Axis center trajectory analysis method and system for time-varying uncertain sliding bearing rotor system

Abstract

The present invention provides a method and system for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system. Applied to the technical field of non-random vibration analysis, the method includes: obtaining the time-varying uncertainty parameters and parameter intervals of the oil film based on the actual operating conditions of the sliding bearing, and calculating the median function of the axis trajectory of the sliding bearing according to the median of the oil film parameters; constructing a multidimensional ellipsoid uncertainty domain based on the time-varying uncertainty parameters of the oil film, sampling the axis trajectory sample set in the multidimensional ellipsoid uncertainty domain, and obtaining the axis trajectory radius function of the sliding bearing based on the geometric characteristics of the ellipse that envelops the sample points; obtaining the upper and lower boundaries of the axis trajectory of the sliding bearing based on the median function of the axis trajectory of the sliding bearing and the axis trajectory radius function of the sliding bearing. In this way, the present invention measures the time-varying uncertainty through a non-probabilistic ellipsoid model, effectively realizes the non-random axis trajectory analysis of the sliding bearing-rotor system, and realizes a non-random trajectory analysis process with few samples and high efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of non-random vibration analysis, and in particular to a method and system for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system. Background Art

[0002] Sliding bearings are the most promising support design scheme for the transmission shaft system of high-power wind turbine gearboxes. Sliding bearings bear strong sudden and heavy loads transmitted by wind turbine gearboxes, presenting a "oil film + contact bearing" state of non-continuous fluids such as large deformation of fixed bearings, oil film slippage at the interface of moving tilted journals, cavitation and contact, etc., rough peak contact, surface wear, rapid increase in friction resistance and lubricating oil temperature rise, change in lubricant viscosity, lubrication failure, and even surface melting, and sticking to each other. As the degree of bearing wear increases, the oil film thickness, pressure, rough peak contact pressure and surface morphology all change accordingly. The oil film parameters such as the radial clearance of the sliding bearing and the viscosity of the lubricating oil have time-varying effects. The oil film excitation load associated with the sliding bearing is also a dynamic uncertainty that changes with time. There is no definite change form and no definite change law, so the axis trajectory generated is an unpredictable non-deterministic process. Lubrication monitoring based on axis trajectory is difficult to accurately estimate. Due to the limitations of time and experimental costs, it is difficult to obtain the probability density function of time-varying uncertain variables such as oil film parameters and axis trajectory, making it difficult to implement non-random axis trajectory analysis based on probability theory. The interval-based uncertainty analysis method expresses the uncertainty of parameters in the form of intervals, but does not require the specific probability density within the parameter value interval. It gradually shows certain advantages in terms of convenience and economy.

[0003] The interval process model derived from the non-probabilistic interval method measures the uncertainty of time-varying parameters in the form of upper and lower boundaries; at any time, the uncertainty of the parameter belongs to a bounded closed interval and is an interval variable that varies with time. The non-probabilistic ellipsoid model is used to quantify the correlation between the mutual influence of time-varying parameters. As a measurement model for time-varying uncertainty parameters, the main characteristic description of the interval process is the upper and lower boundary function and the correlation function. Compared with the random process model, the interval process model is relatively rough in measuring time-varying uncertain parameters and does not involve specific probability measurement information. Therefore, the required parameter observation data is relatively small.

[0004] Therefore, there is an urgent need for a technical solution that can analyze the axis trajectory under non-random axis motion conditions. Summary of the invention

[0005] The present invention provides a method and system for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system. The size and correlation of the time-varying uncertainty of parameters are described by the size and shape of a multi-dimensional ellipsoid, and the upper and lower boundaries of the axis trajectory are finally obtained, which at least solves the technical problems of the existing sliding bearing non-random axis trajectory analysis method having a high degree of dependence on experimental samples and poor analysis effect.

[0006] According to a first aspect of the present invention, there is provided a method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system, comprising the following steps:

[0007] The time-varying uncertainty parameters and parameter intervals of the oil film are obtained based on the actual operating conditions of the sliding bearing, and the median function of the axis trajectory of the sliding bearing is calculated based on the median value of the oil film parameters.

[0008] A multidimensional ellipsoid uncertainty domain based on the time-varying uncertainty parameters of the oil film is constructed, and the axis trajectory sample set is obtained by sampling and calculating in the multidimensional ellipsoid uncertainty domain. The axis trajectory radius function of the sliding bearing is obtained based on the geometric characteristics of the ellipse that envelops the sample points.

[0009] Based on the median function of the sliding bearing axis trajectory and the radius function of the sliding bearing axis trajectory, the upper and lower boundaries of the sliding bearing axis trajectory are obtained to complete the axis trajectory analysis.

[0010] According to the above aspects and any possible implementation, an implementation is further provided, wherein the process of obtaining the time-varying uncertainty parameter and parameter interval of the oil film based on the actual operating condition of the sliding bearing, and calculating the median function of the axis trajectory of the sliding bearing according to the median of the oil film parameter is:

[0011] The time-varying uncertainty parameters and parameter ranges of the oil film are obtained based on the actual operating conditions of the sliding bearing; the Reynolds equation reflecting the relationship between the oil film parameters and the oil film force is constructed based on the flow principle of the lubricating oil in the clearance of the sliding bearing, and the oil film force corresponding to the oil film parameters is obtained based on the Reynolds equation;

[0012] Based on the Reynolds equation, the transfer matrix of the sliding bearing shaft system is established by using the Riccati-Newmark acceleration transfer matrix method and the Newmark acceleration method;

[0013] The median of the oil film parameter interval is selected and substituted into the transfer matrix to calculate the axis trajectory of the sliding bearing-rotor system, and recorded as the median function of the axis trajectory of the sliding bearing.

[0014] According to the above aspects and any possible implementation, an implementation is further provided, wherein the Reynolds equation is specifically:

[0015] ;

[0016] Where h is the oil film thickness; η is the lubricating oil viscosity; U j is the journal speed, U b is the bearing speed; P is the oil film pressure, x and y are the journal center displacements, and the oil film pressure is integrated on the contact surface between the oil film and the journal to obtain the oil film force. For time.

[0017] According to the above aspects and any possible implementation, an implementation is further provided, wherein the construction process of the multidimensional ellipsoid uncertainty domain is as follows:

[0018] Collect a number of samples according to the interval variable of the oil film time-varying uncertainty parameter;

[0019] By enveloping all samples and constructing a covariance matrix, the covariance matrix is ​​inverted to obtain a feature matrix;

[0020] A multi-dimensional ellipsoid uncertainty domain of oil film parameters is constructed based on the characteristic matrix.

[0021] According to the above aspects and any possible implementation, an implementation is further provided, wherein the process of enveloping all samples, constructing a covariance matrix, and performing inversion to obtain a feature matrix is ​​as follows:

[0022] Construct an ellipse with the minimum area that envelops all samples and satisfies the edge area conditions;

[0023] The correlation coefficient of the interval variable of the oil film time-varying uncertainty parameter is calculated based on the geometric characteristics of the ellipse;

[0024] A covariance function is calculated based on the correlation coefficient and different interval variables, and a covariance matrix is ​​constructed based on the covariance function.

[0025] According to the above aspects and any possible implementation, an implementation is further provided, wherein the process of sampling and calculating the axis trajectory sample set in the oil film parameter multidimensional ellipsoid uncertainty domain, and obtaining the axis trajectory radius function of the sliding bearing based on the geometric characteristics of the ellipse of the envelope sample points is:

[0026] Sampling in the oil film parameter multidimensional ellipsoid uncertainty domain to obtain a sample set, and substituting the sample set into the transfer matrix to calculate and obtain a plurality of groups of axis trajectory samples;

[0027] Extract the values ​​of any axis trajectory sample at different times and map them to the plane to obtain the plane sample points;

[0028] Count the plane sample points of all axis trajectory samples to obtain a sample set;

[0029] Constructing a minimum area ellipse that includes the sample set and satisfies the edge interval condition, and calculating the axis trajectory covariance function based on the geometric characteristics of the ellipse;

[0030] The axis trajectory radius function is calculated based on the axis trajectory covariance function.

[0031] According to the above aspects and any possible implementation, an implementation is further provided, wherein the upper and lower boundaries of the axis trajectory of the sliding bearing are obtained based on the median function of the axis trajectory of the sliding bearing and the radius function of the axis trajectory of the sliding bearing, and the process of completing the axis trajectory analysis is:

[0032] Construct the motion differential equations of sliding shaft system parameters and oil film excitation loads;

[0033] The oil film excitation load is expressed by using an interval orthogonal series expansion method to obtain a load function relationship between the oil film excitation load and a median function and a radius function of the time-varying uncertain oil film excitation load;

[0034] Combining the motion differential equation and the load function relationship, a trajectory function relationship between the sliding bearing axis trajectory and the sliding bearing axis trajectory median function and the sliding bearing axis trajectory radius function is obtained;

[0035] The upper and lower boundaries of the axis trajectory are calculated based on the trajectory function relationship.

[0036] According to the above aspects and any possible implementation, an implementation is further provided, wherein the upper and lower boundaries of the axis trajectory are specifically:

[0037] ;

[0038] in, is the median function of the axis trajectory of the sliding bearing, is the radius function of the sliding bearing axis trajectory, is the total response of the axis trajectory of the wind turbine gearbox transmission shaft system response boundary.

[0039] According to a second aspect of the present invention, there is provided a time-varying uncertain sliding bearing rotor system axis trajectory analysis system, comprising: a sliding bearing axis trajectory median function calculation module, a sliding bearing axis trajectory radius function calculation module and an axis trajectory analysis module;

[0040] The sliding bearing axis trajectory median function calculation module is used to obtain the oil film time-varying uncertainty parameters and parameter intervals based on the actual operating conditions of the sliding bearing, and calculate the sliding bearing axis trajectory median function according to the oil film parameter median;

[0041] The sliding bearing axis trajectory radius function calculation module is used to construct a multi-dimensional ellipsoid uncertainty domain based on the time-varying uncertainty parameters of the oil film, sample and calculate the axis trajectory sample set in the multi-dimensional ellipsoid uncertainty domain, and obtain the sliding bearing axis trajectory radius function based on the geometric characteristics of the ellipse enveloping the sample points;

[0042] The axis trajectory analysis module is used to obtain the upper and lower boundaries of the axis trajectory of the sliding bearing based on the axis trajectory median function of the sliding bearing and the axis trajectory radius function of the sliding bearing, and complete the axis trajectory analysis.

[0043] Compared with the prior art, the present invention has the following technical effects:

[0044] (1) The present invention provides a measurement model for time-varying uncertainty parameters in non-random vibration analysis of sliding bearing-rotor systems using interval processes and non-probability ellipsoids. Its main features describe the upper and lower boundary functions and correlation functions of the axis trajectory. Compared with the probability model, since it does not involve specific probability measurement information, the required parameter sampling data is relatively small. When the sample function data is insufficient, the existing information can be used as effectively as possible, which can greatly reduce the dependence on the test sample size, thereby providing an effective mathematical tool for modeling time-varying uncertainty parameters and corresponding structural uncertainty analysis in the absence of experimental information. It can also effectively reduce the computational scale of non-random axis trajectory analysis and improve computational efficiency, thereby greatly reducing the computational cost of non-random vibration of sliding bearing rotor systems.

[0045] (2) The method for analyzing the axis trajectory of a sliding bearing rotor system using a non-probabilistic ellipsoid model to measure the time-varying uncertainty of the proposed invention can replace the axis trajectory samples with samples of easily measurable time-varying uncertain oil film parameters to obtain the axis trajectory upper and lower boundary functions and correlation functions, thereby realizing the evaluation of the oil film vortex and sliding lubrication state without axis trajectory test samples.

[0046] (3) Based on the interval process model, the present invention transforms the axis trajectory analysis of the time-varying uncertain sliding bearing rotor system from uncertainty analysis to two types of deterministic analysis, thereby enhancing the engineering practicality and extensiveness of non-random vibration analysis.

[0047] It should be understood that the contents described in the summary of the invention are not intended to limit the key or important features of the embodiments of the present invention, nor are they intended to limit the scope of the present invention. Other features of the present invention will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The above and other features, advantages and aspects of the embodiments of the present invention will become more apparent with reference to the following detailed description in conjunction with the accompanying drawings. The accompanying drawings are provided for a better understanding of the present invention and do not constitute a limitation of the present invention. In the accompanying drawings, the same or similar reference numerals represent the same or similar elements, wherein:

[0049] Figure 1 A schematic flow chart of a method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system according to an embodiment of the present invention is shown;

[0050] Figure 2 A schematic diagram of the structure of an ellipsoid correlation model of a method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system according to an embodiment of the present invention is shown;

[0051] Figure 3 A schematic diagram of the structure of a system for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system according to an embodiment of the present invention is shown;

[0052] Figure 4 A schematic diagram showing sample points and correlation between bearing radius clearance and dynamic viscosity according to an embodiment of a method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system according to an embodiment of the present invention is shown;

[0053] Figure 5 A schematic diagram of a set of displacement responses and axis trajectory collected in an oil film uncertainty region according to an embodiment of a method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system according to an embodiment of the present invention is shown;

[0054] Figure 6 A schematic diagram of the radius function of the random x, y displacement response of the sliding bearing and the axis trajectory of the rotor system of a time-varying uncertain sliding bearing according to an embodiment of the present invention is shown;

[0055] Figure 7 A schematic diagram of the displacement response and axis center trajectory interval under time-varying uncertain oil film parameters according to an embodiment of a method for analyzing the axis center trajectory of a time-varying uncertain sliding bearing rotor system according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0057] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0058] Studying the stability of the shaft structure to non-random oil film excitation based on the axis trajectory can effectively control the oil film vortex and evaluate the lubrication state of the sliding bearing. It is a development trend of the wind power industry to use sliding bearings instead of rolling bearings in high-power wind turbine gearboxes. Sliding bearings bear non-torsional loads such as the yaw torque transmitted by the wind turbine gearbox, the weight of the wind wheel and its unbalanced load, and strong sudden overloads caused by frequent start-stop impacts. The mixed lubrication state of bearing deformation and wear and rough peak contact causes the friction resistance and lubricating oil temperature to rise rapidly, changing the viscosity of the lubricant, lubrication failure, and even surface melting, and mutual sticking. The oil film parameters such as the radial clearance of the sliding bearing and the viscosity of the lubricating oil have time-varying effects, and the oil film excitation load of the sliding bearing associated with it is also a dynamic uncertainty that changes with time. There is no definite change form and no definite change law, so the axis trajectory generated is an unpredictable non-deterministic process. The probability measurement based on the probability distribution function requires a large number of samples of uncertain parameters, which is difficult or costly to obtain. Different from probability density information, it is usually relatively easy to define the value range of time-varying uncertain parameters such as radial clearance of sliding bearings and viscosity of lubricating oil, and the required parameter sample size is also relatively small. In non-random vibration analysis, the uncertainty of parameters is expressed in the form of intervals, and there is no requirement for the specific probability density within the parameter value interval. The present invention proposes a non-random axis trajectory analysis method for sliding bearing-rotor systems, which measures time-varying uncertain oil film parameters and axis trajectories with an interval process model. The uncertain parameters are represented by interval variables at any time, and the correlation between interval variables at different times is described by an ellipse. The dynamic uncertainty is represented in the form of upper and lower boundary functions, which effectively avoids the acquisition of a large number of time history sample functions, avoids the introduction of probability characteristics, and can reduce problems such as high cost.

[0059] The present invention measures the time-varying uncertainty existing in the axis trajectory analysis process based on an interval process model and a multidimensional ellipsoid model, and converts the non-random axis trajectory analysis into two types of deterministic axis trajectory calculations, namely, a median function and a radius function. One type is to calculate the median function of the axis trajectory according to the median of interval variables such as the radial clearance of the sliding bearing and the viscosity of the lubricating oil; the other type is to sample in the multidimensional ellipsoid uncertainty domain of interval variables such as the radial clearance of the sliding bearing and the dynamic viscosity, calculate the axis trajectory response sample set, and obtain the radius function of the axis trajectory based on the geometric characteristics of the ellipse that envelops the sample points; finally, the upper and lower boundary functions of the axis trajectory are calculated according to the obtained median function and radius function of the axis trajectory.

[0060] This method does not involve specific probability measurement information, so the required parameter sampling data is relatively small. When the sample function data is insufficient, the existing information can be used as effectively as possible, which can greatly reduce the dependence on the sample size, thereby providing an effective mathematical tool for modeling time-varying uncertainty parameters and corresponding structural uncertainty analysis in the absence of experimental information. The method of the present invention broadens the scope of non-random vibration analysis.

[0061] Reference Figure 1 As shown, this embodiment provides a method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system, comprising the following steps:

[0062] S101. Obtaining the time-varying uncertainty parameters and parameter intervals of the oil film based on the actual operating conditions of the sliding bearing, and obtaining the median function of the axis trajectory of the sliding bearing according to the median calculation of the oil film parameters.

[0063] In this embodiment, the magnitude of the oil film force to which the lubricating oil in the sliding bearing flows in the bearing gap is affected by the oil film thickness, the viscosity of the lubricating oil, etc. The radial clearance of the sliding bearing, as the initial value of the oil film thickness, is affected by processing and bearing wear, and is often a time-varying uncertain parameter. The change in lubricating oil viscosity with temperature is also often a time-varying uncertain parameter. These time-varying uncertain parameters make the sliding oil film excitation load have the characteristic of changing with time, but there is no definite form of change, that is, there is no definite change law for each measurement of it. That is, the change process of the oil film excitation load cannot be described by a deterministic function about time.

[0064] For oil film excitation load, the oil film force , , is the journal center displacement and speed The complex nonlinear function of the sliding bearing. When the external force on the journal of the sliding bearing changes at different instants, the axis trajectory at the journal of the sliding bearing will also change. The flow of lubricating oil in the bearing gap obeys the following Reynolds equation:

[0065] (1);

[0066] Where h is the oil film thickness; η is the lubricating oil viscosity; U j is the journal speed, U b is the bearing speed; P is the oil film pressure. The oil film pressure of the sliding bearing is regarded as the superposition of the pressure generated by the dynamic pressure effect and the extrusion effect. The oil film force is obtained by integrating the oil film pressure on the contact surface between the oil film and the journal.

[0067] The commonly used Riccati-Newmark acceleration transfer matrix method uses the Newmark acceleration method to establish the transfer matrix of the shaft system, and uses the Taylor series to estimate the displacement and velocity of the sliding bearing axis at the next moment. The Reynolds equation shown in formula (1) establishes the sliding bearing point transfer matrix to realize the calculation of the axis trajectory of the sliding bearing-rotor system.

[0068] From formula (1), it can be seen that the magnitude of the oil film force is affected by the oil film thickness, lubricant viscosity, etc. The radial clearance of the sliding bearing, as the initial value of the oil film thickness, is affected by processing and bearing wear and is often a time-varying uncertain parameter. The change in lubricant viscosity with temperature is also often a time-varying uncertain parameter. These time-varying uncertain parameters make the sliding oil film excitation load have the characteristics of changing with time, but there is no definite change form, that is, there is no definite change law for each measurement of it. That is, the change process of the oil film excitation load cannot be described by a deterministic function about time.

[0069] S102, constructing a multidimensional ellipsoid uncertainty domain based on the time-varying uncertainty parameters of the oil film, sampling and calculating the axis trajectory sample set in the multidimensional ellipsoid uncertainty domain, and obtaining the axis trajectory radius function of the sliding bearing based on the geometric characteristics of the ellipse that envelops the sample points.

[0070] For deterministic oil film excitation, the differential equation of motion of the wind turbine gearbox transmission shaft system is:

[0071] (2);

[0072] in, , and denote the mass, damping and stiffness matrices of the shaft system respectively, , , are the acceleration, velocity and displacement responses of the axis system, is the oil film excitation load, the sliding bearing supports and lubricates the rotor, and t is the time.

[0073] When the oil film excitation load is uncertain and described by an interval process, i.e. , and are the lower and upper boundary functions of the time-varying uncertain oil film excitation load, respectively. The autocorrelation coefficient function is is the oil film excitation load set, where Represents the oil film excitation load set exist and The autocorrelation coefficient function at two moments. The time-varying uncertain oil film excitation load is represented by the interval orthogonal series expansion method:

[0074] (3);

[0075] in, and They are respectively the time-varying uncertain oil film excitation load The median function and radius function of is a standard interval variable, satisfying , and The autocorrelation coefficient function The eigenvalues ​​and eigenfunctions of .

[0076] The time-varying uncertain oil film excitation load described by equation (3) is Substituting into the wind turbine gearbox transmission shaft system dynamic differential equation, that is, equation (1), we can get:

[0077] (4);

[0078] In formula (4), only is an interval variable, and , , and All are deterministic functions. The axis trajectory response is determined by the median function of the oil film excitation load Caused by , and the uncertainty of the oil film excitation Caused by .

[0079] According to the linear system superposition principle, the axis trajectory responses caused by them can be processed separately and then superimposed to form the total axis trajectory response of the axis system, that is, .

[0080] For the median function of the oil film excitation load Cause axis trajectory response It can be obtained by the calculation method of the axis trajectory of the sliding bearing-rotor system under deterministic oil film excitation.

[0081] As for the uncertain part of oil film excitation because , and are deterministic functions, Instead, it is recorded as:

[0082] (5);

[0083] When the wind turbine gearbox transmission shaft system is a linear system, the time-varying uncertain oil film excitation load is expressed as , in the form of an infinite series, the axis trajectory response is theoretically It should also be about interval variables , an infinite series. In addition, due to , The uncertainty space of the oil film excitation load determined by equation (5) is symmetric about the time axis. Therefore, the uncertainty space of the axis trajectory response must also be symmetric about the time axis. In other words, the axis trajectory response interval process determined by equation (5) is The median function of must always be zero. Assume that the axis trajectory response is , is the deterministic function to be solved. Substitute it into equation (5) and perform Laplace transform on both sides of the equation at the same time. According to the convolution theorem of Laplace transform, we can get:

[0084] (6);

[0085] in, and Displacement and incentives The Laplace transform of It is only related to the mass m', stiffness k and damping c of the system, and fully describes the dynamic characteristics of the system in the s domain. The unit impulse response function is for The inverse Laplace transform of represents the inverse Laplace transform, express and The convolution of For the moment, is the time interval, For motivation.

[0086] According to the nature of the interval process correlation, the total response of the axis trajectory is The autocovariance function of is:

[0087] (7);

[0088] in, The oil film excitation load interval process Equation (7) shows that the autocovariance function of the axis trajectory response is composed of the oil film excitation covariance function and the unit impulse response function Decide.

[0089] Because the median function of the oil film excitation load The axis trajectory response caused For a deterministic response, The autocovariance function is the total response of the axis trajectory The autocovariance function of , we can get the radius function of the axis trajectory response at any time t The total response of the axis trajectory of the wind turbine gearbox transmission shaft system The response boundary is .

[0090] Since the oil film parameters such as the radial clearance of the sliding bearing and the viscosity of the lubricating oil are mutually affected by wear and heat dissipation, there is a certain correlation between the oil film parameters. The non-random axis trajectory generated shows correlation at different times. The non-probabilistic ellipsoid model describes the size and correlation of parameter uncertainty through the size and shape of the multi-dimensional ellipsoid. Figure 2 As shown in the ellipsoid model, the uncertainty domain of the interval variables X1 and X2 is an elliptical domain as shown in the figure, denoted as , where the superscript E represents the ellipsoid model; the correlation between variables X1 and X2 is measured by the geometric characteristics of the ellipse. Its covariance function . The relevant angle θ and the length of the semi-axis of the ellipse and , representing the geometric characteristics of the ellipse.

[0091] When the oil film uncertainty parameter interval variable and (superscript m, r denote median and radius, respectively) into related standard interval variables and When the standard interval variable and The covariance function of and correlation coefficient are equal to , Therefore, for the oil film interval variable, n groups of samples are collected, and the minimum area ellipse that envelops all samples and satisfies the edge interval conditions is used as the estimate of the uncertainty domain of the oil film variable. Based on the geometric characteristics of the ellipse, the correlation coefficient of the oil film interval variable can be calculated. and covariance function . Construct the covariance matrix:

[0092] ,in , . Invert the calculated covariance matrix to obtain the characteristic matrix It can reflect the size and shape of the ellipsoid uncertainty domain, so as to obtain the multidimensional ellipsoid uncertainty domain of the time-varying uncertainty parameters of the oil film: .

[0093] Therefore, in this embodiment, specifically:

[0094] This embodiment obtains the covariance between interval variables based on the sample data of the time-varying uncertainty parameters of the oil film, constructs the covariance matrix, and obtains the characteristic matrix by inversion. Determine the multidimensional ellipsoid uncertainty domain of interval variables such as the radial clearance and dynamic viscosity of the sliding bearing;

[0095] The calculation method of the axis trajectory of the sliding bearing-rotor system under the deterministic oil film excitation is obtained by sampling the multi-dimensional ellipsoid uncertainty domain of the time-varying uncertainty parameters of the oil film. Group axis trajectory samples;

[0096] For any sample axis trajectory , , extract its and time , and maps it to Plane, forming plane sample points ;

[0097] for Group sample axis trajectory , repeat the above steps to obtain the point set ;

[0098] Construct a minimum area ellipse that contains the above point set V and satisfies the edge interval condition based on the geometric characteristics of the ellipse, namely the relevant angle θ and the length of the semi-axis of the ellipse and , calculate the axis trajectory covariance function , the square root is the radius function of the axis trajectory response .

[0099] S103, obtaining the upper and lower boundaries of the axis trajectory of the sliding bearing based on the median function of the axis trajectory of the sliding bearing and the radius function of the axis trajectory of the sliding bearing, and completing the axis trajectory analysis.

[0100] The upper and lower boundaries of the axis trajectory are obtained according to the median function and radius function of the axis trajectory .

[0101] In this embodiment, the axis trajectory under the time-varying uncertainty oil film excitation based on the interval process model measurement includes two parts: the median function and the radius function. The median function part is the median function of the oil film excitation load. The axis trajectory response caused , is a deterministic response, which can be obtained according to the calculation method of the axis trajectory of the sliding bearing-rotor system under deterministic oil film excitation; the radius function part is the axis trajectory response caused by the oil film excitation of the uncertain part The fluctuation of reflects the fluctuation amplitude of the axis trajectory response caused by the uncertain oil film excitation, which is determined by the oil film excitation covariance function.

[0102] like Figure 3 As shown, this embodiment also provides a time-varying uncertain sliding bearing rotor system axis trajectory analysis system, including: a sliding bearing axis trajectory median function calculation module 1, a sliding bearing axis trajectory radius function calculation module 2 and an axis trajectory analysis module 3;

[0103] The sliding bearing axis trajectory median function calculation module 1 is used to obtain the time-varying uncertainty parameters and parameter intervals of the oil film based on the actual operating conditions of the sliding bearing, and calculate the sliding bearing axis trajectory median function according to the median value of the oil film parameters;

[0104] The sliding bearing axis trajectory radius function calculation module 2 is used to construct a multi-dimensional ellipsoid uncertainty domain based on the time-varying uncertainty parameters of the oil film, sample and calculate the axis trajectory sample set in the multi-dimensional ellipsoid uncertainty domain, and obtain the sliding bearing axis trajectory radius function based on the geometric characteristics of the ellipse that envelops the sample points;

[0105] The axis trajectory analysis module 3 is used to obtain the upper and lower boundaries of the axis trajectory of the sliding bearing based on the axis trajectory median function of the sliding bearing and the axis trajectory radius function of the sliding bearing, and complete the axis trajectory analysis.

[0106] Embodiment: The oil film parameters such as bearing clearance and dynamic viscosity in the sliding bearing cross-influence each other, are mutually causal, and are correlated with each other. As a result, the axis trajectory generated by them also has time-varying uncertainty. It is difficult to obtain experimental samples of the axis trajectory of the sliding bearing-rotor system in practice. Based on the very limited sample size, it is difficult to measure the correlation and uncertainty of the axis trajectory by traditional statistical or probabilistic methods. This embodiment introduces a non-probabilistic ellipsoid model to measure the correlation of the time-varying uncertain parameters of the oil film parameters, and gives a quantitative description of the uncertainty domain of the axis trajectory. A single disc rotor system model is used. The rotation speed is 1200r / min, the shaft span L=2000mm, the diameter d=57.4mm, the lumped disc diameter D=100mm, the lumped disc mass is 5kg, and the eccentricity e at the disc is u =1mm, the mass density of the shaft segment is 7.80g / cm 3 , elastic modulus E = 200GPa, Poisson's ratio is 0.3. The shaft segment is divided into 72 segments, with a total of 73 nodes. The two bearings act on the 6th and 66th nodes respectively, and the disk acts on the 36th node. The sliding bearing uses the Capone circular bearing model. Bearing width L c=28.7mm, bearing inner radius 28.7 mm. The uncertain oil film parameters are set as follows: the edge interval of the bearing radius clearance h0 is [26.28, 100] μm, the median value is 63.14 μm, and the interval radius is 36.86 μm; the edge interval of the dynamic viscosity of the oil film is [0.0112, 0.0448], the median value is 0.028 Pa·s, and the interval radius is 0.0168 Pa·s.

[0107] The 20 sets of oil film parameter sample points collected are shown in Table 1. Figure 4 As shown in (a) in the figure, it is converted into Figure 4 As shown in (b) in the figure, the oil film parameter correlation coefficient matrix is ​​obtained by calculating the oil film interval variable correlation coefficient according to the calculation steps:

[0108] , and then we can get the parameter variance matrix And the ellipsoid model characteristic matrix , and then the uncertainty domain of oil film parameters is obtained: The multidimensional ellipsoid model constructed based on the correlation analysis technology can envelop all 20 groups of actual exploration samples in Table 1. The correlation between the oil film uncertainty variables is described as follows: Figure 4 (b) The correlation coefficient between the bearing radius clearance and the dynamic viscosity is 0.571, which reflects the correlation and dependence between the oil film parameters.

[0109] Substituting the above oil film parameter uncertainty domain into the calculation method of the axis trajectory of the sliding bearing-rotor system under the deterministic oil film excitation, 20 sets of axis trajectory samples and displacement response sets are obtained as follows Figure 5 As shown, Figure 5 (a) shows the bearing x-direction displacement response set. Figure 5 (b) shows the bearing y-direction displacement response set. Figure 5 (c) is the set of displacement responses of the bearing axis trajectory. In one cycle (0-0.05s), the time interval is 10 -4 s, discretized into 501 time points. For the 20 groups of sample displacement responses, extract the x and y displacement response values ​​at adjacent time points t_i, t_j, and map them to the μ(t_i)-O-μ(t_j) plane, forming 501 planes consisting of 20 groups of displacement response sample points. For the displacement response sample points of each plane, build an ellipsoid correlation model, and obtain the random x, y displacement response and the radius function of the axis trajectory at each time based on the correlation analysis technology, as shown in Figure 6 As shown, Figure 6 (a) is the random displacement response radius function in the x direction. Figure 6 (b) is the random displacement response radius function in the y direction. Figure 6(c) in the figure is the displacement response radius function of the axis trajectory. Then, the displacement response and the upper and lower boundaries of the axis trajectory are obtained as follows: Figure 7 As shown, Figure 7 (a) is the upper and lower boundaries of the bearing x-axis displacement response. Figure 7 (b) is the upper and lower boundaries of the bearing y-axis displacement response. Figure 7 (c) in the figure is the upper and lower boundaries of the bearing axis trajectory.

[0110] Table 1 Actual survey sample data of oil film parameters

[0111]

[0112] In the specific technical solution of the present invention, it can be known from the calculation method of the axis trajectory of the sliding bearing-rotor system under deterministic oil film excitation that the size of the oil film excitation load is affected by the oil film thickness, lubricating oil viscosity, etc. The oil film excitation load, as an intermediate variable, affects the axis trajectory. It is difficult to determine the interval median and covariance function of the oil film excitation in engineering, while the interval of the oil film time-varying uncertain parameters such as the sliding bearing radius clearance and lubricating oil viscosity can be obtained based on engineering experience and expert opinions. That is, the median of the interval of the oil film time-varying uncertain parameters related to the sliding bearing radius clearance and lubricating oil viscosity is taken, and the transfer matrix of the shaft system is established by the Riccati-Newmark acceleration transfer matrix method using the Newmark acceleration method, and the Taylor series is used to estimate the displacement and velocity of the sliding bearing axis at the next moment. The oil film force in the sliding bearing point transfer matrix is ​​obtained according to the Reynolds equation shown in formula (1), so as to realize the calculation of the median function of the axis trajectory of the sliding bearing-rotor system according to the Riccati-Newmark acceleration transfer matrix method. As for the fluctuation of the oil film excitation load caused by the fluctuation of the time-varying uncertain parameters of the sliding bearing radius clearance and the lubricating oil viscosity oil film, and thus the axis trajectory radius function part, we must first determine the uncertainty domain of the oil film time-varying uncertain parameters, sample in the corresponding uncertainty domain, substitute the calculation method of the axis trajectory of the sliding bearing-rotor system under deterministic oil film excitation to obtain the axis trajectory under different samples, and then obtain the axis trajectory radius function part based on its axis trajectory set. How to obtain the uncertainty domain based on the interval of the determined oil film time-varying uncertain parameters and obtain the axis trajectory radius function with a small sample size is the key to the problem.

[0113] The present invention considers the correlation between interval parameters by using a non-probabilistic ellipsoid model, describes the size and correlation of the time-varying uncertainty of the parameters by the size and shape of the multidimensional ellipsoid, measures the uncertain oil film excitation by using an interval process model, and represents it by an interval series expansion; in the processing of the differential equation of motion of the wind power gearbox transmission shaft system, the motion equation in the time domain is converted to the complex domain by Laplace transform, and an algebraic equation with interval variables is obtained; finally, the upper and lower boundaries of the axis trajectory are derived according to the properties of the axis linear system and the correlation properties of the interval process. The time and economic costs caused by the calculation scale and calculation efficiency of the non-random axis trajectory analysis are avoided.

[0114] It should be noted that, for the above-mentioned method embodiments, for the sake of simplicity, they are all described as a series of action combinations, but those skilled in the art should know that the present invention is not limited by the described order of actions, because according to the present invention, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also know that the embodiments described in the specification are all optional embodiments, and the actions and modules involved are not necessarily required by the present invention.

[0115] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the present invention can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0116] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system, characterized in that: The following steps are involved: The time-varying uncertainty parameters and parameter intervals of the oil film are obtained based on the actual operating conditions of the sliding bearing, and the median function of the axis trajectory of the sliding bearing is calculated based on the median value of the oil film parameters. A multidimensional ellipsoid uncertainty domain based on the time-varying uncertainty parameters of the oil film is constructed, and the axis trajectory sample set is obtained by sampling and calculating in the multidimensional ellipsoid uncertainty domain. The axis trajectory radius function of the sliding bearing is obtained based on the geometric characteristics of the ellipse that envelops the sample points. Based on the median function of the sliding bearing axis trajectory and the radius function of the sliding bearing axis trajectory, the upper and lower boundaries of the sliding bearing axis trajectory are obtained to complete the axis trajectory analysis.

2. The method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system according to claim 1 is characterized in that: The process of obtaining the time-varying uncertainty parameters and parameter intervals of the oil film based on the actual operating conditions of the sliding bearing, and calculating the median function of the axis trajectory of the sliding bearing according to the median value of the oil film parameters is as follows: Obtain the time-varying uncertainty parameters and parameter ranges of the oil film based on the actual operating conditions of the sliding bearing; Based on the flow principle of lubricating oil in the clearance of sliding bearings, a Reynolds equation reflecting the relationship between oil film parameters and the oil film excitation load of sliding bearings is constructed, and the oil film force corresponding to the oil film parameters is obtained based on the Reynolds equation; Based on the Reynolds equation, the transfer matrix of the sliding bearing shaft system is established by using the Riccati-Newmark acceleration transfer matrix method and the Newmark acceleration method; The median of the oil film parameter interval is selected and substituted into the transfer matrix to calculate the axis trajectory of the sliding bearing-rotor system, and recorded as the median function of the axis trajectory of the sliding bearing.

3. The method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system according to claim 2 is characterized in that: The Reynolds equation is specifically: ； Where h is the oil film thickness; η is the lubricating oil viscosity; U j is the journal speed, U b is the bearing speed; P is the oil film pressure, x and y are the journal center displacements, and the oil film pressure is integrated on the contact surface between the oil film and the journal to obtain the oil film force. For time.

4. The method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system according to claim 2 is characterized in that: The construction process of the multidimensional ellipsoid uncertainty domain of the oil film time-varying uncertainty parameters is as follows: Collect a number of samples according to the interval variable of the oil film time-varying uncertainty parameter; By enveloping all samples and constructing a covariance matrix, the covariance matrix is ​​inverted to obtain a feature matrix; Based on the characteristic matrix, a multi-dimensional ellipsoid uncertainty domain of the time-varying uncertainty parameters of the oil film is constructed.

5. The method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system according to claim 4 is characterized in that: The process of enveloping all samples, constructing a covariance matrix, and performing inversion to obtain a feature matrix is ​​as follows: Construct an ellipse with the minimum area that envelops all samples and satisfies the edge area conditions; The correlation coefficient of the interval variable of the oil film time-varying uncertainty parameter is calculated based on the geometric characteristics of the ellipse; A covariance function is calculated based on the correlation coefficient and different interval variables, and a covariance matrix is ​​constructed based on the covariance function.

6. The method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system according to claim 5 is characterized in that: The process of sampling and calculating the axis trajectory sample set in the multidimensional ellipsoid uncertainty domain and obtaining the axis trajectory radius function of the sliding bearing based on the geometric characteristics of the ellipse that envelops the sample points is as follows: Sampling in the multidimensional ellipsoid uncertainty domain to obtain a sample set, and substituting the sample set into the transfer matrix to calculate and obtain a plurality of groups of axis trajectory samples; Extract the values ​​of any axis trajectory sample at different times and map them to the plane to obtain the plane sample points; Count the plane sample points of all axis trajectory samples to obtain a sample set; Constructing a minimum area ellipse that includes the sample set and satisfies the edge interval condition, and calculating the axis trajectory covariance function based on the geometric characteristics of the ellipse; The axis trajectory radius function is calculated based on the axis trajectory covariance function.

7. The method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system according to claim 1, characterized in that: The process of obtaining the upper and lower boundaries of the sliding bearing axis trajectory based on the sliding bearing axis trajectory median function and the sliding bearing axis trajectory radius function to complete the axis trajectory analysis is as follows: Construct the motion differential equations of sliding shaft system parameters and oil film excitation loads; The oil film excitation load is expressed by using an interval orthogonal series expansion method to obtain a load function relationship between the oil film excitation load and a median function and a radius function of the time-varying uncertain oil film excitation load; Combining the motion differential equation and the load function relationship, a trajectory function relationship between the sliding bearing axis trajectory and the sliding bearing axis trajectory median function and the sliding bearing axis trajectory radius function is obtained; The upper and lower boundaries of the axis trajectory are calculated based on the trajectory function relationship.

8. The method for analyzing the axis trajectory of a time-varying uncertain sliding bearing rotor system according to claim 7, characterized in that: The upper and lower boundaries of the axis trajectory are specifically: ； in, is the median function of the axis trajectory of the sliding bearing, is the radius function of the sliding bearing axis trajectory, is the total response of the axis trajectory of the wind turbine gearbox transmission shaft system response boundary.

9. A system for analyzing the axis center trajectory of a time-varying uncertain sliding bearing rotor system, implemented by using the method for analyzing the axis center trajectory of a time-varying uncertain sliding bearing rotor system according to any one of claims 1 to 8, characterized in that: include: A sliding bearing axis trajectory median function calculation module (1), a sliding bearing axis trajectory radius function calculation module (2), and an axis trajectory analysis module (3); The sliding bearing axis trajectory median function calculation module (1) is used to obtain the oil film time-varying uncertainty parameters and parameter intervals based on the actual operating conditions of the sliding bearing, and to calculate the sliding bearing axis trajectory median function based on the oil film parameter median; The sliding bearing axis trajectory radius function calculation module (2) is used to construct a multi-dimensional ellipsoid uncertainty domain based on the time-varying uncertainty parameters of the oil film, sample and calculate the axis trajectory sample set in the multi-dimensional ellipsoid uncertainty domain, and obtain the sliding bearing axis trajectory radius function based on the geometric characteristics of the ellipse that envelops the sample points; The axis trajectory analysis module (3) is used to obtain the upper and lower boundaries of the axis trajectory of the sliding bearing based on the axis trajectory median function of the sliding bearing and the axis trajectory radius function of the sliding bearing, thereby completing the axis trajectory analysis.

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