Eigenvalue analysis of planar linear multibody system under conservative force based on the transfer matrix method

The linear multibody system transfer matrix method(LMSTMM)provides a powerful tool for analyzing the vibration characteristics of a mechanical system.However,the original LMSTMM cannot resolve the eigenvalues of the systems with ideal hinges(i.e.,revolute hinge,sliding hinge,spherical hinge,cylindrical hinge,etc.)or bodies under conservative forces due to the lack of the corresponding transfer matrices.This paper enables the LMSTMM to solve the eigenvalues of the planar multibody systems with ideal hinges or rigid bodies under conservative forces.For a rigid body,the transfer matrix can now consider coupling terms between forces and kinematic state perturbations.Also,conservative forces that contribute to the eigenvalues can be considered.Meanwhile,ideal hinges are introduced to LMSTMM,which enables the treatment of eigenvalues of general multibody systems using LMSTMM.Finally,the comparative analysis with ADAMS software and analytical solutions verifies the effectiveness of the proposed approach in this paper.

FREE VIBRATION ANALYSIS AND PHYSICAL PARAMETER IDENTIFICATION OF NON-UNIFORM BEAM CARRYING SPRING-MASS SYSTEMS

To analyze a multibody system composed of non-uniform beam and spring-mass subsystems, the model discretization is carried on by utilizing the finite element method（FEM）, the dynamic model of non-uniform beam is developed by using the transfer matrix method of multibody system（MS-TMM）, the transfer matrix of non-u- niform beam is derived, and the natural frequencies are computed. Compared with the numerical assembly method （NAM）, the results by MS-TMM have good agreement with the results by FEM, and are better than the results by NAM. When using the high precision method, the global dynamic equations of the complex multibody system are not needed and the orders of involved system matrices are decreased greatly. For the investigation on the re- verse problem of the physical parameter identification of multibody system, MS-TMM and the optimization tech- nology based on genetic algorithms（GAs） are combined and extended. The identification problem is exchanged for an optimization problem, and it is formulated as a global minimum solution of the objective function with respect to natural frequencies of multibody system. At last, the numerical example of non-uniform beam with attach- ments is discussed, and the identification results indicate the feasibility and the effectivity of the proposed aop- proach.

Dynamic model and simulation of aseismatic system about laser gyro strapdown inertial measure assembly based on MSTMM

The precision of the laser gyro used in tactical missiles is poor because of dithering frequency,actuating by vibration,shock and overload in dynamical environment.This paper introduces the transfer matrix method of the multibody system（MSTMM）,establishes the dynamic model of the laser gyro strapdown inertial measure assembly aseismatic system,and analyzes the precision affected by dithering of the laser gyro and shocking of the tactical missile.And the dynamic response of the laser gyro strapdown inertial measure assembly aseismatic system is obtained by simulating the multibody system model.The simulation result indicates a theoretical idea to design the vibration isolation for the laser gyro strapdown inertial measure assembly.

Novel sensitivity analysis method and dynamics optimization for multiple launch rocket systems

This study establishes the launch dynamics method,sensitivity analysis method,and multiobjective dynamic optimization method for the dynamic simulation analysis of the multiple launch rocket system(MLRS)based on the Riccati transfer matrix method for multibody systems(RMSTMM),direct differentiation method(DDM),and genetic algorithm(GA),respectively.Results show that simulation results of the dynamic response agree well with test results.The sensitivity analysis method is highly programming,the matrix order is low,and the calculation time is much shorter than that of the Lagrange method.With the increase of system complexity,the advantage of a high computing speed becomes more evident.Structural parameters that have the greatest influence on the dynamic response include the connection stiffness between the pitching body and the rotating body,the connection stiffness between the rotating body and the vehicle body,and the connection stiffnesses among 14^(#),16^(#),and 17^(#)wheels and the ground,which are the optimization design variables.After optimization,angular velocity variances of the pitching body in the revolving and pitching directions are reduced by 97.84%and 95.22%,respectively.

Transfer matrix method for multibody systems(Rui method) and its applications

The transfer matrix method for multibody systems, namely the "Rui method", is a new method for studying multibody system dynamics, which avoids the global dynamics equations of the system, keeps high computational speed, and allows highly formalized programming. It has been widely applied to scientific research and key engineering of lots of complex mechanical systems in 52 research directions. The following aspects regarding the transfer matrix method for multibody systems are reviewed systematically in this paper: history, basic principles, formulas, algorithm, automatic deduction theorem of overall transfer equation, visualized simulation and design software, highlights, tendency, and applications in 52 research directions in over 100 key engineering products.

Multibody system transfer matrix method:The past, the present, and the future

The multibody system transfer matrix method(MSTMM),a novel dynamics approach developed during the past three decades,has several advantages compared to conventional dynamics methods.Some of these advantages include avoiding global dynamics equations with a system inertia matrix,utilizing low‐order matrices independent of system degree of freedom,high computational speed,and simplicity of computer implementation.MSTMM has been widely used in computer modeling,simulations,and performance evaluation of approximately 150 different complex mechanical systems.In this paper,the following aspects regarding MSTMM are reviewed:basic theory,algorithms,simulation and design software,and applications.Future research directions and generalization to more applications in various fields of science,technology,and engineering are discussed.

Discrete time transfer matrix method for dynamics analysis of complex weapon systems

Efficient, precise dynamic modeling and analysis for complex weapon systems have become more and more important in their dynamic design and performance optimizing. As a new method developed in recent years, the discrete time transfer matrix method of multibody system is highly efficient for multibody system dynamics. In this paper, taking a shipboard gun system as an example, by deducing some new transfer equations of elements, the discrete time transfer matrix method of multibody sys- tem is used to solve the dynamics problems of complex rigid-flexible coupling weapon systems successfully. This method does not need the global dynamic equations of system and has the low order of system matrix, high computational efficiency. The proposed method has advantages for dynamic design of complex weapon systems, and can be carried over straightforwardly to other complex mechanical systems.

An efficient and modular modeling for launch dynamics of tubed rockets on a moving launcher

This paper develops a modular modeling and efficient formulation of launch dynamics with marching fire(LDMF)using a mixed formulation of the transfer matrix method for multibody systems(MSTMM)and Newton-Euler formulation.Taking a ground-borne multiple launch rocket systems(MLRS),the focus is on the launching subsystem comprising the rocket,flexible tube,and tube tail.The launching subsystem is treated as a coupled rigid-flexible multibody system,where the rocket and tube tail are treated as rigid bodies while the flexible tube as a beam with large motion.Firstly,the tube and tube tail can be elegantly handled by the MSTMM,a computationally efficient order-N formulation.Then,the equation of motion of the in-bore rocket with relative kinematics w.r.t.the tube using the Newton-Euler method is derived.Finally,the rocket,tube,and tube tail dynamics are coupled,yielding the equation of motion of the launching subsystem that can be regarded as a building block and further integrated with other subsystems.The deduced dynamics equation of the launching subsystem is not limited to ground-borne MLRS but also fits for tanks,self-propelled artilleries,and other air-borne and naval-borne weapons undergoing large motion.Numerical simulation results of LDMF are given and partially verified by the experiment.

A novel launch dynamics measurement system for multiple launch rocket system and comparative analysis with numerical simulations

In this paper,a novel launch dynamics measurement system based on the photoelectric sensor pair is built.The actual muzzle time(i.e.a time duration that originates from the initial movement to the rocket’s departure from the muzzle)and the muzzle velocity are measured.Compared with the classical methods,the actual muzzle time is obtained by eliminating the ignition delay.The comparative analysis method is proposed with numerical simulations established by the transfer matrix method for multibody systems.The experiment results indicate that the proposed measurement system can effectively measure the actual muzzle time and reduce the error of classical methods,which match well with the simulation results showing the launch dynamics model is reliable and helpful for further analysis and design of the MLRS.

Hybrid multibody system method for the dynamic analysis of an ultra‐precision fly‐cutting machine tool

The dynamics of an ultra‐precision machine tool determines the precision of the machined surface.This study aims to propose an effective method to model and analyze the dynamics of an ultra‐precision fly‐cutting machine tool.First,the dynamic model of the machine tool considering the deformations of the cutter head and the lathe head is developed.Then,the mechanical elements are classified into M subsystems and F subsystems according to their properties and connections.The M‐subsystem equations are formulated using the transfer matrix method for multibody systems(MSTMM),and the F‐subsystem equations are analyzed using the finite element method and the Craig-Bampton reduction method.Furthermore,all the subsystems are assembled by combining the restriction equations at connection points among the subsystems to obtain the overall transfer equation of the machine tool system.Finally,the vibration characteristics of the machine tool are evaluated numerically and are validated experimentally.The proposed modeling and analysis method preserves the advantages of the MSTMM,such as high computational efficiency,low computational load,systematic reduction of the overall transfer equation,and generalization of its computational capability to general flexible‐body elements.In addition,this study provides theoretical insights and guidance for the design of ultra‐precision machine tools.

Reduced multibody system transfer matrix method using decoupled hinge equations

In the multibody system transfer matrix method(MSTMM),the transfer matrix of body elements may be directly obtained from kinematic and kinetic equations.However,regarding the transfer matrices of hinge elements,typically information of their outboard body is involved complicating modeling and even resulting in combinatorial problems w.r.t.various types of outboard body's output links.This problem may be resolved by formulating decoupled hinge equations and introducing the Riccati transformation in the new version of MSTMM called the reduced multibody system transfer matrix method in this paper.Systematic procedures for chain,tree,closed-loop,and arbitrary general systems are defined,respectively,to generate the overall system equations satisfying the boundary conditions of the system during the entire computational process.As a result,accumulation errors are avoided and computational stability is guaranteed even for huge systems with long chains as demonstrated by examples and comparison with commercial software automatic dynamic analysis of the mechanical system.

Dynamic modeling of ultra-precision fly cutting machine tool and the effect of ambient vibration on its tool tip response

The dynamic performances of an ultra-precision fly cutting machine tool(UFCMT)has a dramatic impact on the quality of ultra-precision machining.In this study,the dynamic model of an UFCMT was established based on the transfer matrix method for multibody systems.In particular,the large-span scale flow field mesh model was created;and the variation in linear and angular stiffness of journal and thrust bearings with respect to film thickness was investigated by adopting the dynamic mesh technique.The dynamic model was proven to be valid by comparing the dynamic characteristics of the machine tool obtained by numerical simulation with the experimental results.In addition,the power spectrum density estimation method was adopted to simulate the statistical ambient vibration excitation by processing the ambient vibration signal measured over a long period of time.Applying it to the dynamic model,the dynamic response of the tool tip under ambient vibration was investigated.The results elucidated that the tool tip response was significantly affected by ambient vibration,and the isolation foundation had a good effect on vibration isolation.

电磁轨道炮导轨身管系统动力学分析

针对电磁轨道炮等新概念电磁发射系统发射动力学建模复杂、计算成本高等难题,考虑上下导轨非对称性影响,将上下导轨视为横向振动梁,身管视为在特定位置作用两弹性支撑的横向振动梁,导轨与身管间的相互作用视为连续分布弹簧,建立导轨身管系统三梁动力学模型。利用多体系统传递矩阵法推导系统各部分传递矩阵,组装系统总传递方程,求解系统任意位置在对应频率下的状态矢量。通过毕奥-萨伐尔定律解算导轨间及枢轨间的电磁力作用系数,分析导轨所受电磁力分布规律。利用模态叠加法求解系统静位移和在重力及时变电磁力作用下的动态响应,并与商业有限元软件计算结果比较,验证该方法的有效性和快速性。分析发现当电流较小时,系统在静变形位置附近波动,电流达到峰值平台后,上下导轨间距在“扩张-收缩”的过程中反复震荡;上导轨由于弹性支撑参数等非对称性因素的影响变形量更大,为电磁轨道炮耦合系统动力学分析提供理论支撑。

多体系统传递矩阵法分布式并行计算研究

多体系统传递矩阵法作为一种多体系统动力学新方法,在进行多体系统动力学分析时无需系统总体动力学方程、涉及矩阵阶次低计算速度快的优点,已被广泛用于各种多管火箭、自行火炮、坦克等复杂大型机械系统动力学分析与设计。为了提高多体系统传递矩阵法计算速度,研究了分布式并行计算的原理和方法,将MPI(Message Parallel Interface)分布式并行计算环境引入到多体系统传递矩阵法计算中。针对变截面梁的多体系统传递矩阵法动力学计算算例,设计了并行算法,分析了单机多核和分布式网络环境对计算时间的影响,结果显示通过并行计算能够大幅度提高计算效率。

刚柔耦合多体系统的冲击响应分析方法及应用研究

利用多体系统传递矩阵法建立了刚柔耦合多体系统的动力学模型,并且将冲量模型和碰撞接触模型与多体系统传递矩阵法结合,提出了基于传递矩阵法的刚柔耦合多体系统的冲击响应分析方法。根据柯西方程推导出系统中的柔性梁在冲击载荷作用下的冲击应力分布公式。以某型汽车起重机为例分析了在起吊过程中的冲击载荷特点,计算了该刚柔耦合多体系统的冲击响应及柔性梁的冲击应力分布规律,并与试验结果对比,证实了该方法的正确性。

多体系统传递矩阵法研究进展

作为一种多体系统动力学新方法,多体系统传递矩阵法由于其无需系统总体动力学方程和快速计算的特点,已被广泛用于各种多管火箭、自行火炮、舰炮等复杂大型机械系统动力学分析与设计.本文介绍了该方法的研究进展,包括:线性多体系统传递矩阵法、多体系统离散时间传递矩阵法、二维系统传递矩阵法、受控多体系统传递矩阵法、多体系统传递矩阵法和通常动力学方法的混合方法等,给出了该方法解决自行火炮、多管火箭武器多体系统动力学的重大工程应用实例.

多管火箭发射过程中定向器振动特性研究

为了在多管火箭发射过程中能获得准确的定向器管口振动信号,研究了多管火箭发射过程中定向器管口振动特性;利用多体系统传递矩阵法和发射动力学理论,建立了多管火箭发射动力学模型和仿真系统,通过多管火箭模态试验验证了模型的正确性;仿真获得了在发射过程中定向器管口振动的时域历程,利用离散傅里叶变换(DFT)技术,获得了在发射过程中定向器管口振动位移、速度和加速度信号的频域特性;在此基础上设计了椭圆滤波器,并通过对发射过程中定向器管口的加速度采集信号的滤波前后对比,验证了该研究内容的正确性和重要性,为多管火箭发射过程中定向器运动信号的采集和控制提供了重要参考价值。

自行火炮振动特性的计算

准确计算自行火炮的振动特性是发射动力学研究的重要内容。将自行火炮处理为由多个刚体、集中质量、弹性梁按一定方式铰接而成的刚弹耦合多体系统,建立了自行火炮的动力学模型,用多体系统传递矩阵法计算了其振动特性。计算结果与试验结果吻合较好。文中的方法可方便地推广到其它武器系统和各种机械多体系统。

引信发射环境研究

从炮、弹、药、引信全系统的角度 ,建立了引信发射环境与系统总体布局结构参数之间的定量关系 ,为研究引信机构的响应 ,实现引信系统的仿真和动态设计 。

激光陀螺捷联惯导减振系统动力学建模与仿真

由于激光陀螺固有机抖频率的存在,以及导弹运输、装卸、发射与飞行过程经历的动态环境中振动、冲击、过载等激励,导致激光陀螺在导弹上使用输出精度差。应用多体系统传递矩阵法,建立了激光陀螺捷联惯性测量组合减振多体系统动力学模型,分析激光陀螺固有抖动和导弹振动冲击对激光陀螺输出精度的影响。通过对减振系统动力学模型进行仿真,获得了激光陀螺抖动和导弹冲击环境下激光陀螺捷联惯性测量组合减振系统动态响应。该仿真结果为激光陀螺捷联惯性测量组合减振设计提供理论依据,该分析方法为激光陀螺捷联惯组在导弹上应用提供理论基础。