface, Q is the load, L is the length of the effective contact portion at the inner ring or outer ring, E 'equivalent modulus of elasticity is a _n generatrix direction length to the negative end of the effective contact portion from the origin, it is a _p a generatrix direction length to the positive end of the effective contact portion from the origin.

Images