Nonlinear Dynamics in Drilling and Boring Operations Assisted by Low Frequency Vibration

2007 ◽  
Author(s):  
George F. Moraru
Keyword(s):  
Nonlinear Dynamics ◽  
Harmonic Balance ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Drilling Process ◽  
Process Damping ◽  
Regenerative Effect ◽  
Low Frequency Vibration ◽  
Machining System

The nonlinear dynamics of the drilling process assisted by self-excited axial vibrations is analyzed. Models are developed and discussed, including regenerative effect and various phenomena contributing to the process damping in drilling and boring operations. Stability and bifurcation analysis, using several assumptions on the damping in the cutting process, are carried out using linear analysis tools or simulations. A simple predictive model based on a harmonic balance method is presented. Behavior charts are constructed using simulations. Hypothesis on the nature of the process damping and nonlinear behavior of the machining system are proved by experiments. A possible application to the gundrilling boring process in aircraft drilling and assembly process is presented.

Dynamic Modeling and Output Characteristic Analysis of a Micro Bistable Piezoelectric Generator

2015 ◽  
Vol 645-646 ◽  
pp. 995-1003
Author(s):  
Xin Hua Mao ◽  
Qing He ◽  
Ting Ting Huang
Keyword(s):  
Electromechanical Coupling ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Output Characteristic ◽  
Electromechanical Coupling Coefficient ◽  
Transfer Model ◽  
Characteristic Analysis ◽  
System A ◽  
Low Frequency Vibration ◽  
Piezoelectric Generator

For effectively harvesting the broadband and low-frequency vibration energies in real environment, a micro bistable piezoelectric generator, without containing magnet, is designed. On the basis of analysis the nonlinear behavior of the stiffness, damping and the electromechanical coupling coefficient about the bistable vibration system, a precise mechanical-electric transfer model is built. The output characteristic of the piezoelectric generator is simulated and tested. The results showed that the piezoelectric generator can effectively harvest the broadband and low frequency vibration energies. And the output voltage can meet the electricity demand of a wireless sensor network node. The structure of the piezoelectric generator does not contain magnets, and it is easy to realize miniaturization and integration.

Revealing Nonlinear Dynamics Phenomena in Mooring Due to Slowly-Varying Drift

2005 ◽  
Author(s):  
Michael M. Bernitsas ◽  
Joa˜o Paulo J. Matsuura
Keyword(s):  
Nonlinear Dynamics ◽  
Limit Cycles ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Resonance Phenomenon ◽  
Nonlinear Phenomena ◽  
Mooring System ◽  
Stable Limit ◽  
Dynamic Interactions ◽  
Wave Drift

The effects of slowly-varying wave drift forces on the nonlinear dynamics of mooring systems have been studied extensively in the past 30 years. It has been concluded that slowly-varying wave drift may resonate with mooring system natural frequencies. In recent work, we have shown that this resonance phenomenon is only one of several possible nonlinear dynamic interactions between slowly-varying wave drift and mooring systems. We were able to reveal new phenomena based on the design methodology developed at the University of Michigan for autonomous mooring systems and treating slowly-varying wave drift as an external time-varying force in systematic simulations. This methodology involves exhaustive search regarding the nonautonomous excitation, however, and approximations in defining response bifurcations. In this paper, a new approach is developed based on the harmonic balance method, where the response to the slowly-varying wave drift spectrum is modeled by limit cycles of frequency estimated from a limited number of simulations. Thus, it becomes possible to rewrite the nonautonomous system as autonomous and reveal stability properties of the nonautonomous response. Catastrophe sets of the symmetric principal equilibrium, serving as design charts, define regions in the design space where the trajectories of the mooring system are asymptotically stable, limit cycles, or non-periodic. This methodology reveals and proves that mooring systems subjected to slowly-varying wave drift exhibit many nonlinear phenomena, which lead to motions with amplitudes 2–3 orders of magnitude larger than those resulting from linear resonance. A turret mooring system (TMS) is used to demonstrate the harmonic balance methodology developed. The produced catastrophe sets are then compared with numerical results obtained from systematic simulations of the TMS dynamics.

Numerical Model for Prediction of Cutting Forces in a Vibratory Drilling Process

2014 ◽  
Vol 1016 ◽  
pp. 215-220 ◽  
Author(s):  
Nawel Glaa ◽  
Kamel Mehdi ◽  
Moez Ben Jaber
Keyword(s):  
Cutting Forces ◽  
Three Dimensional ◽  
Low Frequency ◽  
Cutting Parameters ◽  
Forced Vibrations ◽  
Drilling Process ◽  
Drilling Operation ◽  
Low Frequency Vibration ◽  
Cutting Force Components ◽  
Force Components

The drilling operation is considered by manufacturers as complex and difficult process (rapid wear of the cutting edge as well as problems of chip evacuation). Faced with these failures, manufacturers have shifted in recent years towards the drilling process assisted by forced vibrations. This method consist to add an axial oscillation with a low frequency to the classical feed movement of the drill so as to ensure good fragmentation and better chip evacuation. This paper presents a model for prediction of cutting forces during a drilling operation assisted by forced low-frequency vibration. The model allows understanding the interaction between the tool and the workpiece and identifying numerically the three-dimensional evolution of the cutting force components generated by the vibratory drilling operation. The effects of cutting parameters, tool parameters and those of forced vibrations on the cutting forces distributions will be discussed.

Analytical Solution for the Nonlinear Dynamics of Planetary Gears

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
Cheon-Jae Bahk ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Harmonic Balance ◽  
Gear Tooth ◽  
Harmonic Balance Method ◽  
Nonlinear Effects ◽  
Mesh Stiffness ◽  
Planetary Gears ◽  
Parallel Finite Element ◽  
The Impact

Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. At resonance, the resulting vibration causes tooth separation leading to nonlinear effects such as jump phenomena and subharmonic resonance. This work examines the nonlinear dynamics of planetary gears by numerical and analytical methods over the meaningful mesh frequency ranges. Concise, closed-form approximations for the dynamic response are obtained by perturbation analysis. The analytical solutions give insight into the nonlinear dynamics and the impact of system parameters on dynamic response. Correlation between the amplitude of response and external torque demonstrates that tooth separation occurs even under large torque. The harmonic balance method with arclength continuation confirms the perturbation solutions. The accuracy of the analytical and harmonic balance solutions is evaluated by parallel finite element and numerical integration simulations.

Development of Fixing System for 2-Axis Micro Deep Drilling Assisted by Low Frequency Vibration

2014 ◽  
Vol 625 ◽  
pp. 149-154 ◽  
Author(s):  
Ivan Burdukovskyi ◽  
Jun'ichi Kaneko ◽  
Kenichiro Horio
Keyword(s):  
Amplitude Ratio ◽  
Low Frequency ◽  
Two Dimensions ◽  
Drilling Process ◽  
Vibration Source ◽  
Deep Drilling ◽  
Machining Time ◽  
Hard Materials ◽  
Low Frequency Vibration ◽  
Vertical Displacements

Micro deep drilling of hard materials is required to involve step feed in process that grows up machining time. To increase the step feed, a method with low frequency vibration (frequency ~190 Hz, amplitude ~10 μm) by oscillating of workpiece has been proposed. Previous study is focused on method of 1-axis drilling process assisted by low frequency vibration. Introducing the method with low frequency vibration to 2-axis drilling process on a curved surface is required to oscillate the workpiece in two dimensions. Purpose of our study is to design fixing system with the 2-dimansional low frequency vibration. Vibration source is needed to change for providing the 2-dimansional vibration. Fixing system for 2-dimensional vibration (FS2DV) consists of two vibration sources in horizontal and vertical directions with spring systems along it action. The 2-dimensional vibration is controlled by amplitude ratio of the vibrations from each source. As a result, we have succeeded low frequency vibration of the workpiece with assigned direction. The resulting vibration is verified (measuring of instantaneous horizontal and vertical displacements).

scholarly journals The effect of MQL on tool wear progression in low-frequency vibration-assisted  drilling of CFRP/Ti6Al4V stack material

2021 ◽  
Author(s):  
Ramy Hussein ◽  
Ahmad Sadek ◽  
Mohamed Elbestawi ◽  
Helmi Attia
Keyword(s):  
Tool Wear ◽  
Vibration Amplitude ◽  
Cutting Temperature ◽  
Cutting Speed ◽  
Chip Thickness ◽  
Low Frequency ◽  
Drilling Process ◽  
Machining Parameters ◽  
Geometrical Accuracy ◽  
Low Frequency Vibration

Abstract In this paper, the tool wear mechanism in low-frequency vibration-assisted drilling (LF-VAD) of carbon fiber reinforced polymer (CFRP)/Ti6Al4V stacks has been proposed using variably machining parameters. Based on the kinematics analysis, the effect of vibration amplitude on the chip formation, uncut chip thickness, chip radian, and axial velocity was presented. Subsequently, the effect of LF-VAD on the cutting temperature, tool wear, delamination, and geometrical accuracy was presented for different vibration amplitude. The LF-VAD with the utilization of minimum quantity lubricant (MQL) resulted in a successful drilling process of 50 holes, with a 63 % reduction of the cutting temperature. For the rake face, LF-VAD reduced the adhered height of Ti6Al4V by 80 % at low cutting speed and reduced the crater depth by 33 % at the high cutting speed. On the other hand, LF-VAD reduced the flank wear land by 53 %. Furthermore, LF-VAD showed a significant enhancement on the CFRP delamination, geometrical accuracy, and burr formation.

Subharmonic-Response Computation and Stability Analysis for a Nonlinear Oscillator Using a Split-Frequency Harmonic Balance Method

2006 ◽  
Vol 1 (3) ◽  
pp. 221-229 ◽  
Author(s):  
J. F. Dunne
Keyword(s):  
Stability Analysis ◽  
High Frequency ◽  
Harmonic Balance ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Equation Error ◽  
Subharmonic Response ◽  
Split Frequency ◽  
Frequency Harmonic

A split-frequency harmonic balance method (SF-HBM) is developed to obtain subharmonic responses of a nonlinear single-degree-of-freedom oscillator driven by periodic excitation. This method is capable of generating highly accurate periodic solutions involving a large number of solution harmonics. Responses at the excitation period, or corresponding multiples (such as period 2 and period 3), can be readily obtained with this method, either in isolation or as combinations. To achieve this, the oscillator equation error is first expressed in terms of two Mickens functions, where the assumed Fourier series solution is split into two groups, nominally associated with low-frequency or high-frequency harmonics. The number of low-frequency harmonics remains small compared to the number of high-frequency harmonics. By exploiting a convergence property of the equation-error functions, accurate low-frequency harmonics can be obtained in a new iterative scheme using a conventional harmonic balance method, in a separate step from obtaining the high-frequency harmonics. The algebraic equations (needed in the HBM part of the method) are generated wholly numerically via a fast Fourier transform, using a discrete-time formulation to include inexpansible nonlinearities. A nonlinear forced-response stability analysis is adapted for use with solutions obtained with this SF-HBM. Period-3 subharmonic responses are obtained for an oscillator with power-law nonlinear stiffness. The paper shows that for this type of oscillator, two qualitatively different period-3 subharmonic response branches can be obtained across a broad frequency range. Stability analysis reveals, however, that for an increasingly stiff model, neither of these subharmonic branches are stable.

Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers

1997 ◽  
Vol 119 (1) ◽  
pp. 96-103 ◽  
Author(s):  
K. Y. Sanliturk ◽  
M. Imregun ◽  
D. J. Ewins
Keyword(s):  
Harmonic Balance ◽  
Turbine Blades ◽  
Numerical Test ◽  
Harmonic Balance Method ◽  
Nonlinear Behavior ◽  
Friction Damper ◽  
Friction Dampers ◽  
Equivalent Time ◽  
Time Marching ◽  
Detailed Assessment

Although considerable effort has been devoted to the formulation of predictive models of friction damper behavior in turbomachinery applications, especially for turbine blades, the problem is far from being solved due to the complex nonlinear behavior of the contact surfaces. This paper primarily focuses on analytical and numerical aspects of the problem and addresses the problem in the frequency domain while exploring the viability of equivalent time-domain alternatives. The distinct features of this work are: (i) the modelling of nonlinear friction damper behavior as an equivalent amplitude-dependent complex stiffness via a first-order harmonic balance method (HBM), (ii) the use of sine sweep excitation in time-marching analysis, (iii) the application of the methodology to numerical test cases, including an idealised 3D turbine blade model with several friction dampers, (iv) the verification of the numerical findings using experimental data, and (v) a detailed assessment of the suitability of HBM for the analysis of structures with friction dampers.

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