CN106402162A - Noncircular raceway rolling bearing - Google Patents

Abstract

The invention discloses a noncircular raceway rolling bearing. Raceways on the outer ring inner surface of the bearing and the inner ring outer surface of the bearing are noncircular raceways, and rolling bodies are evenly spaced by a holder and roll in the noncircular raceway between a bearing outer ring and a bearing inner ring. The cross sections of the noncircular raceways on the bearing outer ring and the bearing inner ring are one of a normal curve, a parabola, a catenary, a conchoids, an elliptic arc and a versiera, or are the combination of different curves. The radius of curvature in the middle of the raceway on the bearing outer ring is larger than the radius of the curvature in the middle of the raceway on the bearing inner ring. According to the noncircular raceway rolling bearing, the radius of the curvature of the raceways can be reduced, the axial clearance of the bearing is reduced, and vibration of the bearing is reduced. Moreover, the synthetic radius of curvature of the raceways and rollers can be increased, the contact stress of the raceways on the inner ring and the outer ring and the rolling bodies is reduced, the bearing capacity of the bearing is improved, and the contact fatigue life of the bearing is prolonged.

Description

Non-circular raceway rolling bearings

technical field

The invention relates to a rolling bearing, in particular to a non-circular raceway rolling bearing.

Background technique

In rolling bearings, the rolling elements are in contact with the raceways of the inner and outer rings of the bearing. In the design of traditional rolling bearings, the cross section of the raceway is usually designed to be circular, and the ratio of the radius of the raceway to the diameter of the roller is between 0.53 and 0.54. The radius of curvature of the circular raceway section is large, making the bearing The axial clearance is large, which increases the vibration and noise of the bearing. In addition, the comprehensive radius of curvature of the rolling body and the raceway of the circular raceway bearing is small, resulting in excessive contact stress between the rolling body and the inner and outer ring raceways, resulting in a smaller bearing capacity and a shorter service life.

Contents of the invention

In order to solve the problems in the background technology that the radius of curvature of the circular raceway of the general rolling bearing is large, the axial clearance of the bearing is large, the vibration of the bearing is large, the contact stress between the rolling element and the raceway is large, and the contact fatigue life of the bearing is short, the purpose of the present invention is to Provide a non-circular raceway that can reduce the radius of curvature of the raceway, reduce the axial clearance of the bearing, reduce the vibration of the bearing, reduce the contact stress between the rolling elements and the raceway, and improve the bearing capacity and contact fatigue life of the bearing rolling bearings.

The technical scheme adopted in the present invention is:

The present invention includes a bearing outer ring, a bearing inner ring, rolling elements installed between the bearing outer ring and the bearing inner ring, a cage and a lubricant, and the raceways of the inner surface of the bearing outer ring and the outer surface of the bearing inner ring are as follows: Non-circular raceway, the rolling elements are evenly spaced by the cage and roll in the non-circular raceway between the outer ring of the bearing and the inner ring of the bearing.

The cross-sectional shape of the non-circular raceway is one of a normal curve, a parabola, a catenary, a clam curve, an elliptical arc, and a skip line.

The cross-sectional shape of the non-circular raceway of the bearing outer ring and the bearing inner ring is one of normal curve, parabola, catenary line, clam line, ellipse arc, skip line or a combination of the above-mentioned different curves.

The radius of curvature at the middle of the raceway of the outer ring of the bearing (that is, the radius of curvature of the raceway at the symmetrical center point on the curve) is larger than the radius of curvature at the middle of the raceway of the inner ring of the bearing.

The ratio of the radius of curvature at the middle of the raceway of the outer ring of the bearing to the diameter of the rolling body is 0.52-0.53.

The ratio of the radius of curvature at the middle of the raceway of the inner ring of the bearing to the diameter of the rolling body is 0.515-0.52.

The respective non-circular raceways of the bearing outer ring and the bearing inner ring are symmetrical on both sides of the bearing center along the axial direction of the bearing.

The present invention can reduce the radius of curvature of the raceway, reduce the axial clearance of the bearing, and reduce the vibration of the bearing by properly designing the cross-sectional shape of the raceway. The contact stress between the two is reduced, thereby improving the bearing capacity and service life of the rolling bearing. For details, please refer to the following formula for calculating the normal stress σ _H of the contact between two parts.

In the formula: F—the total pressure acting on the contact surface; B—the length of the initial contact line; μ ₁ and μ ₂ —the Poisson’s ratio of the material of part 1 and part 2, respectively; E ₁ and E ₂ —the and the modulus of elasticity of the material of part 2. ρ ₁ and ρ ₂ —the radii of curvature at the initial contact of the first part and the second part, respectively.

Usually, order is called the composite curvature, and Called the composite radius of curvature, where the positive sign is for external contact and the negative sign is for internal contact. In the present invention, the contact conditions between the rollers and the raceways of the inner and outer rings are all internal contact.

The above formula is the formula for calculating the contact stress when two parts are in contact with each other given by elastic mechanics. It can be seen from the above formula that the contact stress between two parts in contact with each other is related to the comprehensive radius of curvature of the two parts at the initial contact line. The larger the combined radius of curvature, the smaller the contact stress. The diameter of the rolling element in the present invention remains unchanged, because it is an internal contact, reducing the radius of curvature of the inner ring and outer ring of the bearing at the contact point with the rolling element will increase the comprehensive radius of curvature and improve the comprehensive radius of curvature, so it can be reduced Contact stress is improved to improve the bearing capacity and service life of rolling bearings.

The beneficial effects that the present invention has are:

1. In the present invention, the cross-sectional shapes of the bearing raceways of the inner and outer rings are respectively designed as normal distribution curves, parabolas, catenary lines, clam lines, elliptical arcs, and skip lines with smaller curvature radii. The radius of curvature of the inner and outer ring bearing raceways is reduced, thereby reducing the axial clearance, vibration and noise of the bearing.

2. In the present invention, the cross-sectional shape of the raceway of the inner and outer ring bearings is respectively designed as a normal distribution curve, a parabola, a catenary, a clam curve, an elliptical arc, a cycloid, and a skip line with a smaller radius of curvature. It can increase the comprehensive radius of curvature of the contact between the rolling body and the inner and outer ring bearing raceways, thereby reducing the contact stress between the rolling body and the inner and outer ring raceways, and improving the bearing capacity and fatigue life of the bearing.

3. The cross-sectional shape of the non-circular raceway is designed to be a normal distribution curve, a parabola, a catenary, a clam curve, an elliptical arc, and a skip line with a small radius of curvature. These curves are easily represented by curve equations, which are convenient for raceway fabrication.

In a word, the present invention reduces the radius of curvature of the raceway, reduces the axial clearance, vibration and noise of the bearing, and also increases the combined radius of curvature of the rolling body and the raceway, reducing the contact stress between the two , thereby improving the bearing capacity and service life of rolling bearings.

Description of drawings

Figure 1 is a schematic diagram of the structure of a non-circular raceway bearing.

Figure 2 is a normal curve diagram.

Fig. 3 is a sectional view of a normal curve raceway rolling bearing.

Figure 4 is a parabolic graph.

Fig. 5 is a sectional view of a parabolic rolling bearing.

Figure 6 is a catenary curve diagram.

Fig. 7 is a sectional view of a catenary raceway rolling bearing.

Fig. 8 is a clam line curve diagram.

Fig. 9 is a cross-sectional view of a clam-shaped raceway rolling bearing.

Figure 10 is an elliptic curve diagram.

Fig. 11 is a sectional view of an elliptical raceway rolling bearing.

Fig. 12 is a curve diagram of skip line.

Fig. 13 is a cross-sectional view of a skip-line raceway rolling bearing.

Among them: 1. Bearing inner ring, 2. Cage, 3. Rolling elements, 4. Bearing outer ring.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

As shown in Fig. 1, the present invention comprises bearing outer ring 4, bearing inner ring 1 and rolling body 3 installed between bearing outer ring 4 and bearing inner ring 1, cage 2 and lubricant, bearing outer ring 4 inner surface The raceway on the outer surface of the bearing inner ring 1 is a non-circular raceway, and the rolling elements 3 are evenly spaced apart by the cage 2 and roll in the non-circular raceway between the bearing outer ring 4 and the bearing inner ring 1 .

The cross-sectional shape of the non-circular raceways of the bearing outer ring 4 and the bearing inner ring 1 is one of normal curve, parabola, catenary line, clam line, elliptical arc, skip line or a combination of the above-mentioned different curves.

The working principle of the present invention is:

After research, it is found that in general rolling bearings, the cross-sectional shape of the raceway of the inner and outer rings of the bearing is designed to be circular, and the ratio of the curvature radius of the raceway to the diameter of the roller is between 0.53 and 0.54. This structural design will make the inner and outer rings of the bearing The raceway has a large radius of curvature, which easily causes the bearing to vibrate. In addition, if the combined radius of curvature of the rolling element and the raceway is too small, the contact stress between the rolling element and the raceway will easily increase and the working life of the bearing will be shortened.

In order to prolong the service life of the bearing and reduce the frictional moment, the present invention designs the cross-sectional shape of the raceway into a non-circular shape, and these non-circular raceways can reduce the axial clearance of the bearing and reduce the vibration of the bearing. In addition, the comprehensive radius of curvature of the contact between the raceway and the rolling body is increased, which reduces the contact stress between the raceway and the rolling body and improves the working life of the bearing.

Embodiments of the present invention are as follows:

As shown in Figure 3, it is a non-circular raceway rolling bearing whose inner and outer ring raceways are designed as normal curves. The normal curve equation of the inner and outer ring raceways is Since the bearing raceway curve is symmetrical in the axial direction of the bearing, the vertex of the normal curve shown in Figure 2 is the symmetrical center point of the raceway section. The radius of curvature here can be calculated by the formula of radius of curvature Calculated. Let μ=0, the formula for calculating the radius of curvature is Given that the diameter D of the roller is 10mm, then from the ratio of the radius of curvature of the raceway to the diameter of the rolling element described in claim 5, the curvature of the raceway of the outer ring of the bearing can be obtained as ρ ₁ =(0.52～0.53)*10, and from the curvature The radius calculation formula is Combining the two formulas, the parameters of the outer ring raceway curve equation σ = 1.275 ~ 1.28 can be obtained. Bring it into the outer ring raceway normal curve equation to get the outer ring curve equation. For the same reason, the radius of curvature of the inner ring raceway is ρ ₂ =(0.515～0.52)*10, the inner ring raceway curve parameter σ=1.271～1.275 can be obtained, and the inner ring raceway curve can be obtained by bringing it into the normal curve equation of the inner ring parametric equation. In addition, the comprehensive curvature radius calculation formula The integrated radius of curvature ρ _1Σ =88.33～130 for the raceway of the outer ring and the rollers can be calculated similarly to the integrated radius of curvature ρ _2Σ =130～171.7 for the raceway of the inner ring and the rollers. In the case where the roller diameter of this example is 10mm, the combined radius of curvature ρ ₁ ' _Σ = 67.5 to 88.3 for the general circular raceway bearing raceway and the roller, which is higher than that between the roller and the raceway in the present invention Comprehensive radius of curvature is small. Therefore, the bearing in the present invention can reduce the vibration of the bearing and the contact stress between the raceway and the roller, and improve the service life of the bearing. In addition, the invention reduces the radius of the raceway, so that the vibration of the bearing is reduced.

Where μ represents the mean of a normal random variable, and σ represents the variance of a normal random variable.

As shown in Figure 5, it is a non-circular raceway rolling bearing whose raceway shape of the inner and outer rings is designed as a parabola. The parabolic equation of the inner and outer raceways is y=at ² . Since the bearing raceway curve is symmetrical in the axial direction of the bearing, the apex of the parabola shown in Figure 4 is the symmetry center of the bearing raceway section. The radius of curvature here can be calculated by the formula of radius of curvature Calculated. Calculate its radius of curvature According to the ratio of the radius of curvature of the raceway to the diameter of the rolling element described in claim 5, given that the diameter of the rolling element is 10mm, the radius of curvature of the outer ring raceway ρ ₃ =(0.52～0.53)*10mm can be determined, and the formula for calculating the radius of curvature Have Combining the two formulas, the parameter a ₁ of the raceway curve equation of the outer ring = 0.094～0.096 can be obtained, that is, the section curve equation of the outer ring of the raceway is determined. Similarly, the parameter a ₂ of the curve equation of the inner ring raceway can be obtained = 0.096-0.097, that is, the section curve equation of the inner ring of the raceway is determined. In the case where the diameter of the roller in this example is 10mm, the comprehensive radius of curvature ρ ₃ ' _Σ = 67.5 to 88.3 for the general circular raceway bearing raceway and the roller, which is higher than that between the roller and the raceway in the present invention Comprehensive radius of curvature is small. Therefore, the bearing in the present invention can reduce the vibration of the bearing and the contact stress between the raceway and the roller, and improve the working life of the bearing. In addition, the present invention reduces the radius of the raceway, so that the vibration of the bearing is reduced.

As shown in Figure 7, it is a non-circular raceway rolling bearing whose raceway shape of the inner and outer rings is designed as a catenary. The catenary line equation of the inner and outer ring raceway is Since the bearing raceway curve is symmetrical in the axial direction of the bearing and symmetrical in the width direction of the bearing, the center of the bearing cross-section raceway is the apex of the catenary line in Figure 6 . The radius of curvature here can be calculated by the formula of radius of curvature Calculated. Calculate its radius of curvature According to the ratio of the radius of curvature of the raceway to the diameter of the rolling body described in claim 5, the radius of curvature of the raceway of the outer ring can be determined when the diameter of the rolling body is 10mm ρ ₄ =(0.52～0.53)*10mm, and the formula for calculating the radius of curvature is: Combining the two formulas, the parameter b ₁ of the raceway curve equation of the outer ring = 0.1887～0.1923 can be obtained, that is, the section curve equation of the outer ring of the raceway is determined. Similarly, the parameter b ₂ of the inner ring raceway curve equation can be obtained = 0.1923 ~ 0.1942, that is, the section curve equation of the inner ring of the raceway is determined. In the case of the roller diameter of this example being 10mm, the comprehensive radius of curvature ρ ₄ ' _Σ = 67.5 to 88.3 for the general circular raceway bearing raceway and the roller, which is higher than that between the roller and the raceway in the present invention Comprehensive radius of curvature is small. Therefore, the bearing in the present invention can reduce the vibration of the bearing and the contact stress between the raceway and the roller, and improve the service life of the bearing. In addition, the invention reduces the radius of the raceway, so that the vibration of the bearing is reduced.

As shown in Figure 9, it is a non-circular raceway rolling bearing whose raceway shape of the inner and outer rings is designed as clam lines. The shell line equation of its inner and outer ring raceway is (xc) ² (x ² +y ² )=d ² x ² . Since the bearing raceway curve is symmetrical in the axial direction of the bearing and symmetrical in the width direction of the bearing, the center of the bearing cross-section raceway is the vertex of the clam line in Figure 8. The radius of curvature here can be calculated by the formula of radius of curvature Calculated. Calculate its radius of curvature ρ=|cd|. According to the ratio of the radius of curvature of the raceway to the diameter of the rolling element described in claim 5, given that the diameter of the rolling element is 10mm, the radius of curvature of the outer ring raceway ρ ₅ =(0.52～0.53)*10mm can be determined, and the formula for calculating the radius of curvature There is ρ=|cd|, let d=1, and the parameter c ₁ =5.2～5.3 of the outer ring raceway curve equation can be obtained, that is, the section curve equation of the outer ring of the raceway is determined. Similarly, the inner ring raceway curve equation parameter c ₂ =5.15~5.2 can be obtained, that is, the inner ring section curve equation of the raceway is determined. In the case where the roller diameter of this example is 10mm, the comprehensive radius of curvature ρ ₅ ' _Σ = 67.5 to 88.3 for the general circular raceway bearing raceway and the roller, which is higher than that between the roller and the raceway in the present invention Comprehensive radius of curvature is small. Therefore, the bearing in the present invention can reduce the vibration of the bearing and the contact stress between the raceway and the roller, and improve the service life of the bearing. In addition, the invention reduces the radius of the raceway, so that the vibration of the bearing is reduced.

As shown in Figure 11, it is a non-circular raceway rolling bearing whose raceway shape of the inner and outer rings is designed as an ellipse. The elliptic equation of the raceway of the inner and outer rings is Since the bearing raceway curve is symmetrical in the axis direction of the bearing and symmetrical in the width direction of the bearing, the center of the bearing cross-section raceway is the vertex of the elliptic curve in Fig. 10 . The radius of curvature here can be calculated by the formula of radius of curvature Calculated. Calculate its radius of curvature According to the ratio of the radius of curvature of the raceway to the diameter of the rolling element described in claim 5, given that the diameter of the rolling element is 10mm, the radius of curvature of the outer ring raceway ρ ₆ = (0.52～0.53)*10mm can be determined, and the formula for calculating the radius of curvature Have If e=1, the parameter f ₁ of the outer ring raceway curve equation can be obtained = 0.1887～0.1923, that is, the section curve equation of the outer ring of the raceway is determined. Similarly, the parameter f ₂ of the curve equation of the inner ring raceway can be obtained = 0.1923-0.1942, that is, the section curve equation of the inner ring of the raceway is determined. In the case where the roller diameter of this example is 10mm, the comprehensive radius of curvature ρ ₆ ' _Σ = 67.5 to 88.3 of the general circular raceway bearing raceway and the roller, which is higher than that between the roller and the raceway in the present invention Comprehensive radius of curvature is small. Therefore, the bearing in the present invention can reduce the vibration of the bearing and the contact stress between the raceway and the roller, and improve the service life of the bearing. In addition, the invention reduces the radius of the raceway, so that the vibration of the bearing is reduced.

As shown in Figure 13, it is a non-circular raceway rolling bearing whose raceway shape of the inner and outer rings is designed as a skip line. The skip line equation of the inner and outer ring raceways is Since the bearing raceway curve is symmetrical in the axial direction of the bearing and symmetrical in the width direction of the bearing, the center of the bearing cross-section raceway is the apex of the skip line in Figure 12. The radius of curvature here can be calculated by the formula of radius of curvature Calculated. Calculate its radius of curvature ρ=16g ² . According to the ratio of the radius of curvature of the raceway to the diameter of the rolling element described in claim 5, given that the diameter of the rolling element is 10mm, the radius of curvature of the outer ring raceway ρ ₇ = (0.52～0.53)*10mm can be determined, and the formula for calculating the radius of curvature There is ρ=16g ² , combining the two formulas can obtain the outer ring raceway curve equation parameter g ₁ =0.570～0.576, that is to determine the outer ring section curve equation of the raceway. Similarly, the parameter g ₂ of the inner ring raceway curve equation can be obtained = 0.567-0.570, that is, the section curve equation of the inner ring of the raceway is determined. In the case where the diameter of the roller in this example is 10mm, the comprehensive radius of curvature ρ ₇ ' _Σ = 67.5 to 88.3 for the general circular raceway bearing raceway and the roller, which is higher than that between the roller and the raceway in the present invention Comprehensive radius of curvature is small. Therefore, the bearing in the present invention can reduce the vibration of the bearing and the contact stress between the raceway and the roller, and improve the service life of the bearing. In addition, the invention reduces the radius of the raceway, so that the vibration of the bearing is reduced.

It can be seen from the above embodiments that the present invention reduces the axial clearance, vibration and noise of the bearing through the improvement of the inner curve of the bearing, can reduce the contact stress, and improves the bearing capacity and service life of the rolling bearing.

The above specific embodiments are used to explain the present invention, rather than to limit the present invention. Within the spirit of the present invention and the protection scope of the claims, any modification and change made to the present invention will fall into the protection scope of the present invention.

Claims (8)

1. A non-circular raceway rolling bearing, comprising a bearing outer ring (4), a bearing inner ring (1), and rolling elements (3) installed between the bearing outer ring (4) and the bearing inner ring (1), retaining frame (2) and lubricant, characterized in that: the raceways on the inner surface of the bearing outer ring (4) and the outer surface of the bearing inner ring (1) are non-circular raceways, and the rolling elements (3) are held by the cage ( 2) Evenly spaced, rolling in the non-circular raceway between the bearing outer ring (4) and the bearing inner ring (1). 2. A non-circular raceway rolling bearing according to claim 1, characterized in that: the cross-sectional shape of the non-circular raceway is a normal curve, a parabola, a catenary, a clam curve, an elliptical arc, or a skip line one of a kind. 3. A non-circular raceway rolling bearing according to claim 2, characterized in that: the cross-sectional shape of the non-circular raceways of the bearing outer ring (4) and the bearing inner ring (1) is a normal curve, a parabola , catenary line, clam line, elliptical arc, skip line, or a combination of the above-mentioned different curves. 4. A non-circular raceway rolling bearing according to claim 2, characterized in that: the radius of curvature at the middle of the raceway of the bearing outer ring (4) is larger than the curvature at the middle of the raceway of the bearing inner ring (1) Large radius. 5. A non-circular raceway rolling bearing according to claim 4, characterized in that the ratio of the radius of curvature at the middle of the raceway of the outer ring (4) of the bearing to the diameter of the rolling body (3) is 0.52- 0.53, the ratio of the radius of curvature at the middle of the raceway of the bearing inner ring (1) to the diameter of the rolling element (3) is 0.515-0.52. 6. A non-circular raceway rolling bearing according to claim 1, characterized in that: the respective non-circular raceways of the bearing outer ring (4) and the bearing inner ring (1) are aligned along the axial direction of the bearing Both sides are symmetrical with the center of the bearing. 7. A non-circular raceway rolling bearing according to claim 1, characterized in that: the circumferential angle formed between the two ends of the cross-sectional shape of the non-circular raceway and the center of the rolling element (3) is 120 degrees. 8. A non-circular raceway rolling bearing according to any one of claims 2-4, characterized in that: The normal curve described is: $\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&mu;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span>$ In the above formula, x represents the axial direction of the bearing, y represents the radial direction of the bearing, μ represents the mean value of a normally distributed random variable, and σ represents the variance of a normally distributed random variable; The parabola described is: y=ax ² In the above formula, x represents the axial direction of the bearing, y represents the radial direction of the bearing, and a is a constant; Described catenary is: $\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; b</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\frac{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; b</span>}}}<span\; class="notranslate">\; )</span>$ In the above formula, x represents the axial direction of the bearing, y represents the radial direction of the bearing, and b is a constant; Described clam line is: (xc) ² (x ² +y ² )＝d ² x ² In the above formula, x represents the axial direction of the bearing, y represents the radial direction of the bearing, and c and d are constants; Described ellipse arc is: $\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}$ In the above formula, x represents the axial direction of the bearing, y represents the radial direction of the bearing, e and f are the major and minor semi-axes of the ellipse, respectively; The skip line is: $\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 8</span>}{\mathrm{<span\; class="notranslate">\; g</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; g</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$ In the above formula, x represents the axial direction of the bearing, y represents the radial direction of the bearing, and g is a constant.