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目录 contents

    摘要

    为了确定固体推进剂生产过程中的各因素对摩擦感度的影响,采用响应面法(RSM)与中心复合试验设计(CCD)相结合,以摆锤角度、滑柱压力、试样温度为影响因素,以固体推进剂摩擦感度值为响应值设计试验,采用摩擦感度测试仪进行试验,并分析试验结果拟合了响应面模型。结果表明,在三个响应面评价精度指标中,相对均方根误差为0.14、决定系数R2为0.9309、校正拟合度Radj2为0.8686,说明方程拟合精度高且误差小;由模型方差分析得方差比值F为14.96,表明模型对响应面的影响程度较高;概率值p为0.0001,表明模型有0.01%的概率对响应面无影响;响应曲面图表明了各因素之间的相互作用;优化模型得到最小摩擦感度值所对应的三因素范围为角度小于45°,压力小于2 MPa,温度小于45 ℃。

    Abstract

    To determine the influence of various factors in the production process of solid propellant on the friction sensitivity, the response surface methodology (RSM) combined with central composite design (CCD) was used to design the experiments based on the pendulum angle, the strut pressure and the sample temperature were taken as influencing factors, and the friction sensitivity value of solid propellant was considered as the response value. The friction sensitivity tester was used to test and analyze, the testing results were fitted to the response surface model. Results show that in three response surface evaluation accuracy indexes, the relative root mean square error RMSE is 0.14, the determination coefficient R2 is 0.9309, and the correction fitting degree Radj2 is 0.8686, showing that the fitting precision of the equation is high and the error is small. The variance ratio F obtained by variance analysis of the model is 14.96, indicating that the model has a higher influence on the response surface. The probability value p is 0.0001, indicating that the probability of 0.01% of the model has no effect on the response surface. The response surface map shows the interaction between the various factors. The three‑factor operating range corresponding to the minimum friction sensitivity value obtained by the model optimization is less than 45° in angle, less than 2 MPa in pressure, and less than 45 ℃ in temperature.

  • 1 引 言

    固体推进剂是指含有燃烧剂和氧化剂,在燃烧过程中能够放出大量炽热气体的固体致密材[1],作为一种高能化学动力提供者,广泛用于现代先进武器系统,同时亦是一种高危险的化学爆炸[2]。热分解作用和碰撞摩擦都会导致推进剂点火或爆[3],因此,引入摩擦感度的概念来评价固体推进剂的危险性能对安全生产具有十分重要的意[4]。目前,国内外测定固体推进剂摩擦感度的仪器主要有柯兹洛夫摩擦摆、BAM摩擦仪、ABL摩擦仪、大型摩擦摆、ROTO摩擦仪[5]。其中,国内应用较多的是柯兹洛夫摩擦摆。利用此摩擦摆进行的炸药摩擦感度实验研究较[6],但是相关的理论研究较少,并且对不同配方的固体推进剂在不同条件下的摩擦感度都需要进行相关实验研究,工作量较大,需要耗费较大的人力物力。此外,实验研究周期较长,一定程度上可能导致实际生产的延后。因此,通过数理模型得到某一固定条件下固体推进剂的摩擦感度是当前面临的主要问题。此外,数值模拟技术已广泛应用于工程应用领域,在节省设计制造成本和研发时间方面发挥了重大作用。目前,火炸药生产过程的数值模拟技术也得到了相关部门的重[7,8,9,10]。但是现有的数值仿真模型都是基于包括速度、压力、温度等参数的流场分析,对采用模型预测不同条件下的感度数值相关理论研究较少,不能满足多条件多类型的固体推进剂生产过程中的安全监控。

    现今广泛应用的正交实验设计法存在实验次数多、周期长等缺[11],并且最终不能回归出一个函数关系式,不能从根本上解决摩擦感度试验次数多的问题,因此选择可以通过设计试验方案回归拟合函数关系的响应面法对摩擦感度试验结果进行分析拟合。响应面法(Response Surface Methodology, RSM)也称响应曲面法,是通过设计合理的试验方案以及相应的试验数据,并分析响应曲面和等高线来寻求最优的工艺参数,采用二次多项式回归拟合相应的函数关系的一种统计方[12,13]。最初由BOX[14]提出用来进行物理试验的设计,现已广泛应用于化工、制药、机械等领[15,16,17]。但是,在感度理论研究方向,大部分集中于换热器等设备上摩擦情况的模[18,19,20],而直接采用响应面法回归固体推进剂摩擦感度模型的研究未见报道。响应面法的优点在于可以连续分析各因素的水平值并给出直观的图形分析以及相应的函数模型。与传统优化方法不同,RSM也考虑到试验的随机误差,并且采用一次或二次多项式来拟合复杂的函数关系,减小了计算量。在摩擦感度测试过程中影响因素较多,随机误差较为明显,采用RSM能够有效的避免随机误差对最终结果的影响。

    RSM试验设计方法有很多种,包括中心复合试验设计(Central Composite Design, CCD)、Box‑Behnken试验设计(BBD)、Koshal试验设计、Hybrid试验设计、A优化准则[21]。其中较为常用的为CCD设计和BBD设计,且在试验设计中应用最为广泛的是CCD试验设计,这是因为在CCD试验设计中合适的轴点坐标能够保证试验的可旋转性以及序贯性,能够在等距点上预测恒定方差,改善预测精度;此外,CCD试验设计中合适的中心试验次数可以使整体试验设计趋于正交设计,更有利于确定最优点的位[22]

    基于此,本研究采用RSM与CCD相结合设计了摩擦感度测试试验,通过设定的响应面方程拟合试验测试结果,得到了固体推进剂摩擦感度的方程,同时分析影响因素及方程的可行性,可为安全测试和生产提供一定程度的指导,为后续的数值仿真预测生产过程中的摩擦感度分布提供理论模型基础。

  • 2 响应面法试验设计

  • 2.1 试验样品及设备

    丁羟三组元推进剂,西安航天化学动力厂。

    摩擦感度测试仪:参照国家军用标准GJB5891.24-2006[23]和国家航天工业部标准QJ2913-1997[24]自制,试验装置简图如图1所示。

    图1
                            摩擦感度测试装置简图

    图1 摩擦感度测试装置简图

    Fig.1 Sketch of friction sensitivity testing device

  • 2.2 试验方法

    摩擦感度测试试验按照国家军用标准GJB5891.24-2006[23]进行。预先在烘箱中将药浆加热保温到测试温度,恒温一定时间;将药浆迅速置于导向套内的下滑柱上,放置上滑柱,移动下柱塞使药料移出导向套;根据表压显示给下滑柱施加一定的推力;在一定角度释放摆锤,击打击杆,击杆撞击上滑柱以一定速率运动并与药浆摩擦进而发生点火;观察并记录有无分解、燃烧、爆炸等现象发生;每组测试标定为25发,以发生爆发的次数除以25即得到摩擦感度。

    根据试验过程选取摆锤角度(A)、滑柱压力(B)、试样温度(C)作为CCD试验设计的影响因素。为保证试验设计的旋转性以及序贯性,在k个因素的情况下,对于轴向点极值(α)的选取应遵循α=2k/4,在每个因素范围内选取5个不同的值进行试验,具体实际参数及水平编码值(Level)如表1所示。

    表1 CCD试验因素、水平及实际值

    Table 1 CCD testing factors, levels and actual values

    levelfactor
    A / (°)B / MPaC / ℃
    -1.68230.001.0030.00
    -142.161.8134.05
    060.003.0045.00
    177.844.1945.95
    1.68290.005.0060.00

    NOTE: A is the pendulum angel; B is the sliding column pressure; C is the spicery temperature.

  • 2.3 试验方案设计

    在满足旋转性的前提下,为保证整个试验区域内的预测值具有一定精度,需要对三因素选择6个中心点。此外,试验方案包括20组试验,其中6个中心点对应6组中心试验,剩余14组为析因试验,试验方案设计如表2所示。根据本试验方案和2.2节所述试验方法,进行摩擦感度测试,得到不同试验条件下的摩擦感度数值。同时,分别分析了以小数表示的结果和以百分数表示的结果,如表3所示,对比两种结果中三个响应面精度评价指标(相对均方根误差RMSE、决定系数R2、校正拟合度Radj2)发现,当摩擦感度以小数表示时,拟合得到的模型可靠性更高。因此,拟合过程摩擦感度数值均以小数表示。

    表2 CCD试验设计方案

    Table 2 Design scheme of CCD testing

    No.factorY
    A / (°)B / MPaC / ℃
    160.003.0045.000.04
    260.003.0045.000.04
    342.161.8136.080.00
    460.005.0045.001.00
    590.003.0045.000.76
    677.841.8136.080.64
    760.003.0045.000.04
    860.001.0045.000.00
    942.161.8153.920.00
    1060.003.0045.000.04
    1177.844.1953.921.00
    1260.003.0030.000.12
    1360.003.0045.000.04
    1442.164.1936.080.64
    1577.841.8153.920.28
    1660.003.0060.000.48
    1777.844.1936.081.00
    1860.003.0045.000.04
    1930.003.0045.000.00
    2042.164.1953.920.36

    NOTE: Y is the friction sensitivity.

    表3 评价指标对比

    Table 3 Comparison of evaluation indexes

    evaluation indexdecimal formpercentage form
    RSME0.1413.75
    R20.93090.9309
    Radj20.86860.8686
  • 3 响应面法结果分析

  • 3.1 摩擦感度模型

    选择合适的响应面模型不仅能够提高最终拟合模型的预测精度,还能较为准确地预测非试验点处的响应面数[25]。常用的响应面法函数形式包括多项式基函数和高斯基函数等,根据摩擦感度的影响因素以及三种因素之间的相互作用,选用二次多项式基函数。这种基函数形式包括不含交叉项的二次多项式和含有交叉项的二次多项式,考虑到摩擦感度影响因素之间的共同作用,选用含有交叉项的二次多项式。二次多项式模[22]如公式(1)和(2)所示:

    不含交叉项:

    y(x)=a0+i=1naixi+i=1naiixi2
    (1)

    含交叉项:

    y(x)=a0+i=1naixi+ij(i<j)naijxixj
    (2)

    式中,a0为常数项待定系数;ai为一次项待定系数;aij为交叉项待定系数;aii为平方项待定系数。

    根据20组试验数据以及所选择的含交叉项的二次多项式,采用试验设计和分析软件对试验结果进行分析,拟合得到仅在三种因素影响下的某固体推进剂摩擦感度与角度、压力、温度之间响应模型,如公式(3)所示:

    Y=4.01473-0.036764A-0.59378B-0.12074C+4.57155×10-4AB-6.36232×10-5AC+9.47186×10-4BC+4.27569×10-4A2+0.12590B2+1.34927×10-3C2
    (3)

    式中,Y为摩擦感度;A为摆锤角度,(°);B为压力,MPa;C为试样温度,℃。

  • 3.2 模型评价与分析

    为保证最终拟合模型预测值的准确性,需要对拟合模型进行分析评价,主要通过方差分析证明方程可靠性,误差分析证明方程预测的准确程度,残差分布证明方程在预测过程中的适应[26]。通过方差分析可以对二次方程中各参数项进行显著性检验,检验结果见表4F为模型的均方与残差的均方的比值,用来比较模型方差与剩余方差,代表了该模型对响应面即摩擦感度的影响程度;p为与该模型F值相关的概率值,表示该模型对响应面没有影响时获得该F值的概率。一般此概率小于0.05时即可将该模型视为对响应面即摩擦感度有重要影响,本模型此概率远小于0.05,因此认为该模型可靠程度很高。F值越大,p值越小代表方程的显著性越高。从表4可以看出,所建立的摩擦感度模型F值为14.96,p值为0.0001,说明该模型对响应面有影响且影响程度不变的概率为99.99%,即该模型对响应面有稳定显著的影响。从表4中各二次项参数的p值可以直观地观察到对拟合模型有显著影响的参数项。此外,自由度(DF)表示回归模型过程中取值不受限制的变量个数,其值为9,表明模型中考虑的影响因素共9个。

    表4 摩擦感度模型方差分析

    Table 4 Variance analysis of friction sensitivity model

    sourcesum of squareDFmean squareFpinfluence degree
    model2.5490.2814.960.0001significant
    A0.7510.7539.54< 0.0001significant
    B1.0411.0454.84< 0.0001significant
    C8.556E-00518.556E-0054.527E-0030.9477
    AB7.644E-00417.644E-0040.0400.8446
    AC8.328E-00418.328E-0040.0440.8380
    BC8.074E-00418.074E-0040.0430.8404
    A20.2710.2714.210.0037significant
    B20.4610.4624.190.0006significant
    C20.1710.178.790.0142significant
    residual0.19100.019
    lack of fit0.1950.038
    pure error0.00050.000

    NOTE: Sum of square is the sum of the squared deviations from the mean due to the effect of this term;DF is the number of variables whose value is not limited;Mean square is the ratio of sum of square to DF, and it is the variance associated with that term; F is the mean square for the term divided by the mean square for the residual; p is the probability of getting an F value of this size if the term did not have an effect on the response.

    误差分析主要是对方程响应面精度评价指标的分析,包括相对均方根误差RMSE、决定系数R2、校正拟合度Radj2。其计算过程如公式(4)(5)(6[25]所示:

    RMSE=1ky¯i=1k(yi-y˜i)2
    (4)
    R2=1-i=1k(yi-y˜i)2i=1k(yi-y¯i)2
    (5)
    Radj2=1-i=1kyi-y˜i2(k-1)i=1kyi-y¯i2(k-p)
    (6)

    式中,y˜i为响应面回归方程的计算值;yi为采样点计算值;y¯为所有实验的平均值;k为试验次数。

    RMSE用来表示计算值与测量值之间的差异, 其值越趋近于0,表示响应面的误差越小,拟合的精度越高。当R2的值越接近1,则表示响应面的拟合精度越高。通常,当R2>0.9时,响应面的拟合精度则被认为可以满足要[27]。此外,当引入多个设计参数时,除决定系数R2之外,还需要考虑校正之后的R2,即校正拟合度Radj2Radj2越大,响应面拟合精度越好。表5为模型误差分析结果,从表5中可以看出RMSE为0.14,R2为0.9309,Radj2为0.8686,因此认为摩擦感度准确度较高。此外,Radj2Rpred2表示工艺过程的影响因素,其值较高且Radj2Rpred2差值小于0.2时可认为除给定因素外没有其他影响因素,但是本试验中差值大于0.2,说明摩擦感度测试过程除摆锤角度、滑柱压力、试样温度三个因素影响之外,还包括其他因素的影响,这与摩擦感度的实际测试过程一致。精密度是信号与噪声之比,由表5可知,其值大于4,表明模型合理。

    表5 摩擦感度模型误差分析

    Table 5 Error analysis of friction sensitivity model

    evaluation indexnumerical value
    RMSE0.14
    R20.9309
    Radj20.8686
    Rpred20.4434
    adeq precision10.760

    NOTE: adeq precisionis a signal to noise ratio;Rpred2 is a measure of how well the model predicts a response value.

    以图2,3,4进一步表征模型方程的适应性。图中数据点代表每一个试验方案,不同的颜色点表示不同的感度数值。图2为残差正态概率分布,由图2可知,不同试验方案的残差概率分布总体呈线性分布,表明摩擦感度模型的适应性良好。图3为残差与预测值分布,上下两条线代表残差的分布范围,从图3中可以看出预测值的残差分布均在此范围之内并且无明显规律,同样可以证明模型的适应性良好。图4为真实值与预测值的分布,从图4中可以观察到大部分数据点分布在y=x这条直线上,表明真实值与预测值基本一致,少数点分布在直线左右,进一步从具体数值表征方程的适应性。

    图2
                            残差正态概率分布图

    图2 残差正态概率分布图

    Fig.2 Distribution diagram of residual normal probability

    图3
                            残差与预测值分布图

    图3 残差与预测值分布图

    Fig.3 Distribution diagram of residual and predicted value

    图4
                            真实值与预测值分布图

    图4 真实值与预测值分布图

    Fig.4 Distribution diagram of actual value and predicted value

    以响应曲面表示各因素对摩擦感度的影响,如图5,6,7所示。从图5可以看出,当温度一定,角度和压力均为最小值时摩擦感度值最小,说明角度和压力之间的相互作用不明显。图6显示,在角度最小时,温度在一定范围之内摩擦感度值较小,说明角度和温度之间的交互作用明显,并且角度对最终摩擦感度的数值影响更加明显。由图7可知,压力和温度对摩擦感度的影响与图6相似,表明这三种因素中角度和压力对摩擦感度的影响较为显著,因此在生产过程中应作为首要考虑因素。

    图5
                            角度和压力对摩擦感度的影响

    图5 角度和压力对摩擦感度的影响

    Fig.5 Influence of angle and pressure on friction sensitivity

    图6
                            角度和温度对摩擦感度的影响

    图6 角度和温度对摩擦感度的影响

    Fig.6 Influence of angle and temperature on friction sensitivity

    图7
                            压力和温度对摩擦感度的影响

    图7 压力和温度对摩擦感度的影响

    Fig.7 Influence of pressure and temperature on friction sensitivity

  • 3.3 模型优化

    对最终拟合模型进行参数优化,拟合摩擦感度最小值所对应的三因素的数值,保证在此三因素作用范围内摩擦感度为0。选定这三因素的作用范围,以及摩擦感度优化值选定最小值,并设定一个本试验中所达不到的最小数值,保证优化结果的准确性。通过优化得出,当角度小于45°,压力小于2 MPa,温度小于45 ℃时,摩擦感度数值为0,即为最优安全操作条件,为通过响应面法优化摩擦感度试验因素提供了可能。

  • 4 结 论

    (1)采用响应面法与摩擦感度试验相结合获得固体推进剂摩擦感度模型,对模型方差、误差以及残差分布进行分析,证明响应面模型的准确性和可靠性。

    (2)模型方差中较大的F值和极小的p值表明了该模型的可靠性;响应面精度评价指标RMSE越小,R2Radj2越大,模型拟合精度越高;残差分布图、真实值与预测值分布满足线性关系,残差与预测值分布无规律表明模型的适应性良好;响应面曲线图表明了各因素之间的相互作用。

    (3) 通过优化模型响应面的最小值得到三种影响因素的安全操作范围:角度小于45°;压力小于2 MPa;温度小于45 ℃。

    (责编:姜 梅)

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邵明旺

机 构:北京理工大学化学与化工学院, 北京 102488

Affiliation:School of Chemistry and Chemical Engineering, Beijing Institute of Technology, Beijing 102488, China

邮 箱:shaomingwang1@126.com

作者简介:邵明旺(1994-),男,硕士研究生,主要从事化学工程与技术研究。e‑mail:shaomingwang1@126.com

王建

机 构:北京化工大学机电工程学院, 北京100029

Affiliation:School of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing 100029, China

角 色:通讯作者

Role:Corresponding author

邮 箱:wjj_0107@163.com

作者简介:王建(1984-),男,教授,主要从事含能材料与高分子材料加工及装备研究。e‑mail:wjj_0107@163.com

乔晓林

机 构:西安航天化学动力厂, 陕西 西安710025

Affiliation:Xi′an Aerospace Chemical Propultion Plant, Xi′an 710025, China

李兴刚

机 构:西安航天化学动力厂, 陕西 西安710025

Affiliation:Xi′an Aerospace Chemical Propultion Plant, Xi′an 710025, China

赵慧

机 构:西安航天化学动力厂, 陕西 西安710025

Affiliation:Xi′an Aerospace Chemical Propultion Plant, Xi′an 710025, China

html/hncl/CJEM2018237/alternativeImage/a7530ca2-3307-447b-aa2b-42b91b9a7fd1-F001.png
levelfactor
A / (°)B / MPaC / ℃
-1.68230.001.0030.00
-142.161.8134.05
060.003.0045.00
177.844.1945.95
1.68290.005.0060.00
No.factorY
A / (°)B / MPaC / ℃
160.003.0045.000.04
260.003.0045.000.04
342.161.8136.080.00
460.005.0045.001.00
590.003.0045.000.76
677.841.8136.080.64
760.003.0045.000.04
860.001.0045.000.00
942.161.8153.920.00
1060.003.0045.000.04
1177.844.1953.921.00
1260.003.0030.000.12
1360.003.0045.000.04
1442.164.1936.080.64
1577.841.8153.920.28
1660.003.0060.000.48
1777.844.1936.081.00
1860.003.0045.000.04
1930.003.0045.000.00
2042.164.1953.920.36
evaluation indexdecimal formpercentage form
RSME0.1413.75
R20.93090.9309
Radj20.86860.8686
sourcesum of squareDFmean squareFpinfluence degree
model2.5490.2814.960.0001significant
A0.7510.7539.54< 0.0001significant
B1.0411.0454.84< 0.0001significant
C8.556E-00518.556E-0054.527E-0030.9477
AB7.644E-00417.644E-0040.0400.8446
AC8.328E-00418.328E-0040.0440.8380
BC8.074E-00418.074E-0040.0430.8404
A20.2710.2714.210.0037significant
B20.4610.4624.190.0006significant
C20.1710.178.790.0142significant
residual0.19100.019
lack of fit0.1950.038
pure error0.00050.000
evaluation indexnumerical value
RMSE0.14
R20.9309
Radj20.8686
Rpred20.4434
adeq precision10.760
html/hncl/CJEM2018237/alternativeImage/a7530ca2-3307-447b-aa2b-42b91b9a7fd1-F002.png
html/hncl/CJEM2018237/alternativeImage/a7530ca2-3307-447b-aa2b-42b91b9a7fd1-F003.png
html/hncl/CJEM2018237/alternativeImage/a7530ca2-3307-447b-aa2b-42b91b9a7fd1-F007.png
html/hncl/CJEM2018237/alternativeImage/a7530ca2-3307-447b-aa2b-42b91b9a7fd1-F004.png
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图1 摩擦感度测试装置简图

Fig.1 Sketch of friction sensitivity testing device

表1 CCD试验因素、水平及实际值

Table 1 CCD testing factors, levels and actual values

表2 CCD试验设计方案

Table 2 Design scheme of CCD testing

表3 评价指标对比

Table 3 Comparison of evaluation indexes

表4 摩擦感度模型方差分析

Table 4 Variance analysis of friction sensitivity model

表5 摩擦感度模型误差分析

Table 5 Error analysis of friction sensitivity model

图2 残差正态概率分布图

Fig.2 Distribution diagram of residual normal probability

图3 残差与预测值分布图

Fig.3 Distribution diagram of residual and predicted value

图4 真实值与预测值分布图

Fig.4 Distribution diagram of actual value and predicted value

图5 角度和压力对摩擦感度的影响

Fig.5 Influence of angle and pressure on friction sensitivity

图6 角度和温度对摩擦感度的影响

Fig.6 Influence of angle and temperature on friction sensitivity

图7 压力和温度对摩擦感度的影响

Fig.7 Influence of pressure and temperature on friction sensitivity

image /

无注解

A is the pendulum angel; B is the sliding column pressure; C is the spicery temperature.

Y is the friction sensitivity.

无注解

Sum of square is the sum of the squared deviations from the mean due to the effect of this term;DF is the number of variables whose value is not limited;Mean square is the ratio of sum of square to DF, and it is the variance associated with that term; F is the mean square for the term divided by the mean square for the residual; p is the probability of getting an F value of this size if the term did not have an effect on the response.

adeq precisionis a signal to noise ratio;Rpred2 is a measure of how well the model predicts a response value.

无注解

无注解

无注解

无注解

无注解

无注解

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