JP2007211861A - Cam follower - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reduce contact pressure of a cam follower by taking a contact condition including misalignment into account. <P>SOLUTION: Drop quantity of crowning formed on both contact surface of a cam 2 or a roller 10 of the cam follower 4 is given by a formula (I) and is automatically optimized by a computer with using at least one of arbitrary optimization methods of parameters K1, K2, zm in the formula (I). In the formula (1) , z(y) is drop quantity of crowning at a position y in a bus line direction of a roller (displacement in a bus line perpendicular direction from the bus line of the roller to a rolling surface of the roller). Also, Q is load, E' is equivalent elastic coefficient, L is length of effective contact part of a bearing raceway ring and the roller, b is Hertz contact half width (half width in a circumference direction of the effective contact part), and "a" is length in a bus line direction from an origin O to an end part of the effective contact part (normally a=L/2). <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a cam follower, and more particularly to a crowning formed on a contact surface between a cam and a roller.

  A cam follower is used in a rocker arm or the like in a valve mechanism of an automobile engine. Since the roller of the cam follower is in pressure contact with the cam, the surface pressure at the contact end may increase due to misalignment caused by a processing error or deformation. By providing the cam or the roller or both with a bulge shape called crowning, the increase in surface pressure can be reduced.

As the crowning shape of the cam follower, those described in Patent Documents 1 to 3 are known in addition to a simple arc shape. Patent Document 1 and Patent Document 2 describe crowning in which a plurality of arcs are combined. In particular, the former defines a range of drop amounts at a plurality of points by a logarithmic function expression. Patent Document 3 describes a trapezoidal crowning in which both ends of an effective contact portion are cut with a straight line.
JP 2003-106111 A JP 2002-039326 A Japanese Patent Laid-Open No. 06-229456 JP 2000-346078 A (see formula (16) and formula (19))

  The contact between the cam follower roller and the cam is a line contact, or according to Lundberg, in the case of a line contact, the axial shape of the contact portion is made logarithmic so that the axial surface pressure distribution is constant. Can do. However, the shape of the function derived by Lundberg is not feasible, and Johns-Gohar shows an improved function. In the Johns-Gohar shape, when the misalignment occurs, the surface pressure at the contact end of the roller increases.

  The main object of the present invention is to reduce the surface pressure of the cam follower in consideration of contact conditions including misalignment.

  The present applicant has previously proposed a method for designing a crowning of a logarithmic roller bearing in consideration of the effect of misalignment (Japanese Patent Application No. 2004-234780). The present invention is an application of this design method to a cam follower. First, the design method for the crowning will be described.

  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 (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. 9, the Johns-Gohar curve of equation (1) is a y-z 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. In equation (1), z (y) is the amount of crowning drop at the position y of the roller in the busbar direction (displacement in the direction perpendicular to the busbar from the roller busbar to the rolling surface of the roller). 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 Equation (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, when the elastic coefficients of the bearing rings and rollers are E ₁ and E ₂ and the Poisson's ratios of the bearing rings and rollers are ν ₁ and ν ₂ , the equivalent elastic coefficient E ′ is obtained by the following equation (4). .

  By the way, as a result of analyzing the contact pressure of the crowning represented by the Johns-Gohar curve of the formula (1), the inventors have confirmed that the contact pressure is slightly increased at the end of the crowning. This is also pointed out in Patent Document 2. Patent Document 4 proposes a crowning curve obtained by improving the Johns-Gohar curve of Equation (1) so that the maximum value of equivalent stress is not distributed in the generatrix direction of the effective contact portion (see Equation (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.

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. The coefficients k ₁ and k ₂ in the equation (5) are determined to give the length L of the effective contact portion and the contact half width b of Hertz as design conditions. Therefore, in equation (5), the safety factor K is a design parameter. Specifically, when the safety factor K is increased, the radius of curvature of the crowning is increased, and when the safety factor K is decreased, the radius of curvature of the crowning is decreased.

  In equation (5), an optimal full crowning can be designed by setting the safety factor K so that the distribution of equivalent stress in the vicinity of the contact surface of the bearing race is substantially uniform. Specifically, if the value of the safety factor K is changed, the equivalent stress in the vicinity of the contact surface of the bearing race is obtained, and if the safety factor K when the maximum equivalent stress is minimum is selected, the equivalent of the bearing race is obtained. It is possible to design an optimal full crowning in which the stress distribution is substantially uniform in the generatrix direction.

  As described above, the crowning formed on the roller bearing includes a full crowning and a cut crowning. Since the full crowning is formed over the entire effective contact portion of the roller and the bearing ring, the length in the busbar direction of the full crowning is equal to the length L in the busbar direction of the effective contact portion. On the other hand, in the case of cut crowning, it is formed outward from one end or both ends of the straight portion formed at the intermediate portion of the effective contact portion. Changes. Further, in the cut crowning, when the length in the bus line direction is changed, the drop amount (maximum drop amount) at the end portion of the effective contact portion is also changed. Therefore, in order to design an optimal crowning assuming both full crowning and cut crowning, it is necessary to introduce not only the curvature of the crowning but also the length of the crowning in the busbar direction and the maximum drop amount into the formula (1) as design parameters. There is.

Thus, the crowning curve of Equation (5) has improved the Johns-Gohar curve by introducing the safety factor K and the factors k ₁ and k ₂ into Equation (1), but the coefficients k ₁ and k ₂ are There is a problem that the degree of freedom in design is low and the design is not suitable for the design of the cut crowning because the parameters are defined only by the safety factor K defined as the above formulas (6) and (7). .

  In the present invention, the logarithmic function formula of Johns-Gohar is improved to introduce three design parameters that define the shape. The surface pressure can be reduced by numerically optimizing these parameters in consideration of contact conditions including misalignment.

That is, the cam follower according to the present invention is characterized in that the sum of the drop amount of the crowning formed on the contact surface of the cam or roller or both is given by equation (8).
However, A = 2K ₁ Q / πLE ′
Q: Load L: Length E ′ of the effective contact portion of the contact surface E ′: Equivalent elastic coefficient a: Length Q from the origin taken on the bus of the contact surface to the end of the effective contact portion Q, L, E ′ Is given as a design condition, and a is determined by the position of the origin.

Applying the Johns-Gohar curve represented by Equation (1) in the conventional example to crowning increases the contact pressure at the end of the effective contact portion, so the coefficients K ₁ and K ₂ ′ are introduced into Equation (1). Then, the constant term was parameterized to obtain the following equation (9).

Expression (9) has the same form as Expression (5) of the conventional example if 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 (9) 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.

  Expression (9) represents a full crowning that is symmetrical with respect to the positive and negative lines with the origin at the center of the effective contact part and the origin as a vertex. In the full crowning, the starting points of the crownings formed toward the negative side or the positive side in the bus line direction coincide with each other. On the other hand, in the cut crowning, the starting points of the crowning formed toward the negative side or the positive side in the generatrix direction do not coincide with each other, and a straight portion is formed between the starting points of the crowning. Therefore, in order to be able to express the cut crowning by translating the curve represented by Equation (9) in the direction of the generatrix, the starting point coordinates (± s, 0) of each crowning are introduced into Equation (9). . In addition, since full crowning and cut crowning are usually formed symmetrically with the positive and negative of the bus direction, it is possible to create a relational expression representing the crowning formed toward either the negative side or the positive side of the bus direction. For example, this formula can be applied to the crowning formed toward the other side. Here, for the sake of convenience, a relational expression representing the crowning formed toward the positive side in the generatrix direction is made, and the starting point coordinates (s, 0) are introduced into the expression (9) and converted into the expression (10). .

Crowning start point coordinates (s, 0), using the generatrix direction length a and the generatrix direction length y _m of the crowning to the end of the effective contact portion from the origin, (s, 0) = ( a-y m , 0) (see FIG. 2). Thereby, Formula (10) can be transformed into Formula (11).

In addition, since the crowning curve represented by Formula (11) is obtained by translating the Crowning curve represented by Formula (9), the crowning represented by Formula (9) and Formula (11) is a bus line. direction and length y _m, drop amount that is, the maximum drop amount z _m at the end of the effective contact portions are the same. Accordingly, the length y _m of the crowning in the expression (11) can be expressed as the expression (12) based on the expression (9).

As in equation (12), the generatrix direction length y _m of the crowning, K _1, K ₂ ', can not be obtained unless given z _m. Therefore, it is difficult to design the crowning based on the equation (11). The coefficient K ₁ in equation (11), since hung on the load Q, can be interpreted as a ratio of the load Q as a physical sense, K ₂ ', the coefficients K ₁ defines a y _m Since the curvature of the crowning curve changes when it is changed, it can be interpreted geometrically as a parameter that determines the curvature of the crowning curve. On the other hand, the physical meaning of the coefficient K ₂ ′ is unclear. Therefore, it is necessary to eliminate the coefficient K ₂ ′ from the equation (11) and introduce a design parameter having a physical meaning.

Therefore, when the coefficient K ₂ ′ obtained from the equation (12) is substituted into the equation (11) and arranged, the following equation (13) is obtained.

Here, the proportion of generatrix direction length y _m of each crowning respect generatrix direction length a to the end of the effective contact portion from the origin is defined as _{K 2 (K 2 = y m} / a), y m = K _{When 2} a is substituted into equation (13) and 2K ₁ Q / πLE ′ = A, the above equation (8) is obtained.

The above formula (8) is the crowning formed toward the positive side in the generatrix direction using a yz coordinate system in which the generatrix of the cam follower on which the crowning is formed is the y-axis and the z-axis is in the generatrix orthogonal direction. The contour line in the axial direction cross section of is shown. In equation (8), the curvature K ₁ of the crowning curve, the ratio K ₂ generatrix direction length y _m of each crowning respect generatrix direction length a to the end of the effective contact portion from the origin, and the maximum drop amount of the crowning Other values (Q, L, E ′, a) excluding z _m are given as design conditions. In the case of full crowning or cut crowning and the length of the straight portion is preset, the value of K ₂ is also given as a design condition. Therefore, in order to design the crowning curve based on Expression (8), it is necessary to determine three design parameters K ₁ , K ₂ , z _m , or two design parameters K ₁ , z _m .

As a method for determining two or three design parameters in Expression (8), a numerical optimization method such as a gradient method, an annealing method, a genetic algorithm, a direct search method, or the like can be used. ). That is, at least one of the parameters K ₁ , K ₂ , and z _m is automatically optimized by a computer using an arbitrary optimization method.

  The gradient method, also known as the hill-climbing method or the gradient method, seeks the solution in the direction of the largest derivative (gradient) (for example, GN Vanderphan, “Numerical Optimization Techniques for Engineering Design: with Applications ”, McGraw-Hill, Inc., New York (1984)).

Simulated annealing (SA, Simulated Annealing) has been devised by annealing and analogy, is a technique to minimize the energy (e.g., WH Press, et al, Numerical Recipes in FORTRAN: the art of scientific computing, 2 nd ed., Cambridge University Press, Cambridge (1992)).

  Genetic Algorithm (GA) is a technique that models the process of biological evolution, and is also called an evolutionary algorithm (Eas, Evolutionary Algorithm) or evolutionary computation (Evolutionary Computation). Therefore, there is a merit that can be applied to multimodal functions (see, for example, DE Goldberg, Genetic Algorithms in Search, Optimization & Machine Learning, Addison-Wesley Publishing Company, Inc., Reading (1989)).

  The direct search method is an optimization method that uses only the value of the objective function without calculating the derivative when the calculation of the derivative is difficult. A representative direct search method is the Rosenbrock method. Rosenbrock's method is a method of finding an optimum value by rotating a vector in a search direction in a better direction (see, for example, H. Sugie et al., “Numerical calculation method by FORTRAN77”, Bafukan, 1986).

  In addition, some of the above numerical optimization methods are included, but linear programming, nonlinear programming, experiment planning, Monte Carlo method, and the like can be cited as optimization methods.

  As described above, various optimization methods have been proposed. However, since there is a merit that it is not necessary to obtain the gradient of the objective function, the optimization of the design parameter of Equation (8) uses the direct search method. It is preferable to employ one Rosenbrock method. The Rosenbrock method is generally dependent on the initial value, and it is necessary to give an appropriate initial value. Therefore, a range of design parameters estimated to include the optimum value, that is, an initial value search range is given, and an objective function is obtained for all combinations of design parameters obtained by dividing the initial value search range into a plurality. A combination of design parameters that optimizes the objective function is adopted as an initial value. The relationship between the design parameter and the objective function obtained when searching for the initial value can be used when a tolerance is given to the design parameter.

  As the objective function, use at least one of the maximum contact pressure applied to the inner ring raceway surface, outer ring raceway surface or roller rolling surface, Mises equivalent stress, Tresca equivalent stress, and rolling fatigue life. be able to. When the maximum contact pressure, Mises equivalent stress, or Tresca equivalent stress is used as an objective function, design parameters are determined so that these values are minimized. When the rolling fatigue life is an objective function, design parameters are determined so that the rolling fatigue life is maximized.

FIG. 10 shows a comparison between a simple arc-shaped crowning and the shape of the logarithmic crowning expressed by the equation (8), and FIG. 11 shows the axial surface pressure distribution. Here, misalignment is given, and logarithmic crowning design parameters K ₁ , K ₂ , and z _m are optimized by using a mathematical optimization method so that the maximum surface pressure is minimized. As shown in FIGS. 10 and 11, the maximum surface pressure is lower in the logarithmic crowning than in the arc crowning, although the drop amount at the end is smaller. Although the maximum surface pressure is used as the optimization objective function here, rolling fatigue life and internal stress can also be used.

  The drop amount given by the equation (8) does not need to be provided on one contact surface, and the sum of the drop amounts on the two contacting surfaces may be the drop amount of the equation (8).

K ₂ is Optimizing usually becomes a value of about 0.9. However, if there is a need for manufacturing, a value of 0 <K ₂ ≦ 1 may be arbitrarily given.

As shown in FIG. 12, when K ₁ and z _m are smaller than the optimum values, the maximum surface pressure is extremely large. This is due to an increase in surface pressure at the edge portion. However, in the case of a value larger than the optimum value, it increases only gradually. Therefore, when giving the tolerance, the optimum value of _{K 1 K 1} opt, the optimum value of _{z m} and _{z m opt, K 1 opt ≦} K 1 and may be set to _{z m} opt ≦ _{z m} (according Item 3).

  According to the present invention, the surface pressure between the cam and the cam follower becomes uniform in the axial direction, and the fatigue life is extended while the crowning is a slight machining amount.

  Embodiments of the present invention will be described below with reference to the drawings. The cam follower 4 for a rocker arm illustrated in FIG. 1A has a shaft 8 spanned between a pair of parallel yokes 6, and a roller 10 is rotatably supported on the shaft 8. The roller 10 is in contact with the cam 2 on its outer peripheral surface. Crowning is formed on the outer peripheral surface of the roller 10, and reference numeral 10a indicates crowning. FIG. 1B shows a state where the roller 10 is misaligned.

  FIG. 2 shows a y-axis in which the generatrix of the roller 10 is the y axis, the origin O is on the generatrix of the roller 10 at the center of the effective contact portion, and the z axis is in the generatrix orthogonal direction (radial direction) An example of the crowning 10a represented by the following formula (14) using a coordinate system is shown. The effective contact portion is a contact portion of the roller 10 when the cut crowning 10a is not formed on the roller 10. Further, since the crowning 10a of the roller 10 is normally formed line-symmetrically with respect to the z-axis passing through the central portion of the effective contact portion, only one crowning 10a is shown in FIG.

However, in the formula (14), A = 2K ₁ Q / πLE ′. Further, since the coordinates of the starting point O ₁ of the crowning 6a are (a−K ₂ a, 0), the range of y in the equation (14) is y> (a−K ₂ a).

In Expression (14), z (y) is a drop amount of the crowning 10 a at the position y in the generatrix direction of the roller 10. In Equation (14), Q is the load, L is the length in the bus contact direction of the effective contact portion, E ′ is the equivalent elastic modulus, and a is the length in the bus bar direction from the origin O to the end of the effective contact portion. These values are given as design conditions. In FIG. 2, since the origin O is located at the center of the effective contact portion, a = L / 2. Further, since the region from the origin O to the starting point O _{1 of the} crowning 10a is a straight portion formed in a cylindrical surface shape, z (y) = 0 when 0 ≦ y ≦ (a−K ₂ a). Become. However, when K ₂ = 1, since the starting point O ₁ coincides with the origin O, the expression (14) represents full crowning without a straight portion.

In Expression (14), K ₁ , K ₂ , and z _m are design parameters. The design parameter K ₁ means the magnification of the load Q, geometrically, the curvature of the crowning 10a. Design parameters K _2, which means the ratio of the generatrix direction length y _m of the crowning 10a against generatrix direction length a from the origin O to the end of the effective contact portions _{(K 2 = y m / a} ). The design parameter z _m means the drop amount at the end of the effective contact portion, that is, the maximum drop amount of the crowning 10a.

When a design condition such as a load Q and an appropriate design parameter K ₁ , K ₂ , z _m are given to the equation (14), one crowning curve is obtained, and one of the design parameters K ₁ , K ₂ , z _m is obtained. The crowning curve can be deformed by changing. Therefore, when the optimum design parameters K ₁ , K ₂ , and z _m are given, an optimum crowning curve is obtained in which the contact pressure of the roller 10 is almost uniform and no edge load occurs.

Hereinafter, optimization of design parameters K ₁ , K ₂ , and z _m when design conditions as shown in Table 1 are given will be described. The data in Table 1 is for the roller bearing disclosed in the previous application (Japanese Patent Application No. 2004-234780).

Various methods for optimizing the design parameters K ₁ , K ₂ , and z _m have been proposed. Here, the Rosenbrock method, which is one of direct search methods, is adopted, and the roller 10 is used as its objective function. The maximum contact pressure P _max is used.

Given the design conditions shown in Table 1, if the maximum contact pressure P _max is simply minimized, the maximum contact pressure P _max is determined for all combinations of the design parameters K ₁ , K ₂ , and z _m. However, if optimization is performed in consideration of the tilt gradient of the roller 10, K ₂ = 1 and the cut crowning 10a cannot be evaluated. In the cut crowning 10a of FIG. 2, the starting point O ₁ is in the region on the positive side of the origin O, so the range of K ₂ is 0-1. Therefore, here, in order to evaluate and examine the cut crowning, it is assumed that K ₂ is 0.5, the tolerance is 0.05, and the allowable range of K ₂ is 0.45 to 0.55.

3 to 5 show the maximum contact pressure P _max for each of the crowning curves obtained by changing the design parameters K ₁ and z _m when K ₂ = 0, 45, 0.50, and 0.55. The result is shown as an isobaric diagram. 3 to 5, the minimum value of the maximum contact pressure P _max is 3.486 GPa at the optimum point M shown in FIG. The values of the design parameters K ₁ and z _{m at} the optimum point M are K ₁ = 2.779 and z _m = 16.253 μm. Assuming that the maximum contact pressure P _{max at} the optimum point M is 1.05 times the allowable range, as shown in FIGS. 3 to 5, K ₁ = 2 to 3, K ₂ = 0.45 to 0.55, z _m = 16 to 38 μm can be selected as the tolerance range D of the design parameter. When the tolerance range D thus obtained is given to the design parameters K ₁ , K ₂ , and z _m of the equation (14), a suitable crowning curve is accommodated in the hatching region shown in FIG. In FIG. 6, a crowning curve indicated by a thick line is an optimum crowning curve obtained from the design parameters K ₁ , K ₂ , and z _{m at} the optimum point M.

As described above, when the crowning 10a of the roller 10 is designed by giving a suitable tolerance range to the design parameters K ₁ , K ₂ , and z _m of the equation (14), the contact pressure of the roller 10 becomes substantially uniform, and the roller 10 No edge loading occurs.

In the above-described embodiment, when the design parameters K ₁ and z _m are optimized with K ₂ = 1, the optimum full crowning with the origin O as the starting point of each crowning 10a and its tolerance range are included. Full crowning can be designed.

As mentioned above, although one embodiment of the crowning design method of the roller bearing according to the present invention has been described, the present invention is not limited to the above-described embodiment, and various modifications can be made. In the embodiment, the crowning 10a is represented using a yz coordinate system in which the origin O is at the center of the effective contact portion. However, as shown in FIG. 7A, the origin O is the center of the effective contact portion. Even for the position offset from C, the contour line of the crowning 10a can be expressed by the equation (14). In this case, the length a in the generatrix direction from the origin O to the end of the effective contact portion is a ≠ L / 2. If K ₂ > 1, the starting point coordinate O ₁ (a−K ₂ a, 0) of the crowning 10a is set on the negative side with respect to the origin O as shown in FIG.

In the above-described embodiment, the crowning 10a having line symmetry with respect to the z axis taken at the center of the effective contact portion has been described. However, the crowning may be non-line symmetrical with respect to the z axis. In this case, the design parameters K ₁ , K ₂ , and z _m of the equation (14) may be optimized independently for each crowning, and one crowning formed toward the positive side in the busbar direction is represented by the following equation: (15) and the other crowning formed toward the negative in the bus direction is expressed by the following equation (16). Design parameters K _1p , K _2p , z _mp in equation (15) and equation (16) The design parameters K _1n , K _2n , and z _{mn in FIG} .

Incidentally, a _p in equation (15) is a generatrix direction length from the origin O to the positive end of the effective contact portions, a _n in the formula (16), the negative end of the effective contact portion from the origin O Is the length in the direction of the bus. In addition, Equation (15) and Equation (16) use K _1p , K _2p , z _mp and K _1n , K _2n , z _mn as design parameter symbols, but are substantially the same as Equation (14). It is a formula.

According to Expression (15) and Expression (16), in addition to cut crowning and full crowning that are line-symmetric with respect to the z axis described in the above embodiment, for example, as shown in FIG. Full crowning of a non-linear object offset from the central portion C of the effective contact portion, or the offset distances of the starting points O ₁ and O ₂ from the central portion C of the effective contact portion are different as shown in FIG. 8B. Various crowning shapes, such as line-symmetric cut crowning, can be represented. Note that the crowning curves shown in FIGS. 8A and 8B include the design parameters K _1p , K _2p , and z _mp in Expression (15) and the design parameters K _1n , K _2n , and z _mn in Expression (16), K _1p ≠ K _1n, satisfies at least any one of _{K 2p a p ≠ K 2n a} n, z mp ≠ z mn. As described above, by using the equations (15) and (16), it is possible to design an optimal crowning and a suitable crowning included in the tolerance range regardless of whether it is line symmetric or non-line symmetric. .

(A) is sectional drawing of the cam follower which shows embodiment of this invention, (B) is the front view of the state which raise | generated the misalignment Yz coordinate diagram showing an example of crowning shape Yz coordinate diagram showing an example of change in curvature of positive side crowning when design parameter K _1p is changed Yz coordinate diagram showing another example of crowning shape Yz coordinate diagram showing another example of crowning shape Yz coordinate diagram showing another example of crowning shape Yz coordinate diagram showing another example of crowning shape Yz coordinate diagram showing another example of crowning shape A yz coordinate diagram showing an example of a conventional crowning shape Graph showing crowning shape Graph showing surface pressure distribution in the axial direction Graph showing the relationship between design parameters and maximum surface pressure

Explanation of symbols

2 Cam 4 Cam follower 6 Yoke 8 Shaft 10 Roller 10a Crowning

Claims (3)

A cam follower in which the sum of the drop amount of crowning formed on the contact surface of the cam or roller or both is given by the formula (I).
The cam follower according to claim 1, wherein at least one of the parameters K ₁ , K ₂ and z _{m in} the formula (I) is automatically optimized by a computer using an arbitrary optimization method. When the optimum value of K ₁ and _{K 1} opt, the optimum value of z _m and _{z m} opt, the cam follower of claim 1, relation holds as represented by _{K 1} opt ≦ _{K 1} and _{z m} opt ≦ _{z m.}