Method for determining eutectic content in solid propellant

Abstract

The invention provides a method for determining the eutectic content in a solid propellant. The method comprises the following steps: determining at least one of the burning rate, the density and the mechanical property of the solid propellant; the content of eutectic in the solid propellant is determined based on at least one of a firing rate, a density, and a mechanical property of the solid propellant. According to the method, the correlation between other parameters of the solid propellant and the content of the eutecticum in the solid propellant is found, and the numerical relationship of the correlation is further optimized, so that the method for determining the content of the eutecticum in the solid propellant by using the other parameters of the solid propellant is determined.

Description

Technical Field

[0001] The present invention relates to the field of propulsion technology, and particularly to a method for determining the content of eutectics in solid propellants. Background Art

[0002] Solid propellants are commonly used types of propellants. With the development of technology and the continuous improvement of performance requirements, high-energy materials such as energetic plasticizers, energetic binders, hexanitrohexaazaisowurtzitane (CL-20), and cyclotetramethylenetetranitramine (HMX) have been used in propellants. During the development of new high-energy solid propellants, it has been found that in the aging process of CL-20 / HMX nitrate plasticized GAP propellants, the burning rate and modulus increase abnormally, while the strength and density decrease abnormally. Current research has found that part of the reason is that in a nitrate environment, CL-20 and HMX continuously form eutectics and precipitate, forming a multi-defect random packing. As an important component of high-energy propellants, the solubility of nitrate in CL-20 and HMX is related to the use safety and storage life of the propellant. If in a high-energy propellant containing CL-20 and HMX, CL-20 and HMX have a large solubility in nitrate and form CL-20 / HMX eutectics and precipitate from the system, it will have an important impact on the engine performance.

[0003] Therefore, a suitable method is needed to determine the content of eutectics in solid propellants. Currently, a known method is to measure whether eutectics appear in the propellant by X-ray diffraction. This is because during the aging process, the CL-20 particles and HMX particles will dissolve, resulting in a decrease in the intensity of their own characteristic peaks. However, the X-ray diffraction method is a qualitative method and cannot accurately quantitatively represent the content of eutectics. At the same time, when the applicant used the peak area method for calculation in the X-ray diffraction method, it was also found that the determined content of eutectics deviated from the actual mass fraction. Therefore, the X-ray diffraction method can only determine the presence of eutectics, but cannot quantitatively determine the mass fraction of eutectics, and thus cannot truly reflect the eutectic changes. Summary of the Invention

[0004] For this reason, the present invention provides a method for determining the content of eutectics in solid propellants, which can more accurately determine the content of eutectics in solid propellants.

[0005] Specifically, the present invention proposes a method for determining the content of eutectics in solid propellants,

[0006] determine at least one of the burning rate, density, and mechanical properties of the solid propellant;

[0007] Determine the content of the eutectic in the solid propellant based on at least one of the burning rate, density, and mechanical properties of the solid propellant.

[0008] According to one example, the mechanical property is represented by the elastic modulus.

[0009] According to one example, let the three independent variables of the burning rate, density, and elastic modulus be density (X1), burning rate (X2), and elastic modulus (X3), and the target dependent variable be the eutectic mass fraction (Y). Assume that the density, burning rate, and elastic modulus follow a Gaussian distribution with a mean of μ and a standard deviation of ζ, specifically as follows:

[0010] X1 ∼ Φ(μ1, ζ1)

[0011] X2 ∼ Φ(μ2, ζ2)

[0012] X3 ∼ Φ(μ3, ζ3)

[0013] In the formula, μ is the true value, ζ is the respective experimental standard deviation, and X is the measured value.

[0014] Set up a multiple linear model, specifically as follows:

[0015] Y1 = k1X1 + b1

[0016] Y2 = k2X2 + b2

[0017] Y3 = k3X3 + b3

[0018] In the formula, k1, k2, and k3 are slopes, and b1, b2, and b3 are intercepts.

[0019] Combining the above two formulas, we obtain:

[0020] Y1 ∼ Φ(k1μ1 + b1, k1ζ1)

[0021] Y2 ∼ Φ(k2μ2 + b2, k2ζ2)

[0022] Y3 ∼ Φ(k3μ3 + b3, k3ζ3)

[0023] Taking the optimization goal of predicting the distribution consistency of Y1, Y2, and Y3, the optimization cost loss function Loss is defined as:

[0024] Loss = D KL (Y1, Y2) + D KL (Y2, Y3) + D KL (Y3, Y1)

[0025] Randomly select data at different temperatures for optimization analysis, and perform an iterative optimization process to continuously adjust k1, k2, k3, b1, b2, b3 to obtain the optimal solution that minimizes the Loss function. The specific formula is:

[0026] (k1, b1, k2, b2, k3, b3) = argmin Loss

[0027] Finally, k1, k2, k3, b1, b2, b3 are determined.

[0028] According to an example, the following formula is used to calculate the content of eutectics in solid propellants:

[0029] Y1 = k1X1 + b1

[0030] Y2 = k2X2 + b2

[0031] Y3 = k3X3 + b3

[0032] Among them, the values of k1, k2, k3, b1, b2, b3 are -0.5197, 0.0471, 0.0089, 0.5253, -0.0426, -0.0063 respectively.

[0033] According to an example, based on the values of burning rate, density, and elastic modulus determined from the aging test, and the values of the content of eutectics obtained by X-ray diffraction method, the correlation between the burning rate, density, and elastic modulus and the content of eutectics is found.

[0034] As can be seen from the above, the present invention proposes a method for determining the content of eutectics in solid propellants. First, through experiments, parameters related to the content of eutectics in existing solid propellant parameters are found, and then a method of jointly optimizing multiple parameters is used. Finally, a characterization method capable of characterizing the content of eutectics in solid propellants is determined, which can quantitatively determine the mass fraction of eutectics, thus truly reflecting the eutectic change.

[0035] Other features and advantages of the present invention will be described below. Brief Description of the Drawings

[0036] Figure 1 is a flowchart of the method for determining the content of eutectics in solid propellants of the present invention.

[0037] Figure 2 is a correlation fitting graph between density and the content of eutectics obtained from the high-temperature aging test.

[0038] Figure 3(a) and Figure 3(b) respectively show the residual analysis results obtained based on the above-mentioned linear function fitting and the model after optimizing three parameters. Detailed implementation manners

[0039] The present invention will be further described below in conjunction with the accompanying drawings and embodiments. It should be understood that the following described embodiments are intended to facilitate the understanding of the present invention, rather than imposing any limitations on it.

[0040] Figure 1 It is a flowchart of the method for determining the eutectic content in solid propellant according to the present invention. Specifically, the method of the present invention includes:

[0041] Determine the density, burning rate and elastic modulus of the solid propellant;

[0042] Use the density, burning rate and elastic modulus of the solid propellant to calculate the eutectic content in the solid propellant.

[0043] Specifically, the present invention proposes to use the following calculation formula to determine the eutectic content in the solid propellant:

[0044] Y1 = k1X1 + b1

[0045] Y2 = k2X2 + b2

[0046] Y3 = k3X3 + b3

[0047] Wherein, X1 represents the density, X2 represents the burning rate, X3 represents the elastic modulus, and Y1, Y2 and Y3 respectively represent the eutectic content determined based on the density, burning rate and elastic modulus; and the values of k1, k2 and k3 as well as b1, b2, b3 in the above three formulas are shown in Table 1 below:

[0048] Table 1

[0049]

[0050] Thus, after determining the density, burning rate and elastic modulus of the solid propellant through experiments, the eutectic content in the solid propellant can be determined.

[0051] The method for obtaining the above-mentioned eutectic content in solid propellant will be described in detail below.

[0052] For solid propellants, there are many performance parameters, such as density, burning rate, maximum elongation, maximum tensile strength, elastic modulus, content of stabilizers (including N-methyl-p-nitroaniline and 2-nitrodiphenylamine, etc.). As described in the background art, although the existence of eutectics can be determined by X-ray diffraction, and the proportion of eutectics can be obtained to a certain extent by methods such as the ratio of characteristic peak areas by the applicant first, the calculation results have large errors and are difficult to be used as accurate and available results.

[0053] To this end, an idea that occurred to the applicant was to determine the content of the eutectic by using other performance parameters of the solid propellant that can be accurately obtained. Since the content of the eutectic changes continuously with the aging of the solid propellant, the applicant conducted aging tests on the solid propellant at multiple temperatures and simultaneously measured parameters such as the density, burning rate, maximum elongation, maximum tensile strength, elastic modulus, and stabilizer content of multiple solid propellants. The change trend of the content of the eutectic obtained by X-ray diffraction at the same temperature and the change trend of the above-mentioned parameters of multiple solid propellants with time at the same temperature were studied. Through experiments and analysis of the experimental results, it was found that the change trends of density, burning rate, and elastic modulus were the same as those of the content of the eutectic obtained by X-ray diffraction, while the change trends of maximum tensile strength, maximum elongation, and stabilizer content were significantly different from those of the content of the eutectic obtained by X-ray diffraction. Based on this, the applicant preliminarily judged that the content of the eutectic could be determined based on density, burning rate, and elastic modulus.

[0054] In order to be able to use the existing parameters as accurately as possible by mathematical methods to accurately determine the content of the eutectic, the applicant first calculated the values of density, burning rate, and elastic modulus obtained from the aging tests conducted at multiple temperatures and performed a correlation analysis on their relationship with the content of the eutectic in the solid propellant under the same test conditions. As a specific calculation method, software was used for correlation analysis. For example, Statistical Product and Service Solutions (SPSS) correlation analysis software was used. With the content of the eutectic as the independent variable and density, burning rate, and elastic modulus as the dependent variables, a bivariate correlation analysis was first performed. The analysis found that the absolute values of Pearson correlations could all reach above 0.9, while the Sig. (two-tailed) values were all significantly less than 0.05. Thus, it was determined that there was a certain correlation between the content of the eutectic and density, burning rate, and elastic modulus.

[0055] Figure 2 It is a correlation fitting graph between the density obtained from the high-temperature aging test and the content of the eutectic. Taking density as an example, generally speaking, it can be fitted with a linear function, and there are also some individual data points with a relatively high degree of deviation. Similarly, the applicant also performed a correlation analysis on the relationship between the data of burning rate and elastic modulus and the content of the eutectic, and found that there was also an obvious correlation. In addition, the applicant also performed a correlation analysis on maximum elongation, maximum tensile strength, stabilizer content, etc., and no obvious correlation was found.

[0056] Therefore, if only the results obtained from the above-mentioned correlation analysis are used as the method for determining the content of the eutectic, there may still be a large inaccuracy. In addition, according to the preliminary model prediction above, since the prediction is carried out based on density, burning rate, and elastic modulus respectively, in addition to the deviation in the prediction itself, the results of the three predictions are also inconsistent. Therefore, it is difficult to be used as a reliable and available determination method. For this reason, the applicant has made further optimizations on the basis of the above work.

[0057] As a specific optimization method, let the three independent variables be density (X1), burning rate (X2), and elastic modulus (X3), and the target dependent variable be the eutectic mass fraction (Y). Considering that there are certain standard deviations in the density, burning rate, and elastic modulus tests, it is assumed that the density, burning rate, and elastic modulus follow a Gaussian distribution with a mean of μ and a standard deviation of ζ. Specifically, as follows:

[0058] X1~Φ(μ1,ζ1)

[0059] X2~Φ(μ2,ζ2)

[0060] X3~Φ(μ3,ζ3)

[0061] In the formula, μ is the true value, ζ is the respective test standard deviation, and X is the measured value.

[0062] According to the linear correlation between the eutectic mass fraction Y and density X1, burning rate X2, and elastic modulus X3, a multiple linear model is set, specifically as follows:

[0063] Y1=k1X1+b1

[0064] Y2=k2X2+b2

[0065] Y3=k3X3+b3

[0066] In the formula, k1, k2, and k3 are slopes, and b1, b2, and b3 are intercepts.

[0067] Combining the above two formulas, we get:

[0068] Y1~Φ(k1μ1+b1,k1ζ1)

[0069] Y2~Φ(k2μ2+b2,k2ζ2)

[0070] Y3~Φ(k3μ3+b3,k3ζ3)

[0071] Taking the consistency of the distributions of Y1, Y2, and Y3 as the optimization goal, the Kullback-Leibler divergence (KL divergence) is used to characterize the pairwise distribution consistency. The KL divergence is defined as follows:

[0072]

[0073] The optimized cost loss function Loss is defined as:

[0074] Loss = D KL (Y1, Y2) + D KL (Y2, Y3) + D KL (Y3, Y1)

[0075] Randomly select 7 groups of data from 13 groups of data at 60°C and 70°C for optimization analysis, and use Python to execute the iterative optimization process. Starting from the initial guess parameters, continuously adjust k1, k2, k3, b1, b2, b3 to make the Loss function reach the optimal solution of the minimum value. The specific formula:

[0076] (k1, b1, k2, b2, k3, b3) = argmin Loss

[0077] After the optimization calculation, the above-mentioned respective parameter values are finally determined as shown in Table 1.

[0078] Figures 3(a) and 3(b) respectively show the residual analysis results obtained based on the above-mentioned linear function fitting and the model after optimizing three parameters. Comparing Figures 3(a) and 3(b), it can be seen that under the same sample conditions, the residuals of the optimized model are all lower than those of the model fitted by the linear function. Compared with the linear function model, the maximum residual of the optimized model is reduced by about 90%, and the residuals of the remaining sample conditions are basically reduced by 50%. Thus, it can be seen that using the optimized model can better reflect the consistency of the predicted eutectic mass fraction.

[0079] For those of ordinary skill in the art, without departing from the creative concept of this application, several variations and improvements can also be made to the embodiments of the present invention, and these all belong to the protection scope of this application.

Claims

1. A method for determining the eutectic content in a solid propellant, characterized in that determining at least one of a burning rate, a density, and a mechanical property of the solid propellant; The content of the eutectic in the solid propellant is determined based on at least one of a burning rate, a density, and a mechanical property of the solid propellant.

2. The method for determining the eutectic content in a solid propellant according to claim 1, characterized in that The mechanical property adopts elastic modulus.

3. The method for determining the eutectic content in a solid propellant according to claim 2, characterized in that Assume that the three independent variables of burning rate, density and elastic modulus are density (X1), burning rate (X2) and elastic modulus (X3), the target dependent variable is the mass fraction of eutectic (Y), and the density, burning rate and elastic modulus are set to obey Gaussian distribution with mean μ and standard deviation ζ, as follows: X1~Φ(μ1,ζ1) X2~Φ(μ2,ζ2) X3~Φ(μ3,ζ3) In the formula, μ is the true value, ζ is the standard deviation of each test, X is the measured value, Set up a multivariate linear model, as follows: Y1=k1X1+b1 Y2=k2X2+b2 Y3=k3X3+b3 In the formula, k1, k2 and k3 are slopes, b1, b2 and b3 are intercepts, Combining the above two equations, we get: Y1~Φ(k1μ1+b1,k1ζ1) Y2~Φ(k2μ2+b2,k2ζ2) Y3~Φ(k3μ3+b3,k3ζ3) Taking the distribution consistency of predicted Y1, Y2, and Y3 as the optimization goal, the optimization cost loss function Loss is defined as: Loss=D KL (Y1,Y2)+D KL (Y2,Y3)+D KL (Y3,Y1) Randomly select data from different temperatures for optimization analysis, and perform an iterative optimization process to continuously adjust k1, k2, k3, b1, b2, and b3 to achieve the optimal solution of the minimum value of the Loss function. The specific formula is: (k1,b1,k2,b2,k3,b3)=argminLoss Finally, k1, k2, k3, b1, b2, and b3 were determined.

4. The method for determining the eutectic content in a solid propellant according to claim 3, characterized in that The following formula is used to calculate the eutectic content in solid propellant: Y1=k1X1+b1 Y2=k2X2+b2 Y3=k3X3+b3 Among them, the values ​​of k1, k2, k3, b1, b2, and b3 are -0.5197, 0.0471, 0.0089, 0.5253, -0.0426, and -0.0063, respectively.

5. The method for determining the eutectic content in a solid propellant according to claim 1, characterized in that: Based on the values ​​of the burning rate, density and elastic modulus determined by the aging test and the value of the eutectic content obtained by X-ray diffraction, a correlation between the burning rate, density and elastic modulus and the eutectic content was found.

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