Method for back-calculation of parameters of propellant combustion model based on time series of bore pressure

Abstract

The application discloses a method for inversely calculating parameters of a propellant combustion model based on a time sequence of bore pressure, and relates to the technical field of material constitutive parameter identification. The method comprises the following steps: obtaining sample values of parameters to be solved in a propellant combustion model; inputting the sample values into a two-dimensional axisymmetric finite element simulation model to obtain output results; establishing a mapping relationship between the parameters to be solved and the output results; obtaining actual bore pressure values and actual muzzle velocities in shooting tests; establishing an inverse calculation target function according to the actual bore pressure values, the actual muzzle velocities and the mapping relationship; and obtaining optimal values of the parameters to be solved according to the inverse calculation target function. The method can greatly reduce the number of tests and costs and ensure the accuracy of the data of the parameters to be solved by only a few actual shooting tests, a two-dimensional axisymmetric finite element simulation model and a calculation inverse calculation method, and finally obtaining the optimal values of the parameters to be solved.

Description

TECHNICAL FIELD

[0001] The present application generally relates to the technical field of material constitutive parameter identification, and particularly relates to a propellant combustion model parameter inversion method based on bore pressure time series. BACKGROUND

[0002] With the development of science and technology, especially the rapid development of propellant technology and numerical simulation technology, the development of optimization design of propellant parameters and structure in the shooting process is greatly promoted. However, in the verification stage of optimization design, due to the difficulty, cost and great danger of shooting test, the numerical simulation method is usually used to verify the accuracy of the optimized parameters. Many scholars at home and abroad have conducted extensive research on the combustion behavior of propellant and constructed many constitutive models of propellant. Among them, the typical model is the propellant combustion model. However, there are many parameters in the propellant combustion model, and it is not easy to determine, therefore, how to accurately and efficiently obtain these propellant parameters has important theoretical significance and practical effect for the research of optimization design in the shooting process.

[0003] At present, some parameters of the propellant combustion model can be determined by experimental means, but some key parameters cannot be directly obtained by experiment, and a large number of experiments are needed to obtain some key parameters through data fitting. Due to the difficulty, test equipment limitation and danger of existing shooting test, it is very time-consuming and laborious to carry out a large number of shooting tests. Therefore, we propose a propellant combustion model parameter inversion method based on bore pressure time series to solve the above problems. SUMMARY

[0004] In view of the above defects or deficiencies in the prior art, it is desirable to provide a propellant combustion model parameter inversion method based on bore pressure time series, which can effectively reduce the number of tests and reduce the test cost.

[0005] The present application provides a propellant combustion model parameter inversion method based on bore pressure time series, comprising the following steps:

[0006] Obtaining sample values of parameters to be solved in the propellant combustion model;

[0007] Inputting the sample values into a two-dimensional axisymmetric finite element simulation model to obtain output results; the output results include: simulated bore pressure value, simulated muzzle velocity, simulated maximum bore pressure, and the time when the simulated maximum bore pressure occurs;

[0008] Establishing a mapping relationship between the parameters to be solved and the output results;

[0009] The actual bore pressure value is obtained by a pressure measuring device, and the actual muzzle velocity is obtained by a high-speed camera device;

[0010] The inverse target function is established according to the actual bore pressure value, the actual muzzle velocity and the mapping relationship;

[0011] The optimal value of the parameter to be solved is obtained according to the inverse target function.

[0012] After the optimal value of the parameter to be solved is obtained, the following steps are further included according to the technical scheme provided by the application:

[0013] The optimal value is input into the two-dimensional axisymmetric finite element simulation model to obtain a simulation bore pressure value and a simulation muzzle velocity;

[0014] An error value is calculated according to the simulation bore pressure value, the simulation muzzle velocity, the actual bore pressure value and the actual muzzle velocity;

[0015] When the error value is in a first preset range, the optimal value is the optimal value of the parameter to be solved.

[0016] According to the technical scheme provided by the application, the error value is calculated according to the following formula (I):

[0017]

[0018] wherein, δ is the error value, P is the actual bore pressure value, P' is the simulation bore pressure value, v is the actual muzzle velocity, v' is the simulation muzzle velocity, t0 is the actual propellant ignition time, t is the actual process time, t0' is the simulation propellant ignition time, and t' is the simulation process time.

[0019] According to the technical scheme provided by the application, the parameter to be solved at least includes a growth parameter, an energy parameter, an ignition rate parameter and a combustion rate coefficient.

[0020] According to the technical scheme provided by the application, the mapping relationship between the parameter to be solved and the output result is represented according to the following formula (II):

[0021]

[0022] wherein, P i ' is the simulation bore pressure value, i is the number of simulation bore pressure values, v' is the simulation muzzle velocity, P' is the simulation bore pressure value, t' is the simulation process time, S is the integral of the simulation bore pressure value with respect to time, G is the growth parameter, Eg is the energy parameter, C max is the simulation bore pressure maximum value, t' pmax is the time at which the simulation bore pressure maximum value is located, and S is the integral of the simulation bore pressure value with respect to time. IFor the ignition rate parameter, A is a combustion rate coefficient.

[0023] According to the technical scheme provided by the application, after the actual bore pressure value and the actual muzzle velocity in the shooting test are obtained, before the inverse target function is obtained, the following steps are further included:

[0024] The simulation bore pressure maximum value, the time at which the simulation bore pressure maximum value occurs, the actual bore pressure maximum value, and the time at which the actual bore pressure maximum value occurs are obtained.

[0025] According to the simulation bore pressure maximum value, the time at which the simulation bore pressure maximum value occurs, the actual bore pressure maximum value, and the time at which the actual bore pressure maximum value occurs, a constraint condition is established.

[0026] Under the constraint condition, the inverse target function is determined.

[0027] According to the technical scheme provided by the application, the constraint condition is expressed according to the following formula (three):

[0028]

[0029] Wherein, P max,min is the minimum value of the square of the difference between the actual bore pressure maximum value and the simulation bore pressure maximum value, P max is the actual bore pressure maximum value, P' max is the simulation bore pressure maximum value, t pmax,min is the minimum value of the square of the difference between the time at which the actual bore pressure maximum value occurs and the time at which the simulation bore pressure maximum value occurs, t pmax is the time at which the actual bore pressure maximum value occurs, t' pmax is the time at which the simulation bore pressure maximum value occurs.

[0030] According to the technical scheme provided by the application, the inverse target function is expressed according to the following formula (four):

[0031]

[0032] Wherein, P i,min is the minimum value of the square of the difference between the actual bore pressure value and the simulation bore pressure value, P i is the actual bore pressure value, P i ' is the simulation bore pressure value, i is the number of bore pressure values, v min is the minimum value of the square of the difference between the actual muzzle velocity and the simulation muzzle velocity, v is the actual muzzle velocity, v' is the simulation muzzle velocity, S min is the minimum value of the square of the difference between the integral of the actual bore pressure value with respect to the actual time and the integral of the simulation bore pressure value with respect to the simulation time.

[0033] In summary, the application discloses a specific process of a propellant combustion model parameter inversion method based on a bore pressure time sequence.

[0034] Compared with a traditional method of obtaining the parameter value through a large number of tests, the application can greatly reduce the test times and cost and ensure the accuracy of the parameter data by obtaining the optimal value of the parameter through only a few actual shooting tests, a two-dimensional axisymmetric finite element simulation model and a calculation inversion method. BRIEF DESCRIPTION OF DRAWINGS

[0035] Other features, objects and advantages of the application will become more apparent with reference to the following detailed description of non-limiting embodiments when taken in conjunction with the accompanying drawings.

[0036] Figure 1 Fig. 1 is a flowchart of a propellant combustion model parameter inversion method based on a bore pressure time sequence.

[0037] Figure 2 Fig. 2 is a flowchart for verifying the optimal value.

[0038] Figure 3 Fig. 3 is a schematic diagram of a two-dimensional axisymmetric finite element simulation model.

[0039] Figure 4 Fig. 4 is a curve graph of actual bore pressure-time.

[0040] Reference signs in the drawings: 1, propellant; 2, projectile; 3, gun barrel area; 4, free boundary. DETAILED DESCRIPTION

[0041] The application will be further described below in conjunction with the drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the related application, and not to limit the application. In addition, it should be noted that only the parts related to the application are shown in the drawings for the convenience of description.

[0042] It should be noted that the embodiments in the application and the features in the embodiments can be combined with each other without conflict. The application will be described in detail below with reference to the drawings and in conjunction with the embodiments.

[0043] Embodiment 1

[0044] Reference should be made to Figure 1The illustrated application provides a flowchart of a method for parameter inversion of a propellant combustion model based on a time series of bore pressure, which comprises the following steps:

[0045] S10, obtaining sample values of parameters to be solved in the propellant combustion model;

[0046] Wherein, the parameters to be solved include at least growth parameters, energy parameters, ignition rate parameters and combustion rate coefficients.

[0047] The propellant combustion model includes m parameters to be solved, which are subject to Gaussian distribution X a ∈N(μ a ,δ a ),a=1,2,...,m;

[0048] Wherein, X is a random variable, N is a Gaussian distribution, μ is a mathematical expectation, also known as an average value, δ is a variance, and a is the number of parameters to be solved in the propellant combustion model.

[0049] And each parameter to be solved includes n sample values

[0050] Wherein, is the sample set of each parameter to be solved, x n is the nth sample value in the sample set, and j is the number of sample values in each parameter to be solved.

[0051] Here, optimal Latin hypercube sampling can be used to obtain sample values of parameters to be solved in the propellant combustion model.

[0052] Wherein, the sample values of the parameters to be solved are, for example, G=0.09, Eg=1.88185×10 6 , C I =500, A=1.2, and the confidence interval of the sampling is 0.25.

[0053] S20, inputting the sample values into a two-dimensional axisymmetric finite element simulation model to obtain output results;

[0054] The two-dimensional axisymmetric finite element simulation model is established based on Autodyn software, as shown in Figure 3 The two-dimensional axisymmetric finite element simulation model includes: propellant 1, projectile 2 and barrel area 3, and the outlet boundary condition of the barrel area 3 is set as a free boundary 4; the two-dimensional axisymmetric finite element simulation model is established by the existing known finite element method.

[0055] The output result includes: a bore pressure response, a muzzle velocity response, a simulated bore pressure maximum value, and a time at which the simulated bore pressure maximum value is located; the bore pressure response refers to a sample value of a to-be-solved parameter input into a two-dimensional axisymmetric finite element simulation model to obtain a bore pressure value, i.e., simulated bore pressure values at different time points; and the muzzle velocity response refers to a muzzle velocity obtained by inputting the sample value of the to-be-solved parameter into the two-dimensional axisymmetric finite element simulation model, i.e., a simulated muzzle velocity.

[0056] S30, a mapping relationship between the to-be-solved parameter and the output result is established.

[0057] Here, a functional function of the to-be-solved parameter and the output result can be established based on a Kriging surrogate model, and the mapping relationship between the to-be-solved parameter and the output result is obtained.

[0058] The mapping relationship between the to-be-solved parameter and the output result is represented by the following formula (two):

[0059]

[0060] P' = P + v' + S + G + Eg + C + A i is a simulated bore pressure value, i is the number of simulated bore pressure values, v' is a simulated muzzle velocity, P' is a simulated bore pressure maximum value, t' is a time at which the simulated bore pressure maximum value is located, S is an integral of the simulated bore pressure value with respect to time, G is a growth parameter, Eg is an energy parameter, C is an ignition rate parameter, and A is a combustion rate coefficient. max pmax I

[0061] S40, actual bore pressure values and actual muzzle velocities in a shooting test are obtained; the actual bore pressure values are obtained by a pressure measuring device; and the actual muzzle velocities are obtained by a high-speed camera device.

[0062] Specifically, whether the insertable electronic pressure gauge is intact is checked and tested, the insertable electronic pressure gauge is powered on after being confirmed to be intact, is placed in the outer cylinder, is tightened, is filled and packaged, i.e., the insertable electronic pressure gauge is placed vertically, and is connected to a short circuit of "RST" and "GND". After the reading port of the insertable electronic pressure gauge is connected to a computer special software, the instrument is detected and powered on. The packaged insertable electronic pressure gauge is sent to a shooting test site.

[0063] A high-speed camera is arranged at a muzzle position to measure the muzzle velocity.

[0064] At the shooting test site, a known shooting test is carried out, the pressure gauge is recovered after the shooting test, the actual bore pressure-time data are read after the outer cylinder is disassembled, as shown in FIG. 4, which is a curve graph of the actual bore pressure-time, and the actual bore pressure value can be obtained in the curve graph. Figure 4

[0065] ​​​​According to the shooting interval of the high-speed camera and the position information of the bullet in the different time in the shooting photos, the actual muzzle velocity of the bullet is calculated;

[0066] Here, the time interval from the ignition of the propellant to the ejection of the bullet can be calculated from the start of the high-speed camera shooting at the ignition, and the shooting interval of the high-speed camera is certain. The number of photos from the start of the high-speed camera shooting at the ignition to the ejection of the bullet is multiplied by the shooting interval of the high-speed camera to calculate. S50, according to the actual chamber pressure value, the actual muzzle velocity and the mapping relationship, the inverse target function is obtained;

[0067] Further, after obtaining the actual chamber pressure value and the actual muzzle velocity in the shooting test, before obtaining the inverse target function, the following steps are further included:

[0068] The simulation chamber pressure maximum value, the time at which the simulation chamber pressure maximum value is located, the actual chamber pressure maximum value, and the time at which the actual chamber pressure maximum value is located are obtained.

[0069] According to the simulation chamber pressure maximum value, the time at which the simulation chamber pressure maximum value is located, the actual chamber pressure maximum value, and the time at which the actual chamber pressure maximum value is located, a constraint condition is established.

[0070] Under the constraint condition, the inverse target function is determined.

[0071] The constraint condition is represented by the following formula (three):

[0072]

[0073] Wherein, P max,min is the minimum value of the square of the difference between the actual chamber pressure maximum value and the simulation chamber pressure maximum value, P max is the actual chamber pressure maximum value, P' max is the simulation chamber pressure maximum value, t pmax,min is the minimum value of the square of the difference between the time at which the actual chamber pressure maximum value is located and the time at which the simulation chamber pressure maximum value is located, t pmax is the time at which the actual chamber pressure maximum value is located, t' pmax is the time at which the simulation chamber pressure maximum value is located.

[0074] The inverse target function is represented by the following formula (four):

[0075]

[0076] Wherein, P i,min is the minimum value of the square of the difference between the actual chamber pressure value and the simulation chamber pressure value, P i is the actual chamber pressure value, P i ' is the simulation chamber pressure value, i is the number of chamber pressure values, v minThe minimum value of the square of the difference between the actual muzzle velocity and the simulation muzzle velocity, v is the actual muzzle velocity, and v' is the simulation muzzle velocity min The minimum value of the square of the difference between the actual chamber pressure value and the simulation chamber pressure value.

[0077] The above constraint condition can ensure that the simulation chamber pressure maximum value (simulation chamber pressure peak value) and the time at which the simulation chamber pressure maximum value (simulation chamber pressure peak time) are consistent, avoid the time at which the simulation chamber pressure peak value is reached being advanced or delayed, and cause the simulation chamber pressure value and the simulation muzzle velocity calculated by the two-dimensional axisymmetric finite element simulation model to be inconsistent with the actual shooting test data, thereby causing a large error.

[0078] S60, obtaining the optimal value of the to-be-solved parameter according to the inverse target function.

[0079] The optimal value can be obtained based on an optimization method of a multi-objective optimization algorithm.

[0080] Compared with the traditional way of obtaining the value of the to-be-solved parameter through a large number of tests, the present application can greatly reduce the number of tests and costs and ensure the accuracy of the to-be-solved parameter data by only a few actual shooting tests, a two-dimensional axisymmetric finite element simulation model, and an inverse target function, and ultimately obtaining the optimal value of the to-be-solved parameter.

[0081] Further, as shown in Figure 2 After obtaining the optimal value of the to-be-solved parameter, the following steps are further included:

[0082] S70, inputting the optimal value into the two-dimensional axisymmetric finite element simulation model to obtain a simulation chamber pressure value and a simulation muzzle velocity;

[0083] S80, calculating an error value according to the simulation chamber pressure value, the simulation muzzle velocity, the actual chamber pressure value, and the actual muzzle velocity;

[0084] The error value is calculated according to the following formula (I):

[0085]

[0086] Wherein, δ is the error value, P is the actual chamber pressure value, P' is the simulation chamber pressure value, v is the actual muzzle velocity, v' is the simulation muzzle velocity, t0 is the actual propellant ignition time, t is the actual process time, t0' is the simulation propellant ignition time, and t' is the simulation process time.

[0087] For example, t0=t0'=0 ms, and t=t'=25 ms.

[0088] S90, when the error value is within a first preset range, the optimal value is the optimal value of the to-be-solved parameter; for example, the first preset range is δ≤±15%.

[0089] The correctness of the optimal value of the parameter to be solved obtained by the reverse calculation is verified by calculating the error value of the simulation result and the test result.

[0090] The above description is only the preferred embodiment of the present application and the explanation of the applied technical principles. It should be understood by those skilled in the art that the scope of the present application is not limited to the technical solutions formed by the specific combinations of the above technical features, and should also cover other technical solutions formed by any combinations of the above technical features or equivalent features without departing from the inventive concept. For example, the technical solutions formed by the mutual replacement of the above features and the technical features disclosed in the present application (but not limited to) having similar functions.

Claims

1. A method for inversely determining propellant combustion model parameters based on chamber pressure time series, characterized in that, Includes the following steps: Obtain sample values ​​of the parameters to be determined in the propellant combustion model; The parameters to be determined include at least: growth parameters, energy parameters, ignition rate parameters, and combustion rate coefficient; The sample values ​​are input into a two-dimensional axisymmetric finite element simulation model to obtain the output results. The output results include: simulated chamber pressure, simulated muzzle velocity, simulated maximum chamber pressure, and the time at which the simulated maximum chamber pressure occurs. Establish a mapping relationship between the parameters to be determined and the output results; The actual chamber pressure and actual muzzle velocity were obtained during the shooting test; the actual chamber pressure was acquired by a pressure measuring device; and the actual muzzle velocity was acquired by a high-speed camera. Based on the actual chamber pressure, the actual muzzle velocity, and the mapping relationship, an inverse objective function is established. The optimal value of the parameter to be determined is obtained by inversely calculating the objective function. The process involves checking and testing the placement electronic pressure gauge to ensure it is intact. Once the gauge is confirmed to be intact, it is powered on, placed in the outer cylinder, tightened, and sealed. The placement electronic pressure gauge is then placed upright. By shorting "RST" and "GND", the reading port of the placement electronic pressure gauge is connected to the computer software. The instrument is then tested and powered on. The sealed placement electronic pressure gauge is then delivered to the shooting test site. A high-speed camera is installed at the muzzle to measure the muzzle velocity; At the shooting test site, conduct existing and well-known shooting experiments, and retrieve the pressure gauge after the shooting experiment. After removing the outer cylinder, read the actual chamber pressure-time data. The actual chamber pressure value can be obtained from the actual chamber pressure-time curve. Then, the actual muzzle velocity of the projectile is calculated based on the shooting interval of the high-speed camera and the projectile position information at different times in the captured photos; Here, the time interval from propellant ignition to projectile exit is calculated by multiplying the number of photos taken by the high-speed camera from the moment of ignition to the moment the projectile exits the barrel by the high-speed camera's shooting time interval. After obtaining the actual chamber pressure and actual muzzle velocity from the shooting test, and before obtaining the inverse objective function, the following steps are also included: Obtain the simulated maximum chamber pressure, the time at which the simulated maximum chamber pressure occurs, the actual maximum chamber pressure, and the time at which the actual maximum chamber pressure occurs; Constraints are established based on the simulated maximum chamber pressure, the time at which the simulated maximum chamber pressure occurs, the actual maximum chamber pressure, and the time at which the actual maximum chamber pressure occurs. Under the constraints, determine the objective function for inverse calculation.

2. The method for inversely determining propellant combustion model parameters based on chamber pressure time series according to claim 1, characterized in that, After obtaining the optimal value of the parameter to be determined, the following steps are also included: The optimal value is input into the two-dimensional axisymmetric finite element simulation model to obtain the simulated chamber pressure and simulated muzzle velocity. The error value is calculated based on the simulated chamber pressure value, the simulated muzzle velocity, the actual chamber pressure value, and the actual muzzle velocity. When the error value is determined to be within a first preset range, the optimal value is the optimal value of the parameter to be determined.

3. The method for inversely determining propellant combustion model parameters based on chamber pressure time series according to claim 2, characterized in that, The error value is calculated using the following formula (I): Formula (1); in, denoted as error value, P as actual chamber pressure value, P' as simulated chamber pressure value, v as actual muzzle velocity, v' as simulated muzzle velocity, t0 as actual propellant ignition time, t as actual process time, t0' as simulated propellant ignition time, and t' as simulated process time.

4. The method for inversely determining propellant combustion model parameters based on chamber pressure time series according to claim 1, characterized in that, The parameters to be determined include at least: growth parameters, energy parameters, ignition rate parameters, and combustion rate coefficients.

5. The method for inversely determining propellant combustion model parameters based on chamber pressure time series according to claim 1, characterized in that, The mapping relationship between the parameters to be determined and the output results can be expressed by the following formula (II): Formula (II); in, Here, i represents the simulated chamber pressure value, and i is the number of simulated chamber pressure values. To simulate muzzle velocity, To simulate the maximum chamber pressure, S represents the time at which the simulated chamber pressure reaches its maximum value, S is the integral of the simulated chamber pressure over time, G is the growth parameter, Eg is the energy parameter, and C is the energy parameter. I Here, A is the ignition rate parameter, and A is the combustion rate coefficient.

6. The method for inversely determining propellant combustion model parameters based on chamber pressure time series according to claim 1, characterized in that, After obtaining the actual chamber pressure and actual muzzle velocity from the shooting test, and before obtaining the inverse objective function, the following steps are also included: Obtain the simulated maximum chamber pressure, the time at which the simulated maximum chamber pressure occurs, the actual maximum chamber pressure, and the time at which the actual maximum chamber pressure occurs; Constraints are established based on the simulated maximum chamber pressure, the time at which the simulated maximum chamber pressure occurs, the actual maximum chamber pressure, and the time at which the actual maximum chamber pressure occurs. Under the given constraints, the objective function for inverse calculation is determined.

7. The method for inversely determining propellant combustion model parameters based on chamber pressure time series according to claim 6, characterized in that, The constraints are expressed by the following formula (III): Formula (III); in, It is the minimum value of the square of the difference between the actual maximum chamber pressure and the simulated maximum chamber pressure. This represents the actual maximum chamber pressure. To simulate the maximum chamber pressure, It is the minimum value of the square of the time difference between the actual maximum chamber pressure and the simulated maximum chamber pressure. This represents the time when the actual maximum chamber pressure occurs. This represents the time when the simulated chamber pressure reaches its maximum value.

8. The method for inversely determining propellant combustion model parameters based on chamber pressure time series according to claim 1, characterized in that, The objective function can be obtained by inverse calculation using the following formula (iv): Formula (IV); in, It is the minimum value of the square of the difference between the actual chamber pressure and the simulated chamber pressure. This is the actual chamber pressure value. The simulated chamber pressure values ​​are given by i, where i is the number of chamber pressure values. It is the minimum value of the square of the difference between the actual muzzle velocity and the simulated muzzle velocity. This is the actual muzzle velocity. To simulate muzzle velocity, It is the minimum value of the square of the difference between the integral of the actual chamber pressure value over actual time and the integral of the simulated chamber pressure value over simulated time.

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