Reliability analysis method for abrasion of side plate of gear pump

Abstract

The invention discloses a reliability analysis method for abrasion of a side plate of a gear pump. The method comprises the following steps: step 1: carrying out stress analysis on a gear pump side plate, step 2: establishing a wear loss formula of the gear pump side plate, step 3: initializing parameters required for calculating a failure probability, step 4: establishing or updating a GPR model, step 5: in an active learning process, adaptively adding points and returning to the step 4 to update the GPR model; step 6, calculating an important direction according to the real design point obtained in the step 5; 7, adaptively adding points in the active learning process, returning to the step 4, and updating the GPR model; 8, according to the intersection point obtained in the step 7, estimating the failure probability of the gear pump side plate with the maximum abrasion loss not exceeding a specified value; according to the method, the problem that an original AGPR-LS method depends on important directions is solved, and the blank in the aspect of reliability analysis of the gear pump side plate is filled up. The problem that the abrasion failure probability of the gear pump side plate is small can be effectively solved for events with the small failure probability.

Description

Technical Field

[0001] The invention relates to the technical field of wear reliability analysis of a fuel gear pump of an aviation engine, and in particular to a reliability analysis method for wear of a side plate of a gear pump. Background Art

[0002] In aircraft engines, the fuel pump plays a key role in delivering fuel to the engine combustion chamber, and its life is an important factor affecting the performance of aircraft engines. External gear pumps have been widely used in light industry, aviation, shipbuilding, automobiles and other mechanical industries due to their advantages such as easy manufacturing, relatively low cost, light weight, long life and high efficiency. However, the axial clearance automatic compensation gear pumps currently used at home and abroad have always had problems such as severe side plate wear and failure of floating side plate end face seal. In order to ensure the reliability, operation stability and extend the service life of the fuel pump, it is of great significance to conduct reliability analysis on the wear failure of the gear pump side plate.

[0003] Domestic and foreign scholars have conducted some research on the modeling and simulation of the side plate lubrication theory. Koc, Hooke and others studied the effects of the running speed, pressure and tilt angle of the floating side plate on the side plate lubrication.

[0004] According to the research of Dhar S, Vacca A, the pressure on both sides of the side plate has a strong dependence on the lubricant film thickness and the micro-motion of the side plate. Therefore, in order to design an axially balanced floating bushing, it is crucial to accurately predict the lubricant film thickness in the axial clearance and the fluid dynamic effects of pressure. However, early studies always involve assumptions about the oil film thickness. Although these methods provide certain insights, no model has been proposed to accurately predict the lubricant film thickness and the axial clearance performance of external gear pumps.

[0005] Dhar and Vacca proposed the first axial lubrication clearance model for external gear pumps that can predict the oil film thickness. As a component of the complete external gear pump simulation tool HYGESim, the model calculates the transient inter-tooth volume (TSV) pressure and provides boundary conditions for the thermal-fluid-solid coupling model. This work proves that the addition of dynamics has a significant impact on the performance of the oil film; however, there are few domestic and foreign literatures that conduct reliability analysis on the model of the gear pump side plate.

[0006] There are many commonly used methods for evaluating structural reliability. Among them, the line sampling method has been widely used in various engineering problems due to its efficiency and high precision.

[0007] The AGPR-LS method proposed by Song Jingwen et al. can estimate small failure probability problems with fewer limit state functions, but its accuracy depends on the important directions calculated by the first-order reliability method, which may lead to non-convergence or unnecessary calculations.

[0008] In summary, the defects of the existing technology are: many reliability algorithms rely on the selection of important directions, and the important directions are obtained based on the design points. The existing technology for calculating the design points has reduced calculation accuracy and may even result in errors for highly nonlinear and small failure probability events. Summary of the invention

[0009] In order to overcome the above technical defects, the purpose of the present invention is to provide a reliability analysis method for gear pump side plate wear, and apply the ConBayOptSub method

[19] that we recently proposed, which can directly, efficiently and accurately calculate the design point, to the AGPR-LS algorithm to evaluate the failure probability of the gear pump side plate. This method not only solves the problem of the original AGPR-LS method's dependence on important directions, but also fills the gap in the reliability analysis of gear pump side plates. It can effectively target small failure probability events, which meets the problem of low failure probability of gear pump side plate wear.

[0010] In order to achieve the above object, the technical solution adopted by the present invention is:

[0011] A reliability analysis method for gear pump side plate wear comprises the following steps;

[0012] Step 1: Perform force analysis on the gear pump side plate, including the force acting on the back, the force acting on the unloading groove, the gear cavity pressure and the clearance oil film pressure;

[0013] Step 2: Based on the stress analysis in step 1 and the Archard wear model, the wear amount formula of the gear pump side plate is established, which is the limit state function in the reliability analysis. The input variables include the gear radius, the axis distance between the two gears, the gear pump speed, the wear coefficient, the yield strength of the material, and the wear height of the output side plate.

[0014] Step 3: Calculate the parameters required for failure probability calculation (such as the number of sample points N in the sample pool, the number of initial training points N 0 , initial failure probability value p 0 , ξ to determine the size of the feasible domain, ε for the fault tolerance of the failure probability, Δ for the stopping threshold of the learning function, α for balancing the exploration and development capabilities, etc.) are initialized for the subsequent execution of the reliability algorithm.

[0015] Step 4: Establish a GPR model based on the initial training sample points generated in step 3 or update the GPR model using the newly added points to replace the limit state function established in step 2 to calculate the failure probability and reduce the calculation cost.

[0016] Step 5: Actively learn the GPR model generated in step 4 to obtain the lth intermediate failure event b land the corresponding intermediate design point Until in some iteration b l ≤0, let b l =0, the real design point can be obtained, and the adaptive addition point is returned to step 4 to update the GPR model during the active learning process;

[0017] Step 6: Calculate the important directions based on the actual design points obtained in step 5;

[0018] Step 7: Convert all point samples into line samples according to the important directions obtained in step 6, and actively learn to find the intersection of each line sample and the failure boundary. In the active learning process, adaptively add points and return to step 4 to update the GPR model;

[0019] Step 8: Based on the intersection point obtained in step 7, the failure probability of the gear pump side plate is estimated with the maximum wear amount not exceeding the specified value;

[0020] Step 1 is as follows:

[0021] During the working process of the gear pump, the forces on the side plate of the gear pump are divided into:

[0022] ① Force acting on the back of the side plate (away from the gear side): The force on the side away from the gear is mainly the pressure of the high-pressure oil. Therefore, this force is expressed as:

[0023] F Back =P HP A Back

[0024] Among them, F Back represents the force acting on the back of the side panel, P HP is the pressure of high pressure oil, A Back is the area of ​​the back of the side panel;

[0025] ② Force acting on the unloading groove: The forces acting on the two unloading grooves are assumed to be high pressure and low pressure respectively and are considered to be evenly distributed. The force is expressed as:

[0026] F Rel，HP =P HP A Rel，HP F Rel，LP =P LP A Rel，LP

[0027] Among them, F Rel，HP and F Rel，LP They represent the forces acting on the unloading groove in the high pressure area and the unloading groove in the low pressure area, respectively. HP and P LP For high pressure and low pressure, A Rel，HP and A Rel，LP They represent the areas of the unloading groove in the high-pressure zone and the unloading groove in the low-pressure zone respectively;

[0028] ③ The pressure acting in a single tooth cavity is obtained by simulation in Pumplinx (assuming that the pressure in each tooth cavity is uniformly distributed), and provides boundary conditions for solving the Reynolds equation;

[0029]

[0030] Among them, F TSV Represents the sum of the forces acting in the tooth cavity, P i and A i They represent the oil pressure in a single tooth cavity and the area of ​​a single tooth cavity respectively, and Z is the number of teeth;

[0031] ④ The force of the Reynolds equation solution caused by the gap oil film is a micro-dynamic force, which is calculated using the unit pressure and area of ​​the finite volume grid:

[0032]

[0033] F Oil is the force of the Reynolds equation solution caused by the gap oil film, P j and A j They represent the unit pressure and area of ​​the finite volume grid, respectively, and nfaces represents the number of grids;

[0034] Step 2 is as follows:

[0035] Based on the force analysis and the Archard model proposed earlier, the wear amount formula is expressed as:

[0036]

[0037] Among them, V is the wear volume of the part, l is the relative sliding distance, K is the wear coefficient related to the material and lubrication, F is the normal load acting on the part, and H represents the Brinell hardness. However, in practice, the yield strength σ of the material is easier to obtain, and H≈3×σ. Therefore, the above formula is expressed as:

[0038]

[0039] Divide both sides of the above equation by the contact area and simplify to obtain the wear model:

[0040]

[0041] Where P = F / A represents the contact stress, and L is the wear distance within one cycle.

[0042] The step 3 is specifically as follows:

[0043] Initialize N, N 0 ,ε,ξ,Δ EI , p0 , δ, and k * Generate N samples and select N from them 0 As the initial training sample set N 0 Set to 8-15;

[0044] ε and Δ EI Respectively represent the tolerance value and stop threshold of the first acquisition function. In order to ensure that the constraints are met The ε value should be very close to zero and is set to (0.5% to 3%) according to experience. y , where σ y is the standard deviation of the limit state function; the stopping threshold Δ EI Typically set to 10 -5 ~10 -8 ξ is a value used to specify the size of the feasible region; p 0 It is used to select the probability value of the intermediate fault event; δ is the fault tolerance value that controls the width of the integration interval of the second acquisition function, k * is the stopping threshold for the second acquisition function.

[0045] The step 4 is specifically as follows:

[0046] Construct an n-dimensional input variable represented as x=(x 1 , x 2 , …, x n ), the limit state function is g(x), and without knowing anything about g(x), we assume that it follows a Gaussian process Where m(x) represents the prior mean function, which can be selected as zero, a constant, or a polynomial; k(x, x′) represents the prior covariance function of any two points x and x′ of g(x);

[0047] Given a training set D = (X, Y), where X is the sample matrix, Y is the column vector of function values, and y (i) =g(x (i) );

[0048] It is known that the vector Y obeys the mean value m(X)=(m(x (1) ), m(x (2) ), …, m(x (N) )) T and a Gaussian distribution with covariance K, where the i-th element of the covariance matrix is ​​represented by k(x (i) , x (j) );

[0049] Then, the likelihood function is expressed as a Gaussian vector joint probability density function with mean function m(x) and covariance function k(x) (i) , x (j)), the hyperparameters are calculated by maximum likelihood estimation.

[0050] According to the above concepts, the posterior GPR model is inferred as:

[0051]

[0052] The posterior information μ g (x) and c g (x, x′) is expressed as:

[0053] μ g (x) = μ(xx) + k(X, x) T K -1 (y-μ(x))

[0054] c g (xx′)=k(x,x′)-k(X,x) T K -1 k(X, x)

[0055] where k(X, x) is a column vector whose i-th element is k(x (i) , x), the posterior variance is

[0056] Use training samples to build or update the GPR model. In this process, it is necessary to properly select the prior mean function and the prior covariance function.

[0057] Then, we get the posterior mean μ g (x) and the posterior variance

[0058] The step 5 is specifically as follows:

[0059] Specify b by Monte Carlo simulation l (l = 1, ..., m), in order to specify b l To find the value of b, we need to generate a set of samples from an independent Gaussian distribution with a variance of 1 and the center at the l-1th design point (MPP). Then we calculate the posterior mean predicted value of N points and sort the result values ​​in descending order. l The value of p is specified as 0 After the GPR model is updated, this value will also be automatically updated. 0 When the predicted value is less than zero, b l The value is set to zero.

[0060] The step 6 is specifically as follows:

[0061] Create a random process:

[0062]

[0063] In which ασ is introduced g Item (x) acts as a soft boundary, represents the average function of the random process h, where

[0064] By maximizing the mean function, we get a reference value x * . The acquisition function is defined as:

[0065]

[0066] By maximizing the acquisition function, the corresponding independent variable value x is obtained + ,if The design point is The significant directions are calculated; otherwise, the corresponding x and y values ​​are added to the training set and the GPR model is continued to be updated.

[0067] The step 7 is specifically as follows:

[0068] The GPR model trained in step 4 provides the posterior information μ g (x) and By solving μ g (x (s)⊥ +x / / e α ), (s=1, ..., N) to obtain the intersection point x of each line with the failure boundary (s)⊥ +ce α ,(s=1,…,N);

[0069] For line samples where no intersection can be found, the remaining lines are used instead. (s) The average value of (s=1, ..., N) is then calculated, and the acquisition function value corresponding to each intersection point is calculated:

[0070]

[0071] Find the minimum value K of the acquisition function min , if K min >k * , go to step 6, otherwise calculate the corresponding x and y values, add them to the training set and return to step 4.

[0072] Step 8 is specifically as follows: after obtaining the intersection point of the line sample and the failure boundary in step 7, the failure probability is calculated according to the reliability index corresponding to the intersection point.

[0073] Beneficial effects of the present invention.

[0074] This invention not only solves the problem of the original AGPR-LS method's dependence on important directions and can effectively evaluate small failure probability events, but also fills the gap in the reliability analysis of the gear pump side plate, which helps to control the entire operation cycle of the gear pump and prevent failures in advance.

[0075] The present invention calculates the failure probability corresponding to the side plate wear when t / T=500000. The algorithm proposed in the present invention only needs about 75 sample points to meet the convergence condition, and the corresponding coefficient of variation is very small. That is to say, compared with other methods, the sample size is greatly reduced, the calculation cost is reduced, and the calculation efficiency is improved while ensuring the calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 Schematic diagram of the ConBaySubOpt algorithm solving the design point.

[0077] Figure 2 is a schematic diagram of the acquisition function, Figure 2 a is the comparison diagram of limit state function, Figure 2 b is a comparison chart of probability density functions.

[0078] Figure 3 This is the flow chart of the Optimization-Based ALS algorithm.

[0079] Figure 4 This is the reliability analysis flow chart of the gear pump side plate.

[0080] Figure 5 This is the force diagram of the gear pump side plate. DETAILED DESCRIPTION

[0081] 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.

[0082] A reliability analysis method for gear pump side plate wear comprises the following steps;

[0083] Step 1: Perform force analysis on the gear pump side plate, including the force acting on the back, the force acting on the unloading groove, the gear cavity pressure and the clearance oil film pressure;

[0084] Step 2: Based on the stress analysis in step 1 and the Archard wear model, the wear amount formula of the gear pump side plate is established, which is the limit state function in the reliability analysis. The input variables include the gear radius, the axis distance between the two gears, the gear pump speed, the wear coefficient, the yield strength of the material, and the wear height of the output side plate.

[0085] Step 3: Calculate the parameters required for failure probability calculation (such as the number of sample points N in the sample pool, the number of initial training points N 0 , initial failure probability value p 0 , ξ to determine the size of the feasible domain, ε for the fault tolerance of the failure probability, Δ for the stopping threshold of the learning function, α for balancing the exploration and development capabilities, etc.) are initialized for the subsequent execution of the reliability algorithm.

[0086] Step 4: Establish a GPR model based on the initial training sample points generated in step 3 or update the GPR model using the newly added points to replace the limit state function established in step 2 to calculate the failure probability and reduce the calculation cost.

[0087] Step 5: Actively learn the GPR model generated in step 4 to obtain the lth intermediate failure event b l and the corresponding intermediate design point Until in some iteration b l ≤0, let b l =0, the real design point can be obtained, and the adaptive addition point is returned to step 4 to update the GPR model during the active learning process;

[0088] Step 6: Calculate the important directions based on the actual design points obtained in step 5;

[0089] Step 7: Convert all point samples into line samples according to the important directions obtained in step 6, and actively learn to find the intersection of each line sample and the failure boundary. In the active learning process, adaptively add points and return to step 4 to update the GPR model;

[0090] Step 8: Based on the intersection point obtained in step 7, the failure probability of the gear pump side plate is estimated with the maximum wear amount not exceeding the specified value;

[0091] Step 1 is as follows:

[0092] During the working process of the gear pump, the forces on the side plate of the gear pump are divided into the following types after analysis: Figure 5 . Explain these forces separately.

[0093] ① Force acting on the back of the side plate (away from the gear side): The force on the side away from the gear is mainly the pressure of the high-pressure oil. Therefore, this force is expressed as:

[0094] F Back =PHP A Back

[0095] Among them, F Back represents the force acting on the back of the side panel, P HP is the pressure of high pressure oil, A Back is the area of ​​the back of the side panel.

[0096] ② Force acting on the unloading groove: The forces acting on the two unloading grooves are assumed to be high pressure and low pressure respectively and are considered to be evenly distributed. The force is expressed as:

[0097] F Rel，HP =P HP A Rel，HP F Rel，LP =P LP A Rel，LP

[0098] Among them, F Rel，HP and F Rel，LP They represent the forces acting on the unloading groove in the high pressure area and the unloading groove in the low pressure area, respectively. HP and P LP For high pressure and low pressure, A Rel，HP and A Rel，LP They represent the areas of the unloading groove in the high-pressure zone and the unloading groove in the low-pressure zone respectively.

[0099] ③ The pressure acting in a single tooth cavity is obtained by simulation in Pumplinx (assuming that the pressure in each tooth cavity is uniformly distributed), and provides boundary conditions for solving the Reynolds equation. Figure 4 It can be seen from the figure that the tooth chamber pressure shows a gradual increase from the inlet to the outlet.

[0100]

[0101] Among them, F TSV Represents the sum of the forces acting in the tooth cavity, P i and A i They represent the oil pressure in a single tooth cavity and the area of ​​a single tooth cavity respectively, and Z is the number of teeth.

[0102] ④ The force of the Reynolds equation solution caused by the gap oil film is a micro-dynamic force, which is calculated using the unit pressure and area of ​​the finite volume grid:

[0103]

[0104] F Oil is the force of the Reynolds equation solution caused by the gap oil film, P j and A j They represent the unit pressure and area of ​​the finite volume grid respectively, and nfaces represents the number of grids.

[0105] Step 2 is as follows:

[0106] Based on the force analysis and the Archard model proposed earlier, the wear amount formula is expressed as:

[0107]

[0108] Among them, V is the wear volume of the part, l is the relative sliding distance, K is the wear coefficient related to the material and lubrication, F is the normal load acting on the part, and H represents the Brinell hardness. However, in practice, the yield strength σ of the material is easier to obtain, and H≈3×σ. Therefore, the above formula is expressed as:

[0109]

[0110] However, in terms of the wear problem of the side plate in the gear pump, it is found that it is more meaningful to study the wear height. Therefore, both sides of the above equation are divided by the contact area and simplified to obtain the wear model:

[0111]

[0112] Where P = F / A represents the contact stress, and L is the wear distance within one cycle.

[0113] The step 3 is specifically as follows:

[0114] Initialize N, N 0 ,ε,ξ,Δ EI , p 0 , δ, and k * Generate N samples and select N from them 0 As the initial training sample set N 0 Set to 8-15;

[0115] ε and Δ EI Respectively represent the tolerance value and stop threshold of the first acquisition function. In order to ensure that the constraints are met The ε value should be very close to zero and is set to (0.5% to 3%) according to experience. y , where σ y is the standard deviation of the limit state function; the stopping threshold Δ EI Typically set to 10 -5 ~10 -8 ξ is the value used to specify the size of the feasible region, and a value of 2-4 is generally recommended; p 0 It is used to select the probability value of the intermediate fault event, which can be set to 0.01-0.05; δ is the fault tolerance value for controlling the integral interval width of the second acquisition function, which is set to (1%~10~)σ y . k *is the stopping threshold of the second acquisition function, which takes a value of 0.985.

[0116] The step 4 is specifically as follows:

[0117] GPR is a nonparametric model that uses a Gaussian prior process to perform regression analysis on data; it constructs an n-dimensional input variable represented by x = (x 1 , x 2 , …, x n ), the limit state function is g(x), and without knowing anything about g(x), we assume that it follows a Gaussian process Where m(x) represents the prior mean function, which can be selected as zero, constant, or polynomial; k(x, x′) represents the prior covariance function of any two points x and x′ in g(x), which can be a polynomial kernel, a square exponential kernel, a matern kernel, etc. Given a training set D = (X, Y), where X is the sample matrix, Y is the column vector of the function value, and y (i) =g(x (i) ). It is known that the vector Y obeys the mean value m(X)=(m(x (1) ), m(x (2) ), …, m(x (N) )) T and a Gaussian distribution with covariance K, where the i-th element of the covariance matrix is ​​represented by k(x (i) , x (j) ). Then, the likelihood function is expressed as a Gaussian vector joint probability density function with mean function m(x) and covariance function k(x) (i) , x (j) ), the hyperparameters are calculated by maximum likelihood estimation.

[0118] According to the above concepts, the posterior GPR model is inferred as:

[0119]

[0120] The posterior information μ g (x) and c g (x, x′) is expressed as:

[0121] g(x)=μ(xx)+k(X,x) T K -1 (y-μ(x))

[0122] c g (x, x′)=k(x, x′)-k(X, x) T K -1 k(X, x)

[0123] where k(X, x) is a column vector whose i-th element is k(x(i) , x), the posterior variance is

[0124] Use training samples to build or update the GPR model. In this process, it is necessary to appropriately select the prior mean function and the prior covariance function.

[0125] Then, we get the posterior mean μ g (x) and the posterior variance

[0126] The step 5 is specifically as follows:

[0127] Specify b by Monte Carlo simulation l (l = 1, ..., m), in order to specify b l To find the value of , we need to generate a set of samples from an independent Gaussian distribution with variance 1 centered at the lth design point (MPP). Then we calculate the posterior mean predicted value of the N points and sort the resulting values ​​in descending order. l The value of p is specified as 0 After the GPR model is updated, this value will also be automatically updated. 0 When the predicted value is less than zero, b l The value is set to zero.

[0128] The step 6 is specifically as follows:

[0129] Create a random process:

[0130]

[0131] In which ασ is introduced g The (x) term acts as a soft boundary, and this additional term provides enough flexibility to the acquisition function to balance the functions of exploration and exploitation. represents the average function of the random process h, where

[0132] By maximizing the mean function, we get a reference value x * . The acquisition function is defined as:

[0133]

[0134] By maximizing the acquisition function, the corresponding independent variable value x is obtained + ,if The design point is Further calculations are performed to obtain important directions. Otherwise, the corresponding x and y values ​​are added to the training set and the GPR model is continued to be updated. Figure 1This is the process of actively learning the design point in layers. In this example, the real design point is found through three layers. The three rectangles of different colors represent the feasible domain of each layer, and the black dots represent the design point of each layer. and express.

[0135] The step 7 is specifically as follows:

[0136] The GPR model trained in step 4 provides the posterior information μ g (x) and Therefore, by solving μ g (x (s)⊥ +x / / e α ), (s=1, ..., N) to obtain the intersection point x of each line with the failure boundary (s)⊥ +ce α , (s = 1, ..., N). For the line samples where no intersection can be found, the remaining lines are used instead. (s) Then calculate the acquisition function value corresponding to each intersection point:

[0137]

[0138] Find the minimum value K of the acquisition function min , if K min >k * , go to step 6, otherwise calculate the corresponding x and y values, add them to the training set and return to step 2, Figure 2 The learning function is illustrated in (a). and For the same sample line and failure surface and Figure (b) is the probability density function corresponding to the two points. We can clearly see that compared to The prediction error is larger, so its mass ratio in the small interval [-δ, δ] is few.

[0139] The step 8 is specifically as follows:

[0140] After calculating the intersection points of each line, the failure probability value is estimated. Then the coefficient of variation (Cov) is calculated, and if its value is greater than 0.05, more line samples are added and return to step 6, otherwise the algorithm ends. Figure 3 The flowchart of the whole calculation process is shown in Figure 2.

[0141] Example:

[0142] At present, the gear pumps with automatic axial clearance compensation used at home and abroad have always had problems such as serious side plate wear and failure of floating side plate end face seal. In order to ensure the reliability, operation stability and service life of the fuel pump, the reliability method proposed in this invention is used to evaluate the reliability of the wear failure of the gear pump side plate. The overall flow chart is as follows: Figure 4 shown.

[0143] During the working process of the gear pump, the forces on the side plate of the gear pump are divided into the following types after analysis: Figure 5 . Explain these forces separately.

[0144] ① Force acting on the back of the side plate (away from the gear side): The force on the side away from the gear is mainly the pressure of the high-pressure oil. Therefore, this force is expressed as:

[0145] F Back =P HP A Back

[0146] Among them, F Back represents the force acting on the back of the side panel, P HP is the pressure of high pressure oil, A Back is the area of ​​the back of the side panel.

[0147] ② Force acting on the unloading groove: The forces acting on the two unloading grooves are assumed to be high pressure and low pressure respectively and are considered to be evenly distributed. The force is expressed as:

[0148] F Rel，HP =P HP A Rel，HP F Rel，LP =P LP A Rel，LP

[0149] Among them, F Rel，HP and F Rel，LP They represent the forces acting on the unloading groove in the high pressure area and the unloading groove in the low pressure area, respectively. HP and P LP For high pressure and low pressure, A Rel，HP and A Rel，LP They represent the areas of the unloading groove in the high-pressure zone and the unloading groove in the low-pressure zone respectively.

[0150] ③ The pressure acting in a single tooth cavity is obtained by simulation in Pumplinx (assuming that the pressure in each tooth cavity is uniformly distributed), and provides boundary conditions for solving the Reynolds equation. Figure 4 It can be seen from the figure that the tooth chamber pressure shows a gradual increase from the inlet to the outlet.

[0151]

[0152] Among them, FTSV Represents the sum of the forces acting in the tooth cavity, P i and A i They represent the oil pressure in a single tooth cavity and the area of ​​a single tooth cavity respectively, and Z is the number of teeth.

[0153] ④ The force of the Reynolds equation solution caused by the gap oil film is a micro-dynamic force, which is calculated using the unit pressure and area of ​​the finite volume grid:

[0154]

[0155] F Oil is the force of the Reynolds equation solution caused by the gap oil film, P j and A j They represent the unit pressure and area of ​​the finite volume grid respectively, and nfaces represents the number of grids.

[0156] Based on the force analysis and the Archard model proposed earlier, the wear amount formula is expressed as:

[0157]

[0158] Among them, V is the wear volume of the part, l is the relative sliding distance, K is the wear coefficient related to the material and lubrication, F is the normal load acting on the part, and H represents the Brinell hardness. However, in practice, the yield strength σ of the material is easier to obtain, and H≈3×σ. Therefore, the above formula is expressed as:

[0159]

[0160] However, in terms of the wear problem of the side plate in the gear pump, it is found that it is more meaningful to study the wear height. Therefore, both sides of the above equation are divided by the contact area and simplified to obtain the wear model:

[0161]

[0162] Where P = F / A represents the contact stress, and L is the wear distance within one cycle.

[0163] The wear state equation of the side plate at the working time t is established based on the fact that the wear height exceeds the specified value, which means failure:

[0164]

[0165] Where h max It represents the maximum allowable wear height of the side plate without failure, and its value is 0.655mm; X is the uncertainty factor in the equation, including gear radius R, shaft center distance d, gear speed n, wear coefficient K, and material yield strength σ.

[0166] The distribution information of these parameters is shown in Table 1.

[0167] Table 1 Distribution information of input parameters

[0168]

[0169]

[0170] Using the Optimization-Based ALS reliability algorithm proposed in the present invention, the wear failure problem of the gear pump side plate is evaluated for reliability, with the maximum wear depth not exceeding a given value as the failure criterion. The failure probability corresponding to the side plate wear when t / T=500000. The calculation results of different methods are shown in Table 2. It can be seen from the table that the calculation results of the four methods are basically similar. The Optimization-Based ALS algorithm only requires about 75 sample points to meet the convergence conditions, and the corresponding coefficient of variation is very small. In comparison, the AGPR-MCMC algorithm consumes 10 more sample points and has a larger coefficient of variation. If the traditional MCS algorithm is used, it will consume 10 7 Sample points are required to achieve satisfactory results, which requires a great deal of time and computational cost. The method adopted by the present invention greatly reduces the number of samples used, improves efficiency, and saves space while ensuring accurate calculation of failure probability.

[0171] Table 2: Comparison of calculation results

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Claims

1. A reliability analysis method for gear pump side plate wear, characterized in that: The steps include: Step 1: Perform force analysis on the gear pump side plate, including the force acting on the back, the force acting on the unloading groove, the gear cavity pressure and the clearance oil film pressure; Step 2: Based on the stress analysis in step 1 and the Archard wear model, the wear amount formula of the gear pump side plate is established, which is the limit state function in the reliability analysis. The input variables include the gear radius, the axis distance between the two gears, the gear pump speed, the wear coefficient, the yield strength of the material, and the wear height of the output side plate. Step 3: Initialize the parameters required for calculating the failure probability for subsequent reliability algorithm execution; Step 4: Establish a GPR model based on the initial training sample points generated in step 3 or update the GPR model using the newly added points to replace the limit state function established in step 2 to calculate the failure probability and reduce the calculation cost; Step 5: Actively learn the GPR model generated in step 4 to obtain the lth intermediate failure event b l and the corresponding intermediate design point Until in some iteration b l ≤0, let b l =0, the real design point can be obtained, and the adaptive addition point is returned to step 4 to update the GPR model during the active learning process; Step 6: Calculate the important directions based on the actual design points obtained in step 5; Step 7: Convert all point samples into line samples according to the important directions obtained in step 6, and actively learn to find the intersection of each line sample and the failure boundary. In the active learning process, adaptively add points and return to step 4 to update the GPR model; Step 8: Based on the intersection point obtained in step 7, estimate the failure probability of the gear pump side plate with the maximum wear amount not exceeding the specified value.

2. A reliability analysis method for gear pump side plate wear according to claim 1, characterized in that: Step 1 specifically includes: During the working process of the gear pump, the forces on the side plate of the gear pump are divided into: ① Force acting on the back of the side plate (away from the gear side): The force on the side away from the gear is mainly the pressure of the high-pressure oil. Therefore, this force is expressed as: F Back =P HP A Back where F Back represents the force acting on the back of the side panel, P HP is the pressure of high pressure oil, A Back is the area of ​​the back of the side panel; ② Force acting on the unloading groove: The forces acting on the two unloading grooves are assumed to be high pressure and low pressure respectively and are considered to be evenly distributed. The force is expressed as: F Rel，HP =P HP A Rel，HP F Rel，LP =P LP A Rel，LP where F Rel，HP and F Rel，LP They represent the forces acting on the unloading groove in the high pressure area and the unloading groove in the low pressure area, respectively. HP and P LP For high pressure and low pressure, A Rel，HP and A Rel，LP They represent the areas of the unloading groove in the high-pressure zone and the unloading groove in the low-pressure zone respectively; ③ The pressure acting in a single tooth cavity is obtained by simulation in Pumplinx (assuming that the pressure in each tooth cavity is uniformly distributed), and provides boundary conditions for solving the Reynolds equation; where F TSV Represents the sum of the forces acting in the tooth cavity, P i and A i They represent the oil pressure in a single tooth cavity and the area of ​​a single tooth cavity respectively, and Z is the number of teeth; ④ The force of the Reynolds equation solution caused by the gap oil film is a micro-dynamic force, which is calculated using the unit pressure and area of ​​the finite volume grid: F Oil is the force of the Reynolds equation solution caused by the gap oil film, P j and A j They represent the unit pressure and area of ​​the finite volume grid respectively, and nfaces represents the number of grids.

3. The reliability analysis method for gear pump side plate wear according to claim 1, characterized in that: Step 2 is as follows: Based on the force analysis and the Archard model proposed earlier, the wear amount formula is expressed as: Among them, V is the wear volume of the part, l is the relative sliding distance, K is the wear coefficient related to the material and lubrication, F is the normal load acting on the part, and H represents the Brinell hardness. However, in practice, the yield strength σ of the material is easier to obtain, and H≈3×σ; so the above formula is expressed as: Divide both sides of the above equation by the contact area and simplify to obtain the wear model: Where P = F / A represents the contact stress, and L is the wear distance within one cycle.

4. A reliability analysis method for gear pump side plate wear according to claim 1, characterized in that: The step 3 is specifically as follows: Initialize N, N0, ε, ξ, Δ EI , p0, δ, and k * Generate N samples and select N0 as the initial training sample set N0 is set to 8-15; ε and Δ EI Respectively represent the tolerance value and stop threshold of the first acquisition function. In order to ensure that the constraints are met The ε value should be very close to zero and is set to (0.5% to 3%) according to experience. y , where σ y is the standard deviation of the limit state function; the stopping threshold Δ EI Typically set to 10 -5 ~10 -8 ξ is a value used to specify the size of the feasible region; p0 is used to select the probability value of the intermediate fault event; δ is the fault tolerance value that controls the width of the integral interval of the second acquisition function, k * is the stopping threshold for the second acquisition function.

5. The reliability analysis method for gear pump side plate wear according to claim 1, characterized in that: The step 4 is specifically as follows: Construct an n-dimensional input variable represented as x = (x1, x2, ..., x n ), the limit state function is g(x), and without knowing anything about g(x), we assume that it follows a Gaussian process Where m(x) represents the prior mean function, which can be selected as zero, a constant, or a polynomial; k(x, x′) represents the prior covariance function of any two points x and x′ of g(x); Given a training set D = (X, Y), where X is the sample matrix, Y is the column vector of function values, and y (i) =g(x (i) ); It is known that the vector Y obeys the mean value m(X)=(m(x (1) ), m(x (2) ), …, m(x (n) )) T and a Gaussian distribution with covariance K, where the i-th element of the covariance matrix is ​​represented by k(x (i) , x (j) ); Then, the likelihood function is expressed as a Gaussian vector joint probability density function with mean function m(x) and covariance function k(x) (i) , x (j) ), the hyperparameters are calculated by maximum likelihood estimation.

6. A reliability analysis method for gear pump side plate wear according to claim 5, characterized in that: According to the above concepts, the posterior GPR model is inferred as: The posterior information μ g (x) and c g (x, x′) is expressed as: μ g (x)=μ(xx)+k(X,x) T K -1 (y-μ(x)) c g (x,x′)=k(x,x′)-k(X,x) T K -1 k(X,x) where k(X, x) is a column vector whose i-th element is k(x (i) , x), the posterior variance is Use training samples to build or update the GPR model. In this process, it is necessary to properly select the prior mean function and the prior covariance function. Then, we get the posterior mean μ g (x) and the posterior variance 7. A reliability analysis method for gear pump side plate wear according to claim 6, characterized in that: The step 5 is specifically as follows: Specify b by Monte Carlo simulation l (l = 1, ..., m), in order to specify b l To find the value of b, we need to generate a set of samples from an independent Gaussian distribution with a variance of 1 and the center at the l-1th design point (MPP). Then we calculate the posterior mean predicted value of N points and sort the result values ​​in descending order. l The value of is specified as the p0th prediction value. After the GPR model is updated, this value will also be automatically updated. When the p0th prediction value is less than zero, b l The value is set to zero.

8. A reliability analysis method for gear pump side plate wear according to claim 7, characterized in that: The step 6 is specifically as follows: Create a random process: In which ασ is introduced g Item (x) acts as a soft boundary, represents the average function of the random process h, where By maximizing the mean function, we get a reference value x * . The acquisition function is defined as: By maximizing the acquisition function, the corresponding independent variable value x is obtained + ,if The design point is The significant directions are calculated; otherwise, the corresponding x and y values ​​are added to the training set and the GPR model is continued to be updated.

9. A reliability analysis method for gear pump side plate wear according to claim 8, characterized in that: The step 7 is specifically as follows: The GPR model trained in step 4 provides the posterior information μ g (x) and By solving Get the intersection of each line with the failure boundary For line samples where no intersection can be found, the remaining lines are used instead. (s) The average value of (s=1, ..., N) is then calculated, and the acquisition function value corresponding to each intersection point is calculated: Find the minimum value K of the acquisition function min , if K min >k * , go to step 6, otherwise calculate the corresponding x and y values, add them to the training set and return to step 4.

10. A reliability analysis method for gear pump side plate wear according to claim 9, characterized in that: Step 8 is specifically as follows: after obtaining the intersection point of the line sample and the failure boundary in step 7, the failure probability is calculated according to the reliability index corresponding to the intersection point.

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