Frequency Domain Updating of Thin-Walled Workpiece Dynamics Using Reduced Order Substructuring Method in Machining

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Oguzhan Tuysuz ◽  
Yusuf Altintas
Keyword(s):  
Frequency Domain ◽  
Equations Of Motion ◽  
Selection Criterion ◽  
Order Reduction ◽  
Fe Model ◽  
Computationally Efficient ◽  
Peripheral Milling ◽  
Reduced Order ◽  
Dynamic Substructuring ◽  
Thin Walled

The structural dynamics of thin-walled parts vary as the material is removed during machining. This paper presents a new, computationally efficient reduced order dynamic substructuring method to predict the frequency response function (FRF) of the workpiece as the material is removed along the toolpath. The contribution of the removed mass to the dynamics of the workpiece is canceled by adding a fictitious substructure having the opposite dynamics of the removed material. The equations of motion of the workpiece are updated, and workpiece FRFs are evaluated by solving the hybrid set of assembled equations of motion in frequency domain as the tool removes the material between two consecutive dynamics update steps. The orders of the initial workpiece structure and the removed substructures are reduced using a model order reduction method with a newly introduced automatic master set selection criterion. The reduced order FRF update model is validated with peripheral milling tests and FRF measurements on a plate-shaped workpiece. It is shown that the proposed model provides ∼20 times faster FRF predictions than the full order finite element (FE) model.

Analysis of Vibration of a Tank Caused by an Explosion

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
M. Utsumi ◽  
H. Tazuke
Keyword(s):  
Fluid Motion ◽  
Three Dimensional ◽  
Longitudinal Axis ◽  
Reduced Order Model ◽  
Fe Model ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order ◽  
Large Tank ◽  
The Galerkin Method

The vibration of a large tank caused by an explosion that occurs at a place apart from the tank is analyzed. Because the tank is double-walled and the liquid is contained in the inner shell, the vibration of the outer shell subjected to the explosion-induced pressure wave that travels outside the tank is analyzed without considering the liquid. A cylindrical tank with a spherical roof is considered as a realistic three-dimensional (3D) model, and a computationally efficient semi-analytical method that is applicable to the 3D geometry of the tank–fluid interface is investigated. First, cylindrical coordinates are introduced such that the longitudinal axis intersects the center of the tank base and is normal to the explosion source plane, thereby defining the inner and outer radii of the analysis domain of the fluid motion. Next, the solutions are expressed in terms of coordinate-dependent eigenvalues and a reduced order model is developed by applying the Galerkin method to the governing equations that take into account the compressibility and nonlinearity of the fluid motion. The method is verified by comparing with earlier results obtained by a numerical method. We also analyze the vibration of the tank shell by developing its finite element (FE) model and transforming the model into modal equations to develop a reduced order model for the fluid–tank system.

scholarly journals A Reduced-Order Model for the Vibration Analysis of Mistuned Blade–Disc–Shaft Assembly

2019 ◽  
Vol 9 (22) ◽  
pp. 4762
Author(s):  
Wang ◽  
Bi ◽  
Zheng
Keyword(s):  
Vibration Analysis ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Normal Modes ◽  
Order Reduction ◽  
Symmetry Analysis ◽  
Reduced Order Model ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Reduced Order

An effective reduced-order model is presented in this paper for the vibration analysis of a mistuned blade–disc–shaft assembly considering the flexibility of the shaft and the rotordynamic effects. For the sake of accurate modeling and quantitative analysis, three-dimensional (3D) finite element models were employed in obtaining the governing equations of motion with the Coriolis force, centrifugal stiffening, and spin softening effects taken into account. Then, an efficient model order reduction technique based on the coordinate projection by normal modes of tuned assembly and cyclic symmetry analysis was developed for mistuned blade–disc–shaft assembly. The criterion of whether one matrix could be incorporated in cyclic symmetry analysis is presented. During the modeling, the mistuning in blade and disc was taken into account and dealt with independently. In mistuning projection, the blade and disc parts were both projected onto their tuned counterparts of the sector model, where the boundary conditions were set to be fixed and free, respectively. Finally, an example of a blade–disc–shaft assembly was employed to validate the effectiveness of the presented method in free and forced vibration analysis.

Time-Domain Modeling of Varying Dynamic Characteristics in Thin-Wall Machining Using Perturbation and Reduced-Order Substructuring Methods

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Oguzhan Tuysuz ◽  
Yusuf Altintas
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
End Milling ◽  
Domain Model ◽  
Mode Shapes ◽  
Thin Wall ◽  
Domain Modeling ◽  
Reduced Order ◽  
Thin Walled ◽  
Five Axis

The dynamic response of thin-walled parts becomes time and tool position dependent due to material removal along the toolpath. This article proposes a new reduced-order workpiece dynamic parameters update model using substructuring and perturbation methods. The removed volumes between discrete locations along the toolpath are defined as substructures of the initial global workpiece. The dynamically reduced-order initial workpiece structure and the removed substructures are obtained with model order reduction techniques. Equations of motion of the workpiece are updated in time-domain by rigidly coupling fictitious substructures having the negative mass and stiffness of the removed material. Instead of solving the generalized eigenvalue problem repeatedly along the toolpath, the mode shapes of the in-process workpiece are perturbed using the mass and stiffness of the removed substructures. Convergence of the perturbation is improved by integrating a vector sequence convergence accelerating algorithm. The corresponding updated mode frequencies are evaluated using Rayleigh Quotient with the perturbed mode shapes. The proposed reduced-order time-domain dynamics update model is verified in five-axis ball-end milling tests on a thin-walled twisted fan blade, and its predictions are also compared against the authors’ previously developed frequency-domain reduced-order model. It is shown that the newly introduced model is ∼4 times more computationally efficient than the frequency-domain model.

Some Techniques for Order Reduction of Nonlinear Time Periodic Systems

2003 ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha ◽  
Eric A. Butcher
Keyword(s):  
Nonlinear Systems ◽  
Invariant Manifold ◽  
Equations Of Motion ◽  
Linear Method ◽  
Order Reduction ◽  
Reduced Order ◽  
Reduction Techniques ◽  
Nonlinear Projection ◽  
Short Period ◽  
Time Periodic

In this paper, some techniques for order reduction of nonlinear systems with time periodic coefficients are introduced. The equations of motion are first trasformed using the Lyapunov-Floquet transformation such that the linear parts of the new set of equations are time-invariant. To reduce the order of this transformed system three model reduction techniques are suggested. The first approach is simply an application of the well-known linear method to nonlinear systems. In the second technique, the idea of singular perturbation and noninear projection are employed, whereas the concept of invariant manifold for time-periodic system forms the basis for the third method. A discussion of nonlinear projection method and time periodic invariant manifold technique is included. The invariant manifold based technique yields a ‘reducibility condition’. This is an important result due to the fact that various types of resonance are present in such systems. If the ‘reducibility condition’ is satisfied only then a nonlinear order reduction is possible. In order to compare the results obtained from various reduced order modeling techniques, an example consisting of two parametrically excited coupled pendulums is included. Reduced order results and full-scale dynamics are used to construct approximate and exact Poincare´ maps, respectively, because it portrays the long-term behavior of system dynamics. This measure is more convincing than just comparing the time traces over a short period of time. It is found that the invariant manifold yields the most accurate results followed by the nonlinear projection and the linear techniques.

Systematic Simulation Method for the Calculation of Maximum Deflections in Peripheral Milling of Thin-Walled Workpieces with Flexible Iterative Algorithms

2014 ◽  
Vol 909 ◽  
pp. 185-191 ◽  
Author(s):  
Yong Gang Kang ◽  
Guo Rong Yang ◽  
Jie Huang ◽  
Jing Hang Zhu
Keyword(s):  
Iterative Algorithms ◽  
Simulation Method ◽  
Milling Process ◽  
Fe Model ◽  
Surface Form ◽  
High Complexity ◽  
Peripheral Milling ◽  
Form Errors ◽  
Simulation Procedure ◽  
Thin Walled

Due to the deflection of tool and workpiece induced by cutting force, there is a high complexity associated with the prediction of surface form errors in the peripheral milling process of thin-walled workpieces. And the prediction of surface form errors induced by cutting deflection is the precondition for process optimization and error compensation. This paper proposes a systematic simulation procedure suitable for surface form errors prediction in peripheral milling of low rigid thin-walled workpiece. Some key algorithms with the judgment of contacts between the cutter and the workpiece, the flexible iterative algorithm as well as the tool/workpieces deflection prediction using FE model are developed and presented in detail. Comparisons of the form errors and cutting forces obtained numerically and experimentally confirm the validity of the proposed algorithms and simulation procedure.

Pretwisted Curved Beams of Thin-Walled Open Section

1972 ◽  
Vol 39 (3) ◽  
pp. 779-785 ◽  
Author(s):  
A. I. Soler
Keyword(s):  
Numerical Technique ◽  
Equations Of Motion ◽  
Highway Bridges ◽  
Major Effect ◽  
Curved Beams ◽  
Open Section ◽  
Straight Beam ◽  
Thin Walled ◽  
Bending Modes ◽  
Axes Of Symmetry

Equations of motion are derived for coupled extension, flexure, and torsion of pretwisted curved bars of thin-walled, open section. The derivation is based on energy principles and includes inertia terms. The major effect of initial pretwist is to allow coupling of all possible beam deformation modes; however, if the bar is straight and has two axes of symmetry, pretwist causes coupling only between the two bending modes, and between extension and torsion. The governing equations are presented in first-order form, and a numerical technique is suggested for the case of space varying pretwist. It is suggested that these equations may form the basis for a simplified study of the effect of superelevation on the static and dynamic response of curved highway bridges. Finally, a simple straight beam with uniform pretwist is studied to compare effects of pretwist and restrained torsion in a thin-walled beam of open section.

scholarly journals Frequency-Domain Robust Performance Condition for Controller Uncertainty in SISO LTI Systems: A Geometric Approach

2009 ◽  
Vol 2009 ◽  
pp. 1-9
Author(s):  
Vahid Raissi Dehkordi ◽  
Benoit Boulet
Keyword(s):  
Frequency Domain ◽  
Linear Time ◽  
Order Reduction ◽  
Geometric Approach ◽  
Geometrical Approach ◽  
Robust Performance ◽  
Linear Time Invariant ◽  
Additive Perturbation ◽  
Plant Uncertainty ◽  
Invariant Control

This paper deals with the robust performance problem of a linear time-invariant control system in the presence of robust controller uncertainty. Assuming that plant uncertainty is modeled as an additive perturbation, a geometrical approach is followed in order to find a necessary and sufficient condition for robust performance in the form of a bound on the magnitude of controller uncertainty. This frequency domain bound is derived by converting the problem into an optimization problem, whose solution is shown to be more time-efficient than a conventional structured singular value calculation. The bound on controller uncertainty can be used in controller order reduction and implementation problems.

scholarly journals Reduced order system identification for UAVs

2015 ◽  
Vol 119 (1218) ◽  
pp. 961-980 ◽  
Author(s):  
P-D. Jameson ◽  
A. K. Cooke
Keyword(s):  
System Identification ◽  
Equations Of Motion ◽  
Real Data ◽  
Flight Test ◽  
Rate Of Change ◽  
Order System ◽  
Parameter Estimates ◽  
Reduced Order Models ◽  
Test Scenario ◽  
Reduced Order

Abstract Reduced order models representing the dynamic behaviour of symmetric aircraft are well known and can be easily derived from the standard equations of motion. In flight testing, accurate measurements of the dependent variables which describe the linearised reduced order models for a particular flight condition are vital for successful system identification. However, not all the desired measurements such as the rate of change in vertical velocity (Ẇ) can be accurately measured in practice. In order to determine such variables two possible solutions exist: reconstruction or differentiation. This paper addresses the effect of both methods on the reliability of the parameter estimates. The methods are used in the estimation of the aerodynamic derivatives for the Aerosonde UAV from a recreated flight test scenario in Simulink. Subsequently, the methods are then applied and compared using real data obtained from flight tests of the Cranfield University Jetstream 31 (G-NFLA) research aircraft.

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