A method for determining the bearing slippage failure threshold based on state information fusion analysis

Abstract

This invention discloses a method for determining the bearing slippage failure threshold based on state information fusion analysis. First, a bearing twin simulation model is constructed, and the bearing cage slippage rate and stress-strain of each component are measured simultaneously. An improved L-P theory is used to construct a bearing life theoretical model and calculate the corresponding PV value. Second, the bearing cage center-of-mass motion trajectory is measured, and its maximum, minimum, average, and standard deviation are calculated to construct a center-of-mass trajectory fusion index to measure the cage motion stability. Bearing vibration acceleration data is measured, and a bearing life prediction state model is constructed based on the ARMA-transfer learning algorithm. Finally, based on the obtained bearing life theoretical model, PV value, center-of-mass motion trajectory fusion index, and bearing life prediction state model, and combined with fuzzy clustering evidence theory, a bearing state information decision-making layer fusion is performed to determine the bearing slippage failure threshold. This invention enables accurate calculation of the bearing slippage threshold under varying operating conditions.

Description

Technical Field

[0001] This invention relates to the field of bearing cage slippage, and in particular to a method for determining the bearing slippage failure threshold based on state information fusion analysis. Background Technology

[0002] As rotating machinery continues to develop towards higher efficiency, stability, and reliability, the DN value (inner ring diameter D (mm) × inner ring speed N (r / min)) of high-end bearings has reached over 3 × 10⁶ mm·r / min. At the same time, increasingly harsh operating environments for bearings lead to frequent bearing failures, such as slippage, fatigue failure, and motion instability. Among these, bearing slippage failure is the most common, accounting for approximately 37% of all failures. Therefore, studying bearing slippage failure is essential.

[0003] Studies have shown that the physical properties of the contact surfaces of various bearing components (such as hardness, thermal stability, and contact strength), lubrication conditions, operating conditions (such as operating temperature, speed, and load), and machining and installation all affect bearing slippage and service life. Therefore, it is crucial to analyze and calculate the bearing slippage failure threshold by combining different bearing structures and operating environments. Since the influence of operating conditions on bearings can be reflected through dynamic performance parameters and temperature analysis results, such as the bearing's PV value, contact stress, slippage rate, cage center of mass trajectory, and vibration acceleration data, these key bearing condition performance parameters can be used as primary failure criteria. This invention also utilizes an improved LP theory to construct a bearing life theoretical model, employs the ARMA-transfer learning algorithm to construct a bearing life prediction state model, and further fuses bearing motion characteristic decision-making layer information based on fuzzy clustering evidence theory to determine the bearing slippage failure threshold. Determining the bearing slippage failure threshold has significant guiding significance for preventing bearing slippage and formulating reasonable bearing maintenance and replacement strategies. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a method for determining the bearing slippage failure threshold based on motion characteristic information fusion analysis. By making full use of information closely related to bearing slippage, such as PV value, contact stress, slippage rate, cage center of mass motion trajectory and vibration acceleration data, a bearing slippage failure model is constructed, which can realize accurate calculation of bearing slippage failure threshold under variable structure and variable working conditions.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for determining the bearing slippage failure threshold based on state information fusion analysis includes the following steps:

[0007] Step S1: Construct a bearing twin simulation model and simultaneously obtain the bearing cage slippage rate, bearing inner ring stress, bearing outer ring stress, roller stress, bearing cage center of mass motion trajectory, and bearing vibration acceleration data.

[0008] Step S2: Based on the bearing cage slippage rate, bearing inner ring stress, bearing outer ring stress and roller stress obtained in step S1, construct a bearing life theoretical model and calculate the PV value using the improved LP theory.

[0009] Step S3: Based on the bearing cage center of mass motion trajectory information obtained in step S1, calculate the four indicators of maximum value, minimum value, average value and standard deviation respectively, and construct the center of mass trajectory fusion index to measure the stability of cage motion;

[0010] Step S4: Based on the bearing vibration acceleration data obtained in step S1, construct a bearing life prediction state model using the life prediction model ARMA and the component migration analysis method.

[0011] Step S5: Based on the bearing life theoretical model and PV value obtained in step S2, the centroid trajectory fusion index obtained in step S3, and the life prediction model ARMA obtained in step S4, the bearing state information is fused at the decision level using the decision-level fusion algorithm of fuzzy clustering and PCR6 evidence theory to construct the bearing slippage failure model, and then the bearing slippage failure threshold is determined.

[0012] Preferably, the implementation process of step S1 is as follows:

[0013] Step S101: First, use Solidworks software to establish a bearing geometric model, then use Hypermesh software to build a bearing twin simulation model, and finally use ADAMS software to perform multibody simulation on the bearing twin simulation model.

[0014] Step S102: Based on the bearing twin simulation model established in step S101, measure the rotational speed of the bearing inner ring and the rotational speed of the bearing cage, and calculate the bearing cage slippage rate S. a :

[0015]

[0016] Where, ω c ω is the actual rotational speed of the bearing cage; cm This is the theoretical rotational speed of the bearing cage; the theoretical rotational speed ω of the bearing cage cm satisfy:

[0017]

[0018] Among them, R wR is the roller radius of the bearing; m It is the pitch circle radius of the bearing; ω im It is the rotational speed of the inner ring of the bearing;

[0019] Step S103: Extract the stress F of the bearing inner ring based on the bearing twin simulation model established in step S101. ir Stress F of the bearing outer ring or and the stress F of the bearing roller b ;

[0020] Step S104: Calculate the centroid motion trajectory of the bearing cage based on the bearing twin simulation model established in step S101.

[0021] In ADAMS software, the motion trajectories of four points uniformly distributed along the circumference on the bearing cage are extracted as x1, x2, x3 and x4, respectively. The motion trajectory x of the center of mass of the bearing cage is calculated as shown in equation (3):

[0022]

[0023] Step S105: Extract bearing vibration acceleration data based on the bearing twin simulation model established in step S101.

[0024] Preferably, the implementation process of step S2 is as follows:

[0025] Step S201, Improved LP bearing life theoretical model:

[0026] Assuming the roller length of the bearing is l, the contact area between the roller and the bearing inner ring raceway and the bearing outer ring raceway is divided into m thin plates; according to the basic rated dynamic load theory, the basic rated dynamic load Q of the contact area between the j-th roller and the bearing inner ring raceway or outer ring raceway thin plate of the k-th bearing inner ring raceway or outer ring raceway is... cnjk for:

[0027]

[0028] When n = μ, it is the inner raceway thin plate; when n = v, it is the outer raceway thin plate; D is the diameter of the roller; Z is the number of rollers; parameter γ nj Satisfying γ nj =Dcosα nj / d m ;α nj d is the contact angle between the j-th roller and either the inner or outer raceway; m The bearing pitch circle diameter;

[0029] Then the contact area between the j-th roller and the inner ring raceway of the bearing has a life L of the thin sheet of the k-th inner ring raceway. μjkThe life L of the contact area between the j-th roller and the outer raceway of the bearing, and the thin sheet of the k-th outer raceway. vjk As shown in equations (5) and (6) respectively:

[0030]

[0031]

[0032] Among them, Q cμjk Q is the basic rated dynamic load of the thin sheet of the k-th inner ring raceway in the contact area between the j-th roller and the inner ring raceway of the bearing; cvjk Q is the basic rated dynamic load of the thin sheet of the k-th outer ring raceway in the contact area between the j-th roller and the outer ring raceway of the bearing; μjk Q is the contact load of the thin sheet of the k-th inner ring raceway in the contact area between the j-th roller and the inner ring raceway of the bearing; vjk The contact load of the thin sheet of the k-th outer ring raceway in the contact area between the j-th roller and the outer ring raceway of the bearing;

[0033] The basic rated dynamic load Q of the contact area between the j-th roller and the inner or outer raceway of the bearing. Rnjk As shown in equation (7):

[0034]

[0035] Then, the bearing life theoretical model L... g The calculation is shown in equation (8):

[0036]

[0037] Where e is the Weibull coefficient; L Rμjk and L Rvjk These represent the basic rated life of the k-th roller sheet in the contact area between the j-th roller and the inner or outer raceway of the bearing; j is a parameter.

[0038] Step S202: Calculate the bearing PV value:

[0039] Based on the bearing cage slippage rate S obtained in step S102 a The bearing roller contact stress F obtained in step S103 b The bearing PV value is obtained by calculating the product of the two in the time domain, as shown in equation (9):

[0040] PV = S a *F b (9)

[0041] Preferably, the implementation process of step S3 is as follows:

[0042] Step S301: Based on the bearing cage center of mass motion trajectory obtained in step S104, calculate the maximum value x. max Minimum value x min Average value x mean and standard deviation x stdev Four indicators:

[0043] x max =MAX(x) (10)

[0044] x min =MIN(x) (11)

[0045] x mean =MEAN(x) (12)

[0046] x stdev =STDEV(x) (13)

[0047] Where MAX(·) represents the function to find the maximum value; MIN(·) represents the function to find the minimum value; MEAN(·) represents the function to find the average value; and STDEV(·) represents the function to find the standard deviation.

[0048] Step S302: Construct a centroid trajectory fusion index to measure the motion stability Θ of the bearing cage, as shown in equation (14):

[0049] Θ = 0.2x max +0.2x min +0.2x mean +0.4x stdev (14)

[0050] Preferably, the implementation process of step S4 is as follows:

[0051] Step S401: Transfer of bearing vibration acceleration data based on compositional migration analysis:

[0052] The bearing vibration acceleration data obtained in step S105 is used as the source domain data D. S ={(y S1 ,ξ S1 ),...,(y Sσ ,ξ Sσ )}, where y S1 ,y S2 ,...,y Sσ It is the input of the source domain data, ξ S1 ,ξ S2 ,...,ξ Sσ It is the output of the source domain data; For target domain data, where It is the input of the target domain data. It is the output of the target domain data; after minimizing the mapping, D S and D T The nonlinear mapping ζ is calculated by the maximum average difference distance, as shown in equation (15):

[0053]

[0054] Among them, Y' S and Y' T This represents the input of the mapped source domain data and the input of the target domain data; Indicates the i-th t Data from one source domain; Indicates the i-th t The target domain data is σ; σ is the number of source domain data. The number of data points in the target domain; ||·|| H D is the distance between the vectors in the reproducing kernel Hilbert space; H (·) represents the maximum average difference distance of the vector;

[0055] Step S402: Construct the bearing life prediction model ARMA:

[0056] For the bearing vibration acceleration sequence {y} obtained in step S105 t The fitted random difference equation is shown in equation (16):

[0057]

[0058] in, The autoregressive parameters are: θ1, θ2, ..., θ η The moving average parameter; sequence {a} t} represents the residual sequence.

[0059] Preferably, the implementation process of step S5 is as follows:

[0060] Step S501: Based on the bearing life theoretical model and PV value obtained in step S2, the centroid trajectory fusion index obtained in step S3, and the life prediction model ARMA obtained in step S4, the bearing state information is fused at the decision level using a decision-level fusion algorithm based on fuzzy clustering and PCR6 evidence theory.

[0061] (1) Fuzzy clustering algorithm:

[0062] The dataset consists of the bearing life theoretical model and PV value obtained in step S2, the centroid trajectory fusion index obtained in step S3, and the life prediction model ARMA obtained in step S4. Perform clustering, dataset Each data point in the dataset has a dimension of ρ. The dataset is then calculated. neighborhood radius ra Thus, the dataset is calculated. The i-th d Dimensional data points density value As shown in equation (17):

[0063]

[0064] Where v is the dimension;

[0065] Based on density value The data point with the highest density value is selected as the first cluster center, and the dataset is calculated. The density values ​​of the remaining data points are shown in equation (18):

[0066]

[0067] in, r is the maximum density value obtained from the previous clustering; b Let J be the new neighborhood radius; add data weights and an inhibition factor to achieve rapid convergence, and construct the objective function J of the dissimilarity index, as shown in equation (19):

[0068]

[0069] in, w is the number of sample points; w is the number of cluster centers; d is the weighted value of each fuzzy membership degree of the sample point to the cluster center; i'j' u is the distance from the i'th sample point to the j'th cluster center; i'j' Let be the membership function of the i'th sample point with respect to the j'th cluster center, as shown in equation (20):

[0070]

[0071] Where, d k'j' Let k' be the distance from the k'th sample point to the j'th cluster center;

[0072] (2) Decision-level fusion algorithm based on PCR6 evidence theory:

[0073] The evidence set was fused using the PCR6 combination rule to obtain the fusion result, wherein the evidence set includes the bearing life theoretical model, PV value, centroid trajectory fusion index and life prediction model ARMA;

[0074] Step S502: Determine the bearing slippage failure threshold:

[0075] The cluster center O is determined based on the density value obtained from formula (18) in step S501. jCalculate the distance CD between cluster centers:

[0076] CD = ||O Δ -O ▽ ||; Δ=1,2,...,w; Δ≠▽ (21)

[0077] If the maximum distance between cluster centers is less than 0.4, the evidence is considered to have little conflict, and the PCR6 combination rule is directly used to obtain the fusion result; if the maximum distance between cluster centers is greater than 0.4, the evidence is considered to have conflict, the evidence with a distance greater than 0.4 between cluster centers is deleted, and the remaining evidence is fused using the PCR6 combination rule; finally, the bearing slippage failure threshold is determined.

[0078] The beneficial effects of this invention are:

[0079] 1. This invention constructs a bearing twin model, which can simultaneously extract multi-source data such as bearing contact stress, slippage rate, cage center of mass motion trajectory and vibration acceleration, fully explore the relationship between bearing slippage and motion characteristics, and further combine the relationship between bearing motion characteristics and service life to establish the connection between bearing slippage and service life for the first time.

[0080] 2. This invention utilizes the vibration acceleration dataset extracted based on the bearing twin model, combined with the bearing vibration data migration method based on component migration analysis and the ARMA life prediction algorithm, to construct a bearing life prediction state model.

[0081] 3. Based on the evidence set including the bearing life theoretical model, PV value, centroid trajectory fusion index and bearing life prediction state model, this invention uses fuzzy clustering evidence theory to realize the decision-level information fusion of bearing motion characteristics.

[0082] 4. This invention constructs a comprehensive and accurate bearing slippage failure model, which can accurately calculate the bearing slippage failure threshold under varying structures and operating conditions, providing a basis for operation and maintenance strategies for bearing slippage-related faults. Attached Figure Description

[0083] Figure 1 This is a schematic diagram of the process for determining the bearing slippage failure threshold based on motion characteristic information fusion analysis provided in Example 1;

[0084] Figure 2 This is a twin model of the deep groove ball bearing in Example 1, where a is the bearing geometric model and b is the bearing mesh model;

[0085] Figure 3The bearing cage slippage rate provided in Example 1 is defined as follows: a is the cage slippage rate at a speed of 10000 r / min and a load of 4000 N; b is the cage slippage rate at a speed of 20000 r / min and a load of 4000 N; and c is the cage slippage rate at a speed of 30000 r / min and a load of 4000 N.

[0086] Figure 4 The following are stress-strain diagrams of the deep groove ball bearing provided in Example 1: a is the stress-strain diagram of the bearing cage at a speed of 10000 r / min and a load of 4000 N; b is the stress-strain diagram of the inner and outer raceways of the bearing at a speed of 10000 r / min and a load of 4000 N; c is the stress-strain diagram of the bearing cage at a speed of 30000 r / min and a load of 4000 N; and d is the stress-strain diagram of the inner and outer raceways of the bearing at a speed of 30000 r / min and a load of 4000 N.

[0087] Figure 5 The force diagrams of the bearing rollers provided in Example 1 are as follows: a is the force diagram of the rollers when the rotation speed is 10000 r / min and the load is 4000 N; b is the force diagram of the rollers when the rotation speed is 20000 r / min and the load is 4000 N; and c is the force diagram of the rollers when the rotation speed is 30000 r / min and the load is 4000 N.

[0088] Figure 6 The diagrams shown are of the cage center of gravity motion trajectory provided in Example 1, where a is the cage center of gravity motion trajectory at a speed of 10000 r / min and a load of 4000 N, b is the cage center of gravity motion trajectory at a speed of 20000 r / min and a load of 4000 N, and c is the cage center of gravity motion trajectory at a speed of 30000 r / min and a load of 4000 N.

[0089] Figure 7 The diagram shows the trajectory of the cage center of mass of the cylindrical roller bearing provided in Example 1. In this diagram, a represents the trajectory of the cage center of mass at a speed of 10000 r / min and a load of 4000 N; b represents the trajectory of the cage center of mass at a speed of 20000 r / min and a load of 4000 N; and c represents the trajectory of the cage center of mass at a speed of 30000 r / min and a load of 4000 N.

[0090] Figure 8The diagram shows the vibration acceleration of the deep groove ball bearing provided in Example 1. In this diagram, a represents the bearing's vibration acceleration in the X direction at a speed of 10000 r / min and a load of 4000 N; b represents the bearing's vibration acceleration in the Y direction at a speed of 10000 r / min and a load of 4000 N; c represents the bearing's vibration acceleration in the Z direction at a speed of 10000 r / min and a load of 4000 N; d represents the bearing's vibration acceleration in the X direction at a speed of 20000 r / min and a load of 4000 N; e represents the bearing's vibration acceleration in the Y direction at a speed of 20000 r / min and a load of 4000 N; f represents the bearing's vibration acceleration in the Z direction at a speed of 20000 r / min and a load of 4000 N; g represents the bearing's vibration acceleration in the X direction at a speed of 30000 r / min and a load of 4000 N; h represents the bearing's vibration acceleration in the Y direction at a speed of 30000 r / min and a load of 4000 N; and i represents the bearing's vibration acceleration in the Z direction at a speed of 30000 r / min and a load of 4000 N.

[0091] Figure 9 The diagram shows the vibration acceleration of the cylindrical roller bearing provided in Example 1. In this diagram, a represents the bearing's vibration acceleration in the X direction at a speed of 10000 r / min and a load of 4000 N; b represents the bearing's vibration acceleration in the Y direction at a speed of 10000 r / min and a load of 4000 N; c represents the bearing's vibration acceleration in the Z direction at a speed of 10000 r / min and a load of 4000 N; d represents the bearing's vibration acceleration in the X direction at a speed of 20000 r / min and a load of 4000 N; e represents the bearing's vibration acceleration in the Y direction at a speed of 20000 r / min and a load of 4000 N; f represents the bearing's vibration acceleration in the Z direction at a speed of 20000 r / min and a load of 4000 N; g represents the bearing's vibration acceleration in the X direction at a speed of 30000 r / min and a load of 4000 N; h represents the bearing's vibration acceleration in the Y direction at a speed of 30000 r / min and a load of 4000 N; and i represents the bearing's vibration acceleration in the Z direction at a speed of 30000 r / min and a load of 4000 N.

[0092] Figure 10 The PV values ​​for the bearings provided in Example 1 are as follows: a is the PV value at a speed of 10000 r / min and a load of 4000 N, b is the PV value at a speed of 20000 r / min and a load of 4000 N, and c is the PV value at a speed of 30000 r / min and a load of 4000 N.

[0093] Figure 11 The ARMA bearing life prediction curve provided in Example 1;

[0094] Figure 12 This is a flowchart of the bearing motion characteristic decision layer information fusion based on fuzzy clustering evidence theory provided in Example 1;

[0095] Figure 13The evidence set clustering results provided in Example 1 are shown, where a is the clustering result of conflicting evidence set and b is the clustering result of non-conflicting evidence set;

[0096] Figure 14 This refers to the safe operating range of bearing cage slippage rate in Example 1. Detailed Implementation

[0097] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0098] Example 1

[0099] See Figures 1-14 This embodiment provides a method for determining the bearing slippage failure threshold based on state information fusion analysis. The process of this method is as follows: Figure 1 As shown, this embodiment uses deep groove ball bearings and cylindrical roller bearings as examples for verification. The strategy specifically includes the following steps:

[0100] Step S1: Construct a bearing twin simulation model and simultaneously measure the bearing cage slippage rate and the stress F of the bearing inner ring. ir Stress F of the bearing outer ring or The stress F of the bearing roller b Information such as the trajectory of the bearing cage's center of mass and bearing vibration acceleration data;

[0101] Specifically, in this embodiment, step S1 includes:

[0102] Step S101: Construct a bearing twin simulation model: First, use Solidworks software to create a bearing geometric model (e.g., ...). Figure 2 As shown in a), secondly, a bearing mesh model was created based on Hypermesh software (as shown in a). Figure 2 (as shown in b), and finally, ADAMS is used to perform multibody simulation of the bearing;

[0103] Step S102: Measure the inner ring speed and cage speed of the bearing, and calculate the cage slippage rate S. a :

[0104]

[0105] Where, ω c It is the actual rotational speed of the bearing cage; ω cm This refers to the theoretical rotational speed of the bearing cage; Sa It is the bearing cage slippage rate; where the theoretical rotational speed ω of the bearing cage is... cm satisfy:

[0106]

[0107] Among them, R w It is the bearing roller radius; R m It is the bearing pitch circle radius; ω im This refers to the inner ring speed of the bearing; the calculated results of the bearing cage slippage rate under different operating conditions are as follows: Figure 3 As shown;

[0108] Step S103: Extract the stress F of the bearing inner ring. ir Stress F of the bearing outer ring or and the stress F of the bearing roller b The stress and strain of deep groove ball bearings under different operating conditions are as follows: Figure 4 As shown, the rollers are subjected to the following forces during bearing operation: Figure 5 As shown;

[0109] Step S104: Calculation of the trajectory of the bearing cage's center of mass:

[0110] In the ADAMS simulation software, the motion trajectories of four points uniformly distributed along the circumference on the bearing cage are extracted as x1, x2, x3 and x4, respectively. The motion trajectory x of the center of mass of the bearing cage is calculated as shown in equation (3):

[0111]

[0112] The trajectory of the center of mass of a deep groove ball bearing under different operating conditions is as follows: Figure 6 As shown, the trajectory of the center of mass of a cylindrical roller bearing under different operating conditions is as follows: Figure 7 As shown;

[0113] Step S105: Extract bearing vibration acceleration data. The vibration acceleration of deep groove ball bearings under different operating conditions is as follows: Figure 8 As shown, the vibration acceleration of cylindrical roller bearings under different operating conditions is as follows: Figure 9 As shown;

[0114] Step S2: Based on the information such as bearing cage slippage rate and stress of each component obtained in step S1, construct a bearing life theoretical model and calculate the corresponding PV value by combining the improved LP theory.

[0115] Specifically, in this embodiment, step S2 includes:

[0116] Step S201: Based on the bearing cage slippage rate and bearing inner ring stress F obtained in step S1 ir Stress F of the bearing outer ring orand the stress F of the bearing roller b Based on this information and the improved LP theory, a bearing life theoretical model is constructed:

[0117] Assuming the roller length of the bearing is l, the contact area between the roller and the inner and outer ring raceways is divided into m thin plates. According to the basic rated dynamic load theory, the basic rated dynamic load Q of the contact area between the j-th roller and the inner or outer ring raceway is... cnjk for:

[0118]

[0119] When n = μ, it is the thin sheet of the inner raceway; when n = v, it is the thin sheet of the outer raceway; D is the diameter of the roller; Z is the number of rollers; parameter γ nj Satisfying γ nj =Dcosα nj / d m ;α nj d is the contact angle between the j-th roller and either the inner or outer raceway; m The bearing pitch circle diameter;

[0120] Then the contact area between the j-th roller and the inner ring raceway of the bearing, and the life L of the thin sheet of the k-th inner ring raceway. μjk The thin-plate life L of the contact area between the j-th roller and the outer raceway of the bearing outer ring and the k-th outer raceway. vjk As shown in equations (5) and (6) respectively:

[0121]

[0122]

[0123] Among them, Q cμjk Q is the basic rated dynamic load of the thin sheet of the k-th inner ring raceway in the contact area between the j-th roller and the bearing inner ring raceway; cvjk Q is the basic rated dynamic load of the thin sheet of the k-th outer ring raceway in the contact area between the j-th roller and the bearing outer ring raceway; μjk Q is the contact load of the thin sheet of the k-th inner ring raceway in the contact area between the j-th roller and the inner ring raceway of the bearing; vjk The contact load is the thin sheet of the k-th outer ring raceway in the contact area between the j-th roller and the outer ring raceway of the bearing.

[0124] The basic rated dynamic load Q of the contact area between the j-th roller and the inner or outer raceway of the bearing. Rnjk As shown in equation (7):

[0125]

[0126] Then, the bearing life theoretical model L... g The calculation is shown in equation (8):

[0127]

[0128] Where e is the Weibull coefficient; L Rμjk and L Rvjk These represent the basic rated life of the k-th roller sheet in the contact area between the j-th roller and the inner or outer raceway of the bearing; j is a parameter.

[0129] Step S202: Calculate the corresponding PV value:

[0130] Based on the bearing cage slippage rate S obtained in step S102 a The bearing roller contact stress F obtained in step S103 b The bearing PV value is obtained by calculating the product of the two in the time domain, as shown in equation (9):

[0131] PV = S a *F (9)

[0132] The calculated PV values ​​of the bearings under different operating conditions are as follows: Figure 10 As shown;

[0133] Step S3: Based on the bearing cage center of mass motion trajectory information obtained in step S1, calculate the four indicators of maximum value, minimum value, average value and standard deviation respectively, and construct the center of mass trajectory fusion index to measure the stability of cage motion;

[0134] Specifically, in this embodiment, step S3 includes:

[0135] Step S301: Based on the bearing cage center of mass motion trajectory information obtained in step S1, calculate the maximum value x. max Minimum value x min Average value x mean and standard deviation x stdev Four indicators:

[0136] x max =MAX(x) (10)

[0137] x min =MIN(x) (11)

[0138] x mean =MEAN(x) (12)

[0139] x stdev =STDEV(x) (13)

[0140] Where MAX(·) represents the function for finding the maximum value; MIN(·) represents the function for finding the minimum value; MEAN(·) represents the function for finding the average value; STDEV(·) represents the function for finding the standard deviation; Table 1 shows the data processing of the center of mass motion trajectory of deep groove ball bearings under different working conditions, and Table 2 shows the data processing of the center of mass motion trajectory of cylindrical roller bearings under different working conditions.

[0141] Table 1. Data processing of the center-of-mass motion trajectory of deep groove ball bearings under different working conditions.

[0142]

[0143] Table 2 Data processing of the center-of-mass motion trajectory of deep groove ball bearings under different working conditions

[0144]

[0145] Step S302: Construct a centroid trajectory fusion index to measure the motion stability of the Θ cage, as shown in equation (14):

[0146] Θ = 0.2x max +0.2x min +0.2x mean +0.4x stdev (14)

[0147] Step S4: Based on the bearing vibration acceleration data obtained in step S1, construct a bearing life prediction state model using the ARMA-transfer learning algorithm;

[0148] Specifically, in this embodiment, step S4 includes:

[0149] Step S401: Bearing vibration data migration based on component migration analysis:

[0150] The bearing vibration acceleration data obtained in step S105 is used as the source domain data D. S ={(y S1 ,ξ S1 ),...,(y Sσ ,ξ Sσ )}, where y S1 ,y S2 ,...,y Sσ It is the input of the source domain data, ξ S1 ,ξ S2 ,...,ξ Sσ It is the output of the source domain data; For target domain data, where It is the input of the target domain data. It is the output of the target domain data; after minimizing the mapping, D S and D TThe nonlinear mapping ζ is calculated by the maximum average difference distance, as shown in equation (15):

[0151]

[0152] Among them, Y' S and Y' T This represents the input of the mapped source domain data and the input of the target domain data; Indicates the i-th t Data from one source domain; Indicates the i-th t The target domain data is σ; σ is the number of source domain data. The number of data points in the target domain; ||·|| H D is the distance between the vectors in the reproducing kernel Hilbert space; H (·) represents the maximum average difference distance of the vector;

[0153] Step S402: Construct a bearing ARMA life prediction model:

[0154] For the bearing vibration acceleration sequence {y} obtained in step S105 t The fitted random difference equation takes the following form:

[0155]

[0156] in, The autoregressive parameters are: θ1, θ2, ..., θ η The moving average parameter; sequence {a} t} represents the residual sequence; the ARMA life prediction curve based on vibration acceleration data extracted from bearing twins is shown below. Figure 11 As shown;

[0157] Step S5: Based on the bearing life theoretical model, PV value, centroid trajectory fusion index and bearing life prediction state model obtained in steps S2, S3 and S4, fuzzy clustering evidence theory is used to perform bearing motion characteristic decision layer information fusion and determine the bearing slippage failure threshold.

[0158] Specifically, in this embodiment, step S4 includes:

[0159] Step S501: Based on the bearing life theoretical model and PV value obtained in step S2, the centroid trajectory fusion index obtained in step S3, and the life prediction model ARMA obtained in step S4, the bearing state information is fused at the decision level using a decision-level fusion algorithm based on fuzzy clustering and PCR6 evidence theory (the process is as follows). Figure 12 As shown):

[0160] (1) Fuzzy clustering algorithm:

[0161] The dataset consists of the bearing life theoretical model and PV value obtained in step S2, the centroid trajectory fusion index obtained in step S3, and the life prediction model ARMA obtained in step S4. Perform clustering, dataset Each data point in the dataset has a dimension of ρ. The dataset is then calculated. neighborhood radius r a Thus, the dataset is calculated. The i-th d Dimensional data points density value As shown in equation (17):

[0162]

[0163] Where v is the dimension;

[0164] Based on density value The data point with the highest density value is selected as the first cluster center, and the dataset is calculated. The density values ​​of the remaining data points are shown in equation (18):

[0165]

[0166] in, r is the maximum density value obtained from the previous clustering; b Let J be the new neighborhood radius; add data weights and an inhibition factor to achieve rapid convergence, and construct the objective function J of the dissimilarity index, as shown in equation (19):

[0167]

[0168] in, w is the number of sample points; w is the number of cluster centers; d is the weighted value of each fuzzy membership degree of the sample point to the cluster center; i'j' u is the distance from the i'th sample point to the j'th cluster center; i'j' Let be the membership function of the i'th sample point with respect to the j'th cluster center, as shown in equation (20):

[0169]

[0170] Where, d k'j' The distance from the k'-th sample point to the j'-th cluster center; the evidence set clustering results are as follows: Figure 13 As shown; (2) Decision-level fusion algorithm based on PCR6 evidence theory:

[0171] The evidence set was fused using the PCR6 combination rule to obtain the fusion result, wherein the evidence set includes the bearing life theoretical model, PV value, centroid trajectory fusion index and life prediction model ARMA;

[0172] Step S502: Determine the bearing slippage failure threshold:

[0173] The cluster center O is determined based on the density value obtained from formula (18) in step S501. j Calculate the distance CD between cluster centers:

[0174] CD = ||O Δ -O ▽ ||; Δ=1,2,...,w; Δ≠▽ (21)

[0175] If the maximum distance between cluster centers is less than 0.4, the evidence is considered to have little conflict, and the PCR6 combination rule is directly used to obtain the fusion result. If the maximum distance between cluster centers is greater than 0.4, the evidence is considered to have conflict, and evidence with a distance greater than 0.4 is deleted. The remaining evidence is then fused using the PCR6 combination rule. Finally, the bearing slippage failure threshold is determined. The determined safe operating range for the bearing cage slippage rate is as follows: Figure 14 As shown.

[0176] Any aspects of this invention not described in detail are well-known to those skilled in the art.

[0177] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for determining the bearing slippage failure threshold based on state information fusion analysis, characterized in that, Includes the following steps: Step S1: Construct a bearing twin simulation model and simultaneously obtain the bearing cage slippage rate, bearing inner ring stress, bearing outer ring stress, roller stress, bearing cage center of mass motion trajectory, and bearing vibration acceleration data. Step S2: Based on the bearing cage slippage rate, bearing inner ring stress, bearing outer ring stress and roller stress obtained in step S1, construct a bearing life theoretical model and calculate the PV value using the improved LP theory. Step S3: Based on the bearing cage center of mass motion trajectory information obtained in step S1, calculate the four indicators of maximum value, minimum value, average value and standard deviation respectively, and construct the center of mass trajectory fusion index to measure the stability of cage motion; Step S4: Based on the bearing vibration acceleration data obtained in step S1, construct a bearing life prediction state model using the life prediction model ARMA and the component migration analysis method. Step S5: Based on the bearing life theoretical model and PV value obtained in step S2, the centroid trajectory fusion index obtained in step S3, and the life prediction model ARMA obtained in step S4, the bearing state information is fused at the decision level using the decision-level fusion algorithm of fuzzy clustering and PCR6 evidence theory to construct the bearing slippage failure model, and then the bearing slippage failure threshold is determined.

2. The method for determining the bearing slippage failure threshold based on state information fusion analysis according to claim 1, characterized in that, The implementation process of step S1 is as follows: Step S101: First, use Solidworks software to establish a bearing geometric model, then use Hypermesh software to build a bearing twin simulation model, and finally use ADAMS software to perform multibody simulation on the bearing twin simulation model. Step S102: Based on the bearing twin simulation model established in step S101, measure the rotational speed of the bearing inner ring and the rotational speed of the bearing cage, and calculate the bearing cage slippage rate S. a : Where, ω c ω is the actual rotational speed of the bearing cage; cm This is the theoretical rotational speed of the bearing cage; the theoretical rotational speed ω of the bearing cage cm satisfy: Among them, R w R is the roller radius of the bearing; m It is the pitch circle radius of the bearing; ω im It is the rotational speed of the inner ring of the bearing; Step S103: Extract the stress F of the bearing inner ring based on the bearing twin simulation model established in step S101. ir Stress F of the bearing outer ring or and the stress F of the bearing roller b ; Step S104: Calculate the centroid motion trajectory of the bearing cage based on the bearing twin simulation model established in step S101. In ADAMS software, the motion trajectories of four points uniformly distributed along the circumference on the bearing cage are extracted as x1, x2, x3 and x4, respectively. The motion trajectory x of the center of mass of the bearing cage is calculated as shown in equation (3): Step S105: Extract bearing vibration acceleration data based on the bearing twin simulation model established in step S101.

3. The method for determining the bearing slippage failure threshold based on state information fusion analysis according to claim 2, characterized in that, The implementation process of step S2 is as follows: Step S201, Improved LP bearing life theoretical model: Assuming the roller length of the bearing is l, the contact area between the roller and the bearing inner ring raceway and the bearing outer ring raceway is divided into m thin plates; according to the basic rated dynamic load theory, the basic rated dynamic load Q of the contact area between the j-th roller and the bearing inner ring raceway or outer ring raceway thin plate of the k-th bearing inner ring raceway or outer ring raceway is... cnjk for: When n = μ, it is the inner raceway thin plate; when n = v, it is the outer raceway thin plate; D is the diameter of the roller; Z is the number of rollers; parameter γ nj Satisfying γ nj =Dcosα nj / d m ;α nj d is the contact angle between the j-th roller and either the inner or outer raceway; m The bearing pitch circle diameter; Then the contact area between the j-th roller and the inner ring raceway of the bearing has a life L of the thin sheet of the k-th inner ring raceway. μjk The life L of the contact area between the j-th roller and the outer raceway of the bearing, and the thin sheet of the k-th outer raceway. vjk As shown in equations (5) and (6) respectively: Among them, Q cμjk Q is the basic rated dynamic load of the thin sheet of the k-th inner ring raceway in the contact area between the j-th roller and the inner ring raceway of the bearing; cvjk Q is the basic rated dynamic load of the thin sheet of the k-th outer ring raceway in the contact area between the j-th roller and the outer ring raceway of the bearing; μjk Q is the contact load of the thin sheet of the k-th inner ring raceway in the contact area between the j-th roller and the inner ring raceway of the bearing; vjk The contact load of the thin sheet of the k-th outer ring raceway in the contact area between the j-th roller and the outer ring raceway of the bearing; The basic rated dynamic load Q of the contact area between the j-th roller and the inner or outer raceway of the bearing. Rnjk As shown in equation (7): Then, the bearing life theoretical model L... g The calculation is shown in equation (8): Where e is the Weibull coefficient; L Rμjk and L Rvjk These represent the basic rated life of the k-th roller sheet in the contact area between the j-th roller and the inner or outer raceway of the bearing; j is a parameter. Step S202: Calculate the bearing PV value: Based on the bearing cage slippage rate S obtained in step S102 a The bearing roller contact stress F obtained in step S103 b The bearing PV value is obtained by calculating the product of the two in the time domain, as shown in equation (9): PV=S a *F b (9)。 4. The method for determining the bearing slippage failure threshold based on state information fusion analysis according to claim 3, characterized in that, The implementation process of step S3 is as follows: Step S301: Based on the bearing cage center of mass motion trajectory obtained in step S104, calculate the maximum value x. max Minimum value x min Average value x mean and standard deviation x stdev Four indicators: x max =MAX(x)(10) x min =MIN(x)(11) x mean =MEAN(x)(12) x stdev =STDEV(x)(13) Where MAX(·) represents the function to find the maximum value; MIN(·) represents the function to find the minimum value; MEAN(·) represents the function to find the average value; and STDEV(·) represents the function to find the standard deviation. Step S302: Construct a centroid trajectory fusion index to measure the motion stability Θ of the bearing cage, as shown in equation (14): Θ=0.2x max +0.2x min +0.2x mean +0.4x stdev (14)。 5. The method for determining the bearing slippage failure threshold based on state information fusion analysis according to claim 4, characterized in that, The implementation process of step S4 is as follows: Step S401: Transfer of bearing vibration acceleration data based on compositional migration analysis: The bearing vibration acceleration data obtained in step S105 is used as the source domain data D. S ={(y S1 ,ξ S1 ),...,(y Sσ ,ξ Sσ )}, where y S1 ,y S2 ,...,y Sσ It is the input of the source domain data, ξ S1 ,ξ S2 ,...,ξ Sσ It is the output of the source domain data; For target domain data, where It is the input of the target domain data. It is the output of the target domain data; after minimizing the mapping, D S and D T The nonlinear mapping ζ is calculated by the maximum average difference distance, as shown in equation (15): Among them, Y′ S and Y′ T This represents the input of the mapped source domain data and the input of the target domain data; Indicates the i-th t Data from one source domain; Indicates the i-th t The target domain data; σ is the number of source domain data; θ is the number of target domain data; ||·|| H D is the distance between the vectors in the reproducing kernel Hilbert space; H (·) represents the maximum average difference distance of the vector; Step S402: Construct the bearing life prediction model ARMA: For the bearing vibration acceleration sequence {y} obtained in step S105 t The fitted random difference equation is shown in equation (16): in, The autoregressive parameters are: θ1, θ2, ..., θ η The moving average parameter; sequence {a} t } represents the residual sequence.

6. The method for determining the bearing slippage failure threshold based on state information fusion analysis according to claim 5, characterized in that, The implementation process of step S5 is as follows: Step S501: Based on the bearing life theoretical model and PV value obtained in step S2, the centroid trajectory fusion index obtained in step S3, and the life prediction model ARMA obtained in step S4, the bearing state information is fused at the decision level using a decision-level fusion algorithm based on fuzzy clustering and PCR6 evidence theory. (1) Fuzzy clustering algorithm: The dataset consists of the bearing life theoretical model and PV value obtained in step S2, the centroid trajectory fusion index obtained in step S3, and the life prediction model ARMA obtained in step S4. Clustering, dataset Each data point in the dataset has a dimension of ρ. The dataset is then calculated. neighborhood radius r a Thus, the dataset is calculated. The i-th d Dimensional data points density value As shown in equation (17): Where v is the dimension; Based on density value The data point with the highest density value is selected as the first cluster center, and the dataset is calculated. The density values ​​of the remaining data points are shown in equation (18): in, r is the maximum density value obtained from the previous clustering; b Let J be the new neighborhood radius; add data weights and an inhibition factor to achieve rapid convergence, and construct the objective function J of the dissimilarity index, as shown in equation (19): in, w is the number of sample points; w is the number of cluster centers; d is the weighted value of each fuzzy membership degree of the sample point to the cluster center; i'j' u is the distance from the i'th sample point to the j'th cluster center; i'j' Let be the membership function of the i'th sample point with respect to the j'th cluster center, as shown in equation (20): Where, d k'j' Let k' be the distance from the k'th sample point to the j'th cluster center; (2) Decision-level fusion algorithm based on PCR6 evidence theory: The evidence set was fused using the PCR6 combination rule to obtain the fusion result, wherein the evidence set includes the bearing life theoretical model, PV value, centroid trajectory fusion index and life prediction model ARMA; Step S502: Determine the bearing slippage failure threshold: The cluster center O is determined based on the density value obtained from formula (18) in step S501. j Calculate the distance CD between cluster centers: If the maximum distance between cluster centers is less than 0.4, the evidence is considered to have little conflict, and the PCR6 combination rule is directly used to obtain the fusion result; if the maximum distance between cluster centers is greater than 0.4, the evidence is considered to have conflict, the evidence with a distance greater than 0.4 between cluster centers is deleted, and the remaining evidence is fused using the PCR6 combination rule; finally, the bearing slippage failure threshold is determined.

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