引用本文 ↓

李科,郑坚,支建庄,等. Kooij方法预估固体火箭发动机中丁羟包覆层老化寿命[J].含能材料,2018,26(9):739-743.

LI Ke,ZHENG Jian,ZHI Jian‑zhuang,et al.Storage Lifetime Prediction of HTPB Coating in Solid Rocket Motor Based on Kooij Method[J].Chinese Journal of Energetic Materials(Hanneng Cailiao),XXXX,XX(XX):739-743.

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    摘要

    为了准确地预估固体火箭发动机中丁羟包覆层的贮存寿命,开展了50,60,70 ℃和80 ℃时的加速老化试验,用对数模型、幂函数模型和指数模型研究了丁羟包覆层的最大延伸率随贮存时间的变化。选取Kooij方程作为丁羟包覆层的老化模型,预估了试样的常温贮存寿命。结果表明, α = 0.4 时的幂函数模型能描述最大延伸率随时间的变化规律。所得老化反应的表观活化能约为29 kJ·mol-1,远小于60 kJ·mol-1,表示在50~80 ℃下进行的老化反应易于发生。以最大延伸率下降50%为失效准则,预估丁羟包覆层的常温贮存寿命为15.62年,能满足包覆层的老化性能要求。

    Abstract

    To accurately predict the storage life of hydroxyl-terminated polybutadiene (HTPB) coating in solid rocket motor, accelerated aging tests at 50, 60, 70 ℃ and 80 ℃ were carried out. Logarithmic model, power function model and exponential model were used to study the maximum elongation of HTPB coating with storage time. Kooij equation was regarded as the aging model, and the storage life of HTPB coating at normal temperature was predicted. Results show that the power function model with α = 0.4 can describe the variation law of maximum elongation with time. The apparent activation energy of the aging reaction obtained is 29 k J m o l - 1 approximately, which is far less than 60 k J m o l - 1 , revealing that the aging reaction during 50 ℃ to 80 ℃ is easy to occur. Taking the maximum elongation decrease of 50% as the failure criterion, the storage life of the estimated HTPB coating at normal temperature is 15.62 years, which can meet the aging performance requirements of the coating.

    LI Ke,ZHENG Jian,ZHI Jian-zhuang,et al. Storage Lifetime Prediction of HTPB Coating in Solid Rocket Motor Based on Kooij Method[J].Chinese Journal of Energetic Materials(Hanneng Cailiao),2018,26(9):739-743.

  • 1 引 言

    1

    丁羟包覆层是在丁羟(端羟基聚丁二烯)橡胶基体加入了耐烧蚀填料等填充剂的高分子复合材料,作为固体火箭发动机中重要的结构组成,其材料必须具有良好的贮存老化性能,以防止包覆层在长期的贮存过程中受应力、辐射、热氧等外界环境载荷的作用而失效,从而导致固体火箭发动机的结构完整性遭到破坏[1,2]。研究包覆层的老化特性并且准确预估其贮存寿命将为固体发动机的结构完整性评估提供重要的参考,可以避免发动机提前退役造成浪费或过度服役导致危害,具有重要的工程应用价值[3]

    对于橡胶类材料的寿命预估,国内外常用的研究方法是将高温加速老化试验与Arrhenius方程结合,建立材料老化性能变化的模型,并外推贮存温度下的老化寿命[4]。如Gillen K T等[5,6,7]利用Arrhenius方程和加速老化试验相结合的方法对某型推进剂的寿命进行了预估,然而Arrhenius方法通常将活化能看作常数,忽略了温度的影响,给材料的贮存寿命预估引入了误差[8]。为了减小预估误差,杜永强[9]等使用分段函数函数来描述推进剂最大延伸率随时间的变化关系,并结合Arrhenius方程外推推进剂的寿命,提高了预估结果的准确性;周洁[10]将Arrhenius方程中的温度参数进行了有效分段,取得了较好的效果。丁羟包覆层的老化是一个非常复杂的过程,受自身材料的构成和外部环境的影响,主要老化过程为分子链的氧化交联与降解断链[11,12],其贮存寿命的准确预测具有一定的难度,预估固体火箭发动机中丁羟包覆层寿命的研究还未见文献报道。

    为此,本研究对不同贮存温度条件下的丁羟包覆层进行了热氧加速老化试验和力学性能测试,用最大延伸率来表征包覆层在老化过程中的性能变化,选取Kooij方程作为丁羟包覆层的老化模型。结合老化试验数据,对老化模型的参数进行了求解,预估了丁羟包覆层的常温贮存寿命,为固体火箭发动机的结构完整性评估提供依据。

  • 2 实验部分

    2
  • 2.1 加速老化实验

    2.1

    试验所用材料为西安国营845厂提供的同一批次的丁羟包覆层样品,试样按照标准QJ916-1985中的1型标准哑铃试件的形状和尺寸制备成标准件。

    参考GB/T 3512-2001的相关方法,进行为期50 d空气热氧化高温加速老化试验。将试样分别自然悬挂于设定温度为50 ℃(323.15 K)、60 ℃(333.15 K)、70 ℃(343.15 K)和80 ℃(353.15 K)的四个DU288型电热油浴恒温箱中,控制温度波动在±1 ℃以内,在恒温箱内放入干燥剂,保持相对湿度小于30%。每隔5 d从各个实验温度下的恒温箱中各取出5个试样,测试最大延伸率。注意在取样时尽量减少打开恒温箱的时间,避免因箱内实验温度变化而影响试样的老化性能。

  • 2.2 最大延伸率测试

    2.2

    从DU288型电热油浴恒温箱中取出试样,置于密闭的干燥器内自然冷却24 h,再使用INSTRON5982型材料试验机按照标准QJ916-1985进行丁羟包覆层的最大延伸率测试。

    测试时,将试件在(20±2) ℃下放置1 h后,把试件垂直对称地夹在材料试验机的上、下夹具上,控制拉伸速率为100 mm·min-1,拉伸试件直至断裂,记录试样在不同老化阶段的最大延伸率。不同温度下的每个老化时间点取样数为5个,采用t检验准则剔除异常数据,并对有效数据取平均值用于求解模型。

  • 3 结果与讨论

    3
  • 3.1 老化丁羟包覆层的最大延伸率

    3.1

    丁羟包覆层的老化性能受诸多因素的影响,其微观结构受到热、氧等环境因素的作用,易发生不可逆的化学反应,主要为分子链的氧化交联和降解断链[13,14]。拉伸强度和最大延伸率都可作为表征丁羟包覆层性能变化的指标。但是,在老化过程中,丁羟包覆层的拉伸强度先增大后减小,而丁羟包覆层的最大延伸率随时间单调递减,更适合用于描述包覆层在不同阶段的老化程度,老化丁羟包覆层的最大延伸率随老化时间变化的曲线见图1

    图1
                            老化丁羟包覆层最大延伸率随时间变化曲线

    图1 老化丁羟包覆层最大延伸率随时间变化曲线

    Fig.1 Variation curves of the maximum elongation with time for aging HTPB coating

    从图1可知,老化试样在4个老化温度下的最大延伸率随时间的变化趋势相同,说明这4种情况下的包覆层遵循相同的老化机理。此外,温度的增高明显提高了老化反应速率,这是因为高温加速了丁羟包覆层的老化进程。从曲线的整体变化趋势来看,最大延伸率的下降速率先快后慢,主要是因为分子链的氧化交联和降解断链共同作用的结果。老化前期,主要为后固化和氧化交联作用使最大延伸率迅速下降;老化中后期,老化反应主要为氧化交联和降解断链,且氧化反应略强于降解断链的作用,表现为最大延伸率的缓慢降低[11]

  • 3.2 老化模型与寿命预估

    3.2
  • 3.2.1 Kooij方法的基本原理

    3.2.1

    国内外常用Arrhenius方程与高温加速寿命试验相结合来预估材料的贮存寿命,Arrhenius方程中的老化表观活化能可表示为[15]

    E a = R T 2 d l n k d T = - R d l n k d ( 1 T )
    (1)

    式中, k 为老化反应速率, % d - 1 E a 为表观活化能, J m o l - 1 T 为绝对温度, K R 为摩尔气体常数, 8.314 J m o l - 1 K - 1 。通常认为指前因子和表观活化能是与温度无关的常数,该假设仅适用于小温度范围内的应用,当外推温度范围较大时,则会引起较大的误差[16]。因此,为保证寿命预估的准确性,有必要对Arrhenius公式进行适当的修正。

    表观活化能 E a 实际上是与温度变量相关的函数,在较为宽泛的温度范围内,可以在Arrhenius方程中加入参数 m ,将其修正成为含有 A E m 三个常数参量的公式,即Kooij方程[17]

    k = A T m e - E / R T
    (2)

    式中, E 为表观活化能中与温度无关的常数部分, J m o l - 1 m 为常数, T m 整体为无量纲量。

    对式(2)的两端同时取对数,得

    l n k = l n A + m l n T - E R T
    (3)

    从式(3)也可以看出,Arrhenius方法中将 l n k 1 T 看作线性关系是不准确的,外推的温度范围越大则产生的误差就越大。将式(3)对 T 微分,得

    d l n k = m d l n T - E R d ( 1 T )
    (4)

    将式(4)代入式(1)中,得到Kooij方法的表观活化能的表达式

    E b = - R m d l n T - E R d ( 1 T ) d ( 1 T ) = E + m R T
    (5)

    式中, E b 为Kooij方法中的表观活化能, J m o l - 1 。从式(5)可知,表观活化能 E b 与温度 T 之间存在着线性关系。

  • 3.2.2 模型求解与寿命预估

    3.2.2

    根据航天工业部标准QJ 2328A-2005,描述丁羟包覆层最大延伸率随时间的变化规律可以选用以下三种数学模型:

    对数模型:

    ε m = ε m 0 - k l g t
    (6)

    幂函数模型:

    ε m = ε m 0 - k t α
    (7)

    指数模型:

    ε m = ε m 0 e x p ( - k t )
    (8)

    式中, ε m 为某一时刻的最大延伸率, % ε m 0 为最大延伸率的初始值, % k 为老化反应速率, % d - 1 t 为老化时间, d α 为常数,当 α = 1 时,幂函数模型表示的是线性模型。

    根据图1加速老化试验结果,借助最小二乘法对三种数学模型进行回归求解,并进行相关性分析,结果见表1。对比4个老化温度下试验数据的拟合效果,发现幂函数模型在 α = 0.4 时的回归效果最好,表1中幂函数的拟合参数为 α = 0.4 时的计算结果。

    表1 三种模型的参数拟合对比

    Table 1 Comparison of the fitting parameters of the three models

    model T / K ε m 0 / % k / % d - 1 r 2
    logarithmic model323.15403.618.590.7615
    333.15382.928.570.9008
    343.15359.339.820.9202
    353.15343.251.090.9069
    power function model( α = 0.4 323.15437.616.220.9748
    333.15428.322.860.9701
    343.15416.930.190.9280
    353.15424.240.870.9755
    exponential model323.15417.43.389×10-30.9119
    333.15397.54.884×10-30.7857
    343.15375.26.941×10-30.6842
    353.15375.61.104×10-20.8263
    表1
                    三种模型的参数拟合对比

    r 2 is judgment coefficient.

    表1可知,在描述最大延伸率随时间的变化规律时,三种数学模型中 α = 0.4 时的幂函数模型的相关性最好。所以,选用幂函数模型作为丁羟包覆层的老化模型。利用表1中幂函数模型的数据对式(3)进行回归求解,得到Kooij方程的参数拟合结果见表2

    表2 Kooij方程的参数拟合结果

    Table 2 The fitting parameters of Kooij equation

    parameters l n ( A / % d - 1 ) m E / J m o l - 1 r 2
    value33.83-2.973.729×1040.9992
    表2
                    Kooij方程的参数拟合结果

    r 2 is judgment coefficient.

    表2中的参数带入式(5),得到不同温度下活化能的表达式

    E b = 3.729 × 10 4 - 2.97 × 8.314 T
    (9)

    为了验证式(9)的准确性,需要将其与Arrhenius方法求得活化能进行对比。用Arrhenius方法求解表观活化能时,把323.15,333.15,343.15,353.15 K下的老化性能数据回归求解的 E a 看作338.15 K的活化能,以323.15,333.15,343.15 K下的数据计算得到的 E a 作为333.15 K的活化能,将333.15,343.15,353.15 K下的数据求解结果作为343.15 K时的活化能。两种方法求解表观活化能的对比结果见表3

    表3 两种方法求得的活化能对比

    Table 3 Comparison of activation energy obtained by the two methods

    T / K E a / J m o l - 1 E b / J m o l - 1 δ /%
    333.1528660290641.41
    338.1528950289400.03
    343.1528395288171.49

    δ is the error of E b relative to E a .

    表3可知,Kooij方法计算不同老化温度下的表观活化能具有一定的参考意义,特别是在338.15 K时两种方法求得的结果几乎相同。Arrhenius方法求得的表观活化能散布无规律可循,主要是因为Arrhenius方法将活化能看作是与温度无关的不变量,且此法求解不同温度下活化能的过程是相互独立的,导致了结果散布的随机性。此外,橡胶材料的热空气老化表观活化能一般为60~90 k J m o l - 1 [14,18],而上述两种方法求得的反应表观活化能约为29 kJ·mol-1,远小于60 k J m o l - 1 ,说明了丁羟包覆层在本研究的加速老化条件下的老化反应很容易发生。

    表2的数据代入式(3)中,求得在标准实验室温度298.15 K下的老化反应速率预估值 k 0 = 6.4539 。在计算过程中难免会因数据的散布造成误差进而导致预估结果不准确,所以需要在计算中考虑随机误差的影响[19]。在显著性水平为0.2的情况下,求得老化反应速率常数的上、下限值,结果分别为 k m a x = 6.7925 % d - 1 k m i n = 6.1153 % d - 1

    在预估橡胶类材料的寿命时,若最大延伸率下降50%,则认为材料失效[15]。本研究将最大延伸率下降50%作为丁羟包覆层的失效判据。基于安全性考虑,在计算过程中,需要使用老化反应速率预估值的上限值进行寿命预估 [20]。将 k m a x = 6.7925 % d - 1 ε m 0 = 432 % ε m = 216 % 代入式(7),计算得到丁羟包覆层的常温298.15 K下的贮存寿命为5702天,即为15.62年。固体火箭发动机的结构完整性评估要求包覆层具有15~20年贮存寿命[21],Kooij方法求得的贮存寿命符合该规定,且该方法预估的寿命比Arrhenius方法的16.70年短了1.08年,相对误差在6.92%以内,表明两种方法的预估结果具有较好的一致性。

  • 4 结 论

    4

    (1) 提出了使用Kooij方法来预估固体火箭发动机中丁羟包覆层的贮存寿命,将 α = 0.4 时的幂函数模型用于描述最大延伸率的变化规律,结合高温加速老化试验的数据对模型的参数进行了求解,得到Kooij方程的表达式为 l n k = 33.83 - 2.97 l n T - 3.729 × 10 4 8.314 T

    (2) Kooij方法求解得到的老化反应表观活化能 E b 是与温度 T 呈线性关系的函数,而Arrhenius方法求得的活化能 E a 数值散布无规律可循,主要是因为Arrhenius方法将 E a 看作与温度无关的不变量,且每个活化能的求解过程相互独立导致结果随机散布。

    (3) Kooij方法和Arrhenius方法这两种方法获取的老化反应的表观活化能远小于60 k J m o l - 1 ,表明丁羟包覆层在50~80 ℃条件下的老化反应很容易发生。

    (4) 以最大延伸率下降50%作为老化失效的准则,使用Kooij方法预估得到丁羟包覆层的贮存寿命为15.62年,比Arrhenius方法求得的寿命短1.08年,相对误差小于6.92%,能够满足固体火箭发动机结构完整性评估对包覆层老化性能的要求。

  • 参考文献

    • 1

      侯林法.复合固体推进剂[M]. 北京:北京宇航出版社,1994:431-446.

      HOU Lin-fa.Composite solid propellant[M]. Beijing:China Aerospace Publishing House,1994:431-446.

    • 2

      孙长印.丁羟包覆层的强制老化试验[J]. 航空兵器,1984(4):30-34.

      SUN Chang-yin.Forced aging test of HTPB inhibitor[J]. Aviation Weapons,1984(4):30-34.

    • 3

      陈汝训.固体火箭发动机设计与研究[M]. 北京:北京宇航出版社,1991:460-472.

      CHEN Ru‑xun.Design and research of solid rocket engine[M]. Beijing:China Aerospace Publishing House,1991:460-472.

    • 4

      杜永强,郑坚,彭威,等. HTPB推进剂贮存老化建模及寿命预估研究综述[J].化工进展,2016,35(增刊):219-224.

      DU Yong-qiang,ZHENG Jian,PENG Wei,et al. Review of the research of aging modeling and life prediction for HTPB propellant[J]. Chemical Industry and Engineering Progress,2016,35(Suppl.):219-224.

    • 5

      Gillen K T,Celinam M,Bernestein.Review of the ultrasensitive oxygen consumption method for making more reliable extrapolated predictions of polymer lifetimes[J]. Ann Tech Conf Soc Plast Eng,2004,62:2289.

    • 6

      HUANG W,DUANE L.An alternative degradation reliability modeling approach using maximum likelihood estimation[J]. IEEE Transactions on Reliability,2005,54(2):310-317.

    • 7

      Celina M,Gillen K T,Assink R A.Accelerated aging and lifetime prediction:review of non-Arrhenius behavior due to two competing processes[J]. Polym Degrad Stab,2005,90:395.

    • 8

      高大元,何碧,何松伟,等.Arrhenius方法的局限性讨论[J]. 含能材料,2006,14(2):132-135.

      GAO Da-yuan,HE Bi,HE Song-wei,et al.Discussion on limitation of the Arrhenius methodology[J]. Chinese Journal of Energetic Materials( Hanneng Cailiao ),2006,14(2):132-135.

    • 9

      杜永强,郑坚,彭威,等.基于分段老化模型的HTPB推进剂贮存寿命[J]. 含能材料,2016,24(10):936-940.

      DU Yong-qiang,ZHENG Jian,PENG Wei,et al.Storage life of HTPB propellant based on segmented aging model[J]. Chinese Journal of Energetic Materials(Hanneng Cailiao),2016,24(10):936-940.

    • 10

      周洁,姚军,宋燕.基于分段非线性Arrhenius的贮存寿命评估方法[J]. 北京航空航天大学学报,2015,41(4):744-750.

      ZHOU Jie,YAO Jun,SONG Yan.Storage life evaluation method based on segmented nonlinear Arrhenius model[J]. Journal of Beijing University of Aeronautics and Astronautics,2015,41(4):744-750.

    • 11

      张兴高.HTPB推进剂贮存老化特性及寿命预估研究[D]. 长沙:国防科学技术大学,2009:79-85.

      ZHANG Xing-gao.Study on the aging properties and storage life prediction of HTPB propellant[D]. Changsha:National University of Defense Technology,2009:79-85.

    • 12

      Cerri S,Bohn M A,Menke K,et al.Aging behavior of HTPB based rocket propellant formulations[J]. Central European Journal of Energetic Materials,2009,6(12):149-165.

    • 13

      丁世俊,王英英.HTPB贮存老化性能[J]. 固体火箭技术,2001,24(4):50-55.

      DING Shi-jun,WANG Ying-ying. Storage aging performance for HTPB[J]. Journal of Solid Rocket Technology,2001,24(4):50-55.

    • 14

      钱艺华,肖红照,赵耀洪,等.模拟变压器工作环境下的丁腈橡胶老化研究及寿命预测[J]. 变压器,2017,54(11):19-25.

      QIAN Yi-hua,XIAO Hong-zhao,ZHAO Yao-hong,et al. Lifetime prediction and research on aging of NBR under operating environment of transformer[J]. Transformer,2017,54(11):19-25.

    • 15

      张检,王海刚.氯丁橡胶的老化和寿命预测研究[J]. 橡塑技术与装备(塑料),2017,43(16):24-26.

      ZHANG Jian,WANG Hai-gang. Study on aging and life prediction of chloroprene rubber[J]. China Rubber/Plastic Technology and Equipment(Plastics),2017,43(16):24-26.

    • 16

      陈海建,滕克难,李波,等.基于修正Arrhenius方法的SRM药柱储存寿命预估[J]. 弹箭与制导学报,2011,31(4):232-239.

      CHEN Hai-jian,TENG Ke-nan,LI Bo,et al.A research of solid rocket motor grain storage life forecast based on modified Arrhenius method[J]. Journal of Projectiles,Rockets,Missiles and Guidance,2011,31(4):232-239.

    • 17

      胡荣祖,赵凤起,高红旭,等.非线性等转换率的微、积分法及其在含能材料物理化学研究中的应用 V.基于Kooij公式的理论和数值方法[J]. 含能材料,2008,16(3):290-308.

      HU Rong-zu,ZHAO Feng-qi,GAO Hong-xu,et al.Differential and integral isoconversional non-linear Methods and their application in Physical Chemistry study of Energetic Materials V. theory and Numerical Method Based on Kooij′s Formula[J]. Chinese Journal of Energetic Materials( Hanneng Cailiao ) ,2008,16(3):290-308.

    • 18

      张昊,罗怀德,杜娟.线性活化能法预估推进剂贮存寿命研究[J]. 固体火箭技术,2002,25(2):56-58.

      ZHANG Hao,LUO Huai-de,DU Juan.Linear activation energy method for predicting service life of propellant[J]. Journal of Solid Rocket Technology,2002,25(2):56-58.

    • 19

      盛骤,谢式千,潘承毅.概率论与数理统计[M]. 北京: 高等教育出版社, 2001: 156-174.

      SHENG Zhou, XIE Shi-qian, PAN Cheng-yi .Probability theory and mathematical statistics[M]. Beijing: Higher Education Press, 2001: 156-174.

    • 20

      曹付齐,刘志成,李小换.某固体火箭发动机装药加速老化试验与贮存寿命预测[J]. 航空兵器,2014(4):58-61.

      CAO Fu-qi,LIU Zhi-cheng,LI Xiao-huan.Research on accelerated aging test and storage life prediction of solid rocket motor charge[J]. Aero Weaponry,2014(4):58-61.

    • 21

      邱哲明.固体火箭发动机材料与工艺[M]. 北京:北京宇航出版社,1995:252-253.

      QIU Zhe‑ming.Solid rocket engine materials and technology[M]. Beijing:China Aerospace Publishing House,1995:252-253.

李科

机 构:陆军工程大学石家庄校区,河北 石家庄 050003

邮 箱:763722187@qq.com

作者简介:李科(1993-),男,硕士研究生,主要从事丁羟包覆层的老化性能研究。e-mail:763722187@qq.com

郑坚

机 构:陆军工程大学石家庄校区,河北 石家庄 050003

角 色:通讯作者

邮 箱:zhjianen@163.com

支建庄

机 构:陆军工程大学石家庄校区,河北 石家庄 050003

吴国瑞

机 构:981部队,湖北 武汉 432200

/html/hncl/CJEM2018035/alternativeImage/149a7a97-9625-4c83-91c3-69a6a9975f47-F001.jpg
model T / K ε m 0 / % k / % d - 1 r 2
logarithmic model323.15403.618.590.7615
333.15382.928.570.9008
343.15359.339.820.9202
353.15343.251.090.9069
power function model( α = 0.4 323.15437.616.220.9748
333.15428.322.860.9701
343.15416.930.190.9280
353.15424.240.870.9755
exponential model323.15417.43.389×10-30.9119
333.15397.54.884×10-30.7857
343.15375.26.941×10-30.6842
353.15375.61.104×10-20.8263
parameters l n ( A / % d - 1 ) m E / J m o l - 1 r 2
value33.83-2.973.729×1040.9992
T / K E a / J m o l - 1 E b / J m o l - 1 δ /%
333.1528660290641.41
338.1528950289400.03
343.1528395288171.49

图1 老化丁羟包覆层最大延伸率随时间变化曲线

Fig.1 Variation curves of the maximum elongation with time for aging HTPB coating

表1 三种模型的参数拟合对比

Table 1 Comparison of the fitting parameters of the three models

表2 Kooij方程的参数拟合结果

Table 2 The fitting parameters of Kooij equation

表3 两种方法求得的活化能对比

Table 3 Comparison of activation energy obtained by the two methods

image /

无注解

无注解

r 2 is judgment coefficient.

r 2 is judgment coefficient.

δ is the error of E b relative to E a .

  • 参考文献

    • 1

      侯林法.复合固体推进剂[M]. 北京:北京宇航出版社,1994:431-446.

      HOU Lin-fa.Composite solid propellant[M]. Beijing:China Aerospace Publishing House,1994:431-446.

    • 2

      孙长印.丁羟包覆层的强制老化试验[J]. 航空兵器,1984(4):30-34.

      SUN Chang-yin.Forced aging test of HTPB inhibitor[J]. Aviation Weapons,1984(4):30-34.

    • 3

      陈汝训.固体火箭发动机设计与研究[M]. 北京:北京宇航出版社,1991:460-472.

      CHEN Ru‑xun.Design and research of solid rocket engine[M]. Beijing:China Aerospace Publishing House,1991:460-472.

    • 4

      杜永强,郑坚,彭威,等. HTPB推进剂贮存老化建模及寿命预估研究综述[J].化工进展,2016,35(增刊):219-224.

      DU Yong-qiang,ZHENG Jian,PENG Wei,et al. Review of the research of aging modeling and life prediction for HTPB propellant[J]. Chemical Industry and Engineering Progress,2016,35(Suppl.):219-224.

    • 5

      Gillen K T,Celinam M,Bernestein.Review of the ultrasensitive oxygen consumption method for making more reliable extrapolated predictions of polymer lifetimes[J]. Ann Tech Conf Soc Plast Eng,2004,62:2289.

    • 6

      HUANG W,DUANE L.An alternative degradation reliability modeling approach using maximum likelihood estimation[J]. IEEE Transactions on Reliability,2005,54(2):310-317.

    • 7

      Celina M,Gillen K T,Assink R A.Accelerated aging and lifetime prediction:review of non-Arrhenius behavior due to two competing processes[J]. Polym Degrad Stab,2005,90:395.

    • 8

      高大元,何碧,何松伟,等.Arrhenius方法的局限性讨论[J]. 含能材料,2006,14(2):132-135.

      GAO Da-yuan,HE Bi,HE Song-wei,et al.Discussion on limitation of the Arrhenius methodology[J]. Chinese Journal of Energetic Materials( Hanneng Cailiao ),2006,14(2):132-135.

    • 9

      杜永强,郑坚,彭威,等.基于分段老化模型的HTPB推进剂贮存寿命[J]. 含能材料,2016,24(10):936-940.

      DU Yong-qiang,ZHENG Jian,PENG Wei,et al.Storage life of HTPB propellant based on segmented aging model[J]. Chinese Journal of Energetic Materials(Hanneng Cailiao),2016,24(10):936-940.

    • 10

      周洁,姚军,宋燕.基于分段非线性Arrhenius的贮存寿命评估方法[J]. 北京航空航天大学学报,2015,41(4):744-750.

      ZHOU Jie,YAO Jun,SONG Yan.Storage life evaluation method based on segmented nonlinear Arrhenius model[J]. Journal of Beijing University of Aeronautics and Astronautics,2015,41(4):744-750.

    • 11

      张兴高.HTPB推进剂贮存老化特性及寿命预估研究[D]. 长沙:国防科学技术大学,2009:79-85.

      ZHANG Xing-gao.Study on the aging properties and storage life prediction of HTPB propellant[D]. Changsha:National University of Defense Technology,2009:79-85.

    • 12

      Cerri S,Bohn M A,Menke K,et al.Aging behavior of HTPB based rocket propellant formulations[J]. Central European Journal of Energetic Materials,2009,6(12):149-165.

    • 13

      丁世俊,王英英.HTPB贮存老化性能[J]. 固体火箭技术,2001,24(4):50-55.

      DING Shi-jun,WANG Ying-ying. Storage aging performance for HTPB[J]. Journal of Solid Rocket Technology,2001,24(4):50-55.

    • 14

      钱艺华,肖红照,赵耀洪,等.模拟变压器工作环境下的丁腈橡胶老化研究及寿命预测[J]. 变压器,2017,54(11):19-25.

      QIAN Yi-hua,XIAO Hong-zhao,ZHAO Yao-hong,et al. Lifetime prediction and research on aging of NBR under operating environment of transformer[J]. Transformer,2017,54(11):19-25.

    • 15

      张检,王海刚.氯丁橡胶的老化和寿命预测研究[J]. 橡塑技术与装备(塑料),2017,43(16):24-26.

      ZHANG Jian,WANG Hai-gang. Study on aging and life prediction of chloroprene rubber[J]. China Rubber/Plastic Technology and Equipment(Plastics),2017,43(16):24-26.

    • 16

      陈海建,滕克难,李波,等.基于修正Arrhenius方法的SRM药柱储存寿命预估[J]. 弹箭与制导学报,2011,31(4):232-239.

      CHEN Hai-jian,TENG Ke-nan,LI Bo,et al.A research of solid rocket motor grain storage life forecast based on modified Arrhenius method[J]. Journal of Projectiles,Rockets,Missiles and Guidance,2011,31(4):232-239.

    • 17

      胡荣祖,赵凤起,高红旭,等.非线性等转换率的微、积分法及其在含能材料物理化学研究中的应用 V.基于Kooij公式的理论和数值方法[J]. 含能材料,2008,16(3):290-308.

      HU Rong-zu,ZHAO Feng-qi,GAO Hong-xu,et al.Differential and integral isoconversional non-linear Methods and their application in Physical Chemistry study of Energetic Materials V. theory and Numerical Method Based on Kooij′s Formula[J]. Chinese Journal of Energetic Materials( Hanneng Cailiao ) ,2008,16(3):290-308.

    • 18

      张昊,罗怀德,杜娟.线性活化能法预估推进剂贮存寿命研究[J]. 固体火箭技术,2002,25(2):56-58.

      ZHANG Hao,LUO Huai-de,DU Juan.Linear activation energy method for predicting service life of propellant[J]. Journal of Solid Rocket Technology,2002,25(2):56-58.

    • 19

      盛骤,谢式千,潘承毅.概率论与数理统计[M]. 北京: 高等教育出版社, 2001: 156-174.

      SHENG Zhou, XIE Shi-qian, PAN Cheng-yi .Probability theory and mathematical statistics[M]. Beijing: Higher Education Press, 2001: 156-174.

    • 20

      曹付齐,刘志成,李小换.某固体火箭发动机装药加速老化试验与贮存寿命预测[J]. 航空兵器,2014(4):58-61.

      CAO Fu-qi,LIU Zhi-cheng,LI Xiao-huan.Research on accelerated aging test and storage life prediction of solid rocket motor charge[J]. Aero Weaponry,2014(4):58-61.

    • 21

      邱哲明.固体火箭发动机材料与工艺[M]. 北京:北京宇航出版社,1995:252-253.

      QIU Zhe‑ming.Solid rocket engine materials and technology[M]. Beijing:China Aerospace Publishing House,1995:252-253.

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