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.

Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space

In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid- flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov- ing in space, the global dynamics equations of system are not needed, the orders of involved matrices of the system are very low and the computational speed is high, irrespec- tive of the size of the system. The new method is simple, straightforward, practical, and provides a powerful tool for multi-rigid-flexible-body system dynamics.

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.

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.

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.

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.

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.

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.

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.

Multi-objective Optimization of Non-uniform Beam for Minimum Weight and Sound Radiation

A multi-objective optimization of non-uniform beams is presented for minimum radiated sound power and weight. The transfer matrix method is used to compute the structural and acoustic responses of a non-uniform beam accurately and efficiently. The multi-objective particle swarm optimization technique is applied to search the Pareto optimal solutions that represent various compromises between weight and sound radiation. Several constraints are imposed, which substantially reduce the volume fraction of feasible solutions in the design space. Two non-uniform beams with different boundary conditions are studied to demonstrate the multi-objective optimal designs of the structure. © 2017, Tianjin University and Springer-Verlag Berlin Heidelberg.

Ballistic Trajectory Extrapolation and Correction of Firing Precision for Multiple Launch Rocket System

The research on multiple launch rocket system(MLRS)is now even more demanding in terms of reducing the time for dynamic calculations and improving the firing accuracy,keeping the cost as low as possible.This study employs multibody system transfer matrix method(MSTMM),to model MLRS.The use of this method provides effective and fast calculations of dynamic characteristics,initial disturbance and firing accuracy.Further,a new method of rapid extrapolation of ballistic trajectory of MLRS is proposed by using the position information of radar tests.That extrapolation point is then simulated and compared with the actual results,which demonstrates a good agreement.The closed?loop fire correction method is used to improve the firing accuracy of MLRS at low cost.

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.

Vector radiative transfer numerical model of coupled ocean-atmosphere system using matrix-operator method

A vector radiative transfer numerical model of the coupled ocean-atmosphere system is developed based on the matrix-operator method, which is named PCOART. Using the Fourier analysis, the vector radiative transfer equation (VRTE) is separated into a set of equations depending only on the observa-tion zenith angle. Using the Gaussian-Quadrature method, VRTE is finally transferred into the matrix equation solved by the adding-doubling method. According to the reflective and refractive properties of the ocean-atmosphere interface, the vector radiative transfer numerical model of the ocean and at-mosphere is coupled in PCOART. Compared with the exact Rayleigh scattering look-up tables of MODIS (Moderate-resolution Imaging Spectroradiometer), it is shown that PCOART is an exactly numerical model, and the processing methods of the multi-scattering and polarization are correct. Also, validated with the standard problems of the radiative transfer in water, it is shown that PCOART can be used to calculate the underwater radiative transfer problems. Therefore, PCOART is a useful tool for exactly calculating the vector radiative transfer of the coupled ocean-atmosphere system, which can be used to study the polarization properties of the radiance in the whole ocean-atmosphere system and the remote sensing of the atmosphere and ocean.

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。

基于多体系统传递矩阵法的多管火箭定向器振动控制

应用多体系统传递矩阵法,建立了全新的多管火箭发射动力学控制模型,以二次型性能指标为成本函数,设计了脉冲推力器为控制执行机构的振动主动控制律,并设计了多管火箭发射系统在燃气流冲击下定向器的振动主动控制系统,获得了最优脉冲控制力幅值和脉冲推力器工作次数.应用设计的控制律数值仿真了某多管火箭定向器无控和受控状态下的振动响应,仿真结果表明该法可有效地降低定向器的振动.该方法易于工程实现,对控制多管火箭发射系统的振动、提高多管火箭射击的精度具有重要意义.

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。

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.

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。

多管火箭武器振动特性研究

本文从理论、计算、试验三方面研究了多管火箭武器 (MLRS)的振动特性 ,用多体系统传递矩阵法 ,解决了通常方法不便于处理的刚弹耦合多管火箭武器多体系统固有振动特性的计算问题。进行了模态试验 。