New Continuous Dynamic Coupling for Three Component Modeling of Tool–Holder–Spindle Structure of Machine Tools With Modified Effected Tool Damping

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Mohammad Faraji Ghanati ◽  
Reza Madoliat
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Beam Theory ◽  
New Method ◽  
Equivalent Diameter ◽  
Dynamic Coupling ◽  
Tool Holder ◽  
Joint Parameters ◽  
Continuous Dynamic ◽  
Element Method

In machine dynamics, the tool point frequency response functions (FRFs) are employed to predict the stable machining conditions. In this paper, a combined analytical–experimental substructuring procedure is proposed to determine the tool point FRFs usable for different holder–tool configurations. Contact interface of holder–spindle and tool–holder is modeled using translational and rotational springs and dampers spread in the length of contact surface. These joint parameters are defined using finite element method. This enables the analyst to introduce the contact stiffness and damping in more detail with taking into consideration the variations of normal pressure in the tool–holder and holder–spindle joints. The dynamic analysis of the holder is done using Timoshenko beam theory by Tchebyshev method. The tool dynamics is modeled based on Euler–Bernoulli beam theory using the method of equivalent diameter. For the purpose of shifting the tool stability lobes to a higher level, tool damping parameter is modified by internal frictional damper and the effect is analyzed by analytical methods and experimental study. After joint parameters are defined continuously by finite element method, a new method for continuous dynamic coupling is presented. The method employs the measured spindle-machine FRFs and analytical models of the tool and holder to predict the tool tip FRFs. In this new method, continuous coupling in two separate domains of response model and modal model is presented. Such structural modeling avoids us to do complex modal tests for a different set of combinations of the holder and tool with specific milling machine. An experimental case study is provided to demonstrate the applicability of the proposed method in dynamic modeling of machine tool.

In-Plane Free Vibration of Curved Beams Using Finite Element Method

2007 ◽  
Author(s):  
F. Yang ◽  
R. Sedaghati ◽  
E. Esmailzadeh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Central Line ◽  
Circular Ring ◽  
Curved Beam ◽  
The Finite Element Method ◽  
Curved Beams ◽  
Element Method

Curved beam-type structures have many applications in engineering area. Due to the initial curvature of the central line, it is complicated to develop and solve the equations of motion by taking into account the extensibility of the curve axis and the influences of the shear deformation and the rotary inertia. In this study the finite element method is utilized to study the curved beam with arbitrary geometry. The curved beam is modeled using the Timoshenko beam theory and the circular ring model. The governing equation of motion is derived using the Extended-Hamilton principle and numerically solved by the finite element method. A parametric sensitive study for the natural frequencies has been performed and compared with those reported in the literature in order to demonstrate the accuracy of the analysis.

Analysis of bimorph piezoelectric beam energy harvesters using Timoshenko and Euler–Bernoulli beam theory

2012 ◽  
Vol 24 (2) ◽  
pp. 226-239 ◽  
Author(s):  
Gang Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Slenderness Ratio ◽  
Beam Theory ◽  
Bernoulli Beam ◽  
Energy Harvesters ◽  
Bernoulli Beam Theory ◽  
Spectral Finite Element ◽  
Euler Bernoulli Beam ◽  
Element Method

Single-degree-of-freedom lumped parameter model, conventional finite element method, and distributed parameter model have been developed to design, analyze, and predict the performance of piezoelectric energy harvesters with reasonable accuracy. In this article, a spectral finite element method for bimorph piezoelectric beam energy harvesters is developed based on the Timoshenko beam theory and the Euler–Bernoulli beam theory. Linear piezoelectric constitutive and linear elastic stress/strain models are assumed. Both beam theories are considered in order to examine the validation and applicability of each beam theory for a range of harvester sizes. Using spectral finite element method, a minimum number of elements is required because accurate shape functions are derived using the coupled electromechanical governing equations. Numerical simulations are conducted and validated using existing experimental data from the literature. In addition, parametric studies are carried out to predict the performance of a range of harvester sizes using each beam theory. It is concluded that the Euler–Bernoulli beam theory is sufficient enough to predict the performance of slender piezoelectric beams (slenderness ratio > 20, that is, length over thickness ratio > 20). In contrast, the Timoshenko beam theory, including the effects of shear deformation and rotary inertia, must be used for short piezoelectric beams (slenderness ratio < 5).

A New Method to Quickly Optimize the Thickness of Multi-Holes Plate

2014 ◽  
Vol 915-916 ◽  
pp. 205-208
Author(s):  
Sheng Bin Wu ◽  
Xiao Bao Liu
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Design Method ◽  
New Method ◽  
The Finite Element Method ◽  
Design Error ◽  
Theory Of Plates ◽  
Plates And Shells ◽  
Element Method

The theory of plates and shells is not adapted to design thickness for the multi-holes plates in engineering. A new method to quickly optimize the thickness based on the finite element method theory was put forward. The method combined the theory of plate with the finite element method to establish a mathematical model and analyzed the influences of load, constraint and complexity on design error. The practices demonstrated that the proposed design method is effective and feasible.

Introduction of a Novel and Powerful Optimization Method Using Genetic Algorithm and Finite Element Method

2012 ◽  
Vol 433-440 ◽  
pp. 746-753
Author(s):  
Payam Karimi ◽  
Shahin Shadlou ◽  
Bahare Nazari
Keyword(s):  
Genetic Algorithm ◽  
Finite Element Method ◽  
Finite Element ◽  
Design Optimization ◽  
Optimization Method ◽  
Fast Convergence ◽  
New Method ◽  
Engineering Structures ◽  
Proposed Model ◽  
Element Method

Optimizing the complicated engineering structures has always been a huge issue. A technique for the design optimization of different components is presented using genetic algorithm and finite element method. To reduce the runtime and increase the efficiently of proposed model a new method of coupling is presented. In addition, two different problems were solved using the presented model and the results showed a great and fast convergence.

Two-Scale Algorithm for Computing the Approximation of the Displacement in Periodic Perforated Structure of Composites

2011 ◽  
Vol 374-377 ◽  
pp. 1226-1229
Author(s):  
Ming Xiang Deng ◽  
Yong Ping Feng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximate Solution ◽  
Higher Order ◽  
New Method ◽  
Approximation Solution ◽  
Scale Method ◽  
Small Periodic ◽  
Element Method

By means of two-scale method, the approximation solution of the displacement for structure of composites with small periodic perforated configuration is built, and the algorithm corresponding to two-scale finite element method is presented. One new method of higher order for computing approximate solution of the displacement in periodic perforated composites is given.

Static Analysis of a Functionally Graded Piezoelectric Beam Using Finite Element Method

2010 ◽  
Author(s):  
Iman Eshraghi ◽  
Aghil Yousefi-Koma
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Deformation ◽  
Static Analysis ◽  
Slenderness Ratio ◽  
Beam Theory ◽  
Functionally Graded ◽  
Bending Behavior ◽  
Functionally Graded Piezoelectric ◽  
Element Method

In this study static analysis of functionally graded piezoelectric material (FGPM) beams is performed using finite element modeling. First order shear deformation beam theory (Timoshenko beam theory) with the assumption of linear strain-displacement relations is used for modeling of displacement and strain fields in the beam. Theoretical formulations are derived employing Hamilton’s principle using linear constitutive relations of piezoelectric materials and including the effect of transverse shear deformation. Finite element method with one dimensional linear continuum isoparametric element, three displacement mechanical degrees of freedom, and one electric potential degree of freedom assigned to each node is then used to investigate the bending behavior of FGPM beam actuator under thermo-electro-mechanical loads. Consequently, a parametric study of the bending behavior of an FGPM beam is performed. The effects of slenderness ratio and fraction of volume of constituent materials, on the thermo-electro-mechanical characteristics are studied. It is shown that under electrical loading the beam represents the so-called non-intermediate behavior.

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