Method for predicting mechanical abrasion loss of artillery barrel based on discrete element method

Abstract

The invention belongs to the technical field of wear prediction of metal interfaces, and discloses a method for predicting mechanical wear loss of an artillery barrel based on a discrete element method. The method comprises the following steps: establishing an artillery barrel triaxial shear numerical model through PFC2D / 3D software, selecting a contact model, and determining calibrated macroscopic and microscopic parameters and ranges thereof; designing a numerical test scheme by using an orthogonal test; carrying out a numerical test by using PFC2D / 3D software according to the test scheme; analyzing the significance of the influence of each mesoscopic parameter on the macroscopic mechanical parameters by adopting a multi-factor variance, and screening out main mesoscopic parameters which influence the macroscopic mechanical indexes; establishing a relational expression between the macroscopic parameter and each main mesoscopic parameter through regression analysis; a calibration problem is converted into a multi-objective function mathematical programming problem to be solved, and a numerical test result and live ammunition test data are compared and verified. The method has the advantages of being suitable for simulation of high-hardness and high-brittleness metal materials and high in model prediction precision.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wear prediction of metal interface, and particularly relates to a method for predicting mechanical wear of a gun barrel based on a discrete element method. BACKGROUND

[0002] Currently, the life and reliability of a gun barrel are key factors that restrict the combat effectiveness of a weapon system. Gun barrel wear mainly includes ablation wear and mechanical wear. Although domestic and foreign scholars have conducted long-term research on gun barrel wear, the existing technology still has the following outstanding problems and limitations:

[0003] (1) Lack of research on mechanical wear: existing research mostly focuses on ablation wear caused by thermal cycling and chemical erosion, and the research attention and depth of mechanical wear caused by bullet extrusion, high-speed friction and other mechanical actions are relatively insufficient.

[0004] (2) Limitations of traditional wear models: current theoretical calculations of mechanical wear are generally based on the Archard wear model. This model is suitable for calculating the wear of relatively soft materials, but a "white layer" microstructure with high hardness and brittleness will form on the inner wall of the gun barrel under high temperature and high pressure. The Archard model cannot accurately describe the wear, cracking and spalling behavior of this brittle material, resulting in significant deviations between theoretical predictions and actual situations.

[0005] (3) Unknown white layer wear mechanism and lack of effective simulation means: research shows that the spalling of the white layer is an important factor in the loss of barrel material, and the position of the most severe wear is directly related to the end of the barrel life. However, due to the complexity of the white layer material properties (high hardness and high brittleness), there is a lack of effective numerical simulation and quantitative analysis methods specifically for the mechanical wear behavior of the white layer, which cannot accurately reveal the wear mechanism and key influence laws of the white layer during bullet extrusion. SUMMARY

[0006] The present application provides a method for predicting the mechanical wear of a gun barrel based on the discrete element method to solve the practical problems existing in the prior art in the background art.

[0007] To solve the above technical problems, the present application adopts the following technical solution: a method for predicting the mechanical wear of a gun barrel based on the discrete element method, which specifically includes the following steps:

[0008] S1) First, determine the macro-mechanical parameter value of the gun barrel metal material to be predicted, and then determine the initial mesoscopic parameter value of the gun barrel metal material to be predicted;

[0009] S2) Determine the macro-mechanical parameter value of the initial mesoscopic parameter value obtained in S1);

[0010] S3) determining the main meso-parameters of the macro-mechanical parameter values obtained in S2) by using multi-factor variance analysis method;

[0011] S4) establishing the relationship between the macro-parameters obtained in S2) and the main meso-parameters obtained in S3) by using regression analysis;

[0012] S5) bringing the predicted macro-mechanical parameter values of the gun barrel metal material itself into the relationship in S4) to solve and obtain the predicted meso-parameters of the gun barrel metal material itself;

[0013] S6) predicting the gun barrel wear amount by using the predicted meso-parameters of the gun barrel metal material itself obtained in S5).

[0014] Further, the macro-mechanical parameters in S1) include: macro-Poisson ratio v, macro-elastic modulus E, macro-compressive strength σ f , macro-tensile strength σ t , macro-cohesion c and macro-internal friction angle φ.

[0015] The meso-parameters include: the meso-parameters required to be inputted in the flat joint contact model include flat joint modulus E c , flat joint stiffness ratio k n / k s , flat joint tensile strength σ b , flat joint cohesion c b , flat joint internal friction angle φ b and flat joint friction coefficient μ b .

[0016] Further, the specific steps of S1) are as follows:

[0017] S1.1) selecting the gun barrel metal material to be predicted, and obtaining the macro-mechanical parameter values of the gun barrel metal material to be predicted by experiment;

[0018] S1.2) setting the meso-parameter value range of the gun barrel metal material to be predicted, and selecting the initial meso-parameter values according to the meso-parameter value range of the gun barrel metal material to be predicted.

[0019] Further, the meso-parameter value range in S1.2) is as follows: flat joint modulus E c = 100-1000 MPa, flat joint stiffness ratio k n / k s = 1-10, flat joint tensile strength σ b = 100-1000 MPa, flat joint cohesion c b = 100-1000 MPa, flat joint internal friction angle φb = 0.1°-20°, flat joint friction coefficient μ b = 0.001-0.2.

[0020] Further, the specific steps of S2) are:

[0021] S2.1) First, a two-dimensional granular assembly model of the gun barrel metal material is established by PFC2D software, in which the flat joint contact model is selected for the contact between particles, and the initial mesoscopic parameter values selected in S1) are inputted;

[0022] S2.2) Then, the model is subjected to uniaxial compression, uniaxial tension, and biaxial compression numerical tests, each time using an un-stretched or un-compressed model, and the steps are as follows: uniaxial compression - generate upper and lower rigid walls, and continuously extrude the granular assembly model at a constant speed of 0.1 m / s, until the model cracks and eventually breaks, and the stress-strain curve can be obtained to obtain the Poisson's ratio v, the elastic modulus E and the compressive strength σ;

[0023] uniaxial tension - the particles at the top and bottom of the model move in the vertical direction in opposite directions at a speed of 0.1 m / s, and the stress peak value of the stress-strain curve is the tensile strength σ of the material;

[0024] biaxial compression - generate upper and lower rigid walls, and the left and right walls are continuously adjusted in radial velocity and direction by servo mechanism, thereby maintaining a constant pressure (two biaxial compression tests are performed, the constant pressures are set to 500 MPa and 700 MPa respectively, and the top and bottom walls compress the granular assembly model at a speed of 0.1 m / s until the model breaks, the compressive strength is obtained each time, according to the Mohr circle equation, the constant pressure and the compressive strength are brought in, and the inclination angle of the strength envelope line obtained is the internal friction angle φ, and the intercept of the envelope line with the y-axis is the cohesion c.

[0025] Further, the specific steps of S3) are:

[0026] S3.1) input the initial mesoscopic parameters selected in S1) as input variables;

[0027] S3.2) take the macro-mechanical parameters obtained by numerical test in S2) as output variables, and construct a data set;

[0028] S3.3) perform multi-factor variance analysis based on the data set, construct F statistics FA by calculating the ratio of inter-group mean square to intra-group mean square of each factor, and compare it with the critical value Fα at a given significance level α; if FA>Fα, it is determined that the factor A has a significant effect on the macro-mechanical parameter and is determined as the main mesoscopic parameter value of the macro-mechanical parameter.

[0029] Further, the specific step of S4) is:

[0030] S4.1) taking the main mesoscopic parameters obtained from S3) as input features,

[0031] S4.2) performing regression analysis on the macro-mechanical parameters to obtain a relationship between the macro-mechanical parameters and the mesoscopic parameters.

[0032] Further, the regression analysis is not limited to linear regression, and other machine learning regression algorithms such as polynomial regression, ridge regression, etc. can also be selected. The model form established includes but is not limited to linear relationship.

[0033] Further, the specific step of S5) is:

[0034] The macro-mechanical parameter value of the predicted gun barrel metal material itself obtained from S1) is brought into the relationship of S4) to solve and obtain the mesoscopic parameter value of the predicted gun barrel metal material itself.

[0035] Further, the specific step of S6) is:

[0036] S6.1) First, a three-dimensional particle assembly model of the predicted gun barrel metal material in a close state and the upper, lower, left and right six walls are established by PFC3D software, a flat joint contact model between particles is selected, and a Rolling resistence model between particles and walls is selected,

[0037] S6.2) input the mesoscopic parameter value of the predicted gun barrel metal material itself in S5), then delete the left wall, and set the speed of all walls except the upper wall to 0 m / s;

[0038] S6.2) Finally, input the moving speed of the upper wall to the left, i.e. the movement speed of the projectile relative to the barrel, 1-50 m / s, and the pressure between the upper wall and the particles, i.e. the load between the projectile and the barrel, 100-1000 MPa, and keep it constant, and input the cycle number 1-1000 times, and calculate, i.e. obtain the wear amount of the gun barrel.

[0039] The beneficial effects of the present application are: due to the above technical scheme, the method of the present application has the advantages of being applicable to simulation of high-hardness and high-brittle metal materials and high model prediction accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 is the discrete element method flow chart of the gun barrel mechanical wear prediction provided by the embodiment of the present application.

[0041] Figure 2 is a schematic diagram of the flat joint contact model provided by the embodiment of the present application.

[0042] Figure 3(a) is a force-displacement law of the contact force of the unbonded flat joint element according to an embodiment of the present application.

[0043] Figure 3(b) is a force-displacement law of the contact force of the bonded flat joint element according to an embodiment of the present application.

[0044] Figure 4 Figure 4 is a schematic diagram of a three-dimensional granular flow numerical model according to an embodiment of the present application.

[0045] Figure 5 Figure 5 is a uniaxial compression numerical simulation curve according to an embodiment of the present application; (a) is a uniaxial compression axial stress-strain curve diagram according to an embodiment of the present application; (b) is a uniaxial compression radial axial strain curve diagram according to an embodiment of the present application.

[0046] Figure 6 Figure 6 is a uniaxial tensile axial stress-strain curve diagram according to an embodiment of the present application.

[0047] Figure 7 Figure 7 is a biaxial compression stress Mohr circle and its envelope diagram according to an embodiment of the present application.

[0048] Figure 8 Figure 8 is a multi-factor variance analysis column chart of the elastic modulus according to an embodiment of the present application.

[0049] Figure 9 Figure 9 is a multi-factor variance analysis column chart of the compressive strength according to an embodiment of the present application.

[0050] Figure 10 Figure 10 is a multi-factor variance analysis column chart of the Poisson's ratio according to an embodiment of the present application.

[0051] Figure 11 Figure 11 is a multi-factor variance analysis column chart of the tensile strength according to an embodiment of the present application.

[0052] Figure 12 Figure 12 is a multi-factor variance analysis column chart of the cohesion according to an embodiment of the present application.

[0053] Figure 13 Figure 13 is a multi-factor variance analysis column chart of the internal friction angle according to an embodiment of the present application.

[0054] Figure 14 Figure 14 is a comparison diagram of the predicted wear thickness and the live ammunition experimental data according to an embodiment of the present application. DETAILED DESCRIPTION

[0055] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] To address the problems existing in the prior art, this invention provides a method for predicting the mechanical wear of artillery barrels based on the discrete element method. The invention will be described in detail below with reference to the accompanying drawings.

[0057] like Figure 1 As shown, this invention provides a method for predicting the mechanical wear of artillery barrels based on the discrete element method. The method specifically includes the following steps:

[0058] S1) First determine the macroscopic mechanical parameters of the metal material of the gun barrel to be predicted, and then determine the initial microscopic parameters of the metal material of the gun barrel to be predicted.

[0059] S2) Determine the macroscopic mechanical parameter values ​​obtained from the initial mesoscopic parameter values ​​in S1);

[0060] S3) Use multifactor analysis of variance to determine the main micro-parameter values ​​of the macroscopic mechanical parameters obtained in S2);

[0061] S4) Use regression analysis to establish the relationship between the macroscopic parameters obtained in S2) and the main microscopic parameters obtained in S3);

[0062] S5) Substitute the predicted macroscopic mechanical parameters of the gun barrel metal material into the relation in S4 to solve for the predicted microscopic parameters of the gun barrel metal material.

[0063] S6) The wear of the gun barrel is predicted by using the microscopic parameter values ​​of the predicted gun barrel metal material obtained in S5).

[0064] Furthermore, the macroscopic mechanical parameters in S1) include: macroscopic Poisson's ratio v, macroscopic elastic modulus E, and macroscopic compressive strength σ. f Macroscopic tensile strength σ t Macroscopic cohesion c and macroscopic internal friction angle φ.

[0065] Furthermore, the mesoscopic parameters in S1) include: the mesoscopic parameters required for the straight joint contact model include the straight joint modulus E. c Straight joint stiffness ratio k n / k s σ of straight joints b Straight joint adhesion c b φ, the internal friction angle of a straight joint bFriction coefficient of flat joint μ b .

[0066] Further, the specific steps of S1) are:

[0067] S1.1) selecting the gun barrel metal material to be predicted, and obtaining the macro-mechanical parameter values of the gun barrel metal material to be predicted by experiment;

[0068] S1.2) setting the mesoscopic parameter value range of the gun barrel metal material to be predicted, and selecting the initial mesoscopic parameter values according to the mesoscopic parameter value range of the gun barrel metal material to be predicted.

[0069] Further, the mesoscopic parameter value range is: flat joint modulus E c = 100 MPa-1000 MPa, flat joint stiffness ratio k n / k s = 1-10, flat joint tensile strength σ b = 100 MPa-1000 MPa, flat joint bonding force c b = 100 MPa-1000 MPa, flat joint internal friction angle φ b = 0.1°-20°, flat joint friction coefficient μ b = 0.001-0.2.

[0070] Further, the specific steps of S2) are:

[0071] S2.1) first, a two-dimensional granular assembly model of the gun barrel metal material to be predicted is established by PFC2D software, in which the flat joint contact model is selected for the contact between particles, and the initial mesoscopic parameter values selected in S1) are inputted;

[0072] S2.2) then the model is subjected to uniaxial compression, uniaxial tension, and biaxial compression numerical tests, and the model is not stretched or compressed each time, and the steps are as follows: uniaxial compression - generate upper and lower rigid walls, and continuously extrude the granular assembly model at a constant speed of 0.1 m / s, until the model cracks and finally breaks, and the stress-strain curve can be obtained to obtain the three macro-mechanical parameters of compressive strength, elastic modulus and Poisson's ratio;

[0073] uniaxial tension - the particles at the top and bottom of the model move in the vertical direction in opposite directions at a speed of 0.1 m / s, and the stress peak value of the stress-strain curve is the macroscopic tensile strength of the material;

[0074] biaxial compression - generate a rigid wall on the top and bottom and left and right, the left and right side wall through the servo mechanism constantly adjust the radial velocity and direction, thus maintain constant pressure (two biaxial compression test, constant pressure settings are 500MPa and 700MPa, the top and bottom wall of the granular assembly model at a speed of 0.1m / s compression, until the model is broken, each test to obtain the compressive strength, according to the Mohr circle equation, with constant pressure and compressive strength, draw the strength envelope line angle is the macroscopic internal friction angle, the intercept of the envelope line and the y axis is the macroscopic cohesion;

[0075] Thus, the macroscopic mechanical parameter value of the initial mesoscopic parameter value determined in S1 is obtained.

[0076] Further, the specific steps of S3) are:

[0077] S3.1) taking the initial mesoscopic parameters selected in S1) as input variables;

[0078] S3.2) taking the macroscopic mechanical parameters obtained by numerical test in S2) as output variables, and constructing a data set;

[0079] S3.3) performing multi-factor analysis of variance based on the data set, constructing F statistics (FA) by calculating the ratio of between-group mean square to within-group mean square of each factor (such as factor A), and comparing it with the critical value Fα at a given significance level α; if FA>Fα, it is determined that the factor A has a significant effect on the macroscopic mechanical parameter and is determined as the main mesoscopic parameter value of the macroscopic mechanical parameter.

[0080] Further, the specific steps of S4) are:

[0081] S4.1) taking the main mesoscopic parameters obtained in S3) as input features,

[0082] S4.2) performing regression analysis on the macroscopic mechanical parameter to obtain the relationship between the macroscopic mechanical parameter and the mesoscopic parameter.

[0083] The regression analysis is not limited to linear regression, but can also use other machine learning regression algorithms such as polynomial regression, ridge regression, etc. The model form established includes but is not limited to linear relationship.

[0084] Further, the specific steps of S5) are:

[0085] The macroscopic mechanical parameter value of the predicted gun barrel metal material itself obtained in S1) is brought into the relationship in S4) to solve and obtain the mesoscopic parameter value of the predicted gun barrel metal material itself.

[0086] In S6, firstly, the three-dimensional granular assembly model of the gun barrel metal material in the compacted state and the upper, lower, left and right, front and back six walls are established by PFC3D software, the flat joint contact model is selected for the contact between the particles, the rolling resistance model is selected for the contact between the particles and the walls, the mesoscopic parameter values of the gun barrel metal material itself in S5 are inputted, and then the left wall is deleted and the speed of all the walls except the upper wall is set to 0 m / s. Finally, the moving speed of the upper wall to the left (i.e. the moving speed of the projectile relative to the barrel, 1-50 m / s) and the pressure between the upper wall and the particles (i.e. the load between the projectile and the barrel, 100-1000 MPa) are inputted and kept constant, and the number of cycles (1-1000 shots) is inputted, and then the calculation and prediction of the gun barrel wear are started.

[0087] Embodiment:

[0088] Firstly, the macroscopic mechanical parameter values of the gun barrel metal material itself to be predicted are determined, and then the initial mesoscopic parameter values of the gun barrel metal material to be predicted are selected and the macroscopic mechanical parameter values of the initial mesoscopic parameter values obtained by numerical simulation are determined. Then, the test results are analyzed by using the method of multi-factor variance analysis, the significance of the influence of the initial mesoscopic parameters on the macroscopic mechanical parameters is analyzed, and the main mesoscopic parameters affecting the macroscopic mechanical parameters are screened. Then, the relationship between the macroscopic mechanical parameters and the main mesoscopic parameters is established by using the method of regression analysis. The macroscopic mechanical parameter values of the gun barrel metal material itself to be predicted are inputted into the relationship to solve, and the mesoscopic parameter values of the gun barrel metal material itself to be predicted are obtained. Finally, the wear of the gun barrel is predicted by using the mesoscopic parameter values of the gun barrel metal material itself to be predicted, and it is found by comparing with the data of the physical test that the predicted wear results are basically consistent with the physical test results, which verifies the feasibility of the prediction method.

[0089] 2. Flat joint contact model

[0090] The physical and mechanical properties of metal materials are largely dependent on the contact properties between particles and particles, and the contact model is a direct reflection of the contact properties. PFC5.0 provides 10 built-in contact models to simulate the contact properties, such as flat joint contact model, linear contact model, linear contact bond model, linear parallel bond model, etc. The flat joint contact model is used between the model particles, as shown in FIG. 1, the particles are in a polygonal structure, and the bond is in a flat plane structure to suppress the rotation between the particles under loading and enhance the interlocking ability. The model simulates the real mechanical properties of metal materials by adjusting the contact and fracture state. When the normal stress exceeds the ultimate strength between the particles, the contact surface is fractured and the particles no longer maintain contact. Figure 2

[0091] The mesoscopic parameters required to be inputted for the flat joint contact model include: flat joint modulus E c ​Straight joint stiffness ratio k n / k s σ of straight joints b Straight joint adhesion c b φ, the internal friction angle of a straight joint b The friction coefficient μ of straight joints b .

[0092] 3. Numerical Model

[0093] The steps of a numerical experiment:

[0094] (1) Sample preparation: The model is a two-dimensional rectangular model in PFC2D, with a length of 3.2 mm and a width of 1.6 mm, consisting of 4527 particles.

[0095] (2) Uniaxial Compression Numerical Simulation: Uniaxial compression simulation can be used to obtain the compressive strength, elastic modulus, and Poisson's ratio of metallic materials. Rigid walls on both sides compress the block at a constant speed of 0.1 meters per second until the material fractures. The stress-strain curve is shown in... Figure 5 As shown in (a), the slope of the material during the elastic deformation stage reflects its elastic modulus. When the material reaches its maximum compressive strength, the axial stress drops rapidly, indicating that the material begins to fracture. The stress peak at this point is the material's compressive strength. To obtain the material's Poisson's ratio more accurately, this paper uses a method without sidewall constraints, measuring the radial and axial strain of the model, such as... Figure 5 As shown in b), the accurate Poisson's ratio is obtained.

[0096] (3) Uniaxial Tensile Numerical Simulation: The tensile strength of a material can be obtained through uniaxial tensile simulation. The tensile force is simulated by the reverse movement of the top and bottom walls. During the tensile process, the stress-strain relationship of the material is initially linear. At this time, the slope of the curve reflects the elastic properties of the material. As the stress increases to the peak strength, the material exhibits brittle fracture, leading to a sudden drop in axial stress and the appearance of obvious cracks in the model. The tensile strength of the material can be determined by the peak stress of the stress-strain curve, such as... Figure 6 As shown.

[0097] (4) Biaxial Compression Numerical Simulation: Biaxial compression simulation aims to determine the internal friction angle and cohesion of the material. Compared with uniaxial tension simulation, biaxial compression applies axial loading under constant confining pressure from the upper and lower walls, which is closer to the complex stress state in the working environment of artillery. In the simulation, the radial velocity of the walls is controlled by a servo mechanism to ensure that the pressure on both sides of the model remains constant. Loading is performed under confining pressures of 500MPa and 700MPa. Under different confining pressures, the compressive strength of the material under multiaxial stress is measured by the peak value of the axial stress-strain curve. The compressive strength data is fitted based on the Mohr's circle theory, such as... Figure 7The macroscopic internal friction angle and cohesion of the material are determined by the slope and intercept of the envelope, respectively.

[0098] 4. Orthogonal test and variance analysis

[0099] In scientific experiments, there are often many factors to be investigated and researched, and the number of levels of the factors is often more than two. If a comprehensive test is conducted by matching each level of each factor, the number of tests will increase exponentially with the increase in the number of factors. If a simple comparison method is used, although the number of tests can be reduced, the matching between the levels of the factors in the test process is uneven, and the uniformity of the distribution of data points is not guaranteed. In this case, false conclusions are often drawn. Orthogonal test design can obtain relatively reliable test results while significantly reducing the number of tests.

[0100] Orthogonal tables are standardized tables designed according to the orthogonal principle and are the basic tools for arranging tests and analyzing test results in orthogonal design. They are generally represented by L n (r m ). Among them, L is the code of the orthogonal table; n is the number of horizontal rows of the orthogonal table (the number of tests); r is the number of factor levels; and m is the number of vertical columns of the orthogonal table (the maximum number of factors that can be arranged). For example, the orthogonal table L8(2 7 ) represents a total of 8 rows and 7 columns, and if it is used to arrange an orthogonal test, a maximum of 7 two-level factors can be arranged, and the number of tests is 8. The orthogonal table has the following important properties: each level appears in any column and appears the same number of times; and all possible combinations of different levels between any two columns appear and appear the same number of times. The above two properties determine the balanced dispersion and comprehensive comparability of the orthogonal test.

[0101] 4.2 Variance analysis

[0102] Variance analysis is used to estimate the size of the error and the importance of the influence of each factor on the test results, and is used in the data analysis of orthogonal tests. Variance analysis analyzes the influencing factors of the total variance fluctuation by decomposing the variance, and divides the influencing factors into within-group error and between-group error according to their sources. The F A statistic is constructed by calculating the ratio of the between-group mean square of factor A to the within-group mean square. For a given significance level α, the critical value F α is looked up, and if F A >F α , it is considered that factor A has a significant impact on the test results, and the larger the F A statistic relative to the F α statistic, the more significant the impact of the factor on the test results.

[0103] The test is designed using the Ln(r m ) orthogonal table, and the test result is yi (i = 1, 2,... n). The basic steps of variance analysis are as follows:

[0104] 1) Calculate the total sum of squares of deviation

[0105]

[0106] Where,

[0107]

[0108] (2) Calculate the sum of squares of deviation of factor j:

[0109]

[0110] Where,

[0111]

[0112] In the formula, k i is the sum of the numerical simulation results of the i level of the j column, n is the number of simulations, and r is the numerical simulation level.

[0113] (3) The sum of squares of deviation of numerical simulation error:

[0114] SS e =∑SS 空列 (7)

[0115] (4) The degrees of freedom of the total sum of squares of deviation SST and the sum of squares of deviation of factor j SSj are respectively:

[0116] f T = n - 1 (8)

[0117] f j = r - 1 (9)

[0118] (5) The degrees of freedom of the error is:

[0119] f e =∑f 空列 (10),

[0120] (6) The F value is:

[0121]

[0122] (7) Significance test

[0123] For a given significance level a, the critical value F is found, if Fj > F, it is considered that the j factor has a significant impact on the test results, and the larger FA is relative to F, the more significant the impact of the factor on the test results.

[0124] 4.3 Selection of test indexes and factor levels

[0125] (1) Selection of test indexes

[0126] The calibration of the mesoscopic parameters of the granular flow triaxial shear is usually based on the stress-strain relationship and the failure envelope of the PFC model, which should be consistent with the laboratory test results. Therefore, the selection of the macroscopic characteristic indexes should follow the following principles: ① The selected indexes should be convenient and easy to obtain from the test; ② The selected indexes should be able to better describe the shape of the calibrated curve.

[0127] The present application focuses on the pre-peak behavior and peak behavior of the stress-strain curve of the triaxial shear test, and therefore selects six parameters, including the macroscopic Poisson's ratio v, the macroscopic elastic modulus E, the macroscopic compressive strength σ f , the macroscopic tensile strength σ t , the macroscopic cohesion c and the macroscopic internal friction angle φ, as the macroscopic indexes.

[0128] Based on the flat joint contact model, the present application selects the mesoscopic parameters required to be input into the flat joint contact model as the mesoscopic parameter indexes of the present numerical test, including the flat joint modulus E c , the flat joint stiffness ratio k n / k s , the flat joint tensile strength σ b , the flat joint cohesion c b , the flat joint internal friction angle φ b , and the flat joint friction coefficient μ b .

[0129] (2) Determination of the levels of each factor in the orthogonal test

[0130] Table 1 Factor levels

[0131]

[0132] 4.4 Result analysis

[0133] 4.4.1 Numerical test results

[0134] According to the number of factors and the factor levels, the present application adopts the L 25 (4 6 ) orthogonal table to perform the numerical test, and the test scheme and test results are shown in Table 2.

[0135] Table 2 Numerical calculation scheme and results based on orthogonal design

[0136]

[0137] 4.4.2 Multi-factor variance analysis

[0138] In order to get the relationship between macroscopic and mesoscopic parameters accurately, the variance analysis is carried out on the orthogonal simulation results (Table 3). The variance analysis is to study whether the factors have significant influence on the results by analyzing the numerical simulation results, and the F value test is used to determine the significance level of the factors. The judgment rules of the influence of each factor on the index are as follows: according to the significance level α, if the mesoscopic parameter α < 0.01, i.e. F 0.01 >F 0.01 >F 0.05 , it is considered that the mesoscopic parameter has a particularly significant influence on the macroscopic parameter, marked as "**"; if the mesoscopic parameter 0.01 < α < 0.05, i.e. F 0.05 <F b <F b , it is considered that the mesoscopic parameter has a significant influence on the macroscopic parameter, marked as "*"; if the mesoscopic parameter α > 0.05, i.e. F < F c , it is considered that the mesoscopic parameter has no significant influence on the macroscopic parameter, and no mark is made. In order to analyze the influence degree of the test factors on the test index more intuitively, the variance analysis results are drawn into a column chart, as shown in Table 3. Figures 7-12

[0139] Table 3 Variance analysis table

[0140]

[0141] Figure 8 It is shown that the tensile strength of flat joint has a particularly significant influence on the macroscopic elastic modulus, and in addition, the friction coefficient of flat joint also has a significant influence on the macroscopic elastic modulus. The influence of other factors on the macroscopic elastic modulus can be completely ignored. The sensitivity of each mesoscopic parameter to the macroscopic elastic modulus is in the order of σ b > μ b > E c > φ b > c b > k n / k s .

[0142]

[0143] Figure 9 It is shown that the bonding force of flat joint and the modulus of flat joint have a significant influence on the macroscopic compressive strength, and the influence of the modulus of flat joint on the macroscopic compressive strength is particularly significant. In addition to the two, the influence of other factors on the macroscopic compressive strength is close and can be ignored. The sensitivity of each mesoscopic parameter to the macroscopic compressive strength σ f is in the order of E c > c b > k n / k s > φ b > σ b > μ b .

[0144] Figure 10It is shown that the effect of the stiffness ratio of the flat joint on the macroscopic Poisson's ratio is particularly significant, and the effect of other factors on the macroscopic Poisson's ratio can be ignored.

[0145] Figure 11 It is shown that the effect of the tensile strength of the flat joint on the macroscopic tensile strength is particularly significant, and the effect of other factors on the macroscopic tensile strength can be ignored.

[0146] Figure 12 It is shown that the effect of the internal friction angle of the flat joint on the macroscopic cohesion is particularly significant, and the effect of the cohesion of the flat joint on the macroscopic cohesion is also significant, while the effects of the internal friction angle between the flat joints, the tensile strength, the stiffness ratio and the modulus on the macroscopic cohesion are low in sensitivity. The sensitivity of the macroscopic cohesion to the micro parameters is in the order of: b >c b >k n / k s >E c >σ b >μ b .

[0147] Figure 13 It is shown that the effect of the internal friction angle of the flat joint on the macroscopic internal friction angle is significant, while the effects of the modulus, the tensile strength, the stiffness ratio, the friction coefficient and the cohesion between the flat joints on the macroscopic internal friction angle are far lower than the micro internal friction angle and can be ignored. The sensitivity of the macroscopic internal friction angle to the micro parameters is in the order of:

[0148] φ b >E c >k n / k s >σ b >μ b >c b .

[0149] 4.4.3 Regression analysis

[0150] According to the results of the variance analysis in 5.2, regression analysis is performed on the significant factors and the macroscopic index, and the corresponding relationship between the macroscopic and micro parameters is obtained as follows:

[0151] σ f = -104.71 + 0.636c b + 1.171E c (12)

[0152] E = 194.279 + 0.146σ b + 398.099μ b (13)

[0153] v = 0.079 + 0.053k n / k s (14)

[0154] σ t =4.319+0.54σ b (15)

[0155]

[0156] 5. Detailed parameter calibration process and verification

[0157] 5.1 Calibration of detailed parameters

[0158] Substituting the experimental data of the white layer and gun steel metal materials into the macro-micro parameter fitting equation, the micro parameters of the metal materials can be obtained, as shown in Tables 4 and 5.

[0159] Table 4. Microscopic parameter values ​​of the white layer

[0160]

[0161] Table 5. Microscopic parameters of gun steel

[0162]

[0163] 5.2 Numerical Verification

[0164] Numerical verification mainly includes the following parts: model building, numerical simulation, and comparative verification.

[0165] 5.2.1 Model Establishment

[0166] The layered compression method effectively solves the problems of excessive instantaneous calculations and uneven density distribution during material generation, generating a cubic model. Figure 4 The model has dimensions of 0.4 mm (length, width, and height) and consists of two layers: an upper layer of white material and a lower layer of gun steel. Based on live-fire results from large-caliber artillery, the thickest white layer at the bore slope is approximately 165 μm, gradually decreasing with increasing axial distance from the bore slope. Therefore, the thickness of the white layer is set at 200 μm. In the model, both layers are 0.2 mm thick, and the particle radius is 0.01 mm. The entire model comprises 9166 particles.

[0167] 5.2.2 Numerical Simulation

[0168] The contact surface between the top and bottom walls and the block in the model is not a smooth plane, so a certain friction needs to be set between the wall and the ball, otherwise the model unit will slip when the top wall is pressurized, so that it cannot be stressed and does not conform to the actual situation. Therefore, when setting the unit model of the white layer cannon steel, the contact between the top and bottom layers of the block and the upper and lower walls is set as a rolling resistance model, thereby increasing the friction between the material and the wall and preventing the model unit from slipping. After completing the preloading and setting the contact model, the rigid wall around the unit extrudes the block according to the servo mechanism, so that the unit model is subjected to a constant force, simulating the pressure of other units around. In the process of numerical simulation, the top wall moves along the negative direction of the z axis, and the unit model is loaded with a normal stress. The force applied is kept constant through the servo mechanism. Through the establishment of the mathematical model of the bullet extrusion, Yi Huaijun calculated the extrusion stress of the 130mm caliber gun bore positive line and the bullet belt. The results show that the extrusion stress of the barrel guide transition side by the bullet belt is in the range of 100-700MPa, so the normal stress is taken as 400MPa in this embodiment. In addition, the bullet extrusion speed into the barrel is about 4-10m / s. In order to simulate the shearing of the bullet belt to the white layer, the model gives the wall a speed of 10m / s along the negative direction of the x axis while pressurizing the top wall. The top wall is considered to simulate a bullet launching process from the beginning of the model to the end of the model.

[0169] 5.2.3 Comparison and verification

[0170] Figure 14 is a comparison chart of the predicted wear thickness in loading and the actual bullet test data. Tian Gujun's research shows that the 130mm caliber gun has a bore wear thickness of 121μm after 15 consecutive shots. Wang Wei's research uses the finite element method to simulate the melting and ablation process of the gun barrel. The research results show that in the first 46 shots, the melting and ablation thickness is 0μm because the surface temperature of the bore is lower than the melting point of the barrel. Therefore, only the mechanical wear thickness needs to be considered, and the total wear thickness after 15 consecutive shots is 115.68μm, which has an error of 4% compared with the actual bullet test data of 121μm, and the model prediction accuracy is relatively high.

[0171] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, and any modification, equivalent replacement and improvement made by any person skilled in the art within the technical range disclosed by the present application, as long as it is within the spirit and principles of the present application, should be covered within the protection scope of the present application.

Claims

1. A method for predicting mechanical wear of a gun barrel based on a discrete element method, characterized in that, The method specifically comprises the following steps: S1) determining the macro-mechanical parameter value of the gun barrel metal material itself to be predicted, and then determining the initial mesoscopic parameter value of the gun barrel metal material to be predicted; S2) determining the macro-mechanical parameter value of the initial mesoscopic parameter value obtained in S1); S3) determining the main mesoscopic parameter value of the macro-mechanical parameter value obtained in S2) by using a multi-factor variance analysis method; S4) establishing a relationship between the macro parameter obtained in S2) and the main mesoscopic parameter obtained in S3) by using regression analysis; S5) bringing the macro-mechanical parameter value of the gun barrel metal material itself to be predicted into the relationship in S4) to solve, so as to obtain the mesoscopic parameter value of the gun barrel metal material itself to be predicted; S6) predicting the gun barrel wear amount by using the mesoscopic parameter value of the gun barrel metal material itself to be predicted obtained in S5).

2. The method of claim 1, wherein, The macroscopic mechanical parameters in S1) include: macroscopic Poisson's ratio v, macroscopic elastic modulus E, macroscopic compressive strength σ f , macroscopic tensile strength σ t , macroscopic cohesion c, and macroscopic internal friction angle φ; The mesoscopic parameters include: the mesoscopic parameters required to be inputted by the flat joint contact model include flat joint modulus E c , flat joint stiffness ratio k n / k s , flat joint tensile strength σ b , flat joint cohesion c b , flat joint internal friction angle φ b and flat joint friction coefficient μ b .

3. The method of claim 1, wherein, The specific steps of S1) are as follows: S1.1) selecting the gun barrel metal material to be predicted, and obtaining the macro-mechanical parameter value of the gun barrel metal material itself to be predicted by searching for literature data, uniaxial compression test or uniaxial tensile test; S1.2) setting the mesoscopic parameter value range of the gun barrel metal material to be predicted, and selecting the initial mesoscopic parameter value according to the mesoscopic parameter value range of the gun barrel metal material to be predicted.

4. The method of claim 3, wherein, The micro parameter in S1.2) ranges from: flat joint modulus E c = 100MPa-1000MPa, flat joint stiffness ratio k n / k s = 1-10, flat joint tensile strength σ b = 100MPa-1000MPa, flat joint bonding force c b = 100MPa-1000MPa, flat joint internal friction angle φ b = 0.1°-20°, flat joint friction coefficient μ b = 0.001-0.

2.

5. The method of claim 2, wherein, The specific steps of S2) are as follows: S2.1) first, a two-dimensional particle assembly model of the gun barrel metal material to be predicted is established by using PFC2D software, the flat joint contact model is selected for the contact between particles in the model, and the initial mesoscopic parameter value selected in S1) is input; S2.2) then, the model is subjected to uniaxial compression, uniaxial tension and biaxial compression numerical tests, and the model that is not stretched or compressed is used in each test, and the steps are as follows: uniaxial compression - two rigid walls are generated on the upper and lower surfaces, and the particle assembly model is continuously extruded at a constant speed of 0.1 m / s, until the model cracks and finally breaks, so that the stress-strain curve is obtained, and the macro Poisson's ratio v, the macro elastic modulus E and the macro compressive strength σ can be obtained; uniaxial tension - the particles at the top and bottom of the model move in the vertical direction at a speed of 0.1 m / s in opposite directions, and the stress peak value of the stress-strain curve is the macro tensile strength σ of the material; biaxial compression - four rigid walls are generated on the upper and lower surfaces, and the left and right surfaces, the left and right walls are continuously adjusted in radial velocity and direction by a servo mechanism, so that a constant pressure is maintained, that is, two biaxial compression tests are carried out, the constant pressures are set to 500 MPa and 700 MPa respectively, and the top and bottom walls compress the particle assembly model at a speed of 0.1 m / s until the model breaks, the compressive strength is obtained in each test, according to the Mohr circle equation, the constant pressure and the compressive strength are brought in, and the inclination angle of the strength envelope line obtained is the macro internal friction angle φ, and the intercept of the envelope line with the y-axis is the macro cohesion c.

6. The method of claim 1, wherein, The specific steps of S3) are as follows: S3.1) taking the initial mesoscopic parameter selected in S1) as an input variable; S3.2) taking the macro-mechanical parameter obtained by the numerical test in S2) as an output variable, and constructing a data set; S3.3) Based on the data set, a multi-factor variance analysis is performed, an F statistic FA is constructed by calculating the ratio of the inter-group mean square to the intra-group mean square of each factor, and is compared with the critical value Fα at a given significance level α; if FA>Fα, it is determined that the factor A has a significant influence on the macro-mechanical parameter and is determined as the main meso-parameter value of the macro-mechanical parameter.

7. The method of claim 1, wherein, The specific steps of the S4) are: S4.1) taking the main meso-parameter obtained in the S3) as an input feature, S4.2) performing a regression analysis on the macro-mechanical parameter to obtain a relationship between the macro-mechanical parameter and the meso-parameter.

8. The method of claim 7, wherein, The regression analysis is not limited to linear regression, and a model form established by a polynomial regression algorithm or a ridge regression algorithm can also be selected.

9. The method of claim 1, wherein, The specific steps of the S5) are: The macro-mechanical parameter value of the predicted gun barrel metal material itself obtained in the S1) is brought into the relationship in the S4) to be solved, and the meso-parameter value of the predicted gun barrel metal material itself is obtained.

10. The method of claim 1, wherein, The specific steps of the S6) are: S6.1) First, a three-dimensional particle assembly model of the predicted gun barrel metal material in a close state and six walls of up, down, left, right, front and back are established by the PFC3D software, a flat joint contact model between particles is selected, and a Rolling resistence model between particles and walls is selected, S6.2) the meso-parameter value of the predicted gun barrel metal material itself in the S5) is input, then the left wall is deleted, and the speed of all walls except the upper wall is set to 0 m / s; S6.2) finally, the moving speed of the upper wall to the left, i.e. the movement speed of the projectile relative to the barrel, 1-50 m / s, and the pressure between the upper wall and the particles, i.e. the load between the projectile and the barrel, 100-1000 MPa, are input and kept constant, and the cycle number 1-1000 shots is input, and calculation is performed, i.e. the wear amount of the gun barrel is obtained.

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