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Article(id=1241408877573493198, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241408875602178849, articleNumber=null, orderNo=null, doi=10.16579/j.issn.1001.9669.2025.08.012, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1702915200000, receivedDateStr=2023-12-19, revisedDate=1709395200000, revisedDateStr=2024-03-03, acceptedDate=null, acceptedDateStr=null, onlineDate=1773904540674, onlineDateStr=2026-03-19, pubDate=1755187200000, pubDateStr=2025-08-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773904540674, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773904540674, creator=13701087609, updateTime=1773904540674, updator=13701087609, issue=Issue{id=1241408875602178849, tenantId=1146029695717560320, journalId=1227999626482147330, year='2025', volume='47', issue='8', pageStart='1', pageEnd='174', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773904540204, creator=13701087609, updateTime=1773904658798, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241409373071798309, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241408875602178849, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241409373071798310, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241408875602178849, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=101, endPage=107, ext={EN=ArticleExt(id=1241408883130946074, articleId=1241408877573493198, tenantId=1146029695717560320, journalId=1227999626482147330, language=EN, title=Research on response characterstic and dynamic modeling of launch vehicle under the cold launch mode, columnId=1228282192162390694, journalTitle=Journal of Mechanical Strength, columnName=Experimental Research·Testing Technology, runingTitle=null, highlight=null, articleAbstract=

To accurately simulate the complicated load transfer pattern of the launch device under cold launch mode, the rigid-flexible coupling dynamic simulation method was adopted to analyze the dynamic response of a launch vehicle, the structural strength was also verified. The finite element flexible body was introduced and a multi-rigid-flexible-body dynamic simulation model of a launch vehicle was constructed. Accuracy of the model was verified by the actual launch test. The influence law between the vibration response and stress state of the launch vehicle and the launch angle was further analyzed. The results show that amplitudes of the transmitted load and stress inside the launcher will reduce when the launch angle is close to 90°. The modeling and analysis approaches proposed in this study can effectively support the optimal design of the launch device.

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ZHOU Yuanchun, E-mail：
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为准确模拟冷发射模式下发射装置内部复杂的载荷传递关系，基于刚柔耦合动力学仿真方法分析车载发射系统在发射载荷下的动态响应，校验结构强度。在采用刚体和模态柔性体的基础上引入有限元柔性体，构建了某型发射车刚柔耦合动力学仿真模型。结合实车冷发射试验数据验证了模型的准确性，并进一步分析了不同发射角度对发射装置振动响应与应力状态的影响规律。结果表明，发射角度接近90°有助于减小发射装置内的载荷传递、降低发射筒附近结构的应力幅值。该研究所采用的建模与分析方法可为发射装置的改进设计提供参考。

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周元春，男，1986年生，江苏东台人，硕士，高级工程师；主要研究方向为发射装置设计与动力学仿真分析；E-mail：。
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周迪，男，1994年生，江苏常熟人，博士，工程师；主要研究方向为发射装置设计与动力学仿真分析；E-mail：。

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周迪，男，1994年生，江苏常熟人，博士，工程师；主要研究方向为发射装置设计与动力学仿真分析；E-mail：。

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周迪，男，1994年生，江苏常熟人，博士，工程师；主要研究方向为发射装置设计与动力学仿真分析；E-mail：。

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1.轮式车辆Wheeled vehicle；2.调平油缸Hydro-cylinder for levelling；3.起竖油缸Hydro-cylinder for erecting；4.回转支座Revolving bed；

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Parameters used in the simulation

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参数 Parameter仿真输入值
Value in simulation
接触刚度系数
Contact stiffness coefficient/（N/mm）		7.5×104
接触刚度指数Contact stiffness index1.5
接触阻尼系数
Contact damping coefficient/（N·s/mm）		16
动态摩擦因数Dynamic friction coefficient0.1
最大穿透深度
Maximum penetration depth/mm		0.1
最大步长因数Maximum step size100
油缸刚度系数
Stiffness coefficient of hydro-cylinders/（N/mm）		5.0×104
油缸阻尼系数
Damping coefficient of hydro-cylinders/（N·s/mm）		25
缓冲装置缓冲载荷均值
Average buffering load of buffer devices/N		2.0×105
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模型参数设置

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参数 Parameter仿真输入值
Value in simulation
接触刚度系数
Contact stiffness coefficient/（N/mm）		7.5×104
接触刚度指数Contact stiffness index1.5
接触阻尼系数
Contact damping coefficient/（N·s/mm）		16
动态摩擦因数Dynamic friction coefficient0.1
最大穿透深度
Maximum penetration depth/mm		0.1
最大步长因数Maximum step size100
油缸刚度系数
Stiffness coefficient of hydro-cylinders/（N/mm）		5.0×104
油缸阻尼系数
Damping coefficient of hydro-cylinders/（N·s/mm）		25
缓冲装置缓冲载荷均值
Average buffering load of buffer devices/N		2.0×105
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Maximum stresses and positions of the launcher and guideway

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发射角度
Launching angle/（°）		发射架 Launcher导轨 Guideway
最大应力
Maximum stress/MPa		位置
Position		最大应力
Maximum stress/MPa		位置
Position
86140.3导轨螺栓孔
Bolt hole of the guideway		652.9螺栓孔
Bolt hole
8877.0导轨螺栓孔
Bolt hole of the guideway		158.4螺栓孔
Bolt hole
9045.8起竖支座
Erecting support		119.8螺栓孔
Bolt hole
9263.1下放油缸支座
Support of hydro-cylinder for touchdown		204.3螺栓孔
Bolt hole
9483.5下放油缸销轴
Pin shaft of hydro-cylinder for touchdown		531.6螺栓孔
Bolt hole
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发射架与导轨的最大应力与位置

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发射角度
Launching angle/（°）		发射架 Launcher导轨 Guideway
最大应力
Maximum stress/MPa		位置
Position		最大应力
Maximum stress/MPa		位置
Position
86140.3导轨螺栓孔
Bolt hole of the guideway		652.9螺栓孔
Bolt hole
8877.0导轨螺栓孔
Bolt hole of the guideway		158.4螺栓孔
Bolt hole
9045.8起竖支座
Erecting support		119.8螺栓孔
Bolt hole
9263.1下放油缸支座
Support of hydro-cylinder for touchdown		204.3螺栓孔
Bolt hole
9483.5下放油缸销轴
Pin shaft of hydro-cylinder for touchdown		531.6螺栓孔
Bolt hole
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冷发射模式下发射车动力学建模与响应特性研究
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周迪 1 , 周元春 1 , 王惠娟 1, 2 , 马张健 1 , 蒋圣鹏 1
机械强度 | 实验研究·测试技术 2025,47(8): 101-107
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机械强度 | 实验研究·测试技术 2025, 47(8): 101-107
冷发射模式下发射车动力学建模与响应特性研究
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周迪1 , 周元春1 , 王惠娟1, 2, 马张健1, 蒋圣鹏1
作者信息
  • 1.上海机电工程研究所，上海　201109
  • 2.南京航空航天大学 航天学院，南京　210016

    • 周迪，男，1994年生，江苏常熟人，博士，工程师；主要研究方向为发射装置设计与动力学仿真分析；E-mail：。

通讯作者:

周元春，男，1986年生，江苏东台人，硕士，高级工程师；主要研究方向为发射装置设计与动力学仿真分析；E-mail：。
Research on response characterstic and dynamic modeling of launch vehicle under the cold launch mode
Di ZHOU1 , Yuanchun ZHOU1 , Huijuan WANG1, 2, Zhangjian MA1, Shengpeng JIANG1
Affiliations
  • 1.Shanghai Mechatronic Engineering Institute, Shanghai 201109, China
  • 2.College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
出版时间: 2025-08-15 doi: 10.16579/j.issn.1001.9669.2025.08.012
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摘要
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为准确模拟冷发射模式下发射装置内部复杂的载荷传递关系，基于刚柔耦合动力学仿真方法分析车载发射系统在发射载荷下的动态响应，校验结构强度。在采用刚体和模态柔性体的基础上引入有限元柔性体，构建了某型发射车刚柔耦合动力学仿真模型。结合实车冷发射试验数据验证了模型的准确性，并进一步分析了不同发射角度对发射装置振动响应与应力状态的影响规律。结果表明，发射角度接近90°有助于减小发射装置内的载荷传递、降低发射筒附近结构的应力幅值。该研究所采用的建模与分析方法可为发射装置的改进设计提供参考。

冷发射  /  发射车  /  刚柔耦合动力学  /  仿真  /  振动

To accurately simulate the complicated load transfer pattern of the launch device under cold launch mode, the rigid-flexible coupling dynamic simulation method was adopted to analyze the dynamic response of a launch vehicle, the structural strength was also verified. The finite element flexible body was introduced and a multi-rigid-flexible-body dynamic simulation model of a launch vehicle was constructed. Accuracy of the model was verified by the actual launch test. The influence law between the vibration response and stress state of the launch vehicle and the launch angle was further analyzed. The results show that amplitudes of the transmitted load and stress inside the launcher will reduce when the launch angle is close to 90°. The modeling and analysis approaches proposed in this study can effectively support the optimal design of the launch device.

Cold launch  /  Launch vehicle  /  Multi-rigid-flexible-body dynamic  /  Simulation  /  Vibration
周迪, 周元春, 王惠娟, 马张健, 蒋圣鹏. 冷发射模式下发射车动力学建模与响应特性研究. 机械强度, 2025 , 47 (8) : 101 -107 . DOI: 10.16579/j.issn.1001.9669.2025.08.012
Di ZHOU, Yuanchun ZHOU, Huijuan WANG, Zhangjian MA, Shengpeng JIANG. Research on response characterstic and dynamic modeling of launch vehicle under the cold launch mode[J]. Journal of Mechanical Strength, 2025 , 47 (8) : 101 -107 . DOI: 10.16579/j.issn.1001.9669.2025.08.012
正文
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0　引言
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利用辅助动力系统使飞行器到达一定高度，飞行器自身发动机点火并按程序飞行的发射模式称为冷发射模式。冷发射模式有助于减少燃料消耗，且发动机产生的高温燃气无须导流、排焰，不会对发射场坪或发射装置产生烧蚀，有利于选择发射阵地和缩小阵地规模，提高发射隐蔽性与快速撤收能力[1]。车载发射则进一步提高了发射的机动性与灵活性，因而车载冷发射逐渐成为了国内外陆基机动发射的重要研究方向。
在冷发射模式下，发射筒内的燃气发生装置产生高压气体，气体通过推弹机构做功将飞行器发射出筒。若提弹机构随飞行器一同发射出筒，将对发射阵地及周围区域造成危害，故发射筒前端通常设置缓冲制动装置对提弹机构的运动进行缓冲吸能[2-3]。在缓冲装置的冲击下，发射筒将产生一定的动态响应，若用于安装发射筒的结构刚度过大，将引起发射系统内结构的破坏。因此，有必要针对发射装置中发射筒的安装结构开展研究，分析其在冲击载荷下的载荷传递规律与动力学响应特征，由此支撑发射装置的结构设计。
目前，针对武器系统发射动力学的研究，主要基于多刚体动力学理论，联合有限元算法求解得到的结构模态信息，开展刚柔耦合动力学仿真，对于结构变形较小或结构变形对关注对象影响不显著的部件采用刚性体进行定义，而对于结构变形影响较大或需要分析其变形模式的则采用柔性体定义，以提高仿真精度[4]。COCHRAN等[5]对火箭弹的发射过程进行了动力学仿真，分析了弹体在发射与飞行过程中的偏角。李敏等[6]基于刚柔耦合模型，开展了发射过程的振动响应分析，研究了发射系统各因子对发射筒姿态的影响程度。高宇等[7]研究了井基冷发射的动力学过程，重点分析了适配器排布、强度与风力等级对飞行器出筒姿态的影响并分类讨论了发射安全性与发射精度。孙船斌等[8]建立了包括起竖系统、发射系统及发射车-地面的冷发射动力学物理模型和振动方程，揭示了适配器刚度、液压支腿刚度与场坪坡度对飞行器出筒姿态的影响规律。
发射引起的结构运动涉及结构接触变形与冲击载荷传递[9]，不同发射角度下结构载荷传递特性及其对承载结构的性能要求将发生变化。以上研究大多聚焦于不同发射模式下，发射装置-飞行器的结构参数、发射场坪状态、风载等因素对飞行器出筒姿态的影响，对于发射过程中，发射筒与附近结构间的载荷传递以及附近结构的动力学响应鲜有报道。
本文针对车载冷发射模式，在多刚体模型中同时引入模态柔性体与有限元柔性体，建立了发射装置刚柔耦合动力学模型，由此考虑发射过程中发射装置内的载荷传递与应力状态，结合发射车冷发射试验数据对该模型进行了验证，分析了不同发射角度对发射装置动力学响应的影响规律。本文的研究方法与结果对验证发射装置结构强度性能、优化结构设计具有一定的参考价值。
1　刚柔耦合系统动力学理论基础
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1.1　多刚体系统动力学方程
合适的坐标系是分析发射装置不同结构间动力学响应与载荷传递的基础，相对坐标系法[10]315-396广泛应用于构建多刚体系统的动力学方程，能够准确描述系统的动力学行为。在惯性参考坐标系（XYZ）下，通过运动副di1j1连接的两刚体（i）和（j）如图1所示。（xiyizi）与（xjyjzj）坐标系分别为随刚体运动的坐标系，刚体的坐标系相对于惯性坐标系的速度与虚位移可定义为
相对速度和虚位移可定义为
式中，A为坐标系（xyz）相对于（XYZ）的转换矩阵。各构件在相对与绝对坐标系下的速度关系为
式中，B为的系数集合矩阵，则
式中，nc和nr分别为绝对坐标系和相对坐标系中的坐标数。
根据速度变换法可得到系统的动力学方程
式中，Φ为雅可比约束矩阵；λ为拉格朗日乘子；M为质量矩阵；Q为力向量。
1.2　刚柔耦合系统动力学方程
为模拟结构间载荷较大的接触过程、同时变形等动力学响应，多柔性体动力学（Multi Flexible Body Dynamic, MFBD）[10]315-396[11]在多刚体系统动力学的基础上耦合了有限元理论，通过构建刚柔耦合系统动力学方程，同时求解刚体运动以及基于有限元法的离散单元节点与刚体间的相互作用。式（8）所示的刚体运动方程可进一步写为
式中，r为刚体的数量；g为刚体间相互关系的数量；h为刚体和柔性体节点间相互关系的数量。刚体间约束方程可由刚体的广义坐标qr表示
相似地，柔性体运动方程可表示为
式中，e为柔性体节点数量；qe为柔性体节点的广义坐标。
刚柔耦合系统动力学的系统矩阵可用式（12）表示，利用稀疏矩阵求解器可对其进行求解。
式中，p为柔性体节点间相互关系的数量。
2　发射车刚柔耦合动力学系统建模
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2.1　发射车结构组成与工作原理
某型发射车主要由轮式车辆、发射架、发射筒弹、液压系统等组成，如图2所示。轮式车辆将各功能进行集成，供各子系统安装固定。液压系统安装于车辆车架上，车辆与发射架等结构在液压系统驱动下，可实现姿态的调节。发射架主要由主体结构、导轨、托架与下放油缸等组成。
在储存或行军状态下，发射筒在导轨与托架的约束作用下固定于发射架上。发射前，发射架在起竖油缸的支撑作用下沿回转支座转动，在达到既定发射角度后，起竖油缸锁止（本文中，发射角度定义为发射筒发射方向与-X轴之间夹角）；随后，下放油缸伸展，发射筒随托架沿导轨向下平移，在发射筒触地后，下放油缸锁止，发射车完成发射前的姿态调整，进入发射准备状态。此时，发射筒主要由地面支撑，发射筒与发射车之间仅通过导轨连接，发射筒可沿导轨平移，避免发射冲击引起的发射筒响应对其连接结构造成破坏。
发射车采用冷发射模式，发射时，燃气发生器在短时间内向发射筒加压，燃气推动尾座与飞行器沿发射筒轴向运动[12]。尾座运动至发射筒筒口时，冲击缓冲装置，缓冲装置基于金属塑性变形进行吸能，使尾座减速并保留于发射筒内，飞行器在惯性作用下继续运动并发射出筒。本文主要研究上述发射过程中，由发射载荷引起的发射架等结构的响应。
2.2　模型简化及假设
根据冷发射系统的物理过程，基于动力学仿真软件RecurDyn构建发射车刚柔耦合动力学模型，本文重点分析发射冲击对发射架的影响，对发射车做如下简化[13]：
1）将车辆底盘动力总成（如发动机、变速箱、分动器）、车桥、悬架等子系统简化为配重质量，与车架固定连接。
2）所有铰约束均为理想约束。
3）将车架与发射架定义为柔性体，车辆其余结构定义为刚体。
4）将地面定义为刚体，在发射筒尾部与地面之间定义接触作用，模拟发射筒与地面间的载荷传递。
5）起竖油缸、下放油缸与调平支腿的内外缸体间通过“弹簧-阻尼”单元进行连接。
6）不考虑燃气发生器点火与气体扩散的过程，将实测压力数据根据筒内截面积转为推力直接施加于尾座上。
7）不考虑尾座冲击发射筒筒口缓冲装置使其产生塑性变形的过程，根据有限元仿真计算所得缓冲载荷，定义尾座与筒口之间的双向力，模拟缓冲装置对尾座的约束作用。
2.3　柔性体建模
为评估发射筒的运动对发射架结构的影响，需准确模拟发射筒与导轨间的接触作用，同时考虑发射架自身的动力学响应情况，因此需对发射架、导轨等结构进行柔性化定义。
考虑到发射架主体结构尺寸较大（单边尺寸3 m以上），且与车架通过铰链连接，与导轨通过固定副连接，不存在接触定义，采用模态柔性体法进行建模，以“四边形壳单元”为主对发射架进行有限元离散化，适用于“小变形”结构的仿真，且计算效率高[10]315-396。
在发射过程中，发射筒在燃气压力与尾座冲击的作用下，将沿发射架导轨产生滑移运动，发射筒支腿与导轨间的接触作用将发射冲击传递至发射架进而传递至发射车，采用有限元柔性体法定义发射架导轨，利用有限元节点的相对变形描述柔性体的响应，可用于描述柔性体的接触及其引起的变形积累等非线性力学行为，对接触与载荷传递的计算精度高。
在动力学仿真中，接触参数的设置将直接影响仿真过程的稳定性与计算结果的准确性，接触力定义为
式中，K为刚度系数；δ为穿透深度；k为刚度指数；C为阻尼系数；为穿透速度。模型中接触力参数[14]与各液压油缸弹簧阻尼等参数设置如表1所示。
3　基于弹射试验的模型验证
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为验证所构建刚柔耦合动力学模型的准确性，将仿真所得结果与实车冷发射试验所测数据进行对比分析。在试验或实战条件下，为避免飞行器下落击中发射装置，通常需选取一大于90°的发射角度以提高发射安全性，本文仿真与试验中发射车发射角度均为92°。在试验过程中，测量了飞行器的运动状态、发射筒的位移与发射架导轨的振动加速度响应，在仿真模型中的相应位置设置测点，开展仿真计算。
将仿真与试验中的点火时刻定义为时间原点，统一时序。飞行器轴向加速度响应如图3所示（图3中统一去除重力加速度），在0.06 s内，加速度响应迅速增长至最大值，该过程对应了尾座在发射筒内尚未产生明显位移，而燃气压力迅速增大的过程。随后，尾座逐渐沿发射筒轴线向上运动，燃气压力的空间体积逐渐增大，压力逐渐降低，飞行器的加速度随之下降。在0.5 s左右，尾座运动至发射筒筒口，在缓冲装置作用下逐渐减速，此时飞行器不再受到尾座的推力作用，与发射筒分离并做惯性运动。试验与仿真中，飞行器最大轴向过载分别为10.15g和10.02g（g=9.8m/s2），相对误差为1.29%。
发射筒与发射架之间的载荷通过固定发射筒的导轨传递，发射筒的动态响应决定了发射架的响应情况。发射筒垂向位移曲线如图4所示。由图4可知，在发射后，发射筒均首先向下产生了一定位移量。在试验中，垂向位移通过布置于发射筒底部的位移传感器进行测量，发射筒底部刚度较高，但在发射冲击载荷作用下，发射筒底部仍将产生一定的弹性变形，同时，发射载荷将减小发射筒与地面之间的间隙。而在仿真中，若将发射筒定义为柔性体以模拟冲击载荷下的微小形变将进一步增大计算成本，因此将发射筒与地面均简化为刚体，两者之间的相对运动（侵入量）则受接触刚度与阻尼影响，两者数值越大，发射筒向下位移越小。由图4可知，两者幅值与趋势较为接近，仿真中的接触定义可在一定程度上模拟初始时刻的相对运动。
在0.5 s时刻，尾座冲击发射筒筒口的缓冲装置，发射筒在该载荷作用下向上运动，当运动至最高点后发射筒沿导轨向下滑动、与地面碰撞（0.85 s）、回弹，数次反复后发射筒进入静止状态。发射筒的首次垂向位移量最大，试验与仿真结果分别为110.8 mm与107.6 mm，相对误差为2.89%。整体而言，发射筒的垂向位移曲线趋势一致性较高，且对发射架影响较大的首次“跳动”最大位移量、位移的开始与再次触地时刻十分接近。
发射架与导轨在冲击载荷的作用下将产生动态响应，对比分析导轨的加速度响应，如图5所示。根据试验数据，加速度曲线主要产生了4个波峰，结合发射筒位移响应的时序可知，各次峰值依次对应：点火后发射筒下沉、尾座制动引起发射筒首次向上运动、发射筒首次落地以及二次落地。仿真所得加速度响应的数个波峰与试验数据基本一致。此外，由导轨的振动响应可知，发射架在点火后1.5~2 s恢复至静止状态。由于加速度响应具有随机性，以采样总数的10%为窗口宽度，计算导轨加速度响应2 s内各时刻的浮动均方根（Root Mean Square, RMS）值，为
式中，N为2 s内采样总数；yi为各采样点幅值。如图6所示，导轨加速度RMS波峰主要位于0.5~1.2 s，可见发射筒首次向上运动与触地使导轨产生了较大的振动响应。在2 s内，试验与仿真所得导轨加速度RMS分别为1.06g和0.98g，相对误差为7.55%。
发射架与导轨的局部应力状态分别如图7、图8所示，根据计算结果，发射架的最大应力约为63.1 MPa，而导轨最大应力约为204.3 MPa。由于发射筒与发射架之间采用了可产生相对滑移的“滑块-导轨”结构，在冲击载荷下发射筒与发射架未产生刚性碰撞，因而发射架与导轨的最大应力较小，最大应力主要出现在连接结构附近。
4　发射角度对发射装置动力学响应的影响
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前文针对单一的发射角度（92°）开展了试验与仿真分析，而在不同的发射角度下，发射筒的姿态及其对发射架导轨传递的载荷将发生变化。其主要表现为：若发射车高度不变并保持发射筒后盖触地，当发射角逐渐增加时，发射筒相对于发射架的初始位置逐渐升高；当发射角度为90°时，发射筒后盖垂直于地面，发射筒后盖与地面接触面积最大，其余角度时接触面积减小；当发射角度由锐角增大至钝角时，发射架在发射前后稳定状态下，逐渐由受压缩载荷转变为受拉伸载荷。为进一步探究发射角度变化时发射冲击对发射架的影响，保持模型其余参数不变，分别设置发射角度为86°、88°、90°与94°进行仿真计算，并与92°仿真的工况进行对比。
在不同发射角度下，发射筒均下放着地，但与地面间的接触位置不同，当发射角度越接近90°时，地面与发射筒间载荷的作用位置越接近中心。且在不同的发射角度下，导轨对发射筒的负载状态将发生变化，这将改变发射筒所受摩擦阻力的大小。由图9可知，在上述因素的综合影响下，发射筒沿导轨产生的位移量与发射角度呈非线性关系，相对于86°，发射角度为88°时位移增长了31.4%。若发射筒在导轨内可用的位移较小，发射筒在缓冲载荷的作用下将与发射架导轨发生碰撞。
以采样总数的10%为窗口宽度，计算导轨加速度响应2 s内的浮动RMS，如图10所示。不同发射角度下，发射架导轨的振动响应主要集中于0.5~1.2 s，RMS波峰呈先减小后增大的趋势，尾座缓冲引起的冲击载荷与发射筒跳起后的触地是引起发射架振动的主要原因。
计算发射后2 s内发射筒与导轨间的垂向载荷与导轨加速度响应的RMS值如图11所示，传递的载荷与导轨振动响应趋势较为接近。当发射角度为90°时，发射筒主要沿竖直方向运动，发射筒缓冲与触地产生的冲击载荷主要沿发射筒轴向，发射架导轨对其约束作用较小；而当角度不等于90°时，发射筒缓冲与触地载荷引起的发射筒振动将对发射筒施加径向载荷，增大导轨所受到的冲击载荷。
将各算例下的结构最大应力汇总，如图12与表2所示，随着发射角度的变化，发射架主体结构与导轨的最大应力同样呈现先减小后增大的趋势。发射架主体结构的应力幅值较小，在不同算例下均不大于140.3 MPa。发射架主体结构功能复杂，其主要承力结构包括：安装导轨的平台、安装下放油缸的支座与销轴、发射架起竖转动支座以及行军时锁定发射架的支座（发射状态下处于自由状态）。根据发射角度的不同，发射架主体结构的最大应力产生位置也存在变化，但均出现在与其他结构的连接点或连接结构上。导轨产生的最大应力为119.8~652.9 MPa，波动范围较大，且均出现在用于安装导轨的螺栓孔附近。由此可见，当发射筒经导轨向发射架传递载荷时，螺栓连接点附近易产生应力集中，而过大或过小的发射角度将进一步增大应力。
5　结论
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通过构建发射车刚柔耦合动力学模型，开展了冷发射动力学仿真计算，分析了发射过程中发射架结构的响应特性，在此基础上研究了不同发射角度对发射装置动力学响应的影响规律，得到如下主要结论：
1）冷发射模式下，发射筒的运动将引起导轨及发射架的振动响应，为准确模拟持续数秒的发射过程与载荷传递过程，评估发射冲击对发射装置的影响，对发射车不同结构分别采用刚体、模态柔性体与有限元柔性体进行了刚柔耦合动力学建模与仿真。与试验数据相比，飞行器最大垂向加速度、发射筒弹跳高度与导轨加速度RMS误差分别为1.29%、2.89%与7.55%，有限元柔性体有效反映了结构间冲击载荷的传递，且能够分析冲击过程中的应力状态，所构建的模型具有较高的置信度。本文的建模方法为模拟飞行器冷发射过程中，冲击作用下的载荷传递与结构变形提供了有效参考。
2）发射架结构复杂、各部位功能差异较大，不同发射角度下最大应力主要出现于各承载结构附近，需合理考虑结构强度，避免因强度不足引起失效。在本研究中，导轨是发射筒向发射架传递冲击载荷的唯一路径，不同发射角度下发射筒相对于导轨的运动距离将产生变化，需根据计算结果合理设计导轨长度，避免因长度不足产生刚性碰撞。此外，导轨通过螺栓与发射架固定连接，导轨螺栓孔附近易出现应力集中的现象，需根据不同设计状态下的应力状态合理优化连接结构。
3）发射角度接近90°可减小发射架及导轨结构由发射载荷引起的振动与应力响应，而在试验或实战条件下，通常需选取一大于90°的发射角度以提高发射安全性。基于本文的研究可知，在考虑发射安全性的同时应根据设计需求合理选取发射角度，使其尽可能接近竖直状态，这对于减小发射装置应力，避免结构破坏，同时提高发射装置的轻量化水平具有积极的意义。
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2025年第47卷第8期
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doi: 10.16579/j.issn.1001.9669.2025.08.012
  • 接收时间：2023-12-19
  • 首发时间：2026-03-19
  • 出版时间：2025-08-15
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  • 收稿日期：2023-12-19
  • 修回日期：2024-03-03
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    1.上海机电工程研究所，上海　201109
    2.南京航空航天大学 航天学院，南京　210016

通讯作者:

周元春，男，1986年生，江苏东台人，硕士，高级工程师；主要研究方向为发射装置设计与动力学仿真分析；E-mail：。
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