Lubricating performance degradation modeling method for sliding bearing of gear pump of aero-engine

Abstract

The invention discloses a lubricating performance degradation modeling method for a sliding bearing of a gear pump of an aero-engine. The method comprises the steps of 1, obtaining model parameters through training data, and further constructing a Markov chain degradation model; 2, combining real-time measurement data, based on a degradation model, constructing a bearing clearance degradation model more fitting the actual condition, and outputting the abrasion loss of degradation at each moment; step 3; the method comprises the following steps: solving a Reynolds equation to obtain oil film pressure distribution on the basis of an over-relaxation iteration mathematical method, solving bearing lubrication characteristic parameters through the pressure distribution, and establishing a sliding bearing lubrication characteristic parameter calculation program; and 4, sequentially substituting the abrasion loss at each degradation moment into a lubricating characteristic parameter calculation program to obtain a process of deepening the change of the lubricating characteristic parameter of the bearing along with the abrasion degradation so as to finish the lubricating performance degradation modeling of the sliding bearing of the gear pump of the aero-engine. The method has the advantage of higher fitting degree with the specific object working condition and the actual degradation condition.

Description

Technical Field

[0001] The invention relates to the technical field of performance modeling and simulation of an aircraft engine gear pump, and in particular to a method for modeling degradation of lubrication performance of a sliding bearing of an aircraft engine gear pump. Background Art

[0002] In aircraft engines, the fuel pump plays a key role in delivering fuel to the engine combustion chamber. In order to meet the operating requirements of aircraft engines under harsh working conditions, the key friction pairs in the fuel pump face severe friction and wear challenges. Monitoring and predicting its degradation process is an important prerequisite for ensuring its reliability.

[0003] However, due to the high cost of conducting actual wear degradation tests on fuel gear pumps, current research on the degradation of lubrication performance of gear pump sliding bearings at home and abroad mainly uses computer simulation and mathematical modeling methods.

[0004] For example, Dowson et al. in their article “A generalized Reynolds equation for fluid-film lubrication” studied the effect of lubricating oil viscosity on oil film pressure and temperature by constructing a generalized Reynolds equation, obtained the changes in bearing dynamic pressure lubrication under temperature effects, and constructed a more realistic sliding bearing performance calculation model, but their model did not consider surface wear.

[0005] Based on the friction experimental data, Altmaier et al. revised the thermoelastic lubrication model used to predict the friction loss and oil temperature in bearing operation, but their model did not take into account the changes in oil film thickness and pressure distribution caused by wear.

[0006] At present, the academic community's modeling research on the degradation of lubrication performance of gear pump sliding bearings is relatively incomplete, and there are few studies that use data-driven modeling methods to describe the degradation process. Summary of the invention

[0007] In order to overcome the above technical problems, the purpose of the present invention is to provide a method for modeling the lubrication performance degradation of a sliding bearing of an aircraft engine gear pump, which has the advantage of a higher degree of fit with specific object working conditions and actual degradation conditions.

[0008] The technical solution adopted by the present invention is:

[0009] A method for modeling lubrication performance degradation of a sliding bearing of an aircraft engine gear pump comprises the following steps;

[0010] Step 1: Obtain model parameters through training data and then construct a Markov chain degradation model;

[0011] Step 2: Combined with real-time measurement data, the degradation model in step 1 is modified based on Bayesian updating to build a bearing clearance degradation model that is more in line with the actual situation, and the wear amount at each degradation moment is output;

[0012] Step 3: Based on the mathematical method of super-relaxation iteration, solve the Reynolds equation to obtain the oil film pressure distribution, and then solve the bearing lubrication characteristic parameters through the pressure distribution, thereby establishing a calculation program for the lubrication characteristic parameters of the sliding bearing;

[0013] Step 4: Substitute the wear amount at each degradation moment output by the bearing clearance degradation model in step 2 into the lubrication characteristic parameter calculation program in step 3 in turn to obtain the change process of the bearing lubrication characteristic parameters as the wear degradation deepens, thereby completing the lubrication performance degradation modeling of the aircraft engine gear pump sliding bearing.

[0014] The step 1 is specifically as follows:

[0015] (1.1) The experimental data of group K measured under the same working conditions are in For working hours The jth group of data measured at each moment in the process is used as the basis for the empirical cumulative distribution function at moment n:

[0016]

[0017] Among them, the experimental data y n After the above conversion, the value range is function is an indicator function. When the input The function value is 1 when , and 0 in other cases;

[0018] (1.2) Assume that the cumulative distribution function of the model obtained by the Markov chain degradation model at time n is as follows, and its value is related to the model parameter θ;

[0019]

[0020] In the formula, x n is the degenerate state quantity predicted by the Markov chain at time n; is the i-th discrete degenerate state quantity at time n; is the state transition probability corresponding to the i-th discrete degenerate state quantity at time n; δ(·) is the switching function, when δ(0)=1, δ(·) is 0 in other cases;

[0021] (1.3) On this basis, define d n (θ) is the measure of the difference between the two cumulative distribution functions at time n, which is:

[0022]

[0023] In the formula, the integral This means that all discrete states predicted by the Markov chain are calculated once and summed;

[0024] For the entire working time, the definition is the d n (θ) composed of a vector (d1(θ), ..., d n (θ),...,d N The bi-norm of (θ)) is a measure of the total gap:

[0025]

[0026] Finding the right model parameters make As small as possible, that is:

[0027]

[0028] By solving the above equation, we can obtain the model parameter θ of the Markov chain degradation model, and bring it into the Markov chain degradation model together with the initial state p0:

[0029] p n =p n-1 Q g′(n)-g′(n-1) ; n = 1, 2..., N

[0030] In the formula, The bearing wear state at time n is in each discrete wear state Probability The vector is composed of, s is the number of discrete wear states; N is the maximum working time contained in the training data; Q is a (s+1)×(s+1) double diagonal transition probability matrix, as follows:

[0031]

[0032] In this way, the prior prediction distribution of each discrete degradation state of the bearing clearance at any time n can be obtained: Vector in That is, the prediction of the Markov chain is taken as the prior distribution P n|n-1 =P n .

[0033] The step 2 is specifically as follows:

[0034] (2.1) Combined with real-time measurement data, the prior distribution p of the output of the Markov chain degradation model is n|n-1 To update:

[0035] According to Bayesian theory, the posterior distribution probability of each damage state at time n is Vector It can be expressed as:

[0036]

[0037] in, From the measurement equation we get:

[0038]

[0039] Here we assume that the measurement error follows a Gaussian distribution The mean is 0 and the variance is σ n ;y n Real-time measurement data at n moments; is the i-th discrete degenerate state quantity at time n;

[0040] (2.2) Based on the updated posterior distribution, the previous Markov chain degradation model is used to predict the future degradation state and construct the bearing clearance degradation model:

[0041] The p in the previous step n|n Substitute the Markov chain degradation model and predict the probability distribution of the bearing wear degradation state at each moment in the future by increasing l in sequence:

[0042] p n+l =p n Q g'(n+l)-g'(n)

[0043] In the formula, in the formula, The bearing wear state at time n is in each discrete wear state Probability The vector composed of s is the number of discrete wear states; N is the maximum working time contained in the training data; Q is the double diagonal transition probability matrix in step (1.3); is the predicted distribution of bearing degradation state at time l in the future.

[0044] On this basis, through p n+l The bearing wear amount a at time n+l during the bearing degradation process can be obtained n+l By increasing l successively, the wear amount at each future moment can be obtained, and thus the bearing clearance degradation model for predicting the degradation state at each moment can be obtained.

[0045] The specific steps of step three are as follows:

[0046] (3.1) For the annular sliding bearing oil film flow field, it is expanded in the circumferential direction and divided into a grid with (m+1)×(n+1) nodes;

[0047] The fluid element at each node follows the Reynolds equation for oil film lubrication of sliding bearings:

[0048]

[0049] Among them, h is the oil film thickness, p is the pressure, μ is the medium viscosity, U is the linear speed of the bearing, R is the journal radius, and all variables are in international standard units;

[0050] (3.2) The change in oil film thickness caused by wear degradation at any time is included in the calculation of the oil film thickness h:

[0051] In general, the equation describing the oil film thickness in the absence of wear is:

[0052]

[0053] The wear amount a of the bearing at a certain time n obtained in step 2 is n Incorporating thickness calculations, the equation for oil film thickness can be written as:

[0054]

[0055] (3.3) Use successive super-relaxation iterations to solve the Reynolds equation and obtain the oil film pressure distribution;

[0056] (3.4) According to the bearing oil film pressure distribution, the bearing lubrication characteristic parameters are solved:

[0057] The four bearing lubrication characteristic parameters are: load capacity, end face leakage, friction and deflection angle. The calculation formula is as follows:

[0058] Bearing capacity F and deflection angle θ:

[0059]

[0060] Among them, p is the oil film pressure distribution obtained in the previous step; B is the bearing width; coordinates y,

[0061] End leakage flow Q:

[0062]

[0063] Among them, v| y＝B / 2 is the axial velocity of the medium at the end surface, Calculated; coordinate z is radial.

[0064] Friction force F t :

[0065]

[0066] Ft =F t1 +F t2

[0067] in, is the oil film rupture position; e ξ is the horizontal distance between the journal and the bearing’s geometric center, e η is the vertical distance; ρ, ρ c is the medium density and the medium density in the oil film rupture zone; τ zx|z＝h is the shear stress at the interface between the journal and the oil film,

[0068] Substitute the oil film pressure distribution and geometric and physical parameters obtained in (3.3) into the above formula to calculate the current oil film thickness distribution h n The four bearing lubrication characteristic parameters under the condition are obtained, thereby obtaining the bearing lubrication characteristic parameter calculation program for time n.

[0069] The step (3.3) is specifically:

[0070] First, the oil film thickness distribution h obtained in (3.2) n The iteration coefficient of each node on the mesh is calculated based on the geometric and physical parameters. The calculation formula of the iteration coefficient is as follows:

[0071]

[0072] In the formula, Δy is the distance between two nodes in two coordinate directions; r is the journal radius; U is the linear speed; c = Rr, where R is the bearing radius; μ is the medium viscosity;

[0073] Then, the iteration coefficient is brought into the iterative format Reynolds equation to calculate the pressure at each node. The equation is as follows:

[0074]

[0075] In the formula, β is the relaxation factor, and its value is usually selected between β=1 and 2; The result of the previous iteration.

[0076] Finally, the iterative convergence accuracy is calculated. If the given accuracy requirement is met, the pressure distribution is output; if not, Recalculate iterations.

[0077] Beneficial effects of the present invention:

[0078] The present invention provides a method for modeling the degradation of lubrication characteristics of sliding bearings of aviation fuel gear pumps that combines theoretical formulas and data-driven methods. Based on the Markov chain degradation model and combined with Bayesian inference, the bearing wear phenomenon in the bearing operation is taken as the research object, and a data-driven degradation model with the function of updating and predicting the damage state is established, which realizes the prediction of the degradation process of lubrication characteristic parameters under specific conditions. Compared with the pure experimental method, since the Markov chain degradation modeling method used in the present invention only needs to provide training data at some time points to simulate and predict the entire degradation process, it has fewer requirements on the amount of experimental data, saving expensive experimental materials and experimental time.

[0079] On the other hand, compared with the traditional simulation calculation method, the method of the present invention is based on the training data set and combines the real-time measurement data, so that the simulation calculation results are more consistent with the actual situation, and have the excellent characteristics of gradually increasing prediction confidence as the updated data increases, which better meets the increasing demand for the confidence of simulation calculation results and their consistency with the actual situation in engineering practice. It has high practical value for analyzing the lubrication characteristics simulation of aviation fuel gear pump sliding bearings and the degradation law of lubrication characteristics with working time. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 Build a flow chart for the bearing clearance degradation model.

[0081] Figure 2 Flowchart for modeling degradation of lubrication properties of journal bearings.

[0082] Figure 3 Schematic diagram of bearing oil film mesh division.

[0083] Figure 4 This is the flow chart for calculating the oil film pressure distribution of sliding bearings.

[0084] Figure 5 Schematic diagram of the training data set.

[0085] Figure 6 The following are the prediction results of the degradation state when the model is updated to different conditions. (a) The prediction result of the model when it is updated to n=400; (b) The prediction result of the model when it is updated to n=1200; (c) The prediction result of the model when it is updated to n=2000; (d) The prediction result of the model when it is updated to n=2800.

[0086] Figure 7 Schematic diagram of the calculation results of oil film thickness and pressure distribution in the initial state.

[0087] Figure 8 This is a graph showing the changing trend of bearing lubrication characteristic parameters with degradation time n. DETAILED DESCRIPTION

[0088] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0089] The main technology used in the present invention is the Markov chain degradation modeling method incorporating Bayesian updating, and its basic principle is summarized as follows:

[0090] The Markov chain model is a random process with discrete state space and discrete time space. For s+1 discrete wear states at time n The state at time n+1 Only with the state at time n The wear state is irreversible, and is independent of the state at other times, which is called the Markov property. Due to the irreversible nature of wear, it is now stipulated that there are only two possible wear states, one is from the state Transfer to Its transition probability is The second is to stay in the original state Its transition probability is

[0091] On this basis, the Markov chain model can be described as:

[0092] p m =p n Q g'(m)-g'(n)

[0093] Here, The bearing wear state at time n is in each discrete wear state Probability The vector composed of , Q is a (s+1)×(s+1) double diagonal transfer probability matrix, as follows:

[0094]

[0095] Among them, p∈[0,1] is the transition probability between two consecutive damage states and is an undetermined model parameter.

[0096] In the Markov chain model, g′(n) is a nonlinear function of time n, defined as:

[0097] g'(n)=N·g(n / N)

[0098] Here, g(·):[0,1]→[0,1] is a monotone cubic Hermitian interpolation function, and the interpolation point coordinate set is {(0,0), (θ1,θ′1),..., (θ j ,θ′ j ), ..., (1, 1)}, where the coordinates of each point satisfy 0<θ j <θ j+1 <1,0<θ′ j <θ′ j+1 <1.

[0099] In summary, the parameters of the Markov chain degradation model used in the present invention are θ={p, θ1, θ′1, ..., θ j ,θ′ j}.

[0100] like Figure 1-Figure 8 As shown, the training data set obtained using the bearing wear experiment The corresponding Markov chain degradation model parameters θ can be obtained by training. The parameters are brought into the Markov chain degradation model to obtain the Markov chain degradation model p(x n |x n-1 ;θ).

[0101] At this time, online measurement data y can be obtained through the real-time detection device 1：n , by comparing the measured wear conditions with the discrete wear states By corresponding, we can get the discrete measurement data distribution p(y n |x n ), on this basis, the likelihood distribution can be obtained through mathematical calculation.

[0102] By taking the previous Markov chain degradation model results as the prior distribution and bringing them into the Bayesian updated recursive filtering equation together with the likelihood distribution, we can obtain the posterior distribution p(x n |y 1：n ), and on this basis, the result p(x n+l |y 1：n ) will be more in line with the actual situation. Thus, the degradation model of bearing clearance is obtained. Substituting the predicted value of the clearance degradation model into the bearing lubrication characteristic parameter calculation program can obtain the change of lubrication characteristic parameters in the whole degradation process, that is, the degradation model of lubrication characteristic parameters is obtained.

[0103] To achieve the above purpose, the technical route provided by the present invention is as follows Figure 2 Shown

[0104] Step 1: Obtain model parameters through training data, and then construct a Markov chain degradation model;

[0105] The step 1 is specifically as follows:

[0106] (1.1) The experimental data of group K measured under the same working conditions are in For working hours The jth group of data measured at each moment in . Based on this data, the empirical cumulative distribution function at moment n can be expressed as:

[0107]

[0108] Among them, the experimental data y n After the above conversion, the value range is function is an indicator function. When the input The function value is 1 when , and 0 otherwise.

[0109] (1.2) Suppose the cumulative distribution function of the model obtained by the Markov chain degradation model at time n is as shown below, and its value is related to the model parameter θ.

[0110]

[0111] (1.3) On this basis, define d n (θ) is the measure of the difference between the two cumulative distribution functions at time n, which is:

[0112]

[0113] Its value is only related to the model parameter θ. In this way, for the entire working time, the definition is composed of d at each moment n (θ) composed of a vector (d1(θ), ..., d n (θ),...,d N The bi-norm of (θ)) is a measure of the total gap:

[0114]

[0115] Therefore, if we want to make the model cumulative distribution function obtained from the model and the empirical cumulative distribution function obtained from the experimental data as close as possible, we should find the appropriate model parameters make As small as possible, that is:

[0116]

[0117] By solving the above equation, we can obtain the model parameter θ of the Markov chain degradation model, and bring it into the Markov chain degradation model together with the initial state p0:

[0118] p n =p n-1 Q g′(n)-g′(n-1) ; n = 1, 2..., N

[0119] From this, we can obtain the prior prediction distribution of each discrete degradation state of the bearing clearance at any time n: Vector

[0120] Step 2: Based on Bayesian updating and combined with real-time measurement data, a bearing clearance degradation model is constructed. This step will provide key input parameters for the prediction of lubrication characteristic parameters of the degradation process in the fourth step.

[0121] The specific steps are as follows:

[0122] (2.1) Combined with real-time measurement data, the prior distribution p of the output of the Markov chain degradation model is n|n-1 To update:

[0123] According to Bayesian theory, the posterior distribution probability of each damage state at time n is Vector It can be expressed as:

[0124]

[0125] in, From the measurement equation we get:

[0126]

[0127] Here we assume that the measurement error follows a Gaussian distribution y n Real-time measurement data.

[0128] (2.2) Based on the updated posterior distribution, the previous Markov chain degradation model is used to predict the future degradation state and construct the bearing clearance degradation model:

[0129] The p in the previous step n|n Substitute the Markov chain degradation model and predict the probability distribution of the bearing wear degradation state at each moment in the future by increasing l in sequence:

[0130] p n+l =p n Q g'(n+l)-g ' (n)

[0131] On this basis, through p n+l The bearing wear amount a at time n+l during the bearing degradation process can be obtained n+lBy increasing l in sequence, the wear amount at each future moment can be obtained. Thus, the bearing clearance degradation model for predicting the degradation state at each moment can be obtained.

[0132] Step 3: Based on mathematical methods such as super-relaxation iteration, solve the Reynolds equation to obtain the oil film pressure distribution, and then solve the bearing lubrication characteristic parameters through the pressure distribution, thereby establishing a calculation program for the lubrication characteristic parameters of the sliding bearing. The calculation program constructed in this step will be used in the fourth step to calculate the lubrication characteristic parameters at each moment of the degradation process.

[0133] The specific steps of step three are as follows:

[0134] (3.1) Figure 3 As shown, for the annular sliding bearing oil film flow field, it is expanded in the circumferential direction and divided into a grid with (m+1)×(n+1) nodes.

[0135] The fluid element at each node follows the Reynolds equation for oil film lubrication of sliding bearings:

[0136]

[0137] Among them, h is the oil film thickness, p is the pressure, μ is the medium viscosity, U is the linear speed of the bearing rotation, R is the journal radius, and all variables are in international standard units.

[0138] (3.2) The change in oil film thickness caused by wear degradation at any time is included in the calculation of the oil film thickness h:

[0139] In general, the equation describing the oil film thickness in the absence of wear is:

[0140]

[0141] The wear amount a of the bearing at a certain time n obtained in step 2 is n Incorporating thickness calculations, the equation for oil film thickness can be written as:

[0142]

[0143] (3.3) Use successive super-relaxation iterations to solve the Reynolds equation and obtain the oil film pressure distribution. The calculation process is as follows: Figure 4 As shown:

[0144] First, the iteration coefficient of each node on the grid is calculated by the oil film thickness distribution hn and geometric and physical parameters obtained in (3.2). The calculation formula of the iteration coefficient is as follows:

[0145]

[0146]

[0147]

[0148] In the formula, Δy is the distance between two nodes in two coordinate directions; r is the journal radius; U is the linear speed; c = Rr, where R is the bearing radius; μ is the medium viscosity;

[0149] Then, the iteration coefficient is brought into the iterative format Reynolds equation to calculate the pressure at each node. The equation is as follows:

[0150]

[0151] In the formula, β is the relaxation factor, and its value is usually selected between β=1 and 2; The result of the previous iteration.

[0152] Finally, the iterative convergence accuracy is calculated. If the given accuracy requirement is met, the pressure distribution is output; if not, Recalculate iterations.

[0153] (3.4) According to the bearing oil film pressure distribution, the bearing lubrication characteristic parameters are solved:

[0154] The four bearing lubrication characteristic parameters are: load capacity, end face leakage, friction and deflection angle. The calculation formula is as follows:

[0155] Bearing capacity F and deflection angle θ:

[0156]

[0157] Among them, p is the oil film pressure distribution obtained in the previous step; B is the bearing width; coordinates y, Reference Figure 3 .

[0158] End leakage flow Q:

[0159]

[0160] Among them, v| y＝B / 2 is the axial velocity of the medium at the end surface, Calculated; coordinate z is radial.

[0161] Friction force F t :

[0162]

[0163] F t =F t1 +F t2

[0164] in, is the oil film rupture position; e ξ is the horizontal distance between the journal and the bearing’s geometric center, e η is the vertical distance; ρ, ρ c is the medium density and the medium density in the oil film rupture zone; τ zx|z＝h is the shear stress at the interface between the journal and the oil film,

[0165] Substituting the oil film pressure distribution and geometric and physical parameters obtained in (3.3) into the above formula, the current oil film thickness distribution h can be calculated: n The four bearing lubrication characteristic parameters under the condition of . Thus, the calculation procedure of bearing lubrication characteristic parameters for time n is obtained.

[0166] Step 4. Substitute the wear amount at each degradation moment output by the bearing clearance degradation model in step 2 into the lubrication characteristic parameter calculation program in step 3 in turn to obtain the change process of the bearing lubrication characteristic parameters as the wear degradation deepens. This completes the lubrication performance degradation modeling of the aircraft engine gear pump sliding bearing.

[0167] Experimental Example: The advantages of the present invention can be further illustrated by the following simulation experiment:

[0168] 1. Simulation parameters

[0169] As a fuel pump with simple structure, low specific mass and strong resistance to fuel pollution, the fuel gear pump is widely used in the main and afterburner combustion chambers of aircraft engines. Table 1 shows the geometric design parameters of the sliding bearing of an aviation fuel gear pump and the physical properties of the working medium.

[0170] Table 1 Bearing geometric parameters and physical parameters

[0171]

[0172]

[0173] To obtain the model parameters in step 1, a training data set consisting of 30 independent sets of data is used here.

[0174] 2. Simulation results

[0175] According to step 1, the model parameters can be calculated through the training data set, and the structure is shown in Table 2:

[0176] Table 2 Calculation results of degradation model parameters

[0177]

[0178] Through step 2, the model prediction status of the real-time measurement data updated to the time when n is 400, 1200, 2000, and 2800 hours is obtained. The real-time measurement data before this time will be used for model update, and the real-time measurement data after this time will be used to compare the state prediction results. The results are as follows Figure 6 shown.

[0179] According to the method of steps three and four, the calculation program of bearing lubrication characteristic parameters is constructed, and the bearing clearance degradation prediction result in the previous step is brought into the calculation program to obtain the degradation process of bearing lubrication characteristic parameters. In order to improve the stability of iterative calculation, the oil film thickness, pressure and bearing characteristic parameters are averaged into dimensionless quantities. It can be obtained that the calculation results of the oil film thickness and pressure distribution in the initial state are as follows: Figure 7 As shown in Figure 2, the simulation results of the bearing lubrication characteristic parameters during the entire degradation process are shown in Figure 2. Figure 8 shown.

[0180] 3. Results Analysis

[0181] Conclusion 1: Comparison Figure 6 The uncertainty bounds in (a)(b)(c)(d) show that the Bayesian update method used in this method is able to predict the evolution of the future degradation phase with quantitative uncertainty after the initial learning phase using limited data. As the data used for updating gradually increases, the 5%-95% uncertainty bound gradually narrows. This indicates that the distribution of predictions is more concentrated, the uncertainty of the model predictions is gradually decreasing, and the confidence level is gradually increasing.

[0182] Conclusion 2: Figure 6 In (a) to (c), the damage evolution predicted by the model (blue circles) after incorporating a limited amount of condition monitoring data is consistent with future damage data (red dots). This correct trend in the prediction results can be attributed to the fact that a sufficient amount of data has been used for model calibration.

[0183] Conclusion 3: Comparison Figure 7 From the simulation data and the test results, it can be concluded that the bearing lubrication characteristic parameter calculation procedure used in the present invention is in line with the actual situation, and the feasibility and effectiveness of the theory and method proposed in the present invention have been verified.

[0184] Conclusion 4: Figure 8 In the present invention, the change of lubrication characteristic parameters with the increase of wear is demonstrated through calculation examples. This degradation process is consistent with the theoretical analysis, which verifies the rationality of the degradation model results and the feasibility of the degradation modeling method used in the present invention.

[0185] The present invention aims at the degradation process of lubrication performance of sliding bearings of gear pumps, combines Markov chain and Bayesian update to construct a bearing clearance degradation model, and based on this, combines the bearing lubrication characteristic parameter model to construct a sliding bearing lubrication characteristic degradation model. Compared with the traditional modeling method based on pure theoretical formula, the modeling method of the present invention innovatively applies the Markov chain degradation model with Bayesian update to the bearing lubrication characteristic modeling, and incorporates the actual experimental data into the model building process, thereby improving the degree of fit of the model to the actual situation and increasing the credibility of the model. It has a high practical value for analyzing the lubrication characteristic simulation of the sliding bearings of aviation fuel gear pumps and the degradation law of the lubrication characteristics with working time. Furthermore, the method for constructing a sliding bearing lubrication characteristic degradation model provided in this article has certain reference significance in predicting the future state of bearing lubrication and establishing a digital twin model, as well as guiding accelerated life tests.

Claims

1. A modeling method for lubrication performance degradation of a sliding bearing of an aircraft engine gear pump, characterized in that: The steps include: Step 1: Obtain model parameters through training data and then construct a Markov chain degradation model; Step 2: Combined with real-time measurement data, the degradation model in step 1 is modified based on Bayesian updating to build a bearing clearance degradation model that is more in line with the actual situation, and the wear amount at each degradation moment is output; Step 3: Based on the mathematical method of super-relaxation iteration, solve the Reynolds equation to obtain the oil film pressure distribution, and then solve the bearing lubrication characteristic parameters through the pressure distribution, thereby establishing a calculation program for the lubrication characteristic parameters of the sliding bearing; Step 4: Substitute the wear amount at each degradation moment output by the bearing clearance degradation model in step 2 into the lubrication characteristic parameter calculation program in step 3 in turn to obtain the change process of the bearing lubrication characteristic parameters as the wear degradation deepens, thereby completing the lubrication performance degradation modeling of the aircraft engine gear pump sliding bearing.

2. The method for modeling lubrication performance degradation of a sliding bearing of an aircraft engine gear pump according to claim 1, characterized in that: The step 1 is specifically as follows: (1.1) The experimental data of the group measured under the same working conditions are recorded as in For working hours The jth group of data measured at each moment in is used as the basis for the empirical cumulative distribution function at moment n: Among them, the experimental data is also converted by the above formula, and the value range is function is an indicator function. When the input The function value is 1 when , and 0 in other cases; (1.2) Assume that the cumulative distribution function of the model obtained by the Markov chain degradation model at time n is as follows, and its value is related to the model parameters; In the formula, x n is the degenerate state quantity predicted by the Markov chain at time n; is the i-th discrete degenerate state quantity at time n; is the state transition probability corresponding to the i-th discrete degenerate state quantity at time n; δ(·) is the switching function, when δ(0)=1, δ(·) is 0 in other cases; (1.3)Define d n (θ) is the measure of the difference between the two cumulative distribution functions at time n, which is: In the formula, the integral This means that all discrete states predicted by the Markov chain are calculated once and summed; For the entire working time, the definition is the d n (θ) composed of a vector (d1(θ), ..., d n (θ),...,d N The bi-norm of (θ)) is a measure of the total gap: Finding the right model parameters make As small as possible, that is: Obtain the model parameter θ of the Markov chain degradation model and bring it into the Markov chain degradation model together with the initial state p0: p n =p n-1 ·Qg' (n)-g′(n-1) ;n=1,2…,N In the formula, The bearing wear state at time n is in each discrete wear state Probability The vector is composed of, s is the number of discrete wear states; N is the maximum working time contained in the training data; Q is a (s+1)×(s+1) double diagonal transition probability matrix, as follows: A priori predicted distribution of each discrete degradation state of bearing clearance at any time n The vector composed of in That is, the prediction of the Markov chain is taken as the prior distribution p nn 1 = p n .

3. The method for modeling lubrication performance degradation of a sliding bearing of an aircraft engine gear pump according to claim 2, characterized in that: The step 2 is specifically as follows: (2.1) Combined with real-time measurement data, the prior distribution p of the output of the Markov chain degradation model is n|n-1 To update: According to Bayesian theory, the posterior distribution probability of each damage state at time n is The vector composed of It can be expressed as: in, From the measurement equation we get: Here we assume that the measurement error follows a Gaussian distribution The mean is 0 and the variance is σ n ;y n Real-time measurement data at time n; is the i-th discrete degenerate state quantity at time n; (2.2) Based on the updated posterior distribution, the previous Markov chain degradation model is used to predict the future degradation state and construct the bearing clearance degradation model; The p in the previous step n|n Bring in the Markov chain degradation model and predict the probability distribution of the bearing wear degradation state at each moment in the future by increasing it in sequence: p n+l =p n ·Q g′(n+l)-g′(n) In the formula, in the formula, The bearing wear state at time n is in each discrete wear state Probability The vector is composed of, s is the number of discrete wear states; N is the maximum working time contained in the training data; Q is the double diagonal transition probability matrix in step (1.3); The predicted distribution of bearing degradation states at future,times; By p n+l Obtain the bearing wear amount a at time n+l during the bearing degradation process n+l , by increasing them successively, the wear amount at each future moment can be obtained, and the bearing clearance degradation model for predicting the degradation state at each moment can be obtained.

4. The method for modeling lubrication performance degradation of a sliding bearing of an aircraft engine gear pump according to claim 1, characterized in that: The specific steps of step three are as follows: (3.1) For the annular sliding bearing oil film flow field, it is expanded in the circumferential direction and divided into a grid with (m+1)×(n+1) nodes; The fluid element at each node follows the Reynolds equation for oil film lubrication of sliding bearings: Among them, h is the oil film thickness, p is the pressure, μ is the medium viscosity, U is the linear speed of the bearing, R is the journal radius, and all variables are in international standard units; (3.2) The change in oil film thickness caused by wear degradation at any time is included in the calculation of the oil film thickness h: The equation describing the oil film thickness in the absence of wear is: The wear amount a of the bearing at a certain time n obtained in step 2 is n Incorporating thickness calculations, the equation for oil film thickness can be written as: (3.3) Use successive super-relaxation iterations to solve the Reynolds equation and obtain the oil film pressure distribution; (3.4) According to the bearing oil film pressure distribution, the bearing lubrication characteristic parameters are solved: The four bearing lubrication characteristic parameters are: load capacity, end face leakage, friction and deflection angle. The calculation formula is as follows: Bearing capacity, and deflection angle θ: Among them, p is the oil film pressure distribution obtained in the previous step; B is the bearing width; coordinates y, End leakage flow Q: Among them, v| y＝B / 2 is the axial velocity of the medium at the end surface, Calculated; coordinate z is radial. Friction force F t : F t =F t1 +F t2 in, is the oil film rupture position; e ξ is the horizontal distance between the journal and the bearing’s geometric center, e η is the vertical distance; ρ, ρ c is the medium density and the medium density in the oil film rupture zone; τ zx | z＝h is the shear stress at the interface between the journal and the oil film, Substitute the oil film pressure distribution and geometric and physical parameters obtained in (3.3) into the above formula to calculate the current oil film thickness distribution h n The four bearing lubrication characteristic parameters under are used to obtain the bearing lubrication characteristic parameter calculation program for time n.

5. The method for modeling lubrication performance degradation of a sliding bearing of an aircraft engine gear pump according to claim 4, characterized in that: The step (3.3) is specifically: First, the oil film thickness distribution h obtained in (3.2) n The iteration coefficient of each node on the mesh is calculated based on the geometric and physical parameters. The calculation formula of the iteration coefficient is as follows: In the formula, Δy is the distance between two nodes in two coordinate directions; r is the journal radius; U is the linear speed; c = R-r, where R is the bearing radius; μ is the medium viscosity; Then, the iteration coefficient is brought into the iterative format Reynolds equation to calculate the pressure at each node. The equation is as follows: In the formula, β is the relaxation factor, and its value is usually selected between β=1 and 2; The result of the previous iteration. Finally, the iterative convergence accuracy is calculated. If the given accuracy requirement is met, the pressure distribution is output; if not, Recalculate iterations.

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