A method for predicting the instability characteristics of a planetary row needle bearing cage

Abstract

The present application relates to a kind of planetary row needle bearing cage instability characteristic prediction method, belong to bearing characteristic analysis technical field, the instability of bearing cage in the prior art is solved in the research of most existing technology Limit to only rotation condition, and only by the method of dynamic modeling or test is predicted, the prediction method of the present application first establishes the coordinate system of planetary gear set, on this basis, the index describing cage instability characteristic is constructed;Using dynamic model, the training data of proxy model is formed;Further, the construction and training method of proxy model is proposed, the instability characteristic of planetary row needle bearing cage can be quickly obtained, can replace the large amount of dynamic calculation involved in bearing optimization design process, can reduce the consumption of computing resources and time, to support the rapid optimization design of high-performance planetary row needle bearing.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bearing characteristic analysis, and particularly relates to a planetary row needle bearing cage instability characteristic prediction method. BACKGROUND

[0002] The needle bearing is used for supporting the planetary wheel and the planetary carrier pin shaft in the planetary row, and under the extreme service condition of high centrifugal acceleration, the cage is prone to instability, on the one hand, due to the reciprocating impact of the roller on the cage under the action of centrifugal force, and on the other hand, due to the more complex movement state of the cage itself under the action of centrifugal force. Therefore, the cage instability is an important content that must be considered in the bearing design under the high centrifugal acceleration condition, and therefore it is necessary to study a method capable of quickly predicting the instability characteristic of the bearing cage. SUMMARY

[0003] In view of the above problems, the present application provides a planetary row needle bearing cage instability characteristic prediction method, which solves the problem that the research on the instability of the bearing cage in the prior art is mostly limited to only the rotation condition, and the instability is predicted by the method of dynamics modeling. These methods have the following disadvantages: 1) the bearing dynamics characteristics of only the rotation condition and the sun-rotation coupling condition of the planetary row are different, the instability law of the cage is different, and the original method cannot be applied; 2) the method of dynamics modeling is extremely time-consuming, and a single calculation often consumes several days of time, so it cannot be used for the analysis of the instability characteristic of the cage in the bearing optimization design process. Therefore, the prior art cannot support the technical problem of quickly predicting the instability characteristic of the planetary row needle bearing cage.

[0004] The present application provides a planetary row needle bearing cage instability characteristic prediction method, and the specific steps are as follows:

[0005] S1, establishing a planetary carrier coordinate system and a bearing coordinate system of a planetary gear set;

[0006] The planetary gear set comprises a sun gear, a planetary carrier, a cage, a roller, a planetary wheel, a ring gear, a pin shaft and a planetary row needle bearing.

[0007] S2, constructing the coordinates of the key components of the planetary gear set in the bearing coordinate system and the coordinates in the planetary carrier coordinate system;

[0008] The key components are the cage and / or the planetary wheel.

[0009] S3, based on the positions of the cage center relative to the planetary wheel center and the pin shaft, respectively, the cage instability characteristic index model of the cage center is obtained under the coordinates of the key components in the bearing coordinate system and the coordinates in the planetary carrier coordinate system.

[0010] S4, obtain the working condition points and parameter points of the planetary row needle bearing in the simulation planetary gear set, obtain the simulation instability characteristic index of the cage under the cage instability characteristic index model of the cage center, form the training data;

[0011] S5, establish a proxy model;

[0012] S6, train the best coefficient vector of the proxy model based on the training data; based on the best coefficient vector, obtain the trained proxy model;

[0013] S7, input the input parameter matrix of the to-be-tested planetary row needle bearing into the trained proxy model, and obtain the prediction result of the instability characteristic of the cage of the planetary row needle bearing.

[0014] Optionally, the key component j is the cage and / or the planet wheel.

[0015] Optionally, the cage instability characteristic index of the cage center includes the average radius of the movement trajectory of the cage center relative to the planet wheel center, the average radius of the pin shaft movement trajectory, and the average speed of the pin shaft.

[0016] Optionally, the specific steps of S3 are as follows:

[0017] S31, obtain the coordinates of the pin shaft in the planetary carrier coordinate system;

[0018] S32, obtain the movement trajectory of the cage center relative to the planet wheel center and the movement trajectory of the pin shaft;

[0019] S33, obtain the radius of the movement trajectory of the cage center relative to the planet wheel center and the radius of the movement trajectory of the cage center relative to the pin shaft;

[0020] S34, obtain the relative speed of the cage center relative to the pin shaft based on the planetary carrier coordinate system;

[0021] S35, based on the values obtained from S31 to S34, obtain the average radius of the movement trajectory of the cage center relative to the planet wheel center, the average radius of the movement trajectory relative to the pin shaft, and the average speed relative to the pin shaft, respectively, as the instability characteristic index model of the cage.

[0022] Optionally, the expression of the proxy model is:

[0023]

[0024] wherein, the instability characteristic index of the input parameter matrix S, such as the average radius and the average speed; denotes the trace of the matrix; denotes the input parameter matrix; is a coefficient matrix; The deviation is represented.

[0025] Optionally, the input parameter matrix comprises a plurality of input parameter combinations, and each input parameter combination comprises a working point and a parameter point of the bearing.

[0026] Optionally, the specific steps of S6 are as follows:

[0027] S61, performing quadratic regression on each input parameter combination to obtain an initial value of the instability characteristic index of each input parameter combination of the coefficient matrix, which is used to form an initial coefficient vector;

[0028] S62, simultaneously performing two loops, loop 1 and loop 2, on the initial coefficient vector, and each loop comprises a plurality of processes based on the particle swarm algorithm, and each process takes the result of the previous process as an initial value to obtain a first optimization result and a second optimization result;

[0029] S63, performing a third loop based on the first optimization result and the second optimization result obtained in S62 to obtain an optimal optimization result;

[0030] S64, performing a fourth loop based on the optimal optimization result to obtain an optimal coefficient vector, and obtaining the trained proxy model based on the optimal coefficient vector.

[0031] Compared with the prior art, the present application has at least the following beneficial effects:

[0032] The prediction method of the present application can quickly obtain the instability characteristics of the planet row needle bearing cage, can replace a large number of dynamic calculations involved in the bearing optimization design process, can reduce the consumption of computing resources and time, and thus supports the rapid optimization design of high-performance planet row needle bearings. BRIEF DESCRIPTION OF DRAWINGS

[0033] The accompanying drawings are only for the purpose of illustrating specific embodiments and are not considered as limiting the present application.

[0034] Figure 1 It is a schematic view of the structure of the planet gear set and the planet needle bearing of the present application;

[0035] Figure 2 It is a schematic view of the planet carrier coordinate system and the bearing coordinate system of the present application;

[0036] Figure 3 It is a process principle diagram of the training of the optimal coefficient vector of the proxy model of the planet row needle bearing cage instability characteristic prediction method of the present application;

[0037] Figure 4 It is a schematic diagram of the selection of bearing design parameters of the planet row needle bearing cage instability characteristic prediction method of the present application;

[0038] Figure 5The schematic diagram of the selection of the working condition of the bearing for the planet row roller bearing cage instability characteristic prediction method of the application.

[0039] Reference signs:

[0040] 1. sun gear; 2. planet carrier; 3. cage; 4. roller; 5. planet gear; 6. ring gear; 7. pin shaft; 8. planet row roller bearing. DETAILED DESCRIPTION

[0041] In order to enable the above-mentioned objects, features and advantages of the application to be more clearly understood, the application will be further described below with reference to the drawings and specific embodiments. It should be noted that the embodiments of the application and the features in the embodiments can be combined with each other without conflict. In addition, the application can also be implemented in other ways different from those described herein, and therefore, the protection scope of the application is not limited by the specific embodiments disclosed below.

[0042] One specific embodiment of the application, as Figures 1-5 , discloses a planet row roller bearing cage instability characteristic prediction method, and the specific steps are as follows:

[0043] S1, as Figure 1 shown, the planet carrier coordinate system (O C XY) and the bearing coordinate system (O P xy) of the planetary gear set are established.

[0044] Further, the planetary gear set includes a sun gear 1, a planet carrier 2, a cage 3, a roller 4, a planet gear 5, a ring gear 6 and a planet row roller bearing 8; the planet row roller bearing 8 includes the cage 3 and the roller 4; the planet carrier 2 is arranged on the outer side of the sun gear 1, the inner side of the ring gear 6, the sun gear 1 and the planet carrier 2 are drivingly connected through the planet gear 5, the ring gear 6 and the planet carrier 2 are drivingly connected through the planet gear 5; the planet row roller bearing 8 is arranged between the planet gear 5 and the planet carrier 2; the planet row roller bearing 8 includes a cage 3, and a plurality of rollers 4 are uniformly distributed on the cage 3.

[0045] Specifically, the origin of the planet carrier coordinate system (O C XY) is located at the theoretical center of the sun gear 1, the Y direction of the planet carrier coordinate system is determined by the negative gravity direction, and the X axis is turned 90 degrees clockwise from the Y axis; the origin of the bearing coordinate system (O P xy) is located at the theoretical center of the planet row roller bearing 8, the X axis direction of the bearing coordinate system is from the theoretical center O C of the sun gear 1 to the theoretical center O P of the planet row roller bearing 8.

[0046] Further, in the planet carrier coordinate system, the position coordinates (0, 0, ΦS ), the position coordinates (0, 0, Φ C ) of the planet carrier 2, and the position coordinates (0, 0, Φ R ) of the ring gear 6, wherein Φ S represents the angle of rotation of the sun gear 1; Φ C represents the angle of rotation of the planet carrier 2; and Φ R represents the angle of rotation of the ring gear 6.

[0047] Further, in the bearing coordinate system, the position coordinates (x P , y P , θ P ) of the planet gear 5 and the position coordinates (x g , y g , θ g ) of the cage are determined, wherein x P , y P and θ P represent the coordinates of the x-axis, the coordinates of the y-axis and the angle of rotation of the planet gear 5 in the bearing coordinate system, respectively; and x g , y g and θ g represent the coordinates of the x-axis, the coordinates of the y-axis and the angle of rotation of the cage 3 in the bearing coordinate system, respectively.

[0048] S2, the coordinates (x j (t), y j (t)) of the key component j at time t in the bearing coordinate system and the coordinates (X j (t), Y j (t)) of the key component j at time t in the planet carrier coordinate system are constructed when the planetary gear set is constructed.

[0049] Further, the expression of the coordinates (X j (t), Y j (t)) of the key component j at time t in the planet carrier coordinate system is:

[0050]

[0051]

[0052] wherein, represents the distance between the origin of the bearing coordinate system and the origin of the planet carrier coordinate system; represents the rotation angle of the key component j at time t in the planet carrier coordinate system; represents the x-axis coordinate of the key component j at time t in the planet carrier coordinate system; represents the y-axis coordinate of the key component j at time t in the planet carrier coordinate system; is the rotation speed of the planet carrier.

[0053] wherein, xj (t) represents the coordinate of the key component j in the x-axis of the bearing coordinate system at time t; y j (t) represents the coordinate of the key component j in the y-axis of the bearing coordinate system at time t.

[0054] Specifically, the key component j is the retainer and / or the planet wheel, j is g or p, when j is g, it represents the retainer; when j is p, it represents the planet wheel.

[0055] S3, based on the positions of the retainer 3 center relative to the planet wheel 5 center and the pin shaft 7 respectively under the coordinates of the key component in the bearing coordinate system and the coordinates in the planet carrier coordinate system, a retainer instability characteristic index model is obtained.

[0056] Further, the S3 specifically comprises:

[0057] S31, the coordinates (X C (t), Y C (t)) of the pin shaft in the planet carrier coordinate system are obtained, and the expression is:

[0058]

[0059] wherein, represents the x-axis coordinate of the pin shaft in the planet carrier coordinate system at time t; represents the y-axis coordinate of the pin shaft in the planet carrier coordinate system at time t; represents the rotation angle of the planet carrier in the planet carrier coordinate system at time t.

[0060] S32, the motion trajectory of the retainer center relative to the planet wheel center and the motion trajectory of the retainer center relative to the pin shaft are obtained, and the expression is:

[0061]

[0062] wherein, represents the relative position of the retainer relative to the planet wheel in the X direction under the planet carrier coordinate system at time t; represents the relative position of the retainer relative to the planet wheel in the Y direction under the planet carrier coordinate system at time t; represents the X-axis coordinate of the retainer in the planet carrier coordinate system at time t; represents the X-axis coordinate of the planet wheel in the planet carrier coordinate system at time t; represents the relative position of the retainer relative to the pin shaft in the X direction under the planet carrier coordinate system at time t; represents the relative position of the retainer relative to the pin shaft in the Y direction under the planet carrier coordinate system at time t; represents the X-axis coordinate of the pin shaft in the planet carrier coordinate system at time t; represents the Y-axis coordinate of the holder at time t in the planetary carrier coordinate system; represents the Y-axis coordinate of the planet at time t in the planetary carrier coordinate system; represents the Y-axis coordinate of the pin shaft at time t in the planetary carrier coordinate system.

[0063] S33, the radius of the motion trajectory of the holder center relative to the planet center, and the radius of the motion trajectory of the holder center relative to the pin shaft are obtained, and the expression is:

[0064]

[0065]

[0066] wherein, is the radius of the motion trajectory of the holder center relative to the planet center at time t, is the radius of the motion trajectory of the holder center relative to the pin shaft at time t.

[0067] S34, based on the planetary carrier coordinate system, the relative speed of the holder center relative to the pin shaft is obtained , and the expression is:

[0068]

[0069] wherein, represents the X-axis velocity component of the holder at time t in the planetary carrier coordinate system; represents the X-axis velocity component of the pin shaft at time t in the planetary carrier coordinate system; represents the Y-axis velocity component of the holder at time t in the planetary carrier coordinate system; represents the Y-axis velocity component of the pin shaft at time t in the planetary carrier coordinate system.

[0070] S35, based on the values obtained in S31 to S34, the average radius of the motion trajectory of the holder center relative to the planet center , the average radius of the motion trajectory of the holder center relative to the pin shaft , and the average value of the speed of the holder center relative to the pin shaft are obtained respectively as the instability characteristic index model of the holder.

[0071] S4, the working points and parameter points of the planetary row needle bearing in the simulation planetary gear set are obtained, and the simulation instability characteristic index of the holder is obtained under the holder instability characteristic index model at the holder center, and the training data is formed.

[0072] Further, S4 specifically comprises:

[0073] S41, a planetary row dynamics model containing planetary needle bearings is established in a dynamics simulation software.

[0074] S42, in the working range of the planetary row needle bearing, uniformly select parameter points and corresponding working condition points, and perform dynamic simulation on the planetary row dynamic model of S41 to extract the coordinates (x j (t), y j (t)) of the key components j in the bearing coordinate system at time t; extract the rotation angle of the planetary carrier at time t in the planetary carrier coordinate system; and obtain the instability characteristic index of the retainer according to the instability characteristic index model of the retainer of S3.

[0075] Specifically, within the design range of bearing parameters (such as bearing radial clearance, pocket clearance, guide clearance, etc.), design parameter points (such as the radial clearance design range of the bearing is 0-50μm, and 0μm, 10μm, 20μm, 30μm, 40μm, 50μm are uniformly selected to form groups of 0-1000rpm, 0-2000rpm, 0-3000rpm, etc. for simulation), dynamic simulation is carried out. After simulation, the positions of the retainer, planetary gear and pin shaft corresponding to the working condition points and parameter points are extracted, and the coordinates (x j (t), y j (t)) of the key components j in the bearing coordinate system at time t are extracted; the rotation angle of the planetary carrier at time t in the planetary carrier coordinate system is extracted; and the simulation average radius of the motion trajectory of the retainer center relative to the planetary gear center , the simulation average radius of the motion trajectory of the retainer center relative to the pin shaft , and the simulation average speed relative to the pin shaft are obtained according to S3 to form training data.

[0076] S5, establish a proxy model.

[0077] Specifically, the expression of the proxy model is:

[0078]

[0079] wherein, represents the instability characteristic index of the input parameter matrix S, such as the average radius and the average speed; represents the trace of the matrix; represents the input parameter matrix; is a coefficient matrix; represents the bias.

[0080] Specifically, the input parameter matrix includes multiple groups of input parameter combinations, and the input parameter combination includes the working condition points and parameter points of the bearing.

[0081] Further, the expression of the coefficient matrix is:

[0082]

[0083] wherein, denotes the coefficient of the l -1th row, 1st column; denotes the coefficient of the l -1th row, 1st column; denotes the coefficient of the l -1th row, 1st column; l denotes the coefficient of the -1th row, 1st column; l denotes the coefficient of the l -1th row, 1st column; denotes the coefficient of the l -1th row, 1st column. l

[0084] S6, training the agent model with the best coefficient vector K based on the training data using the particle swarm algorithm PSA best .

[0085] Further, as shown in Figure 2 , S6 specifically comprises:

[0086] S61, performing quadratic regression on the first input parameter of the input parameter combination to obtain the initial value of the instability characteristic index of each input parameter combination of the coefficient matrix, which is used to form the initial coefficient vector , the expression of which is:

[0087]

[0088] wherein, denotes the initial value of the instability index of the input parameter of the coefficient matrix; and denote the coefficient of the l row, 1st column, and the coefficient of the l row, 1st column, respectively; denotes the coefficient of the row, 2nd column. l

[0089] S62, performing two loops simultaneously: loop 1 and loop 2, both of which contain 5 processes based on the particle swarm algorithm, and each process takes the result of the previous process as the initial value to obtain the first optimization result K1 and the second optimization result K2. Further, when performing the process based on the particle swarm algorithm, the search range is:

[0090] ​​​

[0091]

[0092] wherein, is the region coefficient, and the value in cycle 1 and cycle 2 is 5; denotes the coefficient matrix each parameter minimum value; denotes the coefficient matrix each parameter maximum value.

[0093] S63, based on the first optimization result K1obtained in S62 1 and the second optimization result K2 2 perform a third cycle to obtain the optimal optimization result K3 3 , the specific steps are:

[0094] If the difference between the determination coefficients of the first optimization result K1and the second optimization result K2is less than or equal to a threshold value, perform cycle A: cycle A includes 3 search processes based on the particle swarm algorithm, and the region coefficient is 3; otherwise, perform cycle B, which includes 5 search processes based on the particle swarm algorithm, and the region coefficient is 5; obtain the optimal optimization result K3 3 .

[0095] Further, the difference value expression between the determination coefficients of the first optimization result K1 1 and the second optimization result K2 2

[0096] .

[0097] S64, based on the optimal optimization result K3 3 , perform a fourth cycle: select the one with a larger determination coefficient from the first optimization result K1 1 , the second optimization result K2 2 and the optimal optimization result K3 3 as a temporary maximum optimization result K4 : if the difference between the determination coefficients of the temporary maximum optimization result K4 and the optimal optimization result K3is less than a threshold value, perform cycle A, otherwise, perform cycle B to obtain the optimization result K 4 , which is the best coefficient vector , obtain the trained proxy model; denotes the determination coefficient corresponding to the first optimization result K1; denotes the determination coefficient corresponding to the second optimization result K2.

[0098] Further, the difference value expression between the determination coefficients of the temporary maximum optimization result K4 ​The difference value expression between the optimal optimization result K3 and the determination coefficient is:

[0099]

[0100] Further, the expression of the determination coefficient is:

[0101]

[0102] wherein, m is the number of training data, represents the actual index of the i th parameter combination; represents the predicted index of the i th parameter combination; represents the average value of the actual index.

[0103] It can be understood that when the optimization result K (K 1 or K 2 or K 3 or K best,3 or K best ) is brought into the expression of the surrogate model, the predicted index of all the corresponding parameter combinations can be obtained, and on this basis, the determination coefficient corresponding to the optimization result K can be obtained, which can be written as R 2 (K).

[0104] S7, input the input parameter matrix of the star row needle bearing to be tested into the trained surrogate model, and obtain the prediction result of the instability characteristics of the star row needle bearing retainer.

[0105] In order to illustrate the effectiveness of the method of the present application, the above technical solutions of the present application are described in detail through two specific examples as follows:

[0106] Example 1

[0107] For the case that the bearing revolution speed is 3000 rpm and the torque is 610 Nm, a set of bearing design parameters (pocket clearance, radial clearance) is set, as shown in Figure 4 , the circle is the training data (the result obtained by the dynamic simulation model), and the square frame is the test set, which is used to analyze the accuracy of the surrogate model.

[0108] The model is trained using the training set data, and the training process is as shown in Figure 3 , and the best coefficient vector is obtained as:

[0109]

[0110] Wherein, the superscript A, B, C of K respectively represent the optimal coefficient vector corresponding to the average radius of the raceway center relative to the planetary wheel center movement track, the average radius of the raceway center relative to the pin shaft movement track, and the rotation speed index relative to the pin shaft.

[0111] Example two

[0112] For the case of radial clearance of 30 μm and pocket clearance of 50 μm, a set of working conditions is set, as follows Figure 5 As shown in the figure, the circles are training data (results obtained by the dynamic simulation model), and the square frame is the test set, which is used to analyze the accuracy of the agent model.

[0113] The model is trained using the training set data, and the training process is as shown in Figure 3 The optimal coefficient vector K is obtained as follows

[0114]

[0115] Wherein, the superscript D, E, F of K respectively represent the optimal coefficient vector corresponding to the average radius of the raceway center relative to the planetary wheel center movement track, the average radius of the raceway center relative to the pin shaft movement track, and the rotation speed index relative to the pin shaft.

[0116] Referring to Figure 4 , wherein the circles are training data, and the square frame is the test set; referring to Figure 5 , wherein the circles are training data, and the square frame is the test set.

[0117] The above is only the preferred specific embodiment of the present application, but the protection scope of the present application is not limited to this. Any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application.​

Claims

1. A method for predicting the instability characteristics of a planetary needle roller bearing cage, characterized in that, The specific steps are as follows: S1, establishing a planetary carrier coordinate system and a bearing coordinate system of a planetary gear set; Wherein, the planetary gear set comprises a sun gear, a planetary carrier, a retainer, a roller, a planet gear, a ring gear, a pin shaft and a planetary row needle bearing; S2, constructing the coordinates of the key components of the planetary gear set in the bearing coordinate system and the coordinates in the planetary carrier coordinate system; Wherein, the key components are the retainer and / or the planet gear; S3, based on the positions of the retainer center relative to the planet gear center and the pin shaft in the coordinates of the key components in the bearing coordinate system and the planetary carrier coordinate system, obtaining a retainer instability characteristic index model of the retainer center, the specific steps are as follows: S31, obtaining the coordinates of the pin shaft in the planetary carrier coordinate system; S32, obtaining the motion trajectory of the retainer center relative to the planet gear center and the motion trajectory of the pin shaft; S33, obtaining the radius of the motion trajectory of the retainer center relative to the planet gear center and the radius of the motion trajectory of the retainer center relative to the pin shaft; S34, obtaining the relative velocity of the retainer center relative to the pin shaft based on the planetary carrier coordinate system; S35, based on the values obtained from S31 to S34, obtaining the average radius of the motion trajectory of the retainer center relative to the planet gear center, the average radius of the motion trajectory relative to the pin shaft and the average value of the velocity relative to the pin shaft as the instability characteristic index model of the retainer; S4, obtaining the working points and parameter points of the planetary row needle bearing in the simulated planetary gear set, and obtaining the simulation instability characteristic index of the retainer under the retainer instability characteristic index model of the retainer center, forming training data, the specific steps are as follows: S41, establishing a planetary row dynamics model containing planetary needle bearings in the dynamics simulation software; S42, within the working range of the planetary row needle bearing, uniformly selecting parameter points and corresponding working points, performing dynamics simulation on the planetary row dynamics model of S41, extracting the coordinates of the key components in the bearing coordinate system; extracting the rotation angle of the planetary carrier in the planetary carrier coordinate system, and obtaining the instability characteristic index of the retainer according to the instability characteristic index model of the retainer of S3; S5, establishing a surrogate model, the expression is: wherein, denotes an instability characteristic indicator of the input parameter matrix S; denotes the trace of a matrix; is the coefficient matrix; denotes the bias; S6, training the best coefficient vector of the surrogate model based on the training data; based on the best coefficient vector, obtaining the trained surrogate model; S7, inputting the input parameter matrix of the to-be-tested planetary row needle bearing into the trained surrogate model to obtain the prediction result of the instability characteristic of the planetary row needle bearing retainer.

2. The planetary row needle bearing cage instability characteristic prediction method of claim 1, wherein, The key component j is the retainer and / or the planet gear.

3. The planetary row needle bearing cage instability characteristic prediction method of claim 2, wherein, The retainer instability characteristic index of the retainer center includes the average radius of the motion trajectory of the retainer center relative to the planet gear center, the average radius of the motion trajectory of the pin shaft and the average value of the velocity of the pin shaft.

4. The planetary row needle bearing cage instability characteristic prediction method of claim 1, wherein, The input parameter matrix includes multiple input parameter combinations, and the input parameter combination includes the working points and parameter points of the bearing.

5. The planetary row needle bearing cage instability characteristic prediction method of claim 1, wherein, The specific steps of S6 are as follows: S61, performing quadratic regression on each input parameter combination to obtain the initial value of the instability characteristic index of each input parameter combination of the coefficient matrix, which is used to form an initial coefficient vector; S62, simultaneously performing two cycles on the initial coefficient vector: cycle 1 and cycle 2, both of which include multiple particle swarm algorithm-based processes, each of which takes the previous result as the initial value, to obtain a first optimization result and a second optimization result; S63, performing a third cycle based on the first optimization result and the second optimization result obtained in S62 to obtain an optimal optimization result; S64, based on the optimal optimization result, performing a fourth cycle to obtain a best coefficient vector; and based on the best coefficient vector, obtaining a trained proxy model.

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