A method for evaluating a buffer plate protection based on a velocity and mass distribution of a projectile fragment cloud

Abstract

The present application relates to a kind of buffer plate protection evaluation method based on projectile fragment cloud speed and mass distribution, belong to impact protection evaluation technical field, solve the problem that existing buffer plate evaluation method does not consider shock wave spatial distribution cannot accurately evaluate the protection effect of buffer plate.The method comprises: according to the collision speed of projectile superhigh-speed normal impact buffer plate, projectile radius and material initial sound speed, the initial shock wave wave speed of shock wave formed by any collision contact point on projectile is obtained;Based on initial shock wave wave speed, projectile diameter, buffer plate thickness and material initial sound speed, the shock wave Mach number and shock wave wave speed when shock wave attenuates are obtained, and then the projectile edge material scattering speed is obtained;Based on the speed of projectile edge material scattering speed, the speed of fragment cloud shedding area formed by projectile is calculated, the mass distribution of projectile layer splitting is calculated based on buffer plate thickness, projectile radius, material initial sound speed and collision speed, and then the protection effect of buffer plate is evaluated.

Description

Technical Field

[0001] This invention relates to the field of impact protection assessment technology, and in particular to a buffer plate protection assessment method based on the velocity and mass distribution of projectile fragment clouds. Background Technology

[0002] As humanity continues to explore space, the amount of space debris generated is increasing, making the space environment increasingly harsh. Compared to micrometeoroids, orbital debris poses a serious threat to the normal operation of spacecraft in orbit. Currently, most protective structures are improvements on the Whipple structure. The basic idea is to place a thin plate as a buffer at a certain distance in front of the spacecraft's outer bulkhead. When space debris impacts the buffer plate at extremely high speeds, it breaks apart along with the buffer plate, forming a debris cloud. The debris cloud expands sufficiently in the space behind the buffer plate, resulting in a large-area distributed load when the debris cloud collides with the bulkhead, significantly reducing damage to the spacecraft. When applying the buffer plate protective structure in practice, it is necessary to evaluate the protective effect of the buffer plate to determine whether it meets the protection requirements.

[0003] Currently, the evaluation of the protective effect of shock plates typically involves multiple high-velocity spherical projectile impact tests, which are costly and susceptible to external interference. Theoretical research analyzes the shock wave propagation and interaction during debris cloud formation based on high-velocity spherical projectile impacts on the shock plate, deriving the debris cloud's motion characteristics, and then using these characteristics to determine the shock plate's protective effect. However, current analyses of debris cloud formation primarily rely on the generation of one-dimensional shock waves, neglecting their spatial distribution. This fails to accurately describe the complete shock wave propagation process and its impact on the debris cloud, thus hindering an accurate assessment of the shock plate's protective effect. Summary of the Invention

[0004] In view of the above analysis, the present invention aims to provide a buffer plate protection assessment method based on the velocity and mass distribution of projectile fragment clouds, in order to solve the problem that existing buffer plate assessment methods do not consider the spatial distribution of shock waves and cannot accurately assess the protective effect of buffer plates.

[0005] On one hand, embodiments of the present invention provide a buffer protection assessment method based on the velocity and mass distribution of projectile fragment clouds, the method comprising:

[0006] Based on the collision velocity of the projectile's hypersonic impact with the buffer plate, the projectile's radius, and the material's initial sound velocity, the initial shock wave velocity of the shock wave formed at any point of impact on the projectile is obtained.

[0007] Based on the initial shock wave velocity, projectile diameter, buffer plate thickness, and initial sound velocity of the material, the shock wave Mach number and shock wave velocity at the time of shock wave attenuation are obtained, and then the material dispersion velocity at the edge of the projectile is obtained.

[0008] Based on the material dispersion velocity at the edge of the projectile, the velocity of the fragment cloud shedding zone formed by the projectile is calculated; based on the thickness of the buffer plate, the radius of the projectile, the initial sound velocity of the material, and the collision velocity, the mass distribution of the projectile undergoing delamination is calculated.

[0009] The protective effect of the buffer plate is evaluated based on the velocity of the debris cloud shedding zone and the mass distribution of the delamination.

[0010] Furthermore,

[0011] The protective effect of the buffer plate is evaluated based on the velocity of the debris cloud shedding zone and the mass distribution of the delamination, specifically:

[0012] The velocity distribution of the debris cloud shedding zone formed by the projectile includes the outer contour velocity and the in-contour velocity of the debris cloud.

[0013] The higher the values ​​of the outer contour velocity and the inner contour velocity of the debris cloud peeling area, the more fully the projectile and buffer plate material are broken, and the better the buffer plate protection effect.

[0014] The greater the mass distribution of the projectile that causes delamination, the smaller the proportion of the mass-dense part in the debris cloud, and the better the protection effect of the buffer plate.

[0015] Furthermore, the velocity of the outer contour of the debris cloud includes the translational velocity u. c and expansion velocity u e It can be expressed by the following formula:

[0016]

[0017] In the formula, u fz and u fr These are the particle dispersion velocities at the edge of the projectile. z-axis and r-axis components;

[0018] With the center point of the outer contour of the fragment cloud as the pole, u c The direction is the polar axis direction, u e Establish a polar coordinate system with radius t and counterclockwise direction as positive to obtain any point (r) within the contour. f The velocity of ζ) Represented as:

[0019]

[0020] In the formula, u z and u rThese are the z-axis and r-axis components of the velocity at any point within the contour, respectively. f ζ and ζ represent the polar radius and polar angle of any point within the contour, respectively, and t represents the time elapsed after the projectile collides with the buffer plate.

[0021] Furthermore, the mass distribution η of the projectile undergoing spalling is expressed as:

[0022]

[0023] In the formula,

[0024]

[0025] Where, d p V0 is the depth at which the projectile undergoes delamination, D is the projectile diameter, c0 is the initial sound velocity of the material, and a, b, and d represent the first, second, and third parameters of the material, respectively.

[0026] Furthermore, taking the initial collision point on the projectile as the origin, the direction pointing from the initial collision point to the center of the projectile as the z-axis, and the direction perpendicular to the z-axis as the r-axis, a coordinate system is established that translates with the projectile. The following steps are used to obtain any collision contact point (z) in the projectile. e r e The initial shock wave velocity s0(τ) that forms the shock wave:

[0027] The velocity increment U(τ) behind the shock wave formed at any collision contact point can be obtained using the following system of equations:

[0028]

[0029] In the formula,

[0030]

[0031] Where V0 is the impact velocity of the projectile's hypersonic direct impact with the buffer plate, R is the projectile radius, c0 is the initial sound velocity of the material, α is the interface angle between the projectile tangent and the buffer plate at the impact contact point, and τ is the time interval from the initial impact point to the impact contact point; θ P and θ T λ represents the rotation angle of the material particle after the shock wave from the projectile and the buffer plate, respectively; λ is the linear relationship coefficient between the shock wave velocity and the velocity of the material particle.

[0032] When the two solutions to the above system of equations are not equal, the solution with the smaller value is taken as the wave back velocity increment U(τ);

[0033] When the two solutions of the above system of equations are equal, one solution is taken as the wave back velocity increment U(τ). At the same time, the generation of the shock wave ends, and the time interval τ is taken as the end time t1.

[0034] Based on the waveback velocity increment U(τ), the initial shock wave velocity s0(τ) of the shock wave formed at any collision contact point in the projectile is calculated using the following formula:

[0035] s0(τ)=c0+λU(τ).

[0036] Furthermore, based on the initial shock wave velocity, projectile diameter, buffer plate thickness, and initial sound velocity of the material, the shock wave Mach number and shock wave velocity at shock wave attenuation are obtained, specifically including:

[0037] The critical ratio is calculated based on the initial shock wave velocity and the initial sound velocity of the material at the initial collision point.

[0038] When the ratio of the thickness of the buffer plate to the diameter of the projectile is greater than or equal to the critical ratio, the shock wave Mach number at the time of shock wave attenuation is obtained based on the shock wave Mach number and position on the shock wave at the end of the shock wave generation, and then the shock wave velocity at the time of shock wave attenuation is obtained.

[0039] When the ratio of the thickness of the buffer plate to the diameter of the projectile is less than the critical ratio, the shock wave velocity at the time of shock wave attenuation is obtained based on the time when the shock wave propagates to the back surface of the buffer plate and the position and time when the rarefaction wave front catches up with the shock wave, and then the shock wave Mach number at the time of shock wave attenuation is obtained; wherein, the rarefaction wave is obtained by the buffer plate reflecting the shock wave.

[0040] Furthermore, the critical ratio ξ c Represented as:

[0041]

[0042] In the formula,

[0043]

[0044]

[0045] Where c represents the sound velocity behind the shock wave, and γ represents the state parameter.

[0046] Furthermore, when the ratio of the buffer plate thickness h to the projectile diameter D is greater than or equal to the critical ratio ξ... c When the shock wave decays, the shock wave Mach number M at any point (z, r) on the shock wave front surface is... s Represented as:

[0047]

[0048] In the formula, The value represents the shock wave Mach number at the corresponding point on the shock wave front at time t1; r1(τ,t1) represents the r-axis coordinate of the corresponding point on the shock wave at time t1; l represents the distance between the corresponding point (z1, r1) on the shock wave front at time t1 and the current point (z, r); A1 represents the shock wave area at time t1; and K represents the correlation coefficient.

[0049] Determined according to the following formula K, l, and A1:

[0050]

[0051]

[0052]

[0053]

[0054] In the formula,

[0055]

[0056]

[0057]

[0058] Where s1(τ,t1) represents the shock wave velocity at the corresponding point on the shock wave front at time t1, l wl (τ,t1) represents the wavelet trajectory at the corresponding point on the shock wave front at time t1; k a This represents the linear attenuation coefficient of the shock wave in the material;

[0059] The shock wave velocity during shock wave attenuation is expressed as follows:

[0060] s = c0M s .

[0061] Furthermore, when the ratio of the buffer plate thickness h to the projectile diameter D is less than the critical ratio ξ... c When the shock wave attenuates, the shock wave velocity at any point (z, r) on the shock wave front is expressed as:

[0062]

[0063] In the formula,

[0064]

[0065]

[0066] Among them, t h The moment when the shock wave reaches the back surface of the buffer plate; zr and t r These represent the z-axis position and time at which the rarefaction wavefront catches up with the shock wave, respectively.

[0067] The shock wave Mach number during attenuation is expressed as:

[0068]

[0069] Furthermore, a wave-following coordinate system is established with the point P(z,r) at the edge of the projectile as the origin. The x-axis is tangent to the projectile and points in the direction of the shock wave, and the y-axis points towards the center of the projectile. The velocity of material dispersion at the edge of the projectile is obtained according to the following steps.

[0070] The following formula represents the translational velocity vector of the coordinate system containing the projectile edge point P(z,r).

[0071]

[0072] Where q0 represents the translational velocity of the coordinate system containing the projectile edge point P(z,r); β represents the acute angle between the direction of the translational velocity of the coordinate system containing the projectile edge point P(z,r) and the r-axis.

[0073] The mass dispersion velocity vector at the projectile edge point P(z,r) is determined using the following formula.

[0074]

[0075]

[0076] In the formula,

[0077]

[0078]

[0079]

[0080] Among them, c f q represents the speed of sound of the scattered material. f ω represents the velocity of the material at the edge point P(z,r) of the projectile, ω represents the acute angle between the direction of the velocity of the material at the edge point P(z,r) of the projectile and the z-axis, q and θ represent the velocity of the material particles behind the wave and the rotation angle of the material behind the wave in the wave-following coordinate system when the shock wave moves to the edge point P(z,r) of the projectile; p represents the pressure behind the wave and ρ represents the density behind the wave.

[0081] according to and The dispersion velocity of the material at the edge of the projectile was obtained. Represented as:

[0082]

[0083] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0084] This invention provides a buffer plate protection assessment method based on the velocity and mass distribution of projectile fragment clouds. Based on the initial shock wave velocity generated at any point of impact on the projectile, and considering two shock wave attenuation scenarios, the method calculates the shock wave Mach number and velocity during attenuation, thereby obtaining the projectile edge material dispersion velocity. This method fully considers the influence of shock wave variations over time and spatial distribution, providing a more accurate description of the complete shock wave propagation process and the motion patterns of the projectile edge material. Simultaneously, based on the obtained projectile edge dispersion velocity, this invention obtains the velocity of the projectile fragment cloud spalling zone and the mass distribution of projectile delamination. The protective effect of the buffer plate is then evaluated based on the fragment cloud's motion patterns and the projectile delamination situation, improving the accuracy of the assessment.

[0085] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0086] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0087] Figure 1 This is a flowchart of the buffer plate protection assessment method based on the velocity and mass distribution of projectile fragment clouds in an embodiment of the present invention;

[0088] Figure 2 This is a schematic diagram illustrating the shock wave generated by the projectile impacting the buffer plate in an embodiment of the present invention;

[0089] Figure 3 This is a schematic diagram of the shock wave rays in the projectile in an embodiment of the present invention;

[0090] Figure 4 This is a wave system diagram of the rarefaction wave chasing and unloading shock wave in the projectile in an embodiment of the present invention;

[0091] Figure 5 This is a schematic diagram illustrating the velocity of material scattering at the edge of the projectile in an embodiment of the present invention;

[0092] Figure 6This is a schematic diagram illustrating the delamination of a projectile in an embodiment of the present invention;

[0093] Figure 7 This is a schematic diagram illustrating the velocity of the fragment cloud shedding zone formed by the projectile in an embodiment of the present invention. Detailed Implementation

[0094] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0095] A specific embodiment of the present invention discloses a buffer plate protection assessment method based on the velocity and mass distribution of projectile fragment clouds, the flowchart of which is shown below. Figure 1 As shown, the method includes:

[0096] S1. Based on the collision velocity of the projectile's high-speed impact with the buffer plate, the projectile's radius, and the material's initial sound velocity, the initial shock wave velocity of the shock wave formed at any point of impact on the projectile is obtained; specifically, both the projectile and the buffer plate are made of aluminum alloy.

[0097] S2. Based on the initial shock wave velocity, projectile diameter, buffer plate thickness, and initial sound velocity of the material, the shock wave Mach number and shock wave velocity at the time of shock wave attenuation are obtained, and then the material dispersion velocity at the edge of the projectile is obtained.

[0098] S3. Calculate the velocity of the fragment cloud shedding zone formed by the projectile based on the dispersion velocity of the material at the edge of the projectile; calculate the mass distribution of the projectile undergoing delamination based on the thickness of the buffer plate, the radius of the projectile, the initial sound velocity of the material, and the collision velocity.

[0099] S4. Evaluate the protective effect of the buffer plate based on the velocity of the debris cloud shedding zone and the mass distribution of the delamination.

[0100] The velocity and mass distribution of the projectile fragment cloud after impact are explained in detail below, taking into account the process of the projectile's hypersonic direct impact with the buffer plate:

[0101] Phase 1: The projectile's high-speed direct impact with the buffer plate generates a shock wave.

[0102] In this stage, the calculation of step S1 above is performed to obtain the initial shock wave velocity of the shock wave formed at any collision contact point on the projectile.

[0103] A spherical projectile impacting a buffer plate at high speed will generate a two-dimensional bending shock wave that propagates in both the projectile and the buffer plate medium. The motion and intensity of the two-dimensional shock wave exhibit a non-uniform spatial distribution, altering its motion state and deviating from uniform steady motion. In this embodiment, the shock wave refers to a two-dimensional shock wave considering its spatial distribution. A schematic diagram of the shock wave formation stages is shown below. Figure 2 As shown, the shock wave front in the projectile and the buffer plate is the envelope of a family of circular wavelets generated at the point of impact, as shown by S in the figure. P and S T As shown, the specific construction process is as follows:

[0104] Using the initial collision point on the projectile as the origin, the direction pointing from the initial collision point to the center of the projectile as the z-axis, and the direction perpendicular to the z-axis as the r-axis, a coordinate system is established that translates with the projectile. At time t, the wavelet family consists of the planar curve family S. wl express:

[0105]

[0106] Among them, (z e r e ) represents the coordinates of the point of contact during the collision; l wl (τ,t) represents the wavelet trajectory, which is the trajectory from the initial collision point to the collision contact point at time t. e r e (a function of the time interval τ)

[0107] Collision contact point (z) e r e The coordinate expression for ) is as follows:

[0108]

[0109] In the formula, V0 is the collision velocity of the projectile's hypersonic impact with the buffer plate, and R is the radius of the projectile.

[0110] From the collision contact point (z) e r e The expression for the shock wave velocity s1(τ,t) is as follows:

[0111]

[0112] In the formula, s0(τ) represents the point of impact (z) in the projectile. e r e The initial shock wave velocity of the shock wave is c0, where c0 is the initial sound velocity of the material; k is the initial shock wave velocity of the shock wave. a This represents the linear attenuation coefficient of the shock wave in the material; specifically, k a The variation law of shock wave velocity can be obtained through simulation software AUTODYN. In this embodiment, aluminum alloy material is used, k a Take 0.344.

[0113] The wavelet trajectory is the integral of the corresponding shock wave velocity, obtained according to the following formula:

[0114]

[0115] Specifically, the collision contact point (z) in the projectile is determined through the following steps. e r e The initial shock wave velocity s0(τ) of the shock wave formation is:

[0116] Based on the conservation relations and the material state equations on the shock wave front, the relationship between the rotation angle of the micro-particles of material after the shock wave and the velocity increment U(τ) after the wave is obtained in the projectile and the buffer plate. U(τ) is then obtained through the following set of equations:

[0117]

[0118] In the formula, α is the angle between the tangent of the projectile at the point of impact and the interface of the buffer plate; θ P and θ T λ represents the rotation angle of the material particles after the shock wave from the projectile and the buffer plate, respectively; λ is the linear relationship coefficient between the shock wave velocity and the velocity of the material particles. Specifically, in this embodiment, the material is aluminum alloy, and λ is taken as 1.33.

[0119] When the two solutions of the above equation set (4) are equal, one solution is taken as the wave back velocity increment U(τ). At the same time, the generation of the shock wave ends, and the time interval τ is taken as the end time t1. That is, the time interval τ from the initial collision contact point to the current collision contact point is taken as the end time t1 of the first stage. The value range of τ is 0≤τ≤t1.

[0120] When the two solutions of the above equation set (4) are not equal, the solution with the smaller value is taken as the wave back velocity increment U(τ).

[0121] It should be noted that the system of equations (4) is solved for any given value of τ. Each time the solution is solved, it is necessary to compare and select the solution with the smaller value, and then find the numerical solution according to the specific problem.

[0122] Based on the equality of velocities at the collision interface and the velocity increment U(τ) after the wave, the following formula is used to calculate the velocity increment U(τ) at any collision contact point (z) in the projectile. e r e The initial shock wave velocity s0(τ) is:

[0123] s0(τ)=c0+λU(τ) (5)

[0124] Thus, we obtain the wavelet family formed by different collision positions corresponding to different time intervals τ, and the envelope of the wavelet family is the shock wave front.

[0125] The expression for the shock wave front in a projectile is as follows:

[0126]

[0127] In the formula,

[0128] The expression for the shock wave front in the buffer plate is as follows:

[0129]

[0130] Thus, the shock wave waveform formed by the projectile's hypersonic impact on the buffer plate is obtained, wherein different time intervals τ correspond one-to-one with the positions (z, r) on the shock wave front at time t.

[0131] The shock wave velocity s1(τ,t) at any point (z, r) on the shock wave front is obtained from formula (2), and thus the shock wave pressure at that location, i.e., the shock wave intensity, is obtained:

[0132]

[0133] In the formula, γ represents the state parameter, and its expression is as follows:

[0134]

[0135] Phase Two: Attenuation of Shock Wave Intensity within the Projectile

[0136] In this second stage, step S2 is performed to obtain the shock wave Mach number and shock wave velocity during shock wave attenuation.

[0137] During the propagation of the shock wave within the projectile, one scenario is that the cross-sectional area of ​​the projectile increases, causing the shock wave front to expand and thus attenuating the shock wave intensity. Another scenario is that the rarefaction wave reflected by the buffer plate chases and unloads the shock wave from the projectile, resulting in attenuation of the shock wave intensity. Based on the attenuation mechanism of the shock wave under different conditions, the Mach number and wave velocity of the shock wave at the time of attenuation are obtained, as detailed below:

[0138] The critical ratio is calculated based on the initial shock wave velocity and the initial sound velocity of the material at the initial collision point.

[0139] When the ratio of the thickness of the buffer plate to the diameter of the projectile is greater than or equal to the critical ratio, the shock wave front moves in an expanding motion due to the increase in the cross-sectional area of ​​the projectile, and the shock wave intensity decreases. At this time, the shock wave Mach number at the time of shock wave attenuation is obtained based on the shock wave Mach number and position on the shock wave at the end of the shock wave generation, and then the shock wave velocity at the time of shock wave attenuation is obtained.

[0140] When the ratio of the thickness of the buffer plate to the diameter of the projectile is less than the critical ratio, the rarefaction wave reflected by the buffer plate catches up with the shock wave in the unloaded projectile, causing the shock wave intensity to decrease. At this time, the shock wave velocity at the time of shock wave attenuation is obtained according to the time when the shock wave propagates to the back surface of the buffer plate and the position and time when the rarefaction wave front catches up with the shock wave, and then the shock wave Mach number at the time of shock wave attenuation is obtained; wherein, the rarefaction wave is obtained by the buffer plate reflecting the shock wave.

[0141] Specifically, assuming that the shock wave moves at a uniform speed s0(0) during the collision of the projectile with the buffer plate, and the rarefied wave front chases it at the speed of sound c behind the shock wave, the minimum ratio at which the rarefied wave cannot catch up with the shock wave is taken as the critical ratio ξ. c The expression is as follows:

[0142]

[0143] In the formula, c represents the sound velocity behind the shock wave, and the expression is as follows:

[0144]

[0145] In the formula, s0(0) represents the initial shock wave velocity of the shock wave formed at the initial collision point.

[0146] Specifically, when the ratio of the buffer plate thickness h to the projectile diameter D is greater than or equal to the critical ratio ξ... c At that time, according to existing shock wave dynamics, a point (z, r) on the shock wave front moves along the shock wave ray, and the shock wave ray is the integral curve of the shock wave velocity, as shown in the figure. Figure 3 As shown in the figure, directed line segments P1A, P1B, and P1C represent the shock wave rays in the projectile. Setting the curvature of the shock wave rays to 0, based on the shock wave dynamics equations, we obtain the relationship between the shock wave Mach number M and the curves. s The equation is as follows:

[0147]

[0148] From formula (12), the shock wave Mach number M at any point (z, r) on the shock wave front surface during shock wave attenuation can be obtained. s The expression is as follows:

[0149]

[0150] In the formula, Let r1(τ,t1) represent the shock wave Mach number at the corresponding point on the shock wave front at time t1, r1(τ,t1) represent the r-axis coordinate of the corresponding point on the shock wave front at time t1, l represent the distance between the corresponding point (z1, r1) on the shock wave front at time t1 and the current point (z, r), A1 represent the shock wave area at time t1, and K represent the correlation coefficient. It should be noted that the corresponding point on the shock wave front refers to the point on the shock wave front at time t1 corresponding to any point (z, r) during shock wave attenuation.

[0151] Based on formula (13), the shock wave velocity at any point (z, r) on the shock wave front surface during shock wave attenuation is expressed as:

[0152] s = c0M s (14)

[0153] More specifically, the expression for K is as follows:

[0154]

[0155] More specifically, based on formula (2), the shock wave velocity s1(τ,t1) at the corresponding point on the shock wave front at time t1 is obtained, and the expression is as follows:

[0156]

[0157] Furthermore, the shock wave Mach number at the corresponding point on the shock wave front at time t1 is obtained. The expression is as follows:

[0158]

[0159] More specifically, based on formula (3), the corresponding point wave trajectory l on the shock wave front at time t1 is obtained. wl (τ,t1), the expression is as follows:

[0160]

[0161] Then, based on formula (6), the coordinates of the corresponding point (z1, r1) on the shock wave front at time t1 are obtained, and the expression is as follows:

[0162]

[0163] Furthermore, according to formula (19), the distance l between the corresponding point (z1, r1) on the shock wave front at time t1 and the current point (z, r) is obtained, and the expression is as follows:

[0164]

[0165] More specifically, based on formula (19), the shock wave area A1 at time t1 is obtained by surface integral of rotation, and the expression is as follows:

[0166]

[0167] Specifically, when the ratio of the buffer plate thickness h to the projectile diameter D is less than the critical ratio ξ... c At times, such as Figure 4 As shown, the time t when the shock wave propagates to the back surface of the buffer plate h for:

[0168]

[0169] The rarefaction wavefront catches up with the z-axis position of the shock wave. r and time t r for:

[0170]

[0171] Based on (22) and (23), the shock wave velocity at any point (z, r) on the shock wave front surface during the shock wave attenuation is expressed as follows:

[0172]

[0173] Based on formula (24), the shock wave Mach number M at any point (z, r) on the shock wave front surface during the shock wave attenuation is obtained. s Represented as:

[0174]

[0175] Phase 3: Projectile edge material scattering

[0176] During this stage, step S2 is performed to obtain the velocity of material dispersion at the edge of the projectile.

[0177] When a point on the shock wave front moves to the edge of the projectile, such as Figure 3 Points A, B, and C in the diagram represent locations where the shock wave interacts with the free surface, resulting in reflection and the formation of rarefaction waves. The material at the projectile's edge is first compressed by the shock wave, gaining a certain velocity. Then, the reflected rarefaction waves cause the material particles to disperse. The dispersion velocity of the material at the projectile's edge is calculated as follows:

[0178] A wave-following coordinate system is established with the point P(z,r) on the edge of the projectile as the origin. The x-axis is tangent to the projectile and points in the direction of the shock wave, and the y-axis points towards the center of the projectile. (See diagram below.) Figure 5 As shown, the velocity of material scattering at the edge of the projectile. Represented as:

[0179]

[0180] in, Let P(z,r) be the translational velocity vector of the wave-following coordinate system containing the edge point P(z,r) of the projectile. Let be the velocity vector of the material scattering at point P(z,r) on the edge of the projectile.

[0181] Specifically, the translational velocity vector of the coordinate system containing the projectile edge point P(z,r) The following is an expression:

[0182]

[0183] Where q0 represents the translational velocity of the wave-following coordinate system at the edge point P(z,r) of the projectile; β represents the acute angle between the direction of the translational velocity of the wave-following coordinate system at the edge point P(z,r) of the projectile and the r-axis.

[0184] Based on formula (14) or (24), the shock wave velocity s when the shock wave reaches the edge position P(z,r) of the projectile is obtained, and then the velocity of the back-wave material micro-particle and the back-wave material rotation angle q and θ in the wave-following coordinate system when the shock wave reaches the edge point P(z,r) of the projectile are obtained. The expressions are as follows:

[0185]

[0186] Based on formula (13) or (25), the shock wave Mach number M when the shock wave moves to the edge position P(z,r) of the projectile is obtained. s Thus, the back pressure p and back density ρ are obtained, with the following expressions:

[0187]

[0188] Furthermore, the sound velocity c of the scattered material is obtained. f The expression is as follows:

[0189]

[0190] The mass dispersion velocity q at the edge point P(z,r) of the projectile in the wave-following coordinate system is obtained using the Bernoulli equation. f The expression is as follows:

[0191]

[0192] Based on formulas (27) and (28), the acute angle ω between the direction of the material dispersion velocity at the edge point P(z,r) of the projectile and the z-axis is obtained, and the expression is as follows:

[0193]

[0194] Phase 4: Projectile formation and fragmentation cloud delamination zone

[0195] In this stage, step S3 above is performed to calculate the mass distribution of the projectile undergoing delamination and the velocity of the fragment cloud shedding zone formed by the projectile.

[0196] Material dispersion at the projectile's edge leads to multiple delaminations in the projectile material, forming a fragment cloud-like spalling zone. In this embodiment, the delamination region in the projectile is simplified to a quarter-circle, with a thickness equal to the delamination depth d. p The diagram is as follows Figure 6 As shown.

[0197] The ratio d of the fracture depth to the projectile diameter p The ratio of the collision velocity to the initial sound velocity of the material, V0 / c0, and the ratio of the buffer plate diameter to the projectile diameter, h / D, exhibit a power function relationship:

[0198]

[0199] Where a, b, and d represent the first, second, and third parameters of the material, respectively. Specifically, in this embodiment, the material is aluminum alloy, with a = 0.504, b = 0.477, and d = 0.290.

[0200] Based on formula (33), the mass distribution η of the projectile undergoing spalling is obtained, expressed as:

[0201]

[0202] In the formula, m s m is the mass of the material that undergoes delamination in the projectile. p For the mass of the projectile.

[0203] The fragmented projectile material will form a uniformly expanding fragment cloud sphere. Based on the dispersion velocity of the material at the projectile's edge, a nonlinear fitting algorithm is used to obtain the outer contour of the fragment cloud in the fragment cloud peeling area formed by the projectile, which has a translational velocity u. c and expansion velocity u e The circle, i.e., the velocity of the outer contour of the debris cloud, includes the translational velocity u. c and expansion velocity u e It can be expressed by the following formula:

[0204]

[0205] In the formula, u fz and u fr These are the z-axis and r-axis components of the projectile edge material dispersion velocity, respectively. It can be understood that at this point, the outer contour velocity of the debris cloud, including translational velocity and expansion velocity, is determined using all the projectile edge material dispersion velocities in the third stage.

[0206] The dispersion velocity of matter within the fragment cloud outline of the fragment cloud formed by the projectile exhibits a linear distribution, with the center point of the outer outline of the fragment cloud as the pole. c The direction is the polar axis, u e Establish a polar coordinate system with radius t and counterclockwise as the positive direction, where u c The direction is the same as the z-axis direction, as shown in the diagram. Figure 7 As shown, any point (r) within the contour is obtained. f The velocity u of ζ) = (u z ,u r ), represented as:

[0207]

[0208] Among them, u z and u r These are the z-axis and r-axis components of the velocity at any point within the contour, respectively. f Let ζ and ζ be the polar radius and polar angle of any point within the profile, respectively, and t represent the time elapsed after the projectile collides with the buffer plate. It can be understood that this time t represents the time after the first, second, and third stages have occurred, i.e., the time after the projectile begins to delaminate.

[0209] During implementation, the protective effect of the buffer plate is evaluated based on the velocity of the debris cloud detachment zone and the mass distribution of the resulting delamination. It is understandable that the motion pattern of the debris cloud formed by the projectile after impact with the buffer plate can reflect the protective effect of the buffer plate.

[0210] Specifically, the velocity distribution of the fragment cloud shedding area formed by the projectile includes the outer contour velocity and the velocity within the contour of the fragment cloud. The higher the values ​​of the outer contour velocity and the velocity within the contour of the fragment cloud shedding area, the more fully the projectile and the buffer plate material are broken, and the better the protective effect of the buffer plate. More specifically, a first velocity threshold and a second velocity threshold are set. When the value of the outer contour velocity exceeds the first velocity threshold, that is, the translational velocity or expansion velocity exceeds the first velocity threshold, and the value of the velocity within the contour exceeds the second velocity threshold, it indicates that the projectile and the buffer plate material are broken sufficiently, and the protective effect of the buffer plate reaches a good level, meeting the protection requirements. The first velocity threshold and the second velocity threshold are set according to the protection requirements of the buffer plate in actual applications.

[0211] Preferably, the first velocity threshold can be set to include a translational velocity threshold and an expansion velocity threshold. When the translational velocity is greater than the translational velocity threshold or the expansion velocity is greater than the expansion velocity threshold, the projectile and the buffer plate material are sufficiently broken, and the protective effect of the buffer plate meets the protection requirements. The translational velocity threshold and the expansion velocity threshold are set according to the actual protection requirements of the buffer plate in the application.

[0212] Specifically, the larger the mass distribution of the projectile undergoing spalling, the smaller the proportion of the mass-dense portion in the debris cloud, the weaker the destructive effect on the bulkhead (rear plate), and the better the buffer plate's protective effect. More specifically, a spalling mass threshold is set. When the mass distribution of the projectile undergoing spalling exceeds the spalling mass threshold, it indicates that the projectile has sufficiently spalled, the buffer plate's protective effect is good, and the protection requirements are met. The spalling mass threshold is set according to the buffer plate's protection requirements in actual applications.

[0213] Compared with existing technologies, this invention provides a buffer plate protection assessment method based on the velocity and mass distribution of projectile fragment clouds. Based on the initial shock wave velocity generated at any point of impact on the projectile, and considering two shock wave attenuation scenarios, the method calculates the shock wave Mach number and velocity during attenuation, thereby obtaining the projectile edge material dispersion velocity. This fully considers the influence of the shock wave's temporal variation and spatial distribution, more accurately describing the complete propagation process of the shock wave and the motion law of the projectile edge material. Simultaneously, this invention obtains the velocity of the projectile fragment cloud spalling zone and the mass distribution of projectile delamination based on the obtained projectile edge dispersion velocity. The protective effect of the buffer plate is then evaluated based on the fragment cloud's motion law and the projectile delamination situation, improving the accuracy of the assessment and providing a reference for engineering design, thus possessing significant practical value.

[0214] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0215] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for assessing the protection of a buffer plate based on the velocity and mass distribution of a projectile fragment cloud, characterized in that, The method includes: Based on the collision velocity of the projectile's hypersonic impact with the buffer plate, the projectile's radius, and the material's initial sound velocity, the initial shock wave velocity of the shock wave formed at any point of impact on the projectile is obtained. Based on the initial shock wave velocity, projectile diameter, buffer plate thickness, and initial sound velocity of the material, the shock wave Mach number and shock wave velocity at the time of shock wave attenuation are obtained, and then the material dispersion velocity at the edge of the projectile is obtained. Based on the material dispersion velocity at the edge of the projectile, the velocity distribution of the fragment cloud shedding zone formed by the projectile is calculated; based on the buffer plate thickness, projectile radius, initial sound velocity of the material, and collision velocity, the mass distribution of the projectile undergoing delamination is calculated. The protective effect of the buffer plate is evaluated based on the velocity distribution and mass distribution of the delamination zone in the debris cloud. The velocity distribution of the debris cloud shedding zone formed by the projectile includes the velocity along the outer contour of the debris cloud and the velocity within the contour; the initial impact point on the projectile is taken as the origin, and the direction from the initial impact point to the center of the projectile is taken as... The direction of the axis, and The direction perpendicular to the axis is used as In the axial direction, establish a coordinate system that translates with the projectile; the velocity of the outer contour of the debris cloud includes the translational velocity. and expansion rate It can be expressed by the following formula: ， In the formula, and These are the particle dispersion velocities at the edge of the projectile. of Axial components and Axial components; Taking the center point of the outer contour of the fragment cloud as the pole, The direction is the polar axis direction. Establish a polar coordinate system with radius as the radius and counterclockwise as the positive direction to obtain any point within the contour. speed , is represented as: ， In the formula, and The velocity of any point within the contour is respectively Axial components and Axial components, and Let be the polar radius and polar angle of any point within the contour, respectively. This indicates the time elapsed after the projectile collides with the buffer plate. The mass distribution of the projectile undergoing delamination Represented as: ， In the formula, ， in, The depth at which the projectile undergoes delamination. The impact velocity of the projectile's hypersonic direct impact with the buffer plate. The diameter of the projectile. The initial sound velocity of the material. , and These represent the first, second, and third parameters of the material, respectively. The following steps are used to obtain any collision contact point in the projectile. Initial shock wave velocity that forms the shock wave : The velocity increment behind the shock wave at any point of impact can be obtained using the following system of equations. : ， In the formula, ， in, Let the radius be the projectile radius. The angle between the tangent of the projectile and the interface of the buffer plate at the point of impact is given. The time interval between the initial collision point and the point of contact during the collision; and These are the rotation angles of the material micro-particles after the shock waves from the projectile and the buffer plate, respectively. This is the coefficient representing the linear relationship between the shock wave velocity and the velocity of the material particle; When the two solutions to the above system of equations are not equal, the solution with the smaller value is taken as the waveback velocity increment. ; When the two solutions to the above system of equations are equal, one solution is taken as the waveback velocity increment. At the same time, the generation of the shock wave ends, and this time interval is recorded. As the end ; Based on waveback velocity increment The initial shock wave velocity of the shock wave generated at any point of impact in the projectile is calculated using the following formula. : 。 2. The buffer plate protection assessment method based on the velocity and mass distribution of projectile fragment clouds according to claim 1, characterized in that, The protective effect of the buffer plate is evaluated based on the velocity of the debris cloud shedding zone and the mass distribution of the delamination, specifically: The higher the values ​​of the outer contour velocity and the inner contour velocity of the debris cloud peeling area, the more fully the projectile and buffer plate material are broken, and the better the buffer plate protection effect. The greater the mass distribution of the projectile that causes delamination, the smaller the proportion of the mass-dense part in the debris cloud, and the better the protection effect of the buffer plate.

3. The buffer plate protection assessment method based on the velocity and mass distribution of projectile fragment clouds according to claim 1, characterized in that, Based on the initial shock wave velocity, projectile diameter, buffer plate thickness, and initial sound velocity of the material, the shock wave Mach number and shock wave velocity during shock wave attenuation are obtained, specifically including: The critical ratio is calculated based on the initial shock wave velocity and the initial sound velocity of the material at the initial collision point. When the ratio of the thickness of the buffer plate to the diameter of the projectile is greater than or equal to the critical ratio, the shock wave Mach number at the time of shock wave attenuation is obtained based on the shock wave Mach number and position on the shock wave at the end of the shock wave generation, and then the shock wave velocity at the time of shock wave attenuation is obtained. When the ratio of the thickness of the buffer plate to the diameter of the projectile is less than the critical ratio, the shock wave velocity at the time of shock wave attenuation is obtained based on the time when the shock wave propagates to the back surface of the buffer plate and the position and time when the rarefaction wave front catches up with the shock wave, and then the shock wave Mach number at the time of shock wave attenuation is obtained; wherein, the rarefaction wave is obtained by the buffer plate reflecting the shock wave.

4. The buffer plate protection assessment method based on the velocity and mass distribution of projectile fragment clouds according to claim 3, characterized in that, The critical ratio Represented as: ， In the formula, ， ， in, This represents the speed of sound behind the shock wave. Represents the state parameter.

5. The buffer plate protection assessment method based on the velocity and mass distribution of projectile fragment clouds according to claim 3, characterized in that, When the thickness of the buffer plate With the diameter of the bullet The ratio is greater than or equal to the critical ratio. At that time, the shock wave attenuates at any point on the shock wave front. shock wave Mach number Represented as: ， In the formula, Indicates in The shock wave Mach number at the corresponding point on the shock wave front at any given time. Indicates in The corresponding point on the shock wave at any moment Axis coordinates; express The corresponding point on the shock wave front at time _____ With the current point The distance; express Shock wave area at time; Represents the correlation coefficient; Determined according to the following formula , 、 and : ， ， ， ， In the formula, ， ， ， in, Indicates in Shock wave velocity at a corresponding point on the shock wave front at any given time. Indicates in The wavelet trajectory of the corresponding point on the shock wave front at any given moment; This represents the linear attenuation coefficient of the shock wave in the material; The shock wave velocity during shock wave attenuation is expressed as follows: 。 6. The buffer plate protection assessment method based on the velocity and mass distribution of projectile fragment clouds according to claim 3, characterized in that, When the thickness of the buffer plate With the diameter of the bullet The ratio is less than the critical ratio. At that time, the shock wave attenuates at any point on the shock wave front. The shock wave velocity is expressed as: ， In the formula, ， ， in, This is the moment when the shock wave reaches the back surface of the buffer plate; and These represent the rarefaction wavefront catching up with the shock wave. Axis position and time; The shock wave Mach number during attenuation is expressed as: 。 7. The buffer plate protection assessment method based on the velocity and mass distribution of projectile fragment clouds according to claim 5 or 6, characterized in that, The shockwave travels to the edge of the projectile. Establish a wave-following coordinate system with the origin. The axis is tangent to the projectile and points in the direction of the shock wave. The axis points towards the center of the sphere. The velocity of material scattering at the edge of the projectile is obtained according to the following steps. : The following formula represents the edge point of the projectile. Translational velocity vector of the coordinate system : ， in, Indicates the edge point of the projectile The translational velocity value of the coordinate system in which it is located; Indicates the edge point of the projectile The direction of the translational velocity in the coordinate system is... The acute angle between the axes; The bullet edge point is determined using the following formula. The velocity vector of the material dispersion : ， ， In the formula, ， ， ， in, Indicates the sound velocity of the scattered material. Indicates the edge point of the projectile The velocity of matter dispersion, Indicates the edge point of the projectile The direction of the velocity of the scattered matter is... The acute angle between the axes, and This indicates that the shock wave has reached the edge of the projectile. The velocity and rotation angle of the back-wave material particles in the wave-following coordinate system at that time; Indicates the pressure behind the wave. Indicates the waveback density; according to and The dispersion velocity of the material at the edge of the projectile was obtained. , is represented as: 。

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