A Twin Simulation Method for Rotor System Slippage Considering Uncertainty of Flexible Support

Abstract

This invention discloses a twin simulation method for rotor system slippage considering the uncertainty of flexible supports. First, flexible support components such as flexible bearing housings and flexible couplings are respectively equated as spring-damped units, and the baseline values ​​of equivalent support state parameters are obtained based on static analysis. Second, a rotor system thermo-fluid-structure interaction (TSH) simulation model considering the flexible support state is constructed based on the rotor system dynamics simulation model and thermo-elasto-fluido-lubrication coupling analysis. Then, multi-domain simulation data and multi-domain experimental data are collected under the same time-varying slippage operating conditions, and a slippage consistency metric is constructed based on the time-frequency statistical characteristics of the multi-domain information to calculate the slippage sensitivity. Finally, the uncertainty of the flexible support component state parameters is described based on cross-correlation Bayesian methods, and the identified flexible support state parameters are substituted into the established rotor system TSH simulation model to obtain slippage rate curves under different time-varying operating conditions.

Description

Technical Field

[0001] This invention relates to the field of digital twin technology, and mainly to a twin simulation method for rotor system slippage considering the uncertainty of flexible support. Background Technology

[0002] Rotor system slippage behavior is characterized by weak signal characteristics, significant time-varying properties, and the influence of multiple coupled factors. To address the challenge of weak signal characteristics, it is necessary to fully utilize multi-domain information closely related to rotor system slippage behavior for characterization; to address the challenge of significant time-varying properties, it is necessary to fully consider the impact of parameter uncertainties; and to address the challenge of multiple coupled factors, it is necessary to conduct thermo-fluid-structure interaction (TFS) simulation analysis. However, existing research has failed to address these challenges within a unified framework, making it difficult to achieve accurate rotor system slippage simulation.

[0003] Constructing a unified framework to address the aforementioned challenges simultaneously is a prerequisite for realizing slippage twin simulation of flexible support-rotor systems. Reliable slippage twin simulation results can provide a rich data foundation for analyzing slippage fault mechanisms, performing slippage diagnosis and prediction, and carrying out slippage source tracing and control.

[0004] Currently, the rich knowledge obtained from rotor system slippage twin simulation has been used to construct slippage knowledge graphs and guide the improved design of flexible support-rotor systems, achieving significant results in practical applications. Summary of the Invention

[0005] Purpose of the invention: Based on the problems existing in the above-mentioned background technology, the present invention provides a rotor system slippage twin simulation method that considers the uncertainty of flexible support. Within a unified framework, it realizes the construction of a slippage simulation consistency metric index based on multi-domain information, designs a cross-correlation Bayesian algorithm to describe the uncertainty of the state parameters of flexible support components, and uses a thermo-fluid-structure interaction slippage simulation model to perform multi-factor coupling influence analysis.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A twin simulation method for rotor system slippage considering uncertainties in flexible supports includes the following steps:

[0008] Step S1: Establish finite element models of the rotor system shaft and bearings respectively, and convert flexible support components such as flexible bearing housing and flexible coupling into equivalent spring damping elements. Based on static analysis, obtain the reference values ​​of equivalent support state parameters, and then obtain a rotor system slippage dynamic simulation model considering the flexible support state.

[0009] Step S2: Based on the rotor system slippage dynamics simulation model considering the flexible support state obtained in Step S1 and the thermo-elasto-hydrodynamic lubrication theory, analyze the influence of lubrication state parameters on slippage, and further construct a rotor system thermo-fluid-structure coupling simulation model considering the flexible support state.

[0010] Step S3: Based on the rotor system thermal-fluid-structure interaction simulation model considering the flexible support state established in Step S2 and the flexible support-rotor system slippage test bench, multi-domain simulation data and multi-domain experimental data are collected under the same time-varying slippage working state. Furthermore, a slippage consistency metric index is constructed through time-frequency statistical feature slippage sensitivity analysis.

[0011] Step S4: Based on the slip consistency index of the multi-domain simulation data and multi-domain experimental data obtained in step S3, the uncertainty of the equivalent support state parameter benchmark value obtained in step S1 is described by the cross-correlation Bayes algorithm. The identified flexible support state parameters are then substituted into the rotor system thermo-fluid-structure coupling simulation model established in step S2 to obtain the slip rate curves under different time-varying working conditions.

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

[0013] Step S1.1: Establish finite element models of the shaft and bearings in the slippage test rig of the flexible support-rotor system, and further conduct modal tests and model corrections on the shaft to obtain the modal frequency τ of the shaft. S Damping π S and stiffness parameter κ S It is necessary to ensure that the model correction accuracy of the shaft meets the modal confidence criteria (MAC) for each mode shape. ij If the modal confidence criterion is greater than 85%, it will be calculated as follows:

[0014]

[0015] in, The correlation coefficients between the i-th experimental mode shape and the j-th finite element simulation model mode shape of the shaft in the slippage test bench of the flexible support-rotor system; The i-th experimental mode shape of the shaft on the slippage test bench for the flexible support-rotor system; The j-th simulated mode shape of the shaft on the slippage test bench for the flexible support-rotor system; T is the conjugate transpose;

[0016] Step S1.2: In the flexible support-rotor system slippage test rig, the flexible bearing housing is equivalent to two sets of spring damping units perpendicular to the horizontal and vertical directions in the axial plane. The equivalent damping is expressed as... The equivalent stiffness is expressed as In the slippage test rig for the flexible support-rotor system, the flexible coupling is equivalent to three sets of spring-damped units along the axial direction, in the horizontal direction perpendicular to the axial plane, and in the vertical direction. The equivalent damping is expressed as: The equivalent stiffness is expressed as Furthermore, the stiffness and damping parameter values ​​of the equivalent spring damping unit are obtained based on static analysis, and these values ​​are used as the reference values ​​for the equivalent support state parameters.

[0017] Step S1.3: Combine and assemble the finite element models of the shaft and bearings in the flexible support-rotor system slippage test bench obtained in step S1.1, and the equivalent support state parameter reference values ​​of the flexible support components such as the flexible bearing seat and flexible coupling obtained in step S1.2 to obtain a rotor system slippage dynamic simulation model considering the flexible support state.

[0018] Preferably, the implementation process of step S2 is as follows:

[0019] Step S2.1: Analyze the influence of lubrication state parameters on slippage of the flexible support-rotor system slippage test bench based on thermo-elastohydrodynamic lubrication theory; thermo-elastohydrodynamic lubrication theory includes the Reynolds equation, energy equation, film thickness equation, viscosity-pressure / viscosity-temperature equation, and pressure-temperature-temperature equation. The calculation process of the Reynolds equation in thermo-elastohydrodynamic lubrication theory is as follows:

[0020]

[0021] Where h is the oil film thickness; p is the oil film pressure; η is the lubricating oil viscosity; ρ is the lubricating oil density; U is the entrainment velocity; x and y are the coordinates of the oil film width and length directions; the calculation process of the energy equation in thermo-elastohydrodynamic lubrication theory is as follows:

[0022]

[0023] Among them, c ρ Here, is the specific heat capacity at constant pressure; K is the thermal conductivity coefficient; T is the oil film temperature; z is the coordinate of the oil film thickness direction; u and v are the boundary velocities in the x and y directions, respectively; the calculation process of the film thickness equation in thermo-elastohydrodynamic lubrication theory is as follows:

[0024]

[0025] Where v(x,y) is the deformation term; h0 is the initial oil film thickness; R x and R y Here, radii of curvature along the x and y directions at the contact point are respectively those of the bearing and the oil film; the calculation process of the viscosity-pressure / viscosity-temperature equation in thermo-elastohydrodynamic lubrication theory is as follows:

[0026]

[0027] Where T0 is the initial temperature; η0 is the lubricating oil viscosity corresponding to temperature T0; the calculation process of the pressure-temperature equation in thermo-elastohydrodynamic lubrication theory is as follows:

[0028]

[0029] Where ρ0 is the density of the lubricating oil corresponding to temperature T0;

[0030] Step S2.2: Based on the rotor system slippage dynamics simulation model considering the flexible support state obtained in Step S1 and the thermo-elasto-fluidohydrodynamic lubrication theory in Step S2.1, perform thermo-fluid-structure interaction (THE-STE) simulation to obtain a coupled THE-STE simulation model of the rotor system considering the flexible support state. The specific steps of the THE-STE simulation include:

[0031] First, initial oil film pressure, oil film thickness, and oil film temperature parameters are set, and mechanical and kinematic parameters of the contact micro-region obtained from the dynamic simulation model are imported. Second, the oil film pressure is calculated using the multigrid integration method, and the oil film thickness, viscosity, and density are calculated until the pressure, load, and temperature converge simultaneously. Then, the lubricating oil film stiffness and comprehensive contact stiffness are calculated based on the obtained oil film pressure, thickness, and temperature parameters. Finally, the obtained lubricating oil film stiffness and comprehensive contact stiffness are input into the dynamic simulation model to achieve thermo-fluid-structure interaction simulation.

[0032] Specifically, the overall contact stiffness K θ The calculation is as follows:

[0033]

[0034] Where Z is the number of rolling elements in the bearing; j = 1, 2, ..., Z is the j-th rolling element in the bearing; cos(·) is the cosine function; K cij K represents the contact stiffness between the bearing inner ring and the inner ring oil film at the j-th rolling element. cej K represents the contact stiffness between the bearing outer ring and the outer ring oil film at the j-th rolling element. fij K represents the contact stiffness between the rolling element and the inner ring oil film at the j-th rolling element. fej This represents the contact stiffness between the rolling element and the outer ring oil film at the j-th rolling element.

[0035] Lubricating oil film stiffness K μ The calculation is as follows:

[0036]

[0037] Bearing contact stiffness The calculation is as follows:

[0038]

[0039] Preferably, the implementation process of step S3 is as follows:

[0040] Step S3.1: Based on the rotor system thermo-fluid-structure interaction simulation model established in step S2 considering the flexible support state, collect multi-domain simulation data under time-varying slippage conditions, including torque simulation data. Rotor deflection simulation data Vibration acceleration simulation data and slippage rate simulation data

[0041] Step S3.2: Collect multi-domain experimental data under time-varying slippage conditions based on the slippage test bench of the flexible support-rotor system, including torque experimental data. Rotor deflection test data Vibration acceleration experimental data and slippage rate experimental data

[0042] Step S3.3: Based on the multi-domain simulation data obtained in step S3.1 and the multi-domain experimental data obtained in step S3.2 Time-frequency statistical feature slippage sensitivity analysis was performed to determine the slippage sensitivity statistical features corresponding to multi-domain data. The process of time-frequency statistical feature slippage sensitivity analysis for multi-domain data is as follows:

[0043]

[0044]

[0045] in, For the corresponding torque data Ω T The range of variation of the λ time-frequency statistical features; For the rotor deflection data Ω D The range of variation of the λ time-frequency statistical features; To correspond to the vibration acceleration data Ω A The range of variation of the λ time-frequency statistical features; For slippage rate data The range of variation; For the corresponding torque data Ω T The slip sensitivity of the λ time-frequency statistical features; For the rotor deflection data Ω D The slip sensitivity of the λ time-frequency statistical features; To correspond to the vibration acceleration data Ω A The slip sensitivity of λ time-frequency statistical features; corresponding to the multi-domain data Ω{Ω T ,Ω D ,Ω A,Ω S Statistical characteristics of slippage sensitivity The determination process is as follows:

[0046]

[0047] Where max{·} is the operation for finding the maximum value; For the corresponding torque data Ω T The statistical characteristics of slippage sensitivity; For the rotor deflection data Ω D The statistical characteristics of slippage sensitivity; To correspond to the vibration acceleration data Ω A The statistical characteristics of slippage sensitivity;

[0048] Step S3.4: Determine the slip consistency measurement index based on the slip sensitivity statistical characteristics corresponding to multi-domain data obtained in step S3.3;

[0049] Multi-domain simulation data The construction process of the slip consistency metric χ is as follows:

[0050]

[0051] Where, ω T Torque simulation data The corresponding weight of the slip consistency metric; ω D The weight of the slippage consistency metric corresponding to the rotor deflection simulation data; ω A For vibration acceleration simulation data The corresponding weights for slip consistency metrics; which respectively satisfy:

[0052]

[0053] in, and These correspond to the statistical characteristics of slip sensitivity. The change in quantity; similarly, multi-domain experimental data. The construction process of the slip consistency metric γ is as follows:

[0054]

[0055] Preferably, the implementation process of step S4 is as follows:

[0056] Step S4.1: Based on the slippage consistency index of the multi-domain simulation data and multi-domain experimental data obtained in step S3, the uncertainty of the equivalent support state parameter benchmark value obtained in step S1 is described using the cross-correlation Bayes algorithm; the cross-correlation Bayes calculation is as follows:

[0057]

[0058] in, The uncertainty parameter to be identified is the equivalent support state parameter in step S1. The data includes the slip consistency metric χ² corresponding to multi-domain simulation data and the slip consistency metric γ corresponding to multi-domain experimental data. Let be the prior probability density function; ι represents the posterior probability density function; ι represents the evidence. The likelihood function is designed as a combination of the coherence function, a measure of slippage consistency, and the Pearson correlation coefficient, corresponding to multi-domain simulation data and multi-domain experimental data, satisfying the following:

[0059]

[0060] in, To correspond to the slip consistency metric χ and the coherence function ε χγ The likelihood function; To correspond to the slip consistency metric χ and the Pearson correlation coefficient ρ χγ The likelihood function; the coherence function ε of the slippage consistency metrics χ and γ. χγ The calculation is as follows:

[0061]

[0062] in, The autocorrelation function of χ, a measure of slippage consistency in multi-domain simulation data; The autocorrelation function of γ, a measure of slippage consistency in multi-domain experimental data; ν represents the cross-correlation function of slip consistency metrics χ and γ corresponding to multi-domain simulation data and multi-domain experimental data; ν is the frequency; and ρ is the Pearson correlation coefficient between slip consistency metrics χ and γ. χγ The calculation is as follows:

[0063]

[0064] Where cov[χ(t),γ(t)] is the covariance between the slip consistency metrics χ and γ corresponding to the multi-domain simulation data and the multi-domain experimental data; σ χ The standard deviation of χ², a measure of slip consistency in multi-domain simulation data; σ γ γ represents the standard deviation of the slip consistency metric for multi-domain experimental data; t represents time; further, the coherence function ε can be obtained. χγ likelihood function The following conditions must be met:

[0065]

[0066] Where, ψ τ 1-ε χγ The standard deviation; exp(·) is an exponential function; similarly, the Pearson correlation coefficient ρ χγ likelihood function The following conditions must be met:

[0067]

[0068] Where, δ τ 1-ρ χγ Standard deviation;

[0069] Step S4.2: The maximum value of the posterior probability density distribution function of the equivalent support state parameters obtained in step S4.1 is taken as the identification result of the equivalent support state parameters. The following conditions must be met:

[0070]

[0071] Step S4.3: The identified flexible support state parameters... Substituting the values ​​into the rotor system thermal-fluid-structure interaction simulation model established in step S2, we can obtain the slippage rate curves under different time-varying operating conditions, which are the rotor system slippage twin simulation results.

[0072] Beneficial effects:

[0073] (1) This invention can obtain reliable twin simulation results of slippage of flexible support-rotor system. Within a unified framework, it simultaneously realizes the construction of consistency index of multi-domain slippage information, uncertainty analysis of flexible support parameters and thermal-fluid-structure interaction simulation, providing rich data support for slippage mechanism analysis, diagnosis and prediction and source control research.

[0074] (2) Multi-domain information such as torque, rotor deflection and vibration acceleration data that are closely related to the slippage behavior of the rotor system were extracted in a unified system framework. The time-frequency statistical characteristics of the extracted multi-domain information were further analyzed for slippage sensitivity and a slippage simulation consistency metric was constructed. This metric can comprehensively reflect the slippage characteristics and effectively address the technical problem of weak slippage signal characteristics.

[0075] (3) Based on a unified framework, the uncertainty of the state parameters of the flexible support component is accurately described by the cross-correlation Bayes algorithm. The likelihood function of the cross-correlation Bayes algorithm is designed as a combination of the coherence function and Pearson correlation coefficient of the slippage consistency index corresponding to the multi-domain simulation data and the multi-domain experimental data. Since the coherence function and the Pearson correlation coefficient are sensitive to the energy distribution and time distribution of the consistency index, respectively, the cross-correlation Bayes algorithm can comprehensively measure the consistency of the multi-domain slippage simulation data and the multi-domain slippage experimental data from the perspective of frequency domain and time domain, and thus obtain the accurate state parameters of the flexible support component of the rotor system.

[0076] (4) The coupled simulation of rotor dynamics and thermo-elasto-fluid lubrication was realized, breaking the situation where the two theories were analyzed independently in their respective fields, and a slippage prediction model of flexible support-rotor system considering lubrication effect and rotor characteristics was established with high accuracy. Attached Figure Description

[0077] Figure 1 A flowchart of a rotor system slippage twin simulation method considering the uncertainty of flexible support provided by the present invention;

[0078] Figure 2 This is a structural diagram of a high-speed flexible rotor slippage test bench in an embodiment of the present invention;

[0079] Figure 3 This is a schematic diagram of the equivalent spring damping unit structure of the flexible support component in an embodiment of the present invention;

[0080] Figure 4 This is a diagram showing the static analysis results of the flexible bearing housing in an embodiment of the present invention;

[0081] Figure 5 This is a diagram showing the static analysis results of the flexible coupling in an embodiment of the present invention;

[0082] Figure 6 This is a simulation diagram of the rotor system's thermal-fluid-structure interaction in an embodiment of the present invention;

[0083] Figure 7 This is a graph showing the variation of minimum oil film thickness with rotor system speed under different lubricating oil viscosities in an embodiment of the present invention.

[0084] Figure 8 This is a graph showing the variation of maximum oil film pressure with rotor system speed under different lubricating oil viscosities in an embodiment of the present invention.

[0085] Figure 9 This is a graph showing the variation of the maximum oil film temperature with the rotor system speed under different lubricating oil viscosities in an embodiment of the present invention.

[0086] Figure 10This is a graph showing the variation of minimum oil film thickness with rotor system speed under different radial loads in an embodiment of the present invention.

[0087] Figure 11 This is a graph showing the variation of maximum oil film pressure with rotor system speed under different radial loads in an embodiment of the present invention.

[0088] Figure 12 This is a graph showing the variation of the maximum oil film temperature with the rotor system speed under different radial loads in an embodiment of the present invention.

[0089] Figure 13 This is a schematic diagram of the bearing contact stiffness of a rotor system considering lubricating oil film and flexible support in an embodiment of the present invention;

[0090] Figure 14 This is a graph of torque simulation data collected based on the rotor system thermo-fluid-structure interaction simulation model in this embodiment of the invention;

[0091] Figure 15 This is a simulation data diagram of rotor deflection collected based on the rotor system thermo-fluid-structure interaction simulation model in an embodiment of the present invention;

[0092] Figure 16 This is a simulation data graph of vibration acceleration collected based on the rotor system thermo-fluid-structure interaction simulation model in an embodiment of the present invention;

[0093] Figure 17 This is a graph of torque simulation data collected from a rotor system slippage test bench in an embodiment of the present invention;

[0094] Figure 18 This is a simulation data diagram of rotor deflection collected from a rotor system slippage test bench in an embodiment of the present invention;

[0095] Figure 19 This is a simulation data graph of vibration acceleration collected from a rotor system slippage test bench in an embodiment of the present invention;

[0096] Figure 20 This is a graph showing the results of slippage sensitivity analysis of multi-domain information time-frequency statistical features in an embodiment of the present invention.

[0097] Figure 21 This is a posterior probability density distribution function diagram of the proportional coefficient of the benchmark value of the equivalent support state parameter described by the cross-correlation Bayes algorithm in this embodiment of the invention;

[0098] Figure 22 This is a slip rate curve obtained from a slip test bench based on a flexible support-rotor system in an embodiment of the present invention.

[0099] Figure 23 This is a slippage rate curve obtained from the rotor system thermal-fluid-structure interaction simulation model in an embodiment of the present invention. Detailed Implementation

[0100] The invention will now be further described with reference to the accompanying drawings.

[0101] See Figures 1-23 This embodiment provides a twin simulation method for rotor system slippage considering the uncertainty of flexible supports. The process of this method is as follows: Figure 1 As shown, this embodiment uses a high-speed flexible rotor slippage test bench as an example to verify the algorithm performance. The test bench structure is as follows: Figure 2 As shown. The strategy specifically includes the following steps:

[0102] Step S1: Establish finite element models for the rotor system shaft and bearings respectively. Equivalently represent flexible support components such as flexible bearing housings and flexible couplings as spring-damped elements. The equivalent spring-damped elements are as follows: Figure 3 As shown; based on static analysis, the baseline values ​​of the equivalent support state parameters are obtained, and then a dynamic simulation model of rotor system slippage considering the flexible support state is obtained; among which, the static analysis results of the flexible bearing housing are as follows. Figure 4 As shown, the static analysis results of the flexible coupling are as follows: Figure 5 As shown.

[0103] Specifically, in this embodiment, step S1 includes:

[0104] Step S1.1: Establish finite element models of the shaft and bearings in the slippage test rig of the flexible support-rotor system, and further conduct modal tests and model corrections on the shaft to obtain the modal frequency τ of the shaft. S Damping π S and stiffness parameter κ S It is necessary to ensure that the model correction accuracy of the shaft meets the modal confidence criteria (MAC) for each mode shape. ij If the modal confidence criterion is greater than 85%, it will be calculated as follows:

[0105]

[0106] in, The correlation coefficients between the i-th experimental mode shape and the j-th finite element simulation model mode shape of the shaft in the slippage test bench of the flexible support-rotor system; The i-th experimental mode shape of the shaft on the slippage test bench for the flexible support-rotor system; The j-th simulated mode shape of the shaft on the slippage test bench for the flexible support-rotor system; T is the conjugate transpose;

[0107] Step S1.2: In the flexible support-rotor system slippage test rig, the flexible bearing housing is equivalent to two sets of spring damping units perpendicular to the horizontal and vertical directions in the axial plane. The equivalent damping is expressed as... The equivalent stiffness is expressed as In the slippage test rig for the flexible support-rotor system, the flexible coupling is equivalent to three sets of spring-damped units along the axial direction, in the horizontal direction perpendicular to the axial plane, and in the vertical direction. The equivalent damping is expressed as: The equivalent stiffness is expressed as Furthermore, the stiffness and damping parameters of the equivalent spring-damped unit were obtained based on static analysis, and these parameters were used as the reference values ​​for the equivalent support state parameters. The obtained reference values ​​for the equivalent support state parameters of the flexible support assembly are shown in Table 1.

[0108] Table 1. Reference values ​​of equivalent support state parameters for flexible support components.

[0109]

[0110]

[0111] Step S1.3: Combine and assemble the finite element models of the shaft and bearings in the flexible support-rotor system slippage test bench obtained in step S1.1, and the equivalent support state parameter reference values ​​of the flexible support components such as the flexible bearing seat and flexible coupling obtained in step S1.2 to obtain a rotor system slippage dynamic simulation model considering the flexible support state.

[0112] Step S2: Based on the rotor system slippage dynamics simulation model considering the flexible support state obtained in Step S1 and the thermo-elasto-hydrodynamic lubrication theory, analyze the influence of lubrication state parameters on slippage, and further construct a rotor system thermo-fluid-structure coupling simulation model considering the flexible support state.

[0113] Specifically, in this embodiment, step S2 includes:

[0114] Step S2.1: Analyze the influence of lubrication state parameters on slippage of the flexible support-rotor system slippage test bench based on thermo-elastohydrodynamic lubrication theory; thermo-elastohydrodynamic lubrication theory includes the Reynolds equation, energy equation, film thickness equation, viscosity-pressure / viscosity-temperature equation, and pressure-temperature-temperature equation. The calculation process of the Reynolds equation in thermo-elastohydrodynamic lubrication theory is as follows:

[0115]

[0116] Where h is the oil film thickness; p is the oil film pressure; η is the lubricating oil viscosity; ρ is the lubricating oil density; U is the entrainment velocity; x and y are the coordinates of the oil film width and length directions; the calculation process of the energy equation in thermo-elastohydrodynamic lubrication theory is as follows:

[0117]

[0118] Among them, c ρHere, is the specific heat capacity at constant pressure; K is the thermal conductivity coefficient; T is the oil film temperature; z is the coordinate of the oil film thickness direction; u and v are the boundary velocities in the x and y directions, respectively; the calculation process of the film thickness equation in thermo-elastohydrodynamic lubrication theory is as follows:

[0119]

[0120] Where v(x,y) is the deformation term; h0 is the initial oil film thickness; R x and R y Here, radii of curvature along the x and y directions at the contact point are respectively those of the bearing and the oil film; the calculation process of the viscosity-pressure / viscosity-temperature equation in thermo-elastohydrodynamic lubrication theory is as follows:

[0121]

[0122] Where T0 is the initial temperature; η0 is the lubricating oil viscosity corresponding to temperature T0; the calculation process of the pressure-temperature equation in thermo-elastohydrodynamic lubrication theory is as follows:

[0123]

[0124] Where ρ0 is the density of the lubricating oil corresponding to temperature T0;

[0125] Step S2.2: Based on the rotor system slippage dynamics simulation model considering the flexible support state obtained in Step S1 and the thermo-elasto-hydrodynamic lubrication theory in Step S2.1, perform thermo-fluid-structure interaction (THE-STE) simulation to obtain a coupled THE-STE simulation model of the rotor system considering the flexible support state; the THE-STE simulation process is as follows: Figure 6 As shown, it includes two parts: a thermo-elasto-hydrodynamic lubrication model and a rotor dynamics model. The specific steps are as follows:

[0126] First, initial oil film pressure, oil film thickness, and oil film temperature parameters are set, and mechanical and kinematic parameters of the contact micro-region obtained from the dynamic simulation model are imported. Second, the oil film pressure is calculated using the multigrid integration method, and the oil film thickness, viscosity, and density are calculated until the pressure, load, and temperature converge simultaneously. Then, the lubricating oil film stiffness and comprehensive contact stiffness are calculated based on the obtained oil film pressure, thickness, and temperature parameters. Finally, the obtained lubricating oil film stiffness and comprehensive contact stiffness are input into the dynamic simulation model to achieve thermo-fluid-structure interaction simulation.

[0127] Specifically, the overall contact stiffness K θ The calculation is as follows:

[0128]

[0129] Where Z is the number of rolling elements in the bearing; j = 1, 2, ..., Z is the j-th rolling element in the bearing; cos(·) is the cosine function; K cijK represents the contact stiffness between the bearing inner ring and the inner ring oil film at the j-th rolling element. cej K represents the contact stiffness between the bearing outer ring and the outer ring oil film at the j-th rolling element. fij K represents the contact stiffness between the rolling element and the inner ring oil film at the j-th rolling element. fej This represents the contact stiffness between the rolling element and the outer ring oil film at the j-th rolling element.

[0130] Lubricating oil film stiffness K μ The calculation is as follows:

[0131]

[0132] Bearing contact stiffness The calculation is as follows:

[0133]

[0134] Based on the established rotor system thermo-fluid-structure interaction simulation model, different lubricating oil viscosities (21.3 mm) were obtained. 2 / s, 29.8mm 2 / s, 34.3mm 2 / s, 41.2mm 2 The lubrication conditions under different radial loads (0.5kN, 3kN, 5kN, 7kN) and the curves showing the variation of minimum oil film thickness, maximum oil film pressure, and maximum oil film temperature with rotor system speed are shown below. Figures 7-12 As shown in the figure. The curve of bearing contact stiffness over time in a rotor system considering lubricating oil film and flexible support is shown in the figure. Figure 13 As shown.

[0135] Step S3: Based on the rotor system thermal-fluid-structure interaction simulation model considering the flexible support state established in Step S2 and the flexible support-rotor system slippage test bench, multi-domain simulation data and multi-domain experimental data are collected under the same time-varying slippage working state. Furthermore, a slippage consistency metric index is constructed through time-frequency statistical feature slippage sensitivity analysis.

[0136] Specifically, in this embodiment, step S3 includes:

[0137] Step S3.1: Based on the rotor system thermo-fluid-structure interaction simulation model established in step S2 considering the flexible support state, collect multi-domain simulation data under time-varying slippage conditions, including torque simulation data. Rotor deflection simulation data Vibration acceleration simulation data and slippage rate simulation data Collected torque simulation data Rotor deflection simulation data and vibration acceleration simulation data Each as Figures 14-16 As shown;

[0138] Step S3.2: Collect multi-domain experimental data under time-varying slippage conditions based on the slippage test bench of the flexible support-rotor system, including torque experimental data. Rotor deflection test data Vibration acceleration experimental data and slippage rate experimental data collected torque experimental data Rotor deflection test data Vibration acceleration experimental data Each as Figures 17-19 As shown;

[0139] Step S3.3: Based on the multi-domain simulation data obtained in step S3.1 and the multi-domain experimental data obtained in step S3.2 Time-frequency statistical feature slippage sensitivity analysis was performed to determine the slippage sensitivity statistical features corresponding to multi-domain data. The process of time-frequency statistical feature slippage sensitivity analysis for multi-domain data is as follows:

[0140]

[0141] in, For the corresponding torque data Ω T The range of variation of the λ time-frequency statistical features; For the rotor deflection data Ω D The range of variation of the λ time-frequency statistical features; To correspond to the vibration acceleration data Ω A The range of variation of the λ time-frequency statistical features; For slippage rate data The range of variation; For the corresponding torque data Ω T The slip sensitivity of the λ time-frequency statistical features; For the rotor deflection data Ω D The slip sensitivity of the λ time-frequency statistical features; To correspond to the vibration acceleration data Ω A The slip sensitivity of λ time-frequency statistical features; corresponding to the multi-domain data Ω{Ω T ,Ω D ,Ω A ,Ω S Statistical characteristics of slippage sensitivity The determination process is as follows:

[0142]

[0143] Where max{·} is the operation for finding the maximum value; For the corresponding torque data Ω T The statistical characteristics of slippage sensitivity; For the rotor deflection data Ω D The statistical characteristics of slippage sensitivity; To correspond to the vibration acceleration data Ω A The slippage sensitivity statistical characteristics; the time-frequency statistical characteristics used are shown in Table 2:

[0144] Table 2 Time-Frequency Statistical Characteristics

[0145] Serial Number feature Serial Number feature 1 mean 11 Maximum value 2 Absolute mean 12 Minimum value 3 Root Mean Square 13 Peak Indicator 4 Root amplitude 14 margin index 5 Peak-to-peak value 15 Waveform Indicators 6 variance 16 Pulse index 7 Standard deviation 17 Center of gravity frequency 8 Skewness 18 Root mean square frequency 9 cliff 19 average frequency 10 Energy Index 20 Frequency variance

[0146] The calculated time-frequency statistical characteristics of slippage sensitivity analysis results are as follows: Figure 20 As shown, the torque data Ω can be observed. T The corresponding statistical characteristic of slippage sensitivity is the root mean square, and the rotor deflection data Ω D The corresponding statistical characteristic of slippage sensitivity is variance, and the vibration acceleration data Ω A The corresponding statistical characteristic of slippage sensitivity is the energy index.

[0147] Step S3.4: Determine the slip consistency measurement index based on the slip sensitivity statistical characteristics corresponding to multi-domain data obtained in step S3.3;

[0148] Multi-domain simulation data The construction process of the slip consistency metric χ is as follows:

[0149]

[0150] Where, ω T Torque simulation data The corresponding weight of the slip consistency metric; ω D The weight of the slippage consistency metric corresponding to the rotor deflection simulation data; ω A For vibration acceleration simulation data The corresponding weights for slip consistency metrics; which respectively satisfy:

[0151]

[0152] in, and These correspond to the statistical characteristics of slip sensitivity. The change in quantity; similarly, multi-domain experimental data. The construction process of the slip consistency metric γ is as follows:

[0153]

[0154] Step S4: Based on the slip consistency index of the multi-domain simulation data and multi-domain experimental data obtained in step S3, the uncertainty of the equivalent support state parameter benchmark value obtained in step S1 is described by the cross-correlation Bayes algorithm. The identified flexible support state parameters are then substituted into the rotor system thermo-fluid-structure coupling simulation model established in step S2 to obtain the slip rate curves under different time-varying working conditions.

[0155] Specifically, in this embodiment, step S4 includes:

[0156] Step S4.1: Based on the slippage consistency index of the multi-domain simulation data and multi-domain experimental data obtained in step S3, the uncertainty of the equivalent support state parameter benchmark value obtained in step S1 is described using the cross-correlation Bayes algorithm; the cross-correlation Bayes calculation is as follows:

[0157]

[0158] in, The uncertainty parameter to be identified is the equivalent support state parameter in step S1. The data includes the slip consistency metric χ² corresponding to multi-domain simulation data and the slip consistency metric γ corresponding to multi-domain experimental data. Let be the prior probability density function; ι represents the posterior probability density function; ι represents the evidence. The likelihood function is designed as a combination of the coherence function, a measure of slippage consistency, and the Pearson correlation coefficient, corresponding to multi-domain simulation data and multi-domain experimental data, satisfying the following:

[0159]

[0160] in, To correspond to the slip consistency metric χ and the coherence function ε χγ The likelihood function; To correspond to the slip consistency metric χ and the Pearson correlation coefficient ρ χγ The likelihood function; the coherence function ε of the slippage consistency metrics χ and γ. χγ The calculation is as follows:

[0161]

[0162] in, The autocorrelation function of χ, a measure of slippage consistency in multi-domain simulation data; The autocorrelation function of γ, a measure of slippage consistency in multi-domain experimental data; ν represents the cross-correlation function of slip consistency metrics χ and γ corresponding to multi-domain simulation data and multi-domain experimental data; ν is the frequency; and ρ is the Pearson correlation coefficient between slip consistency metrics χ and γ. χγ The calculation is as follows:

[0163]

[0164] Where cov[χ(t),γ(t)] is the covariance between the slip consistency metrics χ and γ corresponding to the multi-domain simulation data and the multi-domain experimental data; σ χ The standard deviation of χ², a measure of slip consistency in multi-domain simulation data; σ γ γ represents the standard deviation of the slip consistency metric for multi-domain experimental data; t represents time; further, the coherence function ε can be obtained. χγ likelihood function The following conditions must be met:

[0165]

[0166] Where, ψ τ 1-ε χγ The standard deviation; exp(·) is an exponential function; similarly, the Pearson correlation coefficient ρ χγ likelihood function The following conditions must be met:

[0167]

[0168] Where, δ τ 1-ρ χγ Standard deviation;

[0169] Step S4.2: The maximum value of the posterior probability density distribution function of the equivalent support state parameters obtained in step S4.1 is taken as the identification result of the equivalent support state parameters. The following conditions must be met:

[0170]

[0171] Furthermore, based on the cross-correlation Bayesian algorithm, the posterior probability density distribution function of the proportional coefficient of the equivalent support state parameter benchmark value is described as follows: Figure 21 As shown. It is worth noting that, Figure 21 The displayed value is a scaling factor for the baseline value of the equivalent support state parameter. Its product with the baseline value of the equivalent support state parameter of the flexible support assembly in Table 1 is the identification value of the equivalent support state parameter of the flexible support assembly, which satisfies the following:

[0172]

[0173] in, This represents the scaling factor for the baseline values ​​of the equivalent support state parameters obtained based on the cross-correlation Bayesian algorithm. The final identified values ​​of the equivalent support state parameters for the flexible support assembly, considering uncertainties, are shown in Table 3.

[0174] Table 3. Identification values ​​of equivalent support state parameters for flexible support components.

[0175]

[0176] Step S4.3: The flexible support state parameters identified in Table 3... Substituting the values ​​into the rotor system thermal-fluid-structure interaction simulation model established in step S2, we can obtain the slippage rate curves under different time-varying operating conditions, which are the rotor system slippage twin simulation results. Figure 22 The slip rate curves collected by the slip test bench based on the flexible support-rotor system are shown. Figure 23 The slip rate curve obtained based on the rotor system thermo-fluid-structure interaction simulation model is shown. It can be found that the slip test and simulation results have a high degree of consistency, which fully verifies the effectiveness and practicality of the present invention.

[0177] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A twin simulation method for rotor system slippage considering uncertainties in flexible supports, characterized in that, Includes the following steps: Step S1: Establish finite element models of the rotor system shaft and bearings respectively, and equate the flexible support component to a spring damping element. Based on static analysis, obtain the reference values ​​of the equivalent support state parameters and obtain a rotor system slippage dynamic simulation model considering the flexible support state. Step S2: Based on the rotor system slippage dynamics simulation model and thermo-elasto-fluidic lubrication theory, analyze the influence of lubrication state parameters on slippage, and further construct a rotor system thermo-fluid-structure coupling simulation model considering the flexible support state; The specific steps of the thermal-fluid-structure interaction simulation include: First, initial oil film pressure, oil film thickness, and oil film temperature parameters are set, and mechanical and kinematic parameters of the contact micro-region obtained from the dynamic simulation model are imported. Second, the oil film pressure is calculated using the multigrid integration method, and the oil film thickness, viscosity, and density are calculated until the pressure, load, and temperature converge simultaneously. Then, the lubricating oil film stiffness and comprehensive contact stiffness are calculated based on the obtained oil film pressure, thickness, and temperature parameters. Finally, the obtained lubricating oil film stiffness and comprehensive contact stiffness are input into the dynamic simulation model to achieve thermo-fluid-structure interaction simulation. Overall contact stiffness K θ The calculation is as follows: Where Z is the number of rolling elements in the bearing; j = 1, 2, ..., Z is the j-th rolling element in the bearing; cos(·) is the cosine function; K cij K represents the contact stiffness between the bearing inner ring and the inner ring oil film at the j-th rolling element. cej K represents the contact stiffness between the bearing outer ring and the outer ring oil film at the j-th rolling element. fij K represents the contact stiffness between the rolling element and the inner ring oil film at the j-th rolling element. fej This represents the contact stiffness between the rolling element and the outer ring oil film at the j-th rolling element. Lubricating oil film stiffness K μ The calculation is as follows: Bearing contact stiffness The calculation is as follows: Step S3: Based on the rotor system thermal-fluid-structure interaction simulation model and the flexible support-rotor system slippage test bench, multi-domain simulation data and multi-domain experimental data are collected under the same time-varying slippage working conditions. Slippage consistency index is constructed through time-frequency statistical feature slippage sensitivity analysis. Step S4: Based on the slippage consistency metric, the uncertainty of the equivalent support state parameter benchmark value obtained in step S1 is described by the cross-correlation Bayes algorithm. The identified flexible support state parameters are substituted into the rotor system thermal-fluid-structure coupling simulation model established in step S2 to obtain the slippage rate curve under different time-varying working conditions.

2. The twin simulation method for rotor system slippage considering the uncertainty of flexible support according to claim 1, characterized in that, Step S1 is as follows: Step S1.1: Establish finite element models of the shaft and bearings in the slippage test rig of the flexible support-rotor system, and perform modal tests and model corrections on the shaft to obtain the modal frequency τ of the shaft. S Damping π S and stiffness parameter κ S To ensure that the model correction accuracy of the shaft meets the modal confidence criteria (MAC) for each mode shape, ij If the value is greater than the set value, the modal confidence criterion is calculated as follows: in, The correlation coefficients between the i-th experimental mode shape and the j-th finite element simulation model mode shape of the shaft in the slippage test bench of the flexible support-rotor system; The i-th experimental mode shape of the shaft on the slippage test bench for the flexible support-rotor system; The j-th simulated mode shape of the shaft on the slippage test bench for the flexible support-rotor system; T is the conjugate transpose; Step S1.2: In the flexible support-rotor system slippage test rig, the flexible bearing housing is equivalent to two sets of spring damping units perpendicular to the horizontal and vertical directions in the axial plane. The equivalent damping is expressed as... The equivalent stiffness is expressed as In the slippage test rig for the flexible support-rotor system, the flexible coupling is equivalent to three sets of spring-damped units along the axial direction, in the horizontal direction perpendicular to the axial plane, and in the vertical direction. The equivalent damping is expressed as: The equivalent stiffness is expressed as The stiffness and damping parameters of the equivalent spring damping unit are obtained based on static analysis and used as the reference values ​​of the equivalent support state parameters. Step S1.3: After combining and assembling the finite element models of the shaft and bearings in the flexible support-rotor system slippage test bench, and the equivalent support state parameter reference values ​​of the flexible support components such as the flexible bearing housing and flexible coupling, a dynamic simulation model of the rotor system slippage considering the flexible support state is obtained.

3. The twin simulation method for rotor system slippage considering the uncertainty of flexible support according to claim 1, characterized in that, Step S2 is as follows: Step S2.1: Analyze the influence of lubrication state parameters on slippage of the flexible support-rotor system slippage test bench based on thermo-elastohydrodynamic lubrication theory; thermo-elastohydrodynamic lubrication theory includes the Reynolds equation, energy equation, film thickness equation, viscosity-pressure / viscosity-temperature equation, and pressure-temperature-temperature equation. The calculation process of the Reynolds equation in thermo-elastohydrodynamic lubrication theory is as follows: Where h is the oil film thickness; p is the oil film pressure; η is the lubricating oil viscosity; ρ is the lubricating oil density; U is the entrainment velocity; x and y are the coordinates of the oil film width and length directions; the calculation process of the energy equation in thermo-elastohydrodynamic lubrication theory is as follows: Among them, c ρ Here, is the specific heat capacity at constant pressure; K is the thermal conductivity coefficient; T is the oil film temperature; z is the coordinate of the oil film thickness direction; u and v are the boundary velocities in the x and y directions, respectively; the calculation process of the film thickness equation in thermo-elastohydrodynamic lubrication theory is as follows: Where v(x,y) is the deformation term; h0 is the initial oil film thickness; R x and R y Here, radii of curvature along the x and y directions at the contact point are respectively those of the bearing and the oil film; the calculation process of the viscosity-pressure / viscosity-temperature equation in thermo-elastohydrodynamic lubrication theory is as follows: Where T0 is the initial temperature; η0 is the lubricating oil viscosity corresponding to temperature T0; the calculation process of the pressure-temperature equation in thermo-elastohydrodynamic lubrication theory is as follows: Where ρ0 is the density of the lubricating oil corresponding to temperature T0; Step S2.2: Based on the rotor system slippage dynamics simulation model and the thermo-elastohydrodynamic lubrication theory of step S2.1, perform thermo-fluid-solid simulation to obtain a rotor system thermo-fluid-solid coupling simulation model considering the flexible support state.

4. The rotor system slippage twin simulation method considering the uncertainty of flexible support according to claim 1, characterized in that, Step S3 is as follows: Step S3.1: Based on the rotor system's thermo-fluid-structure interaction simulation model, collect multi-domain simulation data under time-varying slippage conditions, including torque simulation data. Rotor deflection simulation data Vibration acceleration simulation data and slippage rate simulation data Step S3.2: Collect multi-domain experimental data under time-varying slippage conditions based on the slippage test bench of the flexible support-rotor system, including torque experimental data. Rotor deflection test data Vibration acceleration experimental data and slippage rate experimental data Step S3.3: Based on the multi-domain simulation data respectively and the multi-domain experimental data Time-frequency statistical feature slippage sensitivity analysis was performed to determine the slippage sensitivity statistical features corresponding to multi-domain data. The process of time-frequency statistical feature slippage sensitivity analysis for multi-domain data is as follows: in, For the corresponding torque data Ω T The range of variation of the λ time-frequency statistical features; For the rotor deflection data Ω D The range of variation of the λ time-frequency statistical features; To correspond to the vibration acceleration data Ω A The range of variation of the λ time-frequency statistical features; For slippage rate data The range of variation; For the corresponding torque data Ω T The slip sensitivity of the λ time-frequency statistical features; For the rotor deflection data Ω D The slip sensitivity of the λ time-frequency statistical features; To correspond to the vibration acceleration data Ω A The slip sensitivity of λ time-frequency statistical features; corresponding to the multi-domain data Ω{Ω T ,Ω D ,Ω A ,Ω S Statistical characteristics of slippage sensitivity The determination process is as follows: Where max{·} is the operation for finding the maximum value; For the corresponding torque data Ω T The statistical characteristics of slippage sensitivity; For the rotor deflection data Ω D The statistical characteristics of slippage sensitivity; To correspond to the vibration acceleration data Ω A The statistical characteristics of slippage sensitivity; Step S3.4: Determine the slip consistency measurement index based on the slip sensitivity statistical characteristics; Multi-domain simulation data The construction process of the slip consistency metric χ is as follows: Where, ω T Torque simulation data The corresponding weight of the slip consistency metric; ω D The weight of the slippage consistency metric corresponding to the rotor deflection simulation data; ω A For vibration acceleration simulation data The corresponding weights for slip consistency metrics; which respectively satisfy: in, and These correspond to the statistical characteristics of slip sensitivity. The change in quantity; similarly, multi-domain experimental data. The construction process of the slip consistency metric γ is as follows:

5. The rotor system slippage twin simulation method considering the uncertainty of flexible support according to claim 1, characterized in that, Step S4 is as follows: Step S4.1: Based on the slippage consistency metric of the multi-domain simulation data and multi-domain experimental data, the uncertainty of the equivalent support state parameter benchmark value obtained in step S1 is described using the cross-correlation Bayes algorithm; the cross-correlation Bayes calculation is as follows: in, The uncertainty parameter to be identified is the equivalent support state parameter in step S1. The data includes the slip consistency metric χ² corresponding to multi-domain simulation data and the slip consistency metric γ corresponding to multi-domain experimental data. Let be the prior probability density function; ι represents the posterior probability density function; ι represents the evidence. The likelihood function is designed as a combination of the coherence function, a measure of slippage consistency, and the Pearson correlation coefficient, corresponding to multi-domain simulation data and multi-domain experimental data, satisfying the following: in, To correspond to the slip consistency metric χ and the coherence function ε χγ The likelihood function; To correspond to the slip consistency metric χ and the Pearson correlation coefficient ρ χγ The likelihood function; the coherence function ε of the slippage consistency metrics χ and γ. χγ The calculation is as follows: in, The autocorrelation function of χ, a measure of slippage consistency in multi-domain simulation data; The autocorrelation function of γ, a measure of slippage consistency in multi-domain experimental data; ν represents the cross-correlation function of slip consistency metrics χ and γ corresponding to multi-domain simulation data and multi-domain experimental data; ν is the frequency; and ρ is the Pearson correlation coefficient between slip consistency metrics χ and γ. χγ The calculation is as follows: Where cov[χ(t),γ(t)] is the covariance between the slip consistency metrics χ and γ corresponding to the multi-domain simulation data and the multi-domain experimental data; σ χ The standard deviation of χ², a measure of slip consistency in multi-domain simulation data; σ γ γ represents the standard deviation of the slip consistency metric for multi-domain experimental data; t represents time; further, the coherence function ε can be obtained. χγ likelihood function The following conditions must be met: Where, ψ τ 1-ε χγ The standard deviation; exp(·) is an exponential function; similarly, the Pearson correlation coefficient ρ χγ likelihood function The following conditions must be met: Where, δ τ 1-ρ χγ Standard deviation; Step S4.2: The maximum value of the posterior probability density distribution function of the equivalent support state parameters obtained in step S4.1 is taken as the identification result of the equivalent support state parameters. The following conditions must be met: Step S4.3: The identified flexible support state parameters... Substituting the values ​​into the rotor system thermal-fluid-structure interaction simulation model established in step S2, we can obtain the slippage rate curves under different time-varying operating conditions, which are the rotor system slippage twin simulation results.

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