电磁轨道发射装置导轨动力学响应分析
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摘要
为分析电磁轨道发射装置中导轨在发射过程的动力学响应,将分布式移动电磁载荷作用下的导轨简化为伯努利-欧拉梁,建立了悬臂支撑约束下的导轨振动控制方程。采用分离变量法求解高阶偏微分方程,通过模态叠加导出了给定初边界条件下的导轨振动解析解和临界速度表达式。分别计算分析了电枢匀速运动、典型电流驱动下变加速运动时导轨的动力学响应特征,讨论了导轨振动响应的临界速度效应。结合电枢在膛内的运动过程,分析了导轨的振动挠度、速度和横向加速度等参量的变化规律。研究结果可为发射器封装结构的设计提供一定的理论依据。
In order to analyze the dynamic responses of the conducting rails in an electromagnetic rail launcher(EMRL),the rails subjected to the distributed moving electromagnetic forces were simplified as a Bernoulli-Euler beam,and the governing vibration equations of the rails under cantilever support constraints were established.The method of separation of variables was applied to solve the higher order partial differential equations.The analytical solutions and the critical speed expression of the rail vibration under the given initial boundary conditions were derived through modal superposition.The dynamic responses of the rails were calculated and analyzed in the case of an uniform motion of the armature and in the case of variable acceleration driven by a typical current,respectively.The critical velocity effect of the vibration response of the rails was also discussed.Especially,the characterization of the vibration deflection,velocity and lateral acceleration of the rails was analyzed combined with the movement of armature.This study will provide some theoretical support for the design of package structure of the launcher.
In order to analyze the dynamic responses of the conducting rails in an electromagnetic rail launcher(EMRL),the rails subjected to the distributed moving electromagnetic forces were simplified as a Bernoulli-Euler beam,and the governing vibration equations of the rails under cantilever support constraints were established.The method of separation of variables was applied to solve the higher order partial differential equations.The analytical solutions and the critical speed expression of the rail vibration under the given initial boundary conditions were derived through modal superposition.The dynamic responses of the rails were calculated and analyzed in the case of an uniform motion of the armature and in the case of variable acceleration driven by a typical current,respectively.The critical velocity effect of the vibration response of the rails was also discussed.Especially,the characterization of the vibration deflection,velocity and lateral acceleration of the rails was analyzed combined with the movement of armature.This study will provide some theoretical support for the design of package structure of the launcher.
引文
[1]Marshall R A,Wang Y.Railguns:Their Science and Technology[M].Beijing:Weapons Industry Press,2004.
[2]Fair H D.Advances in electromagnetic launch science and technology and its applications[J].IEEE Transactions on Magnetics,2014,45(1):225-230.
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[6]Tzeng J T.Dynamic response of electromagnetic railgun due to projectile movement[J].IEEE Transactions on Magnetics,2003,39(1):472-475.
[7]Tzeng J T,Sun W.Dynamic response of cantilevered railguns attributed to projectile/gun interaction-theory[J].IEEE Transactions on Magnetics,2007,43(1):207-213.
[8]陈铁宁,白春艳,张益男,等.电枢运动引起电磁发射轨道的动态响应[J].动力学与控制学报,2010,8(04):360-364.Chen Tiening,Bai Chunyan,Zhang Yinan,et al.Dynamic response of electromagnetic railgun due to armature movement[J].Journal of Dynamics and Control,2010,8(04):360-364.
[9]刘郑国,田福庆.电磁轨道发射装置结构动力学特性分析[J].船舶力学,2010,(10):1158-1164.Liu Zhenguo,Tian Fuqing.Structure dynamic characteristic analysis of electromagnetic rail launcher[J].Journal of Ship Mechanics,2010,(10):1158-1164.
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[11]田振国,白象忠,杨阳.电磁轨道发射状态下导轨的动态响应[J].振动与冲击,2012,31(2):10-14.Tian Zhenguo,Bai Xiangzhong,Yang Yang.Dynamic response of rail under a launching state of an electromagnetic rail[J].Journal of Vibration and Shock,2012,31(2):10-14.
[12]田振国,孟晓永,安雪云,等.电磁轨道发射状态下的复合导轨动态响应研究[J].兵工学报,2017,38(4):651-657.Tian Zhenguo,Meng Xiaoyong,An Xueyun,et al.Dynamic response of composite rail during launch process of electromagnetic railgun[J].Acta Armamentarii,2017,38(4):651-657.
[13]Johnson A J,Moon F C.Elastic waves and solid armature contact pressure in electromagnetic launchers[J].IEEE Transactions on Magnetics,2006,42(3):422-429.
[14]Johnson A J,Moon F C.Elastic waves in electromagnetic launchers[J].IEEE Transactions on Magnetics,2007,43(1):141-144.
[15]杨琳,聂建新,任明,等.移动电磁载荷作用下曲面轨道/电枢动力特性[J].高电压技术,2014,(4):1091-1096.YANG Lin,NIE Jianxin,REN Min,et al.Dynamic characteristics of armature and rail with cambered surface under moving electromagnetic load[J].High Voltage Engineering,2014,(4):1091-1096.
[16]Johnson A J,Haran T,Moon F C,et al.Stress wave measurements in an electromagnetic launcher[C].14th Symposium on Electromagnetic Launch Technology,2008:354-359.
[17]Lee Y,Kim S,An S,et al.Dynamic response of an electromagnetic launcher accelerating a C-shaped armature[J].IEEE Transactions on Plasma Science,2017,45(7):1639-1643.
[18]Schuppler C,Tumonis L,Kacianauskas R,et al.Experimental and numerical investigations of vibrations at a railgun with discrete supports[J].IEEE Transactions on Plasma Science,2013,41(5):1508-1513.
[19]吴金国,林庆华,弯港,等.基于物质点法的轨道炮刨削机理三维数值研究[J].爆炸与冲击,2017,37(2):307-314.Wu Jinguo,Lin Qinghua,Wan Gang,et al.3Dnumerical research of railgun gouging mechanism based on material point method[J].Explosion and Shock Waves,2017,37(2):307-314.
[2]Fair H D.Advances in electromagnetic launch science and technology and its applications[J].IEEE Transactions on Magnetics,2014,45(1):225-230.
[3]Barber J P,Bauer D P,Jamison K,et al.A survey of armature transition mechanisms[J].IEEE Transactions on Magnetics,2003,39(1):47-51.
[4]Watt T J,Clay C E,Bassett P M,et al.The effect of surface indentations on gouging in railguns[J].Wear,2014,310(1-2):41-50.
[5]Nechitailo N V,Lewis K B.Critical velocity for rails in hypervelocity launchers[J].International Journal of Impact Engineering,2006,33:485-495.
[6]Tzeng J T.Dynamic response of electromagnetic railgun due to projectile movement[J].IEEE Transactions on Magnetics,2003,39(1):472-475.
[7]Tzeng J T,Sun W.Dynamic response of cantilevered railguns attributed to projectile/gun interaction-theory[J].IEEE Transactions on Magnetics,2007,43(1):207-213.
[8]陈铁宁,白春艳,张益男,等.电枢运动引起电磁发射轨道的动态响应[J].动力学与控制学报,2010,8(04):360-364.Chen Tiening,Bai Chunyan,Zhang Yinan,et al.Dynamic response of electromagnetic railgun due to armature movement[J].Journal of Dynamics and Control,2010,8(04):360-364.
[9]刘郑国,田福庆.电磁轨道发射装置结构动力学特性分析[J].船舶力学,2010,(10):1158-1164.Liu Zhenguo,Tian Fuqing.Structure dynamic characteristic analysis of electromagnetic rail launcher[J].Journal of Ship Mechanics,2010,(10):1158-1164.
[10]田振国,白象忠,杨阳.电磁轨道发射状态下导轨侧面的局部接触应力分析[J].固体力学学报,2011,32(1):74-81.Tian Zhenguo,Bai Xiangzhong,Yang Yang.The analysis of local contact stress on the side of rail when the electromagnetic rail is at a launching state[J].Chinese Journal of Solid Mechanics,2011,32(1):74-81.
[11]田振国,白象忠,杨阳.电磁轨道发射状态下导轨的动态响应[J].振动与冲击,2012,31(2):10-14.Tian Zhenguo,Bai Xiangzhong,Yang Yang.Dynamic response of rail under a launching state of an electromagnetic rail[J].Journal of Vibration and Shock,2012,31(2):10-14.
[12]田振国,孟晓永,安雪云,等.电磁轨道发射状态下的复合导轨动态响应研究[J].兵工学报,2017,38(4):651-657.Tian Zhenguo,Meng Xiaoyong,An Xueyun,et al.Dynamic response of composite rail during launch process of electromagnetic railgun[J].Acta Armamentarii,2017,38(4):651-657.
[13]Johnson A J,Moon F C.Elastic waves and solid armature contact pressure in electromagnetic launchers[J].IEEE Transactions on Magnetics,2006,42(3):422-429.
[14]Johnson A J,Moon F C.Elastic waves in electromagnetic launchers[J].IEEE Transactions on Magnetics,2007,43(1):141-144.
[15]杨琳,聂建新,任明,等.移动电磁载荷作用下曲面轨道/电枢动力特性[J].高电压技术,2014,(4):1091-1096.YANG Lin,NIE Jianxin,REN Min,et al.Dynamic characteristics of armature and rail with cambered surface under moving electromagnetic load[J].High Voltage Engineering,2014,(4):1091-1096.
[16]Johnson A J,Haran T,Moon F C,et al.Stress wave measurements in an electromagnetic launcher[C].14th Symposium on Electromagnetic Launch Technology,2008:354-359.
[17]Lee Y,Kim S,An S,et al.Dynamic response of an electromagnetic launcher accelerating a C-shaped armature[J].IEEE Transactions on Plasma Science,2017,45(7):1639-1643.
[18]Schuppler C,Tumonis L,Kacianauskas R,et al.Experimental and numerical investigations of vibrations at a railgun with discrete supports[J].IEEE Transactions on Plasma Science,2013,41(5):1508-1513.
[19]吴金国,林庆华,弯港,等.基于物质点法的轨道炮刨削机理三维数值研究[J].爆炸与冲击,2017,37(2):307-314.Wu Jinguo,Lin Qinghua,Wan Gang,et al.3Dnumerical research of railgun gouging mechanism based on material point method[J].Explosion and Shock Waves,2017,37(2):307-314.