Rotor system slipping twinborn simulation method considering uncertainty of flexible support

Abstract

The invention discloses a rotor system slipping twinborn simulation method considering uncertainty of a flexible support. The method comprises the steps that firstly, flexible supporting assemblies such as a flexible bearing seat and a flexible coupler are equivalent to spring damping units, and equivalent supporting state parameter reference values are obtained based on statics analysis; secondly, constructing a rotor system thermal-fluid-solid coupling simulation model considering the flexible supporting state based on a rotor system dynamics simulation model and thermal elastohydrodynamic lubrication coupling analysis; then, respectively collecting multi-domain simulation data and multi-domain experimental data in the same time-varying slip working state, and calculating and constructing a slip consistency measurement index based on the time-frequency statistical characteristic slip sensitivity of the multi-domain information; and finally, the uncertainty of the state parameters of the flexible supporting assembly is described based on cross-correlation Bayesian, and the identified flexible supporting state parameters are substituted into the established rotor system heat-fluid-solid coupling simulation model so as to obtain a slip rate curve under different time-varying working conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of digital twins, and in particular to a rotor system slip twin simulation method taking into account the uncertainty of flexible supports. Background Art

[0002] The slip behavior of the rotor system has the significant characteristics of weak signal characteristics, significant time-varying characteristics, and multi-factor coupling effects. In the face of the challenge of weak signal characteristics, it is necessary to make full use of the multi-domain information closely related to the slip behavior of the rotor system for characterization; in the face of the challenge of significant time-varying characteristics, it is necessary to fully consider the influence of parameter uncertainty; in the face of the challenge of multi-factor coupling effects, thermal-fluid-solid coupling simulation analysis is required. However, existing studies have failed to address the above challenges in a unified framework, making it difficult to achieve accurate rotor system slip simulation.

[0003] Building a unified framework to simultaneously address the above challenges is a prerequisite for realizing the slip twin simulation of the flexible support-rotor system. Reliable slip twin simulation results can provide a rich data basis for analyzing the slip fault mechanism, conducting slip diagnosis and prediction, and carrying out slip source tracing and control.

[0004] At present, the rich knowledge obtained from the rotor system slip twin simulation has been used to construct a slip knowledge graph and guide the improved design of the flexible support-rotor system, and has achieved remarkable 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 twin simulation method for rotor system slippage taking into account the uncertainty of flexible support, which realizes the construction of slippage simulation consistency measurement indicators based on multi-domain information within a unified framework, designs a cross-correlation Bayesian algorithm to describe the uncertainty of state parameters of flexible support components, and uses a thermal-fluid-solid coupling slippage simulation model to perform multi-factor coupling influence analysis and other functions.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A rotor system slip twin simulation method considering the uncertainty of flexible support comprises the following steps:

[0008] Step S1, respectively establishing finite element models of the rotor system shaft and bearing, equating flexible support components such as a flexible bearing seat and a flexible coupling to spring damping units, and obtaining equivalent support state parameter reference values ​​based on static analysis, thereby obtaining a rotor system slip dynamics simulation model considering the flexible support state;

[0009] Step S2, based on the rotor system slip dynamics simulation model considering the flexible support state obtained in step S1 and the thermoelastic-hydrodynamic lubrication theory, analyzing the influence of lubrication state parameters on slip, further constructing a rotor system thermal-fluid-solid coupling simulation model considering the flexible support state;

[0010] Step S3, respectively collecting multi-domain simulation data and multi-domain experimental data under the same time-varying slip working state based on the rotor system thermal-fluid-solid coupling simulation model considering the flexible support state and the flexible support-rotor system slip test bench established in step S2, and further constructing a slip consistency measurement index through time-frequency statistical feature slip sensitivity analysis;

[0011] Step S4, based on the slip consistency metric of the multi-domain simulation data and the multi-domain experimental data obtained in step S3, the uncertainty of the reference value of the equivalent support state parameter obtained in step S1 is described using the cross-correlation Bayesian algorithm, and the identified flexible support state parameters are substituted into the thermal-fluid-solid coupling simulation model of the rotor system established in step S2 to obtain the slip rate curve under different time-varying working conditions.

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

[0013] Step S1.1, respectively establish the finite element model of the shaft and bearing in the flexible support-rotor system slip test bench, and further perform modal test and model correction on the shaft to obtain the modal frequency τ of the shaft S 、Damping π S and the stiffness parameter κ S ; It is necessary to ensure that the model correction accuracy of the axis meets the modal confidence criteria MAC of each modal vibration mode ij is greater than 85%, the modal assurance criterion is calculated as follows:

[0014]

[0015] in, is the correlation coefficient between the i-th experimental modal vibration shape and the j-th finite element simulation model modal vibration shape of the shaft in the flexible support-rotor system slip test bench; is the i-th experimental modal vibration shape of the shaft in the flexible support-rotor system slip test bench; is the j-th order simulation mode vibration shape of the shaft in the flexible support-rotor system slip test bench; T is the conjugate transpose;

[0016] Step S1.2, the flexible bearing seat in the flexible support-rotor system slip test bench is equivalent to two sets of spring damping units perpendicular to the horizontal and vertical directions in the axis plane, and the equivalent damping is expressed as The equivalent stiffness is expressed as The flexible coupling in the flexible support-rotor system slip test bench is equivalent to three sets of spring damping units along the axial direction, the horizontal direction perpendicular to the axis plane, and the vertical direction. The equivalent damping is expressed as The equivalent stiffness is expressed as Further, based on the static analysis, the stiffness and damping parameter values ​​of the equivalent spring damping unit are obtained and used as the reference values ​​of the equivalent support state parameters;

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

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

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

[0020]

[0021] Among them, h is the oil film thickness; p is the oil film pressure; η is the viscosity of the lubricating oil; ρ is the density of the lubricating oil; U is the entrainment velocity; x and y are the coordinates of the width and length of the oil film; the calculation process of the energy equation in the thermal elastic hydrodynamic lubrication theory is as follows:

[0022]

[0023] Among them, c ρ is the constant pressure specific heat capacity; K is the heat transfer 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 the thermoelastic 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 are the curvature radii of the bearing and the oil film at the contact point along the x and y directions respectively; the calculation process of the viscosity-pressure-viscosity-temperature equation in the thermoelastic-hydrodynamic lubrication theory is as follows:

[0026]

[0027] Where T0 is the initial temperature; η0 is the viscosity of the lubricating oil corresponding to temperature T0; the calculation process of the density pressure-density temperature equation in the thermoelastic 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 slip dynamics simulation model considering the flexible support state obtained in step S1 and the thermal elastic-hydrodynamic lubrication theory of step S2.1, a thermal-fluid-solid simulation is performed to obtain a rotor system thermal-fluid-solid coupling simulation model considering the flexible support state; the specific steps of the thermal-fluid-solid coupling simulation include:

[0031] First, the initial oil film pressure, oil film thickness and oil film temperature parameters are set, and the mechanical parameters and motion parameters of the contact micro-area parameters obtained based on the dynamic simulation model are imported; secondly, the oil film pressure is calculated using the multi-grid 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 realize the thermal-fluid-solid coupling simulation;

[0032] Specifically, the comprehensive 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 jth rolling element in the bearing; cos(·) is the cosine function; K cij K is the contact stiffness between the inner ring of the bearing and the inner ring oil film corresponding to the jth rolling element; cej K is the contact stiffness between the outer ring of the bearing and the outer ring oil film at the jth rolling element; fij K is the contact stiffness between the rolling element and the inner ring oil film at the jth rolling element; fej is the contact stiffness between the rolling element and the outer ring oil film corresponding to the jth 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:

[0040] Step S3.1: Based on the rotor system thermal-fluid-solid coupling simulation model considering the flexible support state established in step S2, multi-domain simulation data under the time-varying slip working state is collected, including torque simulation data. Rotor deflection simulation data Vibration acceleration simulation data and slip rate simulation data

[0041] Step S3.2: Collect multi-domain experimental data under time-varying slip working state based on the flexible support-rotor system slip test bench, including torque experimental data Rotor deflection test data Vibration acceleration test data And slip 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 Perform time-frequency statistical characteristics slip sensitivity analysis to determine the slip sensitivity statistical characteristics corresponding to multi-domain data; the slip sensitivity analysis process of multi-domain data time-frequency statistical characteristics is as follows:

[0043]

[0044]

[0045] in, Corresponding to the torque data Ω T The variation range of λ time-frequency statistical characteristics; Corresponding to the rotor deflection data Ω D The variation range of λ time-frequency statistical characteristics; Corresponding to the vibration acceleration data Ω A The variation range of λ time-frequency statistical characteristics; Slip rate data The range of changes; Corresponding to the torque data Ω T The slip sensitivity of the λ time-frequency statistical characteristics; Corresponding to the rotor deflection data Ω D The slip sensitivity of the λ time-frequency statistical characteristics; Corresponding to the vibration acceleration data Ω A The slip sensitivity of the λ time-frequency statistical features of the multi-domain data Ω{Ω T ,Ω D ,Ω A,Ω S}'s slip sensitivity statistical characteristics The determination process is as follows:

[0046]

[0047] Among them, max{·} is the operation of taking the maximum value; Corresponding to the torque data Ω T Statistical characteristics of slip sensitivity; Corresponding to the rotor deflection data Ω D Statistical characteristics of slip sensitivity; Corresponding to the vibration acceleration data Ω A Statistical characteristics of slip sensitivity;

[0048] Step S3.4, determining a slip consistency measurement index based on the slip sensitivity statistical features corresponding to the 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] Among them, ω T Torque simulation data The corresponding slip consistency metric weight; ω D is the weight of the slip consistency metric corresponding to the rotor deflection simulation data; ω A Vibration acceleration simulation data The corresponding slip consistency measurement index weights satisfy:

[0052]

[0053] in, and They correspond to the statistical characteristics of slip sensitivity The amount of change; 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:

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

[0057]

[0058] in, is the uncertainty parameter to be identified, i.e., the equivalent support state parameter in step S1; is the observed data, including the slip consistency metric χ corresponding to the multi-domain simulation data and the slip consistency metric γ corresponding to the multi-domain experimental data; is the prior probability density function; is the posterior probability density function; ι is the evidence; is a likelihood function, which is designed as a combination of the coherence function and the Pearson correlation coefficient of the slip consistency metric corresponding to the multi-domain simulation data and the multi-domain experimental data, satisfying the following:

[0059]

[0060] in, is the coherence function ε corresponding to the slip consistency metric χ and γ χγ The likelihood function of ; is the Pearson correlation coefficient ρ corresponding to the slip consistency metric χ and γ χγ Likelihood function of slip consistency measure χ and coherence function ε of γ χγ The calculation is as follows:

[0061]

[0062] in, is the autocorrelation function of the slip consistency metric χ of multi-domain simulation data; is the autocorrelation function of the slip consistency metric γ of multi-domain experimental data; is the cross-correlation function of the slip consistency metrics χ and γ corresponding to the multi-domain simulation data and the multi-domain experimental data; ν is the frequency; the Pearson correlation coefficient ρ of the 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 is the standard deviation of the slip consistency metric χ for multi-domain simulation data; σ γ is the standard deviation of the slip consistency metric γ of the multi-domain experimental data; t is time; further, the coherence function ε χγ The likelihood function Satisfy the following:

[0065]

[0066] Among them, ψ τ 1-ε χγ The standard deviation of; exp(·) is the exponential function; similarly, the Pearson correlation coefficient ρ χγ The likelihood function Satisfy the following:

[0067]

[0068] Among them, δ τ =1-ρ χγ The standard deviation of

[0069] Step S4.2: Taking the maximum value of the posterior probability density distribution function of the equivalent support state parameters obtained in step S4.1 as the identification result of the equivalent support state parameters Satisfy the following:

[0070]

[0071] Step S4.3: The identified flexible support state parameters Substitute the rotor system thermal-fluid-solid coupling simulation model established in step S2 to obtain the slip rate curve under different time-varying working conditions, which is the rotor system slip twin simulation result.

[0072] Beneficial effects:

[0073] (1) The present invention can obtain reliable twin simulation results of the slip of the flexible support-rotor system, and simultaneously realize the construction of multi-domain slip information consistency measurement indicators, flexible support parameter uncertainty analysis and thermal-fluid-solid coupling simulation in a unified framework, providing rich data support for slip mechanism analysis, diagnosis prediction and traceability control research;

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

[0075] (3) On the basis of a unified framework, the uncertainty of the state parameters of the flexible support assembly is accurately described based on the cross-correlation Bayesian algorithm. The likelihood function of the cross-correlation Bayesian is designed as a combination of the coherence function and the Pearson correlation coefficient of the slip consistency metric 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 the time series distribution of the consistency metric, respectively, the cross-correlation Bayesian algorithm can comprehensively measure the consistency of the multi-domain slip simulation data and the multi-domain slip experimental data from the perspective of the frequency domain and the time domain, and thus obtain the accurate state parameters of the flexible support assembly of the rotor system.

[0076] (4) The coupled simulation of rotor dynamics and thermal elastic-hydrodynamic lubrication is realized, breaking the situation where the two theories are analyzed independently in their respective fields. A slip prediction model of the flexible support-rotor system considering the lubrication effect and rotor characteristics with high accuracy is established. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

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

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

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

[0082] Figure 6 This is a diagram of the thermal-fluid-solid coupling simulation process of the rotor system in an embodiment of the present invention;

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

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

[0085] Fig. 9 is a curve diagram showing the variation of the maximum oil film temperature with the rotation speed of the rotor system under different lubricating oil viscosities in an embodiment of the present invention;

[0086] Fig.10is a curve diagram showing the variation of the minimum oil film thickness with the rotation speed of the rotor system under different radial loads in an embodiment of the present invention;

[0087] Fig.11 is a curve diagram showing the variation of the maximum oil film pressure with the rotation speed of the rotor system under different radial loads in an embodiment of the present invention;

[0088] Fig.12 is a curve diagram showing the variation of the maximum oil film temperature with the rotation speed of the rotor system under different radial loads in an embodiment of the present invention;

[0089] Fig.13 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] Fig.14 This is a torque simulation data diagram collected based on the thermal-fluid-solid coupling simulation model of the rotor system in an embodiment of the present invention;

[0091] Fig.15 This is a diagram of rotor deflection simulation data collected based on a thermal-fluid-solid coupling simulation model of a rotor system in an embodiment of the present invention;

[0092] Fig.16 This is a diagram of vibration acceleration simulation data collected based on a thermal-fluid-solid coupling simulation model of a rotor system in an embodiment of the present invention;

[0093] Fig.17 This is a torque simulation data diagram collected based on a rotor system slip test bench in an embodiment of the present invention;

[0094] Fig.18 This is a diagram of rotor deflection simulation data collected based on a rotor system slip test bench in an embodiment of the present invention;

[0095] Fig.19 This is a diagram of vibration acceleration simulation data collected based on a rotor system slip test bench in an embodiment of the present invention;

[0096] Fig. 20 This is a diagram showing the slip sensitivity analysis results of the time-frequency statistical characteristics of multi-domain information in an embodiment of the present invention;

[0097] Fig.21 It is a posterior probability density distribution function diagram of the proportional coefficient of the reference value of the equivalent support state parameter based on the cross-correlation Bayesian algorithm in the embodiment of the present invention;

[0098] Fig. 22 A slip rate curve diagram collected based on a flexible support-rotor system slip test bench in an embodiment of the present invention;

[0099] Fig.23 It is a slip rate curve obtained based on the thermal-fluid-solid coupling simulation model of the rotor system in an embodiment of the present invention. DETAILED DESCRIPTION

[0100] The present invention will be further described below in conjunction with the accompanying drawings.

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

[0102] Step S1, respectively establish the finite element model of the rotor system shaft and bearing, and equate the flexible support components such as the flexible bearing seat and the flexible coupling to the spring damping unit. The equivalent spring damping unit is as follows: Figure 3 As shown in the figure; based on the static analysis, the equivalent support state parameter benchmark value is obtained, and then the rotor system slip dynamics simulation model considering the flexible support state is obtained; among them, the static analysis results of the flexible bearing seat are shown in the figure Figure 4 As shown in the figure, the static analysis results of the flexible coupling are as follows Figure 5 shown.

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

[0104] Step S1.1, respectively establish the finite element model of the shaft and bearing in the flexible support-rotor system slip test bench, and further perform modal test and model correction on the shaft to obtain the modal frequency τ of the shaft S 、Damping π S and the stiffness parameter κ S ; It is necessary to ensure that the model correction accuracy of the axis meets the modal confidence criteria MAC of each modal vibration mode ij is greater than 85%, the modal assurance criterion is calculated as follows:

[0105]

[0106] in, is the correlation coefficient between the i-th experimental modal vibration shape and the j-th finite element simulation model modal vibration shape of the shaft in the flexible support-rotor system slip test bench; is the i-th experimental modal vibration shape of the shaft in the flexible support-rotor system slip test bench; is the j-th order simulation mode vibration shape of the shaft in the flexible support-rotor system slip test bench; T is the conjugate transpose;

[0107] Step S1.2, the flexible bearing seat in the flexible support-rotor system slip test bench is equivalent to two sets of spring damping units perpendicular to the horizontal and vertical directions in the axis plane, and the equivalent damping is expressed as The equivalent stiffness is expressed as The flexible coupling in the flexible support-rotor system slip test bench is equivalent to three sets of spring damping units along the axial direction, the horizontal direction perpendicular to the axis plane, and the vertical direction. The equivalent damping is expressed as The equivalent stiffness is expressed as Further based on the static analysis, the stiffness damping parameter value of the equivalent spring damping unit is obtained and used as the reference value of the equivalent support state parameter; the reference value of the equivalent support state parameter of the obtained flexible support component is shown in Table 1:

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

[0109]

[0110]

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

[0112] Step S2, based on the rotor system slip dynamics simulation model considering the flexible support state obtained in step S1 and the thermoelastic-hydrodynamic lubrication theory, analyzing the influence of lubrication state parameters on slip, further constructing a rotor system thermal-fluid-solid coupling simulation model considering the flexible support state;

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

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

[0115]

[0116] Among them, h is the oil film thickness; p is the oil film pressure; η is the viscosity of the lubricating oil; ρ is the density of the lubricating oil; U is the entrainment velocity; x and y are the coordinates of the width and length of the oil film; the calculation process of the energy equation in the thermal elastic hydrodynamic lubrication theory is as follows:

[0117]

[0118] Among them, c ρis the constant pressure specific heat capacity; K is the heat transfer 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 the thermoelastic 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 are the curvature radii of the bearing and the oil film at the contact point along the x and y directions respectively; the calculation process of the viscosity-pressure-viscosity-temperature equation in the thermoelastic-hydrodynamic lubrication theory is as follows:

[0121]

[0122] Where T0 is the initial temperature; η0 is the viscosity of the lubricating oil corresponding to temperature T0; the calculation process of the density pressure-density temperature equation in the thermoelastic 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 slip dynamics simulation model considering the flexible support state obtained in step S1 and the thermal elastic hydrodynamic lubrication theory of step S2.1, a thermal-fluid-solid simulation is performed to obtain a rotor system thermal-fluid-solid coupling simulation model considering the flexible support state; the thermal-fluid-solid coupling simulation process is as follows: Figure 6 As shown in the figure, it includes two parts: thermal elastohydrodynamic lubrication model and rotor dynamics model. The specific steps are as follows:

[0126] First, the initial oil film pressure, oil film thickness and oil film temperature parameters are set, and the mechanical parameters and motion parameters of the contact micro-area parameters obtained based on the dynamic simulation model are imported; secondly, the oil film pressure is calculated using the multi-grid 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 realize the thermal-fluid-solid coupling simulation;

[0127] Specifically, the comprehensive 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 jth rolling element in the bearing; cos(·) is the cosine function; K cijK is the contact stiffness between the inner ring of the bearing and the inner ring oil film corresponding to the jth rolling element; cej K is the contact stiffness between the outer ring of the bearing and the outer ring oil film at the jth rolling element; fij K is the contact stiffness between the rolling element and the inner ring oil film at the jth rolling element; fej is the contact stiffness between the rolling element and the outer ring oil film corresponding to the jth 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 thermal-fluid-solid coupling simulation model, the different lubricating oil viscosities (21.3 mm 2 / s, 29.8mm 2 / s、34.3mm 2 / s、41.2mm 2 / s) and different radial loads (0.5kN, 3kN, 5kN, 7kN), the minimum oil film thickness, maximum oil film pressure and maximum oil film temperature change with the rotor system speed are shown in the figure below: Figure 7-Figure 12 The variation curve of the contact stiffness of the rotor system bearing with time considering the lubricating oil film and flexible support is shown in Fig.13 shown.

[0135] Step S3, respectively collecting multi-domain simulation data and multi-domain experimental data under the same time-varying slip working state based on the rotor system thermal-fluid-solid coupling simulation model considering the flexible support state and the flexible support-rotor system slip test bench established in step S2, and further constructing a slip consistency measurement index through time-frequency statistical feature slip sensitivity analysis;

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

[0137] Step S3.1: Based on the rotor system thermal-fluid-solid coupling simulation model considering the flexible support state established in step S2, multi-domain simulation data under the time-varying slip working state is collected, including torque simulation data. Rotor deflection simulation data Vibration acceleration simulation data and slip rate simulation data Collected torque simulation data Rotor deflection simulation data and vibration acceleration simulation data Respectively Figure 14-16 As shown;

[0138] Step S3.2: Collect multi-domain experimental data under time-varying slip working state based on the flexible support-rotor system slip test bench, including torque experimental data Rotor deflection test data Vibration acceleration test data And slip rate experimental data Collected torque test data Rotor deflection test data And vibration acceleration experimental data Respectively Figure 17-Figure 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 Perform time-frequency statistical characteristics slip sensitivity analysis to determine the slip sensitivity statistical characteristics corresponding to multi-domain data; the slip sensitivity analysis process of multi-domain data time-frequency statistical characteristics is as follows:

[0140]

[0141] in, Corresponding to the torque data Ω T The variation range of λ time-frequency statistical characteristics; Corresponding to the rotor deflection data Ω D The variation range of λ time-frequency statistical characteristics; Corresponding to the vibration acceleration data Ω A The variation range of λ time-frequency statistical characteristics; Slip rate data The range of changes; Corresponding to the torque data Ω T The slip sensitivity of the λ time-frequency statistical characteristics; Corresponding to the rotor deflection data Ω D The slip sensitivity of the λ time-frequency statistical characteristics; Corresponding to the vibration acceleration data Ω A The slip sensitivity of the λ time-frequency statistical features of the multi-domain data Ω{Ω T ,Ω D ,Ω A ,Ω S}'s slip sensitivity statistical characteristics The determination process is as follows:

[0142]

[0143] Among them, max{·} is the operation of taking the maximum value; Corresponding to the torque data Ω T Statistical characteristics of slip sensitivity; Corresponding to the rotor deflection data Ω D Statistical characteristics of slip sensitivity; Corresponding to the vibration acceleration data Ω A The time-frequency statistical features used are shown in Table 2:

[0144] Table 2 Time-frequency statistical characteristics

[0145] Serial number feature Serial number feature 1 Mean 11 Maximum 2 Absolute mean 12 Minimum 3 RMS 13 Peak Index 4 Square root amplitude 14 Margin index 5 Peak-to-Peak 15 Waveform indicators 6 variance 16 Pulse Indicator 7 Standard Deviation 17 Center of gravity frequency 8 Skewness 18 RMS frequency 9 Kurtosis 19 Average frequency 10 Energy indicators 20 Frequency variance

[0146] The calculated time-frequency statistical characteristics slip sensitivity analysis results are as follows: Fig. 20 As shown, the torque data Ω can be found T The corresponding slip sensitivity statistical characteristics are root mean square, rotor deflection data Ω D The corresponding slip sensitivity statistical characteristics are variance, vibration acceleration data Ω A The corresponding slip-sensitive statistical feature is the energy index.

[0147] Step S3.4, determining a slip consistency measurement index based on the slip sensitivity statistical features corresponding to the 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] Among them, ω T Torque simulation data The corresponding slip consistency metric weight; ω D is the weight of the slip consistency metric corresponding to the rotor deflection simulation data; ω A Vibration acceleration simulation data The corresponding slip consistency measurement index weights satisfy:

[0151]

[0152] in, and They correspond to the statistical characteristics of slip sensitivity The amount of change; 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 metric of the multi-domain simulation data and the multi-domain experimental data obtained in step S3, the uncertainty of the reference value of the equivalent support state parameter obtained in step S1 is described using the cross-correlation Bayesian algorithm, and the identified flexible support state parameters are substituted into the thermal-fluid-solid coupling simulation model of the rotor system established in step S2 to obtain the slip rate curve under different time-varying working conditions.

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

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

[0157]

[0158] in, is the uncertainty parameter to be identified, i.e., the equivalent support state parameter in step S1; is the observed data, including the slip consistency metric χ corresponding to the multi-domain simulation data and the slip consistency metric γ corresponding to the multi-domain experimental data; is the prior probability density function; is the posterior probability density function; ι is the evidence; is a likelihood function, which is designed as a combination of the coherence function and the Pearson correlation coefficient of the slip consistency metric corresponding to the multi-domain simulation data and the multi-domain experimental data, satisfying the following:

[0159]

[0160] in, is the coherence function ε corresponding to the slip consistency metric χ and γ χγ The likelihood function of ; is the Pearson correlation coefficient ρ corresponding to the slip consistency metric χ and γ χγ Likelihood function of slip consistency measure χ and coherence function ε of γ χγ The calculation is as follows:

[0161]

[0162] in, is the autocorrelation function of the slip consistency metric χ of multi-domain simulation data; is the autocorrelation function of the slip consistency metric γ of multi-domain experimental data; is the cross-correlation function of the slip consistency metrics χ and γ corresponding to the multi-domain simulation data and the multi-domain experimental data; ν is the frequency; the Pearson correlation coefficient ρ of the 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 is the standard deviation of the slip consistency metric χ for multi-domain simulation data; σ γ is the standard deviation of the slip consistency metric γ of the multi-domain experimental data; t is time; further, the coherence function ε χγ The likelihood function Satisfy the following:

[0165]

[0166] Among them, ψ τ 1-ε χγ The standard deviation of; exp(·) is the exponential function; similarly, the Pearson correlation coefficient ρ χγ The likelihood function Satisfy the following:

[0167]

[0168] Among them, δ τ =1-ρ χγ The standard deviation of

[0169] Step S4.2: Taking the maximum value of the posterior probability density distribution function of the equivalent support state parameters obtained in step S4.1 as the identification result of the equivalent support state parameters Satisfy the following:

[0170]

[0171] The posterior probability density distribution function of the reference value proportional coefficient of the equivalent support state parameter is further described based on the cross-correlation Bayesian algorithm as follows: Fig.21 It is worth pointing out that Fig.21 What is shown is the proportional coefficient of the reference value of the equivalent support state parameter. The product of the proportional coefficient and the reference 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, is the proportional coefficient of the reference value of the equivalent support state parameter obtained based on the cross-correlation Bayesian algorithm. The final identification value of the equivalent support state parameter of the flexible support component considering uncertainty is shown in Table 3.

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

[0175]

[0176] Step S4.3: The identified flexible support state parameters in Table 3 are Substitute the rotor system thermal-fluid-solid coupling simulation model established in step S2 to obtain the slip rate curve under different time-varying working conditions, which is the rotor system slip twin simulation result. Fig. 22 The slip rate curve collected based on the flexible support-rotor system slip test bench is shown. Fig.23 The slip rate curve obtained based on the thermal-fluid-solid coupling simulation model of the rotor system is shown, and it can be found that the slip test and simulation results are highly consistent, which fully verifies the effectiveness and practicality of the present invention.

[0177] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A rotor system slip twin simulation method considering the uncertainty of flexible support, characterized in that: The following steps are involved: Step S1, respectively establishing finite element models of the rotor system shaft and bearing, equating the flexible support assembly to a spring damping unit, obtaining a reference value of an equivalent support state parameter based on static analysis, and obtaining a rotor system slip dynamics simulation model considering a flexible support state; Step S2, analyzing the influence of lubrication state parameters on slip based on the rotor system slip dynamics simulation model and the thermoelastic-hydrodynamic lubrication theory, and further constructing a rotor system thermal-fluid-solid coupling simulation model considering the flexible support state; Step S3, respectively collecting multi-domain simulation data and multi-domain experimental data based on the rotor system thermal-fluid-solid coupling simulation model and the flexible support-rotor system slip test bench under the same time-varying slip working state, and constructing a slip consistency measurement index through time-frequency statistical feature slip sensitivity analysis; Step S4, based on the slip consistency metric, use the cross-correlation Bayesian algorithm to describe the uncertainty of the reference value of the equivalent support state parameter obtained in step S1, substitute the identified flexible support state parameters into the thermal-fluid-solid coupling simulation model of the rotor system established in step S2 to obtain the slip rate curve under different time-varying working conditions.

2. A rotor system slip twin simulation method considering the uncertainty of flexible support according to claim 1, characterized in that: Step S1 is specifically as follows: Step S1.1, respectively establish the finite element model of the shaft and bearing in the flexible support-rotor system slip test bench, perform modal test and model correction on the shaft to obtain the modal frequency τ of the shaft S 、Damping π S and the stiffness parameter κ S ; In order to ensure that the model correction accuracy of the shaft meets the modal confidence criteria MAC of each modal vibration mode ij is greater than the set value, the modal confidence criterion is calculated as follows: in, is the correlation coefficient between the i-th experimental modal vibration shape and the j-th finite element simulation model modal vibration shape of the shaft in the flexible support-rotor system slip test bench; is the i-th experimental modal vibration shape of the shaft in the flexible support-rotor system slip test bench; is the j-th simulation mode shape of the shaft in the flexible support-rotor system slip test bench; T is the conjugate transpose; Step S1.2, the flexible bearing seat in the flexible support-rotor system slip test bench is equivalent to two sets of spring damping units perpendicular to the horizontal and vertical directions in the axis plane, and the equivalent damping is expressed as The equivalent stiffness is expressed as The flexible coupling in the flexible support-rotor system slip test bench is equivalent to three sets of spring damping units along the axial direction, the horizontal direction perpendicular to the axial plane, and the vertical direction. The equivalent damping is expressed as The equivalent stiffness is expressed as Based on static analysis, the stiffness and damping parameter values ​​of the equivalent spring damping unit are obtained and used as the reference values ​​of the equivalent support state parameters; Step S1.3, after assembling the finite element model of the shaft and bearing in the flexible support-rotor system slip test bench, and the equivalent support state parameter reference values ​​of flexible support components such as the flexible bearing seat and the flexible coupling, a rotor system slip dynamics simulation model considering the flexible support state is obtained.

3. The rotor system slip twin simulation method considering the uncertainty of flexible support according to claim 1 is characterized in that: Step S2 is specifically as follows: Step S2.1, based on the thermoelastic-hydrodynamic lubrication theory, the influence of lubrication state parameters on the slippage of the flexible support-rotor system slippage test bench is analyzed; the thermoelastic-hydrodynamic lubrication theory includes the Reynolds equation, the energy equation, the film thickness equation, the viscosity-pressure-viscosity-temperature equation and the density-pressure-density-temperature equation. The calculation process of the Reynolds equation in the thermoelastic-hydrodynamic lubrication theory is as follows: Among them, h is the oil film thickness; p is the oil film pressure; η is the viscosity of the lubricating oil; ρ is the density of the lubricating oil; U is the entrainment velocity; x and y are the coordinates of the width and length of the oil film; the calculation process of the energy equation in the thermal elastohydrodynamic lubrication theory is as follows: Among them, c ρ is the constant pressure specific heat capacity; K is the heat transfer 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 the thermoelastic 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 are the curvature radii of the bearing and the oil film at the contact point along the x and y directions respectively; the calculation process of the viscosity-pressure-viscosity-temperature equation in the thermoelastic-hydrodynamic lubrication theory is as follows: Where T0 is the initial temperature; η0 is the viscosity of the lubricating oil corresponding to temperature T0; the calculation process of the density pressure-density temperature equation in the thermoelastic 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 slip dynamics simulation model and the thermal elastic hydrodynamic lubrication theory of step S2.1, a thermal-fluid-solid simulation is performed to obtain a rotor system thermal-fluid-solid coupling simulation model that takes into account the flexible support state.

4. The rotor system slip twin simulation method considering the uncertainty of flexible support according to claim 3 is characterized in that: The specific steps of the thermal-fluid-solid coupling simulation include: First, the initial oil film pressure, oil film thickness and oil film temperature parameters are set, and the mechanical parameters and motion parameters of the contact micro-area parameters obtained based on the dynamic simulation model are imported; secondly, the oil film pressure is calculated using the multi-grid 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 realize the thermal-fluid-solid coupling simulation; Comprehensive 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 jth rolling element in the bearing; cos(·) is the cosine function; K cij K is the contact stiffness between the inner ring of the bearing and the inner ring oil film corresponding to the jth rolling element; cej K is the contact stiffness between the outer ring of the bearing and the outer ring oil film at the jth rolling element; fij K is the contact stiffness between the rolling element and the inner ring oil film at the jth rolling element; fej is the contact stiffness between the rolling element and the outer ring oil film corresponding to the jth rolling element; Lubricating oil film stiffness K μ The calculation is as follows: Bearing contact stiffness The calculation is as follows:

5. The rotor system slip twin simulation method considering the uncertainty of flexible support according to claim 1, characterized in that: Step S3 is specifically as follows: Step S3.1: Collect multi-domain simulation data under time-varying slip working state based on the thermal-fluid-solid coupling simulation model of the rotor system, including torque simulation data Rotor deflection simulation data Vibration acceleration simulation data and slip rate simulation data Step S3.2: Collect multi-domain experimental data under time-varying slip working state based on the flexible support-rotor system slip test bench, including torque experimental data Rotor deflection test data Vibration acceleration test data And slip rate experimental data Step S3.3: Based on the multi-domain simulation data And the multi-domain experimental data Perform time-frequency statistical characteristics slip sensitivity analysis to determine the slip sensitivity statistical characteristics corresponding to multi-domain data; the slip sensitivity analysis process of multi-domain data time-frequency statistical characteristics is as follows: in, Corresponding to the torque data Ω T The variation range of the λ time-frequency statistical characteristics; Corresponding to the rotor deflection data Ω D The variation range of λ time-frequency statistical characteristics; Corresponding to the vibration acceleration data Ω A The variation range of the λ time-frequency statistical characteristics; Slip rate data The range of changes; Corresponding to the torque data Ω T The slip sensitivity of the λ time-frequency statistical characteristics; Corresponding to the rotor deflection data Ω D The slip sensitivity of the λ time-frequency statistical characteristics; Corresponding to the vibration acceleration data Ω A The slip sensitivity of the λ time-frequency statistical features of the multi-domain data Ω{Ω T ,Ω D ,Ω A ,Ω S Statistical characteristics of slip sensitivity The determination process is as follows: Among them, max{·} is the operation of taking the maximum value; Corresponding to the torque data Ω T Statistical characteristics of slip sensitivity; Corresponding to the rotor deflection data Ω D Statistical characteristics of slip sensitivity; Corresponding to vibration acceleration data} A Statistical characteristics of slip sensitivity; Step S3.4, determining a 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: Among them, ω T Torque simulation data The corresponding slip consistency metric weight; ω D is the weight of the slip consistency metric corresponding to the rotor deflection simulation data; ω A Vibration acceleration simulation data The corresponding slip consistency measurement index weights satisfy: in, and They correspond to the statistical characteristics of slip sensitivity The amount of change; similarly, multi-domain experimental data The construction process of the slip consistency metric γ is as follows:

6. The rotor system slip twin simulation method considering the uncertainty of flexible support according to claim 1, characterized in that: Step S4 is specifically as follows: Step S4.1: Based on the slip consistency metric of the multi-domain simulation data and the multi-domain experimental data, the uncertainty of the reference value of the equivalent support state parameter obtained in step S1 is described using the cross-correlation Bayesian algorithm; the cross-correlation Bayesian calculation is as follows: in, is the uncertainty parameter to be identified, i.e., the equivalent support state parameter in step S1; is the observed data, including the slip consistency metric χ corresponding to the multi-domain simulation data and the slip consistency metric γ corresponding to the multi-domain experimental data; is the prior probability density function; is the posterior probability density function; l is the evidence; is a likelihood function, which is designed as a combination of the coherence function and the Pearson correlation coefficient of the slip consistency metric corresponding to the multi-domain simulation data and the multi-domain experimental data, satisfying the following: in, is the coherence function ε corresponding to the slip consistency metric χ and γ χγ The likelihood function of ; is the Pearson correlation coefficient ρ corresponding to the slip consistency metric χ and γ χγ Likelihood function of slip consistency measure χ and coherence function ε of γ χγ The calculation is as follows: in, is the autocorrelation function of the slip consistency metric χ of multi-domain simulation data; is the autocorrelation function of the slip consistency metric γ of multi-domain experimental data; is the cross-correlation function of the slip consistency metrics χ and γ corresponding to the multi-domain simulation data and the multi-domain experimental data; ν is the frequency; the Pearson correlation coefficient ρ of the 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 is the standard deviation of the slip consistency metric χ for multi-domain simulation data; σ γ is the standard deviation of the slip consistency metric γ of the multi-domain experimental data; t is time; further, the coherence function ε χγ The likelihood function Satisfy the following: Among them, ψ τ 1-ε χγ The standard deviation of; exp(·) is the exponential function; similarly, the Pearson correlation coefficient ρ χγ The likelihood function Satisfy the following: Among them, δ τ 1-ρ χγ The standard deviation of Step S4.2: Taking the maximum value of the posterior probability density distribution function of the equivalent support state parameters obtained in step S4.1 as the identification result of the equivalent support state parameters Satisfy the following: Step S4.3: The identified flexible support state parameters Substitute the rotor system thermal-fluid-solid coupling simulation model established in step S2 to obtain the slip rate curve under different time-varying working conditions, which is the rotor system slip twin simulation result.

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