Automobile differential free fine-tuning main cone bearing unit and assembling method

Abstract

The application discloses a kind of automobile differential free fine adjustment main cone bearing unit and assembly method, including a bearing seat, two bearing inner rings, two rows of tapered rollers, two cages and a bearing outer ring, wherein, two bearing inner rings are installed on the gear shaft of driving gear side by side, two rows of tapered rollers are installed on the taper surface of two bearing inner rings respectively and are positioned by cage, and bearing outer ring is installed on the circumferential outside of two rows of tapered rollers;When assembling, the locking nut on the gear shaft of driving gear is fastened with set torque to tighten main cone bearing unit, so that all tapered rollers in two rows are in uniform contact with bearing inner and outer ring raceway, and bearing unit realizes design pre-tightening.The bearing unit of the application can accurately realize constant pressure pre-tightening, so that the main reduction differential assembly is convenient, not only the service life of driving gear shafting is high, but also the assembly production efficiency is greatly improved, and it is beneficial to the development of assembly automation and intelligentization.

Description

Technical Field

[0001] This invention belongs to the field of bearing technology, and in particular relates to a main tapered bearing for automotive differentials. Background Technology

[0002] The power from the car engine is output through the transmission and then transmitted to the final drive. The driving bevel gear, through meshing, transfers power to the driven bevel gear. For example... Figure 1 As shown, a traditional main reducer assembly includes a lock nut 1, a main gear flange 2, an oil seal 3, a bearing housing 4, a drive gear 5, a shim 6, a front bearing 7, a bushing 8, a rear bearing 9, and an adjusting shim 10. The drive gear 5 has the bearing housing 4, the front bearing 7, the bushing 8, and the rear bearing 9 mounted on its gear shaft. An adjusting shim 10 is placed between the rear bearing 9 and the drive gear 5. The lock nut 1, the main gear flange 2, and the oil seal 3 are installed at the shaft end. The lock nut 1 secures the main gear flange 2, and the shim 6 is placed between the main gear flange 2 and the front bearing 7. The slewing bearing of the drive bevel gear uses two sets of single-row tapered roller bearings of different sizes, with a bushing 8 in between. The bushing increases the distance between the two bearing support points to improve the load-bearing capacity and rigidity of the shaft system, while also transmitting the axial force between the two rows of bearings. Without bushings, the distance between the support points of the two rows of bearings is 40mm, and its calculated life is 40E+06 revolutions; with bushings, the span increases to 85mm, and the calculated life of the bearings reaches 80E+06 revolutions; the life increases by 1 time.

[0003] According to the theoretical design, when the nut at the end of the main bevel gear shaft of the main reducer-differential is tightened to the specified torque, the main / driven gears will mesh perfectly, and at the same time the clearance (preload) of the two rows of support bearings will be at its optimal level, so that the drive gear shaft system can be put into perfect operation.

[0004] However, in practical applications, the dimensional deviations of various components and the deformation caused by assembly are not adequately considered. Bearing design is based entirely on ideal conditions, resulting in unsuitable meshing clearances between the primary and driven gears in the assembled main reducer assembly. Bearing preload also varies, requiring repeated adjustments of shims to readjust bearing preload and gear meshing clearance—a tedious and inaccurate process that prevents the entire system from reaching its design life. This also leads to low production and assembly efficiency for the main reducer-differential assembly. Furthermore, the presence of low-carbon steel tubing bushings sandwiched between the two rows of bearings causes significant fluctuations in deformation under axial load Fa. For example, in this case, after 10 compressions under the pressure of the tightening force rectangle, the axial displacement range was 68 μm, more than twice the bearing clearance. Therefore, the traditional main bevel gear shaft system exhibits poor stability, significantly impacting bearing life.

[0005] In addition, in the traditional structure, the lubrication of the front bearing is achieved by the gear oil being agitated when the gear rotates, splashing onto the bearing to form lubrication; while the lubrication of the rear bearing is achieved by the oil being swirled up when the gear speed reaches 400 rpm or more, with some of the oil flowing into the oil passage of the housing and being introduced into the rear bearing. However, the rear bearing has an open space, which is not conducive to the retention of lubricating oil and may lead to the risk of insufficient oil. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a fine-tuning-free main tapered bearing unit for automotive differentials, thereby improving the lifespan, reliability, and assembly efficiency of the main tapered bearing.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: a fine-adjustment-free main tapered bearing unit for automotive differentials, comprising a bearing housing, two bearing inner rings, two rows of tapered rollers, two cages, and a bearing outer ring, wherein the two bearing inner rings are mounted side by side on the gear shaft of the drive gear, the two rows of tapered rollers are respectively mounted on the tapered surfaces of the two bearing inner rings and positioned by the cages, and the bearing outer ring is mounted on the circumferential outer side of the two rows of tapered rollers.

[0008] Preferably, the axially connected sides of the inner rings of the bearings are provided with annular extensions, and the end faces of the annular extensions of the two inner rings of the bearings are connected.

[0009] Preferably, the outer ring of the bearing has at least two oil holes distributed circumferentially in the middle position, and the bearing housing has an oil passage communicating with the oil holes, through which lubricating oil enters the interior of the non-adjustable taper bearing unit.

[0010] Preferably, the outer ring of the bearing has a groove extending along the entire circumference at the middle position of its outer circumference, and the oil hole is formed in the groove.

[0011] Preferably, a meshing adjustment shim is provided between the drive gear and the inner ring of the bearing, and the axial outer side of the inner ring of the bearing away from the drive gear is pressed and positioned by a positioning ring.

[0012] Preferably, the positioning ring is pressed by the main tooth flange of the drive gear shaft, the shaft end of the drive gear shaft is provided with a threaded section, the threaded section is threadedly connected with a lock nut, and the main tooth flange is locked and fixed by the lock nut.

[0013] This invention also provides a method for assembling a car differential main tapered bearing unit without fine-tuning. During assembly, the locking nut on the gear shaft of the drive gear is tightened with a set torque to secure the main tapered bearing unit, so that all the tapered rollers in both rows are in uniform contact with the inner and outer raceways of the bearing, and the bearing unit achieves the designed preload.

[0014] The technical solution adopted in this invention has the following beneficial effects:

[0015] During assembly, the locking nut on the gear shaft of the drive gear tightens the main tapered bearing unit with a set torque, ensuring that all the tapered rollers in both rows make uniform contact with the inner and outer raceways of the bearing, achieving the designed preload for the bearing unit. Therefore, the bearing unit can accurately achieve constant pressure preload—with a fixed assembly height and a fixed axial preload force applied, it possesses a definite and controllable preload, thus achieving the designed rigidity, load-bearing capacity, and service life.

[0016] Since the bearings do not require any adjustment, they can be directly assembled to obtain appropriate preload and enter the optimal working state, which makes the main reducer-differential assembly convenient. This not only extends the life of the drive gear shaft system but also greatly improves assembly production efficiency and is conducive to the development of assembly automation and intelligence.

[0017] The two inner ring end faces of the bearing unit are in direct contact without an intermediate bushing, which not only facilitates assembly, but also allows for precise and stable control of the preload of the bearing unit by the gear shaft end locking nut. It also eliminates the risk of failure caused by the yielding deformation of the intermediate bushing when the axial stress increases.

[0018] The outer ring of the bearing unit is a single piece, so the two raceways can be machined simultaneously using a single reference surface, resulting in high precision and good consistency.

[0019] The two rows of bearings in the bearing unit are made completely symmetrical. After pre-tightening, the two inner rings are in direct contact, resulting in high overall rigidity and uniform load distribution on the two rows of bearings, thus increasing the overall load-bearing capacity. Due to the increased load-bearing capacity, the design span of the bearing unit can be appropriately reduced for the same load conditions and life requirements, thereby achieving the goal of weight reduction.

[0020] The lubrication of the inner raceway of the bearing unit initially utilizes the splashed oil from the rotation of the drive gear, while the oil flows through oil passages in the bearing housing. It then flows into the bearing unit through eight evenly distributed oil holes in the center of the outer ring, filling the entire inner cavity. Because a semi-enclosed space is formed between the two rows of rolling elements and the inner and outer rings, the lubricating oil flowing into the bearing unit can fully penetrate between the two raceways, which is highly beneficial for bearing operation lubrication.

[0021] The specific technical solution of the present invention and its beneficial effects will be described in detail in the following specific embodiments in conjunction with the accompanying drawings. Attached Figure Description

[0022] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0023] Figure 1 A schematic diagram of the installation of a traditional automotive differential bearing.

[0024] Figure 1In the middle: 1. Locking nut, 2. Main gear flange, 3. Oil seal, 4. Bearing housing, 5. Drive gear, 6. Shim, 7. Front bearing, 8. Bushing, 9. Rear bearing, 10. Adjusting shim;

[0025] Figure 2 This is a schematic diagram of the installation of the automotive differential fine-adjustment-free main cone bearing unit of the present invention;

[0026] Figure 2 In the middle: 1. Locking nut, 2. Main gear flange, 3. Oil seal, 4. Bearing housing, 5. Drive gear, 6. Pressing shim, 7. Fine-tuning-free main tapered bearing, 8. Adjusting shim;

[0027] Figure 3 This is a structural diagram of the automotive differential's fine-tuning-free main cone bearing of the present invention;

[0028] Figure 3 In the middle: 101. Bearing outer ring, 102. Bearing inner ring, 103. Tapered roller, 104. Cage;

[0029] Figure 4 The distribution of abnormally high contact stress at the roller ends along the generatrix when the bearing is subjected to ultimate load;

[0030] Figure 5 This invention relates to the contact stress distribution after the raceway has been optimized and modified. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] Those skilled in the art will understand that, without conflict, the features in the following embodiments and implementations can be combined with each other.

[0033] The terminology used in this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. For example, terms such as "inner" and "outer" indicating orientation or positional relationship are based solely on the orientation or positional relationship shown in the accompanying drawings and are used only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device / element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention.

[0034] Example 1

[0035] refer to Figure 2 and Figure 3 As shown, a car differential non-adjustable main tapered bearing unit includes a bearing housing 4 and a non-adjustable main tapered bearing 7. The non-adjustable main tapered bearing 7 includes two inner bearing rings 102, two rows of tapered rollers 103, two cages 104, and a bearing outer ring 101. The two inner bearing rings 102 are mounted side-by-side on the gear shaft of the drive gear 5. The two rows of tapered rollers 103 are respectively mounted on the tapered surfaces of the two inner bearing rings 102 and positioned by the cages 104. The bearing outer ring is mounted circumferentially outside the two rows of tapered rollers.

[0036] The bearing inner rings are provided with an annular extension on their axially connected sides, and the end faces of the annular extensions of the two bearing inner rings are connected.

[0037] The bearing unit of this invention is a constant pressure preload type, that is, the assembly height of the bearing unit is constant, and the axial preload applied to it is constant, which means that it has a definite and controllable preload, thereby having the rigidity, load-bearing capacity and service life expected in the design.

[0038] Since the bearings do not require any adjustment, they can be directly assembled to obtain appropriate preload and enter the optimal working state, which makes the main reducer-differential assembly convenient. This not only extends the life of the drive gear shaft system but also greatly improves assembly production efficiency and is conducive to the development of assembly automation and intelligence.

[0039] The two inner ring end faces of the bearing unit are in direct contact without an intermediate bushing. The gear shaft end locking nut provides precise and stable control over the preload of the bearing unit, while also eliminating the risk of failure caused by the yielding deformation of the intermediate bushing when axial stress increases.

[0040] The outer ring of the bearing unit is a single piece, so the two raceways can be machined simultaneously using a single reference surface, resulting in high precision and good consistency.

[0041] The two rows of bearings in the bearing unit are made completely symmetrical. After pre-tightening, the two inner rings are in direct contact, resulting in high overall rigidity and uniform load distribution on the two rows of bearings, thus increasing the overall load-bearing capacity. Due to the increased load-bearing capacity, the design span of the bearing unit can be appropriately reduced for the same load conditions and life requirements, thereby achieving the goal of weight reduction.

[0042] In addition, similar to existing technologies, you can refer to Figure 1 The conventional automotive differential bearing installation shown includes an adjusting shim 8 between the drive gear and the inner ring of the bearing. The inner ring of the bearing, axially away from the drive gear, is pressed and positioned by a pressing shim 6. The pressing shim is pressed by a main gear flange 2, which is locked in place by a lock nut 1. An oil seal 3 is located on the outer side of the bearing.

[0043] To improve lubrication, the outer ring of the bearing has at least two oil holes distributed circumferentially in the middle position, for example, six or eight; in this embodiment, an eight-hole structure is used. The bearing housing has oil channels communicating with the oil holes, through which lubricating oil enters the interior of the non-adjustable taper bearing unit. The outer ring of the bearing has a groove extending circumferentially in the middle position, and the oil holes are located within this groove. Initially, the inner raceway lubrication of the bearing unit utilizes the splashed oil from the rotation of the drive gear, while simultaneously flowing through the oil channels in the bearing housing. The oil flows into the bearing unit through the eight evenly distributed oil holes in the middle of the outer ring, filling the entire inner cavity of the bearing unit. Because a semi-enclosed space is formed between the two rows of rolling elements and the inner and outer rings, the lubricating oil flowing into the bearing unit can fully penetrate between the two rows of raceways, which is highly beneficial for bearing operation lubrication. Therefore, in actual operation, a multi-hole spring-like oil supply pattern is formed.

[0044] Example 2

[0045] A method for assembling a car differential main tapered bearing unit without fine-tuning: During assembly, the locking nut on the gear shaft of the drive gear is tightened with a set torque to secure the main tapered bearing unit, ensuring that all the tapered rollers in both rows are in uniform contact with the inner and outer raceways of the bearing, and achieving the designed preload of the bearing unit.

[0046] Of course, in order to achieve the above assembly method, it is necessary to optimize the algorithm and introduce new design parameters, accurately design the reasonable tolerance range and clearance control range of each part, and ensure that while the fastening nut of the main bevel gear shaft fastens the bearing unit with the specified torque, all the tapered rollers inside it are in uniform contact with the inner and outer raceways, and the bearing unit reaches the design preload, that is, achieves the best load-bearing capacity and rolling operation state.

[0047] Explanation of parameter symbols in the following calculation formulas

[0048] Table 1. Explanation of Parameter Symbols

[0049]

[0050]

[0051] First, the bearing raceway profile is optimized using an algorithm with the objective function of minimizing maximum contact stress. This ensures that the rollers have high load-bearing capacity and suppress overload stress at the edge of the contact area. It also provides good rolling contact line skew correction and anti-slip capability.

[0052] The bearing is decomposed into k slices rotating around an axis, with a slice width of ω, where kω is the rolling contact length of the bearing. There is a relationship between the normal contact pressure p at point (x', y') on the elastic half-space surface and the deformation at point (x, y):

[0053]

[0054] Integrating equation (1), let c be the raceway convexity, z j Let j be the ordinate of the highest (convexity) point. The relationship between the contact stress, deformation, and approach δ of the two contacting bodies, the roller and the raceway, is established as follows:

[0055]

[0056] Let δ j c represents the deformation of the roller at point j under radial load. λ To account for the deformation caused by the raceway crown on the λ-th slice, we introduce the static equilibrium equation for the tapered roller bearing (each roller):

[0057]

[0058] This allows us to solve for the relationship between contact stress and contact deformation of any roller, and to minimize the maximum possible stress by optimizing the raceway generatrix. For details, please refer to existing technologies. The contact stress σ in equation (2) can be optimized by varying Z and ρ. Based on the analytical equation, this numerical model is repeatedly calculated using the orthogonal optimization method, mainly to control stress concentration at the large end of the raceway.

[0059] For example Figure 4 The bearing shown exhibits abnormally high contact stress at the roller ends when subjected to its ultimate load. Figure 5 As shown, after the raceway was optimized and modified, the roller contact stress distribution was significantly improved under the same load, and the peak stress decreased by 26%.

[0060] Secondly, new design parameters are introduced to calculate the effects of "additional radial preload", "skewness", and "external load".

[0061] a. Due to the relatively thin outer ring of the bearing and the reducer housing, the interference fit during installation will cause slight deformation in both, resulting in additional radial preload on the bearing. Assume that the deformation at various points on the circumference of the bearing ring conforms to the displacement principle of a thin-walled ring relative to its center:

[0062]

[0063] And in the formula:

[0064]

[0065]

[0066]

[0067] Solving the differential equation yields a series expression for the deformation of the outer ring of the bearing element.

[0068] That is, the radial displacement u at any angle ψ :

[0069]

[0070] in:

[0071]

[0072]

[0073]

[0074] b. If the inner ring of the bearing is press-fitted into the main bevel gear shaft with an interference fit, deformation will occur, causing displacement of the inner ring raceway. According to the theory of elastic wall thickness rings, the increase in the outer diameter (raceway diameter) of the inner ring of a bearing mounted on a solid shaft due to the press fit is:

[0075]

[0076] c. The geometric parameters and deformation relationships of tapered roller bearings under radial, axial, and moment loads are divided into three parts:

[0077] c.1 Torque balance equation of rollers in the radial plane

[0078]

[0079] c.2 Equilibrium equations for starting and resisting moments related to roller skew

[0080]

[0081] c.3 Equilibrium equations for forces and moments in the inner ring of the bearing

[0082]

[0083]

[0084]

[0085] By combining equations (7) to (11) and substituting equations (2) and (8) into the constraint analysis, a function for clearance and bearing parameters is established:

[0086]

[0087] δ ψ =δ r cosψ-u ψi (δ1, δ2, ... δ) z )+u ψe (δ1, δ2, ... δ) z(13)

[0088] A brief explanation of the numerical calculation for axial preload.

[0089] a. Additional radial preload 1: u ψ Equation (5)

[0090] b. Additional radial preload 2: u is Equation (6)

[0091] c. Skew and external load correction: δ ψ Equation (13)

[0092] Finally, response analysis was conducted using product clearance (preload) as a key design variable.

[0093] This invention relates to a double-row tapered roller structure. In practical applications, clearance must be eliminated to achieve line-to-line matching of the two rows of rolling elements under no-load conditions. Therefore, bearing design optimization ultimately comes down to the calculation of clearance.

[0094]

[0095] In the formula:

[0096]

[0097]

[0098]

[0099]

[0100]

[0101] Equation (14) is a general formula for bearing design geometric parameters, load, and axial preload. It can be used as a reference for existing technologies. Theoretically,

[0102] δ=δ0+δ ψ +f(G r -u ψ -u is )

[0103] δ0: Theoretical preload

[0104] G r Theoretical calculation of radial clearance

[0105] f(G r -u ψ -u is ): Convert the radial clearance variation function into axial displacement.

[0106] As for double row bearings

[0107]

[0108]

[0109] After solving the J-integral, the control function for the axial clearance of the bearing in the factory under the application conditions can be established:

[0110] G a =f(G r δ ψ δ a u ψ u is (15)

[0111] According to the control function of equation (15), the machining parameters can be controlled during the bearing manufacturing process in the factory, thereby controlling the axial clearance.

[0112] The beneficial effects of this design are:

[0113] The bearing unit can accurately achieve constant pressure preload—the assembly height of the bearing unit is constant, and the axial preload applied to it is constant, that is, it has a definite and controllable preload, thus having the rigidity, load-bearing capacity and service life expected in the design.

[0114] Because this structure does not require bushings, it eliminates the risk of failure caused by bushing yielding and deformation when axial stress increases.

[0115] No adjustment of the main bevel gear bearing unit clearance is required, simplifying installation, effectively improving the assembly efficiency of the main reducer-differential assembly, and facilitating the development of assembly automation and intelligence.

[0116] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Those skilled in the art should understand that the present invention includes, but is not limited to, the content described in the above specific embodiments. Any modifications that do not depart from the functional and structural principles of the present invention will be included within the scope of the claims.

Claims

1. An assembly method for a fine-tuning-free main tapered bearing unit for an automotive differential, characterized in that: The bearing assembly includes a bearing housing, two inner bearing rings, two rows of tapered rollers, two cages, and an outer bearing ring. The two inner bearing rings are mounted side-by-side on the gear shaft of the driving gear. The two rows of tapered rollers are respectively mounted on the tapered surfaces of the two inner bearing rings and positioned by the cages. The outer bearing ring is mounted circumferentially outside the two rows of tapered rollers. The axially joined sides of the inner bearing rings have annular extensions, and the end faces of the annular extensions of the two inner bearing rings are joined together. The outer bearing ring has at least two oil holes distributed circumferentially at its center position. The bearing housing has oil passages communicating with the oil holes, allowing lubricating oil to enter the interior of the non-adjustable main tapered bearing unit through the oil holes. The outer bearing ring also has an extension along its entire circumference at its center position. The groove extends, and the oil hole is opened in the groove; a meshing adjustment shim is provided between the drive gear and the inner ring of the connected bearing; the inner ring of the bearing away from the drive gear is axially pressed and positioned by a positioning ring on the outer side; the positioning ring is pressed by the main tooth flange that is ring-fitted on the gear shaft of the drive gear; the end of the gear shaft of the drive gear is provided with a threaded section, and the threaded section is threadedly connected to a lock nut; the main tooth flange is locked and fixed by the lock nut; when assembling the fine-tuning main tapered bearing unit of the automotive differential, the lock nut on the gear shaft of the drive gear tightens the main tapered bearing unit with a set torque, so that all the tapered rollers in both rows are in uniform contact with the inner and outer raceways of the bearing, and the bearing unit achieves the designed preload; The bearing is decomposed into k slices rotating around the axis, with a slice width of ω, where kω is the rolling contact length of the bearing; there is a relationship between the normal contact pressure p at point (x', y') on the elastic half-space surface and the deformation at point (x, y): Let c be the raceway convexity, z j Let (x, y) be the ordinate of the point where the convexity is highest at point j; where: ν is the Poisson's ratio of the material, E is the elastic modulus of the material, and (x, y) are the coordinates of the contact point, (x... j ',y j ') represents the coordinates of the elastic half-space surface at the point of highest convexity; The relationship between the contact stress, deformation, and approach value δ of the two contacting bodies, the roller and the raceway, is established as follows: Where δ j c represents the deformation of the roller at point j under radial load. λ The deformation caused by the raceway convexity on the λ-th slice, ν is the material Poisson's ratio, E is the material elastic modulus, and z j ρ is the y-coordinate of the point with the highest convexity at node j, and y is the coordinate. y The principal curvature of the contact point between the roller and the raceway at point y is D. u It is the toroidal deformation coefficient, σ j Let i be the contact stress, i = 1, 2, 3... n. Divide the contact surface into 2g equal parts along the y-axis and 2c equal parts along the x-axis to form rectangular small pieces. The center of each piece is node i. Assuming that the pressure of each piece is constant, the influence of the contact pressure of this node on point j is the sum of the ring influence coefficient and the stress product of point j. Functions for establishing clearance and bearing parameters: Where: δ r It is the deformation caused by radial load, Δ j It is the deformation caused by radial load at roller position j, l is the roller length, θ is the bearing tilt angle, φ is 1 / 2 rolling element angular clearance, φ j λ is the 1 / 2 rolling element angular clearance at node j, λ is the slice position, and Gr is the theoretical radial clearance. ； Where: δ ψ It represents the deflection and external load displacement at any position angle ψ, where ψ is the contact position angle, and δ is the displacement at any position angle. r It is the deformation caused by radial load, u ψi It is the radial displacement of the inner circle at any position angle ψ, u ψe It is the radial displacement of the outer ring at any position angle ψ, δ1... z It is the deformation of the first to the Zth rolling elements; For double row bearings: ； Among them: J r This is the radial integral of the load distribution in a double-row tapered roller bearing; J a This is the axial integral of the load distribution in a double-row tapered roller bearing. Q max1 This represents the maximum rolling element load on bearing number 1; Q max2 This represents the maximum rolling element load on bearing 2. J r (ε1) is the radial integral of the load distribution of bearing column 1; J a (ε1) is the axial integral of the load distribution of bearing column 1; J r (ε2) is the radial integral of the load distribution of bearing column 2; J a (ε2) is the axial integral of the load distribution of bearing column 2; For a double-row tapered roller bearing, its overall load distribution radial integral J r (ε) is the radial integral J of bearing column 1. r (ε1) and the radial integral J of bearing column 2 r (ε2), and the maximum rolling element load Q of bearing column 1. max1 The maximum rolling element load Q of the bearing in column 2 max2 The function whose overall load distribution axial integral J a (ε) is the axial integral J of bearing column 1. a (ε1) and the axial integral J of bearing column 2 a (ε2), and the maximum rolling element load Q of bearing column 1. max1， The maximum rolling element load Q of the bearing in column 2 max2 The function.

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