基于响应面中心复合设计的固体推进剂摩擦感度理论
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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R~2为0.9309、校正拟合度R_(adj)~2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℃。
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 ana-lyze,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 R~2 is 0.9309,and the correction fitting degree R_(adj)~2 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.
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 ana-lyze,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 R~2 is 0.9309,and the correction fitting degree R_(adj)~2 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.
引文
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[15] Gullón B,Gullón P,Lú-Chau T A,et al. Optimization of sol-vent extraction of antioxidants from eucalyptus globulus leaves by response surface methodology:characterization and assess-ment of their bioactive properties[J]. Industrial Crops&Prod-ucts,2017,108:649-659.
[16]陆森林,任栉翔.基于响应面法的车内噪声分析与优化[J].郑州大学学报(工学版),2017,38(5):65-70.LU Sen-lin,REN Zhi-xiang. Analysis and optimization of interi-or noise based on response surface method[J].Chinese Journal of Zhengzhou University,2017,38(5):65-70.
[17] Alexandre E M C,Araújo P,Duarte M F,et al. Experimental design,modeling,and optimization of high-pressure-assisted extraction of bioactive compounds from pomegranate peel[J].Food&Bioprocess Technology,2017,10(5):886-900.
[18] Ghasemi N,Aghayari R,Maddah H. Optimizing the param-eters of heat transmission in a small heat exchanger with spiral tapes cut as triangles and aluminum oxide nanofluid using cen-tral composite design method[J]. Heat and Mass Transfer,2018,54(7):2113-2130.
[19] Zheng N,Liu P,Shan F,et al. Sensitivity analysis and multi-objective optimization of a heat exchanger tube with conical strip vortex generators[J]. Applied Thermal Engineer-ing,2017,122:642-652.
[20] Zheng N,Liu P,Liu Z,et al. Numerical simulation and sensi-tivity analysis of heat transfer enhancement in a flat heat ex-changer tube with discrete inclined ribs[J]. International Jour-nal of Heat&Mass Transfer,2017,112:509-520.
[21]王永菲,王成国.响应面法的理论与应用[J].中央民族大学学报(自然科学版),2005,14(3):236-240.WANG Yong-fei,WANG Cheng-guo. Theory and application of response surface method[J]. Chinese Journal of the Central University for Nationalities(Natural Science Edition),2005,14(3):236-240.
[22] Jeffwu C F,Michael H.试验设计与分析及参数优化[M].北京:中国统计出版社,2003:362-365.Jeffwu C F,Michael H. Experimental design and analysis and parameter optimization[M]. Beijing:China Statistics Press,2003:362-365.
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[25]秦玉灵,孔宪仁,罗文波.多铺层碳纤维蜂窝板模型修正[J].航空学报,2011,32(4):636-648.QIN Yu-ling,KONG Xian-ren,LUO Wen-bo. Multi-layer car-bon fiber honeycomb panel model correction[J]. Chinese Jour-nal of Aviation,2011,32(4):636-648.
[26]李莉,张赛,何强,等.响应面法在试验设计与优化中的应用[J].实验室研究与探索,2015,34(8):41-45.LI Li,ZHANG Sai,HE Qiang,et al. Application of response surface method in experimental design and optimization[J].Chinese Journal of Laboratory research and exploration,2015,34(8):41-45.
[27]马迪.粒子群响应面建模法在ASPEN多因素优化中的应用[D].山西:太原理工大学,2016.MA Di. Application of particle swarm response surface model-ing method in ASPEN multi-factor optimization[D]. Shanxi:Taiyuan University of Technology,2016.
[2]王照波,野延年,李丽珍.固体推进剂摩擦感度测试方法研究探讨[C]//四川:中国宇航学会固体火箭推进年会. 2005.WANG Zhao-bo,YE Yan-nian,LI Li-zhen. Research on test method of friction sensitivity of solid propellant[C]//Sichuan:China Aerospace Society Solid Rocket Propulsion Annual Meeting. 2005.
[3]秦能,裴江峰,王明星.一种RDX-CMDB推进剂危险性能研究[J].含能材料,2011,19(6):725-729.QIN Neng,PEI Jiang-feng,WANG Ming-xing. Study on Haz-ard Performance of RDXvCMDB Propellant[J]. Chinese Jour-nal of Energetic Materials(Hanneng Cailiao),2011,19(6):725-729.
[4]陈协坤,张喜芳.固体火箭复合推进剂摩擦感度测试技术研究[J].推进技术,1984,5(2):1-5.CHEN Xie-kun,ZHANG Xi-fang. Research on friction sensitivi-ty testing technology of solid rocket composite propellant[J].Chinese Journal of Propulsion technology 1984,5(2):1-5.
[5]郑孟菊.炸药的性能及测试技术[M].北京:兵器工业出版社,1990.ZHENG Meng-ju. Explosive properties and testing techniques[M]. Beijing:Weapon Industry Press,1990.
[6]董海山,周芬芬.高能炸药及相关物性能[M].北京:科学出版社,1989:104-109.DONG Hai-shan,ZHOU Fen-fen. High-energy explosives and related properties[M]. Beijing:Science Press,1989:104-109.
[7]林文洲,洪滔.高能炸药摩擦感度的数值模拟[J].爆炸与冲击,2016,36(6):745-751.LIN Wen-zhou,HONG Tao. Numerical simulation of friction sensitivity of high energy explosives[J]. Chinese Journal of Ex-plosion and Shock,2016,36(6):745-751.
[8]张家希,李世鹏,隋欣,等.某固体推进剂摩擦试验过程数值模拟[C]//西安:中国航天空天动力联合会议. 2016:422-430.ZHANG Jia-xi,LI Shi-peng,SUI Xin,et al. Numerical simula-tion of friction test process of a solid propellant[C]//Xi'an:China Airlines Sky Sky Power Joint Conference. 2016:422-430.
[9]林文洲,洪滔.高能炸药摩擦感度理论初步研究[J].含能材料,2007,15(1):12-15.LIN Wen-zhou,HONG Tao. Preliminary study on the theory of friction sensitivity of high energy explosives[J]. Chinese Journal of Energetic Materials(Hanneng Cailiao),2007,15(1):12-15.
[10] Jiang X B,Guo S,Yao M,et al. Novel method for determin-ing the dynamic friction coefficient of explosives[J]. Combus-tion Explosion&Shock Waves,2014,50(1):118-123.
[11]张泽志,韩春亮,李成未.响应面法在试验设计与优化中的应用[J].河南教育学院学报(自然科学版),2011,20(4):34-37.ZHANG Ze-zhi,HAN Chun-liang,LI Cheng-wei. Application of response surface method in experimental design and optimi-zation[J]. Chinese Journal of Henan Institute of Education(Natural Science Edition),2011,20(4):34-37.
[12] Heller B. Statistics for experimenters,an introduction to de-sign, data analysis, and model building[J]. Mathematical Modelling,1986,7(9):1657-1658.
[13] Montgomery D C.实验设计与分析:第三版[M].北京:中国统计出版社,1998:612-623.Montgomery D C,Experimental design and analysis:the third edition[M]. Beijing:China Statistics Press,1998:612-623.
[14] Box G E P,Wilson K B. On the experimental attainment of op-timum conditions[J]. Journal of the Royal Statistical Society,1951,13(1):1-45.
[15] Gullón B,Gullón P,Lú-Chau T A,et al. Optimization of sol-vent extraction of antioxidants from eucalyptus globulus leaves by response surface methodology:characterization and assess-ment of their bioactive properties[J]. Industrial Crops&Prod-ucts,2017,108:649-659.
[16]陆森林,任栉翔.基于响应面法的车内噪声分析与优化[J].郑州大学学报(工学版),2017,38(5):65-70.LU Sen-lin,REN Zhi-xiang. Analysis and optimization of interi-or noise based on response surface method[J].Chinese Journal of Zhengzhou University,2017,38(5):65-70.
[17] Alexandre E M C,Araújo P,Duarte M F,et al. Experimental design,modeling,and optimization of high-pressure-assisted extraction of bioactive compounds from pomegranate peel[J].Food&Bioprocess Technology,2017,10(5):886-900.
[18] Ghasemi N,Aghayari R,Maddah H. Optimizing the param-eters of heat transmission in a small heat exchanger with spiral tapes cut as triangles and aluminum oxide nanofluid using cen-tral composite design method[J]. Heat and Mass Transfer,2018,54(7):2113-2130.
[19] Zheng N,Liu P,Shan F,et al. Sensitivity analysis and multi-objective optimization of a heat exchanger tube with conical strip vortex generators[J]. Applied Thermal Engineer-ing,2017,122:642-652.
[20] Zheng N,Liu P,Liu Z,et al. Numerical simulation and sensi-tivity analysis of heat transfer enhancement in a flat heat ex-changer tube with discrete inclined ribs[J]. International Jour-nal of Heat&Mass Transfer,2017,112:509-520.
[21]王永菲,王成国.响应面法的理论与应用[J].中央民族大学学报(自然科学版),2005,14(3):236-240.WANG Yong-fei,WANG Cheng-guo. Theory and application of response surface method[J]. Chinese Journal of the Central University for Nationalities(Natural Science Edition),2005,14(3):236-240.
[22] Jeffwu C F,Michael H.试验设计与分析及参数优化[M].北京:中国统计出版社,2003:362-365.Jeffwu C F,Michael H. Experimental design and analysis and parameter optimization[M]. Beijing:China Statistics Press,2003:362-365.
[23]国防科学技术工业委员会. GJB 5891.24-2006:火工品药剂试验方法第24部分:摩擦感度试验[S].北京:中国标准出版社,2006.National Defense Science and Technology Industry Commit-tee. GJB 5891.24-2006:Pyrotechnics-Test methods-Part 24:Friction sensitivity test[S]. Beijing:China Standard Press,1996.
[24]中国航天工业总公司. QJ 2913-1997:复合固体推进剂摩擦感度测试方法[S].北京:中国标准出版社,1997.China Aerospace Industry Corporation. QJ 2913-97:Compos-ite solid propellant friction sensitivity test method[S]. Beijing:China Standard Press,1996.
[25]秦玉灵,孔宪仁,罗文波.多铺层碳纤维蜂窝板模型修正[J].航空学报,2011,32(4):636-648.QIN Yu-ling,KONG Xian-ren,LUO Wen-bo. Multi-layer car-bon fiber honeycomb panel model correction[J]. Chinese Jour-nal of Aviation,2011,32(4):636-648.
[26]李莉,张赛,何强,等.响应面法在试验设计与优化中的应用[J].实验室研究与探索,2015,34(8):41-45.LI Li,ZHANG Sai,HE Qiang,et al. Application of response surface method in experimental design and optimization[J].Chinese Journal of Laboratory research and exploration,2015,34(8):41-45.
[27]马迪.粒子群响应面建模法在ASPEN多因素优化中的应用[D].山西:太原理工大学,2016.MA Di. Application of particle swarm response surface model-ing method in ASPEN multi-factor optimization[D]. Shanxi:Taiyuan University of Technology,2016.
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