Spherical roller bearing and method and system for calculating the limit value of the unnotched rib diameter

Abstract

The application belongs to the technical field of bearings, and particularly relates to a self-aligning roller bearing and a method and system for calculating a diameter limit value of a gapless rib of the self-aligning roller bearing. The method calculates, according to cage data, inner ring data and roller data, a radial movement amount of the roller in the cage pocket, a roller tilting and lifting movement amount, a radial movement amount of the cage relative to the inner ring, and an original maximum gap between the roller and the inner ring raceway. The sum of the roller radial chamfer and twice the above movement amount is added to the diameter of the intersection point between the inner ring raceway and the rib to obtain a result which is used as the outer diameter limit value of the inner ring rib. Based on the obtained outer diameter limit value of the inner ring rib, when the self-aligning roller bearing is manufactured, only the way of ensuring that the diameter of the self-aligning roller bearing rib is not lower than the limit value is needed to manufacture the self-aligning roller bearing. The process of trial processing to determine the diameter of the gapless rib is avoided, and the difficulty of bearing manufacturing is reduced.

Description

Technical Field

[0001] This invention belongs to the field of bearing technology, specifically relating to a self-aligning roller bearing and a method and system for calculating the limit value of the diameter of its unnotched flange. Background Technology

[0002] In the bearing industry, self-aligning roller bearings possess the unique ability to respond to misalignment of the support shaft and are widely used in components such as industrial gearboxes, vibrating screens, rail vehicles, rolling mill machinery, printing machinery, and petroleum machinery. The CA type is a structural type of self-aligning roller bearing that uses a brass cage. To facilitate roller assembly, CA type self-aligning roller bearings typically have roller notches designed on the inner ring's small flange. From a product design perspective, the flange notch has no impact or beneficial effect on bearing performance; it is merely for manufacturing convenience, and the machining of the notch increases bearing manufacturing costs. Furthermore, due to improper design or manufacturing of the notch, rollers frequently fall off during bearing use, as described in Chinese utility model patent CN201866101U.

[0003] Therefore, to ensure ease of manufacturing and avoid increasing bearing manufacturing costs by designing roller notches on the inner ring small flanges of CA type self-aligning roller bearings, new technologies without roller notches have emerged in recent years. Existing technologies, while eliminating the ball-loading notch, reduce the outer diameter of the small flanges to ensure smooth roller assembly without increasing manufacturing costs, thus facilitating the manufacturing process of self-aligning roller bearings. For example, Chinese utility model patent CN206668746U discloses a self-aligning roller bearing with a support roller without a ball-loading notch, described as having small flanges on both sides of the outer circumference of the inner ring, without ball-loading notches, and the outer diameter of the small flanges is reduced by 8-10% compared to the original notched small flanges; bearing contact angle... The contact angle is increased by 10-20° compared to the original notched bearing; the overall length of the cage claws is shortened by 10-12% compared to the original notched bearing cage claws. This makes the bearing assembly process easier, reduces scratches caused during assembly, and increases bearing life by 15-20%.

[0004] Although existing technologies have provided ways to reduce the outer diameter of the small flange to make the installation of rollers in self-aligning roller bearings easier, the degree of reduction in the outer diameter of the small flange is still determined by trial machining. That is, the required small flange outer diameter is obtained through a process of trial assembly-rework-trial assembly. Therefore, although this method avoids the problem of increased bearing manufacturing costs associated with designing roller notches on the inner ring small flange, the flange size is currently determined by trial machining, and a definite value cannot be given in the design. This undoubtedly increases the difficulty of bearing manufacturing. Furthermore, because the flange size is obtained through experiments, and there is no definite basis for the flange size, there is also a risk of rollers falling off even with the reduced flange size, which seriously hinders the development of new technologies for self-aligning roller bearings with notched flanges. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for calculating the limit value of the diameter of the self-aligning roller bearing and its unnotched flange, so as to solve the problem that the existing method of determining the flange size based on trial machining increases the difficulty of bearing manufacturing.

[0006] To solve the above technical problems, the present invention provides a method for calculating the limit value of the diameter of the notched flange of a self-aligning roller bearing, comprising the following steps:

[0007] 1) Calculate the radial movement of the roller in the cage pocket, the radial movement of the cage relative to the inner ring, the roller overturning and lifting movement, and the original maximum clearance between the roller and the inner ring raceway based on the cage data, inner ring data, and roller data.

[0008] 2) The result obtained by adding twice the sum of the roller radial chamfer, the roller radial movement in the cage pocket, the cage radial movement relative to the inner ring, the roller overturning and lifting movement, and the original maximum clearance between the roller and the inner ring raceway, and then adding it to the diameter of the intersection point of the inner ring raceway and the flange, is taken as the limit value of the outer diameter of the inner ring flange.

[0009] The beneficial effects are as follows: Because the radial movement within the cage pocket, the roller overturning and lifting movement, the radial movement of the cage relative to the inner ring, and the original maximum clearance between the roller and the inner ring raceway all limit the maximum diameter of the self-aligning roller bearing chamfer, the method of this invention fully considers the data affecting the roller movement and obtains the maximum diameter of the self-aligning roller bearing chamfer based on this data. Specifically, starting from the intersection of the inner raceway and the chamfer, the roller movement is calculated step by step, and finally, the total radial lifting of the roller chamfer is determined, which is the height value of the notched chamfer. Since this invention determines the maximum diameter of the self-aligning roller bearing chamfer through calculation, the chamfer diameter of the self-aligning roller bearing to be manufactured can be determined based on this maximum value, thus avoiding the process of determining the chamfer diameter through trial machining, thereby reducing the difficulty of bearing manufacturing. Furthermore, by calculating the maximum value, this invention ensures that the actual manufactured chamfer diameter is not lower than this maximum value during the manufacturing process, thereby avoiding the risk of rollers falling off due to an excessively low chamfer diameter.

[0010] Furthermore, the radial movement of the roller within the cage pocket is determined by the distance OO' between the bearing center O and the roller center O' based on the inner ring rolling to the pressure line diameter N and the maximum diameter Da of the self-aligning roller. Then, within a right triangle with OA as the hypotenuse formed by the intersection point A of the cage outer diameter and the pocket and the bearing center O, the distance is calculated using the cage outer diameter Dc and the bearing contact angle. The distance OA between the bearing center and the intersection of the cage outer diameter and the pocket is obtained. Then, in the triangle formed by points O, O', and A, the geometric relationship of the triangle is used to obtain the amount of movement of the roller along the OO' direction. This amount of movement along the OO' direction is then converted into the amount of movement along the radial direction.

[0011] Furthermore, the radial movement δ1 of the roller within the cage pocket is obtained by the following calculation formula:

[0012] ;

[0013] ;

[0014] ;

[0015] ;

[0016] ;

[0017] ;

[0018] ;

[0019] Where O'A is the pocket radius, Dp is the pocket diameter, and Da is the maximum diameter of the self-aligning roller.

[0020] This invention utilizes cage data, inner ring data, and roller data to obtain the final radial movement of the roller within the cage pocket. From the above formula, it can be seen that, given the inner ring diameter N (reaching the pressure line), the maximum diameter Da of the self-aligning roller, the cage outer diameter Dc, and the bearing contact angle... The radial movement of the roller within the cage pocket can be obtained by considering the pocket diameter Dp. The other parameters in the above formula are intermediate parameters; that is, by combining them, the radial movement δ1 within the cage pocket can be obtained, along with N, Da, Dc, and... And the relationship between Dp:

[0021] ,in .

[0022] Furthermore, the radial movement of the cage relative to the inner ring is obtained based on the difference between the inner diameter of the cage and the diameter of the flange in the inner ring.

[0023] There is a gap between the cage and the inner ring, and the cage will move radially. This amount of movement is calculated using the inner diameter dc of the cage and the diameter 2yE of the flange in the inner ring. That is, the radial movement δ2 of the cage relative to the inner ring in this invention is:

[0024] .

[0025] Furthermore, the roller overturning and lifting movement is obtained by acquiring the position H of one end of the roller before overturning and lifting and the position H' of that end when it is overturned and lifted to the limit position, and the difference between the radial distance of the position H and the position H' is taken as the roller overturning and lifting movement.

[0026] The roller overturning and lifting movement of the present invention takes into account the outward displacement of the roller. By obtaining the position H of one end of the roller before overturning and lifting and the position H' of the end when it is overturned and lifted to the limit position, the difference between the radial distance of the position H and the position H' is taken as the roller overturning and lifting movement.

[0027] Furthermore, the roller overturning and lifting movement δ3 is obtained through the following calculation formula:

[0028] ;

[0029] ;

[0030] ;

[0031] δ3=y(H)-y(H'), where L rR is the total length of the roller, r1 is the axial chamfer of the roller, R is the radius of curvature of the roller surface, Da is the maximum diameter of the self-aligning roller, b is the radius of curvature of the inner ring raceway, δ1 is the radial movement of the roller in the cage pocket, and δ2 is the radial movement of the cage relative to the inner ring.

[0032] The method of this invention obtains the roller overturning and lifting movement by measuring the longitudinal position difference between the roller at the non-overturning and overturning limits. Furthermore, this method utilizes coordinate calculations to ultimately obtain the roller overturning and lifting movement δ3. As shown in the above formula, given the total roller length L... r The roller overturning and lifting movement δ3 can be obtained by taking the roller axial chamfer r1, the roller surface radius of curvature R, the maximum diameter Da of the self-aligning roller, and the inner raceway radius of curvature b. The remaining parameters are intermediate parameters; by combining them, the roller overturning and lifting movement δ2 can be obtained. r The relationship between r1, R, Da, and b is as follows:

[0033] ,

[0034] in .

[0035] Furthermore, the formula for calculating the original maximum clearance δ4 between the roller and the inner ring raceway is as follows:

[0036] ;

[0037] Where L r R is the total length of the roller, r1 is the axial chamfer of the roller, R is the radius of curvature of the roller surface, and b is the radius of curvature of the inner raceway.

[0038] Furthermore, when calculating the radial movement of the roller within the cage pocket, the radial movement of the cage relative to the inner ring, the roller overturning and lifting movement, and the original maximum clearance between the roller and the inner ring raceway, the cage data, inner ring data, and roller data used are all limit values ​​within the data error range.

[0039] This invention takes into account that since all dimensional values ​​have tolerance ranges during the design process, in order to determine the limit value of the flange, the dimensional limit value of the data used should be considered when applying the corresponding data, that is, when the roller movement is at its maximum. The calculated value is the limit value of the flange diameter without a notch. At this time, the roller shape should be at its minimum, the chamfer should be at its maximum, the cage pocket should be at its maximum, and the gap between the cage and the inner ring should be at its maximum. Therefore, the flange diameter limit value obtained by using this dimensional limit value is more accurate, and the situation of the roller not falling off can be better avoided based on this limit value.

[0040] To solve the above-mentioned technical problems, the present invention also provides a system for calculating the limit value of the flange diameter of a self-aligning roller bearing without notch, including a memory and a processor. The processor is used to execute instructions to implement the calculation method steps of the limit value of the flange diameter of the self-aligning roller bearing described above, and achieve the same beneficial effect as the method.

[0041] To solve the above-mentioned technical problems, the present invention also provides a self-aligning roller bearing, including an inner ring, rollers, an outer ring, and a cage, wherein the inner ring flange is not notched, and the diameter of the inner ring flange is not less than the limit value of the diameter of the self-aligning roller bearing without notched flange. The limit value of the diameter of the self-aligning roller bearing without notched flange is obtained by the calculation method steps of the limit value of the diameter of the self-aligning roller bearing without notched flange described above. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the bearing structure of the present invention;

[0043] Figure 2a , Figure 2b , Figure 2c This is a simplified diagram showing the calculation of the radial movement of the roller within the cage pocket of the present invention in different view directions;

[0044] Figure 3 This is a simplified diagram for calculating the roller overturning and lifting movement of the present invention;

[0045] Figure 4 This is a simplified diagram for calculating the radial movement of the cage relative to the inner ring of the present invention;

[0046] Figure 5 This is a simplified diagram for calculating the original maximum clearance between the roller and the inner raceway of this invention.

[0047] Figure 6 This is a simplified diagram for calculating the diameter of the notch-free flange of the present invention;

[0048] Figure 7 This is a flowchart illustrating the calculation method for the limit value of the flange diameter of the self-aligning roller bearing according to the present invention.

[0049] The components are: 1. Inner ring; 2. Roller; 3. Outer ring; 4. Cage. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0051] Example of a self-aligning roller bearing:

[0052] In this embodiment, the self-aligning roller bearing is a CA type self-aligning roller bearing without notched flanges, such as... Figure 1As shown, it includes an inner ring 1, a roller 2, an outer ring 3, and a cage 4. In this embodiment, the cage is made of copper, the inner ring flange has no notch, and the bearing is of CA structure type.

[0053] To simplify the assembly of rollers and avoid the manufacturing difficulties caused by trial machining to determine the flange dimensions in the production of self-aligning roller bearings, this embodiment utilizes data from the inner ring, rollers, cage, and outer ring to determine the limit value of the unnotched flange diameter for the self-aligning roller bearing. Therefore, during the manufacturing process, it is only necessary to ensure that the unnotched flange diameter is not lower than this limit value. Since this embodiment determines the limit value of the unnotched flange diameter through calculation, the flange diameter of the self-aligning roller bearing to be manufactured can be determined based on this limit value, thus avoiding the process of determining the flange diameter through trial machining and reducing the difficulty of bearing manufacturing. Furthermore, by calculating the limit value, this embodiment ensures that the actual manufactured flange diameter is not lower than this limit value during the manufacturing process, thereby avoiding the risk of rollers falling off due to an excessively low flange diameter.

[0054] The basic idea of ​​the design method for the diameter of the notched flange is as follows: starting from the intersection of the inner raceway and the flange, the amount of roller movement is calculated step by step, and finally the total radial lift of the roller chamfer is determined, which is the height value of the notched flange. Based on this, the known dimensional values ​​in the calculation equation are replaced with design limit values ​​instead of nominal values, and the result is the height limit value of the notched flange.

[0055] The stepwise calculation of the roller's movement specifically includes four parts: the radial movement of the roller within the cage pocket δ1, the radial movement of the cage relative to the inner ring δ2, the roller's overturning and lifting movement δ3, and the initial maximum clearance between the roller and the inner ring raceway δ4. Therefore, the equation for calculating the outer diameter Di1 of the inner ring flange is:

[0056] ;

[0057] Where 2yG is the diameter of the intersection of the inner raceway and the flange (e.g., ...). Figure 6 As shown, r2 is the diameter value corresponding to the intersection point, and r2 is the radial chamfer of the roller.

[0058] In this embodiment, it is also considered that all dimensions have tolerance ranges during the design process. Therefore, in order to find the limit value of the flange, this tolerance range should be considered in the calculation process, that is, the limit value of the outer diameter of the inner ring flange is calculated by using the corresponding dimensional limit value.

[0059] Specifically, such as Figure 7 The calculation method for the limit value of the notched flange diameter of the self-aligning roller bearing in this embodiment includes the following steps:

[0060] 1) Calculate the radial movement δ1 of the roller within the cage pocket.

[0061] First, in the main view Figure 2a In the diagram, O is the bearing center, O' is the roller center, and A is the intersection of the cage outer diameter and the pocket. The bearing center is determined by the inner ring rolling to the pressure line diameter N and the maximum diameter Da of the self-aligning rollers (e.g., ...). Figure 2a In this context, Da refers to... Figure 2a The distance between the bearing center and the roller center is obtained by multiplying the distance between point B and point O' by 2. Then, within the right triangle with OA as the hypotenuse, the outer diameter Dc of the cage and the bearing contact angle are used to determine the bearing contact angle. The distance OA from the bearing center to the intersection of the cage outer diameter and the pocket is obtained, i.e. .

[0062] The roller cross-section along the OO' direction is as follows Figure 2b As shown, in triangle AOO', by the Law of Cosines, we have:

[0063] In the formula, O'A is the radius of the pocket.

[0064] Then, from O'E⊥AE, we get:

[0065]

[0066] like Figure 2c As shown in the enlarged image:

[0067] ;

[0068] ;

[0069] Where Dp is the diameter of the pocket; Da is the maximum diameter of the self-aligning roller.

[0070] Then, based on AE and DE, the roller's movement AD along the OO' direction is obtained, and converted into radial movement (e.g.) Figure 2a As shown, this radial direction is the same as the straight line direction shown by OC in the figure).

[0071] .

[0072] 2) Calculate the radial movement δ2 of the cage relative to the inner ring.

[0073] like Figure 4 As shown, there is a gap between the cage and the inner ring, causing the cage to move radially. This movement is calculated using the cage inner diameter dc and the inner ring flange diameter 2yE, i.e.:

[0074] .

[0075] 3) Calculate the amount of roller overturning and lifting movement δ3 (i.e., δ3).

[0076] like Figure 3 This is a schematic diagram showing the roller before and after it overturns; that is, the roller overturns around the center point O', and the end near the outer edge rises. For example... Figure 3 As shown, one end of the roller descends from point H to point H', and the amount of descent between these two points represents the amount of elevation of the outer side. First, due to the movement of the roller δ1 and δ2, a gap (δ1+δ2) / cosα will be created between the roller and the inner raceway.

[0077] like Figure 3 As shown, the radius of rotation O'H (or O'H') is calculated by the distance from point H (or H') to the line containing points O1 and O', and the distance between the intersection of the perpendiculars from point O' and point H (or H') to the lines containing points O1 and O'. Specifically:

[0078] L r R is the total length of the roller, r1 is the axial chamfer of the roller, R is the radius of curvature of the roller surface, and Da is the maximum diameter of the self-aligning roller (e.g., ...). Figure 3 As shown, the value of O'F here is half of Da.

[0079] With O' as the origin, a coordinate system is established with the x-direction horizontally along the center line of the roller and the y-direction vertically downward. Then, the coordinates of the centers of each circle can be obtained: O' (0,0), O1 (0,R-0.5Da), O2 (0, b-0.5Da-(δ1+δ2) / cosα).

[0080] The equations for each circular arc can be established:

[0081] Roller rotating arc (center O'): ;

[0082] Roller arc surface (center O1): ;

[0083] Inner raceway arc surface (center O2): x 2 +[y-b+0.5Da+(δ1+δ2) / cosα] 2 =b 2 Where b is the radius of curvature of the inner raceway;

[0084] The coordinates of point H are the intersection of the roller arc surface (center O1) and the roller rotation arc (center O'):

[0085] ;

[0086] Solve for the y-coordinate of point H:

[0087] ;

[0088] The coordinates of point H' are the intersection of the roller rotation arc (center O') and the inner raceway arc (center O2):

[0089]

[0090] Solve for the y-coordinate of point H':

[0091] ;

[0092] Therefore, the radial distance the roller is raised is: δ3=y(H)-y(H').

[0093] 4) Calculate the original maximum clearance δ4 between the roller and the inner raceway.

[0094] like Figure 5 As shown, there is an initial maximum clearance between the roller and the inner raceway; this initial maximum clearance is... Figure 5 The distance between points M1 and M2 is shown. This distance is calculated by taking triangle O2M'M2, then triangle O1MM1, and finally bR to obtain O1O2. This allows us to obtain the original maximum clearance δ4 between the roller and the inner raceway (i.e., M1M2 = O2M2 - O1M1 - O1O2). The specific calculation formula is as follows:

[0095] .

[0096] 5) Determine the limit value of the outer diameter of the inner ring flange based on δ1, δ2, δ3 and δ4.

[0097] like Figure 6 As shown, the roller, including the chamfer r2, must not exceed the flange dimension Di1. Therefore, the outer diameter of the flange is:

[0098] ;

[0099] That is, the outer diameter of the flange is equal to twice the diameter of the intersection of the inner raceway and the flange, plus the sum of the roller radial chamfer, the roller radial movement direction, the radial distance of the roller lifting, the cage radial movement distance, and the original maximum clearance between the roller and the inner raceway.

[0100] Based on the obtained limit value of the inner ring flange outer diameter, when manufacturing self-aligning roller bearings, it is only necessary to ensure that the flange diameter of the self-aligning roller bearing is not lower than this limit value. This avoids the process of determining the flange diameter through trial machining, thereby reducing the difficulty of bearing manufacturing. Furthermore, in this embodiment, by calculating the limit value, the actual flange diameter value manufactured is ensured not to be lower than this limit value during the manufacturing process, thus avoiding the risk of rollers falling off due to an excessively low flange diameter.

[0101] This embodiment takes into account that all dimensional values ​​have tolerance ranges during the design process. In order to determine the limit value of the flange, the dimensional limit value should be used in the aforementioned calculation equation. When the roller movement is at its maximum, the calculated value is the limit value of the unnotched flange diameter. At this time, the roller profile should be at its minimum, the chamfer at its maximum, the cage pocket at its maximum, and the clearance between the cage and the inner ring at its maximum. The dimensions in the above equation should be replaced with the dimensions in Table 1 below.

[0102] Table 1

[0103]

[0104] Taking the 23072CA / W33 self-aligning roller bearing as an example, the bearing parameters are shown in Table 2 below:

[0105] Table 2

[0106]

[0107] The results obtained through the aforementioned algorithm are shown in Table 3 below:

[0108] Table 3

[0109]

[0110] The calculation results show that the limit value of the flange diameter is 413.8 mm, and the design value must not be lower than this value. Therefore, it can be marked as 413.8 (-0.44~0) on the engineering drawings, and the tolerance is given by experience.

[0111] Example of a system for calculating the limit value of the notched flange diameter of a self-aligning roller bearing:

[0112] The system in this embodiment includes a memory and a processor. The processor is used to execute instructions to implement the calculation method steps for the limit value of the diameter of the notched flange of the self-aligning roller bearing. The specific calculation method steps for the limit value of the diameter of the notched flange of the self-aligning roller bearing have been described in detail in the self-aligning roller bearing embodiment, and will not be repeated here.

[0113] Example of a method for calculating the limit value of the notched flange diameter of a self-aligning roller bearing:

[0114] The method in this embodiment calculates the radial movement of the roller within the cage pocket, the roller overturning and lifting movement, the radial movement of the cage relative to the inner ring, and the original maximum clearance between the roller and the inner ring raceway based on cage data, inner ring data, and roller data. The method then takes twice the sum of the roller radial chamfer, the radial movement of the roller within the cage pocket, the roller overturning and lifting movement, the radial movement of the cage relative to the inner ring, and the original maximum clearance between the roller and the inner ring raceway, and adds this sum to the diameter of the intersection point of the inner ring raceway and the flange. The result obtained is used as the limit value of the outer diameter of the inner ring flange. The specific steps for calculating the limit value of the diameter of the notched flange of the self-aligning roller bearing have been described in detail in the embodiments of the self-aligning roller bearing and will not be repeated here.

[0115] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. The scope of patent protection of the present invention shall be determined by the claims. Similarly, any equivalent structural changes made based on the description and drawings of the present invention shall also be included within the scope of protection of the present invention.

Claims

1. A method for calculating the limit value of the diameter of the notched flange of a self-aligning roller bearing, characterized in that, Includes the following steps: 1) Calculate the radial movement of the roller in the cage pocket, the radial movement of the cage relative to the inner ring, the roller overturning and lifting movement, and the original maximum clearance between the roller and the inner ring raceway based on the cage data, inner ring data, and roller data. 2) The result obtained by adding twice the sum of the roller radial chamfer, the roller radial movement in the cage pocket, the cage radial movement relative to the inner ring, the roller overturning and lifting movement, and the original maximum clearance between the roller and the inner ring raceway, and then adding it to the diameter of the intersection point of the inner ring raceway and the flange, is taken as the limit value of the outer diameter of the inner ring flange.

2. The method for calculating the limit value of the diameter of the notched flange of a self-aligning roller bearing according to claim 1, characterized in that, The radial movement of the roller within the cage pocket is determined by the distance OO' between the bearing center O and the roller center O' based on the inner ring raceway pressure line diameter N and the maximum diameter Da of the self-aligning roller. Then, within a right triangle with OA as the hypotenuse formed by the intersection point A of the cage outer diameter and the pocket and the bearing center O, the radial movement is determined by the cage outer diameter Dc and the bearing contact angle. The distance OA between the bearing center and the intersection of the cage outer diameter and the pocket is obtained. Then, in the triangle formed by points O, O', and A, the geometric relationship of the triangle is used to obtain the amount of movement of the roller along the OO' direction. This amount of movement along the OO' direction is then converted into the amount of movement along the radial direction.

3. The method for calculating the limit value of the diameter of the notched flange of a self-aligning roller bearing according to claim 2, characterized in that, The radial movement δ1 of the roller within the cage pocket is obtained by the following formula: ； ； ； ； ； ； ； Where O'A is the pocket radius, Dp is the pocket diameter, and Da is the maximum diameter of the self-aligning roller.

4. The method for calculating the limit value of the diameter of the notched flange of a self-aligning roller bearing according to claim 1, characterized in that, The radial movement of the cage relative to the inner ring is obtained based on the difference between the inner diameter of the cage and the diameter of the flange in the inner ring.

5. The method for calculating the limit value of the diameter of the notched flange of a self-aligning roller bearing according to claim 1, characterized in that, The roller overturning and lifting movement is obtained by taking the position H of one end of the roller before overturning and lifting and the position H' of that end when it is overturned and lifted to the limit position, and the difference between the radial distance of the two positions H and H' is taken as the roller overturning and lifting movement.

6. The method for calculating the limit value of the diameter of the notched flange of a self-aligning roller bearing according to claim 5, characterized in that, The roller overturning and lifting movement δ3 is obtained by the following calculation formula: ； ； ； L r R is the total length of the roller, r1 is the axial chamfer of the roller, R is the radius of curvature of the roller surface, Da is the maximum diameter of the self-aligning roller, b is the radius of curvature of the inner ring raceway, δ1 is the radial movement of the roller in the cage pocket, and δ2 is the radial movement of the cage relative to the inner ring.

7. The method for calculating the limit value of the diameter of the notched flange of a self-aligning roller bearing according to claim 1, characterized in that, The formula for calculating the original maximum clearance δ4 between the roller and the inner ring raceway is: ； Where L r R is the total length of the roller, r1 is the axial chamfer of the roller, R is the radius of curvature of the roller surface, and b is the radius of curvature of the inner raceway.

8. The method for calculating the limit value of the diameter of the notched flange of a self-aligning roller bearing according to claim 3, 5, 6 or 7, characterized in that, When calculating the radial movement of the roller within the cage pocket, the radial movement of the cage relative to the inner ring, the roller overturning and lifting movement, and the original maximum clearance between the roller and the inner ring raceway, the cage data, inner ring data, and roller data used are all limit values ​​within the data error range.

9. A system for calculating the limit value of the diameter of the notched flange of a self-aligning roller bearing, characterized in that, It includes a memory and a processor, the processor being used to execute instructions to implement the steps of the method for calculating the limit value of the unnotched flange diameter of a self-aligning roller bearing as described in any one of claims 1 to 8.

10. A self-aligning roller bearing, comprising an inner ring, rollers, an outer ring, and a cage, wherein the inner ring flange has no notch, characterized in that, The diameter of the inner ring flange is not less than the limit value of the diameter of the unnotched flange of the self-aligning roller bearing, and the limit value of the diameter of the unnotched flange of the self-aligning roller bearing is obtained by the calculation method steps of the limit value of the diameter of the unnotched flange of the self-aligning roller bearing as described in any one of claims 1 to 8.

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