A method and system for calculating the dispersion angle of prefabricated fragments considering the relative positions of fragments

Abstract

The present invention proposes a method and system for calculating the dispersion angle of prefabricated fragments taking into account the relative position of the fragments, obtains a calculation model for the dispersion angle of fragments under cylindrical shell charge when one end is centrally detonated, and obtains a corrected complete formula for calculating the axial fragment dispersion distribution based on the test data analysis, which is used to predict the dispersion angle of the fragment warhead under the condition of single-end detonation; the formula takes into account the ratio of charge mass to shell mass, charge diameter and aspect ratio, axial sparse effect and the influence of the relative position of the shell on the dispersion angle; finally, the universal applicability of the formula is verified through tests under other working conditions and compared with other empirical models. The calculation results are in good agreement with the test data, indicating that the formula has high accuracy in predicting the dispersion angle of cylindrical shell fragments under one-end detonation and meets the deviation requirements of engineering calculations.

Description

Technical Field

[0001] The invention belongs to the field of ammunition design, and in particular to a method and system for calculating the dispersion angle of prefabricated fragments taking into account the relative positions of the fragments. Background Art

[0002] The cylindrical charge warhead filled with fragments is one of the commonly used structures in warhead design, which is called a fragment warhead. After the charge explodes, the high-pressure detonation products drive the fragments to move at high speed, which is the main damage factor. In order to improve the warhead design, it is necessary to accurately predict the speed and dispersion angle of the fragments. Therefore, a series of empirical formulas are proposed to estimate the performance of this typical warhead.

[0003] Gurney's formula is a representative formula for calculating fragment velocity. It takes into account the ratio of charge mass to shell mass. Huang et al. proposed a more accurate formula to estimate the fragment velocity of a cylindrical sleeve detonated at one end. This is the Gurney formula modified by the axial rarefaction wave effect, and is currently widely used. Taylor proposed a very representative analytical formula to predict the dispersion angle of the warhead. Many test data show that the formula is inaccurate for predicting the dispersion angle of the fragments, especially the dispersion angle of the fragments at the two ends. Flix proposed a function of the initial dispersion angle of the fragments constructed according to the expansion shape of the shell. This formula requires the reduction of the fragment dispersion angle at the end plate and the position of the maximum fragment velocity. On the one hand, it is difficult to obtain in the experiment. On the other hand, the relative position and reduction accuracy of the construction are mostly assumed values, and the corrected function curve has certain limitations.

[0004] Considering that the research on the influence of axial sparsity effect on fragment dispersion distribution is still lacking and limited, it is urgent to propose a prediction model for the dispersion distribution of cylindrical warheads under one-end detonation considering the axial sparsity effect and the relative position of the shell. Summary of the invention

[0005] The object of the present invention is to provide a method and system for calculating the dispersion angle of prefabricated fragments taking into account the relative positions of the fragments, taking into account the axial sparse effect and the relative position of the shell to predict the dispersion distribution of a cylindrical warhead under one-end detonation, so as to more accurately predict the dispersion distribution of fragments at various axial positions of the cylindrical fragment warhead, especially at the detonation end and the non-detonation end.

[0006] The technical solution to achieve the purpose of the present invention is:

[0007] A prefabricated fragment dispersion angle calculation system considering the relative positions of fragments, comprising a parameter input module and a fragment dispersion angle calculation module;

[0008] The parameter input module is used to input the input parameters for calculating the fragment dispersion angle, including the distance x between the fragment and the detonation end, the warhead charge diameter d, the warhead length L, the fragment initial velocity V0, and the explosive detonation velocity D;

[0009] The fragment dispersion angle calculation module is used to calculate the fragment dispersion angle by the following formula:

[0010]

[0011] A method for calculating the dispersion angle of prefabricated fragments taking into account the relative positions of the fragments, wherein the dispersion angle of the fragments is calculated by the following formula:

[0012]

[0013] Among them, x is the distance between the fragment and the detonation end, d is the diameter of the warhead charge, L is the length of the warhead, V0 is the initial velocity of the fragment, D is the detonation velocity of the explosive, and φ is the angle formed by the normal line of the detonation wave and the symmetry axis of the projectile.

[0014] Compared with the prior art, the present invention has the following significant advantages:

[0015] The present invention takes into account the ratio of charge mass to shell mass (V0 is determined by this), charge diameter and aspect ratio, axial rarefaction effect and the influence of the relative position of the shell on the dispersion angle, and can more accurately predict the fragment dispersion distribution at various axial positions of the cylindrical fragment warhead, especially at the detonation end and the non-detonation end. The universal applicability of the formula was verified by tests under other working conditions and compared with other empirical models. The calculation results are in good agreement with the test data, indicating that the formula has a high accuracy in predicting the dispersion angle of cylindrical shell fragments under one-end detonation, and meets the deviation requirements of engineering calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a schematic diagram of the sample test arrangement and sample structure.

[0017] Figure 2 It is the process of prefabricated fragments penetrating the target driven by an explosion in the sample.

[0018] Figure 3 This is a picture of the treatment of the holes on the witness board after the test.

[0019] Figure 4 This is a diagram of the distribution of sample fragments.

[0020] Figure 5 are the sample fitting result diagrams, (a~c) are the 50mm caliber fitting result diagrams, 70mm caliber fitting result diagrams, and 89mm caliber fitting result diagrams, respectively.

[0021] Figure 6It is the error analysis diagram of the fragmentation scattering distribution model, (a~c) are the axial relative position error diagram, the scattering distribution error statistics diagram, and the percentile error analysis diagram respectively.

[0022] Figure 7 It is a comparison chart of the present invention and other empirical models in verification experiments. DETAILED DESCRIPTION

[0023] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0024] A prefabricated fragment scattering angle calculation system considering the relative position of fragments in this embodiment is based on a computer system and includes a parameter input module, a fragment scattering angle calculation module, and a fragment scattering distribution curve fitting module;

[0025] The parameter input module is used to input the input parameters for calculating the fragment dispersion angle, including the distance x between the fragment and the detonation end, the warhead charge diameter d, the warhead length L, the fragment initial velocity V0, and the angle φ formed by the normal line of the detonation wave and the symmetry axis of the projectile; φ is determined by the distance x between the fragment and the detonation end and the warhead charge diameter d:

[0026] φ=tan -1 (d / 2x).

[0027] The fragment dispersion angle calculation module calculates the fragment dispersion angle by the following formula:

[0028]

[0029] The fragment scattering distribution curve fitting module generates a scattering angle distribution curve by fitting according to the multiple groups of input parameters input by the parameter input module and the scattering angles corresponding to the multiple groups of input parameters calculated by the fragment scattering angle calculation module.

[0030] In order to study the axial dispersion characteristics of fragments driven by explosion, Figure 1 (a) A static explosion test is carried out on the explosive device shown in Figure 1, and the spatial distribution of the fragments is determined by the impact perforation position of the fragments on the witness plate. The sample is placed on a wooden flat support, 1.5m above the ground. The witness plate is made of carbon structural steel, with dimensions of 1570mm long, 3000mm high and 3mm thick. The covering angle between the warhead and the witness plate is 18°, and the witness plate is placed 5m outside the warhead from the explosion center. The warhead is detonated by one end center detonation, and the test sample is placed vertically with the detonation end facing upwards.

[0031] Six groups of cylindrical specimens with different inner diameters and different aspect ratios were prepared. Figure 1(b) shows a cylindrical sample filled with JH-2 explosive and equipped with a 3mm thick 45 steel casing, a 5mm side end cap and a 5mm steel ball. The charge was pressed at a pressure of 300Mpa using a 300-ton pressing device to obtain a charge density greater than 1.69g / cm3. The inner and outer casings were fixed by threaded connections. The 5mm steel ball fragments were placed in the casing in sequence and then injected with epoxy resin for fixation. The 8701 explosive density and casing thickness of all samples were the same. The aspect ratios of the six groups of specimens were 2:1, 1.8:1, and 1.6:1, respectively, and the charge diameters were 56mm, 70mm, and 89mm, respectively. The C / M ratios of the specimens were 0.778, 0.579, and 0.743, respectively. The detailed specifications of the samples are shown in the table below.

[0032]

[0033]

[0034] The moment when the fragments hit the target is captured by high-speed photography, and the fragment speed at a given distance is calculated based on the time mark on the photo. After the test, the image is converted into a grayscale bitmap and the brightness and contrast are adjusted through the data acquisition system connected to the high-speed photography to obtain the fragment penetration process, such as Figure 2 shown.

[0035] Set the frame before the fire to 0, and you can see that after the explosion, the witness plate has a bright spot at 30.8ms. Calculate according to the law of fragment motion, assuming that the horizontal trajectory of the fragment is a straight line, ignoring the influence of air lift and its own gravity, and only considering the effect of air resistance, according to the fragment velocity attenuation formula, its motion equation is:

[0036]

[0037] Where: v is the instantaneous velocity of the fragment, c f is the air resistance coefficient of the fragment flight, and c is taken as the spherical prefabricated fragment f =0.97, is the average windward area of ​​the fragments, m f is the mass of the fragment, t is the time, and ρ0 is the air density. Integrating the above formula gives the fragment flight speed v f With flight time t f The relationship between

[0038]

[0039] According to the above formula, the speed v of the speed measuring point f The initial velocity V0 of the fragments is obtained by reverse calculation.

[0040] After the test, the fragmentation and witness plate perforation were counted. The image was segmented, the target area was identified, and the area shape was extracted by using the sudden change of the gray value of the edge pixel of the hole area on the witness plate. The IPP (Image-Pro Plus) and Image J image analysis software were used to measure and locate the hole contour of the witness plate, and the statistics were performed, such as Figure 3 shown.

[0041] Since the size and shape of the perforation of the fragments when they penetrate the target are basically the same as those of the fragments, the prefabricated fragment perforation can be effectively extracted through IPP. The position statistics of the fragments formed on the witness target under the six schemes are obtained, and the fragment scattering distribution is obtained as follows: Figure 4 As shown in the figure, the fragment dispersion consistency is good under the same caliber and the same aspect ratio, and the experimental data has no error, which is used to establish the dispersion distribution estimation model.

[0042] From the above-mentioned dispersion distribution test results, it can be clearly found that the fragment dispersion distribution curve has the same function change characteristics as the original hyperbolic sine (Sinhx) curve. It can be considered that the hyperbolic sine curve is translated and the coefficients are transformed accordingly so that the curve between the variables 0 and 1 (axial relative position) has positive and negative values. Therefore, the new function is assumed to be a hyperbolic sine curve. Because the fragment dispersion distribution curve obtained from the test has negative values, the empirical model cannot be constructed using the hyperbolic cosine curve. Detonation end correction term

[0043] f(x)=(a1+sinh(b1·x / d))

[0044] Correction for non-detonating end:

[0045] f(y)=(a2+sinh(b2·(Lx) / d))

[0046] Among them, a1 and b1 are the correction coefficients of the rarefaction wave effect from the detonation end, a2 and b2 are the correction coefficients of the rarefaction wave effect from the non-detonation end, x is the distance of the fragment from the detonation end, L is the warhead length, and d is the warhead charge diameter.

[0047] The detonation correction term f(x) and the non-detonation correction term f(y) plus the ideal fragmentation distribution model θ are the complete dispersion prediction model. Substituting the test data into the dispersion prediction model constructed above, the nonlinear least squares regression equation can be used to fit. The corrected dispersion angle distribution function curve is shown in Figure 5 As shown, the four correction coefficients are determined by the test data, and the fitting correction results are:

[0048]

[0049] Where V0 is the initial velocity of the fragments, D is the detonation velocity of the explosive, and φ is the angle between the normal of the detonation wave and the axis of symmetry of the projectile; φ is determined by the distance x from the fragment to the detonation end and the diameter d of the warhead charge:

[0050] φ=tan -1 (d / 2x).

[0051] The R-square of the fitting parameters is 0.9885, indicating that the equation fits the test data well and can describe the fragmentation distribution under the influence of the rarefaction wave effect under different calibers and different aspect ratio charges, especially the dispersion at the detonation end and the non-detonation end is reasonable, which greatly improves the prediction of the warhead damage capability. For the parameter meaning of x / d and (Lx) / d, the fragmentation distribution at each axial position of the cylindrical fragmentation warhead under one-end detonation can be obtained more accurately, which means that the results of this model are more accurate and applicable.

[0052] Figure 6 The relative difference between the model results and the experimental results is shown. The DF, sum of squares and mean square values ​​of the residuals are 72, 12.86 and 0.19938 respectively. The residuals of the axial relative position and the fitted Y value are mostly distributed between -1 and 1.5, such as Figure 6 As shown in (a) and (b), with (-0.93, 0.66) (0.93.99.33) as the reference line, the conventional residual of the percentile does not exceed 0.3, such as Figure 6 (c) The model fitting results are relatively accurate and consistent with the test results. The relative error of 97% of the data points in the relative axial position is within 3%, and the average error of the 6 sets of data is calculated to be ±2%. The large relative error is due to the sparse wave effect from the detonation end and the non-detonation end, which causes the fragments to be unevenly stressed, so the scattered distribution is unstable, but this model also avoids the influence of errors to a large extent. In general, this model can be used as an empirical calculation model for the scattered distribution of fragments of cylindrical charges detonated at one end under the consideration of the sparse wave effect.

[0053] In order to verify the general applicability of the above fragment dispersion distribution formula, a set of verification tests was designed according to sample tests. The initial velocity of the fragments was substituted into the empirical model of the present invention to predict the dispersion angle. The obtained results were compared with those of other models. Figure 7 The fitting results of the model of the present invention are relatively accurate and well consistent with the test results. The relative error of 97% of the data points in the relative axial position is within 6%, and the average error of the two groups of data is calculated to be ±7%, which meets the error requirements and is well consistent with the test data. It has a high accuracy in predicting the flying angle of the cylindrical shell fragments under one-end detonation, which meets the deviation requirements of engineering calculations.

Claims

1. A prefabricated fragment dispersion angle calculation system taking into account the relative positions of the fragments, characterized in that: It includes parameter input module and fragment dispersion angle calculation module; The parameter input module is used to input the input parameters for calculating the fragment dispersion angle, including the distance x between the fragment and the detonation end, the warhead charge diameter d, the warhead length L, the fragment initial velocity V0, and the explosive detonation velocity D; The fragment dispersion angle calculation module is used to calculate the fragment dispersion angle by the following formula: in It is the angle between the detonation wave normal and the symmetry axis of the projectile.

2. The prefabricated fragment dispersion angle calculation system according to claim 1, characterized in that: It also includes a fragment scattering distribution curve fitting module, which is used to fit and generate a scattering angle distribution curve according to the scattering angles corresponding to the multiple groups of input parameters input by the parameter input module and the multiple groups of input parameters calculated by the fragment scattering angle calculation module.

3. The prefabricated fragment dispersion angle calculation system according to claim 1, characterized in that: The fragment initial velocity V0 is obtained by reverse calculation using the following calculation formula: Among them, c f is the air resistance coefficient of the fragment flight, ρ0 is the air density, v f is the fragment flight speed at the measuring point, is the average windward area of ​​the fragments, t f is the flight time, m f The quality of the fragments.

4. The prefabricated fragment dispersion angle calculation system according to claim 1, characterized in that: The angle between the detonation wave normal and the projectile symmetry axis Determined by the distance x between the fragment and the detonation end and the warhead charge diameter d:

5. A method for calculating the dispersion angle of prefabricated fragments taking into account the relative positions of the fragments, characterized in that: include: Input parameters for calculating the fragment dispersion angle include the distance x between the fragment and the detonation end, the warhead charge diameter d, the warhead length L, the fragment initial velocity V0, and the explosive detonation velocity D; The fragment dispersion angle is calculated using the following formula: in It is the angle between the detonation wave normal and the symmetry axis of the projectile.

6. The method for calculating the dispersion angle of prefabricated fragments according to claim 5, characterized in that: The fragment initial velocity V0 is obtained by reverse calculation using the following calculation formula: Among them, c f is the air resistance coefficient of the fragment flight, ρ0 is the air density, v f is the fragment flight speed at the measuring point, is the average windward area of ​​the fragments, t f is the flight time, m f The quality of the fragments.

7. The method for calculating the dispersion angle of prefabricated fragments according to claim 5, characterized in that: The angle between the detonation wave normal and the projectile symmetry axis Determined by the distance x between the fragment and the detonation end and the warhead charge diameter d:

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