Substructure Synthesis Method Research Articles

Efficient model updating of shaft-raft-hull system using multi-stage convolutional neural network combined with sensitivity analysis

Model updating for marine shaft-raft-hull systems presents significant challenges due to the numerous components and the resulting inaccessible parameters. This study introduces an advanced framework for updating the model parameters of these complex coupling systems using convolutional neural networks (CNNs). Rapid analysis technique based on the substructure synthesis method is employed to enhance the efficiency of generating the CNN training dataset. Global sensitivity analysis is then utilized to identify critical parameters across various frequency bands. Informed by parameter sensitivity, the frequency bands are segmented, and a multi-stage CNN model updating strategy is proposed. The effectiveness of this method is validated through numerical simulations and experimental studies on a scaled shaft-raft-hull model. The findings demonstrate that segmenting the dataset based on global sensitivity analysis results markedly improves the convergence of CNNs, providing a robust solution for model updating in complex marine systems.

Study on the Vibration Characteristics of Yaw Gear System for Large-Capacity Offshore Wind Turbine

Vibration and noise must be considered to maximize the efficiency of a yaw system and reduce the fatigue load acting on a wind turbine. This study investigated a method for analyzing yaw-system vibration based on the change in the load-duration distribution (LDD). A substructure synthesis method was combined with a planetary gear train rotational vibration model and finite element models of the housing and carriers. For the vibration excitation sources, the mass imbalance, gear mesh frequency, and bearing defect frequency were considered, and a critical speed analysis was performed. The analysis results showed that the critical speed did not occur within the operating speed range, but a defect occurred in the bearing of the first-stage planetary gear system. It was found that the bearing stiffness and first natural frequency increased with the LDD load. In addition, no vibration occurred in the operating speed range under any of the LDD loads. Because the rolling bearing stiffness changed with the LDD, it was necessary to consider the LDD when analyzing the wind turbine vibration.

Evolution of lower-order vibration mode of the slender ball screw feed system

Dynamic performance characterized by lower-order natural frequency and lower-order vibration mode is vital for the dynamic positioning accuracy of the ball screw feed system. This paper focuses on the evolution between the lateral vibration mode and the axial vibration mode of the slender ball screw feed system (SBSFS). Firstly, it is proved the first-order vibration mode transformation of the SBSFS is subject to the position of the nut based on an elastodynamic model. This model is established using substructure synthesis method considering the axial, torsional, and lateral deformation of the screw simultaneously through dealing with the screw as Timoshenko Beam elements. By comparing with the experimental results, the validity and accuracy of the established dynamic model are verified. The effects of the stiffness of the kinematic joints on the dynamic performance of SBSFS are then analyzed. The results demonstrate that the dynamic behavior evolution of the SBSFS undergoes the coupling effects from the kinematics joints’ stiffness. Furthermore, a dynamic index ( RSP) is proposed considering the evolution of the first-order vibration mode. On the basis of RSP, three optimization schemes are illustrated. The results show that the RSP can be used to evaluate the dynamic performance of the SBSFS considering the vibration mode.

Audible sound analysis of parametric speaker by concentrated mass model (Steady-state response analysis for cylindrical acoustic space by substructure synthesis method)

Audible sound analysis of parametric speaker by concentrated mass model (Steady-state response analysis for cylindrical acoustic space by substructure synthesis method)

A Substructure Synthesis Method with Nonlinear ROM Including Geometric Nonlinearities

Large flexible aircraft are often accompanied by large deformations during flight leading to obvious geometric nonlinearities in response. Geometric nonlinear dynamic response simulations based on full-order models often carry unbearable computing burden. Meanwhile, geometric nonlinearities are caused by large flexible wings in most cases and the deformation of fuselages is small. Analyzing the whole aircraft as a nonlinear structure will greatly increase the analysis complexity and cost. The analysis of complicated aircraft structures can be more efficient and simplified if subcomponents can be divided and treated. This paper aims to develop a hybrid interface substructure synthesis method by expanding the nonlinear reduced-order model (ROM) with the implicit condensation and expansion (ICE) approach, to estimate the dynamic transient response for aircraft structures including geometric nonlinearities. A small number of linear modes are used to construct a nonlinear ROM for substructures with large deformation, and linear substructures with small deformation can also be assembled comprehensively. The method proposed is compatible with finite element method (FEM), allowing for realistic engineering model analysis. Numerical examples with large flexible aircraft models are calculated to validate the accuracy and efficiency of this method contrasted with nonlinear FEM.

Review of the theory of hybrid modeling

This paper reviews the research theory of domestic and foreign hybrid modeling dynamic substructure and frequency response, and then introduces the basic principle of Jetmundsen, Ren substructure synthesis method, mechanical impedance admittance method, mechanical admittance method of interchange-ability and FBS substructure method. In the end, the scope and limitations of the method are compared and analyzed, and a new direction of hybrid modeling of dynamic substructure theory is put forward.

Coupled free vibration of a functionally graded pre-twisted blade-shaft system reinforced with graphene nanoplatelets

The free vibration of a rotating functionally graded (FG) pre-twisted blade-shaft assembly reinforced with graphene nanoplatelets (GPLs) is analytically investigated based on the coupled model proposed in this paper. The effective material properties of the blade and shaft are assumed to vary continuously along their thickness and radius directions, respectively, and are determined by Halpin-Tsai micromechanics model and the rule of mixture. Within the framework of the Rayleigh beam theory and Euler-Bernoulli beam theory, the governing equations of motion are derived by using Lagrange’s equation. The substructure synthesis method and assumed modes method are utilized to determine the natural frequencies of the system. A comprehensive parametric study is conducted to examine the effects of GPL weight fraction, distribution pattern, geometry and dimensions as well as the blade length, location and pre-twist angle, the shaft length and rotating speed on the natural frequencies. The research findings shed an important light on the design of novel graphene reinforced blade-shaft system for remarkably improved dynamic performance.

Improved substructure synthesis method using experimental modal analysis technique to solve analysis and design problems based on security issues

A substructure synthesis method based on frequency response functions is improved to solve a security-issue-based analysis problem and is applied to an optimal design problem for a finished product consisting of two substructures. While geometry information is provided for one substructure, a limited number of frequency response functions are provided for the other substructure instead of its geometry information. The dynamic stiffness matrix of the latter is estimated from the provided frequency response functions using an experimental modal analysis technique. It is combined with the mass and stiffness matrices of the former to predict the vibration natural frequency of a finished product. The improved substructure synthesis method is used to predict the frequency response functions of a T-shaped beam consisting of a doubly clamped beam and a cantilever beam. Additionally, in a vehicle steering module, it is applied to a size optimization problem that is formulated to maximize its natural frequency. Numerical analysis and design results indicate the effectiveness of the improved substructure synthesis method for industrial applications.

Interface vibration characteristics of rolling mill components based on power flow

ABSTRACT First, the flexibility matrix of the rolling mill interfaces is extracted with Jetmundsen substructure synthesis method, and the power flow mode of the interfaces is obtained and discussed when the property of components of the interface changes with the analytical method. Second, finite element analysis (FEA) method is applied to analyse the power flow harmonic response in each interface of the rolling mill components and their power flow conductivities. The relation among the stiffness, the length of rodless cavity of the Hydraulic Gauge Control cylinder of the mill and the conductivity is discussed. Then, the power flow experimental result shows that the Hydraulic Gauge Control cylinder vibrates violently when the length of rodless cavity of the cylinder approaches 50 and 100 mm. Finally, the result comparison among analytical, FEA and experimental method is introduced.

Research Progress of Synthesis and Modification Methods Based on Dynamic Substructures

In the process of model modification of large and complex structures, substructure synthesis method and modal reduction method have been widely used, but there are still some difficulties in precision control and engineering application in the process of model updating. In order to better study the dynamic response of the vibration substructure, the synthesis and correction method of the classical dynamic substructure is described in this paper, which provides a new idea for further engineering development. In the aspect of substructure synthesis method, the modal reduction of substructures, two methods of classical substructure synthesis, mechanical impedance method, singular value decomposition method, rigidity-flexibility equivalence, and transformation of degree of freedom are analyzed. The advantages and disadvantages of the above methods are discussed. In terms of substructure modification, the reference datum method, function dynamic modification method, neural network model modification, and frequency response function modification are analyzed, and the shortcomings of the dynamic substructure modification method are summarized. Finally, the development trend of dynamic substructure synthesis and modification algorithm is proposed.

Order reduction and bifurcation analysis of a flexible rotor system supported by a full circular journal bearing

Journal bearing has been widely used in the wide range of rotating machineries to support large loads and to add significant damping to the system. Conventionally, its fluid film force is represented by the linear model of spring and damper around its equilibrium position in the vibration analysis of the rotor system. However, the fluid film force of the journal bearing is essentially nonlinear, and it is necessary to consider its nonlinearity to expect the characteristics of the limit cycle at around the instability point. This paper investigated the order reduction and bifurcation analysis of a flexible rotor system supported by a full circular journal bearing. The fluid film force is derived under the conditions of both infinitesimal length approximation and half-Zommerfeld boundary condition, and its polynomial function approximation expression is used. Order reduction in the FEM rotor model retaining the nonlinearity of the journal bearing was performed by utilizing the substructure synthesis method. Then, its bifurcation phenomena at around the instability point are investigated by applying the center manifold theory and using the normal form theory. The influences of various parameters, such as kinematic viscosity, bearing length, and the disk position, on the bifurcation phenomena at around the instability point were investigated and explained. Furthermore, the validity of the derived analytical observation was confirmed by numerical simulation and experiment. By invoking these analytical techniques and obtained results, the bifurcation characteristics can be expected theoretically at the design stage of the journal bearing and rotor system.

Vibration analysis of machine tool using FRF-based substructure synthesis method

Vibration analysis of machine tool using FRF-based substructure synthesis method

Damped Vibration Absorbers for Multi-mode Longitudinal Vibration Control of a Hollow Shaft

The present work adopted damped vibration absorbers (DVAs) to attenuate multi-mode longitudinal vibration of the hollow shaft. The dynamic behavior of a shaft is analyzed for the guidance to the initial parameter design of DVAs and the parameters of DVAs are optimized. Subsequently, specific structures of DVAs are designed taking into account the hollow characteristic of the shaft. Furthermore, finite element stimulation of solid modeling has been performed. In this work, with the aid of the transfer matrix method (TMM) in conjunction with the substructure synthesis method (SSM), a dynamic model of the shaft incorporating multiple DVAs is established. The proposed method is developed for the calculation of dynamics character of the coupled system and estimation of absorption effectiveness of DVAs. To demonstrate the validity of theoretical result obtained from the TMM proposed in this paper, a simulation of the shaft vibration by means of the finite element method (FEM) is also carried out. Theoretical and stimulation results both demonstrate that the resonance peaks of the shaft longitudinal vibration are suppressed obviously with the application of those DVAs, which verify the effectiveness of the absorption performance of DVAs.

Vibration Characteristics of Heavy‐Duty CNC Machine Tool‐Foundation Systems

Vibration characteristics of heavy CNC machine tools are directly affected by their foundations. To analyze vibrations of heavy CNC machine tools caused by internal and external loads, a system dynamics model of a rigid‐flexible coupled heavy‐duty CNC machine tool‐foundation system was established based on the multibody transfer matrix method. Since joint surfaces can seriously affect the accuracy of system mechanics models, the substructure synthesis method was first used to establish a dynamic model of the joint surface. The frequency response function was then used to identify model parameters. Moreover, to improve the accuracy of parameter identification of the joint surface, a residual frequency compensation function was used to reconstruct the frequency response function. Finally, the multibody system model was implemented by combining surface elements. To verify the system dynamics model, an experimental model of the heavy‐duty machine‐foundation system was built, taking into consideration joint surface factors, and the theoretical model was validated by comparing theoretical, simulation, and experimental results. Using the theoretical model, the influence of different forms of concrete foundations, materials, and soil properties on the vibration characteristics of heavy‐duty CNC machine tools was analyzed, thus providing a theoretical basis for optimizing and improving CNC machine tools.

Coupled dynamics of a viscoelastically supported infinite string and a number of discrete mechanical systems moving with uniform speed

The mutual interaction between a number of multi degrees of freedom mechanical systems moving with uniform speed along an infinite taut string supported by a viscoelastic layer has been studied using the substructure synthesis method when base excitations of a common frequency are given to the mechanical systems. The mobility or impedance matrices of the string have been calculated analytically by Fourier transform method as well as wave propagation technique. The above matrices are used to calculate the response of the discrete mechanical systems. Special attention is paid to the contact forces between the discrete and the continuous systems which are estimated by numerical simulation. The effects of phase difference, the distance between the systems and different base excitation amplitudes on the collective behaviour of the mechanical systems are also studied. The present study has relevance to the coupled dynamic problem of more than one railway pantographs and an overhead catenary system where the pantographs are modelled as discrete systems and the catenary is modelled as a taut string supported by continuous viscoelastic layer.

A new method using double distributed joint interface model for three-dimensional dynamics prediction of spindle-holder-tool system

The cutting process stability strongly depends on dynamics of the spindle-holder-tool system, which often changes and is determined by impact hammer testing in general. In order to avoid repeated and time-consuming impact hammer testing on different spindle-holder-tool combinations, this paper proposes a new method for three-dimensional dynamics prediction of spindle-holder-tool system. The system is modeled using Timoshenko’s beam theory and substructure synthesis method. The tool-holder connection is regarded as a double distributed joint interface model including a collet, a holder-collet joint interface and a tool-collet joint interface. The two joint interfaces are further modeled as two sets of independent spring-damper elements, while the collet and tool are modeled as Timoshenko beams with varying cross-sections. The substructure synthesis method is adopted to obtain the equation of motion of the spindle-holder-tool system. Finally, experiments of bending, torsional, and axial FRFs are carried out to verify the proposed method. Good agreements show that the new method is capable of predicting tool point FRFs more accurately compared with the existing methods.

Self-Excited Vibration of a Flexibly Supported Shafting System Induced by Friction

Self-excited vibration of a flexibly supported shafting system in a gravity water tunnel was observed in the testing of friction of water-lubricated rubber bearings. The measured vibrations indicated that the self-excited vibration, characterized by a single-mode vibration modulated by the shaft speed, emerged at a specific speed and grew stronger as the shaft speed decreased, but it would cease at a very low-speed. To explain the mechanism of instability, a dynamic model of the system was built. The substructure synthesis method was employed to model the dynamics of the shafting system, which was divided into two subsystems: the flexible support and the shaft. Before the synthesis, natural frequencies and modes of the subsystems were computed by the finite element method. According to the modal parameters and connecting conditions, a synthesized model was built to take into account the friction between the shaft and the bearing. The fourth-order Runge–Kutta method was used to solve the dynamic equations, and the influences of physical parameters on vibration stability were analyzed. The results have shown that certain vibration modes of the flexible support tend to be unstable under the excitation of the friction. Both the simulation and experimental results have exhibited that the unstable modes are associated with the torsional vibration of the flexible support, which are in fact lightly damped and accordingly can be easily excited by the circumferential friction. Therefore, the coupling between the torsional vibration of the flexible support and the friction of the water-lubricated rubber bearing is the main factor leading to the vibration instability.

Control-Oriented Modeling of a Polymeric Soft Robot

Abstract This article describes an efficient control-oriented model of a soft robot made of electroactive polymers. The proposed soft robot is constructed from two flexible links and has a multiphysics dynamic model consisting of both an electrochemical and electromechanical model. The electrochemical model is based on a distributed RC line approach, and the electromechanical model, considering the continuum vibration of the robot, is derived based on Hamilton's principle. The governing equation of the soft robot is solved by means of the Rayleigh-Ritz-Meirovitch substructure synthesis method, and the Laplace operator is used to obtain the transfer function of the soft robot as a 2 by 2 multiple-input multiple-output system.

등가정하중법과 부분구조합성법을 이용한 구조최적설계

Structural optimization pursues improved performance of structures. Nowadays, structural optimization is applied to the design of huge and complex structures such as an airplane. As the number of the finite elements is increased, the analysis solution becomes more accurate. However, the design cost using the finite element model is significantly increased. The component mode synthesis method that is using the substructure synthesis method is frequently employed in order to keep the accuracy and reduce the cost. A new design method for structural optimization is proposed to reduce the design cost and to consider the dynamic effect of the structure. The proposed method reduces the design cost by applying the equivalent static loads on the design domain. An example of linear dynamic response optimization is solved and the efficiency of the proposed method is demonstrated.

Elastodynamic modeling and joint reaction prediction for 3-PRS PKM

To gain a thorough understanding of the load state of parallel kinematic machines (PKMs), a methodology of elastodynamic modeling and joint reaction prediction is proposed. For this purpose, a Sprint Z3 model is used as a case study to illustrate the process of joint reaction analysis. The substructure synthesis method is applied to deriving an analytical elastodynamic model for the 3-PRS PKM device, in which the compliances of limbs and joints are considered. Each limb assembly is modeled as a spatial beam with non-uniform cross-section supported by lumped virtual springs at the centers of revolute and spherical joints. By introducing the deformation compatibility conditions between the limbs and the platform, the governing equations of motion of the system are obtained. After degenerating the governing equations into quasi-static equations, the effects of the gravity on system deflections and joint reactions are investigated with the purpose of providing useful information for the kinematic calibration and component strength calculations as well as structural optimizations of the 3-PRS PKM module. The simulation results indicate that the elastic deformation of the moving platform in the direction of gravity caused by gravity is quite large and cannot be ignored. Meanwhile, the distributions of joint reactions are axisymmetric and position-dependent. It is worthy to note that the proposed elastodynamic modeling method combines the benefits of accuracy of finite element method and concision of analytical method so that it can be used to predict the stiffness characteristics and joint reactions of a PKM throughout its entire workspace in a quick and accurate manner. Moreover, the present model can also be easily applied to evaluating the overall rigidity performance as well as statics of other PKMs with high efficiency after minor modifications.