高速火箭橇—轨道系统耦合动力学研究
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摘要
本文针对高速火箭橇-轨道系统这一介于室内与室外之间的大型地面试验设备,对其耦合动力学进行了详细研究。首先对高精度试验轨道不平顺及其对火箭橇的影响进行了研究；然后运用动力学相关基础理论,推导建立了高度非线性的火箭橇-轨道耦合动力学一般模型；基于面象对象方法,开发了火箭橇-轨道耦合动力学计算软件RSTdyn (Rocket Slet-Track dynamics);对相关参数获取方法、动力学模型及计算软件进行了验证；以某单轨火箭橇-轨道系统为对象,进行了耦合动力学的应用研究。主要研究工作如下：
(1)根据轨道不平顺功率谱密度分析方法,编制C++程序对美国HHSTT实测轨道不平顺功率谱密度(PSD)曲线进行了数据处理与分析,采用粒子群优化算法获得了高精度轨道的PSD函数及参量值；采用速度法和运动法对轨道短程不平顺影响火箭橇进行了计算与分析,提出了轨道长程不平顺影响火箭橇的PSD量纲分析法,完成了三种方法计算结果的对比分析。研究表明,高精度轨道不平顺高频特性更为明显、不平顺幅值更小、功率集中在高频段、平顺性更好,火箭橇速度越高要求的轨道长程与短程不平顺度的数值越小、波长越大,轨道建造的精度要求亦越高；火箭橇设计时应首先避开轨道的短波高频干扰段。
(2)根据火箭橇在轨道上运动的物理过程,首先运用相对坐标法建立了火箭橇-轨道系统的动力学坐标系,采用方向余弦矩阵实现了各坐标系间的转换；然后运用矢量力学Newton-Euler方法对火箭橇、钢轨与轨道枕板进行了受力分析,考虑了系统所受到的气动力、风速、火箭推力、碰撞接触力、冲击制动力、靴轨间隙等非线性因素；运用动力学相关基础理论推导建立了火箭橇-轨道耦合动力学一般模型,获得相应的动力学矢量、矩阵和标量形式的数学方程组。所建立的动力学模型为火箭橇-轨道系统动力学响应的计算与分析奠定了基础。
(3)基于火箭橇-轨道耦合动力学模型,采用面象对象技术Visual C++6.0开发了橇-轨耦合动力学计算软件RSTdyn,其动力学模型求解算法采用自适应步长Runge-Kutta-Fehlberg方法；以国内外现有相关火箭橇-轨道系统分析与试验结果为基础,对火箭发动机推力模型、轨道不平顺Blackman-Tukey (B-T)重构方法、火箭橇气动参数计算流体力学(CFD)获取方法、靴-轨冲击参数有限元分析(FEA)获取方法、火箭橇-刚性轨道耦合动力学模型及橇-轨耦合动力学计算软件RSTdyn进行了验证。研究表明,所建立动力学模型、参数获取方法及计算软件,具有良好的可靠性和可信度,可以应用于新火箭橇-轨道系统的分析与设计。
(4)利用火箭橇-轨道耦合动力学模型与计算软件RSTdyn,对某单轨火箭橇-轨道系统进行了耦合动力学响应的应用研究。在发动机星形装药几何燃烧规律的基础上推导了该火箭橇质心相对矢径、运动速度与加速度及转动惯量的计算公式。采用CAD、FEA、CFD及B-T等方法获得了单轨火箭橇-轨道系统参数,计算得到了橇-轨系统的加速度、速度、位移、接触力等动态响应结果,并与其它方法结果进行了对比,最后研究了靴-轨间隙、轨道不平顺及地面风速等三个参数对系统响应的影响,总结得到了相关动态响应规律。研究表明,火箭橇低速运动时,呈现出低频振动特性且随着火箭橇速度的增加其振动减弱；火箭橇高速运动时,则呈现出高频振动特性且随着火箭橇速度的增加其振动不断加强；钢轨、轨枕构成的轨道,呈现高频振动特性,随着火箭橇速度的增加其振动不断加强；轨道缓冲作用使得橇-轨动态接触力比准静态接触力更小,按准静态方法设计的火箭橇安全系数较高,可进一步优化减轻火箭橇重量；火箭橇设计时应避开动态高频振动段,与轨道长程不平顺PSD量纲分析法得出的结论一致；靴-轨间隙、轨道不平顺对动态响应影响较大,系统设计时应选取一个与橇-轨匹配的合理值,而地面风速则影响较小,设计时可以忽略该因素。
所采用的方法和得到的结果可以满足火箭橇-轨道系统设计与分析需要,通过研究加深了对高速火箭橇-轨道系统这一动态地面设备的认识,研究成果成功应用到了实际设备的工程研制之中。
The coupled dynamics of high speed rocket sled-track system is researched in detail, which is one type of large ground equipments between indoor and outdoor test. The irregularity of high precision test track and its influences on rocket sled are studied firstly. Then the general models are established for rocket sled-track coupled nonlinear dynamics, which are derived from dynamics theories. The computation software RSTdyn (Rocket Sled-Track dynamics) for rocket sled-track coupled dynamics is developed on object oriented technique. The getparms methods, system coupled dynamics models and computation codes are validated. Finally the coupled dynamics are applied to one monorail rocket sled-track system. The main works are as follows:
(1) According as the method of track random irregularity analysis, the USA HHSTT track testing random irregularity Power Spectrum Density (PSD) curves are processed using C++ to gain the high precision track PSD functions and parameters by Particle Swarm Optimization method. The influences of track short range irregularities to sled are theoretically analyzed by velocity method and motion method; the PSD dimension method is put forward for long range rail irregularities affecting sled; the results of three methods are compared. These researches show that: the high precision track irregularities have clearer high frequent character, smaller irregularity amplitude, more concentrative high frequent powers and better regularity; with rocket sled velocity increasing, the long and short range irregularity magnitudes are smaller, the wave lengths are longer, the track precisions are higher, which are needed by track; rocket sled design should avoid the disturber of track high frequent short wave.
(2) On the basis of rocket sled moving on track process, the dynamics coordinates are established for rocket sled-track system by relative coordinate method and transformed by direction cosine matrix. The mechanical analyses are carried out for rocket sled, rail and rail sleep by vector mechanics Newton-Euler method. The general models of rocket sled coupled track dynamics are derived by dynamics theories, which consider the nonlinear factors such as aerodynamics, ground winds, rocket thrusts, collision contact forces, impact braking forces and gaps of sled shoes to rail. The mathematical equations of dynamics are gained by the types of vector, matrix and scalar, which support the computation of the rocket sled-track system dynamical responses.
(3) Based on the rocket sled-track coupled dynamics model, the dynamics computation codes are developed by object oriented Visual C++6.0, which solves the equations using self-adaption step algorithm of Runge-Kutta-Fehlber. The rocket motor thrusts model, track irregularity samples reconstruction method of Blackman-Tukey (B-T), sled aerodynamics coefficient obtaining method of computation fluid dynamics (CFD), getparms method of finite element analysis (FEA) for sled shoes impacting to rail, system coupled dynamics model and RSTdyn codes are validated by analysis and test results of existing rocket sled-track system. These researches show that:the dynamics model, getparms methods and codes have well reliability and credibility, which can be used in new rocket sled-track system analysis and design.
(4) The dynamical responses of a certain monorail rocket sled-track system are gained by rocket sled-track coupled dynamics models and RSTdyn codes. The relative radius vector, velocity, acceleration of rocket sled centroid and inertia moments are formulated by rocket motor charge geometric burning law. The parameters of monorail rocket sled-track system are obtained by CAD, FEA, CFD and B-T methods. Then the dynamics results of sled and track are achieved such as accelerations, velocities, displacements and contact forces, which are compared with other methods'results. The parameters of shoe-rail gaps, track irregularities and ground winds are analyzed with the influences to system responses. Finally the dynamical characters of sled-track are analyzed with those results and relative dynamics laws are obtained. These researches show that:when sled runs under lower velocity, sled's vibration presents low frequency and weakens as its velocity increases; but when sled runs under higher velocity, its vibration presents high frequency and enhances with sled velocity arguments; the rail and sleep of track vibrate high frequently and enhance with its velocity grows; the dynamical contact forces are smaller than the quasi-static contact forces because of track's damping and sled designed by quasi-static method has higher safety factors, so the sled can be optimized to reduce weight hereunder; sled design should avoid the dynamical high frequent vibration, which is similar with the conclusion of track PSD dimension method; the gaps of shoe-rail and track irregularities affect the dynamical responses seriously, which should be chosen as proper values that match the sled-track during system design; ground winds have little influences to system and can be ignored.
The methods and results can meet the demand of rocket sled-track design and analysis. These researches enhance the cognition to the ground equipment sof rocket sled-track system. The achievements are applied to the engineering prototype developments.
(1)根据轨道不平顺功率谱密度分析方法,编制C++程序对美国HHSTT实测轨道不平顺功率谱密度(PSD)曲线进行了数据处理与分析,采用粒子群优化算法获得了高精度轨道的PSD函数及参量值；采用速度法和运动法对轨道短程不平顺影响火箭橇进行了计算与分析,提出了轨道长程不平顺影响火箭橇的PSD量纲分析法,完成了三种方法计算结果的对比分析。研究表明,高精度轨道不平顺高频特性更为明显、不平顺幅值更小、功率集中在高频段、平顺性更好,火箭橇速度越高要求的轨道长程与短程不平顺度的数值越小、波长越大,轨道建造的精度要求亦越高；火箭橇设计时应首先避开轨道的短波高频干扰段。
(2)根据火箭橇在轨道上运动的物理过程,首先运用相对坐标法建立了火箭橇-轨道系统的动力学坐标系,采用方向余弦矩阵实现了各坐标系间的转换；然后运用矢量力学Newton-Euler方法对火箭橇、钢轨与轨道枕板进行了受力分析,考虑了系统所受到的气动力、风速、火箭推力、碰撞接触力、冲击制动力、靴轨间隙等非线性因素；运用动力学相关基础理论推导建立了火箭橇-轨道耦合动力学一般模型,获得相应的动力学矢量、矩阵和标量形式的数学方程组。所建立的动力学模型为火箭橇-轨道系统动力学响应的计算与分析奠定了基础。
(3)基于火箭橇-轨道耦合动力学模型,采用面象对象技术Visual C++6.0开发了橇-轨耦合动力学计算软件RSTdyn,其动力学模型求解算法采用自适应步长Runge-Kutta-Fehlberg方法；以国内外现有相关火箭橇-轨道系统分析与试验结果为基础,对火箭发动机推力模型、轨道不平顺Blackman-Tukey (B-T)重构方法、火箭橇气动参数计算流体力学(CFD)获取方法、靴-轨冲击参数有限元分析(FEA)获取方法、火箭橇-刚性轨道耦合动力学模型及橇-轨耦合动力学计算软件RSTdyn进行了验证。研究表明,所建立动力学模型、参数获取方法及计算软件,具有良好的可靠性和可信度,可以应用于新火箭橇-轨道系统的分析与设计。
(4)利用火箭橇-轨道耦合动力学模型与计算软件RSTdyn,对某单轨火箭橇-轨道系统进行了耦合动力学响应的应用研究。在发动机星形装药几何燃烧规律的基础上推导了该火箭橇质心相对矢径、运动速度与加速度及转动惯量的计算公式。采用CAD、FEA、CFD及B-T等方法获得了单轨火箭橇-轨道系统参数,计算得到了橇-轨系统的加速度、速度、位移、接触力等动态响应结果,并与其它方法结果进行了对比,最后研究了靴-轨间隙、轨道不平顺及地面风速等三个参数对系统响应的影响,总结得到了相关动态响应规律。研究表明,火箭橇低速运动时,呈现出低频振动特性且随着火箭橇速度的增加其振动减弱；火箭橇高速运动时,则呈现出高频振动特性且随着火箭橇速度的增加其振动不断加强；钢轨、轨枕构成的轨道,呈现高频振动特性,随着火箭橇速度的增加其振动不断加强；轨道缓冲作用使得橇-轨动态接触力比准静态接触力更小,按准静态方法设计的火箭橇安全系数较高,可进一步优化减轻火箭橇重量；火箭橇设计时应避开动态高频振动段,与轨道长程不平顺PSD量纲分析法得出的结论一致；靴-轨间隙、轨道不平顺对动态响应影响较大,系统设计时应选取一个与橇-轨匹配的合理值,而地面风速则影响较小,设计时可以忽略该因素。
所采用的方法和得到的结果可以满足火箭橇-轨道系统设计与分析需要,通过研究加深了对高速火箭橇-轨道系统这一动态地面设备的认识,研究成果成功应用到了实际设备的工程研制之中。
The coupled dynamics of high speed rocket sled-track system is researched in detail, which is one type of large ground equipments between indoor and outdoor test. The irregularity of high precision test track and its influences on rocket sled are studied firstly. Then the general models are established for rocket sled-track coupled nonlinear dynamics, which are derived from dynamics theories. The computation software RSTdyn (Rocket Sled-Track dynamics) for rocket sled-track coupled dynamics is developed on object oriented technique. The getparms methods, system coupled dynamics models and computation codes are validated. Finally the coupled dynamics are applied to one monorail rocket sled-track system. The main works are as follows:
(1) According as the method of track random irregularity analysis, the USA HHSTT track testing random irregularity Power Spectrum Density (PSD) curves are processed using C++ to gain the high precision track PSD functions and parameters by Particle Swarm Optimization method. The influences of track short range irregularities to sled are theoretically analyzed by velocity method and motion method; the PSD dimension method is put forward for long range rail irregularities affecting sled; the results of three methods are compared. These researches show that: the high precision track irregularities have clearer high frequent character, smaller irregularity amplitude, more concentrative high frequent powers and better regularity; with rocket sled velocity increasing, the long and short range irregularity magnitudes are smaller, the wave lengths are longer, the track precisions are higher, which are needed by track; rocket sled design should avoid the disturber of track high frequent short wave.
(2) On the basis of rocket sled moving on track process, the dynamics coordinates are established for rocket sled-track system by relative coordinate method and transformed by direction cosine matrix. The mechanical analyses are carried out for rocket sled, rail and rail sleep by vector mechanics Newton-Euler method. The general models of rocket sled coupled track dynamics are derived by dynamics theories, which consider the nonlinear factors such as aerodynamics, ground winds, rocket thrusts, collision contact forces, impact braking forces and gaps of sled shoes to rail. The mathematical equations of dynamics are gained by the types of vector, matrix and scalar, which support the computation of the rocket sled-track system dynamical responses.
(3) Based on the rocket sled-track coupled dynamics model, the dynamics computation codes are developed by object oriented Visual C++6.0, which solves the equations using self-adaption step algorithm of Runge-Kutta-Fehlber. The rocket motor thrusts model, track irregularity samples reconstruction method of Blackman-Tukey (B-T), sled aerodynamics coefficient obtaining method of computation fluid dynamics (CFD), getparms method of finite element analysis (FEA) for sled shoes impacting to rail, system coupled dynamics model and RSTdyn codes are validated by analysis and test results of existing rocket sled-track system. These researches show that:the dynamics model, getparms methods and codes have well reliability and credibility, which can be used in new rocket sled-track system analysis and design.
(4) The dynamical responses of a certain monorail rocket sled-track system are gained by rocket sled-track coupled dynamics models and RSTdyn codes. The relative radius vector, velocity, acceleration of rocket sled centroid and inertia moments are formulated by rocket motor charge geometric burning law. The parameters of monorail rocket sled-track system are obtained by CAD, FEA, CFD and B-T methods. Then the dynamics results of sled and track are achieved such as accelerations, velocities, displacements and contact forces, which are compared with other methods'results. The parameters of shoe-rail gaps, track irregularities and ground winds are analyzed with the influences to system responses. Finally the dynamical characters of sled-track are analyzed with those results and relative dynamics laws are obtained. These researches show that:when sled runs under lower velocity, sled's vibration presents low frequency and weakens as its velocity increases; but when sled runs under higher velocity, its vibration presents high frequency and enhances with sled velocity arguments; the rail and sleep of track vibrate high frequently and enhance with its velocity grows; the dynamical contact forces are smaller than the quasi-static contact forces because of track's damping and sled designed by quasi-static method has higher safety factors, so the sled can be optimized to reduce weight hereunder; sled design should avoid the dynamical high frequent vibration, which is similar with the conclusion of track PSD dimension method; the gaps of shoe-rail and track irregularities affect the dynamical responses seriously, which should be chosen as proper values that match the sled-track during system design; ground winds have little influences to system and can be ignored.
The methods and results can meet the demand of rocket sled-track design and analysis. These researches enhance the cognition to the ground equipment sof rocket sled-track system. The achievements are applied to the engineering prototype developments.
引文
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