An experimental method for obtaining the relationship between the projectile velocity and penetration depth of a rigid projectile

Abstract

The present invention belongs to the technical field of terminal ballistic efficiency tests, and particularly relates to a test method for obtaining the relationship between the projectile velocity and penetration depth of a rigid projectile. This method belongs to a prediction method combining theory and experiment. Based on the dynamic cavity expansion theory and combined with Newton's second law, a relational expression between the penetration depth and the projectile velocity is obtained. By integrating the parameters and unknown constants that are difficult to directly obtain, a new relational expression between the penetration depth and velocity of the projectile is obtained. A system of simultaneous equations is established and solved through the test data of the penetration depth and projectile velocity of two projectiles, and finally the definite relationship between the projectile velocity and penetration depth is given. On the premise of only knowing three easily measurable projectile-target parameters and conducting a small number (not less than two) of projectile-target tests, this method can obtain the relationship between the predicted penetration depth and projectile velocity of a rigid projectile, greatly reducing the test volume and test cost, and this method has universal applicability to different materials such as metals, concretes, and polymers.

Description

Technical Field

[0001] The present invention belongs to the technical field of terminal ballistic performance tests, and particularly relates to a test method for obtaining the relationship between the projectile velocity and penetration depth of a rigid projectile body. Background Art

[0002] The penetration and damage of a projectile body to media such as metal, concrete, and rock are important research contents in the fields of weaponry, engineering, and armor protection, and are key issues that must be solved to improve the striking ability and defense ability of weaponry. A rigid projectile refers to a projectile body that does not deform or lose mass or has very little deformation and mass loss during the process of penetrating a target plate. In the range of conventional projectile velocities, the penetration process of a metal projectile body with relatively high strength into low-strength metals, concrete, rock, and polymer materials can be considered as a rigid projectile penetration process.

[0003] The penetration depth of a rigid projectile into various media at different projectile velocities is an important research content in the national defense field. For the relationship between the projectile velocity and penetration depth of rigid projectile penetration, existing technologies usually adopt technical solutions such as theoretical analysis, empirical formulas, and semi-empirical formulas. The theoretical analysis method is usually relatively complex, requires a high theoretical level and mathematical calculation ability of technical personnel, is not convenient for engineering applications, and usually involves empirical parameters that need to be determined manually in the theoretical method, otherwise the accuracy is insufficient; the empirical formula method is directly constructed based on the analysis of test data and is a pure empirical formula without theoretical support. A reliable empirical formula requires not only a large amount of test data but also a small application range; the semi-empirical formula method is based on theoretical analysis, combines test data to determine the undetermined coefficients in the formula, and then can give a semi-empirical formula for the penetration depth and projectile velocity.

[0004] The semi-empirical formula method is a commonly used method in current engineering applications, but the following problems are found in actual applications: First, for different metal target plates and concrete target plates, the forms of the semi-empirical formulas are different and do not have universality; second, the semi-empirical formula involves many projectile-target parameters and empirical coefficients. The projectile-target parameters include the projectile body diameter and mass, target plate density, and dynamic compressive strength, and the empirical coefficients include fitting parameters (not less than 3), warhead shape coefficients, projectile-target dynamic friction coefficients, etc. Among them, except for the projectile body diameter, projectile body mass, and target plate density that can be simply measured, other parameters and coefficients need to be obtained through experimental research analysis or fitting.

[0005] Therefore, from the perspective of existing technologies, if a good mapping relationship between the projectile velocity and penetration depth of a rigid projectile body is to be obtained, a large amount of test data is required as a prerequisite for obtaining empirical constants or undetermined coefficients, and a large amount of time, manpower, and material resources need to be consumed. Summary of the Invention

[0006] Aiming at the deficiencies of the existing technology, the present invention provides a test method for obtaining the relationship between the projectile velocity and penetration depth of a rigid projectile. By using this method, based on a small number of projectile-target penetration tests, the curve relationship between penetration depth and projectile velocity can be obtained, and it has universal applicability to different types of materials such as metals, concretes, and polymers.

[0007] The object of the present invention is achieved as follows: Based on the dynamic cavity expansion theory, the penetration resistance formula of the warhead by the target plate in the penetration direction is obtained: Combined with Newton's second law, the relationship between penetration depth and projectile velocity is obtained: In this formula, the parameters mp (projectile mass), d p (projectile diameter), ρ t (target plate density) are easily measured. The parameters Y t (dynamic compressive strength of the target plate) and the unknown constants A, B, N1, and N2, which are difficult to directly obtain, are integrated. Let k1 = AY t N1, k2 = BN2, and then a new relationship (1) between the penetration depth and velocity of the projectile is obtained: There are only two unknown parameters k1 and k2 in this formula. Therefore, the values of k1 and k2 can be obtained by establishing a system of simultaneous equations from the test data of the penetration depth and projectile velocity of two projectiles, and finally the definite relationship between projectile velocity and penetration depth is given.

[0008] The specific technical solution adopted by the present invention is as follows:

[0009] A test method for obtaining the relationship between the projectile velocity and penetration depth of a rigid projectile, comprising the following steps:

[0010] Step S1: Collect relevant data of the projectile and the target plate, including: projectile mass m p , projectile diameter d p , target plate density ρ t ;

[0011] Step S2: Complete projectile-target penetration tests at two different projectile velocities, and measure the projectile velocities v1, v2 and the corresponding penetration depths p1, p2;

[0012] Step S3: Substitute the test data obtained in Step S1 and Step S2 into the new relationship (1) between the penetration depth and velocity of the projectile to establish a system of simultaneous equations (2):

[0013]

[0014]

[0015] Step S4: Solve the system of simultaneous equations (2) to obtain the values of the unknown parameters k1 and k2;

[0016] Step S5: Substitute the parameters of Steps S1 and S2, and the values of k1 and k2 into the new relational expression (1) to obtain the definite functional relational expression between the penetration depth of the projectile and the velocity:

[0017]

[0018] In the formula:

[0019] v i — Projectile velocity, m / s;

[0020] p i — Penetration depth of the projectile into the target plate when the projectile velocity is v, m; i

[0021] m p — Projectile mass, kg;

[0022] d p — Projectile diameter, m;

[0023] ρ t — Target plate density, kg / m 3 ;

[0024] k1 — Unknown parameter related to the warhead shape, projectile-target friction and target plate strength, Pa;

[0025] k2 — Parameter related to the warhead shape and target plate, dimensionless.

[0026] The test method for obtaining the relationship between the velocity of a rigid projectile and its penetration depth provided by the present invention belongs to a prediction method combining theory and experiment. On the premise of only knowing 3 easily measurable projectile-target parameters and conducting a small number (not less than 2) of projectile-target tests, the relationship between the predicted penetration depth of a rigid projectile and its velocity can be obtained, thus greatly reducing the test volume and test cost. Moreover, this method has universal applicability to different materials such as metals, concrete, and polymers. The present invention provides a fast and effective technical solution for weapon equipment, engineering, and armor protection design. Description of the Drawings

[0027] Figure 1 It is the relationship diagram between the penetration depth of a rigid projectile and its velocity in Embodiment 1

[0028] Figure 2 It is the relationship diagram between the penetration depth of a rigid projectile and its velocity in Embodiment 2

[0029] Figure 3 It is the relationship diagram between the penetration depth of a rigid projectile and its velocity in Embodiment 3 Detailed Embodiments

[0030] The present invention will be further described in detail below with reference to specific embodiments. ​

[0031] The test data of the embodiments are used as samples from the published literature to verify the implementation effect of the present invention, where:

[0032] The test data of Example 1 are from the literature [FORRESTAL M J, BRARN S, LUKVK. Penetration of Strain-Hardening Targets With Rigid Spherical-Nose Rods[J]. Journal of Applied Mechanics, 1991, 58(1): 7-10.];

[0033] The test data of Example 2 are from the literature [FORRESTAL M J, FREW D J, HANCHAK S J, et al. Penetration of grout and concrete targets with ogive-nose steel projectiles[J]. International Journal of Impact Engineering, 1996, 18(5): 465-76.];

[0034] The test data of Example 3 are from the literature [WEISS A, VIZEL A, DURBAN D. An experimental investigation of deep penetration into polycarbonate targets[J]. Proceedings - 27th International Symposium on Ballistics, BALLISTICS 2013, 2013, 2: 1241-51.].

[0035] Examples 1, 2, and 3 respectively select the test data of rigid projectiles against aluminum alloy, concrete, and polycarbonate target plates, as shown in Table 1. The test data marked with * in Table 1 are the input data used in the calculation of the present invention, and the test data without * are the verification data of the implementation effect of the present invention.

[0036] Table 1 Test data samples of the embodiments (from published literature)

[0037]

[0038]

[0039] Example 1

[0040] Taking the penetration of a rigid projectile into an aluminum alloy target plate as an example, a test method for obtaining the relationship between the velocity and penetration depth of a rigid projectile includes the following steps:

[0041] Step S1: Collect relevant data of the projectile and the target plate, including: the mass m of the projectile p , the diameter d of the projectile p , and the density ρ of the target plate t ;

[0042] Step S2: Conduct two projectile-target penetration tests at different velocities, and measure the velocities v1, v2 and the corresponding penetration depths p1, p2;

[0043] Step S3: Substitute the test data obtained in Step S1 and Step S2 into the new relationship formula (1) between the penetration depth and velocity of the projectile to establish a system of simultaneous equations (2):

[0044]

[0045] Step S4: Solve the system of simultaneous equations (2) to obtain the numerical values of the unknown parameters k1 and k2;

[0046] Step S5: Substitute the parameters in Step S1, S2 and S4 into the new relationship formula (1) between the penetration depth and velocity of the projectile to obtain the definite functional relationship between the two.

[0047] For the 1# and 2# projectile-target combinations in Example 1, use the two sets of test data marked with * in Table 1 as the input data for the calculation of this method, and substitute them into the system of simultaneous equations (2). After calculation, the functional relationships between the penetration depth and the projectile velocity of the 1# and 2# projectile-target combinations are respectively:

[0048] p i1 = 0.226532ln(1 + 7.53681E-07v i 2 ) (4)

[0049] p i2 = 0.069146ln(1 + 1.8741E-06v i 2 ) (5)

[0050] Figure 1 The functional curves of the penetration depth and the projectile velocity for the projectile-target combination in Example 1 and the verification data are given.

[0051] Example 2

[0052] Taking the penetration of a rigid projectile into a concrete target plate as an example, a test method for obtaining the relationship between the velocity and penetration depth of a rigid projectile includes the following steps:

[0053] Step S1: Collect relevant data of the projectile and the target plate, including: the mass m of the projectilep 、Projectile diameter d p 、Target plate density ρ t ;

[0054] Step S2: Conduct projectile - target penetration tests at two different projectile velocities, and measure the projectile velocities v1, v2 and the corresponding penetration depths p1, p2;

[0055] Step S3: Substitute the test data obtained in Step S1 and Step S2 into the new relationship formula (1) between the projectile penetration depth and velocity to establish a system of simultaneous equations (2):

[0056]

[0057] Step S4: Solve the system of simultaneous equations (2) to obtain the values of the unknown parameters k1 and k2;

[0058] Step S5: Substitute the parameters in Step S1, S2 and S4 into the new relationship formula (1) between the projectile penetration depth and velocity to obtain the definite functional relationship between the two.

[0059] For the 3# and 4# projectile - target combinations in Example 2, use the two groups of test data marked with * in Table 1 as the input data for the calculation of this method, substitute them into the system of simultaneous equations (2), and after calculation, the functional relationships between the penetration depth of the projectile - target combination and the projectile velocity are respectively:

[0060] p i3 = 1.207786ln(1 + 8.05562E - 07v i 2 ) (6)

[0061] p i4 = 1.920446ln(1 + 4.99913E - 07v i 2 ) (7)

[0062] Figure 2 The function curves of the penetration depth of the projectile - target combination and the projectile velocity for Example 2 and the verification data are given.

[0063] Example 3

[0064] Taking the penetration of a rigid projectile into a polycarbonate target plate as an example, a test method for obtaining the relationship between the velocity and penetration depth of a rigid projectile includes the following steps:

[0065] Step S1: Collect relevant data of the projectile and the target plate, including: projectile mass m p 、Projectile diameter d p 、Target plate density ρ t ;

[0066] Step S2: Conduct penetration tests on the projectile and target at two different projectile velocities, and measure the projectile velocities v1, v2 and the corresponding penetration depths p1, p2;

[0067] Step S3: Substitute the test data obtained in Step S1 and Step S2 into the new relationship (1) between the penetration depth and velocity of the projectile to establish a system of simultaneous equations (2):

[0068]

[0069] Step S4: Solve the system of simultaneous equations (2) to obtain the values of the unknown parameters k1 and k2;

[0070] Step S5: Substitute the parameters in Step S1, S2 and S4 into the new relationship (1) between the penetration depth and velocity of the projectile to obtain the definite functional relationship between the two.

[0071] For the 5# and 6# projectile-target combinations in Example 3, use the two sets of test data marked with * in Table 1 as the input data for the calculation of this method, substitute them into the system of simultaneous equations (2), and after calculation, the functional relationships between the penetration depth of the projectile-target combination and the projectile velocity are respectively:

[0072] p i5 = 6.042229ln(1 + 6.25766E-08v i 2 ) (8)

[0073] p i6 = 0.262139ln(1 + 4.38743E-07v i 2 ) (9)

[0074] Figure 3 The functional curves of the penetration depth of the projectile-target combination and the projectile velocity for Example 3 and the verification data are given.

[0075] From Figure 1 , Figure 2 and Figure 3 it can be seen that according to a test method for obtaining the relationship between the projectile velocity and penetration depth of a rigid projectile proposed by the present invention, the functional relationship between the rigid projectile velocity and penetration depth can be obtained when only two projectile-target tests are carried out, and the predicted value can be in good agreement with the test value. In addition, this method is applicable to rigid projectiles penetrating different types of materials such as metals, concrete, and polymers, and has general applicability.

Claims

1. An experimental method for obtaining the relationship between the projectile velocity and penetration depth of a rigid projectile, characterized in that: including the following steps: S1: Collect relevant data of the projectile and the target plate, including: the mass m of the projectile p , the diameter d of the projectile p , the density ρ of the target plate t ; S2: Conduct penetration tests of the projectile against the target at two different projectile velocities, measure the projectile velocities v1, v2 and the corresponding penetration depths p1, p2; S3: Substitute the test data obtained in step S1 and step S2 into the new relationship (1) between the penetration depth and velocity of the projectile to establish a system of simultaneous equations (2): S4: Solve the system of simultaneous equations (2) to obtain the numerical values of the unknown parameters k1 and k2; S5: Substitute the parameters in step S1, S2, and the values of k1 and k2 into the new relationship (1) to obtain the determined functional relationship between the penetration depth and velocity of the projectile: where: v i — Projectile velocity, m / s; p i — Penetration depth of the projectile into the target plate when the projectile velocity is v, m; i ​ m p — Mass of the projectile, kg; d p — Projectile diameter, m; ρ t — Target plate density, kg / m 3 ; k1 - an unknown parameter related to the shape of the warhead, friction between the projectile and the target, and the strength of the target plate, Pa; k2 - a parameter related to the shape of the warhead and the target plate, dimensionless.

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