CN108763836B - Method for acquiring trajectory limit equation of space fragment protection structure under cylindrical projectile impact - Google Patents

Method for acquiring trajectory limit equation of space fragment protection structure under cylindrical projectile impact Download PDF

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CN108763836B
CN108763836B CN201810769770.0A CN201810769770A CN108763836B CN 108763836 B CN108763836 B CN 108763836B CN 201810769770 A CN201810769770 A CN 201810769770A CN 108763836 B CN108763836 B CN 108763836B
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武强
龚自正
张品亮
曹燕
田东波
宋光明
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Abstract

The invention discloses a method for obtaining a ballistic limit equation of a space fragment protection structure under the impact of cylindrical projectiles, which comprises the steps of equivalent principle conversion, simulation calculation, speed segmentation point determination, shape coefficient definition, shape coefficient equation fitting, cylindrical projectile ballistic limit equation obtaining and the like, wherein the ballistic limit equation capable of representing the impact effect of the cylindrical projectiles with different length-diameter ratios is obtained by respectively substituting the shape coefficient equation into the simulation calculation equation. The cylindrical projectile trajectory limit equation obtained by the method can provide reference for engineering design only by carrying out calibration and correction through a small amount of tests, and has obvious practical value.

Description

Method for acquiring trajectory limit equation of space fragment protection structure under cylindrical projectile impact
Technical Field
The invention belongs to the technical field of space fragment protection, and particularly relates to a method for acquiring a ballistic limit equation of a space fragment protection structure under the impact of cylindrical projectiles.
Background
In practical application, the space debris protective structure is firstly subjected to impact risk assessment, so that whether the protective structure meets the protection requirement is determined, safety is guaranteed, over-design is avoided, and unnecessary quality and cost of the spacecraft are increased. The ballistic limit is an important form of the existing protective structure evaluation scheme, and is used for describing a critical failure state of the protective structure under the impact of space debris, a common definition form includes the diameter and impact speed of a projectile, the thickness of a plate, the protective distance, bulkhead strength and the like, a relational expression between related parameters is a ballistic limit equation, and a curve drawn through the relational expression is a ballistic limit curve.
The most of the ballistic limit characteristics corresponding to the current space debris protection structure are obtained through a spherical projectile impact test. The shapes of the real space fragments can be arbitrary, and the number of the spherical fragments is extremely small, so that the fragments are not representative per se. A large number of researches show that the non-spherical projectile has stronger damage capability than a spherical projectile with the same mass under the same impact condition, so that the impact of the projectile shape effect is not considered in a ballistic limit equation applied in the current space debris risk assessment, the ultrahigh-speed impact damage characteristic of the protective structure cannot be accurately predicted and assessed, and the design of the protective structure of the spacecraft has unknown risk. Meanwhile, the launching speed of the spherical projectile is difficult to reach more than 8km/s due to the limitation of the launching capacity of the traditional light gas gun system. In order to obtain ballistic limit data of the space debris protection structure at a speed of over 8km/s through experiments, other novel ultra-high-speed launching technologies can be only utilized, and the corresponding projectile is in a non-spherical shape such as a flyer and a cylinder. Therefore, by means of shape effect analysis, ballistic extreme limits corresponding to columnar projectiles with different length-diameter ratios are equivalent to ballistic extreme limits corresponding to spheres, evaluation on the protective performance of the protective structure is achieved, and therefore a more accurate ballistic extreme equation is obtained in a speed range of more than 8 km/s.
Disclosure of Invention
In view of the existing problems, the invention aims to provide an impact limit equation capable of describing impact damage characteristics of cylindrical shots with different length-diameter ratios and an acquisition method thereof.
The invention adopts the following technical scheme:
the method for acquiring the ballistic limit equation of the space fragment protection structure under the impact of the cylindrical projectile comprises the following steps:
(1) conversion of equivalence principle
By adopting a mass equivalence principle, the columnar shots with different length-diameter ratios are uniformly converted into spheres with the same mass, and the corresponding equivalent spherical shot diameters are obtained, wherein the conversion relation is as follows:
dc＝(6M/πρp)1/3
where M is the mass of the cylindrical projectile, ρpIs the density of the cylindrical shot material, dcThe equivalent spherical shot diameter;
(2) simulation calculation
Based on a fluid dynamics simulation system, selecting proper state equations and constitutive models for protective structure materials, carrying out simulation calculation on the basis of validity verification of the simulation models, taking the spalling or perforation of the rear walls of the protective structures after impact as failure criteria, wherein the corresponding projectile mass is called critical projectile mass, and the corresponding projectile diameter is called equivalent critical projectile diameter;
(3) determining a speed segmentation point
Determining corresponding speed segmentation points of the cylindrical projectile under different length-diameter ratios based on the variation trend of the equivalent critical projectile diameter of the cylindrical projectile along with the impact speed;
(4) defining shape factor
The classical ballistic limit equation is divided into three regions according to different speeds, namely a ballistic region, a crushing region and a melting/vaporizing region, wherein the ballistic region and the melting/vaporizing region are all penetration equations established based on solid particles; wherein a shape coefficient K (f) based on a dimensionless aspect ratio f is introduced in the ballistic zone equation, the melting/vaporization zone equation:
Figure GDA0003560237750000031
in the formula dc＝(6Mcy/πρp)1/3Converting the non-spherical projectile into a diameter corresponding to a spherical projectile with the same mass by using a mass equivalent principle; rhopPellet density (g/cm 3); ρ is a unit of a gradientbA shield density (g/cm 3); t is twIs the back plate thickness (cm); s is a guard spacing (cm); v. of0The projectile impact velocity (km/s); theta is an included angle (DEG) between the impact speed and the normal direction of the target plate; σ is the back plate yield strength (ksi); substituting the equivalent critical projectile diameter, the protection structure parameters, the impact speed and the corresponding speed segmentation points under different length-diameter ratios obtained by simulation into an equation 1 to obtain a shape coefficient K (f) under the corresponding speed condition;
(5) form factor equation fitting
No matter in a ballistic region or a melting/vaporizing region, the shape coefficient of the cylindrical projectile changes obviously along with the length-diameter ratio, but the shape coefficient does not change greatly along with the impact speed under the same length-diameter ratio, so that the shape coefficient of the cylindrical projectile is only related to the length-diameter ratio and is not related to the impact speed, and the shape coefficients of the ballistic region and the melting/vaporizing region are fitted to obtain a shape coefficient equation related to the length-diameter ratio f;
(6) obtaining a cylindrical projectile trajectory limit equation
Equation K of shape coefficient1(f)、K2(f) And (3) respectively substituting the equation (1) to obtain a ballistic limit equation capable of representing the impact effect of the columnar projectile with different length-diameter ratios.
The mass equivalence principle can analyze penetration capability of different shapes on the protection structure on the premise of ensuring consistent impact kinetic energy of the projectile.
Further, a corresponding trajectory limit is established based on the diameter of the equivalent spherical projectile, and comparability of penetration capacity of the non-spherical cylindrical projectile and the spherical projectile is achieved.
In the simulation calculation, in order to determine the critical penetration quality corresponding to the cylindrical projectile with different length-diameter ratios at different impact speeds, the diameter of the equivalent spherical projectile is taken as a variable, the diameter change step length is 0.2mm, the impact speed is fixed, the equivalent projectile diameter is changed, and the average projectile diameter between the failure and non-failure of the protection structure is taken as the equivalent critical projectile diameter, so that the equivalent critical projectile diameter corresponding to the space fragment protection structure at different speeds is obtained.
Wherein, protective structure chooses Whipple protective structure for use, and the protection interval is 100mm, and aluminum plate is chooseed for use to the protective screen.
Wherein, the cylindrical pill materials are LY-12 aluminum, and the length-diameter ratio is 0.5, 1 and 2 respectively.
And taking the average projectile diameter between the failure and non-failure of the protective structure as the equivalent critical projectile diameter.
According to the method for obtaining the ballistic limit equation of the space debris protective structure under the impact of the cylindrical projectile, the ballistic limit corresponding to the cylindrical projectile is equivalent to the ballistic limit corresponding to the sphere according to the mass equivalence principle, the ballistic limit equation capable of representing the impact effect of the cylindrical projectile with different length-diameter ratios is obtained by combining the definition of the shape coefficient and the fitting of the shape coefficient equation, and the evaluation on the protective performance of the space debris protective structure under the impact of the cylindrical projectile is realized.
The cylindrical projectile trajectory limit equation obtained by the method can provide reference for engineering design only by carrying out calibration and correction through a small amount of tests, and has obvious practical value.
Drawings
FIG. 1 is a graph showing the variation of the equivalent critical projectile diameter with impact velocity in an embodiment of the present invention;
FIG. 2 is a ballistic zone shape coefficient curve obtained by fitting in an embodiment of the present invention;
FIG. 3 is a melting/vaporization region shape factor curve fit to an embodiment of the present invention;
figure 4 is a graph of the ballistic limit curves of three aspect ratio cylindrical projectiles obtained in an example of the invention.
Detailed Description
The invention is described in detail below with reference to the figures and the specific embodiments. The examples are not to be construed as limiting the scope of the invention and equivalent methods are within the scope of the invention.
A typical Whipple protective structure is selected, the protective distance is 100mm, a 2A12 aluminum plate with the thickness of 1.5mm is selected as the protective screen, and a 5A06 aluminum plate with the thickness of 2.5mm is adopted as the rear plate. The cylindrical shot materials are LY-12 aluminum, the length-diameter ratio is 0.5, 1 and 2 respectively, and the impact mode is positive collision. Based on the equivalence principle, the equivalence relation between the cylindrical aluminum shot and the sphere is shown in table 1.
TABLE 1 equivalent relationship between cylindrical aluminum pellets of different length-diameter ratios and spherical aluminum pellets
Figure GDA0003560237750000051
And (3) selecting an SPH algorithm suitable for calculating the ultra-high-speed collision problem of the space debris to establish a simulation calculation model. Because the melting point and the gas point of aluminum are lower, the aluminum alloy can be melted and even vaporized in the ultra-high speed collision, a Tillotson physical state equation which can describe the coexistence problem of large deformation and multiple phases under high pressure is selected, and Johnson-Cook models are selected as constitutive models.
The critical projectile diameter is generally between the corresponding projectile diameters when the protective structure is not in effect and when it is not. Under the same impact speed, the equivalent projectile diameter is changed, the change step length is 0.2mm, and the average projectile diameter between the failure and non-failure of the protection structure is taken as the equivalent critical projectile diameter. The equivalent critical projectile diameters at the speed of 11km/s for the three aspect ratio cylindrical projectiles 2-are shown in Table 2. The corresponding trend of the equivalent critical projectile diameter with impact velocity is shown in fig. 1.
TABLE 2 equivalent critical projectile diameters of cylindrical projectiles at different speeds
Figure GDA0003560237750000052
Figure GDA0003560237750000061
Figure 1 can judge the speed segmentation point V of the ballistic limit under three length-diameter ratiosLAnd VH. When the length-diameter ratio of the cylindrical projectile is 0.5, the velocity segmentation point V of the ballistic region and the crushing regionL3km/s, the velocity division point of the crushing zone and the melting/vaporizing zone is VH6.5 km/s; when the length-diameter ratio of the cylindrical projectile is 1, the speed segmentation point of the ballistic region and the crushing region is VL3km/s, the velocity division point of the crushing zone and the melting/vaporizing zone is V H7 km/s; when the length-diameter ratio of the cylindrical projectile is 2, the speed segmentation points of the ballistic region and the crushing region and the speed segmentation points of the crushing region and the melting/vaporizing region are greatly increased and are respectively VL6km/s and VH＝10km/s.
The equivalent critical projectile diameter, the protection structure parameters, and the corresponding velocity segmentation points under different aspect ratios are substituted into equation 1, and the shape coefficient K under the corresponding conditions can be obtained. Table 3 shows the ballistic section shape coefficient, and table 4 shows the melting/vaporization section shape coefficient.
TABLE 3 ballistic section shape factor
Figure GDA0003560237750000062
TABLE 4 melting/vaporizing section shape factor
Figure GDA0003560237750000063
As can be seen from tables 3-4, the shape factor of the cylindrical pellets, whether in the ballistic zone or in the melting/vaporization zone, varies significantly with the aspect ratio, while the shape factor does not vary much for the same aspect ratio.
Fitting the shape coefficients of the ballistic region and the melting/vaporization region by a polynomial fitting method, wherein the fitting curves are shown in fig. 2-3, and the following can be obtained:
the ballistic section shape coefficient equation is:
K1(f)＝2.129-0.034f-0.159f2 (2)
the melting/vaporization section form factor equation is:
K2(f)＝0.613+1.537f-0.714f2 (3)
equation K of shape coefficient1(f)、K2(f) And (3) respectively substituting the equation (1) to obtain a ballistic limit equation capable of representing the impact effect of the columnar shots with different length-diameter ratios:
when V is0cosθ≤VLThe method comprises the following steps:
Figure GDA0003560237750000071
when V is0cosθ≥VHThe method comprises the following steps:
Figure GDA0003560237750000072
when V isLcosθ<VHThen, linear interpolation is performed on the equations (4) and (5), and the corresponding crushing zone equation is obtained:
Figure GDA0003560237750000073
the ballistic limit curves for the three aspect ratio cylindrical pellets are shown in figure 4.
Although particular embodiments of the invention have been described and illustrated in detail, it should be understood that various equivalent changes and modifications can be made to the above-described embodiments according to the inventive concept, and that it is intended to cover such modifications as would come within the spirit of the appended claims and their equivalents.

Claims (6)

1. The method for acquiring the ballistic limit equation of the space fragment protection structure under the impact of the cylindrical projectile comprises the following steps:
(1) conversion of equivalence principle
By adopting a mass equivalence principle, the columnar shots with different length-diameter ratios are uniformly converted into spheres with the same mass, and the corresponding equivalent spherical shot diameters are obtained, wherein the conversion relation is as follows:
dc＝(6M/πρp)1/3
where M is the mass of the cylindrical projectile, ρpIs the density of the cylindrical shot material, dcThe equivalent spherical projectile diameter;
(2) simulation calculation
Based on a fluid dynamics simulation system, a protection structure material selects a state equation and a constitutive model, the corresponding state equation is a Tillotson equation, the constitutive model is a Johnson-Cook model, and the geometric parameters of the protection structure are the same as the test working conditions; carrying out simulation calculation on the basis of validity verification of a simulation model, taking the occurrence of spalling or perforation of the rear wall of the protection structure after impact as a failure criterion, wherein the corresponding shot mass is called critical shot mass, and the corresponding shot diameter is called equivalent critical shot diameter;
(3) determining a speed segmentation point
Determining corresponding speed segmentation points of the cylindrical projectile under different length-diameter ratios based on the variation trend of the equivalent critical projectile diameter of the cylindrical projectile along with the impact speed;
(4) defining shape factor
The classical ballistic limit equation is divided into three regions according to different speeds, namely a ballistic region, a crushing region and a melting/vaporizing region, wherein the ballistic region and the melting/vaporizing region are all penetration equations established based on solid particles; wherein a shape coefficient K (f) based on a dimensionless aspect ratio f is introduced in the ballistic zone equation, the melting/vaporization zone equation:
Figure FDA0003560237740000021
in the formula dc＝(6Mcy/πρp)1/3Converting the non-spherical projectile into a diameter corresponding to a spherical projectile with the same mass by using a mass equivalent principle; rhopPellet density (g/cm 3); rhobA shield density (g/cm 3); t is twIs the back plate thickness (cm); s is a guard spacing (cm); v. of0The projectile impact velocity (km/s); theta is an included angle (DEG) between the impact speed and the normal direction of the target plate; σ is the back plate yield strength (ksi); equivalent critical ammunition obtained by simulationSubstituting the diameter of the pill, the parameters of a protective structure, the impact speed and corresponding speed segmentation points under different length-diameter ratios into an equation (1) to obtain a shape coefficient K (f) under the corresponding speed condition;
(5) form factor equation fitting
No matter in a ballistic region or a melting/vaporizing region, the shape coefficient of the cylindrical projectile changes obviously along with the length-diameter ratio, but the shape coefficient does not change greatly along with the impact speed under the same length-diameter ratio, so that the shape coefficient of the cylindrical projectile is only related to the length-diameter ratio and is not related to the impact speed, and the shape coefficients of the ballistic region and the melting/vaporizing region are fitted to obtain a shape coefficient equation related to the length-diameter ratio f;
(6) obtaining a cylindrical projectile trajectory limit equation
Equation K of shape coefficient1(f)、K2(f) And (3) respectively substituting the equation (1) to obtain a ballistic limit equation capable of representing the impact effect of the columnar projectile with different length-diameter ratios.
2. The method of claim 1, wherein the mass equivalence principle enables analysis of penetration ability of different shapes into the protective structure while ensuring consistent kinetic energy of projectile impact.
3. The method of claim 1, wherein establishing corresponding ballistic limits based on equivalent spherical projectile diameters achieves comparability of non-spherical cylindrical projectile to spherical projectile penetration capability.
4. The method of claim 1, wherein in simulation calculation, in order to determine the critical penetration quality corresponding to the cylindrical projectile with different length-diameter ratios at different impact speeds, the equivalent spherical projectile diameter is used as a variable, the diameter change step is 0.2mm, the impact speed is fixed, the equivalent projectile diameter is changed, and the average projectile diameter between the failure and non-failure of the protection structure is used as the equivalent critical projectile diameter, so as to obtain the equivalent critical projectile diameter corresponding to the space debris protection structure at different speeds.
5. A method according to any one of claims 1 to 4, wherein the protective structure is a Whipple protective structure, the distance between the shields is 100mm, and the shield is an aluminium plate.
6. The method according to any one of claims 1 to 4, wherein the cylindrical shot material is LY-12 aluminum with aspect ratios of 0.5, 1, 2, respectively.
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