CN117874964B - Dynamic analysis method for evolution of rough surface morphology of pocket hole of ball bearing retainer - Google Patents
Dynamic analysis method for evolution of rough surface morphology of pocket hole of ball bearing retainer Download PDFInfo
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Abstract
A dynamic analysis method for the evolution of the rough surface morphology of a pocket hole of a ball bearing retainer belongs to the technical field of analysis of the surface morphology of the ball bearing retainer. The method aims at the problem that the contact position of the ball and the retainer pocket changes in real time in the running process of the ball bearing, and the whole pocket surface is used as a solving domain to influence the accuracy of the prediction of the morphology evolution rule. The method comprises the steps of obtaining the positions and the surface initial shapes of the ball and the retainer pocket; calculating the position vector of the ball and the retainer pocket and the elastic deformation of the interaction of the ball and the retainer pocket; calculating the contact half length and the contact half width so as to determine an adaptive solving domain; determining a pressure step updating step length based on the initial pressure matrix, and calculating the pressure value of each node to obtain a corrected pressure matrix p, a real contact area and a corrected contact area; calculating the abrasion height of each node, and updating the surface morphology of the ball and the retainer pocket; and then the next surface appearance updating calculation is carried out until the end. The method is used for analyzing the evolution of the surface morphology of the retainer pocket.
Description
Technical Field
The invention relates to a dynamic analysis method for the evolution of the rough surface morphology of a pocket hole of a ball bearing retainer, and belongs to the technical field of analysis of the surface morphology of the ball bearing retainer.
Background
During operation of the ball bearing, complex, severe and random impacts exist on internal parts, particularly on the balls and the pocket of the retainer, and the impact forces lead to the absence of a stable oil film in the pocket, so that the pocket surface of the retainer is worn. In addition, the surface of the machined part is not ideal and smooth, the surface roughness is different under different machining processes, and it is important for the rough surface of the retainer pocket to define the abrasion condition and the surface evolution rule of the surface in the working period. In addition, in order to improve the calculation efficiency, the whole pocket surface cannot be used as a solving domain for solving, a smaller solving domain is adopted, so that the contact position of the ball and the retainer pocket is required to be obtained in real time, and then the solving domain is divided on the basis of the contact position, so that the non-contact part is prevented from interfering with the calculation efficiency.
The existing morphology analysis method for the rough surface of the cage pocket cannot adjust the solving domain aiming at the change adaptability of the contact position of the ball and the cage pocket in the running process of the ball bearing, so that the accuracy of predicting the morphology evolution rule of the cage pocket is poor.
Disclosure of Invention
Aiming at the problem that the contact position of a ball and a cage pocket changes in real time in the running process of the ball bearing, the whole pocket surface is used as a solving domain to influence the accuracy of the prediction of the morphology evolution law, the invention provides a dynamic analysis method for the morphology evolution of the rough surface of the ball bearing cage pocket.
The invention relates to a dynamic analysis method for the evolution of the rough surface morphology of a ball bearing retainer pocket hole, which comprises the following steps,
Step one: obtaining the positions and the surface initial shapes of the ball and the retainer pocket at the moment T 0;
Step two: calculating the position vectors of the ball and the retainer pocket according to the positions of the ball and the retainer pocket at the moment T 0, and calculating the elastic deformation of the interaction of the ball and the retainer pocket; if the elastic deformation is larger than 0, calculating the contact force, the contact half length and the contact half width of the ball and the retainer pocket;
Step three: determining the self-adaptive solving domain of the ball and the retainer pocket according to the contact half length and the contact half width;
step four: determining an initial pressure matrix p 0 and solving accuracy according to self-adaptive solving domain of ball and retainer pocket ；
Step five: determining a real contact area based on an initial pressure matrix p 0, calculating the current distance between the ball surface in the real contact area and the pocket surface of the retainer, and then calculating the updating step length of the pressure step; according to the updating step length of the pressure step and the iterative calculation of the relaxation coefficient, a corrected pressure matrix p is determined, and a corrected contact area in the self-adaptive solving domain is determined; calculating relative errors from all node pressure values in the corrected pressure matrix p and the initial pressure matrix p 0 until the relative errors are smaller than the solving accuracy；
Step six: calculating the abrasion height of each node in the real contact area according to the corrected pressure matrix p; updating the surface morphology of the ball and the retainer pocket in the real contact area based on the abrasion height; and then taking the updated surface morphology of the ball and the retainer pocket as the initial surface morphology of the ball and the retainer pocket at the next moment and taking the corrected pressure matrix p as the initial pressure matrix p 0 at the next moment, returning to the step one for continuous calculation until the end.
According to the dynamic analysis method for the evolution of the rough surface morphology of the ball bearing retainer pocket hole, in the second step, the position vectors of the ball and the retainer pocket hole are expressed as：
（1），
Wherein [ T cp ] is a conversion matrix from a cage coordinate system to a pocket coordinate system; [ T Ic ] is a conversion matrix from an inertial coordinate system to a retainer coordinate system; is the vector of the spherical center relative to the center of the inertial coordinate system under the inertial coordinate system,/> The vector is the vector of the cage centroid relative to the inertial coordinate system center under the inertial coordinate system; /(I)Is the vector of the center of the pocket relative to the center of the retainer in the retainer coordinate system.
According to the dynamic analysis method for the evolution of the rough surface morphology of the ball bearing retainer pocket, in the second step, the method for calculating the contact half length and the contact half width of the ball and the retainer pocket comprises the following steps:
Based on position vectors Calculate the elastic deformation δ bc of the ball-cage pocket interaction:
（2），
In the middle of Is the pocket radius,/>Is the radius of the sphere;
If the elastic deformation delta bc is larger than 0, calculating macroscopic contact force Q bc between the ball and the retainer pocket:
（3），
wherein K is the contact stiffness;
the contact half-length a bc and the contact half-width b bc are calculated based on macroscopic contact force Q bc according to Hertz contact theory.
According to the dynamic analysis method for the evolution of the rough surface morphology of the pocket hole of the ball bearing retainer, in the third step, the calculation method of the self-adaptive solving domain comprises the following steps:
（4），
Wherein l x is the self-adaptive solution domain length, and l z is the self-adaptive solution domain width; for self-adaptive solving of vector/>, in pocket coordinate system, of nodes in domain X-axis component of/>For self-adaptive solving of vector of intra-domain node under pocket coordinate systemThe Z-axis component of (2); the nodes are contact points of the balls and the retainer pockets;
Vector quantity According to position vectorsAnd (3) calculating to obtain:
（5），
In the middle of Is a conversion matrix from a spherical coordinate system to a pocket coordinate system,/>Is the vector of the node relative to the geometric center of the sphere under the spherical coordinate system,/>Is a conversion matrix from a spherical coordinate system to a contact coordinate system.
According to the dynamic analysis method for the evolution of the rough surface morphology of the ball bearing retainer pocket hole, in the fifth step, the current distance between the inner ball surface and the retainer pocket hole surface is adaptively solved as g:
（6），
In the middle of An initial distance between the ball surface and the cage pocket surface;
is normal deformation of the ball and the pocket surface of the retainer:
（7），
In the middle of To influence coefficient matrix one,/>The second influence coefficient matrix is obtained;
Adaptive solution domain Internal initial pressure/>An area formed by all nodes larger than 0 is taken as a real contact area, and the node set/>Average spacing of all nodes/>The method comprises the following steps:
（8），
In the middle of For adaptively solving the number of nodes in the domain,/>Representing node coordinates, wherein/>For self-adaptive solving of node abscissa under domain coordinate system,/>Solving the ordinate of the node under the domain coordinate system for self-adaption; /(I)For node in current spacing gThe distance between the ball surface of the retainer pocket surface; /(I)For the corresponding node/>, in the initial pressure matrix p 0 Is an element of (2);
by average spacing The current spacing g is adjusted to obtain updated current spacing g:
（9）。
according to the dynamic analysis method for the evolution of the rough surface morphology of the pocket hole of the ball bearing retainer, in the fifth step, the calculation method for the updating step length of the pressure step is as follows:
calculating the conjugate gradient direction t (i, j) from the updated current distance g:
setting intermediate variables The method comprises the following steps:
（10），
（11），
（12），
In the middle of The initial value is 0 for the relaxation coefficient;
Obtaining conjugate gradient direction vector from conjugate gradient directions t (i, j) of all nodes ；
From conjugate gradient direction vectorsSetting intermediate variables/>：
（13），
Recalculating intermediate variablesAverage value/>：
（14），
In the middle ofIs an intermediate variable/>Corresponding node/>Is an element of (2);
According to the average value Updating intermediate variables/>Is the value of (1):
（15），
Then calculating to obtain the updated step length of the pressure step ：
（16）。
According to the dynamic analysis method for the evolution of the rough surface morphology of the pocket hole of the ball bearing retainer, in the fifth step, the corrected pressure matrix p is obtained by the following steps:
along the direction of conjugate gradient Correcting the pressure of the nodes in the real contact area and enabling the pressure of the nodes outside the real contact area to be zero:
（17），
In the middle of For the corresponding node/>, in the corrected pressure matrix pIs an element of (2);
According to Taking an area formed by all nodes with the ball surface and retainer pocket surface spacing smaller than 0 as a correction contact area, wherein the node set in the correction contact area is omega o1;
updating the pressure of the nodes in the node set omega o1:
（18），
（19），
If it is Then update the relaxation coefficient/>Otherwise/>; Wherein/>Representing an empty set;
Calculating the current contact load of two surfaces ：
（20），
In the middle ofThe grid length corresponding to the nodes in the domain is solved for self-adaption;
Re-pairing Updating to obtain the element/>, in the corrected pressure matrix p：
（21）。
According to the dynamic analysis method for the evolution of the rough surface morphology of the ball bearing retainer pocket hole, in the fifth step, the relative error is calculated：
（22）。
According to the dynamic analysis method for the evolution of the rough surface morphology of the ball bearing retainer pocket hole, in the step six, nodes are formedExpressed as/>：
（23），
In the middle ofFor node/>Is an Archard micro wear coefficient; /(I)For node/>Is used for the hardness of the material,For the relative sliding speed u s node/>Is a relative sliding speed of (a);
The calculation method of the relative sliding speed u s is as follows:
the relative sliding speed u s is:
（24），
In the middle of The speed of the ball is the inertial coordinate system; the speed of the cage under the inertial coordinate system; The angular velocity of the ball in the spherical coordinate system; [ T cs ] is the transformation matrix of the cage coordinate system to the contact coordinate system, The angular velocity of the retainer in the retainer coordinate system; Is the inverse of [ T cp ].
According to the dynamic analysis method for the evolution of the rough surface morphology of the ball bearing retainer pocket, in the step six, the method for updating the surface morphology of the ball and the retainer pocket comprises the following steps:
（25），
（26），
In the middle of Is the spherical surface node/>Is of the initial morphology of/>Wear the ball surface to a high degree; /(I)The surface morphology of the ball is updated;
for cage pocket surface node/> Is of the initial morphology of/>The surface of the pocket hole of the retainer is worn to a high degree; /(I)The surface morphology of the pocket hole of the retainer is updated;
In the middle of According to the formula (23), the material hardness of the corresponding ball is obtained through calculation; /(I)And (3) calculating according to a formula (23) to obtain the material hardness of the corresponding retainer pocket.
The invention has the beneficial effects that: the method utilizes the self-adaptive solving domain to dynamically analyze the evolution of the rough surface morphology of the cage pocket in the running process of the ball bearing, and simulates the real-time contact force and the contact position between the ball of the ball bearing and the cage pocket on the basis of considering the dynamic effect, so that the method has good universality and good analysis and calculation capability.
According to the method, the rough surface of the pocket of the ball bearing retainer is considered, the impact force between the pockets of the ball bearing retainer obtained by ball bearing dynamics is taken as a calculated initial value, the contact center is taken as a calculation domain center, a self-adaptive solving domain is established, the precise abrasion condition of the rough surface of the pocket of the retainer is further obtained, meanwhile, the influence of time-varying factors is considered, and the shape evolution rule of the rough surface of the pocket of the ball bearing retainer can be accurately predicted.
Drawings
FIG. 1 is a flow chart of a dynamic analysis method for the evolution of the rough surface morphology of the pocket of the ball bearing retainer;
FIG. 2 is a schematic diagram of a simulation of the ball to cage pocket contact relationship; in the figure, O b is the origin of a spherical coordinate system, and x bybzb is the spherical coordinate system; o c is the origin of the cage coordinate system, x cyczc is the cage coordinate system; o I is the origin of the inertial coordinate system, x IyIzI is the inertial coordinate system;
FIG. 3 is a geometric schematic of the ball-cage pocket contact relationship; x pypzp in the figure is a cage pocket coordinate system;
FIG. 4 is a schematic view of a domain position adaptive solution for cage pockets; x syszs in the figure is the contact coordinate system; h c is cage thickness;
fig. 5 is a schematic view of the evolution of the rough surface of the cage pocket.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The invention is further described below with reference to the drawings and specific examples, which are not intended to be limiting.
The first embodiment provides a full life cycle ball bearing dynamics and surface evolution coupling analysis method, which solves the problems of blank in the aspect of exploring the evolution law of the main bearing surface of a bearing in a traditional model, limitation of difficult combination with complex variable working conditions in the full life cycle of the bearing and the like. The coupling analysis is based on a ball bearing complete dynamics model, so that dynamic characteristics such as contact force, relative sliding speed of a micro-area and the like between a bearing sphere and a main bearing surface of a raceway are obtained, and the limitation brought by classical quasi-statics or quasi-dynamics in the past is solved. After the dynamic performance is obtained, the dynamic performance is taken into a main bearing rough surface contact model as an initial value condition so as to obtain main bearing surface contact stress distribution and normal clearance considering the real surface morphology. After accurate contact stress distribution is obtained, two behaviors of benign abrasion caused by complete elastic contact and severe abrasion caused by plastic deformation are considered, and the actual shape evolution rule of the main bearing surface is obtained by coupling with the rotation number of the bearing on the basis of updating the surface shape.
The invention provides a dynamic analysis method for the evolution of the rough surface morphology of a ball bearing retainer pocket, which is shown in figures 1 to 4, and comprises the following steps,
Step one: obtaining the positions and the surface initial shapes of the ball and the retainer pocket at the moment T 0;
Step two: calculating the position vectors of the ball and the retainer pocket according to the positions of the ball and the retainer pocket at the moment T 0, and calculating the elastic deformation of the interaction of the ball and the retainer pocket; if the elastic deformation is larger than 0, calculating the contact force, the contact half length and the contact half width of the ball and the retainer pocket;
Step three: determining the self-adaptive solving domain of the ball and the retainer pocket according to the contact half length and the contact half width;
step four: determining an initial pressure matrix p 0 and solving accuracy according to self-adaptive solving domain of ball and retainer pocket ；
Step five: determining a real contact area based on an initial pressure matrix p 0, calculating the current distance between the ball surface in the real contact area and the pocket surface of the retainer, and then calculating the updating step length of the pressure step; according to the updating step length of the pressure step and the iterative calculation of the relaxation coefficient, a corrected pressure matrix p is determined, and a corrected contact area in the self-adaptive solving domain is determined; calculating relative errors from all node pressure values in the corrected pressure matrix p and the initial pressure matrix p 0 until the relative errors are smaller than the solving accuracy；
Step six: calculating the abrasion height of each node in the real contact area according to the corrected pressure matrix p; updating the surface morphology of the ball and the retainer pocket in the real contact area based on the abrasion height; and then taking the updated surface morphology of the ball and the retainer pocket as the initial surface morphology of the ball and the retainer pocket at the next moment and taking the corrected pressure matrix p as the initial pressure matrix p 0 at the next moment, returning to the step one for continuous calculation until the end.
Further, as shown in fig. 2 and 3, in the second step, the position vector of the ball and the retainer pocket is expressed as：
（1），
Wherein [ T cp ] is a conversion matrix from a cage coordinate system to a pocket coordinate system; [ T Ic ] is a conversion matrix from an inertial coordinate system to a retainer coordinate system; is the vector of the spherical center relative to the center of the inertial coordinate system under the inertial coordinate system,/> The vector is the vector of the cage centroid relative to the inertial coordinate system center under the inertial coordinate system; /(I)Is the vector of the center of the pocket relative to the center of the retainer in the retainer coordinate system.
In the second step of this embodiment, the method for calculating the contact half length and the contact half width between the ball and the retainer pocket is as follows:
Based on position vectors Calculate the elastic deformation δ bc of the ball-cage pocket interaction:
（2），
In the middle of Is the pocket radius,/>Is the radius of the sphere;
If the elastic deformation delta bc is larger than 0, calculating macroscopic contact force Q bc between the ball and the retainer pocket:
（3），
wherein K is the contact stiffness;
the contact half-length a bc and the contact half-width b bc are calculated based on macroscopic contact force Q bc according to Hertz contact theory.
Still further, referring to fig. 4, in step three, the calculation method of the adaptive solution domain is as follows:
（4），
Wherein l x is the self-adaptive solution domain length, and l z is the self-adaptive solution domain width; for self-adaptive solving of vector/>, in pocket coordinate system, of nodes in domain X-axis component of/>For self-adaptive solving of vector of intra-domain node under pocket coordinate systemThe Z-axis component of (2); the nodes are contact points of the balls and the retainer pockets;
the self-adaptive solving domain determined by the embodiment ensures that the ball and the retainer pocket are not contacted beyond the range of the self-adaptive solving domain;
Vector quantity According to position vectorsAnd (3) calculating to obtain:
（5），
In the middle of Is a conversion matrix from a spherical coordinate system to a pocket coordinate system,/>Is the vector of the node relative to the geometric center of the sphere under the spherical coordinate system,/>Is a conversion matrix from a spherical coordinate system to a contact coordinate system.
In the fifth step of this embodiment, the current distance between the ball surface and the cage pocket surface in the domain is adaptively solved as g:
（6），
In the middle of An initial distance between the ball surface and the cage pocket surface;
is normal deformation of the ball and the pocket surface of the retainer:
（7），
In the middle of To influence coefficient matrix one,/>The second influence coefficient matrix is obtained;
Adaptive solution domain Internal initial pressure/>An area formed by all nodes larger than 0 is taken as a real contact area, and the node set/>Average spacing of all nodes/>The method comprises the following steps:
（8），
In the middle of For adaptively solving the number of nodes in the domain,/>Representing node coordinates, wherein/>For self-adaptive solving of node abscissa under domain coordinate system,/>Solving the ordinate of the node under the domain coordinate system for self-adaption; /(I)For node in current spacing gThe distance between the ball surface of the retainer pocket surface; /(I)For the corresponding node/>, in the initial pressure matrix p 0 Is an element of (2);
by average spacing The current spacing g is adjusted to obtain updated current spacing g:
（9）。
In the fifth step, the method for calculating the update step length of the pressure step is as follows:
calculating the conjugate gradient direction t (i, j) from the updated current distance g:
setting intermediate variables The method comprises the following steps:
（10），
（11），
（12），
In the middle of The initial value is 0 for the relaxation coefficient;
Obtaining conjugate gradient direction vector from conjugate gradient directions t (i, j) of all nodes ；
From conjugate gradient direction vectorsSetting intermediate variables/>：
（13），
Recalculating intermediate variablesAverage value/>：
（14），
In the middle ofIs an intermediate variable/>Corresponding node/>Is an element of (2);
According to the average value Updating intermediate variables/>Is the value of (1):
（15），
Then calculating to obtain the updated step length of the pressure step ：
（16）。
In the fifth step, the method for obtaining the corrected pressure matrix p comprises the following steps:
along the direction of conjugate gradient Correcting the pressure of the nodes in the real contact area and enabling the pressure of the nodes outside the real contact area to be zero:
（17），
In the middle of For the corresponding node/>, in the corrected pressure matrix pIs an element of (2);
According to Taking an area formed by all nodes with the ball surface and retainer pocket surface spacing smaller than 0 as a correction contact area, wherein the node set in the correction contact area is omega o1;
updating the pressure of the nodes in the node set omega o1:
（18），
（19），
If it is Then update the relaxation coefficient/>Otherwise/>; Wherein/>Representing an empty set;
Calculating the current contact load of two surfaces ：
（20），
In the middle ofThe grid length corresponding to the nodes in the domain is solved for self-adaption;
Re-pairing Updating to obtain the element/>, in the corrected pressure matrix p：
（21）。
In step five, calculate the relative error：
（22）。
Performing convergence judgment once according to the result of each iteration process; when (when)Ending the iterative process, and calculating the abrasion height; otherwise, the positions of the updated ball and the pocket surface of the retainer are returned to carry out the next iterative calculation.
In the sixth step, the improved microscopic Archard wear law is used to quantitatively analyze the benign wear of the main bearing surface after the ball bearing rolls for a certain number of times, and the wear height of any node in the real contact area is expressed as：
（23），
In the middle ofFor node/>Is an Archard micro wear coefficient; /(I)For node/>Is used for the hardness of the material,For the relative sliding speed u s node/>Is a relative sliding speed of (a);
The calculation method of the relative sliding speed u s is as follows:
the relative sliding speed u s is:
（24），
In the middle of The speed of the ball is the inertial coordinate system; the speed of the cage under the inertial coordinate system; The angular velocity of the ball in the spherical coordinate system; [ T cs ] is the transformation matrix of the cage coordinate system to the contact coordinate system, The angular velocity of the retainer in the retainer coordinate system; Is the inverse of [ T cp ].
Finally, in the step six, the method for updating the surface morphology of the ball and the retainer pocket comprises the following steps:
（25），
（26），
In the middle of Is the spherical surface node/>Is of the initial morphology of/>Wear the ball surface to a high degree; /(I)The surface morphology of the ball is updated;
for cage pocket surface node/> Is of the initial morphology of/>The surface of the pocket hole of the retainer is worn to a high degree; /(I)The surface morphology of the pocket hole of the retainer is updated;
In the middle of According to the formula (23), the material hardness of the corresponding ball is obtained through calculation; /(I)And (3) calculating according to a formula (23) to obtain the material hardness of the corresponding retainer pocket.
After the surface morphology of the ball and the retainer pocket is updated once, checking whether the specified calculation time T end is reached, if so, stopping calculation and storing all results; otherwise, the calculation result of the current step is stored and enters the next time step T=T 0 +DeltaT, and the circulation is continued; wherein DeltaT is a time step, n is a time step number, and is a positive integer.
In this embodiment, the update range of the surface morphology of the ball and the cage pocket each time includes a real contact area and a corrected contact area, and the morphology continues to be in the original state if the other adaptive solution area areas consider that no collision occurs.
Specific examples:
taking a certain aero-engine main shaft bearing as an example, the structural parameters are shown in table 1.
Table 1 main ball bearing parameters
As shown in fig. 2 and 3, the ball and cage geometry can be determined for the contact force Q bc, the contact half-length a bc, and the contact half-width b bc of the ball and any one of the cage pockets. From this information, the adaptive solution domain range can be obtained on the cage pocket expansion surface, as shown in fig. 4. And further calculating to obtain the surface morphology of the cage pocket after evolution, wherein the surface morphology is shown in figure 5.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.
Claims (10)
1. A dynamic analysis method for the evolution of the rough surface morphology of the pocket hole of a ball bearing retainer is characterized by comprising the steps of,
Step one: obtaining the positions and the surface initial shapes of the ball and the retainer pocket at the moment T 0;
Step two: calculating the position vectors of the ball and the retainer pocket according to the positions of the ball and the retainer pocket at the moment T 0, and calculating the elastic deformation of the interaction of the ball and the retainer pocket; if the elastic deformation is larger than 0, calculating the contact force, the contact half length and the contact half width of the ball and the retainer pocket;
Step three: determining the self-adaptive solving domain of the ball and the retainer pocket according to the contact half length and the contact half width;
step four: determining an initial pressure matrix p 0 and solving accuracy according to self-adaptive solving domain of ball and retainer pocket ；
Step five: determining a real contact area based on an initial pressure matrix p 0, calculating the current distance between the ball surface in the real contact area and the pocket surface of the retainer, and then calculating the updating step length of the pressure step; according to the updating step length of the pressure step and the iterative calculation of the relaxation coefficient, a corrected pressure matrix p is determined, and a corrected contact area in the self-adaptive solving domain is determined; calculating relative errors from all node pressure values in the corrected pressure matrix p and the initial pressure matrix p 0 until the relative errors are smaller than the solving accuracy；
Step six: calculating the abrasion height of each node in the real contact area according to the corrected pressure matrix p; updating the surface morphology of the ball and the retainer pocket in the real contact area based on the abrasion height; and then taking the updated surface morphology of the ball and the retainer pocket as the initial surface morphology of the ball and the retainer pocket at the next moment and taking the corrected pressure matrix p as the initial pressure matrix p 0 at the next moment, returning to the step one for continuous calculation until the end.
2. The dynamic analysis method for the evolution of the rough surface morphology of the pockets of the ball bearing retainer according to claim 1, wherein in the second step, the position vectors of the balls and the pockets of the retainer are expressed as：
（1），
Wherein [ T cp ] is a conversion matrix from a cage coordinate system to a pocket coordinate system; [ T Ic ] is a conversion matrix from an inertial coordinate system to a retainer coordinate system; is the vector of the spherical center relative to the center of the inertial coordinate system under the inertial coordinate system,/> The vector is the vector of the cage centroid relative to the inertial coordinate system center under the inertial coordinate system; /(I)Is the vector of the center of the pocket relative to the center of the retainer in the retainer coordinate system.
3. The dynamic analysis method for the evolution of the rough surface morphology of the pockets of the ball bearing retainer according to claim 2, wherein in the second step, the method for calculating the contact half length and the contact half width of the ball and the pockets of the retainer is as follows:
Based on position vectors Calculate the elastic deformation δ bc of the ball-cage pocket interaction:
（2），
In the middle of Is the pocket radius,/>Is the radius of the sphere;
If the elastic deformation delta bc is larger than 0, calculating macroscopic contact force Q bc between the ball and the retainer pocket:
（3），
wherein K is the contact stiffness;
the contact half-length a bc and the contact half-width b bc are calculated based on macroscopic contact force Q bc according to Hertz contact theory.
4. The dynamic analysis method for the evolution of the rough surface morphology of the pockets of the ball bearing retainer according to claim 3, wherein in the third step, the calculation method of the self-adaptive solving domain is as follows:
（4），
Wherein l x is the self-adaptive solution domain length, and l z is the self-adaptive solution domain width; for self-adaptive solving of vector/>, in pocket coordinate system, of nodes in domain X-axis component of/>For self-adaptive solving of vector/>, in pocket coordinate system, of nodes in domainThe Z-axis component of (2); the nodes are contact points of the balls and the retainer pockets;
Vector quantity According to the position vector/>And (3) calculating to obtain:
（5），
Wherein [ T bp ] is a conversion matrix from a spherical coordinate system to a pocket coordinate system, Is the vector of the node relative to the geometric center of the sphere under the spherical coordinate system,/>Is a conversion matrix from a spherical coordinate system to a contact coordinate system.
5. The dynamic analysis method for the evolution of the rough surface morphology of the pockets of the ball bearing retainer according to claim 4, wherein in the fifth step, the current distance between the inner ball surface and the pocket surface of the retainer is adaptively solved to be g:
（6），
In the middle of An initial distance between the ball surface and the cage pocket surface;
is normal deformation of the ball and the pocket surface of the retainer:
（7），
In the middle of To influence coefficient matrix one,/>The second influence coefficient matrix is obtained;
Adaptive solution domain Internal initial pressure/>An area formed by all nodes larger than 0 is taken as a real contact area, and the node set/>Average spacing of all nodes/>The method comprises the following steps:
（8），
In the middle of For adaptively solving the number of nodes in the domain,/>Representing node coordinates, wherein/>For self-adaptive solving of node abscissa under domain coordinate system,/>Solving the ordinate of the node under the domain coordinate system for self-adaption; /(I)For node/>, in current spacing gThe distance between the ball surface of the retainer pocket surface; /(I)For the corresponding node/>, in the initial pressure matrix p 0 Is an element of (2);
by average spacing The current spacing g is adjusted to obtain updated current spacing g:
（9）。
6. the dynamic analysis method for the evolution of the rough surface morphology of the pockets of the ball bearing retainer according to claim 5, wherein in the fifth step, the calculation method for the update step length of the pressure step is as follows:
calculating the conjugate gradient direction t (i, j) from the updated current distance g:
setting intermediate variables The method comprises the following steps:
（10），
（11），
（12），
In the middle of The initial value is 0 for the relaxation coefficient;
Obtaining conjugate gradient direction vector from conjugate gradient directions t (i, j) of all nodes ；
From conjugate gradient direction vectorsSetting intermediate variables/>：
（13），
Recalculating intermediate variablesAverage value/>：
（14），
In the middle ofIs an intermediate variable/>Corresponding node/>Is an element of (2);
According to the average value Updating intermediate variables/>Is the value of (1):
（15），
Then calculating to obtain the updated step length of the pressure step ：
（16）。
7. The dynamic analysis method for the evolution of the rough surface morphology of the pockets of the ball bearing retainer according to claim 6, wherein in the fifth step, the corrected pressure matrix p is obtained by the following method:
along the direction of conjugate gradient Correcting the pressure of the nodes in the real contact area and enabling the pressure of the nodes outside the real contact area to be zero:
（17），
In the middle of For the corresponding node/>, in the corrected pressure matrix pIs an element of (2);
According to Taking an area formed by all nodes with the ball surface and retainer pocket surface spacing smaller than 0 as a correction contact area, wherein the node set in the correction contact area is omega o1;
updating the pressure of the nodes in the node set omega o1:
（18），
（19），
If it is Then update the relaxation coefficient/>Otherwise/>; Wherein/>Representing an empty set;
Calculating the current contact load of two surfaces ：
（20），
In the middle ofThe grid length corresponding to the nodes in the domain is solved for self-adaption;
Re-pairing Updating to obtain the element/>, in the corrected pressure matrix p：
（21）。
8. The dynamic analysis method for the evolution of the rough surface morphology of the pockets of the ball bearing retainer according to claim 7, wherein in the fifth step, the relative error is calculated：
（22）。
9. The dynamic analysis method for the evolution of the rough surface morphology of the pockets of the ball bearing retainer according to claim 8, wherein in the step six, the nodes areExpressed as/>：
（23），
In the middle ofFor node/>Is an Archard micro wear coefficient; /(I)For node/>Material hardness of/>For the relative sliding speed u s node/>Is a relative sliding speed of (a);
The calculation method of the relative sliding speed u s is as follows:
the relative sliding speed u s is:
（24），
In the middle of The speed of the ball is the inertial coordinate system; /(I)The speed of the cage under the inertial coordinate system; /(I)The angular velocity of the ball in the spherical coordinate system; [ T cs ] is the transformation matrix of the cage coordinate system to the contact coordinate system,/>The angular velocity of the retainer in the retainer coordinate system; /(I)Is the inverse of [ T cp ].
10. The dynamic analysis method for the evolution of the rough surface morphology of the pockets of the ball bearing retainer according to claim 9, wherein in the sixth step, the method for updating the surface morphology of the balls and the pockets of the retainer is as follows:
（25），
（26），
In the middle of Is the spherical surface node/>Is of the initial morphology of/>Wear the ball surface to a high degree; /(I)The surface morphology of the ball is updated;
for cage pocket surface node/> Is of the initial morphology of/>The surface of the pocket hole of the retainer is worn to a high degree; The surface morphology of the pocket hole of the retainer is updated;
In the middle of According to the formula (23), the material hardness of the corresponding ball is obtained through calculation; /(I)And (3) calculating according to a formula (23) to obtain the material hardness of the corresponding retainer pocket.
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| JP2012172820A (en) * | 2011-02-24 | 2012-09-10 | Nsk Ltd | Double row angular ball bearing and retainer for rolling bearing |
| CN114519239A (en) * | 2022-02-18 | 2022-05-20 | 青岛理工大学 | Non-uniform collision and abrasion prediction method for ball bearing retainer pocket |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2012172820A (en) * | 2011-02-24 | 2012-09-10 | Nsk Ltd | Double row angular ball bearing and retainer for rolling bearing |
| CN114519239A (en) * | 2022-02-18 | 2022-05-20 | 青岛理工大学 | Non-uniform collision and abrasion prediction method for ball bearing retainer pocket |
Non-Patent Citations (2)
| Title |
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| 姚廷强 ; 王立华 ; 迟毅林 ; 黄亚宇 ; .球轴承-螺旋锥齿轮系统多体接触动力学分析.振动工程学报.2013,(05),全文. * |
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