A method for calculating the axial distribution of the initial velocity of fragments in a cubic composite structure.

Abstract

This invention discloses a method for calculating the axial distribution of the initial velocity of fragments in a cubic composite structure, aiming to solve the problem that existing models cannot accurately describe the axial distribution of the initial velocity of fragments in a cubic composite structure. This invention first obtains the Gurney initial velocity of natural fragments and pre-formed fragments based on the Gurney formula, and then, combined with end-effects, introduces the influence coefficient of detonation product leakage to perform a first correction on the initial velocities of the two types of fragments. Subsequently, it classifies the fragments according to the initiation point location. If the detonation occurs from the pre-formed fragment side, the radial leakage effect of detonation products at the pre-formed fragment needs to be considered additionally, resulting in a second correction on the initial velocity of the natural fragments. Numerical simulation using LS-DYNA software verifies that this invention can accurately predict the axial distribution of the initial velocity of fragments, providing support for warhead yield assessment.

Description

Technical Field

[0001] This invention belongs to the field of fragment force simulation, specifically relating to a method for calculating the axial distribution of the initial velocity of fragments in a cubic composite structure. Background Technology

[0002] Early high-explosive fragmentation warheads used fragments generated naturally from the outer casing under explosive detonation. However, these fragments had complex parameters and poor velocity retention. To improve kill efficiency, pre-fabricated fragments were typically installed around the explosive charge according to a certain pattern. However, due to practical considerations, the number of pre-fabricated fragments installed on the projectile was limited, and a certain thickness of outer casing still needed to be maintained in other axial positions of the projectile for support. Therefore, the explosion of a pre-fabricated fragmentation warhead would produce two types of fragments. These two types of fragments would disperse together to form a kill cluster, known as a combined fragmentation structure.

[0003] Currently, there is relatively complete research on the dispersion of single fragments in cylindrical charges. In his article "Axial Distribution of Initial Velocity of Fragments in Cylindrical Sleeves with Different Length-to-Diameter Ratios," Bi Weixin studied the initial velocity distribution of fragments under different L / d conditions through numerical simulation and proposed a calculation model for the axial distribution of initial velocity of fragments considering different L / d conditions. This model can calculate the initial velocity distribution of fragments under different L / d conditions with a relatively accurate average error of no more than 6%. However, due to the temporal nature of the explosive charge, the two types of fragments influence each other, making it impossible to accurately describe the axial distribution of the initial velocity of fragments using existing calculation models. Summary of the Invention

[0004] This invention proposes a method for calculating the axial distribution of the initial velocity of fragments in a cubic composite structure. It comprehensively considers the end leakage of cylindrical charges and the differences in circumferential leakage of different types of fragments. Based on the Gurney formula, it determines the initial velocity distribution of two types of fragments at different axial positions under different proportions and different initiation point positions, so as to obtain the initial velocity of fragments at different axial positions.

[0005] The technical solution for achieving the present invention is as follows: a method for calculating the axial distribution of the initial velocity of fragments in a cubic composite structure, comprising the following steps:

[0006] Step 1: After the explosion of the warhead loaded with cubic pre-fragmented fragments, pre-fragmented fragments and shell fragments are produced. The shell fragments are called natural fragments. The pre-fragmented fragments and natural fragments disperse together to form a fragment cluster with a combined structure. The initial Gurney velocities v of the two types of fragments are calculated according to the Gurney formula. 0i i represents the type of fragment, i=1 represents natural fragments, i=2 represents pre-made fragments, proceed to step 2.

[0007] Step 2: Determine the detonation point. If the detonation is initiated from the shell end, proceed to step 3; if the detonation is initiated from the prefabricated end, proceed to step 4.

[0008] Step 3: When the detonation point is located at the end of the casing, the initial Gurney velocity v of the two types of fragments is... 0i After correction, the axial distribution of the initial velocity of the fragments is obtained. ;

[0009] ,

[0010] In the formula, x is the axial distance between the fragment element and the detonation point, and f i (x) is the axial distribution correction factor that takes into account the end effect.

[0011] Step 4: When the detonation point is located at the precast end, the initial velocities of the precast fragments and the naturally occurring fragments are corrected separately, specifically as follows:

[0012] The axial distribution of the pre-fragmented fragment initial velocity was obtained through calculations based on the corrected initial velocity of the pre-fragmented fragments. :

[0013] ,

[0014] The initial velocity correction for spontaneous fragments needs to consider the effect of radial leakage of detonation products at the pre-formed fragment location, and the axial distribution of the corrected initial velocity of spontaneous fragments. :

[0015] ,

[0016] In the formula, g(x) is the correction factor for the radial leakage effect of detonation products at the pre-fragmentation site.

[0017] Compared with the prior art, the significant advantages of this invention are:

[0018] (1) This invention takes into account the end leakage of cylindrical charge and the difference in circumferential leakage of different types of fragments. Based on the Gurney formula, it determines the initial velocity distribution of two types of fragments at different axial positions under different proportions and different initiation point positions, so as to obtain the initial velocity of fragments at different axial positions.

[0019] (2) The present invention proposes an expression for the influence coefficient g(x) of radial leakage at the pre-formed fragment on the initial velocity of the natural fragment. When the warhead detonates from the pre-formed end, the natural fragment needs to be corrected by g(x) for a second time. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the calculation method for the axial distribution of the initial velocity of fragments in a cubic composite structure as described in this invention.

[0021] Figure 2 It refers to the geometric dimensions of the prefabricated cubic fragments used.

[0022] Figure 3 These are two-dimensional model diagrams of different scale models, where (a) is a model diagram with 8 pre-fragmented fragments installed axially, (b) is a model diagram with 16 pre-fragmented fragments installed axially, and (c) is a model diagram with 24 pre-fragmented fragments installed axially.

[0023] Figure 4 The figures show a comparison between numerical simulation and formula calculation of pre-fabricated end detonation. (a) is a model diagram with 8 pre-fabricated fragments installed axially, (b) is a model diagram with 16 pre-fabricated fragments installed axially, and (c) is a model diagram with 24 pre-fabricated fragments installed axially.

[0024] Figure 5 The figures show a comparison between numerical simulation and formula calculation for natural end detonation. (a) is a model diagram with 8 pre-fragmented fragments installed axially, (b) is a model diagram with 16 pre-fragmented fragments installed axially, and (c) is a model diagram with 24 pre-fragmented fragments installed axially. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. 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.

[0026] The technical solutions of the various embodiments of the present invention can be combined with each other, but only if they can be implemented by those skilled in the art. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0027] The following section will further introduce the specific implementation method, as well as the technical difficulties and inventive points of this invention, using this design example as an example.

[0028] Combination Figure 1 The method for calculating the axial distribution of the initial velocity of a cubic composite structure fragment according to the present invention comprises the following steps:

[0029] Step 1: After the explosion of the warhead loaded with cubic pre-fragmented fragments, pre-fragmented fragments and shell fragments are produced. The shell fragments are called natural fragments. The pre-fragmented fragments and natural fragments disperse together to form a fragment cluster with a combined structure. The initial Gurney velocities v of the two types of fragments are calculated according to the Gurney formula. 0i i represents the type of fragment, i=1 represents natural fragments, and i=2 represents pre-made fragments.

[0030] Among them, the initial Gurney velocities v of the two types of fragments formed according to the Gurney formula are... 0i The details are as follows:

[0031] ,

[0032] In the formula, v 0i Let C be the initial Gurney velocity of the fragment, C be the mass of the charge, and M be the mass of the fragment. This is Gurney's constant.

[0033] The charge shape of the object being calculated is cylindrical, and the pre-fragmented type is cubic.

[0034] Proceed to step 2.

[0035] Step 2: Determine the detonation point. If the detonation is initiated from the shell end, proceed to step 3; if the detonation is initiated from the prefabricated end, proceed to step 4.

[0036] Step 3: When the detonation point is located at the end of the casing, the initial Gurney velocity v of the two types of fragments is... 0i After correction, the axial distribution of the initial velocity of the fragments is obtained. ;

[0037] ,

[0038] In the formula, x is the axial distance between the fragment element and the detonation point, and f i (x) is the axial distribution correction factor that takes into account the end effect.

[0039] The aforementioned correction factors are as follows:

[0040] ,

[0041] ,

[0042] In the formula, x is the distance between the fragment and the plane where the detonation point is located, L is the total length of the explosive charge, and d is the diameter of the explosive charge.

[0043] Step 4: When the detonation point is located at the precast end, the initial velocities of the precast fragments and the naturally occurring fragments are corrected separately, specifically as follows:

[0044] The axial distribution of the pre-fragmented fragment initial velocity was obtained through calculations based on the corrected initial velocity of the pre-fragmented fragments. :

[0045] ,

[0046] The initial velocity correction for spontaneous fragments needs to consider the effect of radial leakage of detonation products at the pre-formed fragment location, and the axial distribution of the corrected initial velocity of spontaneous fragments. :

[0047] ,

[0048] In the formula, g(x) is the correction factor for the radial leakage effect of detonation products at the pre-fragmentation site.

[0049] The expression for the influence coefficient g(x) of radial leakage from pre-formed fragments is as follows:

[0050] ,

[0051] in, This represents the ratio of the overall axial length of the pre-fragmented material to the diameter of the propellant grain. , This indicates the overall axial length of the prefabricated fragment.

[0052] Example 1

[0053] This invention provides a method for calculating the axial distribution of the initial velocity of fragments in a cubic composite structure, as detailed below:

[0054] The initial velocities of the two types of fragments were obtained according to the Gurney formula, and the calculation formula is as follows:

[0055] ,

[0056] In the formula, v0 is the initial Gurney velocity of the fragment (m / s), C is the mass of the charge (kg), and M is the mass of the fragment (kg). For Gurney.

[0057] According to explosives theory, the relationship between Gurney energy and detonation velocity is as follows:

[0058] ,

[0059] Where D is the detonation velocity of the explosive (m / s).

[0060] Given the mass of the explosive, the mass of the fragments, and the detonation velocity of the explosive, the Gurney initial velocity of the two types of fragments can now be calculated.

[0061] Gurney provides an ideal formula for calculating the initial velocity of fragments, which can reflect the influence of explosive mass, fragment mass, and explosive detonation velocity on the initial velocity of fragments to a certain extent. However, in practical applications, due to the end effect, the initial velocity of fragments at different locations is not a single value calculated by the Gurney formula. Furthermore, due to the different circumferential leakage degrees of pre-formed fragments and natural fragments, their respective axial distributions are also different.

[0062] Based on the above reasons, considering the end effect, the pre-fragmented fragments and natural fragments are corrected for the first time, with i=1 representing the natural fragments and i=2 representing the pre-fragmented fragments, respectively. The initial velocity axial distributions of the two types of fragments without mutual influence are obtained as follows:

[0063] ,

[0064] In the formula, f i (x) is the influence coefficient considering the end effect, and the specific calculation formula is as follows:

[0065] ,

[0066] ,

[0067] In the formula, x is the distance (mm) from the fragment to the plane where the detonation point is located, L is the total length of the explosive charge (mm), and d is the diameter (mm) of the explosive charge.

[0068] Thus, we have obtained the calculation formulas for the axial distribution of initial velocity when there are two types of single fragment distributions. Based on this, it is necessary to classify and discuss different detonation point positions. If the detonation is initiated from the center point of the side end face of the natural fragment, only the first correction is required.

[0069] If the detonation is initiated from the center point of the pre-fragmented fragment's side end face, the impact of detonation product leakage at the pre-fragmented fragment on the initial velocity of the natural fragment must be considered. A second correction is then made to the initial velocity of the natural fragment, resulting in the following axial distribution of the corrected initial velocity:

[0070] ,

[0071] In the formula, g(x) represents the effect of radial leakage of detonation products at the pre-fragmentation site on the natural initial velocity, and its specific expression is as follows:

[0072] ,

[0073] in, This represents the ratio of the overall axial length of the pre-fragmented material to the diameter of the propellant grain. , This indicates the overall axial length of the prefabricated fragment.

[0074] Example 2:

[0075] To verify the accuracy of the above calculation formula, this embodiment 2 provides a numerical simulation for verifying the initial velocity of the fragments.

[0076] The numerical simulation verification of this invention uses the commercial LS-DYNA finite element analysis software, and the algorithm adopts the ALE multi-material fluid-structure interaction algorithm.

[0077] The charge material used in the numerical simulation verification of this invention is Comp B explosive. The model adopts the high-energy explosive combustion material model HIGH_EXPLOSIVE_BURN and the JWL equation of state, and its parameters are shown in Table 1.

[0078]

[0079] Both the pre-formed fragments and the naturally formed fragments were made of 45# steel. The Gruneison equation of state and the Johnson-Cook constitutive equation were used, and their parameters are shown in Table 2.

[0080]

[0081] The dimensions of the pre-formed fragments are as follows: Figure 2 As shown, the number of circumferentially arranged units is 50.

[0082] The geometric dimensions of the charge model used to calculate the axial distribution of the initial velocity of the combined fragment structure are as follows: Figure 3 As shown.

[0083] Numerical simulations were used to verify the calculated and simulated results of the axial initial velocity distribution of the fragments after detonation loading. A detailed comparison is shown below. Figure 4 and Figure 5 As shown.

[0084] Figure 4 To compare the results of detonation from the pre-fragmented end, the detonation point is set as zero. A vertical dotted line is shown as the dividing line in the figure. The pre-fragmented fragment is to the left of the dividing line, and the natural fragment is to the right of the dividing line. After comparison, the initial velocity calculation formula of the first pre-fragmented fragment near the detonation point has an error of about 8% compared with the numerical simulation, while the maximum error of the calculation formula of the other positions is less than 4%.

[0085] Figure 5 To compare the results of detonation from the spontaneous fragmentation end, the detonation point is set at zero. A vertical dotted line is used as the dividing line in the figure. Figure 4 Conversely, the left side of the dividing line represents naturally occurring fragments, while the right side represents pre-formed fragments; the error between numerical simulation and formula calculation is less than 10%.

[0086] The comparative calculation results show that the method for calculating the axial distribution of the initial velocity of fragments proposed in this invention, by distinguishing between the detonation point and the type of fragments and considering the mutual influence between the two types of fragments, can accurately predict the initial velocity distribution of fragments.

Claims

1. A method for calculating the axial distribution of the initial velocity of fragments in a cubic composite structure, characterized in that, The steps are as follows: Step 1: After the explosion of the warhead loaded with cubic pre-fragmented fragments, pre-fragmented fragments and shell fragments are produced. The shell fragments are called natural fragments. The pre-fragmented fragments and natural fragments disperse together to form a fragment cluster with a combined structure. The initial Gurney velocities of the two types of fragments are calculated according to the Gurney formula. i represents the type of fragment, i=1 represents natural fragments, i=2 represents pre-made fragments, proceed to step 2; Step 2: Determine the detonation point. If the detonation occurs at the shell end, proceed to Step 3; if the detonation occurs at the prefabricated end, proceed to Step 4. Step 3: When the detonation point is located at the end of the casing, the initial Gurney velocities of the two types of fragments are... After correction, the axial distribution of the initial velocity of the fragments is obtained. ; ， In the formula, x is the axial distance between the fragment element and the detonation point. A correction factor for axial distribution considering end effect; Step 4: When the detonation point is located at the precast end, the initial velocities of the precast fragments and the naturally occurring fragments are corrected separately, specifically as follows: The axial distribution of the initial velocity of the pre-fragmented fragments was obtained through calculations to correct the initial velocity. : ， The initial velocity correction for spontaneous fragments needs to consider the effect of radial leakage of detonation products at the pre-formed fragment location, and the axial distribution of the corrected initial velocity of spontaneous fragments. : ， In the formula, g(x) is the correction factor for the radial leakage effect of detonation products at the pre-fragmentation site.

2. The method for calculating the axial distribution of the initial velocity of a cubic composite structure fragment according to claim 1, characterized in that, In step 1, the initial Gurney velocities v of the two types of fragments formed are calculated according to the Gurney formula. 0i The details are as follows: ， In the formula, Let C be the initial Gurney velocity of the fragment, C be the mass of the charge, and M be the mass of the fragment. This is Gurney's constant.

3. The method for calculating the axial distribution of the initial velocity of a cubic composite structure fragment according to claim 2, characterized in that: The charge shape of the object being calculated is cylindrical, and the pre-fragmented type is cubic.

4. The method for calculating the axial distribution of the initial velocity of a cubic composite structure fragment according to claim 3, characterized in that, In step 3, the correction factor is specifically as follows: ， ， In the formula, x is the distance between the fragment and the plane where the detonation point is located, L is the total length of the explosive charge, and d is the diameter of the explosive charge.

5. The method for calculating the axial distribution of the initial velocity of a cubic composite structure fragment according to claim 4, characterized in that, In step 4, the influence coefficient g(x) of radial leakage of pre-fragmented fragments is expressed as follows: ， in, This represents the ratio of the overall axial length of the pre-fragmented material to the diameter of the propellant grain. , This indicates the overall axial length of the prefabricated fragment.

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