A method for simulating the momentum field of natural fragmentation projectiles at the moment of detonation

Abstract

The present invention discloses a method for simulating the momentum field of natural fragmentation projectiles at the moment of detonation. The method adopts a random variable generation method to realize the uniform distribution of fragments in each calculation unit, establishes a prime number spatial distribution model of fragments, and on this basis, couples and superimposes the spatial position distribution of fragments with the fragment velocity field to establish a fragment momentum field, thereby realizing the damage assessment prediction of projectiles. Compared with the prior art, the method for simulating the momentum field of natural fragmentation projectiles at the moment of detonation can realize the damage assessment prediction of projectiles.

Description

Technical Field

[0001] The invention relates to the technical field of system simulation, and in particular to a method for simulating momentum fields of natural fragment projectiles at the moment of explosion. Background Art

[0002] As the most important damaging element in grenades, fragments play a decisive role in the damaging power of grenades. The design of ammunition achieves the purpose of increasing the power by changing factors such as the mass, quantity distribution, velocity and spatial distribution, fragment shape, and detonation method of fragments. At present, the grenade power prediction technology at home and abroad mainly uses finite element algorithms to predict fragments and velocity distribution, establish fragment momentum fields, and complete the power prediction of ammunition according to damage criteria.

[0003] Since the finite element algorithm cannot solve the problems of mass loss caused by mesh disappearance and random generation of projectile fragments, in order to make up for the theoretical defects in the mass, quantity and spatial distribution technology of ammunition fragments, foreign countries use expert systems to correct the calculation results and construct fragment momentum fields. For example, the FATEPEN simulation software in the United States and the AVAL simulation software in Sweden use the finite element calculation method to obtain relatively ideal results, but there are no relevant reports on the solution technology used by these two software to avoid mass loss caused by mesh elimination. At present, domestic ammunition power assessment software uses the method of artificially setting fragment mass and spatial distribution to construct fragment momentum fields, and its scope of application and accuracy cannot meet the requirements of projectile design and damage capability assessment. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a method for simulating the momentum field of natural fragment projectile fragments at the moment of detonation, which can realize the damage assessment prediction of the projectile, in view of the current status of the prior art.

[0005] The technical solution adopted by the present invention to solve the technical problem is: a method for simulating the momentum field of natural fragment projectiles at the moment of detonation, characterized in that:

[0006] According to the geometric characteristics of the projectile to be predicted, the projectile is divided into N calculation units along the projectile axis. The i-th calculation unit forms K after detonation. i a fragment;

[0007] The simulation method comprises the following steps:

[0008] S1. Use random variable generation method to achieve uniform distribution of fragments in each computing unit, establish prime number spatial distribution model of fragments, and obtain coordinates A of any fragment j in computing unit i. ij (x ij ,y ij ,z ij ), where 1≤i≤N, 1≤j≤K i ;

[0009] S2. Use the Gurney velocity formula and Shapiro formula to calculate the velocity and scattering angle of the fragments, establish the velocity field of the fragments, and obtain the initial velocity V of any fragment j in the calculation unit i. d (A ij ), memory speed V dL (A ij ) and the scattered direction angle

[0010] S3. Superimpose and couple the fragments of different masses and quantities in each projectile segment with the velocity field, and verify it using the theorem of conservation of momentum. Use statistical methods to accumulate the superimposed coupling field of the fragments of each projectile segment with the velocity field, establish a fragment momentum field model, and form a data file that meets the requirements of the grenade damage prediction system.

[0011] In order to more accurately predict the spatial distribution of fragments, the specific steps of S1 are as follows:

[0012] S1-1. Determine the starting section radius R of the i-th calculation unit i-1 and the end section radius R i If R i-1 =R i , it is determined that the i-th computing unit is cylindrical, and S1-2 is executed; otherwise, it is determined that the i-th computing unit is truncated cone, and S1-3 is executed;

[0013] S1-2, according to the random uniform distribution function in the two-dimensional plane coordinate system, the random distribution point formed by the j-th fragment of the i-th calculation unit is obtained, and the spatial position of the j-th fragment of the i-th calculation unit at the moment of detonation is obtained through the mapping and inverse mapping relationship between the three-dimensional space coordinates of the projectile shell and the plane rectangular coordinates;

[0014] S1-3. According to the random uniform distribution function in the two-dimensional plane coordinate system, the random distribution points formed by the j-th fragment of the i-th calculation unit are obtained. Through the mapping and inverse mapping relationship between the three-dimensional spatial coordinates of the projectile shell and the polar coordinates, the spatial position of the j-th fragment of the i-th calculation unit at the moment of detonation is obtained.

[0015] In order to more accurately predict the speed of the fragments, the specific steps of S2 are as follows:

[0016] S2-1. Establish static explosion velocity field:

[0017] (1) Calculate the initial velocity of fragments under static explosion conditions:

[0018]

[0019] In the formula, V0(A ij ) is the initial velocity of fragment j under static explosion conditions;

[0020] is the Gurney constant, D e is the charge detonation velocity, where the dimension of each parameter is mm / μs;

[0021] β i is the charge mass ratio of calculation unit i;

[0022] (2) Calculate the fragment velocity under static explosion conditions:

[0023]

[0024] Where: V L (A ij ) is the storage velocity of fragment j under static explosion conditions;

[0025] L ij is the flight distance of fragment j;

[0026] α ij is the velocity attenuation coefficient of fragment j, with dimension m -1 ;

[0027] (3) Calculate the fragment scattering angle under static explosion conditions:

[0028]

[0029]

[0030] Where: is the scattering direction angle of fragments j under static explosion conditions;

[0031] is the angle between the outer normal n of the shell surface of the calculation unit where the fragment is located and the missile axis;

[0032] It is the angle between the propagation direction of the detonation wave or the detonation velocity direction De and the missile axis;

[0033] θ s (A ij ) is the fragment scattering direction or initial velocity V0(A ij ) is the deflection angle caused by the direction of the explosion wave propagating away from the outer normal direction of the shell;

[0034] S2-2. Establish dynamic explosion velocity field:

[0035] (1) Calculate the initial velocity of fragments under dynamic explosion conditions:

[0036]

[0037] Where: Vd (A ij ) is the initial velocity of fragment j under dynamic explosion conditions;

[0038] Vm is the speed of the warhead in the air;

[0039] a is the angle between the velocity vector direction and the projectile axis;

[0040] (2) Calculation of fragment velocity under dynamic explosion conditions:

[0041]

[0042] Where: V dL (A ij ) is the storage velocity of fragment j under dynamic explosion conditions;

[0043] (3) Calculate the fragment scattering angle under dynamic explosion conditions:

[0044]

[0045] Where: is the scattering direction angle of fragments under dynamic explosion conditions.

[0046] Preferably, in S2-1, the β i The expression is:

[0047] β i =C i / M i ;

[0048] Where: C i is the charge mass of calculation unit i, M i is the metal shell mass of calculation unit i.

[0049] Preferably, in S2-1, the α ij The expression is:

[0050]

[0051] Where: S ij is the average frontal area of ​​fragment j;

[0052] ρ a is the local air density;

[0053] C D is the aerodynamic drag coefficient;

[0054] m ij is the mass of fragment j.

[0055] Preferably, in S2-1, the and The expression is:

[0056]

[0057]

[0058] Where: Z i-1 and Z i The distances from the starting section and the ending section of unit i to the origin are calculated respectively;

[0059] R i-1 and R i are the radii of the start and end sections respectively.

[0060] In order to more accurately predict the momentum of the fragments, the specific steps of S3 are as follows:

[0061] S3-1. Calculate the momentum of fragments:

[0062]

[0063] Among them, p(A ij ) is the momentum of fragment j;

[0064] m ij is the mass of fragment j;

[0065] is the velocity vector of fragment j;

[0066] S3-2. In each calculation unit i, the starting section is used as the reference datum and the axis of the missile is used as the rotation axis. The calculation unit is divided into 2n equal parts. N consecutive parts are randomly selected to calculate the momentum field of the fragments. The momentum field of the remaining part is obtained by the coordinate transformation method, thereby forming a complete momentum field of the fragments.

[0067] Of course, it can also be achieved mathematically through other ways, such as the rotation matrix method, which superimposes the calculated fragment momentum field with the rotation matrix to obtain the remaining momentum field, thereby forming a complete fragment momentum field.

[0068] Preferably, the fragment momentum field is constructed as follows:

[0069] (1) Obtain the momentum of all fragments in one of the selected parts of the calculation unit i. The momentum of these fragments constitutes a momentum field, denoted as P i1 ,but

[0070] (2) According to the above step (1), the momentum fields of the remaining n-1 fragments of the selected part are calculated in sequence, which are denoted as P i2 , P i3 , P i4 ...Pin ;

[0071] (3) According to the coordinate transformation method, the above n fragment momentum fields are transformed to obtain the remaining n fragment momentum fields, which are denoted as P i(n+1) , P i(n+2) , P i(n+3) ...P i(2n-1) , P i(2n) , thereby obtaining the complete fragment momentum field of calculation unit i;

[0072] (4) Repeat the above steps (1) to (3) to calculate the fragment momentum fields of the remaining calculation units in turn, thereby obtaining the fragment momentum field of the complete projectile.

[0073] Compared with the prior art, the advantages of the present invention are:

[0074] (1) By using the relationship between the shape structure of each shell segment and the spatial coordinates, the three-dimensional spatial coordinates are converted into XZ two-dimensional plane coordinates with the Z axis as the reference axis. The two-dimensional coordinates of the fragments are obtained by using the characteristic that the fragments meet the random uniform distribution. Combined with the inverse mapping relationship between the two-dimensional space and the three-dimensional space, the spatial position coordinates of the fragments at the moment of explosion are obtained, making it possible to simulate and analyze the spatial position distribution of natural fragment projectiles at the moment of explosion, filling the gap in the previous lack of independent research on fragment spatial distribution technology, and providing a feasible operation for the research on the power of projectiles;

[0075] (2) The technical method of the present invention can be used to establish a natural fragment momentum field based on momentum conservation, avoiding the problems of mass loss caused by finite element calculation or the limited scope of application and accuracy caused by the artificial setting of fragment mass and spatial distribution method, thereby achieving damage assessment prediction that is relatively consistent with the results of live ammunition explosion. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 This is a schematic diagram of the pellet segmentation of this application;

[0077] Figure 2 It is a schematic diagram of the structure of a right-handed Cartesian coordinate system;

[0078] Figure 3 This is a schematic diagram of a fan-shaped structure formed by unfolding the truncated cone-shaped shell of the present application in the XZ plane;

[0079] Figure 4 This is a schematic diagram of the spatial position relationship of the truncated cone-shaped shell of the present application in three-dimensional space;

[0080] Figure 5 This is a schematic diagram of a rectangular structure formed by unfolding the cylindrical shell of the present application in the XZ plane;

[0081] Figure 6This is a schematic diagram of the fragmentation angle under static explosion conditions of this application;

[0082] Figure 7 This is a schematic diagram of the fragmentation angle under dynamic explosion conditions of this application;

[0083] Figure 8 This is a schematic diagram of selecting fragments after the calculation unit is equally divided for this application;

[0084] Fig. 9 It is an output table of fragment space coordinate data of a certain mass segment in the embodiment of the present application;

[0085] Fig.10 A schematic diagram of a fragment momentum field model according to an embodiment of the present application;

[0086] Fig.11 for Fig.10 Schematic diagram of corresponding fragment markings;

[0087] Fig.12 for Fig.11 A partial enlarged view of . DETAILED DESCRIPTION

[0088] The present invention is further described in detail below with reference to the accompanying drawings.

[0089] This application claims protection for a method for simulating the momentum field of natural fragmentation projectile fragments at the moment of detonation. Before fully disclosing the method of this application in detail, it should be mentioned that this method is based on the following assumptions generally recognized in the field of projectile natural fragment damage assessment: (1) the projectile shell is fully broken at the moment of detonation to form natural fragments; (2) the formation position of each natural fragment in the shell is random; (3) the position distribution of all fragments on the surface of the projectile shell is uniform. The acquisition of the coordinates of the fragments in two-dimensional space and the coordinate transformation between two-dimensional space and three-dimensional space in the following text are also based on this premise.

[0090] According to the geometric characteristics of the projectile to be predicted, the projectile is divided into N calculation units along the projectile axis. The i-th calculation unit forms K after detonation. i A fragment.

[0091] The above-mentioned method for simulating the momentum field of natural fragment projectile fragments at the moment of detonation comprises the following steps:

[0092] S1. Use random variable generation method to achieve uniform distribution of fragments in each computing unit, establish prime number spatial distribution model of fragments, and obtain coordinates A of any fragment j in computing unit i. ij (x ij ,y ij ,z ij ), where 1≤i≤N, 1≤j≤K i ;

[0093] S2. Use the Gurney velocity formula and Shapiro formula to calculate the velocity and scattering angle of the fragments, establish the velocity field of the fragments, and obtain the initial velocity V of any fragment j in the calculation unit i. d (A ij ), memory speed V dL (A ij ) and the scattered direction angle

[0094] S3. Superimpose and couple the fragments of different masses and quantities in each projectile segment with the velocity field, and verify it using the theorem of conservation of momentum. Use statistical methods to accumulate the superimposed coupling field of the fragments of each projectile segment with the velocity field, establish a fragment momentum field model, and form a data file that meets the requirements of the grenade damage prediction system.

[0095] Among them, the specific steps of S1 are as follows:

[0096] S1-1. Determine the starting section radius R of the i-th calculation unit i-1 and the end section radius R i If R i-1 =R i , it is determined that the i-th computing unit is cylindrical, and S1-2 is executed; otherwise, it is determined that the i-th computing unit is truncated cone, and S1-3 is executed;

[0097] S1-2, according to the random uniform distribution function in the two-dimensional plane coordinate system, the random distribution point formed by the j-th fragment of the i-th calculation unit is obtained, and the spatial position of the j-th fragment of the i-th calculation unit at the moment of detonation is obtained through the mapping and inverse mapping relationship between the three-dimensional space coordinates of the projectile shell and the plane rectangular coordinates;

[0098] S1-3. According to the random uniform distribution function in the two-dimensional plane coordinate system, the random distribution points formed by the j-th fragment of the i-th calculation unit are obtained. Through the mapping and inverse mapping relationship between the three-dimensional spatial coordinates of the projectile shell and the polar coordinates, the spatial position of the j-th fragment of the i-th calculation unit at the moment of detonation is obtained.

[0099] In order to simulate the spatial position of the projectile, the present application divides the complete projectile shell into N segments along the projectile axis according to the geometric structure characteristics of the projectile, and each segment can be approximated as a truncated cone or a cylinder, such as Figure 1 For the convenience of calculation, the three-dimensional space of the fragments of the projectile shell uses the right-handed Cartesian coordinate system, as shown in Figure 2 As shown, the top end (small end) of the projectile is placed at the origin of the coordinate system, and the projectile axis is the positive Z axis.

[0100] Assume that the cone / column i, 1≤i≤N, and the coordinates of the two sections along the positive Z axis are Z i-1 , Zi The radius of the cross-section circle is R i-1 , Ri, the radius R i-1 , R i It is obtained by adding the average value of the inner and outer diameters of the projectile shell. i-1 =R i When , the shell segment i is a cylinder, otherwise it is a truncated cone. Because the shapes formed by the truncated cone or cylinder when unfolded in a two-dimensional plane are different, the coordinate conversion relationship is also different. Therefore, when performing spatial position analysis and conversion on a specific fragment, it is necessary to first determine the shape of the i-th segment of the projectile shell that forms the fragment, which is presented in step S1-1.

[0101] Regarding the spatial position coordinates of the fragments, the approach adopted in this application is that, since two-dimensional coordinates are easier to obtain than three-dimensional space coordinates, the three-dimensional space is first reduced in dimension to obtain the conversion relationship between three-dimensional and two-dimensional coordinates. Then, after obtaining the two-dimensional plane random coordinates, the three-dimensional space coordinates of the fragments are calculated back through inverse mapping.

[0102] Specifically, when it is determined that the shell of the i-th projectile is truncated cone-shaped, the mapping of the three-dimensional space coordinates of the truncated cone-shaped shell to the two-dimensional space coordinates and the inverse mapping have the following relationship:

[0103] (1) Mapping of three-dimensional space coordinates to two-dimensional plane, where the two-dimensional plane coordinate system uses polar coordinates

[0104] like Figure 3 As shown, the truncated cone shell is cut along the generatrix of the first hexagram section in the XZ plane, and the first, second, third, and fourth hexagrams are unfolded in sequence along the direction of the right index finger around the Z axis to form a fan surface, and the fan arc is β j , assuming the center of the sector is the origin of polar coordinates, then,

[0105] Length of round busbar

[0106] Corresponding small cone generatrix length

[0107] Corresponding small cone height

[0108] The angle between the corresponding small cone generatrix and the elastic axis

[0109] Sector arc

[0110] The cone vertex corresponding to the truncated cone shell is translated to the origin along the Z axis. Then the vertical coordinate Z after translation is i-1 , Z i becomes Z' i-1 ,Z' i , translation distance di = Zi-1 -h min,i Of course, it is easy to understand that a positive di number means a translation in the negative direction of the Z axis, and a negative di number means a translation in the positive direction of the Z axis.

[0111] It should also be mentioned here that the spatial position of the projectile shell listed in this application makes R i-1 <R i Can also be replaced by R i-1 >R i , but at this time, the larger end surface of the projectile shell is located at the origin, that is, it is just upside down with the upper and lower end surfaces of the projectile in the three-dimensional space established in this application. In this case, when performing coordinate mapping conversion, only a simple coordinate transformation process is required, which will not be repeated here;

[0112] (2) Inverse mapping from two-dimensional plane coordinates to three-dimensional space coordinates

[0113] The total number of fragments formed after the detonation of the i-th truncated cone shell is K i ,like Figure 4 As shown in the figure, the polar coordinates of any fragment j in the unfolded fan area are (ρ ij ,θ ij ), 0≤θ ij ≤β i , 1≤j≤K i , then from polar coordinates to three-dimensional rectangular coordinate system coordinates (x ij ,y ij , z ij ) is as follows:

[0114] Z-axis coordinate z′ after translation ij =ρ ij *cosδ i ;

[0115] ρ ij The length of the projected line segment in the XY plane is ρ′ ij =ρ ij *sinδ i ;

[0116] θ ij Conic projection circumference in the XY plane

[0117] X-axis coordinate of fragment j

[0118] Y-axis coordinate of fragment j

[0119] The Z-axis coordinate z of fragment j before translation ij = z′ ij +di .

[0120] When it is determined that the shell of the i-th projectile is cylindrical, the mapping and inverse mapping of the three-dimensional space coordinates of the cylindrical shell to the two-dimensional space coordinates have the following relationship:

[0121] (1) Mapping of three-dimensional space coordinates to two-dimensional plane coordinates, where the two-dimensional coordinate system uses plane rectangular coordinates LZ'

[0122] like Figure 5 As shown, the i-th cylindrical shell is cut along the generatrix of the first quadrant section of the XZ plane, and the first, second, third, and fourth quadrants are unfolded in sequence around the Z axis along the direction of the right index finger to form a two-dimensional rectangle. The X / Z axis corresponds to the L / Z' axis respectively. In the plane rectangular coordinate system LZ', the side of the rectangle corresponding to the generatrix of the cylinder coincides with the positive direction of the Z' axis, and the side of the rectangle corresponding to the unfolded circumference of the cylinder is parallel to the X axis, that is, it coincides with the extension line of the axial section of the cylinder in the rectangular coordinate system LZ'. The coordinates of any point in the rectangle are expressed as (l ij ,z ij '), where 0≤l ij ≤2πR i-1 ,Z i-1 ≤z′ ij ≤ Z i ;

[0123] (2) Inverse mapping from two-dimensional plane coordinates to three-dimensional space coordinates

[0124] The total number of fragments formed after the explosion of the i-th cylindrical shell is K i , the plane rectangular coordinates of the particle point of any fragment j in the unfolded rectangular area are (l ij ,z' ij ), 1≤j≤K i , then its coordinates from the two-dimensional plane to the three-dimensional rectangular coordinate system (x ij ,y ij , z ij ) is converted as follows:

[0125] The angle between the radius projection of fragment j on the XY plane and the X axis

[0126] X-axis coordinate of fragment j

[0127] Y-axis coordinate of fragment j

[0128] The Z-axis coordinate z of fragment j before translation ij = z′ ij , Z i-1 With Z iis the Z-axis coordinate of the upper and lower sections of the i-th cylindrical shell.

[0129] Under the premise that the shell fragments obey uniform distribution, this method uses the more classic random variable generation method in statistical theory - the inverse transformation method to solve the problem of random uniform distribution of fragments in the two-dimensional plane area. Specifically,

[0130] When the shell of the i-th projectile is truncated cone, the corresponding random uniform distribution function in the two-dimensional plane coordinate system is:

[0131] (ρ ij ,θ ij ) obeys the fan-shaped area D = {(ρ ij ,θ ij )|l min，i ≤ρ ij ≤l i , 0≤θ ij ≤β i} uniform distribution, where ρ ij and θ ij The density function distribution of is:

[0132]

[0133] And ij With θ ij Independent of each other,

[0134] At this time, the specific method of obtaining the random distribution points formed by the jth fragment of the i-th projectile shell is:

[0135] (1) Generate U(0, 1) uniform random numbers independently and j=1,2,3…,K i ;

[0136] (2) By Get {θ ij}, in [0,β i ] is evenly distributed on Get {ρ ij}, in l min，i , l i ] are evenly distributed on the surface.

[0137] When the shell of the i-th projectile is cylindrical, the corresponding random uniform distribution function in the two-dimensional plane coordinate system is: (L, Z') in the rectangular area [0, 2πR i-1 ]×[Z i-1 , Z i ] obeys uniform distribution, where L~U[0,2πR i-1],Z'~U[Z i-1 , Z i ], and L and Z' are independent of each other.

[0138] In this case, the specific random distribution point of the jth fragment of the i-th projectile shell is formed as follows:

[0139] (1) Generate U(0, 1) uniform random numbers independently and

[0140] (2) By and We can get [0, 2πR i-1 ] and [Z i-1 , Z i ] are randomly distributed points uniformly distributed within, j = 1, 2, 3, …, Ki.

[0141] In this way, the spatial position scattering problem of fragments is solved by converting between the three-dimensional space position coordinates and the two-dimensional plane position coordinates, and the random uniform distribution theory method is used to solve the random uniform distribution problem of fragments in the two-dimensional plane area. Then, the three-dimensional space coordinates are converted into XZ two-dimensional plane coordinates with the Z axis as the reference axis by utilizing the relationship between the shape structure of each section of the shell and the spatial coordinates. The two-dimensional coordinates of the fragments are obtained by utilizing the characteristic that the fragments satisfy the random uniform distribution. Combined with the inverse mapping relationship between the two-dimensional space and the three-dimensional space, the spatial position coordinates of the fragments at the moment of explosion are obtained, making it possible to simulate and analyze the spatial position distribution of natural fragment projectiles at the moment of explosion, filling the gap of the previous lack of independent research on fragment spatial distribution technology, and providing a feasible operation for the research on the power of projectiles.

[0142] The specific steps of S2 are as follows:

[0143] S2-1. Establish static explosion velocity field:

[0144] (1) Calculate the initial velocity of fragments under static explosion conditions:

[0145] The Gurney energy method is the most basic method for deriving the relationship between fragment initial velocity, Gurney specific energy and explosive to metal mass ratio (C / M). As a classic semi-theoretical and semi-empirical method, it has clear physical meaning and simple model form. It can obtain satisfactory calculation accuracy for most charge materials and structures and a fairly wide range of C / M values ​​(0.1-5).

[0146] According to the Gurney formula, the initial velocity of any fragment j in calculation unit i is calculated as follows:

[0147]

[0148] In the formula, V0(A ij) is the initial velocity of fragment j;

[0149] is the Gurney constant, D e is the charge detonation velocity, where the dimension of each parameter is mm / μs;

[0150] β i is the charge mass ratio of calculation unit i, β i =c i / M i , C i is the charge mass of calculation unit i, M i is the mass of the metal shell of calculation unit i;

[0151] In this application, the β required to calculate the initial velocity of the fragments is i It takes different values ​​with different calculation units i, which is different from the classic Gurney formula in which β is the average charge mass ratio of the entire projectile;

[0152] (2) Calculate the fragment velocity under static explosion conditions:

[0153] After the fragments acquire the initial velocity and escape from the effect of the detonation products, they fly in the air and are affected by both gravity and air resistance. Gravity causes the trajectory of the fragments to bend, while air resistance causes the velocity of the fragments to decay. Since the distance from the fragments to the target is not too long and the time is very short, the effect of gravity can be ignored and the trajectory of the fragments can be approximately regarded as a straight line.

[0154] According to the fragment storage speed calculation formula, the flight distance of any fragment j in unit i is calculated to be L ij When , the storage speed expression is:

[0155]

[0156] Where: V L (A ij ) is the storage speed of fragment j;

[0157] V0(A ij ) is the initial velocity of fragment j;

[0158] L ij is the flight distance of fragment j;

[0159] α ij is the velocity attenuation coefficient of fragment j, the expression is as follows, the dimension is m -1 ;

[0160] The expression of the velocity attenuation coefficient is:

[0161]

[0162] Where: S ij is the average frontal area of ​​fragment j;

[0163] ρ a is the local air density;

[0164] C D is the aerodynamic drag coefficient;

[0165] m ij is the mass of fragment j;

[0166] (3) Calculate the fragment scattering angle under static explosion conditions:

[0167] Since there are many factors that affect the scatter angle, such as shell shape, explosive detonation velocity and detonation position, the calculation of the fragment scatter angle is usually approximated according to the Shapiro formula;

[0168] like Figure 6 As shown, point O is taken as the detonation position. After detonation, the detonation wave propagates forward along the sphere. Assume that the angle between the outer normal line n of the shell surface of the calculation unit where the fragment is located and the missile axis is The angle between the propagation direction of the detonation wave or the detonation velocity direction De and the missile axis is The direction of fragment scattering or the direction of initial velocity V0 deviates from the outer normal direction of the shell due to the influence of the propagation direction of the explosion wave, resulting in a deflection angle θ s , called the fragmentation deflection angle; the angle between the fragmentation direction and the missile axis It is called the fragmentation scattering angle;

[0169]

[0170]

[0171] According to the above expression, the deflection angle θ of the fragment j is calculated respectively: s (A ij ) and the scattered direction angle

[0172] The shell taper of calculation unit i where fragment j is located:

[0173] The angle between the outer normal n of the shell surface of calculation unit i where fragment j is located and the missile axis:

[0174] The angle between the detonation velocity direction De and the missile axis when the detonation wave propagates to fragment j is:

[0175] Fragment scattering deflection angle:

[0176] Fragment scattering angle:

[0177] S2-2. Establish dynamic explosion velocity field:

[0178] The θ scattered by static explosion fragments s and The direction of fragment scattering under dynamic explosion conditions can be deduced. Figure 7 As shown, the warhead's speed in the air is Vm, and the angle between the velocity vector direction and the missile axis is a (called the angle of attack). Under dynamic explosion conditions, the angle between the fragment scattering direction and the missile axis is It is called the dynamic scattering direction angle of fragments.

[0179] The initial velocity of fragments under dynamic conditions is:

[0180]

[0181] In the case of a dynamic explosion, the speed of the fragments flying to a point L from the explosion center is V dL , the expression is as follows:

[0182] V dL =V d e -αL ;

[0183] According to the above expressions, the scattering direction angle of fragment j in the case of dynamic explosion is calculated respectively: and initial velocity V d (A ij ) and memory speed V dL (A ij );

[0184] (1) Calculate the initial velocity of fragments under dynamic explosion conditions:

[0185]

[0186] (2) Calculation of fragment velocity under dynamic explosion conditions:

[0187]

[0188] (3) Calculate the fragment scattering angle under dynamic explosion conditions:

[0189]

[0190] The specific steps of S3 are as follows:

[0191] S3-1. According to the momentum formula, the momentum of any fragment j in unit i is calculated as p(A ij ),but

[0192]

[0193] Among them, m ij is the mass of fragment j;

[0194] is the velocity vector of fragment j;

[0195] S3-2. In this technology, the projectile is an axisymmetric structure. A part of it is selected for calculation, and the calculation results of the remaining parts are obtained by coordinate transformation method. In each calculation unit i, the starting section is used as the reference datum, and the axis of the projectile is used as the rotation axis. The calculation unit is divided into 2n equal parts (n≥1), and n consecutive parts are randomly selected to calculate the momentum field of the fragments (such as Figure 8 As shown in Figure 2, the momentum field of the remaining part is obtained by coordinate transformation method, thereby forming a complete momentum field of fragments;

[0196] This application establishes the fragment momentum field through the coordinate transformation method to achieve the conservation of fragment momentum;

[0197] Specifically, the above fragment momentum field is constructed as follows:

[0198] (1) Obtain the momentum of all fragments in one of the selected parts of the calculation unit i. The momentum of these fragments constitutes a momentum field, denoted as P i1 ,but

[0199] (2) According to the above step (1), the momentum fields of the remaining n-1 fragments of the selected part are calculated in sequence, which are denoted as P i2 , P i3 , P i4 ...P in ;

[0200] (3) According to the coordinate transformation method, the above n fragment momentum fields are transformed to obtain the remaining n fragment momentum fields, which are denoted as P i(n+1) , P i(n+2) , P i(n+3) ...P i(2n-1) , P i(2n) , thereby obtaining the complete fragment momentum field of calculation unit i;

[0201] (4) Repeat the above steps (1) to (3) to calculate the fragment momentum fields of the remaining calculation units in turn, thereby obtaining the fragment momentum field of the complete projectile.

[0202] Example:

[0203] This application is described in detail using a real missile as an example.

[0204] The calculation indicators such as the type and density of the projectile material, the density of the explosive, the AB value, and the geometric dimensions of the projectile unit are imported into the "Visual Simulation System for Damage Assessment of Killing Bombs" in the form of a spreadsheet file to perform fragment momentum field model prediction verification, and the following is obtained: Fig. 9 Results shown.

[0205] According to the momentum formula, the momentum of any fragment j is recorded as p(A ij ),but

[0206]

[0207] Among them, m ij is the mass of fragment j;

[0208] is the velocity vector of fragment j;

[0209] The set of momentums of all calculation unit fragments is called the fragment momentum field, denoted by P, then: P = {p1, p2, p3...p N}.

[0210] The projectile is divided into 10 calculation units according to its geometric dimensions, ie, N=10.

[0211] P i ={p i1 , p i2 , p i3 …… i(2n-1) , p i(2n)}, where 1≤i≤10,

[0212]

[0213] from Fig. 9 Randomly select a few points in Fig.10 You can get corresponding fragments in it.

[0214] like Fig.11 As shown, in Fig. 9 Two points are randomly selected from the matrix, with serial numbers 951 and 1105, and the corresponding fragments are recorded as 1 and 2 respectively.

[0215] from Fig.12 It can be seen that each fragment corresponds to a velocity vector, combined with Fig. 9 The mass of the fragments can be used to obtain the momentum of each fragment, and the collection formed by this is the fragment momentum field of the projectile.

[0216] A live-fire detonation test was carried out on the projectile. By comparing the simulation data with the live-fire detonation test data, it was calculated that the error of the fragment model prediction value was within 10%. It can be seen that the technical method of the present invention can achieve damage assessment prediction that is relatively consistent with the live-fire detonation result.

Claims

1. A method for simulating the momentum field of natural fragments at the moment of projectile detonation, characterized in that: According to the geometric characteristics of the projectile to be predicted, the projectile is divided into N calculation units along the projectile axis. The i-th calculation unit forms K after detonation. i a fragment; The simulation method comprises the following steps: S1. Use random variable generation method to achieve uniform distribution of fragments in each computing unit, establish prime number spatial distribution model of fragments, and obtain coordinates A of any fragment j in computing unit i. ij (x ij ,y ij ,z ij ), where 1≤i≤N, 1≤j≤K i ; S2. Use the Gurney velocity formula and Shapiro formula to calculate the velocity and scattering angle of the fragments, establish the velocity field of the fragments, and obtain the initial velocity V of any fragment j in the calculation unit i. d (A ij ), memory speed V dL (A ij ) and the scattered direction angle S3, superimpose and couple the fragments of different masses and quantities in each projectile segment with the velocity field, and verify it by using the momentum conservation theorem; use statistical methods to accumulate the fragments of each projectile segment and the velocity superposition coupling field, establish a fragment momentum field model, and form a data file that meets the requirements of the grenade damage prediction system; The specific steps of S1 are as follows: S1-1. Determine the starting section radius R of the i-th calculation unit i-1 and the end section radius R i If R i-1 =R i , it is determined that the i-th computing unit is cylindrical, and S1-2 is executed; otherwise, it is determined that the i-th computing unit is truncated cone, and S1-3 is executed; S1-2, according to the random uniform distribution function in the two-dimensional plane coordinate system, the random distribution point formed by the j-th fragment of the i-th calculation unit is obtained, and the spatial position of the j-th fragment of the i-th calculation unit at the moment of detonation is obtained through the mapping and inverse mapping relationship between the three-dimensional space coordinates of the projectile shell and the plane rectangular coordinates; S1-3, according to the random uniform distribution function in the two-dimensional plane coordinate system, the random distribution point formed by the j-th fragment of the i-th calculation unit is obtained, and the spatial position of the j-th fragment of the i-th calculation unit at the moment of detonation is obtained through the mapping and inverse mapping relationship between the three-dimensional space coordinates of the projectile shell and the polar coordinates; Specifically, when it is determined that the shell of the i-th projectile is truncated cone-shaped, the mapping of the three-dimensional space coordinates of the truncated cone-shaped shell to the two-dimensional space coordinates and the inverse mapping have the following relationship: (1) Mapping of three-dimensional space coordinates to two-dimensional plane, where the two-dimensional plane coordinate system uses polar coordinates: Cut the truncated cone shell along the first quadrant section generatrix of the XZ plane, and unfold the first, second, third, and fourth quadrants in sequence around the Z axis in the direction of the right index finger to form a fan surface, and the fan arc is β i , assuming the center of the sector is the origin of polar coordinates, then, Length of round busbar Corresponding small cone generatrix length Corresponding small cone height The angle between the corresponding small cone generatrix and the elastic axis Sector arc The cone vertex corresponding to the truncated cone shell is translated to the origin along the Z axis. Then the vertical coordinate Z after translation is i-1 , Z i becomes Z' i-1 ,Z' i , translation distance di = Z i-1 -h min,i ; (2) Inverse mapping from two-dimensional plane coordinates to three-dimensional space coordinates: The total number of fragments formed after the detonation of the i-th truncated cone shell is K i , the polar coordinates of any particle j in the expanded fan area are (ρ ij ,θ ij ), 0≤θ ij ≤β i , 1≤j≤K i , then from polar coordinates to three-dimensional rectangular coordinate system coordinates (x ij ,y ij , z ij ) is as follows: Z-axis coordinate z′ after translation ij =ρ ij *cosδ i ; ρ ij The length of the projected line segment in the XY plane is ρ′ ij =ρ ij *sinδ i ; θ ij Conic projection circumference in the XY plane X-axis coordinate of fragment j Y-axis coordinate of fragment j The Z-axis coordinate z of fragment j before translation ij = z′ ij +d i ; When it is determined that the shell of the i-th projectile is cylindrical, the mapping and inverse mapping of the three-dimensional space coordinates of the cylindrical shell to the two-dimensional space coordinates have the following relationship: (1) Mapping of three-dimensional space coordinates to two-dimensional plane coordinates, where the two-dimensional coordinate system uses plane rectangular coordinates LZ' The i-th cylindrical shell is cut along the generatrix of the first quadrant section of the XZ plane, and the first, second, third, and fourth quadrants are unfolded in sequence around the Z axis along the direction of the right index finger to form a two-dimensional rectangle. The X / Z axis corresponds to the L / Z' axis respectively. In the plane rectangular coordinate system LZ', the side of the rectangle corresponding to the generatrix of the cylinder coincides with the positive direction of the Z' axis, and the side of the rectangle corresponding to the unfolded circumference of the cylinder is parallel to the X axis, that is, it coincides with the extension line of the axial section of the cylinder in the rectangular coordinate system LZ'. The coordinates of any point in the rectangle are expressed as (l ij ,z′ ij ), where 0≤l ij ≤2πR i-1 ,Z i-1 ≤z′ ij ≤Z i ; (2) Inverse mapping from two-dimensional plane coordinates to three-dimensional space coordinates The total number of fragments formed after the i-th cylindrical shell is detonated is K i , the plane rectangular coordinates of the particle point of any fragment j in the unfolded rectangular area are (l ij ,z' ij ), 1≤j≤K i , then its coordinates from the two-dimensional plane to the three-dimensional rectangular coordinate system (x ij ,y ij , z ij ) is converted as follows: The angle between the radius projection of fragment j on the XY plane and the X axis X-axis coordinate of fragment j Y-axis coordinate of fragment j The Z-axis coordinate z of fragment j before translation ij = z′ ij , Z i-1 With Z i is the Z-axis coordinate of the upper and lower sections of the i-th cylindrical shell.

2. The method for simulating momentum field of natural fragmentation projectiles at the moment of detonation according to claim 1 is characterized in that: The specific steps of S2 are as follows: S2-1. Establish static explosion velocity field: (1) Calculate the initial velocity of fragments under static explosion conditions: In the formula, V0(A ij ) is the initial velocity of fragment j under static explosion conditions; is the Gurney constant, De is the charge detonation velocity, where the dimensions of each parameter are mm / μs; β i is the charge mass ratio of calculation unit i; (2) Calculate the fragment velocity under static explosion conditions: Where: V L (A ij ) is the storage velocity of fragment j under static explosion conditions; L ij is the flight distance of fragment j; α ij is the velocity attenuation coefficient of fragment j, with dimension m -1 ; (3) Calculate the fragment scattering angle under static explosion conditions: Where: is the scattering direction angle of fragments j under static explosion conditions; is the angle between the outer normal n of the shell surface of the calculation unit where the fragment is located and the missile axis; It is the angle between the propagation direction of the detonation wave or the detonation velocity direction De and the missile axis; θ s (A ij ) is the fragment scattering direction or initial velocity V0(A ij ) is the deflection angle caused by the direction of the explosion wave propagating away from the outer normal direction of the shell; S2-2. Establish dynamic explosion velocity field: (1) Calculate the initial velocity of fragments under dynamic explosion conditions: Where: V d (A ij ) is the initial velocity of fragment j under dynamic explosion conditions; Vm is the speed of the warhead in the air; a is the angle between the velocity vector direction and the projectile axis; (2) Calculation of fragment velocity under dynamic explosion conditions: Where: V dL (A ij ) is the storage velocity of fragment j under dynamic explosion conditions; (3) Calculate the fragment scattering angle under dynamic explosion conditions: Where: is the scattering direction angle of fragments under dynamic explosion conditions.

3. The method for simulating momentum field of natural fragmentation projectiles at the moment of detonation according to claim 2 is characterized in that: In S2-1, the β i The expression is: b i =C i / M i ; Where: C i is the charge mass of calculation unit i, M i is the metal shell mass of calculation unit i.

4. The method for simulating momentum field of natural fragmentation projectiles at the moment of detonation according to claim 2 is characterized in that: In S2-1, the α ij The expression is: Where: S ij is the average frontal area of ​​fragment j; ρ a is the local air density; C D is the aerodynamic drag coefficient; m ij is the mass of fragment j.

5. The method for simulating momentum field of natural fragmentation projectiles at the moment of detonation according to claim 2 is characterized in that: In S2-1, and The expression is: Where: Z i-1 and Z i The distances from the starting section and the ending section of unit i to the origin are calculated respectively; R i-1 and R i are the radii of the starting section and the ending section respectively; θ i锥 is the shell taper of calculation unit i where fragment j is located.

6. The method for simulating momentum field of natural fragmentation projectiles at the moment of detonation according to claim 1 is characterized in that: The specific steps of S3 are as follows: S3-1. Calculate the momentum of fragments: Among them, p(A ij ) is the momentum of fragment j; m ij is the mass of fragment j; is the velocity vector of fragment j; S3-2. In each calculation unit i, the starting section is used as the reference datum and the axis of the missile is used as the rotation axis. The calculation unit is divided into 2n equal parts. N consecutive parts are randomly selected to calculate the momentum field of the fragments. The momentum field of the remaining part is obtained by the coordinate transformation method, thereby forming a complete momentum field of the fragments.

7. The method for simulating the momentum field of natural fragmentation projectiles at the moment of detonation according to claim 6 is characterized in that: The fragment momentum field is constructed as follows: (1) Obtain the momentum of all fragments in one of the selected parts of the calculation unit i. The momentum of these fragments constitutes a momentum field, denoted as P i1 ,but (2) According to the above step (1), the momentum fields of the remaining n-1 fragments of the selected part are calculated in turn, which are denoted as P i2 , P i3 , P i4 ...P in ; (3) According to the coordinate transformation method, the above n fragment momentum fields are transformed to obtain the remaining n fragment momentum fields, which are denoted as P i(n+1) , P i(n+2) , P i(n+3) ...P i(2n-1) , P i(2n) , thereby obtaining the complete fragment momentum field of calculation unit i; (4) Repeat the above steps (1) to (3) to calculate the fragment momentum fields of the remaining calculation units in turn, thereby obtaining the fragment momentum field of the complete projectile.

Images