Substructuring: Definition of the Analytical Dynamic Model of a Complex System During its Design Stage

1995 ◽  
Author(s):  
Fabrice Llorca ◽  
Alain Gerard ◽  
Denis Hennequin ◽  
Dominique Brenot
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Least Square Method ◽  
Close Correlation ◽  
Least Square ◽  
Component Mode Synthesis ◽  
Design Stage ◽  
Synthesis Methods ◽  
Rectangular Plates

Abstract A structure is often an assembly of several components coupled by various joints such as bolted or riveted joints. Component mode synthesis methods are very practical tools to define a dynamic model. But, several points have to be examined and improved in order to give a complet representation of the modal behaviour of the whole structure. For example, rotational degrees of freedom on connecting points between adjacent substructures should be estimated to give a better representation of the multidirectional connecting forces. These informations may be evaluated through a method based on both interpolation and spatial derivation of the experimental translational displacements of the components. Unlike many other structural elements, the dynamic properties of a connection are very difficult to evaluate. So, we propose a method of determining joint stiffness characteristics. We consider only the conservative problem so the damping properties of the different components of the considered assembly are not taken into account. The joint characteristics are extracted comparing experimental modal data base and component mode synthesis simulation. The updating procedure is based on a nonlinear iterative least-square method. Results are presented concerning a particular assemblie of rectangular plates. Structural modification is applied for one component. We show that the joint properties stay the same if the connecting interface is not modified. The close correlation between predicted and experimental results demonstrate that this method is well adaptated to the study of structural modifications.

scholarly journals Joints dynamic identification and modeling based on FRFs data

2018 ◽  
Vol 189 ◽  
pp. 01010
Author(s):  
Guanhua Dong ◽  
Wei Wu ◽  
Jianhui Zhou
Keyword(s):  
Frequency Response ◽  
Dynamic Model ◽  
Dynamic Properties ◽  
Dynamic Stiffness ◽  
Least Square Method ◽  
Least Square ◽  
Experimental Results ◽  
Response Functions ◽  
Dynamic Identification ◽  
Inconsistent Equation

The problem of joints dynamic identification and modeling is discussed in this paper. The theoretical dynamic model of joints is established by FRFs (frequency response functions) data, and formulas for identifying the joints dynamic properties is deduced. The equivalent value of dynamic stiffness is extracted by solving the inconsistent equation using the least square method. The experimental example is provided to validate the feasibility and accuracy of the proposed method, the predicted result showing good fitting with experimental results.

scholarly journals Component Mode Synthesis Using Undeformed Interface Coupling Modes to Connect Soft and Stiff Substructures

2013 ◽  
Vol 20 (1) ◽  
pp. 157-170 ◽  
Author(s):  
Eskil Lindberg ◽  
Nils-Erik Hörlin ◽  
Peter Göransson
Keyword(s):  
Degrees Of Freedom ◽  
Component Mode Synthesis ◽  
Vehicle Suspension ◽  
Synthesis Methods ◽  
Test Case ◽  
Rotation Axes ◽  
Acoustic Modelling ◽  
Stiffness Properties ◽  
Rubber Bushing ◽  
Vehicle Suspension System

Classical component mode synthesis methods for reduction are usually limited by the size and compatibility of the coupling interfaces. A component mode synthesis approach with constrained coupling interfaces is presented for vibro-acoustic modelling. The coupling interfaces are constrained to six displacement degrees of freedom. These degrees of freedom represent rigid interface translations and rotations respectively, retaining an undeformed interface shape. This formulation is proposed for structures with coupling between softer and stiffer substructures in which the displacement is chiefly governed by the stiffer substructure. Such may be the case for the rubber-bushing/linking arm assembly in a vehicle suspension system. The presented approach has the potential to significantly reduce the modelling size of such structures, compared with classical component mode synthesis which would be limited by the modelling size of the interfaces. The approach also eliminates problems of nonconforming meshes in the interfaces since only translation directions, rotation axes and the rotation point need to be common for the coupled substructures. Simulation results show that the approach can be used for modelling of systems that resemble a vehicle suspension. It is shown for a test case that adequate engineering accuracy can be achieved when the stiffness properties of the connecting parts are within the expected range of rubber connected to steel.

Identification of Two Degree of Freedom Robot Arm’s Joints’ Time-Varying Stiffness

2012 ◽  
Vol 241-244 ◽  
pp. 1880-1884
Author(s):  
Rui Xu ◽  
Qiang Chen ◽  
Guo Lai Yang
Keyword(s):  
Degrees Of Freedom ◽  
Least Square Method ◽  
Identification Problem ◽  
Degree Of Freedom ◽  
Least Square ◽  
Analytical Mechanics ◽  
Time Varying ◽  
Robot Arm ◽  
Whole Process ◽  
Two Degree Of Freedom

This paper is concerned with the identification problem of two degree of freedom robot arm’s joints’ time-varying stiffness. The dynamic equation of two degrees of freedom robot arm can be obtained by using analytical mechanics method. Then by choosing limited memory least square method, time-varying stiffness can be identified. Finally, the calculative stiffness is compared to the “real” stiffness which is simulated in ADAMS. The whole process shows that the robot arm’s dynamic model and the method of identification are both effective.

A wavelet transform and substructure algorithm for tracking the abrupt stiffness degradation of shear structure

2018 ◽  
Vol 22 (5) ◽  
pp. 1136-1148 ◽  
Author(s):  
Chao Wang ◽  
Demi Ai ◽  
Wei-Xin Ren
Keyword(s):  
Wavelet Transform ◽  
Degrees Of Freedom ◽  
Least Square Method ◽  
Least Square ◽  
Stiffness Degradation ◽  
Discrete Wavelet ◽  
Time Varying ◽  
Engineering Structures ◽  
Shear Structure ◽  
Stiffness And Damping

Time-varying parameter identification is an important research topic for structural health monitoring, performance evaluation, damage diagnosis, and maintenance. Practical civil engineering structures usually contain multiple degrees of freedom; however, damage often locally occurs. In this study, a discrete wavelet transform and substructure algorithm is presented for tracking the abrupt stiffness degradation of shear structures. A substructure model is built by the extraction of the local structure which may contain damaged region. Time-varying stiffness and damping are expanded into multi-scales using discrete wavelet analysis. An optimization method based on Akaike information criterion is introduced to select the decomposition scale. The expanded scale coefficients are evaluated using least square method, then the original time-varying stiffness or damping parameter is identified by reconstructing from the scale coefficients. To validate the proposed method, a numerical example of seven-story shear structure with time-varying stiffness and damping is proposed. Experiment for a three-story shear-type structure with abrupt stiffness degradation is also tested in the laboratory. Both numerical and experimental results indicate that the proposed method can effectively identify the abrupt degradation of stiffness parameter with a satisfactory accuracy.

Experiment and Dynamic Model of Motor for Rotary-Screw-Driven Dispensing System

2012 ◽  
Vol 220-223 ◽  
pp. 1071-1076 ◽  
Author(s):  
Shu Zhen Liu ◽  
Yu Bao Zhang ◽  
Xiong Biao Chen
Keyword(s):  
Dynamic Model ◽  
Model Simulation ◽  
Applied Pressure ◽  
Selection Criterion ◽  
Least Square Method ◽  
Input Voltage ◽  
Angular Speed ◽  
Least Square ◽  
Order System ◽  
Rotary Screw

Motor plays an important role in the dynamic property of the rotary-screw-driven dispensing system. Dynamic model of the motor was developed and validated in this paper. The output angle displacement and input voltage were measured from photoelectric digital encoder which is used to measure the angle displacement of the motor. In order to realize data smooth processing, Alpha-Beta filter was used. Discrete model of the motor was developed based on the Least Square Method and Model Selection criterion. Computational studies show that the system is equivalent to second order system. Moreover, the model was validated based on the experiment results under the different applied pressure and angular speed of motor. It is revealed that there is a good fit between experiment data and model simulation.

scholarly journals Generalized Sparse Polarization Array for DOA Estimation Using Compressive Measurements

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Tao Chen ◽  
Jian Yang ◽  
Weitong Wang ◽  
Muran Guo
Keyword(s):  
Degrees Of Freedom ◽  
Elevation Angle ◽  
Least Square Method ◽  
Estimation Algorithm ◽  
Doa Estimation ◽  
Least Square ◽  
Polarization Angle ◽  
Estimation Performance ◽  
The Difference ◽  
Cramer Rao Bound

The compressive array method, where a compression matrix is designed to reduce the dimension of the received signal vector, is an effective solution to obtain high estimation performance with low system complexity. While sparse arrays are often used to obtain higher degrees of freedom (DOFs), in this paper, an orthogonal dipole sparse array structure exploiting compressive measurements is proposed to estimate the direction of arrival (DOA) and polarization signal parameters jointly. Based on the proposed structure, we also propose an estimation algorithm using the compressed sensing (CS) method, where the DOAs are accurately estimated by the CS algorithm and the polarization parameters are obtained via the least-square method exploiting the previously estimated DOAs. Furthermore, the performance of the estimation of DOA and polarization parameters is explicitly discussed through the Cramér-Rao bound (CRB). The CRB expression for elevation angle and auxiliary polarization angle is derived to reveal the limit of estimation performance mathematically. The difference between the results given in this paper and the CRB results of other polarized reception structures is mainly due to the use of the compression matrix. Simulation results verify that, compared with the uncompressed structure, the proposed structure can achieve higher estimated performance with a given number of channels.

Dynamic Parameters Identification for Tong & Tong-Carrier of a Forging Manipulator

2011 ◽  
Vol 121-126 ◽  
pp. 2006-2010
Author(s):  
Ning Bo Cheng ◽  
Li Wen Guan ◽  
Li Ping Wang ◽  
Jian Han
Keyword(s):  
Dynamic Model ◽  
Relative Error ◽  
Linear Form ◽  
Least Square Method ◽  
Least Square ◽  
Dynamic Parameters ◽  
Mass Center ◽  
Simulation Results ◽  
Forging Manipulator ◽  
Center Parameter

This paper deals with the dynamic parameters of the combination of the tong, the tong-carrier and (or without) a forging (link TCF). Two linear form equations of the dynamic model of link TCF about the dynamic parameters are obtained. And then based on two linear form equations, the least square method is adopted to identify the parameters. Simulation results show that the identified dynamic parameters, mass m, moment of inertia IL and the mass center parameter b1, have a small relative error that no more than 5%.

scholarly journals Stabilized Solution to Spurious Mode Problem and Ill-Conditioning in Interface Force Based Substructure Coupling Method

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Hui-hua Feng ◽  
Xiao-long Mou ◽  
Khaled Teffah
Keyword(s):  
Degrees Of Freedom ◽  
Component Mode Synthesis ◽  
Coupling Method ◽  
Synthesis Methods ◽  
Assembly Method ◽  
Spurious Mode ◽  
Ill Conditioning ◽  
Fixed Interface ◽  
Matrix Problems ◽  
Value Decomposition

There are two major types of substructure mode synthesis methods, i.e., the fixed-interface component mode synthesis and free-interface component mode synthesis. There are two coupling methods, the interface degrees of freedom based coupling method and the interface force based coupling method, the former one is referred to as the primary assembly method, and the latter is referred to as the dual assembly method. However, the dual assembly method is theoretically shown to be unstable in this research, such reduced stiffness matrix is indefinite, this fatal weakness can be conquered by further interface reduction, and the interface compatibility is therefore rigorously enforced. Unfortunately, Craig’s method leads to another numerical instability when inverting a submatrix of residual flexibility on the interface degrees of freedom, this problem is neglectable in small dimensional matrix problems, but it is prominent in large models when the number of interface degrees of freedom is large, this ill-conditioning problem may be circumvented by truncated singular value decomposition technique; here, a more efficient strategy is proposed, the substructure reduction is modified, this modification proves to be numerically stable, and it can be even more accurate than the prevailing Craig-Bampton method; the numerical examples validate the suggestion.

Evaluation of free interface-based reduction techniques for nonlinear forced response analysis of shrouded blades

2019 ◽  
Vol 233 (23-24) ◽  
pp. 7459-7475 ◽  
Author(s):  
Fahimeh Mashayekhi ◽  
Stefano Zucca ◽  
Ali S Nobari
Keyword(s):  
Degrees Of Freedom ◽  
Turbine Blades ◽  
Computational Cost ◽  
Forced Response ◽  
Contact Forces ◽  
Component Mode Synthesis ◽  
Response Analysis ◽  
Synthesis Methods ◽  
Free Interface ◽  
Reduction Techniques

The efficient dynamic stress assessment of turbine blades is of prime importance in turbomachinery design. An accurate prediction of forced response level of shrouded blades requires a very detailed finite element model in addition to a nonlinear solver. In order to perform nonlinear forced response analysis of blades at an affordable computational cost, applying a model order reduction technique is essential. The appeal for component mode synthesis methods in dimension reduction of structures with friction contacts is due to the possibility of retaining a subset of physical degrees of freedom (e.g. the contact degrees of freedom) in the set of generalized coordinates. In this paper, a reduction method recently developed for nonlinear forced response analysis of structures with local nonlinearity is evaluated and compared with two classical component mode synthesis reduction techniques. All three methods have the same projection basis, which includes residual flexibility attachment modes and free interface modes, but different implementation. The response is computed in the frequency domain using multiharmonic balance method and periodic contact forces are modeled with a node-to-node 3D friction contact model. In order to demonstrate the efficiency of the three formulations, a rod and a simplified shrouded turbine blade are considered as case studies.

scholarly journals A Conceptual Investigation of a Large Radio Telescope Support Point Number Effect on Its Pointing Accuracy

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Song Xue ◽  
Kaitong Ma ◽  
Congsi Wang ◽  
Peiyuan Lian ◽  
Yan Wang ◽  
...  
Keyword(s):  
Radio Telescope ◽  
Least Square Method ◽  
Support Point ◽  
Least Square ◽  
Design Stage ◽  
Pointing Error ◽  
Large Radio Telescope ◽  
Point Number ◽  
Pointing Accuracy ◽  
Fourier Function

The purpose of this paper is to investigate a large radio telescope support point number effect on its pointing accuracy and provide a useful guideline for the large radio telescope design engineer. In a large radio telescope system, the azimuth track is used to support the whole telescope structure and the mounting error as well as the telescope wheel-track contact in a long term can cause unevenness on the azimuth track, which can further deteriorate the telescope pointing accuracy. Even though various compensation methods have been proposed to compensate for this pointing error, it remains as one of the challenges for the telescope pointing error reduction. In this paper, a general telescope pointing error estimation formula has been proposed to investigate different telescope support-point number designs on its pointing accuracy. In this approach, the azimuth track unevenness has been modelled as the Fourier function using the least square method after the raw track profile has been measured. Next, the elevation position matrix, azimuth position matrix, and the azimuth profile matrix can be constructed for different telescope support point numbers, and the telescope pointing error can then be obtained based on the proposed general formula. The telescope pointing error root mean square (RMS) value is used to quantify the effect of the telescope support point number on the pointing accuracy. Two interesting results can be observed in the numerical example. The first one is that the telescope pointing error curves have different dominant peaks during one azimuth track rotation, which is corresponding to the support point number. Another interesting finding is that the RMS value experienced a complex trend with the support point number change, and they are not a simple monotonous increasing or decreasing relationship with the support number. All the results in this paper can provide a useful guideline for reducing the telescope pointing error in the initial design stage.

Sign in / Sign up

Export Citation Format

Share Document