Sliding mechanism

Abstract

To provide a sliding mechanism with reduced friction. [Solution] The sliding mechanism comprises a ring 20 and a disc 10 that slide against each other, and is configured such that lubricating oil can be interposed between a first sliding surface 20A, which is the sliding surface of the ring 20 facing the disc 10, and a second sliding surface 10A, which is the sliding surface of the disc 10 facing the ring 20. The first sliding surface 20A has a undulation 21. The undulation 21 includes an inclination 21A such that the distance between the first sliding surface 20A and the second sliding surface 10A decreases as it moves in the sliding direction D of the ring 20 relative to the disc 10.

Description

Technical Field

[0001] The present invention relates to a sliding mechanism including a first member and a second member that slide relative to each other.

Background Art

[0002] The sliding mechanism described in Patent Document 1 includes a plurality of dimples having a dimple opening diameter of 5 μm to 50 μm and a dimple depth of 0.5 μm to 10.0 μm on the sliding surface of at least one of a pair of sliding members. The ratio of the area of the plurality of dimples to the area of the entire sliding surface is 10% to 30%. The lubricating oil intervening between the pair of sliding members contains organic molybdenum.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] On the other hand, since the demand for extending the service life of the sliding mechanism is increasing, reduction of friction is still required in the above-described sliding mechanism.

Means for Solving the Problems

[0005] A sliding mechanism that solves the above problems comprises a first member and a second member that slide against each other, and is configured such that lubricating oil can be interposed between a first sliding surface, which is the sliding surface of the first member facing the second member, and a second sliding surface, which is the sliding surface of the second member facing the first member, and the sliding mechanism is configured such that lubricating oil can be interposed between them, and the sliding length is defined as the length in the sliding direction in the portion where the distance between the first sliding surface and the second sliding surface that slides in the sliding direction via the lubricating oil is 10 μm or less, and the first sliding surface contains at least one convex peak and one concave peak of a undulation that are aligned with the sliding direction of the first member relative to the second member and have wavelength components shorter than the sliding length, and the undulation is configured such that the surface roughness of the first sliding surface in the sliding direction is defined as σ, and the distance between the convex peak and the concave peak is defined as the height of the undulation, and the value obtained by adding 3σ to the height of the undulation is 3.3σ or more and 30σ or less.

[0006] According to the above configuration, when the first member slides against the second member, an oil film reaction force is generated between the first and second members due to the wedge effect caused by the lubricating oil interposed between the two members. Regarding this wedge effect, if the undulation is configured such that the value obtained by adding 3σ to the undulation height is 3.3σ or more and 30σ or less, the oil film reaction force will be high. As a result, friction between the first and second members will be reduced.

[0007] In the sliding mechanism, the undulation may be configured such that the value obtained by adding 3σ to the height of the undulation is 3.9σ or more and 15σ or less. In the sliding mechanism, the undulation may be configured such that the value obtained by adding 3σ to the height of the undulation is 6.6σ or greater.

[0008] In the sliding mechanism, the sliding length may be between 0.1 mm and 50 mm. Furthermore, in the sliding mechanism, two undulations may be included within the sliding length. In the sliding mechanism, the undulation includes a first convex peak which is adjacent to the concave peak in the sliding direction, a second convex peak which is adjacent to the concave peak and is located in the opposite direction to the first convex peak with respect to the concave peak in the sliding direction, a first inclination in which the distance between the first sliding surface and the second sliding surface decreases as it moves from the concave peak toward the first convex peak, and a second inclination in which the distance between the first sliding surface and the second sliding surface decreases as it moves from the concave peak toward the second convex peak, and a recess in which the lubricating oil accumulates may be provided in at least one of the first inclination and the second inclination.

[0009] In the sliding mechanism, a plurality of recesses are provided, and the total opening area of ​​the plurality of recesses may be 5% to 15% of the area of ​​the first sliding surface. [Effects of the Invention]

[0010] According to the present invention, friction on the sliding surface can be reduced by the reaction force of the oil film. [Brief explanation of the drawing]

[0011] [Figure 1] Figure 1 is a perspective view showing the configuration of one embodiment of a sliding mechanism. [Figure 2] Figure 2 is a plan view showing the sliding surface of the ring. [Figure 3] Figure 3 is a graph showing the waviness curve of the sliding surface. [Figure 4] Figure 4 is a table showing the relationship between surface roughness and cutoff value. [Figure 5] Figure 5 is a schematic diagram illustrating the oil film reaction force in a sliding mechanism. [Figure 6] Figure 6 is a schematic diagram showing a sliding mechanism with a single undulation on the sliding surface. [Figure 7] Figure 7 is a schematic diagram showing a sliding mechanism with two undulations on the sliding surface. [Figure 8] Figure 8 is a graph showing the dependence of Cp on the gap ratio m. [Figure 9]Figure 9 is a graph showing a ring curve and a disk curve. [Figure 10] Figure 10 is a graph showing a composite curve. [Figure 11] Figure 11 is a table showing oil film reaction forces in the sliding mechanisms of each calculation example. [Figure 12] Figure 12 is an operational diagram showing a sliding mechanism having two undulations on the sliding surface. [Figure 13] Figure 13 is an operational diagram showing a sliding surface having undulations and a reservoir groove. [Figure 14] Figure 14 is an operational diagram showing a sliding surface having undulations and dimples. [Figure 15] Figure 15 is a table showing the surface properties of the sliding surfaces in each test example. [Figure 16] Figure 16 is a graph showing the coefficient of friction with respect to the rotational speed of the sliding mechanism. [Figure 17] Figure 17 is a diagram showing an example of applying the sliding mechanism to a bearing mechanism. [Figure 18] Figure 18 is a diagram showing an example of applying the sliding mechanism to a speed reduction mechanism. [Figure 19] Figure 19 is an enlarged view of a part of Figure 18. [Figure 20] Figure 20 is a diagram showing an example of applying the sliding mechanism to a hydraulic pump. [Figure 21] Figure 21 is a diagram showing a curve for analyzing the sliding surface. [Figure 22] Figure 22 is a diagram showing the curve for analyzing the sliding surface divided into a plurality of motifs. [Figure 23] Figure 23 is a diagram showing an envelope curve. [Figure 24] Figure 24 is a diagram showing the analysis result of Fourier transform.

Embodiments for Carrying Out the Invention

[0012] An embodiment of the sliding mechanism will be described below with reference to Figures 1 to 16. The sliding mechanism comprises a first member and a second member that slide against each other. The undulation of the first sliding surface of the first member includes a slope such that the distance between the first sliding surface and the second sliding surface of the second member decreases as it moves in the sliding direction. To help understand the friction suppression achieved by the undulation of the sliding surfaces, this embodiment first shows an example in which the second sliding surface is a mirror surface with extremely low flatness and planarity. Next, the case in which the first sliding surface and the second sliding surface each have undulations will be described.

[0013] (Sliding mechanism) As shown in Figure 1, the sliding mechanism is applied to the ring-on-disk test. The sliding mechanism comprises a disc 10, which is an example of a second member, and a ring 20, which is an example of a first member. The disc 10 and ring 20 are made of, for example, metal. Hereinafter, the direction along the rotation axis of the ring 20 will be simply referred to as the axial direction. The circumferential direction around the rotation axis of the ring 20 will be simply referred to as the circumferential direction. The radial direction around the rotation axis of the ring 20 will be simply referred to as the radial direction.

[0014] The disc 10 is fixed to a device equipped with a sliding mechanism. The first sliding surface 20A, which is the lower surface of the ring 20, rests on the second sliding surface 10A, which is the upper surface of the disc 10. A predetermined amount of lubricating oil is interposed between the first sliding surface 20A and the second sliding surface 10A. In the ring-on-disk test, the ring 20 is rotated around its central axis while a load F is applied to the ring 20 along its axial direction. As the ring 20 rotates, the first sliding surface 20A slides against the second sliding surface 10A. Hereinafter, the sliding direction of the first sliding surface 20A relative to the second sliding surface 10A will simply be referred to as the sliding direction D.

[0015] Both sliding surfaces 10A and 20A intersect the rotation axis of the ring 20. More specifically, both sliding surfaces 10A and 20A are approximately perpendicular to the rotation axis of the ring 20. Both sliding surfaces 10A and 20A face each other in the axial direction. Here, the distance between the first sliding surface 20A and the second sliding surface 10A in the axial direction is 10 μm or less at any point on the first sliding surface 20A in both the radial and circumferential directions. In other words, both sliding surfaces 10A and 20A are configured such that the distance between them is 10 μm or less at any position. And both sliding surfaces 10A and 20A slide while maintaining a distance of 10 μm or less from each other at any position. Note that the distance between the first sliding surface 20A and the second sliding surface 10A relates to the axial direction and, consequently, the direction perpendicular to the second sliding surface 10A. In the following, the distance between the first sliding surface 20A and the second sliding surface 10A may simply be referred to as the distance between the two sliding surfaces 10A and 20A.

[0016] As shown by the shading of the dots in Figure 2, the first sliding surface 20A has irregularities formed by processing. That is, in Figure 2, the areas with dark dots are located closer to the viewer than the areas with light dots. In other words, the areas with dark dots bulge out towards the second sliding surface 10A more than the areas with light dots. In Figure 2, the areas with the darkest dots and the areas with lighter dots alternate along the sliding direction D. The area with the darkest dots and the areas with lighter dots adjacent to it constitute a single undulation. That is, in the example shown in Figure 2, the first sliding surface 20A has a first undulation 21 and a second undulation 22. For example, the first undulation 21 and the second undulation 22 are arranged at equal intervals along the sliding direction D. Details such as the dimensions of the irregularities treated as "undulations" in this embodiment will be described later. For example, the undulation can be obtained by buffing the first sliding surface 20A while rotating the ring 20. For example, the undulation can also be obtained by laser processing using a phetosecond laser, or by etching utilizing corrosive action. For example, the undulation can also be obtained by surface processing that combines etching with lithography, which involves partial exposure by masking.

[0017] (Evaluation process) The surface properties of the first sliding surface 20A will be described below. In describing these surface properties, we consider an evaluation path PA, which is a specific path along the first sliding surface 20A, as shown in Figure 2. The evaluation path PA is a single circle virtually drawn along the sliding direction D. In this embodiment, corresponding to the first sliding surface 20A sliding in the rotational direction, the evaluation path PA is a circle centered on the rotational center of the ring 20.

[0018] The first sliding surface 20A has a first undulation 21 and a second undulation 22 within the evaluation path PA. In other words, the evaluation path PA can be described as a path that passes through both undulations 21 and 22 and extends in the sliding direction D (circumferential direction in this embodiment). In this embodiment, both undulations 21 and 22 are located approximately in the radial center of the first sliding surface 20A. The evaluation path PA has a diameter approximately half the outer diameter of the first sliding surface 20A. The first undulation 21 and the second undulation 22 are arranged at equal intervals along the sliding direction D.

[0019] Note that multiple evaluation paths PA may be set. For example, the first swell 21 and the second swell 22 may be formed at different radial positions. Multiple evaluation paths PA with different radii may be set to match these differences in swell positions. In short, it is sufficient that the evaluation paths PA are set to pass through at least one swell.

[0020] (Wavy curve) Figure 3 shows the cross-sectional curve of the evaluation path PA. The cross-sectional curve shows the height of the first sliding surface 20A at each position in the evaluation path PA, for each phase angle, which is the central angle of the ring 20. In other words, the horizontal axis in Figure 3 represents the phase angle. The phase angle is set to advance in the sliding direction D. The vertical axis in Figure 3 represents the depth of the depression of the first sliding surface 20A from the reference position. In other words, in Figure 3, the larger the positive value on the vertical axis, the greater the distance between the first sliding surface 20A and the second sliding surface 10A. Put another way, in Figure 3, the distance between the two sliding surfaces 10A and 20A becomes shorter towards the bottom. The height of "0" indicating the reference position is determined in conjunction with the observation position of the measuring instrument and does not necessarily coincide with the lowest end of the first sliding surface 20A, i.e., the position of the flat part on the first sliding surface 20A where no depression is formed. Note that Figure 3 is, strictly speaking, a undulation curve obtained by filtering the cross-sectional curve, as described later.

[0021] The cross-sectional curve is obtained by setting the sliding direction D in the measurement direction and following a method compliant with JIS B 0601:2013 and JIS B 0633:2001. That is, the cross-sectional curve is the contour of the first sliding surface 20A when the ring 20 is cut axially along the evaluation path PA. For example, the cross-sectional curve can be obtained from the measurement results of a white light interference microscope NewView8300 (manufactured by Zygo). White light interference microscopes are suitable for obtaining the surface properties of the entire first sliding surface 20A because they can observe a wide area quickly.

[0022] The cross-sectional curve of the evaluation path PA includes roughness and waviness components among the irregularities formed on the first sliding surface 20A. The waviness component is an irregularity with wavelength components longer than those of the roughness component. The roughness component and the waviness component can be separated by applying filtering to the cross-sectional curve to extract a specific wavelength range. The roughness component is separated from the cross-sectional curve as a roughness curve by applying a first cutoff value λc as a high-pass filter to the cross-sectional curve. The waviness component is separated from the cross-sectional curve by applying a first cutoff value λc as a low-pass filter to the cross-sectional curve, and also by applying a second cutoff value λf, which is greater than the first cutoff value λc, as a high-pass filter to the cross-sectional curve. In other words, "waviness" refers to an irregularity in the cross-sectional curve obtained by an evaluation device capable of evaluating minute surface irregularities, which has wavelength components longer than the first cutoff value λc and shorter than the second cutoff value λf. In the following explanation, the curve separated using both cutoff values ​​λc and λf will be referred to as the waviness curve.

[0023] In this embodiment, for the sake of ease of understanding, we will use as an example a case where the irregularities indicating "undulation" are clearly visible in the undulation curve. For example, in the undulation curve shown in Figure 3, it can be visually observed that there are two undulations, with the valleys appearing near 120 degrees and 300 degrees in the circumferential direction serving as the boundary.

[0024] (First cutoff value) The first cutoff value λc is the boundary value between the roughness component and the waviness component. The first cutoff value λc is obtained by a method conforming to JIS B 0633:2001. Figure 4 shows reference values ​​for the first cutoff value λc. The first cutoff value λc is predetermined in correspondence with the arithmetic mean roughness Ra. The first cutoff value λc is determined for each range of arithmetic mean roughness Ra.

[0025] The arithmetic mean roughness Ra is obtained from the roughness curve using a method compliant with JIS B 0601:2013. Specifically, the arithmetic mean roughness Ra is obtained as the average value of the height of the roughness curve at a given length, when a first cutoff value λc is set for the given length. The arithmetic mean roughness Ra represents the surface roughness of the first sliding surface 20A within the range of the first cutoff value λc in the sliding direction D.

[0026] When separating the waviness curve from the cross-sectional curve, an appropriate value is selected from among the multiple first cutoff values ​​λc shown in Figure 4, corresponding to the roughness of the first sliding surface 20A. For example, if a desired arithmetic mean roughness Ra exists for the first sliding surface 20A, depending on the specifications of the application, the first cutoff value λc is set to correspond to the desired arithmetic mean roughness Ra. For example, if the desired arithmetic mean roughness Ra is 0.01 μm, the first cutoff value λc is set to 0.08 mm from the reference values ​​in Figure 4. For example, even if the desired arithmetic mean roughness Ra is a different value, the corresponding first cutoff value λc is selected from Figure 4. For example, the desired arithmetic mean roughness Ra can be obtained using a stylus-type roughness and shape measuring instrument SEF800-N (manufactured by Kosaka Laboratory). Although the measurement range of the stylus-type roughness and shape measuring instrument is localized, it can provide precise information about roughness.

[0027] Furthermore, when selecting the first cutoff value λc, the maximum height roughness Rz can be used instead of the arithmetic mean roughness Ra. The maximum height roughness Rz is obtained from the roughness curve using a method compliant with JIS B 0601:2013. That is, it is obtained as the average value of the height of the roughness curve at the reference length. The maximum height roughness Rz is obtained as the sum of the maximum peak height and the maximum valley depth in the roughness curve at the reference length when the first cutoff value λc is set for the reference length.

[0028] (Second cutoff value) The second cutoff value λf is the boundary value between the undulation component and wavelength components longer than the undulation component. More specifically, the second cutoff value λf is the sliding length R, which will be explained later. As shown in JIS B 0633:2001, even when the sliding length R is set as the second cutoff value λf, the filtered undulation curve will not include the component of the sliding length R, but will only extract wavelength components shorter than the sliding length R. This is because the amplitude transmission rate related to filtering is attenuated in the vicinity of the second cutoff value λf. Alternatively, wavelength components shorter than the sliding length R can be separated from the cross-sectional curve by setting the second cutoff value λf to a value slightly smaller than the sliding length R. In short, it is sufficient to separate wavelength components shorter than the sliding length R from the cross-sectional curve.

[0029] The sliding length R is the length in the sliding direction D in the portion where the distance between the first sliding surface 20A and the second sliding surface 10A, which slide in the sliding direction D via lubricant, is 10 μm or less. As described above, in this embodiment, the distance between the first sliding surface 20A and the second sliding surface 10A is 10 μm or less at any position. In relation to this, in this embodiment, the length of the evaluation path PA becomes the sliding length R. The sliding length R can also be said to be the length over which the first sliding surface 20A slides against the second sliding surface 10A during one rotation of the ring 20. When the operation of one rotation of the ring 20 is considered as a unit operation, the sliding length R can also be said to be the length over which both sliding surfaces 10A and 20A slide during one period of the unit operation. Note that the length of the evaluation path PA changes depending on the radial position of the first sliding surface 20A. Therefore, the sliding length R changes depending on the evaluation position. The sliding length R is, for example, about 10 mm to 50 mm.

[0030] Based on the first cutoff value λc and the second cutoff value λf described above, if the arithmetic mean roughness Ra of the first sliding surface 20A is greater than 0.006 μm and less than or equal to 0.02 μm, then the "undulation" is an irregularity having wavelength components longer than 0.08 mm and shorter than the sliding length R.

[0031] Similarly, if the arithmetic mean roughness Ra of the first sliding surface 20A is greater than 0.02 μm and 0.1 μm or less, the "undulation" is an irregularity having wavelength components longer than 0.25 mm and shorter than the sliding length R. If the arithmetic mean roughness Ra of the first sliding surface 20A is greater than 0.1 μm and 2 μm or less, the "undulation" is an irregularity having wavelength components longer than 0.8 mm and shorter than the sliding length R. If the arithmetic mean roughness Ra of the first sliding surface 20A is greater than 2 μm and 10 μm or less, the "undulation" is an irregularity having wavelength components longer than 2.5 mm and shorter than the sliding length R. If the arithmetic mean roughness Ra of the first sliding surface 20A is greater than 10 μm and 80 μm or less, the "undulation" is an irregularity having wavelength components longer than 8 mm and shorter than the sliding length R.

[0032] As shown in Figure 3, the first sliding surface 20A has two "undulations" that satisfy one of these conditions. Note that it is sufficient for the first sliding surface 20A to have one or more "undulations," and the number of "undulations" is not limited to two.

[0033] (Details of the swell) As shown in Figure 3, the first swell 21 has a concave peak 21m, convex peaks 21p and 21q, and a first slope 21A and a second slope 21B.

[0034] The concave peak 21m is the most recessed point in the first undulation 21 located on the evaluation path PA. In other words, the concave peak 21m is the point in the first undulation 21 located on the evaluation path PA that is furthest from the second sliding surface 10A. The distance between the concave peak 21m and the second sliding surface 10A is 10 μm or less. That is, the undulation of the first sliding surface 20A is configured such that the maximum distance between the two sliding surfaces 10A and 20A is 10 μm or less.

[0035] The convex peaks 21p and 21q correspond to the circumferential ends of the first undulation 21. The convex peaks 21p and 21q are located near the second sliding surface 10A in the first undulation 21. More specifically, at least one of the convex peaks 21p and 21q is the closest point in the first undulation 21 to the second sliding surface 10A. For the sake of explanation, of the two convex peaks 21p and 21q, the one located in the sliding direction D relative to the concave peak 21m will be called the first convex peak 21p, and the one located in the opposite direction to the sliding direction D relative to the concave peak 21m will be called the second convex peak 21q. In other words, the first convex peak 21p is a convex peak adjacent to the concave peak 21m in the sliding direction D. The second convex peak 21q is a convex peak adjacent to the concave peak 21m, located in the opposite direction to the first convex peak 21p relative to the concave peak 21m in the sliding direction D. Note that the height positions of the biconvex peaks 21p and 21q may be the same or different.

[0036] Both inclined surfaces 21A and 21B are positioned on either side of the concave peak 21m. The first inclined surface 21A connects the concave peak 21m and the first convex peak 21p. In this case, the first circumferential end of the first inclined surface 21A is the concave peak 21m, and the second circumferential end of the first inclined surface 21A is the first convex peak 21p. The first end of the first inclined surface 21A is the point furthest from the second sliding surface 10A, and the second end of the first inclined surface 21A is the point closest to the second sliding surface 10A.

[0037] The first inclination 21A is inclined such that the distance between the first sliding surface 20A and the second sliding surface 10A decreases as it moves from the concave peak 21m towards the first convex peak 21p. Note that the first inclination 21A only needs to be inclined as a whole, and may include parts where the distance is constant locally. The first inclination 21A is located in the sliding direction D with respect to the concave peak 21m. The first inclination 21A is located in the direction opposite to the sliding direction D with respect to the first convex peak 21p.

[0038] The second inclination 21B connects the concave peak 21m and the second convex peak 21q. The second inclination 21B is inclined such that the distance between the first sliding surface 20A and the second sliding surface 10A decreases as it moves from the concave peak 21m towards the second convex peak 21q. Note that the second inclination 21B only needs to be inclined as a whole, and may include parts where the distance is constant locally. The second inclination 21B is located in the opposite direction to the sliding direction D with respect to the concave peak 21m. The second inclination 21B is located in the sliding direction D with respect to the second convex peak 21q.

[0039] In this embodiment, the circumferential lengths of both inclined surfaces 21A and 21B, in other words, the phase angles occupied by both inclined surfaces 21A and 21B, are set to be the same. However, this is not limited to this, and the circumferential lengths of both inclined surfaces 21A and 21B may be different.

[0040] As shown in Figure 3, the second swell 22 has a concave peak 22m, convex peaks 22p and 22q, and a first slope 22A and a second slope 22B. The concave peak 22m is the most recessed point in the second swell 22 that lies on the evaluation path PA. In other words, the concave peak 22m is the point in the second swell 22 that lies on the evaluation path PA and lies furthest from the second sliding surface 10A. The distance between the concave peak 22m and the second sliding surface 10A is 10 μm or less, similar to the case of the concave peak 21m of the first swell 21.

[0041] The convex peaks 22p and 22q correspond to the circumferential ends of the second undulation 22. The convex peaks 22p and 22q are located near the second sliding surface 10A in the second undulation 22. More specifically, at least one of the convex peaks 22p and 22q is the closest point in the second undulation 22 to the second sliding surface 10A. For the sake of explanation, of the two convex peaks 22p and 22q, the one located in the sliding direction D relative to the concave peak 22m will be called the first convex peak 22p, and the one located in the opposite direction to the sliding direction D relative to the concave peak 22m will be called the second convex peak 22q. In other words, the first convex peak 22p is a convex peak adjacent to the concave peak 22m in the sliding direction D. The second convex peak 22q is a convex peak adjacent to the concave peak 22m, located in the opposite direction to the first convex peak 22p relative to the concave peak 22m in the sliding direction D. Note that the height positions of the biconvex peaks 22p and 22q may be the same or different.

[0042] In this embodiment, both swells 21 and 22 are arranged continuously in the circumferential direction. As a result, the first convex peak 21p of the first swell 21 and the second convex peak 22q of the second swell 22 are at the same position, and the first convex peak 22p of the second swell 22 and the second convex peak 21q of the first swell 21 are at the same position.

[0043] The two inclined surfaces 22A and 22B of the second undulation 22 are located on both sides of the concave peak 22m. The first inclined surface 22A connects the concave peak 22m and the first convex peak 22p. In this case, the first circumferential end of the first inclined surface 22A is the concave peak 22m, and the second circumferential end of the first inclined surface 22A is the first convex peak 22p. The first end of the first inclined surface 22A is the point furthest from the second sliding surface 10A, and the second end of the first inclined surface 22A is the point closest to the second sliding surface 10A.

[0044] The first inclination 22A is inclined such that the distance between the first sliding surface 20A and the second sliding surface 10A decreases as it moves from the concave peak 22m towards the first convex peak 22p. Note that the first inclination 22A only needs to be inclined as a whole, and may include parts where the distance is constant locally. The first inclination 22A is located in the sliding direction D with respect to the concave peak 22m. The first inclination 22A is located in the direction opposite to the sliding direction D with respect to the first convex peak 22p.

[0045] The second inclination 22B connects the concave peak 22m and the second convex peak 22q. The second inclination 22B is inclined such that the distance between the two sliding surfaces 10A and 20A decreases as it moves from the concave peak 22m towards the second convex peak 22q. Note that the second inclination 22B only needs to be inclined as a whole, and may include parts where the distance is constant locally. The second inclination 22B is located in the opposite direction to the sliding direction D with respect to the concave peak 22m. The second inclination 22B is located in the sliding direction D with respect to the second convex peak 22q.

[0046] In this embodiment, the circumferential lengths of both inclined surfaces 22A and 22B, in other words, the phase angles occupied by both inclined surfaces 22A and 22B, are set to be the same. However, this is not limited to this, and the circumferential lengths of both inclined surfaces 22A and 22B may be different.

[0047] In the undulation curve obtained from the cross-sectional curve of the evaluation path PA, the phase angle of the portion corresponding to the first undulation 21 is the first phase angle θ1. In the undulation curve obtained from the cross-sectional curve of the evaluation path PA, the phase angle of the portion corresponding to the second undulation 22 is the second phase angle θ2 (= 360° - first phase angle θ1). In this embodiment, both phase angles θ1 and θ2 are the same. Focusing on this point, both undulations 21 and 22 in this embodiment can be said to be periodic irregularities having a phase angle obtained by dividing 360° by the number of undulations.

[0048] (Oil film reaction force) Both undulations 21 and 22 serve to reduce friction between the two sliding surfaces 10A and 20A. This function will be explained using the first undulation 21 as an example. As described above, in the first undulation 21, the first inclination 21A is inclined with respect to the second sliding surface 10A in the sliding direction D. As a result, as shown in Figure 5, the first inclination 21A forms a wedge shape that shortens the distance between the second sliding surface 10A and the first sliding surface 20A as the sliding direction D approaches. When such a wedge shape is formed, the lubricating oil between the second sliding surface 10A and the first sliding surface 20A is drawn into the minimum gap between the first sliding surface 20A and the second sliding surface 10A as the ring 20 rotates, exhibiting a so-called wedge effect. This wedge effect generates an oil film reaction force P that separates the first sliding surface 20A from the second sliding surface 10A. The minimum gap between the first sliding surface 20A and the second sliding surface 10A is located at the position where the distance to the second sliding surface 10A is shortest on the first inclination 21A, i.e., at the first convex peak 21p. In Figure 5, the flow of lubricating oil is indicated by the symbol K.

[0049] As shown in equation (1) below, the oil film reaction force P acting on the first sliding surface 20A from the lubricating oil is derived from the gap ratio m, outlet distance h2, wedge distance L, viscosity μ of the lubricating oil, sliding speed U, and distributed constant Cp. The gap ratio m is the ratio of the inlet distance h1 to the outlet distance h2, as shown in equation (2). The distributed constant Cp is derived by applying the gap ratio m to equation (3) below. The oil film reaction force P derived from equation (1) is preferably large from the viewpoint of suppressing friction, and more preferably exceeds the load F. When the oil film reaction force P exceeds the load F, fluid lubrication between the disc 10 and the ring 20 greatly reduces friction.

[0050]

number

[0051] The wedge distance L is the length in the sliding direction D from the concave peak 21m to the first convex peak 21p. In other words, the wedge distance L is the circumferential length of the first incline 21A. If the first convex peak 21p is the point in the first undulation 21 closest to the second sliding surface 10A, then the wedge distance L can also be said to be the length in the sliding direction D between the point in the first undulation 21 where the distance to the second sliding surface 10A is longest and the point where the distance to the second sliding surface 10A is shortest.

[0052] Note that equation (1) is strictly speaking a formula for calculating the oil film reaction force P assuming that the two sliding surfaces 10A and 20A are rectangular in shape. In this embodiment, a portion of the circumferential direction of the ring-shaped first sliding surface 20A, i.e., the first inclination 21A, is approximately considered as a rectangle, and the oil film reaction force P is calculated from equation (1). Also, equation (1) is a formula for calculating the oil film reaction force P for a single wedge. If there are multiple wedges on the evaluation path PA, the total oil film reaction force P can be obtained by deriving the oil film reaction force P for each wedge from equation (1) and adding them together.

[0053] (Oil film reaction force and swell distance) As can be seen from equation (1), the oil film reaction force P is a value that reflects the magnitude of the undulation distance L. The undulation distance L is related to the number of undulations present on the first sliding surface 20A. The following describes the preferred number of undulations for obtaining a high oil film reaction force P.

[0054] As shown in Figure 6, if only the first undulation 21 is present in the evaluation path PA, only the first incline 21A generates a wedge effect within the first sliding surface 20A. The wedge distance L of this first incline 21A is the circumferential length of the first incline 21A. Assuming that the circumferential lengths of both inclines 21A and 21B of the first undulation 21 are the same, the wedge distance L corresponds to half of the sliding length R. In other words, if the length of the sliding length R is R, then the wedge distance L is R / 2.

[0055] As shown in Figure 7, when a first undulation 21 and a second undulation 22 are present in the evaluation path PA, both the first incline 21A of the first undulation 21 and the first incline 22A of the second undulation 22 generate a wedge effect within the first sliding surface 20A. Assuming that the circumferential length of all inclines is the same, the wedge distance L corresponds to 1 / 4 of the sliding length R. In other words, when the length of the sliding length R is R, the wedge distance L is R / 4.

[0056] The oil film reaction force P is proportional to the square of the wedge distance L, as shown in equation (1). Therefore, if we consider the oil film reaction force P1 when there is only one swell in the evaluation path PA, then when there are two swells in the evaluation path PA, the oil film reaction force P per swell will be P2 (= P1 × 1 / 4). In other words, the more swells there are, the lower the oil film reaction force P per swell becomes. As mentioned above, when there are multiple wedges in the evaluation path PA, the oil film reaction force P for the entire evaluation path PA is the sum of the oil film reaction forces P of each swell. Therefore, when there are two swells in the evaluation path PA, the total oil film reaction force P is P1 × 1 / 2. In other words, the more swells there are, the lower the oil film reaction force P becomes even when considering the entire evaluation path PA. Therefore, from the viewpoint of increasing the oil film reaction force P, it is preferable to have fewer undulations. For example, there are two undulations per sliding length R.

[0057] Furthermore, if there are multiple swells within the evaluation path PA, and the wedge distances L of each swell are different from each other, then at least one swell distance L may be greater than or equal to the sliding length R / 6, and may also be greater than or equal to the sliding length R / 4.

[0058] (Oil film reaction force and inlet distance) This section explains the conditions for the inlet distance h1 necessary to obtain a high oil film reaction force P. As a prerequisite, the relationship between the distributed constant Cp and the gap ratio m is explained. Figure 8 shows the theoretical relationship between the distributed constant Cp and the gap ratio m obtained from equation (3). As shown in equation (1), the larger the distributed constant Cp, the larger the oil film reaction force P; therefore, a large distributed constant Cp is preferable from the viewpoint of suppressing friction.

[0059] As shown in Figure 8, the distribution constant Cp exhibits a unimodal distribution with respect to the gap ratio m, with a maximum value when the gap ratio m is around 2. When the pair of the gap ratio m and the distribution constant Cp obtained from it is denoted as [m,Cp], the distribution constant Cp increases sharply with increasing gap ratio m, passing through [1.1,0.049] and [1.3,0.10]. The distribution constant Cp has a maximum value at [2.19,0.16] and decreases exponentially with increasing gap ratio m, passing through [5.0,0.11] and [10,0.049].

[0060] From the viewpoint of obtaining a distribution constant Cp of 0.049 or higher, the gap ratio m is preferably 1.1 or more and 10 or less, more preferably 1.3 or more and 5 or less, and even more preferably 2.2 or more. Also, as mentioned above, since the exit distance h2 is usually considered to be 3σ, the gap ratio m derived by equation (2) is considered to be the entrance distance h1 / 3σ. For this reason, the entrance distance h1 is preferably 3.3 times (=1.1×3σ) or more and 30 times (=10×3σ) or less the arithmetic mean roughness Ra in the evaluation path PA. Furthermore, the entrance distance h1 is more preferably 3.9 times (=1.3×3σ) or more and 15 times (=5×3σ) or less the arithmetic mean roughness Ra in the evaluation path PA, and even more preferably 6.6 times (=2.2×3σ) or more.

[0061] The first swell 21 is constructed to satisfy these conditions for the inlet distance h1. That is, as shown in Figure 5, the height of the first convex peak 21p relative to the concave peak 21m is defined as the swell height h3. The swell height h3 is the distance between the first convex peak 21p and the concave peak 21m in the axial direction and thus perpendicular to the second sliding surface 10A. The swell height h3 can also be described as the difference in height between the two ends of the first incline 21A. As shown in Figure 5, the inlet distance h1 depends on the swell height h3, and more specifically, it is the value obtained by adding the outlet distance h2 to the swell height h3.

[0062] In this configuration, the first swell 21 is configured to satisfy the following height condition. That is, when the arithmetic mean roughness Ra is σ, the height condition is such that, considering that the exit distance h2 is usually 3σ, the sum of the swell height h3 and 3σ is between 3.3 and 30 times the arithmetic mean roughness Ra. A more preferred aspect of the height condition is that the above sum is between 3.9 and 15 times the arithmetic mean roughness Ra, and more specifically, that the sum is 6.6 times or more.

[0063] Furthermore, it is preferable that the second swell 22, like the first swell 21, be configured to satisfy the above height conditions. However, this is not limited to this, and instead of each of the swells 21 and 22 satisfying the height conditions, one swell height h3 representing both swells 21 and 22 may be defined, and the first sliding surface 20A may be configured such that this representative height satisfies the height conditions. An example of a representative height is the average value of each swell height h3, or the higher value among the each swell height h3. A representative height can be defined in the same manner if there are three or more swells on the evaluation path PA.

[0064] As described above, multiple evaluation paths PA with different diameters may be set on the first sliding surface 20A. The first sliding surface 20A may be configured such that the average value of the waviness height h3 of each evaluation path PA satisfies the height condition. When setting multiple evaluation paths PA, for example, it is conceivable to set three evaluation paths PA as follows. Here, the value 10% of the value obtained by subtracting the inner diameter from the outer diameter of the first sliding surface 20A is called the first value. The first evaluation path PA is a path near the inner peripheral edge of the ring-shaped first sliding surface 20A. Specifically, the first evaluation path PA is a virtual circle whose diameter is the sum of the inner diameter of the first sliding surface 20A and the first value. The second evaluation path PA is a path in the center between the inner and outer peripheral edges of the first sliding surface 20A. Specifically, the second evaluation path PA is a virtual circle whose diameter is the sum of the inner diameter of the first sliding surface 20A and five times the first value. The third evaluation path PA is the path near the outer edge of the first sliding surface 20A. Specifically, the third evaluation path PA is a virtual circle whose diameter is the value obtained by subtracting the first value from the outer diameter of the first sliding surface 20A.

[0065] In the above examples, the rightward direction in Figures 5 to 7 was used as the sliding direction D. However, if the sliding direction D is reversed, the wedge effect will be produced by the second incline 21B instead of the first incline 21A. In this case, the wedge distance L will be the circumferential length of the second incline 21B. The undulation height h3 will be the height difference of the second incline 21B, i.e., the height from the concave peak 21m to the second convex peak 21q.

[0066] Here, the undulation curve may contain multiple irregularities of different heights. In this case, the maximum height undulation Wz1 in the evaluation path PA may be used to define the irregularities having an undulation height h3 that satisfies the following equation (4).

[0067] Wz1 / 2 ≤ swell height h3 ≤ Wz1 …(4) In other words, for convex areas where the swell height h3 is 50% or less of the maximum swell height Wz1, the resulting oil film reaction force P is negligibly small compared to swells exceeding 50% of the maximum swell height Wz1. Therefore, such irregularities do not need to be considered as swells. Note that irregularities are those having concave peaks and convex peaks.

[0068] The maximum height swell Wz1 is obtained from the swell curve using a method compliant with JIS B 0601:2013. Specifically, the maximum height swell Wz1 is obtained as the sum of the maximum peak height and the maximum trough depth in the swell curve.

[0069] (Synthetic undulation) This section describes the configuration of the undulations necessary to obtain a high oil film reaction force P when the first sliding surface 20A and the second sliding surface 10A each have their own undulations. First, the definition of the parameters necessary for describing this configuration is explained, and then the conditions required for these parameters are explained. When the first sliding surface 20A and the second sliding surface 10A each have their own undulations, it is necessary to understand the surface properties of both sliding surfaces 10A and 20A by relating their undulations to each other. Therefore, an evaluation path PA is set not only for the first sliding surface 20A but also for the second sliding surface 10A. The evaluation path PA for the second sliding surface 10A is set at a position opposite to the evaluation path PA for the first sliding surface 20A. The length of this evaluation path PA becomes the sliding length R that defines the undulation. As a premise for the following explanation, it is assumed that the undulations of both sliding surfaces 10A and 20A are configured such that the maximum distance between the two sliding surfaces 10A and 20A during one rotation of the ring 20 is 10 μm or less. For example, when the concave peak of the undulation of the first sliding surface 20A and the concave peak of the undulation of the second sliding surface 10A face each other, the distance between these two concave peaks is 10 μm or less. Here, let's assume that no undulations are formed on either the first sliding surface 20A or the second sliding surface 10A, and that both sliding surfaces 10A and 20A are flat. And let's assume that these two sliding surfaces 10A and 20A are in surface contact. In this case, the two sliding surfaces 10A and 20A are referred to as virtual reference surfaces. In the explanation of composite undulation, the distance between the two sliding surfaces 10A and 20A is the length in the direction perpendicular to the virtual reference surface. In this embodiment, the direction perpendicular to the virtual reference plane is the axial direction.

[0070] Let the undulation curve of the evaluation path PA on the first sliding surface 20A be the ring curve. Similarly, let the undulation curve of the evaluation path PA on the second sliding surface 10A be the disk curve. Now, let's assume that the ring 20 is in a specific rotational position. Figure 9 shows a simplified example of the ring curve 101 and disk curve 102 in this case. The ring curve 101 and disk curve 102 shown in Figure 9 are merely for convenience to explain the surface properties in an easy-to-understand manner and do not necessarily correspond to the actual values. The vertical axis in Figure 9 is set so that the value increases in the direction in which the ring 20 is positioned relative to the disk 10. In other words, the absolute value of the ring curve 101 increases as the depth of the depression from the first sliding surface 20A increases. Similarly, the absolute value of the disk curve 102 increases as the depth of the depression from the second sliding surface 10A increases.

[0071] In the example shown in Figure 9, the ring curve 101 has two undulations. Each undulation contains a convex peak and a concave peak. Similarly, the disk curve 102 also has two undulations. Each undulation contains a convex peak and a concave peak. Note that the ring curve 101 only needs to contain one or more undulations. The disk curve 102 also only needs to contain one or more undulations.

[0072] As shown in Figure 10, the composite curve 103 is obtained by combining the ring curve 101 and the disk curve 102 with its sign reversed. The composite curve 103 shows the distance between the first sliding surface 20A and the second sliding surface 10A for each phase angle. Hereafter, the height shown by the composite curve 103 will be referred to as the composite height.

[0073] The following describes the parameters of each component, focusing on the composite curve 103. As shown in Figure 10, the composite curve 103 has two composite swells 110 and 120. The composite swells 110 and 120 are arranged side by side in the circumferential direction.

[0074] The first composite swell 110 includes a composite concave peak 110m, composite convex peaks 110p and 110q, and a first composite slope 110A and a second composite slope 110B. The composite concave peak 110m is the point in the first composite swell 110 located on the evaluation path PA where the distance between the two sliding surfaces 10A and 20A is longest. The composite convex peaks 110p and 110q correspond to the circumferential ends of the first composite swell 110. The composite convex peaks 110p and 110q are points in the first composite swell 110 where the distance between the two sliding surfaces 10A and 20A is shortest. More specifically, at least one of the composite convex peaks 110p and 110q is the point in the first composite swell 110 where the distance between the two sliding surfaces 10A and 20A is shortest. For the sake of explanation, of the two composite convex peaks 110p and 110q, the one located in the sliding direction D relative to the composite concave peak 110m is referred to as the first composite convex peak 110p, and the one located in the direction opposite to the sliding direction D relative to the composite concave peak 110m is referred to as the second composite convex peak 110q. In other words, the first composite convex peak 110p is a composite convex peak adjacent to the composite concave peak 110m in the sliding direction D. The second composite convex peak 110q is a composite convex peak adjacent to the composite concave peak 110m in the sliding direction D, in the opposite direction to the first composite convex peak 110p with respect to the composite concave peak 110m. The height positions of both composite convex peaks 110p and 110q may be the same or different.

[0075] The two composite inclines 110A and 110B are positioned on both sides of the composite concave peak 110m. The first composite incline 110A connects the composite concave peak 110m and the first composite convex peak 110p. In this case, the first circumferential end of the first composite incline 110A is the composite concave peak 110m, and the second circumferential end of the first composite incline 110A is the first composite convex peak 110p. The first end of the first composite incline 110A is the point where the distance between the two sliding surfaces 10A and 20A is longest, and the second end of the first composite incline 110A is the point where the distance between the two sliding surfaces 10A and 20A is shortest.

[0076] The first composite inclination 110A is inclined such that the distance between the two sliding surfaces 10A and 20A decreases as it moves from the composite concave peak 110m towards the first composite convex peak 110p. The first composite inclination 110A only needs to be inclined as a whole; it may include localized areas where the distance is constant. The first composite inclination 110A is located in the sliding direction D relative to the composite concave peak 110m. The first composite inclination 110A is located in the direction opposite to the sliding direction D relative to the first composite convex peak 110p.

[0077] The second composite inclination 110B is inclined such that the distance between the two sliding surfaces 10A and 20A decreases as it moves from the composite concave peak 110m towards the second composite convex peak 110q. The second composite inclination 110B only needs to be inclined overall; it may include localized areas where the distance is constant. The second composite inclination 110B is located in the opposite direction to the sliding direction D relative to the composite concave peak 110m. The second composite inclination 110B is located in the sliding direction D relative to the second composite convex peak 110q.

[0078] Thus, the first composite undulation 110 is derived from the change in distance between the two sliding surfaces 10A and 20A in the sliding direction D. In this embodiment, the circumferential lengths of both composite inclines 110A and 110B, in other words, the phase angles occupied by both composite inclines 110A and 110B are set to be the same. However, this is not limited to this, and the circumferential lengths of both composite inclines 110A and 110B may be different.

[0079] The second composite swell 120 includes a composite concave peak 120m, composite convex peaks 120p and 120q, and a first composite slope 120A and a second composite slope 120B. Since these are the same as the corresponding configurations of the first composite swell 110, a detailed explanation is omitted.

[0080] In this configuration, the oil film reaction force P generated by the first composite swell 110 is determined based on equation (1). In this case, the inlet distance h1 is the distance between the first sliding surface 20A and the second sliding surface 10A at the position of the composite concave peak 110m of the first composite swell 110. The outlet distance h2 is the distance between the first sliding surface 20A and the second sliding surface 10A at the first composite convex peak 110p. The inlet distance h1 is the sum of the swell height h3 of the first composite swell 110 and the outlet distance h2. The outlet distance h2 is usually considered to be 3σ, where σ is the arithmetic mean roughness Ra of the first sliding surface 20A. Therefore, the inlet distance h1 is the sum of the swell height h3 of the first composite swell 110 and 3σ. Furthermore, the inlet distance h1, outlet distance h2, and swell height h3 related to the first composite swell 110 are lengths in the axial direction and are lengths in the direction perpendicular to the virtual reference plane mentioned above.

[0081] The swell height h3 of the first composite swell 110 is the height of the first composite convex peak 110p relative to the composite concave peak 110m, and can also be said to be the height of the first composite slope 110A. Furthermore, in the first composite swell 110, the wedge distance L that contributes to the wedge effect is the circumferential length of the first composite slope 110A.

[0082] Furthermore, when the sliding direction D is reversed, the oil film reaction force P depends on the undulation height h3 of the second composite slope 110B. The undulation height h3 of the second composite slope 110B is the height of the second composite convex peak 110q relative to the composite concave peak 110m, and the wedge distance L is the circumferential length of the second composite slope 110B.

[0083] Here, the relative position in the sliding direction D between the undulating portion of the first sliding surface 20A and the undulating portion of the second sliding surface 10A changes according to the rotation of the ring 20. Consequently, the shape of the composite undulations 110 and 120, which are the irregularities formed by the undulations of the first sliding surface 20A and the second sliding surface 10A, also changes. In other words, the shape of the composite undulations 110 and 120 and their height h3 change as the two sliding surfaces 10A and 20A slide against each other.

[0084] To account for these changes in shape, the composite curve 103 is generated for various rotational positions during one rotation of the ring 20. For example, the composite curve 103 is generated for each case where the rotational position of the ring 20 is changed by a predetermined angle. An example of a predetermined angle is 10 degrees. In this case, 36 composite curves 103 are generated. For each of these multiple composite curves 103, the values ​​of each parameter that characterizes the undulation are determined.

[0085] More specifically, for each of the multiple composite curves 103, in other words, for each rotation position, the swell height h3 (inlet distance h1), outlet distance h2, and wedge distance L of the first composite swell 110 are derived. Thus, multiple swell heights h3, multiple inlet distances h1, multiple outlet distances h2, and multiple wedge distances L are derived. The averages of these are called the average swell height h3a, average inlet distance h1a, average outlet distance h2a, and average wedge distance La, respectively. The average swell height h3a is the average value of each swell height h3 when the ring 20 is rotated once. The average inlet distance h1a is the average value of each inlet distance h1 when the ring 20 is rotated once. The average outlet distance h2a is the average value of each outlet distance h2 when the ring 20 is rotated once. The average wedge distance La is the average value of each wedge distance L when the ring 20 is rotated once.

[0086] In a similar manner to the exit distance h2 already explained, the average exit distance h2a is usually considered to be 3σ, where σ is the arithmetic mean roughness Ra of the first composite swell 110. Here, the arithmetic mean roughness Ra of the first composite swell 110 is the combined value of the surface roughness of the first sliding surface 20A and the surface roughness of the second sliding surface 10A. More specifically, the arithmetic mean roughness Ra is the square root of the sum of the square of the arithmetic mean roughness Ra of the first sliding surface 20A and the square of the arithmetic mean roughness Ra of the second sliding surface 10A.

[0087] Furthermore, from the same perspective as the inlet distance h1, the average inlet distance h1a in the first composite swell 110 is preferably 3.3 times or more and 30 times or less the arithmetic mean roughness Ra in the evaluation path PA. More preferably, the average inlet distance h1a is 3.9 times or more and 15 times or less the arithmetic mean roughness Ra in the evaluation path PA, and even more preferably 6.6 times or more. The swells of both sliding surfaces 10A and 20A are configured to satisfy these conditions for the average inlet distance h1a. That is, the swells of both sliding surfaces 10A and 20A are configured such that the value obtained by adding 3σ to the average swell height h3a is 3.3 times or more and 30 times or less the arithmetic mean roughness Ra in the evaluation path PA.

[0088] Similar to the wedge length L, a longer average wedge distance La is preferable. When the sliding length R is R, the average wedge distance La may be, for example, R / 6 or greater, or R / 4 or greater.

[0089] Incidentally, as shown in Figure 10, if there are multiple composite swells 110 and 120 within a single composite curve 103, the necessary parameters (swell height h3, wedge distance L, etc.) may be derived for each composite swell 110 and 120. Then, representative values ​​may be determined. For example, the representative value of swell height h3 may be the average value of the swell height h3 of both composite swells 110 and 120, or the maximum value.

[0090] In determining the values ​​of each parameter that characterizes the composite swell, multiple evaluation paths PA with different diameters may be set. For example, three evaluation paths PA may be set: a first evaluation path PA, a second evaluation path PA, and a third evaluation path PA, as explained in relation to the case where only the first sliding surface 20A of the two sliding surfaces 10A and 20A has swell. When setting these three evaluation paths PA, for example, a representative value such as the average or maximum value is calculated for each evaluation path PA with respect to a certain parameter. Then, the average of the representative values ​​in each of the three evaluation paths PA can be taken as the final value. For example, if the swell height is h3, the average swell height h3a is calculated for each of the three evaluation paths PA using the calculation method already explained. Then, the average value of the average swell height h3a in each of the three evaluation paths PA is determined as the final value.

[0091] (Example of theoretical calculation) As shown in Figure 11, the oil film reaction force P when the number of undulations or the undulation height h3 of the first sliding surface 20A is changed, with a mirror surface having extremely low flatness and planarity, will be explained using a theoretical calculation example. The arithmetic mean roughness Ra of the second sliding surface 10A is assumed to be 0.01 [μm].

[0092] The oil film reaction force P for Calculation Example 1 was obtained by setting various parameters as follows. The oil film reaction force P for Calculation Example 1 was 4360 [N]. • Ring 20 diameter: 16 [mm] • Inner diameter of ring 20: 5 [mm] • Diameter of evaluation path PA: 10.5 [mm] • Length of evaluation path PA (= sliding length R): 33.0 [mm] • Viscosity of lubricating oil μ: 7.17 × 10 -8 [N / mm 2 ·s] • Sliding speed U: 1 [mm / s] • Number of undulations: 2 per sliding length R • Swell distance L:R / 4 • Swell height h3: 130 [nm] (<15σ) • Arithmetic mean roughness Ra of the first sliding surface 20A: 0.01 [μm] Next, the number of undulations was changed to eight, which are arranged at equal intervals in the sliding direction D, and the undulation distance L was changed to R / 16. All other settings were kept the same as in Calculation Example 1 to obtain the oil film reaction force P for Calculation Example 2. The oil film reaction force P for Calculation Example 2 was 1090 [N], which was 1 / 4 of the oil film reaction force P for Calculation Example 1. From a comparison between Calculation Example 1 and Calculation Example 2, it was found that when a higher oil film reaction force P is required, the number of undulations should be small, while still being one or more.

[0093] Next, the peak height h3 of the swell was changed to 1 [μm] (>30σ), and all other parameters were kept the same as in Calculation Example 1 to obtain the oil film reaction force P for Calculation Example 3. The oil film reaction force P for Calculation Example 3 was 460 [N], which was less than 1 / 6 of the oil film reaction force P for Calculation Example 1. From the comparison between Calculation Example 1 and Calculation Example 3, it is preferable that the peak height h3 of the swell be 30 times or less the arithmetic mean roughness Ra, and more preferably 15 times or less.

[0094] (Supply of lubricating oil) The first sliding surface 20A described above may have a recess for storing lubricating oil. The recess for storing lubricating oil will be described below.

[0095] For the oil film reaction force P to be generated by the wedge effect, a sufficient amount of lubricating oil must be present in the wedge-shaped space between the first inclined surface 21A and the second sliding surface 10A. Therefore, as shown in Figure 13, the second undulation 22 may be provided with a storage groove 23 as an example of a recess for storing lubricating oil.

[0096] More specifically, as already explained, the second incline 22B of the second swell 22 is connected to the first incline 21A of the first swell 21. More specifically, as shown in Figure 12, the second incline 22B of the second swell 22 is an inclined surface with the first convex peak 21p of the first swell 21 and the concave peak 22m of the second swell 22 at its ends, and the distance between the first sliding surface 20A and the second sliding surface 10A increases as the sliding direction D is moved from the first convex peak 21p of the first swell 21.

[0097] As the two sliding surfaces 10A and 20A slide against each other, the lubricating oil flows through the following positions in the circumferential direction: namely, the lubricating oil flows in the following order: concave peak 21m of the first swell 21 → first slope 21A of the first swell 21 → first convex peak 21p of the first swell 21 → second slope 22B of the second swell 22 → concave peak 22m of the second swell 22 → first slope 22A of the second swell 22 → first convex peak 22p of the second swell 22.

[0098] In this configuration, as shown in Figure 13, the storage groove 23 is recessed near the boundary between the second incline 22B and the first incline 22A. The storage groove 23 straddles the second incline 22B and the first incline 22A. The storage groove 23 has approximately the same cross-sectional area at each position in the direction in which the recess deepens. The storage groove 23 supplies lubricating oil to the region between the first incline 22A and the second sliding surface 10A. As a result, the shortage of lubricating oil is suppressed in this region and the oil film reaction force P increases. Consequently, the frictional resistance is reduced. Note that in Figure 13, the size of the storage groove 23 is exaggerated and shown as larger than its actual size.

[0099] Furthermore, as shown in Figure 14, the second undulation 22 may be provided with dimples 24 as an example of recesses for storing lubricating oil. The dimples 24 are recessed in both the first incline 22A and the second incline 22B. The cross-sectional area of ​​the dimples 24 decreases as the recesses deepen. The dimples 24 supply lubricating oil to the region between the second undulation 22 and the second sliding surface 10A. This suppresses a shortage of lubricating oil in this region and increases the oil film reaction force P. In the example in Figure 14, the state after the dimples 24 on the second incline 22B have supplied lubricating oil is shown. After this, the dimples 24 store lubricating oil again. The dimples 24 repeat this process of supplying and storing lubricating oil. Note that the dimples 24 on one of the first incline 22A and the second incline 22B may be omitted.

[0100] In the example shown in Figure 14, dimples 24 are also present in the first incline 21A and the second incline 21B of the first undulation 21. These dimples 24 function similarly to the dimples 24 of the second undulation 22. Therefore, a shortage of lubricating oil in the region between the first undulation 21 and the second sliding surface 10A is suppressed. Note that in Figure 14, the size of the dimples 24 is exaggerated to appear larger than their actual size.

[0101] As described above, multiple dimples 24 may be provided on the first sliding surface 20A. When multiple dimples 24 are provided on the first sliding surface 20A, the total opening area of ​​the multiple dimples 24 may be 5% to 15% of the area of ​​the first sliding surface 20A. However, this is not limited to this example, but providing multiple dimples 24 is preferable for preventing a shortage of lubricating oil.

[0102] Here, the storage groove 23 illustrated in Figure 13 and the dimple 24 illustrated in Figure 14 are irregularities in the cross-sectional curve of the evaluation path PA that have wavelength components longer than the first cutoff value λc and shorter than the third cutoff value λd. The third cutoff value λd is greater than the first cutoff value λc and less than the second cutoff value λf. For example, the third cutoff value λd is half of the second cutoff value λf. The two undulations 21 and 22 may be identified from the undulation curve filtered using such a third cutoff value λd. That is, by filtering the cross-sectional curve using the third cutoff value λd, wavelength components excluding the irregularities of the storage groove 23 or the dimple 24 can be obtained. The depth of the dimple 24 as a recess is greater than the arithmetic mean roughness Ra of the first sliding surface 20A and less than the undulation height h3 of the second undulation 22.

[0103] (Effects of this embodiment) Next, the effects of this embodiment will be described. (1) When one or more undulations are formed on the first sliding surface 20A, when the first sliding surface 20A slides against the second sliding surface 10A, an oil film reaction force P due to the wedge effect is generated between the two sliding surfaces 10A and 20A. In the configuration of this embodiment, the undulations are configured such that the value obtained by adding 3σ to the height h3 of the undulations is 3.3σ or more and 30σ or less. In this case, the oil film reaction force P due to the wedge effect becomes particularly high. Therefore, friction between the two sliding surfaces 10A and 20A can be reduced.

[0104] (2) When the value obtained by adding 3σ to the swell height h3 is 3.9σ or greater and 15σ or less, the first sliding surface 20A and the second sliding surface 10A slide against each other in the range in which the oil film reaction force P increases sharply in relation to the swell height h3. Therefore, a significant reduction in friction due to the oil film reaction force P is possible.

[0105] (3) If the value obtained by adding 3σ to the swell height h3 is 6.6σ or greater, the effectiveness of obtaining the effect similar to (2) increases. (4) If recesses are provided in the first incline 22A and the second incline 22B of the second undulation 22, the lubricating oil stored in the recesses is supplied, thereby forming the necessary oil film between the two sliding surfaces 10A and 20A. Specifically, the supply of lubricating oil from the recesses causes the two sliding surfaces 10A and 20A to be in a fluid-lubricated state. This makes it possible to obtain the desired oil film reaction force P between the two sliding surfaces 10A and 20A. The recesses of the first undulation 21 have a similar effect.

[0106] (5) When the total opening area of ​​the multiple recesses for storing lubricating oil is 5% to 15% of the area of ​​the first sliding surface 20A, a sufficient amount of lubricating oil can be stored in the multiple recesses to obtain a high oil film reaction force P. By supplying this lubricating oil to the wedge-shaped portion, a significant reduction in friction due to the oil film reaction force P can be achieved.

[0107] (Example test) A test example of the sliding mechanism will be described with reference to Figures 15 and 16. [Test Example 1] In Test Example 1, the waviness height h3 and waviness distance L of the ring 20 are 0.109 [μm] and 1 / 4 of the sliding length R (=R / 4), respectively. In Test Example 1, the waviness height h3 and waviness distance L of the disc 10 are 0.105 [μm] and half of the sliding length R (=R / 2), respectively. In the sliding mechanism of Test Example 1, the average waviness height h3a and average waviness distance La are 0.2 [μm] and 1 / 4 of the sliding length R (=R / 4), respectively. The ring 20 in Test Example 1 is equipped with a storage groove 23 for storing lubricating oil. The surface roughness Ra of the ring 20 and disc 10 in Test Example 1 is 0.01 [μm].

[0108] [Test Example 2] In Test Example 2, the waviness height h3 and waviness distance L of the ring 20 are 0.057 [μm] and half the sliding length R (= R / 2), respectively. In Test Example 2, the waviness height h3 and waviness distance L of the disk 10 are 0.076 [μm] and half the sliding length R (= R / 2), respectively. In the sliding mechanism of Test Example 2, the average waviness height h3a and average waviness distance La are 0.122 [μm] and 1 / 8 of the sliding length R (= R / 8). The surface roughness of the ring 20 and disk 10 in Test Example 2 is the same as in Test Example 1. The ring 20 in Test Example 2 is equipped with dimples 24 for storing lubricating oil. The volume of the dimples 24 is 2617 [μm]. 3 ]. The theoretically required dimple volume is 1648 [μm³]. 3] The theoretically required dimple volume can be calculated, for example, as follows. Hereinafter, we assume that the ring 20 is viewed in plan with the axial direction.As a premise, we assume that multiple dimples 24 are arranged on the ring 20 at approximately equal intervals from one another.Here, we assume that the entire sliding surface is virtually divided into multiple equal regions.A dimple 24 is located at the center of one region.And we assume that each region is assigned as a region to which one dimple 24 should supply lubricating oil.If each dimple 24 can supply a sufficient amount of lubricating oil to the region assigned to it, it can be expected that a sufficient oil film reaction force P will be generated at each position on the sliding surface to achieve friction reduction.The area of ​​the above region assigned to one dimple 24 is called the cover area.That is, with respect to a particular dimple 24, the cover area is the area of ​​the region surrounding the dimple 24 on the sliding surface, and is the area of ​​the sliding surface to which the dimple 24 should supply lubricating oil. In the ring 20 of this embodiment, the spacing between adjacent dimples 24 is determined such that the covering area is, for example, 10 times the opening area of ​​the dimples 24. The theoretically required dimple volume can be calculated as the product of the covering area and 6σ. That is, the theoretically required dimple volume is the volume of the dimples 24 assuming that lubricating oil equivalent to a height of 6σ (=2 × outlet distance h2(3σ)) is supplied to the entire covering area.

[0109] [evaluation] For each of the above test examples, the dependence of the friction coefficient on the rotational speed of ring 20 was evaluated. As shown in Figure 16, the friction coefficients for test examples 1 and 2 continuously decrease from 300 [rpm] towards 10 [rpm]. This trend in the friction coefficient reflects a fluid lubrication state in which both sliding surfaces 10A and 20A are completely separated by an oil film due to the supply of lubricating oil from the recess. The friction coefficient of test example 1 shows a steep increase below 10 [rpm], while the friction coefficient of test example 2 does not show a steep increase below 10 [rpm] and continues to decrease from 300 [rpm] towards the minimum rotational speed. In other words, if the recess has a volume assuming a height of 6σ as described above, friction can be significantly suppressed even in the low-speed range of 10 [rpm] or less on both sliding surfaces 10A and 20A.

[0110] The sliding mechanism may include a drive unit that slides the first member against the second member. The drive unit may continuously slide the first member against the second member so that the rotational speed of the first sliding surface 20A against the second sliding surface 10A is 250 [rpm] or less. Alternatively, the drive unit may continuously slide the first member against the second member so that the sliding speed U of the first sliding surface 20A against the second sliding surface 10A is 0.17 [m / sec] (= diameter of the evaluation path PA (0.013 [m]) × 3.14 × 250 [rpm] / 60) or less.

[0111] (Other embodiments) The above embodiment can be implemented with the following modifications. The above embodiment and the following modifications can be combined with each other to the extent that they do not contradict each other technically.

[0112] At least one of the first sliding surface 20A and the second sliding surface 10A may be provided with at least one of the storage groove 23 and the dimple 24. At least one of the first inclined surfaces 21A, 22A and the second inclined surfaces 21B, 22B may be provided with at least one of the storage groove 23 and the dimple 24.

[0113] At least one of the first sliding surface 20A and the second sliding surface 10A may be provided with grooves, such as herringbone patterns, leading to the area where lubricant is to be introduced, so that lubricant can be supplied from around it. According to this modification, the sliding speed U is increased by the amount of lubricant supplied from the grooves, while the oil film reaction force P is increased.

[0114] If a high sliding speed U is not required, the first sliding surface 20A and the second sliding surface 10A may omit recesses for storing lubricating oil, such as storage grooves 23 or dimples 24.

[0115] When both sliding surfaces 10A and 20A slide in only one direction, the circumferential length of the inclination that exhibits a wedge effect with respect to the sliding direction D among the first inclinations 21A and 22A and the second inclinations 21B and 22B may be made longer than the circumferential length of the inclination that does not exhibit a wedge effect. This makes it possible to obtain a larger oil film reaction force P with respect to the sliding direction D.

[0116] The length of the sliding length R is not limited to the examples of the embodiments described above. The sliding length R may vary depending on the product in question. The length of the sliding length R is, for example, about 0.1 mm to 50 mm. However, the length of the sliding length R is not limited to this example.

[0117] The sliding mechanism may be applied to tests other than ring-on-disk testing. As shown in Figure 17, for example, the sliding mechanism may be applied to a bearing mechanism 200. In this case, the bearing mechanism 200 comprises a rotating shaft 220 as a first member and a bearing 210 as a second member.

[0118] The bearing 210 is ring-shaped. The bearing 210 is fixed in a position that prevents it from moving. The rotating shaft 220 is cylindrical. The rotating shaft 220 passes through the bearing 210. The rotating shaft 220 is rotatably supported by the inner circumferential surface of the bearing 210. The rotating shaft 220 rotates relative to the bearing 210 about its own central axis.

[0119] The portion of the rotating shaft 220's side surface facing the inner circumferential surface of the bearing 210 constitutes the first sliding surface 220A. That is, the first sliding surface 220A is the portion of the rotating shaft 220's side surface located inside the bearing 210. On the other hand, the inner circumferential surface of the bearing 210 constitutes the second sliding surface 210A. The diameter of the rotating shaft 220 is slightly smaller than the diameter of the bearing 210. The distance between the two sliding surfaces 210A, 220A is 10 μm at any position in the circumferential and radial directions around the central axis of the rotating shaft 220. Note that in Figure 17, the distance between the two sliding surfaces 210A, 220A is exaggerated and shown as larger. Lubricating oil is present throughout the entire area between the two sliding surfaces 210A, 220A. The two sliding surfaces 210A, 220A slide together as the rotating shaft 220 rotates. The rotation direction of the rotating shaft 220 corresponds to the sliding direction D of the first sliding surface 220A relative to the second sliding surface 210A.

[0120] Multiple undulations 222 are formed on the first sliding surface 220A. These undulations 222 are arranged in the circumferential direction. In Figure 17, the multiple undulations 222 are shown by six dotted lines for convenience; however, this does not indicate the number of undulations 222, but rather schematically represents the presence of undulations. Similar to the first sliding surface 220A, multiple undulations 212 are formed on the second sliding surface 210A. These undulations 212 are arranged in the circumferential direction. Similar to the first sliding surface 220A, in Figure 17, the undulations 212 of the second sliding surface 210A are shown by six dotted lines for convenience. The undulations 212, 222 on both sliding surfaces 210A, 220A are formed at positions opposite each other in the radial direction. The undulations 212 and 222 of both sliding surfaces 210A and 220A are configured to satisfy the conditions for the combined undulation described in the above embodiment. The evaluation path PA for extracting the undulation 222 of the first sliding surface 220A is set as a path connecting the sides of the rotating shaft 220 for one full turn in the circumferential direction. The evaluation path PA for the second sliding surface 210A is set as a path connecting the inner circumferential surface of the bearing 210 for one full turn in the circumferential direction. The sliding length R that defines the undulation in the bearing mechanism 200 is the inner circumferential dimension of the inner circumferential surface of the bearing 210. For example, the sliding length R is about 50 mm. Depending on the size of the gap between the outer circumferential surface of the rotating shaft 220 and the inner circumferential surface of the bearing 210, the following may occur: That is, due to the weight of the rotating shaft 220, the rotating shaft 220 may be shifted downward relative to the central axis of the bearing 210. Consequently, only the portion of the outer surface of the rotating shaft 220 that is lower to the central axis may be in contact with the inner surface of the bearing 210. In this case, the sliding length R becomes shorter than the inner circumference of the bearing 210.

[0121] Similar to the above embodiment, a recess for storing lubricating oil may be provided in the undulation of at least one of the first sliding surface 220A and the second sliding surface 210A. The undulation may be formed on only one of the first sliding surface 220A and the second sliding surface 210A. In this case, the undulation only needs to be configured to satisfy the height conditions of the above embodiment.

[0122] As shown in Figure 18, for example, a sliding mechanism may be applied to the reduction mechanism 250. The reduction mechanism 250 comprises an output wheel 260, an oscillating gear 270, and a plurality of rotating shafts 280. The output wheel 260 is ring-shaped. The output wheel 260 has a plurality of arcuate grooves 262. The arcuate grooves 262 are recessed in the inner circumferential surface of the output wheel 260. The plurality of arcuate grooves 262 are arranged at equal intervals in the circumferential direction around the central axis of the output wheel 260. In a plan view facing in the direction along the central axis of the output wheel 260, the arcuate grooves 262 are semicircular. That is, the arcuate grooves 262 are curved.

[0123] A rotating shaft 280 is provided for each arc groove 262. The rotating shaft 280 is cylindrical. The diameter of the rotating shaft 280 is slightly smaller than the diameter of the arc groove 262. The rotating shaft 280 is located within the arc groove 262. The central axis of the rotating shaft 280 passes through a position that approximately coincides with the center of the arc groove 262. Approximately half of the circumferential portion of the rotating shaft 280 faces the arc groove 262. The remaining portion of the rotating shaft 280 is exposed from the arc groove 262. The rotating shaft 280 is rotatably supported by the arc groove 262. The rotating shaft 280 rotates relative to the arc groove 262 with its own central axis as the center. The distance between the side surface of the rotating shaft 280 and the surface defining the arc groove 262 is 10 μm or less at any point in the circumferential and radial directions of the rotating shaft 280. Lubricating oil is interposed between the rotating shaft 280 and the arc groove 262.

[0124] The oscillating gear 270 is located inside the output wheel 260. The outer surface of the oscillating gear 270 is curved in a wave-like manner. That is, the outer surface of the oscillating gear 270 has a repeating smooth uneven surface. The number of recesses on the outer surface of the oscillating gear 270 is one less than the number of recesses on the rotating shaft 280. Of these multiple recesses, the recesses in a portion of the circumferential range of the oscillating gear 270 mesh with the rotating shaft 280. The oscillating gear 270 oscillates in accordance with the rotation of an input shaft (not shown), such that the circumferential range in which it meshes with the rotating shaft 280 changes. The oscillation of the oscillating gear 270 is transmitted to the output wheel 260 via the rotating shaft 280. The output wheel 260 rotates at a rotational speed lower than the rotational speed of the input shaft.

[0125] Figure 19 shows a magnified view of the area around one of the multiple rotating shafts 280. In the reduction mechanism 250, the rotating shaft 280 constitutes the first member of the sliding mechanism. The output wheel 260 constitutes the second member of the sliding mechanism. The side surface of the rotating shaft 280 constitutes the first sliding surface. Of the output wheel 260, the surface that demarcates the arc groove 262 constitutes the second sliding surface. Here, the rotating shaft 280 rotates in response to its contact with the oscillating gear 270. As the rotating shaft 280 rotates, the first sliding surface and the second sliding surface slide against each other. The direction of rotation of the rotating shaft 280 corresponds to the sliding direction of the first sliding surface relative to the second sliding surface.

[0126] Multiple undulations may be formed on at least one of the first and second sliding surfaces of the reduction mechanism 250. Figure 19 shows an example in which undulations are formed on both the first and second sliding surfaces. In Figure 19, multiple undulations 285 formed on the side surface of the rotating shaft 280 are shown by three dotted lines for convenience. The multiple undulations 285 are arranged in the circumferential direction. Also in Figure 19, multiple undulations 265 formed in the arc groove 262 are shown by two dotted lines for convenience. The multiple undulations 265 are arranged in the circumferential direction. The undulations 265 and 285 on both sliding surfaces are formed at positions facing each other in the radial direction. The undulations 265 and 285 on both sliding surfaces are configured to satisfy the conditions for a composite undulation described in the above embodiment. The evaluation path PA of the first sliding surface is set as a path connecting one full rotation of the side surface of the rotating shaft 280. The evaluation path PA of the second sliding surface is set to connect both ends of the arc groove 262 in the circumferential direction centered on the center of the arc groove 262. The sliding length R that defines the undulation in these evaluation paths PA is the circumferential length of the arc groove 262 in the circumferential direction centered on the center of the arc groove 262. For example, the sliding length R is about 20 mm. As in the above embodiment, a recess for storing lubricating oil may be provided in the undulation on at least one of the two sliding surfaces. Also, if undulation is formed on only one of the two sliding surfaces, the undulation only needs to satisfy the height condition.

[0127] The sliding mechanism is not limited to applications involving rotational motion; it may also apply to applications involving linear motion. For example, as shown in Figure 20, in the hydraulic pump 300, the piston 310 reciprocates linearly within a cylindrical recess 322 partitioned in the cylinder block 320. As a result of this reciprocating motion, the outer circumferential surface of the piston ring 340, which is attached to the side of the piston 310, slides against the circumferential surface 322A of the recess 322. The gap between the outer circumferential surface of the piston ring 340 and the circumferential surface 322A of the recess 322 is 10 μm or less, and lubricating oil is interposed between them. One or more undulations may be formed on at least one of the outer circumferential surface of the piston ring 340 and the circumferential surface 322A of the recess 322. That is, as illustrated in Figure 20, it is conceivable to form multiple undulations 323 on the circumferential surface 322A of the recess 322, or to form multiple undulations 343 on the outer circumferential surface of the piston ring 340. The sliding length R that defines the undulation at this time can be treated as the length of the piston ring 340 in the direction along the central axis of the piston ring 340. The direction along the central axis of the piston ring 340 corresponds to the sliding direction D of the piston ring 340 with respect to the circumferential surface 322A of the recess 322. In Figure 20, the multiple undulations 323 formed on the circumferential surface 322A of the recess 322 are shown by four dotted lines for convenience. Also in Figure 20, the multiple undulations 343 formed on the piston ring 340 are shown by one dotted line for convenience.

[0128] The definition of "undulation," and consequently the method of calculating each parameter that characterizes "undulation," is not limited to the examples of the embodiments described above. Not limited to the examples of the embodiments described above, a cluster of large irregularities appearing in the cross-sectional curve of a particular evaluation path PA may be treated as "undulation."

[0129] For example, the following envelope method may be used to identify the "undulation" and calculate the parameters related to the undulation. In explaining this envelope method, the sliding mechanism consisting of the ring 20 and the disk 10 described in the above embodiment will be used as an example below. Furthermore, the following example will be used in the case where undulation exists only on the first sliding surface 20A of the two sliding surfaces 10A. Furthermore, the following example will be used in the case where three evaluation paths PA are set.

[0130] In the enveloping method, the first step is performed first. In the first step, the cross-sectional curves of the first evaluation path PA, the second evaluation path PA, and the third evaluation path PA are obtained. The definitions of these three evaluation paths PA are as described in the above embodiment. That is, the first evaluation path PA is the path near the inner peripheral edge of the first sliding surface 20A. The second evaluation path PA is the path in the center between the inner and outer peripheral edges of the first sliding surface 20A. The third evaluation path PA is the path near the outer peripheral edge of the first sliding surface 20A. The cross-sectional curves of each evaluation path PA can be obtained by observation using a white light interference microscope. After obtaining the cross-sectional curves of each evaluation path PA in the first step, the following steps 2 to 5 are performed individually on each of these cross-sectional curves. Below, steps 2 to 5 will be explained using one evaluation path PA as an example.

[0131] In the second step, a first cutoff value λc is applied to the cross-sectional curve as a low-pass filter. This results in obtaining the analytical curve ZL shown in Figure 21. The horizontal axis of Figure 21, as in Figure 3, represents the phase angle. The vertical axis of Figure 21, as in Figure 3, represents the depth of the indentation in the first sliding surface 20A from the reference position. That is, the larger the positive value on the vertical axis, the greater the distance between the first sliding surface 20A and the second sliding surface 10A. As in Figure 3, the reference position is determined in conjunction with the observation position of the measuring instrument. An example of a first cutoff value λc used to obtain the analytical curve ZL is 0.08 mm. Other values ​​may be used as the first cutoff value λc in correspondence with Figure 4. The analytical curve ZL may also be a undulation curve. That is, the analytical curve ZL may be obtained by applying the first cutoff value λc as a low-pass filter to the cross-sectional curve, and also by applying the second cutoff value λf as a high-pass filter to the cross-sectional curve. The second cutoff value λf is the sliding length R. As shown in Figure 21, the analytical curve ZL contains numerous fine irregularities corresponding to the storage groove 23 or dimple 24.

[0132] In the third step, as shown in Figure 22, the so-called motif method is applied to the analytical curve ZL to divide the numerous irregularities appearing in the analytical curve ZL into multiple motifs ZM. One motif ZM is a cluster of large convexities obtained by ignoring small convexities below a certain level among the convexities appearing in the analytical curve ZL. The motif method conforms to JIS B 0631:2000. One example of the maximum circumferential width of one motif ZM is 1 / 20th of the sliding length R. In the third step, after dividing the analytical curve ZL into multiple motifs ZM, the envelope ZQ is generated by sequentially connecting the circumferential ends of each motif ZM. In Figure 22, the envelope ZQ is shown as a thick solid line. Figure 23 shows an enlarged view of this envelope ZQ. The envelope ZQ shown in Figure 23 is obtained by dividing the value of the envelope ZQ at each position in the circumferential direction by the average value over the entire circumferential region.

[0133] In the fourth step, the envelope ZQ obtained in the third step is subjected to a Fourier transform. Figure 24 shows the amplitude magnitudes for each order obtained by the Fourier transform. The order is the wave number. In the fifth step, the provisional index value ZUA is calculated. The provisional index value ZUA is obtained by dividing the sum of the amplitudes from the first order to a specific order, obtained by the Fourier transform, by the sum of the amplitudes from the first order to the 20th order. An example of a specific order is the fourth order. The analysis from the second to the fifth step above is performed for each of the three evaluation paths PA. This calculates the provisional index value ZUA for each evaluation path PA. After this, the sixth step is performed.

[0134] In the sixth step, the average of the provisional index values ​​ZUA for each of the three evaluation paths PA is calculated as the final index value ZU. If this final index value ZU is greater than or equal to a threshold, the irregularities appearing in the cross-sectional curve are treated as having "undulation." An example of a threshold is 0.4. The threshold should be set to a value that, in conjunction with the specific order mentioned above, allows us to consider that a reasonably large block of wave exists in the envelope ZQ. Here, each index value, referred to as the provisional index value ZUA or the final index value ZU, indicates the contribution rate of the amplitude of wave components with wavenumbers from 1 to 4 among the amplitudes of various wave components contained in the envelope ZQ. In other words, a large index value indicates that the contribution rate of wave components with small wavenumbers is large in the envelope ZQ. Furthermore, a large index value means that the entire envelope ZQ constitutes a wave exhibiting a single block of irregularities. When this single block of irregularities is considered as "undulation," the larger the index value, the longer the wavelength of this undulation and, consequently, the longer the "wedge distance L" explained in the above embodiment. In other words, the index value can be considered an indicator of the magnitude of the "wedge distance L".

[0135] If swells are found to exist in step 6, step 7 is performed. In step 7, the swell height h3 is calculated. Specifically, as shown in Figure 23, for the envelope ZQ of a certain evaluation path PA, the range from the minimum value to the maximum value of the envelope ZQ height is calculated as the provisional swell height Zh3. In determining the maximum and minimum values ​​of the envelope ZQ height, a moving average or the like may be applied to the envelope ZQ to smooth out the fine irregularities that appear in the envelope ZQ. Then, the provisional swell height Zh3 may be calculated. In step 7, these provisional swell heights Zh3 are calculated for each of the three evaluation paths PA. Then, the average of the provisional swell heights Zh3 of the three evaluation paths PA is calculated as the final swell height h3. If the sum of the swell height h3 and the arithmetic mean roughness Ra is between 3.3 and 30 times the arithmetic mean roughness Ra in the evaluation path PA, a high oil film reaction force P can be obtained. Note that the point where the height of the envelope ZQ is at its maximum can be considered a "concave peak" of the swell. The point where the height of the envelope ZQ is at its minimum can be considered a "convex peak" of the swell.

[0136] Furthermore, when calculating the provisional swell height h3 in step 7, the following approach may be adopted. That is, by applying the Fourier transform and inverse Fourier transform to the envelope ZQ generated in step 3, a specific envelope is generated in which only certain wavenumber components are extracted from the various fluctuation components contained in the envelope ZQ. Specifically, the specific envelope is a curve obtained by extracting waves with wavenumbers from, for example, 1 to 4 from the original envelope ZQ. The width from the minimum to the maximum height of such a specific envelope may be taken as the provisional swell height h3. At the same time, the width in the sliding direction D of the specific envelope, which is the width from the minimum to the maximum height, may be treated as the swell distance L.

[0137] When the above envelope method is applied to a sliding mechanism in which the first sliding surface 20A and the second sliding surface 10A each have their own undulations, the following analysis is performed. Here, for ease of understanding, we will take the example of setting a single evaluation path PA. In the above embodiment, when both sliding surfaces 10A and 20A each have their own undulations, a composite undulation curve representing the distance between the two sliding surfaces 10A and 20A is generated for each rotation position during one rotation of the ring 20, and the analysis is performed. When using the envelope method, a composite envelope is generated instead of a composite undulation curve. The composite envelope is a curve obtained by combining the envelope ZQ of the first sliding surface 20A and the curve obtained by inverting the envelope ZQ of the second sliding surface 10A. The envelope ZQ for each of the two sliding surfaces 10A and 20A can be generated by the method of the third step described above. Such a composite envelope is generated for each rotation position during one rotation of the ring 20. Then, steps 4 and 5 described above are performed for each composite envelope. That is, for a given composite envelope, a Fourier transform is applied to the composite envelope, and a provisional index value ZUA is calculated based on the analysis results of the Fourier transform. In this manner, provisional index values ​​ZUA are calculated for each rotation position during one rotation of the ring 20. After obtaining the provisional index values ​​ZUA for each rotation position, their average value is calculated as the composite index value. If this composite index value is greater than or equal to the threshold value described above, for example, 0.4, it can be treated as if "swell" exists. If "swell" exists, the provisional swell height Zh3 at each rotation position is calculated based on the composite envelope of each rotation position. Then, the average value of these multiple provisional swell heights Zh3 is calculated as the average swell height h3a. If the sum of the average undulation height h3a and the arithmetic mean roughness Ra is between 3.3 and 30 times the arithmetic mean roughness Ra, a high oil film reaction force P can be obtained. The arithmetic mean roughness Ra referred to here is the combined value of the arithmetic mean roughness Ra of both sliding surfaces 10A and 20A, as explained in relation to the composite undulation in the above embodiment.

[0138] Furthermore, if undulation exists on both the first sliding surface 20A and the second sliding surface 10A, multiple evaluation paths PA may be set. In this case, a combined index value should be calculated for each evaluation path PA, and their average value should be treated as the final combined index value. Additionally, the average undulation height h3a should be calculated for each evaluation path PA, and their average value should be treated as the final average undulation height h3a.

[0139] In the above embodiment, a structure composed of multiple objects may be integrated, or conversely, a structure composed of a single object may be divided into multiple objects. Whether or not the objects are integrated, the structure should be configured in a way that achieves the objective of the invention. [Explanation of symbols]

[0140] 10…Disk 10A…Second sliding surface 20... Ring 20A...First sliding surface 21...First swell 21A…1st slope 21B…Second slope 21m…concave peak 21p…First convex peak 21q…Second convex peak 22...Second swell 22A…1st slope 22B…Second slope 22m…concave peak 22p…First peak 22q…Second convex peak 23... Storage trench 24... Dimple

Claims

1. A sliding mechanism comprising a first member and a second member that slide against each other, wherein lubricating oil can be interposed between a first sliding surface, which is the sliding surface of the first member facing the second member, and a second sliding surface, which is the sliding surface of the second member facing the first member, If the length in the sliding direction of the portion where the distance between the first sliding surface and the second sliding surface that slides in the sliding direction via the lubricating oil is 10 μm or less is defined as the sliding length, The first sliding surface includes at least one convex peak and one concave peak of undulation that are aligned with the sliding direction of the first member relative to the second member and have wavelength components shorter than the sliding length. Let σ be the surface roughness of the first sliding surface in the aforementioned sliding direction. If the distance between the convex peak and the concave peak is defined as the height of the undulation, The swell is configured such that the value obtained by adding 3σ to the height of the swell is 3.3σ or more and 30σ or less. Sliding mechanism.

2. The swell is configured such that the value obtained by adding 3σ to the height of the swell is 3.9σ or more and 15σ or less. The sliding mechanism according to claim 1.

3. The swell is constructed such that the value obtained by adding 3σ to the height of the swell is 6.6σ or greater. The sliding mechanism according to claim 2.

4. The sliding length is 0.1 mm to 50 mm. The sliding mechanism according to claim 1.

5. The aforementioned undulation is contained in two parts within the aforementioned sliding length. The sliding mechanism according to claim 1.

6. The aforementioned swell is, A first convex peak is a convex peak adjacent to the concave peak in the sliding direction, In the sliding direction, a second convex peak is located in the opposite direction to the first convex peak with respect to the concave peak and is adjacent to the concave peak, A first incline in which the distance between the first sliding surface and the second sliding surface decreases as it moves from the concave peak toward the first convex peak, It includes a second incline in which the distance between the first sliding surface and the second sliding surface decreases as it moves from the concave peak toward the second convex peak, At least one of the first incline and the second incline is provided with a recess in which the lubricating oil accumulates. The sliding mechanism according to claim 1.

7. Multiple recesses are provided, and the total opening area of ​​the multiple recesses is 5% to 15% of the area of ​​the first sliding surface. The sliding mechanism according to claim 6.

Images