Rolling bearing quasi-static fast convergence method based on error control strategy

Abstract

A kind of rolling bearing quasi-static quick convergence method based on error control strategy belongs to the field of rolling bearing design and analysis.The present application is aimed at the method for solving bearing quasi-static equilibrium equation, and the problem of large iterative calculation amount is not conducive to multiple calls. It includes establishing absolute coordinate system to estimate the initial position of rolling body and bearing inner ring; establishing rolling body force balance equation and bearing inner ring force balance equation and setting corresponding error limit; based on corresponding error limit, respectively iteratively calculate rolling body equation error and bearing inner ring equation error, and update rolling body position and bearing inner ring position; judge whether the current two error limits are simultaneously less than corresponding target absolute error limit; and according to the comparison result, the next round of iterative calculation is carried out, until the bearing inner ring iteration times is 1 in a certain round of iterative calculation, and the final position is output. The present application realizes the quick convergence of rolling bearing quasi-static equation based on error control, and realizes position determination.

Description

Technical Field

[0001] This invention relates to a rapid convergence method for quasi-statics of rolling bearings based on error control strategies, and belongs to the field of rolling bearing design and analysis. Background Technology

[0002] The quasi-static analysis method for rolling bearings takes into account the centrifugal force on the rolling elements and can effectively analyze the internal stress of the bearing under combined loads. It is an important tool for rolling bearing design.

[0003] Currently, the Newton-Raphson algorithm is commonly used to solve the quasi-static equilibrium equations of bearings. However, due to the inherent clearance in the bearings, improper initial values ​​or special operating conditions can easily lead to separation of the rolling elements from the raceways, or excessive contact between the rolling elements and raceways, resulting in a large computational burden or even divergence in the equations when convergence is achieved. Wang Yanzhong, in "Improved Quasi-Static Analysis of Angular Contact Ball Bearings under Combined Loads [J]. Bearings, 2022(11):13-17." (DOI:10.19533 / j.issn1000-3762.2022.11.003), introduced complex geometric constraints for obtaining initial values. Nevertheless, convergence is still difficult under certain operating conditions. To address this, the current common practice is to set a maximum number of iteration steps, and the calculation result after reaching the maximum number of iteration steps is used as the final position of the rolling elements and raceways. Summary of the Invention

[0004] Existing methods for solving the quasi-static equilibrium equations of bearings suffer from problems such as large iterative computation and inconvenience for repeated calls. This invention provides a fast convergence method for the quasi-static equilibrium of rolling bearings based on an error control strategy.

[0005] The present invention provides a fast convergence method for quasi-statics of rolling bearings based on an error control strategy, comprising:

[0006] Step 1: Establish an absolute coordinate system based on the absolute stationarity of the bearing outer ring;

[0007] Step 2: Estimate the initial positions of the rolling elements and the inner ring of the bearing in the absolute coordinate system;

[0008] Step 3: Based on the initial position, according to the quasi-static theory, analyze the interaction forces between the rolling elements and the inner and outer rings of the bearing, and establish the rolling element force balance equation and the bearing inner ring force balance equation respectively; set the initial value of the error limit ERROR_EB of the rolling element force balance equation and the initial value of the error limit ERROR_IR of the bearing inner ring force balance equation.

[0009] Step 4: Based on the current position of the bearing inner ring, iteratively solve the rolling element force balance equation for each rolling element using the Newton-Raphson algorithm, calculate the remainder of the rolling element equation, and calculate the rolling element equation error until the rolling element equation error of each rolling element is less than the current error limit ERROR_EB, then end the iteration; update the position of each rolling element based on the calculation results of the rolling element force balance equation.

[0010] Step 5: Based on the current rolling element position, iteratively solve the bearing inner ring force balance equation using the Newton-Raphson algorithm, calculate the remainder of the bearing inner ring equation, and calculate the bearing inner ring equation error until the bearing inner ring equation error is less than the current error limit ERROR_IR, then end the iteration; update the bearing inner ring position based on the calculation results of the bearing inner ring force balance equation.

[0011] Step Six: Determine whether the current error limit ERROR_EB and the current error limit ERROR_IR are both less than the corresponding target absolute error limit:

[0012] If so, in the current loop calculation process of steps four and five, if the number of iterations of the bearing inner ring is 1, output the current rolling element position and the current bearing inner ring position as the final position; if the number of iterations of the bearing inner ring is greater than 1, return to step four to perform the next loop calculation process.

[0013] If not, further determine whether the current error limit ERROR_IR is greater than the target absolute error limit IR_TARGET of the bearing inner ring. If so, halve the current error limit ERROR_IR as the new error limit ERROR_IR; otherwise, continue to use the current error limit ERROR_IR as the new error limit ERROR_IR. Then determine whether the current error limit ERROR_EB is greater than the target absolute error limit EB_TARGET of the rolling element. If so, halve the current error limit ERROR_EB as the new error limit ERROR_EB; otherwise, continue to use the current error limit ERROR_EB as the new error limit ERROR_IR. Based on the determined current error limit ERROR_IR and current error limit ERROR_EB, return to step four to perform the next iterative calculation process; until the final position is determined.

[0014] According to the fast convergence method of quasi-static rolling bearing based on error control strategy of the present invention, in step one, the absolute coordinate system is fixed on the outer ring of the bearing, wherein the X-axis coincides with the bearing rotation axis, the Y-axis points outward along the bearing radial direction, and the Z-axis is determined according to the right-hand screw rule.

[0015] According to the rapid convergence method for quasi-static rolling bearings based on error control strategy of the present invention, the initial position in step two is estimated based on the bearing's geometric parameters, material properties and input operating conditions.

[0016] For the quasi-static fast convergence method of rolling bearings based on the error control strategy according to the present invention, the calculation method of the initial position in step two is as follows:

[0017] Taking the positions of the rolling elements, the inner ring, and the outer ring of the bearing without external loads as the initial positions, we get:

[0018]

[0019]

[0020]

[0021] Z ir = 0, (4)

[0022] In the formula is the initial axial position of the rolling element, R go is the curvature radius of the outer ring raceway of the bearing, d is the diameter of the rolling element, α

[0023] is the initial contact angle of the rolling element, is the initial radial position of the rolling element, D m is the pitch diameter;

[0024] is the initial axial position of the inner ring of the bearing, R gi is the curvature radius of the inner ring raceway of the bearing, Z ir is the initial Z - coordinate of the inner ring of the bearing.

[0025] For the quasi-static fast convergence method of rolling bearings based on the error control strategy according to the present invention, in step three, the initial value of the error limit ERROR_EB of the rolling element force balance equation and the initial value of the error limit ERROR_IR of the inner ring force balance equation of the bearing are both set to half of the maximum absolute value of the axial load and the radial load borne by the bearing.

[0026] For the quasi-static fast convergence method of rolling bearings based on the error control strategy according to the present invention, in step four, the rolling element equation remainder is [RESex, RESer], where RESex is the axial residual of the rolling element force balance equation and RESer is the radial residual of the rolling element force balance equation. Then the rolling element equation error erroreb is:

[0027] erroreb = (RESex 2 + RESer 2 ) 0.5 ; (5)

[0028] Iterate cyclically until erroreb < ERROR_EB, and the rolling element force balance equation reaches convergence, then end the iteration.

[0029] In the fast convergence method of quasi-static mechanics of rolling bearings based on an error control strategy according to the present invention, in step five, the remainder of the inner ring equation of the bearing is [RESrx, RESrr], where RESrx is the axial residual of the force balance equation of the inner ring of the bearing, and RESrr is the radial residual of the force balance equation of the inner ring of the bearing. Then, the error error_ir of the inner ring equation of the bearing is:

[0030] errorir = (RESrx 2 + RESrr 2 ) 0.5 ; (6)

[0031] Perform cyclic iteration until errorir < ERROR_IR, the force balance equation of the inner ring of the bearing reaches convergence, and end the iteration.

[0032] Advantages of the present invention: The method of the present invention enables the motion law and force state between the rolling elements and the outer ring of the rolling bearing to converge rapidly under the action of external loads.

[0033] The method of the present invention is based on an error control strategy, which reduces the difficulty of selecting the initial calculation value and reduces the number of convergence iteration calculations of the quasi-static balance equation. Through comparison with examples, the method of the present invention can achieve a high convergence accuracy and significantly reduce the number of equation iterations in specific implementations, which is beneficial for the quasi-static mechanics model of the rolling bearing to be frequently called as a subroutine.

[0034] The method of the present invention controls the error limits of the force balance equation of the rolling elements and the force balance equation of the inner ring of the bearing respectively, enabling the rolling elements and the inner ring of the bearing to gradually approach high-precision convergence multiple times, rather than the force balance equation of the rolling elements and the force balance equation of the inner ring of the bearing converging to a high precision at one time as required by the traditional method. The method of the present invention greatly reduces the convergence difficulty of the model. Therefore, it reduces the difficulty of selecting the initial calculation value and can directly use the positions of the rolling elements and the inner ring of the bearing when the bearing is unloaded as the initial calculation value. At the same time, it also reduces the number of calculation iterations of the equation. Compared with the traditional method for solving the quasi-static mechanics model, the number of iterative calculations of the equation of the method of the present invention is reduced by approximately half. Description of the Drawings

[0035] Figure 1 is a schematic flow chart of the fast convergence method of quasi-static mechanics of rolling bearings based on an error control strategy according to the present invention;

[0036] Figure 2 is a schematic diagram of the interaction positions of the rolling elements, the inner ring, and the outer ring of the bearing; in the figure, O is the origin of the absolute coordinate system. Detailed Embodiment

[0037] 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. 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.

[0038] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0039] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0040] Specific Implementation Method 1: Combination Figure 1 and Figure 2 As shown, this invention provides a fast convergence method for quasi-statics of rolling bearings based on an error control strategy, including:

[0041] Step 1: Establish an absolute coordinate system based on the absolute stationarity of the bearing outer ring;

[0042] Step 2: Estimate the initial positions of the rolling elements and the inner ring of the bearing in the absolute coordinate system;

[0043] Step 3: Based on the initial position, according to the quasi-static theory, analyze the interaction forces between the rolling elements and the inner and outer rings of the bearing, and establish the rolling element force balance equation and the bearing inner ring force balance equation respectively; set the initial value of the error limit ERROR_EB of the rolling element force balance equation and the initial value of the error limit ERROR_IR of the bearing inner ring force balance equation.

[0044] Step 4: Based on the current position of the bearing inner ring, iteratively solve the rolling element force balance equation for each rolling element using the Newton-Raphson algorithm, calculate the remainder of the rolling element equation, and calculate the rolling element equation error until the rolling element equation error of each rolling element is less than the current error limit ERROR_EB, then end the iteration; update the position of each rolling element based on the calculation results of the rolling element force balance equation.

[0045] Step 5: Based on the current rolling element position, iteratively solve the bearing inner ring force balance equation using the Newton-Raphson algorithm, calculate the remainder of the bearing inner ring equation, and calculate the bearing inner ring equation error until the bearing inner ring equation error is less than the current error limit ERROR_IR, then end the iteration; update the bearing inner ring position based on the calculation results of the bearing inner ring force balance equation.

[0046] Step Six: Determine whether the current error limit ERROR_EB and the current error limit ERROR_IR are both less than the corresponding target absolute error limit:

[0047] If so, in the current loop calculation process of steps four and five, if the number of iterations of the bearing inner ring is 1, output the current rolling element position and the current bearing inner ring position as the final position; if the number of iterations of the bearing inner ring is greater than 1, return to step four to perform the next loop calculation process.

[0048] If not, further determine whether the current error limit ERROR_IR is greater than the target absolute error limit IR_TARGET of the bearing inner ring. If so, halve the current error limit ERROR_IR as the new error limit ERROR_IR; otherwise, continue to use the current error limit ERROR_IR as the new error limit ERROR_IR. Then determine whether the current error limit ERROR_EB is greater than the target absolute error limit EB_TARGET of the rolling element. If so, halve the current error limit ERROR_EB as the new error limit ERROR_EB; otherwise, continue to use the current error limit ERROR_EB as the new error limit ERROR_IR. Based on the determined current error limit ERROR_IR and current error limit ERROR_EB, return to step four to perform the next iterative calculation process; until the final position is determined.

[0049] Furthermore, in step one, the absolute coordinate system is fixed on the outer ring of the bearing, where the X-axis coincides with the bearing's rotation axis, the Y-axis points outward along the bearing's radial direction, and the Z-axis is determined according to the right-hand screw rule.

[0050] The rolling elements of the bearing have axial and radial degrees of freedom, the inner ring of the bearing has X-axis and Y-axis degrees of freedom, and the yaw angle of the inner ring of the bearing relative to the outer ring of the bearing is fixed.

[0051] The initial position in step two is estimated based on the bearing's geometric parameters, material properties, and input operating conditions.

[0052] The method for calculating the initial position in step two is as follows:

[0053] Using the initial positions of the rolling elements, the inner ring of the bearing, and the outer ring of the bearing under no external load, we obtain:

[0054]

[0055]

[0056]

[0057] Z ir =0, (4)

[0058] In the formula R is the initial axial position of the rolling element. gois the curvature radius of the outer raceway groove of the bearing, d is the diameter of the rolling element, α is the initial contact angle of the rolling element, is the initial radial position of the rolling element, D m is the pitch diameter;

[0059] is the initial axial position of the inner ring of the bearing, R gi is the curvature radius of the inner raceway groove of the bearing, Z ir is the initial coordinate of the inner ring of the bearing in the Z direction.

[0060] Furthermore, the initial value of the error limit ERROR_EB of the rolling element force balance equation and the initial value of the error limit ERROR_IR of the inner ring force balance equation in step three are both set to half of the maximum absolute value of the axial load and radial load borne by the bearing.

[0061] Both initial values can be set to max(abs(F x ), abs(F r )) / 2, where F x is the axial load borne by the bearing, and F r is the radial load borne by the bearing.

[0062] In step four of this embodiment, the rolling element equation remainder is [RESex, RESer], where RESex is the axial residual of the rolling element force balance equation and RESer is the radial residual of the rolling element force balance equation. Then the rolling element equation error erroreb is:

[0063] erroreb = (RESex 2 + RESer 2 ) 0.5 ; (5)

[0064] Perform cyclic iteration until erroreb < ERROR_EB, the rolling element force balance equation converges, and the iteration ends; update the current rolling element position.

[0065] In step five, the inner ring equation remainder is [RESrx, RESrr], where RESrx is the axial residual of the inner ring force balance equation and RESrr is the radial residual of the inner ring force balance equation. Then the inner ring equation error errorir is:

[0066] errorir = (RESrx 2 + RESrr 2 ) 0.5 ; (6)

[0067] Perform cyclic iteration until errorir < ERROR_IR, the inner ring force balance equation converges, and the iteration ends; and update the current inner ring position.

[0068] In actual implementation, step six of this embodiment presents four possible scenarios:

[0069] Case 1: Both ERROR_EB and ERROR_IR are less than the target absolute error limit EB_TARGET for the rolling element and the target absolute error limit IR_TARGET for the bearing inner ring. This means both the rolling element force balance equation and the bearing inner ring force balance equation have converged to the target absolute error limits. In this case, determine whether the Newton-Raphson algorithm was used to solve the bearing inner ring force balance equation only once. If so, it indicates that the position of the bearing inner ring has not been updated, and the current position information of the rolling element and the bearing inner ring can be directly output. Otherwise, it indicates that the position of the bearing inner ring has been updated, and in this case, it is necessary to return to step four, calculate the rolling element force balance equation under the current bearing inner ring position, and continue the process.

[0070] Case 2: ERROR_EB is less than EB_TARGET, while ERROR_IR is greater than IR_TARGET. In this case, the rolling element balance force equation has reached the target absolute error limit, while the bearing inner ring force balance equation has not. In this situation, ERROR_IR needs to be halved. Since the bearing inner ring position has been updated, it is necessary to return to step four, recalculate the rolling element force balance equation, and continue the process.

[0071] Scenario 3: ERROR_EB is greater than EB_TARGET, while ERROR_IR is less than IR_TARGET. In this case, the bearing inner ring force balance equation has reached the target absolute error limit, while the rolling element force balance equation has not. In this situation, ERROR_EB needs to be halved. Since the bearing inner ring position has been updated, it is necessary to return to step four, recalculate the rolling element force balance equation, and continue the process.

[0072] Scenario 4: ERROR_EB is greater than EB_TARGET, while ERROR_IR is greater than IR_TARGET. In this case, neither the bearing inner ring force balance equation nor the rolling element force balance equation has reached the target absolute error limit. Therefore, both ERROR_EB and ERROR_IR need to be halved. Since the bearing inner ring position has been updated, it is necessary to return to step four, recalculate the rolling element force balance equation, and continue the process.

[0073] Thus, a fast convergence method for quasi-static rolling bearings based on error control strategy was established.

[0074] Specific embodiment: For a certain type of angular contact ball bearing, the method of the present invention is used for control: The specific process is as follows:

[0075] 1. Assume that the outer ring of the bearing is always absolutely stationary. Fix the absolute coordinate system on the outer ring of the bearing, with the X-axis coinciding with the axis of rotation of the bearing, the Y-axis pointing radially outwards, and the Z-axis determined by the right-hand screw rule. The rolling elements of the bearing have axial and radial degrees of freedom, the inner ring has degrees of freedom in the X-axis and Y-axis directions, and the yaw angle of the inner ring relative to the outer ring is 0.

[0076] 2. Take the positions of the rolling elements, the inner ring, and the outer ring of the bearing without any external loads as the initial positions, and calculate the initial values of the positions of the rolling elements and the inner ring of the bearing:

[0077]

[0078]

[0079]

[0080] Z ir = 0.

[0081] In this embodiment, R go is 11.45 mm, d is 22.225 mm, α is 25°, D m is 167.5375 mm, R gi is 11.55 mm. The angular contact ball bearing has 20 rolling elements, and the rotational speed of the inner ring of the bearing is 12000 r / min.

[0082] 3. The axial load borne by the bearing is 9000 N, and the radial load is 1000 N. Set the error limit of the rolling element force balance equation ERROR_EB = 1000 / 2 = 500 N, and the error limit of the inner ring force balance equation of the bearing ERROR_IR = 1000 / 2 = 500 N.

[0083] 4. According to the quasi-static theory, analyze the interaction forces between the rolling elements and the inner ring of the bearing one by one, and establish the force balance equations of the rolling elements and the inner ring of the bearing respectively.

[0084] 5. Calculate the error of the current rolling element equation, and perform iterative loops until the equation converges when erroreb < ERROR_EB.

[0085] 6. Calculate the error of the inner ring equation of the bearing and perform iterative loops until the equation converges when errorir < ERROR_IR.

[0086] 7. According to step 6, determine whether the current error limit ERROR_EB of the rolling element balance equation and the current error limit ERROR_IR of the raceway balance equation meet the target absolute error limit, analyze in four cases, and continue the process.

[0087] The maximum error in the final solution of the rolling element force balance equation is 2.25e-009N, and the maximum error in the bearing inner ring force balance equation is 5.6e-009N. The axial positions of the 20 rolling elements obtained from the solution are as follows (in meters): [156.497086314469e-006

[0088] 156.495854295342e-006

[0089] 156.492277990316e-006

[0090] 156.486705256490e-006

[0091] 156.479678849454e-006

[0092] 156.471884340512e-006

[0093] 156.464083857408e-006

[0094] 156.457041809809e-006

[0095] 156.451449743179e-006

[0096] 156.447857797583e-006

[0097] 156.446619804288e-006

[0098] 156.447857797583e-006

[0099] 156.451449743179e-006

[0100] 156.457041809809e-006

[0101] 156.464083857408e-006

[0102] 156.471884340512e-006

[0103] 156.479678849454e-006

[0104] 156.486705256490e-006

[0105] 156.492277990316e-006

[0106] 156.495854295342e-006];

[0107] The radial positions of the 20 rolling elements obtained from the solution are (in meters): [83.7700346139814e-003

[0108] 83.7700051959339e-003

[0109] 83.7699198223198e-003

[0110] 83.7697868524219e-003

[0111] 83.7696193051304e-003

[0112] 83.7694335834697e-003

[0113] 83.7692478680659e-003

[0114] 83.7690803371553e-003

[0115] 83.7689473875052e-003

[0116] 83.7688620302720e-003

[0117] 83.7688326184815e-003

[0118] 83.7688620302720e-003

[0119] 83.7689473875052e-003

[0120] 83.7690803371553e-003

[0121] 83.7692478680659e-003

[0122] 83.7694335834697e-003

[0123] 83.7696193051304e-003

[0124] 83.7697868524219e-003

[0125] 83.7699198223198e-003

[0126] 83.7700051959339e-003].

[0127] The axial position of the bearing inner ring is obtained as follows (in meters): 3.64276892819920e-004;

[0128] The Z-axis coordinate of the bearing inner ring is obtained as follows (in meters): 1.28547269874770e-006;

[0129] The rolling body force balance equation was calculated 879 times, and the bearing inner ring force balance equation was iterated 21 times.

[0130] Under the same operating conditions, using existing methods, the rolling body force balance equation requires 1751 calculations, and the bearing inner ring force balance equation requires 96 iterations. Therefore, the method of this invention significantly reduces the number of iterations for the equations, achieving excellent results.

[0131] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A fast convergence method for quasi-static rolling bearings based on an error control strategy, characterized in that... include, Step 1: Establish an absolute coordinate system based on the absolute stationarity of the bearing outer ring; Step 2: Estimate the initial positions of the rolling elements and the inner ring of the bearing in the absolute coordinate system; Step 3: Based on the initial position, according to the quasi-static theory, analyze the interaction forces between the rolling elements and the inner and outer rings of the bearing, and establish the rolling element force balance equation and the bearing inner ring force balance equation respectively; set the initial value of the error limit ERROR_EB of the rolling element force balance equation and the initial value of the error limit ERROR_IR of the bearing inner ring force balance equation. Step 4: Based on the current position of the bearing inner ring, iteratively solve the rolling element force balance equation for each rolling element using the Newton-Raphson algorithm, calculate the remainder of the rolling element equation, and calculate the rolling element equation error until the rolling element equation error of each rolling element is less than the current error limit ERROR_EB, then end the iteration; update the position of each rolling element based on the calculation results of the rolling element force balance equation. Step 5: Based on the current rolling element position, iteratively solve the bearing inner ring force balance equation using the Newton-Raphson algorithm, calculate the remainder of the bearing inner ring equation, and calculate the bearing inner ring equation error until the bearing inner ring equation error is less than the current error limit ERROR_IR, then end the iteration; update the bearing inner ring position based on the calculation results of the bearing inner ring force balance equation. Step Six: Determine whether the current error limit ERROR_EB and the current error limit ERROR_IR are both less than the corresponding target absolute error limit: If so, in the current loop calculation process of steps four and five, if the number of iterations of the bearing inner ring is 1, output the current rolling element position and the current bearing inner ring position as the final position; if the number of iterations of the bearing inner ring is greater than 1, return to step four to perform the next loop calculation process. If not, further determine whether the current error limit ERROR_IR is greater than the target absolute error limit IR_TARGET of the bearing inner ring. If so, halve the current error limit ERROR_IR as the new error limit ERROR_IR; otherwise, continue to use the current error limit ERROR_IR as the new error limit ERROR_IR. Then determine whether the current error limit ERROR_EB is greater than the target absolute error limit EB_TARGET of the rolling element. If so, halve the current error limit ERROR_EB as the new error limit ERROR_EB; otherwise, continue to use the current error limit ERROR_EB as the new error limit ERROR_IR. Based on the determined current error limit ERROR_IR and current error limit ERROR_EB, return to step four to perform the next iterative calculation process; until the final position is determined.

2. The method for rapid convergence of quasi-static rolling bearings based on error control strategy according to claim 1, characterized in that, In step one, the absolute coordinate system is fixed on the outer ring of the bearing, with the X-axis coinciding with the bearing's rotation axis, the Y-axis pointing outward along the bearing's radial direction, and the Z-axis determined according to the right-hand screw rule.

3. The method for rapid convergence of quasi-static rolling bearings based on error control strategy according to claim 1, characterized in that, The initial position in step two is estimated based on the bearing's geometric parameters, material properties, and input operating conditions.

4. The method for rapid convergence of quasi-static rolling bearings based on error control strategy according to claim 3, characterized in that, The method for calculating the initial position in step two is as follows: Using the initial positions of the rolling elements, the inner ring of the bearing, and the outer ring of the bearing under no external load, we obtain: Z ir ＝0， (4) In the formula R is the initial axial position of the rolling element. go d is the radius of curvature of the bearing outer ring raceway, d is the diameter of the rolling element, and α is the initial contact angle of the rolling element. D is the initial radial position of the rolling element. m The diameter of the pitch circle; R represents the initial axial position of the bearing inner ring. gi Z is the radius of curvature of the bearing inner ring raceway. ir The initial coordinates of the bearing inner ring in the Z direction are given.

5. The method for rapid convergence of quasi-static rolling bearings based on error control strategy according to claim 4, characterized in that, In Step 3, the initial values of the error limit ERROR_EB of the rolling body force balance equation and the error limit ERROR_IR of the inner ring force balance equation of the bearing are both set to half of the maximum absolute value of the axial load and the radial load borne by the bearing.

6. The method for rapid convergence of quasi-static rolling bearings based on error control strategy according to claim 5, characterized in that, In Step 4, the rolling body equation remainder is [RESex, RESer], where RESex is the axial residual of the rolling body force balance equation and RESer is the radial residual of the rolling body force balance equation. Then the rolling body equation error erroreb is: erroreb=(RESex 2 +RESer 2 ) 0.5 (5) Iterate cyclically until erroreb < ERROR_EB, the rolling body force balance equation converges, and the iteration ends.

7. The quasi-static fast convergence method for rolling bearings based on an error control strategy according to claim 5, wherein In Step 5, the inner ring equation remainder of the bearing is [RESrx, RESrr], where RESrx is the axial residual of the inner ring force balance equation of the bearing and RESrr is the radial residual of the inner ring force balance equation of the bearing. Then the inner ring equation error errorir is: error_ir=(RESrx 2 +RESrr 2 ) 0.5 ;(6) Perform cyclic iteration until errorir < ERROR_IR, the inner ring force balance equation of the bearing converges, and the iteration ends.

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