Bearing selection method based on rotor system critical speed characteristics and slip suppression

Abstract

The present invention discloses a bearing selection method based on the critical speed characteristics and slip suppression of a rotor system. First, the global stiffness and damping of the bearing are solved by combining elastohydrodynamic lubrication and Hertz contact theory, and the influence of different structural parameters on the global stiffness and damping of the bearing is studied. Secondly, a twin model of the bearing-rotor system considering the influence of the lubricating oil film is established based on the global stiffness and damping of the bearing, and the actual critical speed of bearing-rotor systems with different structures is calculated. Then, a full-speed range slip test is performed on the bearing-rotor system test bench, and the slip rate of the bearing cage at different speeds is measured. The influence of the critical speed on the slip rate is studied, and the expected critical speed is determined based on the actual operating conditions of the bearing-rotor system and the half-power bandwidth theory. Finally, the actual critical speed of the rotor system is made equal to the expected critical speed by modifying the bearing structure, and the optimal bearing structural parameters that meet the requirements are obtained based on a multi-objective grey wolf optimization algorithm.

Description

Technical Field

[0001] The present invention relates to the field of bearing retainer slippage, and in particular to a bearing selection method based on the critical speed characteristics of a rotor system and slippage suppression. Background Art

[0002] As bearing operating environments become increasingly harsh, bearing failures become more frequent. These include slippage, fatigue failure, and motion instability. Bearing slippage is the most common, accounting for approximately 37% of all failures. Therefore, research on bearing slip reduction strategies is crucial. Current research on slip rates primarily focuses on individual bearings, failing to consider the impact of the rotor system. Consequently, the resulting conclusions often differ significantly from actual conditions. Research has shown that the critical speed of the bearing-rotor system significantly influences the bearing slip rate. Numerous factors influence the critical speed of the bearing-rotor system, including bearing structural parameters. The most representative bearing structural parameters are global stiffness and global damping. Previous calculations of bearing global stiffness and damping considered only the Hertz contact between the bearing rollers and the inner and outer rings, ignoring the effects of the lubricant film on bearing stiffness and damping parameters. With the continuous advancement of elastohydrodynamic lubrication theory, the influence of the lubricant film on bearing global stiffness and damping cannot be ignored. Calculating bearing global stiffness and damping by comprehensively considering the lubricant film and further developing twin simulation models of the bearing-rotor system are becoming increasingly valuable. At the same time, structural parameters such as bearing stiffness and damping are significantly affected by the number, diameter, and length of bearing rollers. Therefore, exploring the relationship between bearing structural parameters such as the number, diameter, and length of bearing rollers and the critical speed of the bearing-rotor system, and using this as a basis to determine the bearing matching method based on the actual operating conditions of the bearing-rotor system, is important for improving the performance of the bearing-rotor system and preventing bearing slippage. Summary of the Invention

[0003] In view of this, the purpose of the present invention is to provide a bearing selection method based on the critical speed characteristics and slip suppression of the rotor system, which can effectively avoid the bearing slip caused by the critical speed of the bearing-rotor system and improve the working performance of the bearing-rotor system.

[0004] In order to achieve the above object, the present invention adopts the following technical solutions:

[0005] A bearing selection method based on the critical speed characteristics and slip suppression of a rotor system, the method comprising:

[0006] Step S1, solving the global stiffness and global damping of the bearing;

[0007] Step S2: In the simulation part, based on the global bearing stiffness and damping obtained in step S1, a finite element twin simulation model of the bearing-rotor system is established, which takes into account the influence of the lubricating oil film. The actual critical speed of the finite element twin model of the bearing-rotor system with different structures is calculated, and the actual critical speed curve of the bearing-rotor system with different bearing structural parameters is plotted.

[0008] Step S3: In the test section, a slip test is performed on the bearing-rotor system test bench over the entire speed range, the bearing slip rate at different speeds is measured, the inner ring speed and bearing cage slip rate curves are plotted, and the expected critical speed is determined;

[0009] Step S4: Based on the actual critical speed curve of the bearing-rotor system under different bearing structural parameters obtained in step S2, the twin simulation model is run to extract the bearing time-domain vibration acceleration signal. The optimization goal is to minimize the energy of the bearing time-domain vibration acceleration signal and make the expected critical speed and the actual critical speed closest to each other, and use the optimization algorithm to obtain the optimal bearing structural parameters that meet the requirements.

[0010] Preferably, the step S1 includes:

[0011] Step S101: Calculate the global bearing stiffness by combining the elastohydrodynamic lubrication theory and the Hertz contact theory:

[0012] (1) Calculation of bearing oil film stiffness

[0013] The minimum oil film thickness between the roller and the inner ring raceway is:

[0014]

[0015] The minimum oil film thickness between the roller and the outer ring raceway is:

[0016]

[0017] Where: D w is the roller diameter; n i is the speed of the bearing inner ring; n e is the outer ring speed of the bearing; E0 is the elastic modulus of the material; τ is the pressure index of viscosity; η0 is the dynamic viscosity of the lubricating oil at normal pressure; l is the effective contact length; d m is the bearing pitch diameter; F r is the radial load; γ i and γ e are dimensionless parameters related to the inner and outer rings, respectively, satisfying:

[0018]

[0019]

[0020] Where: αi is the contact angle between the roller and the inner raceway; α e is the contact angle between the roller and the outer raceway;

[0021] The sum of the minimum oil film thickness h formed between the roller and the inner and outer raceways is:

[0022]

[0023] The introduced coefficient S is as follows:

[0024]

[0025] Then formula (5) is expressed as:

[0026]

[0027] Taking into account the factors of elastic fluid lubrication, the calculation expression of the oil film stiffness of the bearing is as follows:

[0028]

[0029] (2) Calculation of bearing roller contact stiffness

[0030] Contact stiffness between roller and inner ring:

[0031]

[0032] Where: δ1 is the elastic deformation between the roller and the inner ring; Z is the number of rollers; R1 is the inner raceway radius; r is the roller radius;

[0033] Contact stiffness between roller and outer ring:

[0034]

[0035] Where: R2 is the outer raceway radius; δ2 is the elastic deformation between the roller and the outer ring;

[0036] Cylindrical roller bearing contact stiffness K c The calculation is as follows:

[0037]

[0038] (3) Calculation of bearing global stiffness

[0039]

[0040] Step S102: Combine the elastohydrodynamic lubrication theory and the Hertz contact theory to solve the bearing global damping:

[0041] Damping between the roller and the inner raceway at the maximum load:

[0042]

[0043] Where: R x1 is the equivalent curvature radius of the contact between the roller and the inner raceway;

[0044] Damping between the roller and the outer raceway at the maximum load:

[0045]

[0046] Where: R x2 is the equivalent curvature radius of the contact between the roller and the outer raceway;

[0047] The global damping expression of the roller at the maximum load is as follows:

[0048]

[0049] Preferably, the step S2 includes:

[0050] Step S201: Based on the global stiffness and global damping obtained in step S1, a finite element twin simulation model of the bearing-rotor system is established taking into account the influence of the lubricating oil film:

[0051] A bearing-rotor system geometric model is established using SolidWorks software, and a bearing-rotor system mesh model is established using Hypermesh software. Furthermore, a multi-body simulation twin model of the bearing-rotor system is established based on ADAMS software. Twin simulation models are established for bearings with different roller diameters, numbers of rollers, and roller lengths, and the stiffness and damping parameters obtained in step S1 are used to set the bearing twin model parameters.

[0052] Step S202: Calculate the actual critical speed of the finite element twin simulation model of the bearing-rotor system with different structures:

[0053] The actual critical speed v of the finite element twin model of the bearing-rotor system with different structures obtained based on the Workbench calculation step S201 real , draw the critical speed curve of the bearing-rotor system under different bearing structural parameters.

[0054] Preferably, step S3 includes:

[0055] Step S301: In the test part, adjust the speed of the bearing-rotor system test bench from 0 to the rated value, perform a slip test on the bearing-rotor system test bench in the full speed range, and measure the bearing cage slip rate at different speeds. The bearing cage slip rate S a The calculation formula is as follows:

[0056]

[0057] Where: ω c is the actual speed of the bearing cage; ω cm is the theoretical speed of the bearing cage, which satisfies:

[0058]

[0059] Where: R w is the bearing roller radius; R m is the bearing pitch radius; ω i is the bearing inner ring speed;

[0060] Step S302: Based on the measured slip test results of the bearing-rotor system test bench over the full speed range, a bearing slip curve is plotted with the bearing inner ring speed as the abscissa and the bearing cage slip rate as the ordinate. The speed corresponding to the maximum slip rate is the critical speed of the bearing-rotor system.

[0061] Step S303: Determine the expected critical speed based on the actual operating condition requirements of the bearing-rotor system test bench and the half-power bandwidth theory:

[0062] Combined with the bearing slip curve obtained in step S302, the stable operating speed range of the bearing-rotor system test bench is determined according to the half-power bandwidth theory; assuming that the maximum bearing slip rate is S max And the corresponding critical speed is v cri , then according to the half-power bandwidth theory, the slip rate needs to be determined as The corresponding smaller bearing inner ring speed v poz and the larger bearing inner ring speed v poy ; When the inner ring speed is less than the inner ring speed v of the bearing poz Or greater than the bearing inner ring speed v poy When the bearing-rotor system test bench runs smoothly, when the inner ring speed is between the smaller bearing inner ring speed v poz and the larger bearing inner ring speed v poy When the speed range is between , the bearing-rotor system test bench will run unstably. The calculation of the speed range threshold Π of the bearing-rotor system test bench running unstably is as follows:

[0063]

[0064] When the bearing-rotor system test bench speed v satisfies When the bearing-rotor system test bench runs unsteadily, the bearing-rotor system test bench speed v satisfies When the bearing-rotor system test bench runs smoothly; according to the actual operating conditions of the bearing-rotor system test bench, the operating speed range of the bearing-rotor system test bench is [0,v α], combined with the unstable operation speed interval threshold Π of the bearing-rotor system test bench to determine the ideal critical speed v of the rotor test bench ideal for:

[0065]

[0066] Where: v α It is the upper limit of the operating speed range of the bearing-rotor system test bench.

[0067] Preferably, step S4 includes:

[0068] Step S401: Extract the bearing time domain vibration acceleration signal a based on the ADAMS twin model established in step S2. acc , the bearing time domain vibration acceleration signal energy E acc Minimum and expected critical speed v ideal and the actual critical speed v real The closest optimization goal is:

[0069]

[0070] J2=|v ideal -v real | (21)

[0071] Where: t is time; J1 is the bearing time domain vibration acceleration signal energy E acc The objective function; J2 is the desired critical speed v ideal and the actual critical speed v real The absolute value of the difference;

[0072] Step S402: Using the number of bearing rollers, roller diameter, and roller length as optimization parameters, combined with the actual critical speed curves of the bearing-rotor system under different bearing structural parameters obtained in step S2, a multi-objective Grey Wolf optimization algorithm is used to obtain the optimal bearing structural parameters that meet the requirements:

[0073] The speed and position component update formulas of the multi-objective gray wolf optimization algorithm are as follows:

[0074]

[0075] Where, is the gray wolf population movement speed; is the inertia factor; c VSGWO1 , c VSGWO2 and c VSGWO3 They are learning factor; r VSGWO1 =random(0,1), r VSGWO2 =random(0,1) and r VSGWO3 =random(0,1) are random numbers respectively; is the current position of the gray wolf; t GWO is the number of iterations; and are intermediate auxiliary variables respectively.

[0076] The beneficial effects of the present invention are:

[0077] 1. Comprehensively consider the elastohydrodynamic lubrication theory and Hertz contact theory to solve the bearing stiffness and damping parameters to obtain more accurate bearing global stiffness and global damping;

[0078] 2. The bearing slip law is studied in conjunction with the bearing-rotor system. The influence of different bearing structural parameters on the critical speed of the bearing-rotor system and the influence of the critical speed of the bearing-rotor system on the bearing slip rate are analyzed. The half-power bandwidth theory is creatively used to determine the unstable operation threshold of the bearing-rotor system.

[0079] 3. Taking the minimum energy of the bearing time-domain vibration acceleration signal and the closest approach between the expected critical speed and the actual critical speed as the optimization goal, the multi-objective Grey Wolf optimization algorithm is used to obtain the optimal bearing structural parameters that meet the requirements, providing theoretical guidance for bearing selection for slip suppression and further improving the operating performance of the bearing-rotor system. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 This is a flow chart of the bearing selection method based on the critical speed characteristics and slip suppression of the rotor system provided in Example 1;

[0081] Figure 2 Schematic diagram of the bearing-rotor system used in Example 1;

[0082] Figure 3 This is a graph showing the effect of the number and radius of rollers on the global stiffness of a cylindrical roller bearing provided in Example 1;

[0083] Figure 4 Graph showing the effect of roller length on the global stiffness of a cylindrical roller bearing provided in Example 1;

[0084] Figure 5 This is a graph showing the effect of the number and radius of rollers on the global damping of a cylindrical roller bearing provided in Example 1;

[0085] Figure 6 Graph showing the effect of roller length on global damping of a cylindrical roller bearing provided in Example 1;

[0086] Figure 7 A diagram of a cylindrical roller bearing model provided in Example 1;

[0087] Figure 8This is a diagram showing the effect of the number and radius of rollers on the critical speed of the bearing-rotor system provided in Example 1;

[0088] Figure 9 This is a graph showing the effect of roller length on the critical speed of the bearing-rotor system provided in Example 1;

[0089] Figure 10 The bearing slip curve of the bearing-rotor system provided in Example 1;

[0090] Figure 11 This is the optimization result diagram of the multi-objective variable speed gray wolf optimization algorithm provided in Example 1. DETAILED DESCRIPTION

[0091] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0092] Example 1

[0093] See also Figures 1-11 This embodiment provides a bearing selection method based on the critical speed characteristics and slip suppression of the rotor system. The process of this method is as follows: Figure 1 As shown, this embodiment adopts Figure 2 The algorithm performance is verified using the bearing-rotor system shown in FIG. The strategy specifically includes the following steps:

[0094] Step S1, combining elastohydrodynamic lubrication theory and Hertz contact theory to solve the global stiffness and global damping of the bearing;

[0095] Specifically, in this embodiment, step S1 includes:

[0096] Step S101: Calculate the global bearing stiffness by combining the elastohydrodynamic lubrication theory and the Hertz contact theory:

[0097] (1) Calculation of bearing oil film stiffness

[0098] The minimum oil film thickness between the roller and the inner ring raceway is:

[0099]

[0100] The minimum oil film thickness between the roller and the outer ring raceway is:

[0101]

[0102] Where: D w is the roller diameter; n i is the speed of the bearing inner ring; n e is the outer ring speed of the bearing; E0 is the elastic modulus of the material; τ is the pressure index of viscosity; η0 is the dynamic viscosity of the lubricating oil at normal pressure; l is the effective contact length; d m is the bearing pitch diameter; F r is the radial load; γ i and γ e are dimensionless parameters related to the inner and outer rings, respectively, satisfying:

[0103]

[0104]

[0105] Where: α i is the contact angle between the roller and the inner raceway; α e is the contact angle between the roller and the outer raceway;

[0106] The sum of the minimum oil film thickness formed between the roller and the inner raceway and the outer raceway (i.e. the minimum oil film thickness of the bearing) h is:

[0107]

[0108] The introduced coefficient S is as follows:

[0109]

[0110] Then formula (5) can be expressed as:

[0111]

[0112] Taking into account the factors of elastic fluid lubrication, the calculation expression of the bearing oil film stiffness is as follows:

[0113]

[0114] Where: Δ represents the change in the variable;

[0115] (2) Calculation of bearing roller contact stiffness

[0116] Contact stiffness between roller and inner ring:

[0117]

[0118] Where: δ1 is the elastic deformation between the roller and the inner ring; Z is the number of rollers; R1 is the inner raceway radius; r is the roller radius;

[0119] Contact stiffness between roller and outer ring:

[0120]

[0121] Where: R2 is the outer raceway radius; δ2 is the elastic deformation between the roller and the outer ring;

[0122] Cylindrical roller bearing contact stiffness K c The calculation is as follows:

[0123]

[0124] (3) Calculation of bearing global stiffness

[0125]

[0126] The structural parameters of the bearing roller studied in Example 1 of the present invention are shown in Table 1:

[0127] Table 1 Bearing roller structural parameters For the cylindrical roller bearing in Example 1 of the present invention, the influence of roller parameters on the global stiffness of the bearing is calculated based on formula (12):

[0128] The influence of roller diameter and number of rollers: The influence of roller diameter and number on the radial comprehensive stiffness of roller bearings is as follows: Figure 3 As shown in Figure 2, as the roller diameter increases, the contact area between the roller and the inner and outer raceways increases, which can improve the overall stiffness of the bearing. At the same time, the number of rollers the bearing can accommodate decreases, which reduces the bearing stiffness. Therefore, the roller diameter and number are mutually exclusive.

[0129] The influence of roller length: Figure 4 It can be seen that as the length of the circular bearing roller increases, the contact area between the roller and the raceway also increases accordingly, resulting in an increase in the radial comprehensive stiffness of the bearing.

[0130] Step S102: Combine the elastohydrodynamic lubrication theory and the Hertz contact theory to solve the bearing global damping:

[0131] Damping between the roller and the inner raceway at the maximum load:

[0132]

[0133] Where: R x1 is the equivalent curvature radius of the contact between the roller and the inner raceway;

[0134] Damping between the roller and the outer raceway at the maximum load:

[0135]

[0136] Where: R x2is the equivalent curvature radius of the contact between the roller and the outer raceway;

[0137] The comprehensive damping expression of the roller at the maximum load is as follows:

[0138]

[0139] For the cylindrical roller bearing in Example 1 of the present invention, the influence of roller parameters on the global damping of the bearing is calculated based on formula (15):

[0140] The influence of roller diameter and number of rollers: Figure 5 It can be seen that the damping of the bearing increases with the increase in the number of rollers and also increases with the increase in the roller radius.

[0141] The influence of roller length: Figure 6 It can be seen that the damping of the bearing gradually increases with the increase of roller length.

[0142] Step S2: In the simulation part, based on the global bearing stiffness and damping obtained in step S1, a finite element twin simulation model of the bearing-rotor system is established, which takes into account the influence of the lubricating oil film. The actual critical speed of the finite element twin model of the bearing-rotor system with different structures is calculated, and the actual critical speed curve of the bearing-rotor system with different bearing structural parameters is plotted.

[0143] Specifically, in this embodiment, step S2 includes:

[0144] Step S201: Based on the global stiffness and global damping obtained in step S1, a finite element twin simulation model of the bearing-rotor system is established taking into account the influence of the lubricating oil film:

[0145] The bearing-rotor system geometric model was established using SolidWorks software, and the bearing-rotor system mesh model was established using Hypermesh software. A multi-body simulation twin model of the bearing-rotor system was further established based on ADAMS software. Among them, twin simulation models with different roller diameters, roller numbers, and roller lengths were established for the bearings (such as Figure 7 As shown), and the bearing twin model parameters are set according to the stiffness parameters and damping parameters obtained in step S1;

[0146] Step S202: Calculate the actual critical speed of the finite element twin simulation model of the bearing-rotor system with different structures:

[0147] The actual critical speed v of the finite element twin model of the bearing-rotor system with different structures obtained based on the Workbench calculation step S201 real , draw the critical speed curve of the bearing-rotor system under different bearing structural parameters;

[0148] The influence of different bearing structural parameters on the critical speed of the bearing-rotor system is analyzed for the bearing-rotor system in Example 1 of the present invention:

[0149] Influence of roller radius and number: Figure 8 Figure 2 shows the effect of roller radius and number on the critical speed of a cylindrical roller bearing-rotor system. It can be seen that the critical speed of the bearing-rotor system increases slightly with increasing roller radius and number of rollers, with the number of rollers having a more pronounced effect on the critical speed.

[0150] Effect of roller length: Figure 9 Figure 2 shows the effect of cylindrical roller length on the critical speed of the bearing-rotor system. It can be seen that the critical speed of the bearing-rotor system increases with the increase of roller length.

[0151] Step S3: In the test portion, a slip test is performed on the bearing-rotor system test bench over the entire speed range, the bearing slip rate at different speeds is measured, inner ring speed and bearing cage slip rate curves are plotted, and the expected critical speed is determined based on the actual operating conditions of the bearing-rotor system and the half-power bandwidth theory;

[0152] Specifically, in this embodiment, step S3 includes:

[0153] Step S301: In the test part, adjust the speed of the bearing-rotor system test bench from 0 to the rated value, perform a slip test on the bearing-rotor system test bench in the full speed range, and measure the bearing cage slip rate at different speeds. The bearing cage slip rate S a The calculation formula is as follows:

[0154]

[0155] Where: ω c is the actual speed of the bearing cage; ω cm is the theoretical speed of the bearing cage, which satisfies:

[0156]

[0157] Where: R w is the bearing roller radius; R m is the bearing pitch radius; ω i is the bearing inner ring speed;

[0158] Step S302: Based on the measured slip test results of the bearing-rotor system test bench over the full speed range, a bearing slip curve is plotted with the bearing inner ring speed as the horizontal axis and the bearing cage slip rate as the vertical axis. It can be found that the bearing slip curve is a parabola, and the speed corresponding to the maximum slip rate is the critical speed of the bearing-rotor system; Figure 10As shown, it is the bearing slip curve of the rotor used in this embodiment.

[0159] Step S303: Determine the expected critical speed based on the actual operating condition requirements of the bearing-rotor system test bench and the half-power bandwidth theory:

[0160] Combined with the bearing slip curve obtained in step S302, the stable operating speed range of the bearing-rotor system test bench is determined according to the half-power bandwidth theory; assuming that the maximum bearing slip rate is S max And the corresponding critical speed is v cri , then according to the half-power bandwidth theory, the slip rate needs to be determined as The corresponding smaller bearing inner ring speed v poz and the larger bearing inner ring speed v poy ; It can be considered that when the inner ring speed is less than the inner ring speed v of the bearing poz Or greater than the bearing inner ring speed v poy When the bearing-rotor system test bench runs smoothly, when the inner ring speed is between the smaller bearing inner ring speed v poz and the larger bearing inner ring speed v poy When the speed range is between , the bearing-rotor system test bench will run unstably. The calculation of the speed range threshold Π of the bearing-rotor system test bench running unstably is as follows:

[0161]

[0162] When the bearing-rotor system test bench speed v satisfies When the bearing-rotor system test bench runs unsteadily, the bearing-rotor system test bench speed v satisfies When the bearing-rotor system test bench runs smoothly; according to the actual operating conditions of the bearing-rotor system test bench, the operating speed range of the bearing-rotor system test bench is [0,v α ], combined with the stable and unstable operation speed range threshold Π of the bearing-rotor system test bench, the ideal critical speed v of the rotor test bench is determined ideal for:

[0163]

[0164] Where: v α is the upper limit of the operating speed range of the bearing-rotor system test bench; the unstable operation speed interval threshold value Π of the bearing-rotor system test bench used in this embodiment satisfies the following formula:

[0165]

[0166] The operating speed range of the bearing-rotor system test bench is [0r / min, 10000r / min], then v α=10000r / min. The ideal critical speed v of the bearing-rotor test bench can be obtained ideal for:

[0167]

[0168] That is, the bearing structure needs to be adjusted so that the actual critical speed of the bearing-rotor test bench changes from 8543 r / min to 11746 r / min.

[0169] Step S4: Based on the actual critical speed curve of the bearing-rotor system under different bearing structural parameters obtained in step S2, the bearing time-domain vibration acceleration signal is extracted based on the ADAMS running twin model. The optimal bearing structural parameters that meet the requirements are obtained using the multi-objective Grey Wolf optimization algorithm, with the minimum energy of the bearing time-domain vibration acceleration signal and the closest proximity between the expected critical speed and the actual critical speed as the optimization goal. The optimization results are as follows: Figure 11 shown.

[0170] Specifically, in this embodiment, step S4 includes:

[0171] Step S401: Extract the bearing time domain vibration acceleration signal a based on the ADAMS twin model established in step S2. acc , the bearing time domain vibration acceleration signal energy E acc Minimum and expected critical speed v ideal and the actual critical speed v real The closest optimization goal is as follows:

[0172]

[0173] J2=|v ideal -v real | (23) Where: t is time; J1 is the bearing time domain vibration acceleration signal energy E acc The objective function; J2 is the desired critical speed v ideal and the actual critical speed v real The absolute value of the difference;

[0174] Step S402: Using the number of bearing rollers, roller diameter, and roller length as optimization parameters, combined with the actual critical speed curves of the bearing-rotor system under different bearing structural parameters obtained in step S2, a multi-objective Grey Wolf optimization algorithm is used to obtain the optimal bearing structural parameters that meet the requirements:

[0175] The speed and position component update formulas of the multi-objective gray wolf optimization algorithm are as follows:

[0176]

[0177] Where, is the gray wolf population movement speed; is the inertia factor; c VSGWO1 , c VSGWO2 and c VSGWO3 They are learning factor; r VSGWO1 =random(0,1), r VSGWO2 =random(0,1) and r VSGWO3 =random(0,1) are random numbers respectively; is the current position of the gray wolf; t GWO is the number of iterations; and are intermediate auxiliary variables. The optimal bearing structural parameters obtained by the multi-objective Grey Wolf optimization algorithm are: number of rollers 14, roller diameter 4mm and roller length 25mm.

[0178] Anything not described in detail in the present invention is well known to those skilled in the art.

[0179] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A bearing selection method based on the critical speed characteristics and slip suppression of the rotor system, characterized in that: The method includes: Step S1, solving the global stiffness and global damping of the bearing; Step S2: In the simulation part, based on the global bearing stiffness and damping obtained in step S1, a finite element twin simulation model of the bearing-rotor system is established, which takes into account the influence of the lubricating oil film. The actual critical speed of the finite element twin model of the bearing-rotor system with different structures is calculated, and the actual critical speed curve of the bearing-rotor system with different bearing structural parameters is plotted. Step S3: In the test section, a slip test is performed on the bearing-rotor system test bench over the entire speed range, the bearing slip rate at different speeds is measured, the inner ring speed and bearing cage slip rate curves are plotted, and the expected critical speed is determined; Step S4: Based on the actual critical speed curve of the bearing-rotor system under different bearing structural parameters obtained in step S2, the twin simulation model is run to extract the bearing time-domain vibration acceleration signal. The optimization goal is to minimize the energy of the bearing time-domain vibration acceleration signal and make the expected critical speed and the actual critical speed closest to each other, and use the optimization algorithm to obtain the optimal bearing structural parameters that meet the requirements.

2. The bearing selection method based on the critical speed characteristics and slip suppression of the rotor system according to claim 1, characterized in that: The step S1 comprises: Step S101: Calculate the global bearing stiffness by combining the elastohydrodynamic lubrication theory and the Hertz contact theory: (1) Calculation of bearing oil film stiffness The minimum oil film thickness between the roller and the inner ring raceway is: The minimum oil film thickness between the roller and the outer ring raceway is: Where: D w is the roller diameter; n i is the speed of the bearing inner ring; n e is the outer ring speed of the bearing; E0 is the elastic modulus of the material; τ is the pressure index of viscosity; η0 is the dynamic viscosity of the lubricating oil at normal pressure; l is the effective contact length; d m is the bearing pitch diameter; γ i and γ e are dimensionless parameters related to the inner and outer rings respectively; F r is the radial load; The sum of the minimum oil film thickness h formed between the roller and the inner and outer raceways is: The introduced coefficient S is as follows: Taking into account the factors of elastic fluid lubrication, the calculation expression of the bearing oil film stiffness is as follows: Where: Δ represents the change of the variable; (2) Calculation of bearing roller contact stiffness Contact stiffness between roller and inner ring: Where: δ1 is the elastic deformation between the roller and the inner ring; Z is the number of rollers; R1 is the inner raceway radius; r is the roller radius; Contact stiffness between roller and outer ring: Where: R2 is the outer raceway radius; δ2 is the elastic deformation between the roller and the outer ring; Cylindrical roller bearing contact stiffness K c The calculation is as follows: (3) Calculation of bearing global stiffness Step S102: Combine the elastohydrodynamic lubrication theory and the Hertz contact theory to solve the bearing global damping: Damping between the roller and the inner raceway at the maximum load: Where: R x1 is the equivalent curvature radius of the contact between the roller and the inner raceway; Damping between the roller and the outer raceway at the maximum load: Where: R x2 is the equivalent curvature radius of the contact between the roller and the outer raceway; The global damping expression of the roller at the maximum load is as follows:

3. The bearing selection method based on the critical speed characteristics and slip suppression of the rotor system according to claim 1, characterized in that: The step S2 comprises: Step S201: Based on the global stiffness and global damping obtained in step S1, a finite element twin simulation model of the bearing-rotor system is established taking into account the influence of the lubricating oil film: A bearing-rotor system geometric model is established using SolidWorks software, and a bearing-rotor system mesh model is established using Hypermesh software. Furthermore, a multi-body simulation twin model of the bearing-rotor system is established based on ADAMS software. Twin simulation models are established for bearings with different roller diameters, numbers of rollers, and roller lengths, and the stiffness and damping parameters obtained in step S1 are used to set the bearing twin model parameters. Step S202: Calculate the actual critical speed of the finite element twin simulation model of the bearing-rotor system with different structures: The actual critical speed v of the finite element twin model of the bearing-rotor system with different structures obtained based on the Workbench calculation step S201 real , draw the critical speed curve of the bearing-rotor system under different bearing structural parameters.

4. The bearing selection method based on the critical speed characteristics and slip suppression of the rotor system according to claim 1, characterized in that: The step S3 comprises: Step S301: In the test part, adjust the speed of the bearing-rotor system test bench from 0 to the rated value, perform a slip test on the bearing-rotor system test bench in the full speed range, and measure the bearing cage slip rate at different speeds. The bearing cage slip rate S a The calculation formula is as follows: Where: ω c is the actual speed of the bearing cage; ω cm is the theoretical speed of the bearing cage, which satisfies: Where: R w is the bearing roller radius; R m is the bearing pitch radius; ω i is the bearing inner ring speed; Step S302: Based on the measured slip test results of the bearing-rotor system test bench over the full speed range, a bearing slip curve is plotted with the bearing inner ring speed as the abscissa and the bearing cage slip rate as the ordinate. The speed corresponding to the maximum slip rate is the critical speed of the bearing-rotor system. Step S303: Determine the expected critical speed based on the actual operating condition requirements of the bearing-rotor system test bench and the half-power bandwidth theory: Combined with the bearing slip curve obtained in step S302, the stable operating speed range of the bearing-rotor system test bench is determined according to the half-power bandwidth theory; assuming that the maximum bearing slip rate is S max And the corresponding critical speed is v cri , then according to the half-power bandwidth theory, the slip rate needs to be determined as The corresponding smaller bearing inner ring speed v poz and the larger bearing inner ring speed v poy ; When the inner ring speed is less than the inner ring speed v of the bearing poz Or greater than the bearing inner ring speed v poy When the bearing-rotor system test bench runs smoothly, when the inner ring speed is between the smaller bearing inner ring speed v poz and the larger bearing inner ring speed v poy When the speed range is between , the bearing-rotor system test bench will run unstably. The calculation of the speed range threshold Π of the bearing-rotor system test bench running unstably is as follows: When the bearing-rotor system test bench speed v satisfies When the bearing-rotor system test bench runs unsteadily, the bearing-rotor system test bench speed v satisfies When the bearing-rotor system test bench runs smoothly; according to the actual operating conditions of the bearing-rotor system test bench, the operating speed range of the bearing-rotor system test bench is [0,v α ], combined with the unstable operation speed interval threshold Π of the bearing-rotor system test bench to determine the ideal critical speed v of the bearing-rotor system test bench ideal for: Where: v α It is the upper limit of the operating speed range of the bearing-rotor system test bench.

5. The bearing selection method based on the critical speed characteristics and slip suppression of the rotor system according to claim 1, characterized in that: The step S4 comprises: Step S401: Extract the bearing time domain vibration acceleration signal a based on the ADAMS twin model established in step S2. acc , the bearing time domain vibration acceleration signal energy E acc Minimum and expected critical speed v ideal and the actual critical speed v real The closest optimization goal is: J2=|v ideal -v real | (18) Where: t is time; J1 is the bearing time domain vibration acceleration signal energy E acc The objective function; J2 is the desired critical speed v ideal and the actual critical speed v real The absolute value of the difference; Step S402: Using the number of bearing rollers, roller diameter, and roller length as optimization parameters, combined with the actual critical speed curves of the bearing-rotor system under different bearing structural parameters obtained in step S2, a multi-objective Grey Wolf optimization algorithm is used to obtain the optimal bearing structural parameters that meet the requirements: The speed and position component update formulas of the multi-objective gray wolf optimization algorithm are as follows: Where, is the gray wolf population movement speed; is the inertia factor; c VSGWO1 , c VSGWO2 and c VSGWO3 They are learning factor; r VSGWO1 =random(0,1), r VSGWO2 =random(0,1) and r VSGWO3 =random(0,1) are random numbers respectively; is the current position of the gray wolf; t GWO is the number of iterations; and are intermediate auxiliary variables respectively.

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