Nonlinear Vibration of a Thin-Plate Workpiece During High Speed Milling Under 1:1 Internal Resonance Condition

2012 ◽  
Author(s):  
Wei Zhang ◽  
Rui Zhou ◽  
Jean W. Zu ◽  
Qian Wang
Keyword(s):  
Nonlinear Vibration ◽  
Thin Plate ◽  
Internal Resonance ◽  
High Speed ◽  
Plate Theory ◽  
Resonance Condition ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Milling Process ◽  
Phase Portraits

In this paper, the nonlinear vibration of a thin-plate workpiece during milling process is investigated. The thin-plate workpiece is modeling as a cantilevered thin plate. The equations of motion for the thin-plate workpiece are derived based on the Kirchhoff-plate theory and the von Karman strain-displacement relations by using the Hamilton’s principle. By applying the Galerkin’s approach, the resulting equations are reduced to a two-degree-of-freedom nonlinear system with external excitations. Considering the case of 1:1 internal resonance, the method of Asymptotic Perturbation method is utilized to obtain the averaged equations of the cantilevered thin-plate workpiece. Numerical method is used to study nonlinear dynamics of the cantilevered thin plate and get the two-dimensional phase portraits, waveforms phase, three-dimensional phase and frequency spectrum phase. The result shows that the cantilevered thin-plate workpiece exhibits the complex dynamic behavior with the increase of the amplitude of the forcing excitation.

Chaotic Motion of a Functionally Graded Materials Square Thin Plate

2012 ◽  
Vol 531 ◽  
pp. 593-596
Author(s):  
Shuang Bao Li ◽  
Yu Xin Hao
Keyword(s):  
Thin Plate ◽  
Functionally Graded Materials ◽  
Chaotic Motion ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Third Order ◽  
Graded Materials ◽  
Steady State Heat ◽  
Steady State Heat Transfer

Chaotic motion of a simply supported functionally graded materials (FGM) square thin plate under one-to-two internal resonance is studied in this paper. The FGM plate is subjected to the transversal and in-plane excitations. Material properties are assumed to be temperature-dependent and change continuously throughout the thickness of the plate. The temperature variation is assumed to occur in the thickness direction only and satisfy the steady-state heat transfer equation. Based on the Reddy’s third-order plate theory and Hamilton’s principle, the nonlinear governing equations of motion for the FGM plate are derived by using the Galerkin’s method to describe the transverse oscillation in the first two modes Numerical simulations illustrate that there exist chaotic motion for the FGM rectangular plate.

Development of a machining simulator considering machine behaviour

2003 ◽  
Vol 217 (9) ◽  
pp. 1333-1339 ◽  
Author(s):  
A Dugas ◽  
J J Lee ◽  
M Terrier ◽  
J Y Hascoët
Keyword(s):  
High Speed ◽  
Dynamic Behaviour ◽  
Three Dimensional ◽  
Milling Process ◽  
High Speed Machining ◽  
Tracking Errors ◽  
Tool Paths ◽  
Milling Operation ◽  
Dynamic Errors ◽  
Tool Deflections

High-speed machining gives much potential for increasing the efficiency of the milling operation, but it requires very careful preparation for the milling process to use this potential. A machining simulator has been developed that can analyse dynamic errors due to tool deflections and machine dynamic behaviour using a three-dimensional solid simulation model. This kind of simulator would be a useful tool to apply in high-speed machining where it is necessary to obtain very well prepared part programs considering dynamic errors as well as geometrical errors. In this short communication, an algorithm will be introduced to estimate the dynamic errors caused by machine dynamic behaviour. Specifically, this algorithm predicts real feed rates and tracking errors considering the limits of numerical controllers and machine tools. The efficiency of the algorithm has been verified through several experiments with various tool paths. In addition, the algorithm has been integrated into the machining simulator. Some results obtained from the machining simulator concerning the estimation of tracking errors will be reported.

Analysis and Research of High Speed Milling of Thin-Walled Bracket Part Based on UG NX

2010 ◽  
Vol 129-131 ◽  
pp. 256-260
Author(s):  
Yi Shu Hao ◽  
Chuang Hai ◽  
Xin Xing Zhu
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Structural Features ◽  
Milling Process ◽  
Analysis Method ◽  
Three Dimensional Model ◽  
Machining Processes ◽  
Element Analysis ◽  
High Speed Milling ◽  
Tool Paths

Treating high speed milling theory as the guidance, this paper researched high speed milling process of bracket part based on UG NX. Combined with the structural features of bracket part, three dimensional model is built by UG NX CAD and machining processes are worked out after analysis. UG CAM module was applied to fabricate tool paths. At last, finite element analysis method is introduced to study the processing deformation by UG NX NASTRAN module, based on which measures to restrain processing deformations is advanced and processing sequences are optimized.

Static Performance Analysis of Foil Thrust Bearing Based on Thin Plate Theory

2014 ◽  
Vol 621 ◽  
pp. 437-442
Author(s):  
Jian Jun Zhu ◽  
Jian Jun Du ◽  
Bing Li ◽  
Chang Lin Li ◽  
Dun Liu
Keyword(s):  
Thin Plate ◽  
Rotational Speed ◽  
High Speed ◽  
Plate Theory ◽  
Load Capacity ◽  
Structural Parameters ◽  
Structural Deformation ◽  
Foil Thickness ◽  
Frictional Torque ◽  
Eccentricity Ratio

The thrust foil bearing, as one of the key parts in high-speed rotating machineries, is used to sustain the axial force, and its load performance has a crucial relationship with the structural parameters and working condition. In this paper the top foil is modeled as a thin plate supported by the bumps underneath. The finite element method (FEM) is used to calculate the structural deformation coupled with the pressure distribution obtained through the solution of Reynolds equation by the finite difference method (FDM). The effects of structural and operating parameters, such as rotational speed, eccentricity ratio, top foil thickness and bump foil thickness on the load capacity and frictional torque are discussed in detail. The results show that the increase of rotational speed, eccentricity ratio and bump foil thickness is beneficial to increase the load capacity and frictional torque. The effect of variation of top foil thickness on load capacity is not obvious, which implies that the top foil plays a role in building the lubricant surface rather than providing supporting stiffness.

scholarly journals Nonlinear interactions in deformable container cranes

2015 ◽  
Vol 230 (1) ◽  
pp. 5-20 ◽  
Author(s):  
Andrea Arena ◽  
Walter Lacarbonara ◽  
Matthew P Cartmell
Keyword(s):  
Rigid Body ◽  
Internal Resonance ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Higher Order ◽  
Mode Shapes ◽  
Lagrange Equations ◽  
Internal Resonances ◽  
Container Cranes ◽  
Bending Mode

Nonlinear dynamic interactions in harbour quayside cranes due to a two-to-one internal resonance between the lowest bending mode of the deformable boom and the in-plane pendular mode of the container are investigated. To this end, a three-dimensional model of container cranes accounting for the elastic interaction between the crane boom and the container dynamics is proposed. The container is modelled as a three-dimensional rigid body elastically suspended through hoisting cables from the trolley moving along the crane boom modelled as an Euler-Bernoulli beam. The reduced governing equations of motion are obtained through the Euler-Lagrange equations employing the boom kinetic and stored energies, derived via a Galerkin discretisation based on the mode shapes of the two-span crane boom used as trial functions, and the kinetic and stored energies of the rigid body container and the elastic hoisting cables. First, conditions for the onset of internal resonances between the boom and the container are found. A higher order perturbation treatment of the Taylor expanded equations of motion in the neighbourhood of a two-to-one internal resonance between the lowest boom bending mode and the lowest pendular mode of the container is carried out. Continuation of the fixed points of the modulation equations together with stability analysis yields a rich bifurcation behaviour, which features Hopf bifurcations. It is shown that consideration of higher order terms (cubic nonlinearities) beyond the quadratic geometric and inertia nonlinearities breaks the symmetry of the bifurcation equations, shifts the bifurcation points and the stability ranges, and leads to bifurcations not predicted by the low order analysis.

An Efficient Numerical Method for Dynamic Interaction Analysis of Shinkansen Train and Railway Structure During an Earthquake

2007 ◽  
Author(s):  
M. Tanabe ◽  
N. Matsumoto ◽  
H. Wakui ◽  
M. Sogabe ◽  
H. Okuda ◽  
...  
Keyword(s):  
Numerical Method ◽  
High Speed ◽  
Large Scale ◽  
Interaction Analysis ◽  
Plastic Material ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Material Model ◽  
Dynamic Interaction ◽  
Contact Dynamics

In this paper, a simple and efficient numerical method to solve for the dynamic interaction of a Shinkansen train (high-speed train in Japan) and railway structure during an earthquake is given. The motion of the train is modeled in multibody dynamics with nonlinear springs and dampers used to connect components. An efficient mechanical model for contact dynamics between wheel and rail during an earthquake is presented. The railway structure is modeled with various finite elements. A three-dimensional nonlinear spring element based on a trilinear elastic-plastic material model is given for the concrete railway structure during an earthquake. A loop structure model has been devised to obtain an approximated combined motion of the train and railway structure during an earthquake. A modal method has been developed to solve large-scale nonlinear equations of motion of the train and railway structure effectively. Based on the present method, a computer program DIASTARS for the dynamic interaction of a Shinkansen train and railway structure during an earthquake has been developed. Numerical examples are demonstrated.

scholarly journals A Method for Determining the Thicknesses of the Reserved Protective Layers in Complex Goafs Using a Joint-Modeling Method of GTS and Flac3D

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Xin Zhao ◽  
Dianshu Liu ◽  
Shenglin Li ◽  
Meng Wang ◽  
Shuaikang Tian ◽  
...  
Keyword(s):  
Thin Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Joint Modeling ◽  
Modeling Method ◽  
Underground Cavity ◽  
Protective Layers ◽  
Safe Production ◽  
Thin Plate Theory ◽  
The Stability

In this study, a C-ALS underground cavity scanner was used to detect the shapes of mining goafs. In addition, GTS software was adopted to establish a three-dimensional geological model based on the status of the stopes, geological data, and mechanical parameters of each rock mass and to analyze the roof areas of the goafs. In regard to the morphology of the study area, based on a thin plate theory and the obtained field sampling data, a formula was established for the thicknesses of the reserved protective layers in the goafs. In addition, a formula for the thicknesses of the protective layers in the curved gobs was obtained. The thickness formula of the protective layers was then successfully verified. The detection results showed that the roof shapes of the goafs in the Yuanjiacun Iron Mine were mainly arc-shaped, and the spans of the goafs were generally less than 20 m. The stability of the arc-shaped roofs was found to be greater than that of the plate-shaped roofs. Therefore, by reducing the thicknesses of the protective layers in mining goafs, the ore recovery rates can be increased on the basis of safe production conditions. The formula of the thickness of the security layers obtained through the thin plate theory was revised based on the statistical results of the roof shapes of the goafs and then combined using GTS and FLAC3D. The modeling method successfully verified the stability of the mined-out areas. It was found that the verification results were good, and the revised formula was able to improve the recovery rate of the ore under the conditions of meeting safe production standards. Also, it was found that the revised formula could be used in the present situation. At the same time, it was also determined that the complexity of the rock masses obstructed the full identification of the joints and fissures in the present orebodies. Therefore, it is necessary to incorporate C-ALS underground cavity scanners to regularly observe the shapes of the goafs in order to ensure that stability and safety standards are maintained.

Dynamic solution for vehicle–track interaction considering the elastoplasticity of track slabs

2020 ◽  
pp. 107754632094729
Author(s):  
Lei Xu ◽  
Zhiwu Yu
Keyword(s):  
Plate Theory ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mindlin Plate ◽  
Suspension Systems ◽  
Stiffness Matrices ◽  
Track System ◽  
The Time Domain ◽  
Stress Dependent ◽  
Track Slab

In this work, an entire multi-rigid-body system with two-stage suspension systems is assumed to run on a slab track system, where the elastoplasticity of the track slab is modeled by Mindlin plate theory considered in a framework of three-dimensional vehicle–track dynamic system. Considering the elastoplasticity of track slabs, the nonlinearity and time- and stress-dependent track slab stiffness matrices must be accounted for in the time-domain dynamic solutions; therefore, a two-step iterative algorithm separating the vehicle–track system into vehicle–rail subsystem and track slab system is developed to solve the dynamic equations of motion for vehicle–track interactions. The numerical studies have shown the accuracy and efficiency of this method in calibrating the vehicle–track dynamic behavior in conditions of track slab elastoplastic deformation. Besides, it has shown that the longitudinal unevenness of the track support stiffness has significant influence on the plasticity of track slabs.

Simulation of Three-Dimensional Dynamic Cutting Forces and Chatter Stability in Ball-End Milling

2010 ◽  
Vol 443 ◽  
pp. 302-307
Author(s):  
Jun Zhao ◽  
Xiao Feng Zhang ◽  
Han Bing Luo
Keyword(s):  
High Speed ◽  
End Milling ◽  
Three Dimensional ◽  
Milling Process ◽  
Ball End Milling ◽  
Parameters Selection ◽  
Nonlinear Dynamics Model ◽  
Dynamic Components ◽  
The Stability ◽  
Milling Forces

By taking into account the regenerative chatter vibration, a nonlinear dynamics model for high speed ball-end milling is proposed. The effect of dynamic components of milling forces on chatter is analyzed. A method to predict the stability limits of high speed ball-end milling process is proposed and the stability lobes diagram is simulated. The comparison of experimental milling forces with the simulation results indicates the high accuracy of the model and the effectiveness of the simulation algorithms. The proposed method provides a theoretical instruction for parameters selection and optimization in milling processing.

Modal Analysis of Ballooning Strings With Small Sag

1999 ◽  
Author(s):  
Rongjun Fan ◽  
Sushil K. Singh ◽  
Christopher D. Rahn
Keyword(s):  
Steady State ◽  
High Speed ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Theoretical Predictions ◽  
Nonlinear Equations Of Motion

Abstract During the manufacture and transport of textile products, yarns are rotated at high speed and form balloons. The dynamic response of the balloon to varying rotation speed, boundary excitation, and disturbance forces governs the quality of the associated process. Resonance, in particular, can cause large tension variations that reduce product quality and may cause yarn breakage. In this paper, the natural frequencies and mode shapes of a single loop balloon are calculated to predict resonance. The three dimensional nonlinear equations of motion are simplified via small steady state displacement (sag) and vibration assumptions. Axial vibration is assumed to propagate instantaneously or in a quasistatic manner. Galerkin’s method is used to calculate the mode shapes and natural frequencies of the linearized equations. Experimental measurements of the steady state balloon shape and the first two natural frequencies and mode shapes are compared with theoretical predictions.

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