Stability Analysis of a Variable Spindle Speed Milling Process

2005 ◽  
Author(s):  
X.-H. Long ◽  
B. Balachandran
Keyword(s):  
Milling Process ◽  
Spindle Speed ◽  
Depth Of Cut ◽  
Infinite Dimensional ◽  
Dimensional Matrix ◽  
Finite Dimensional ◽  
Milling Operations ◽  
Milling Operation ◽  
The Stability ◽  
Delay Differential

In this effort, a stability treatment is presented for a milling process with a variable spindle speed (VSS). This variation is caused by superimposing a sinusoidal modulation on a nominal spindle speed. The dynamics of the VSS milling process is described by a set of delay differential equations (DDEs) with time varying periodic coefficients and a time delay. A semi-discretization scheme is used to discretize the system over one period, and the infinite dimensional transition matrix is converted to a finite dimensional matrix over this period. The eigenvalues of this finite dimensional matrix are used to determine the stability of the VSS milling operation with respect to selected control parameters, such as the axis depth of cut and the nominal spindle speed. The benefits of VSS milling operations are discussed by comparing the stability charts obtained for VSS milling operations with those obtained for constant spindle speed (CSS) milling operations.

Stability of Up-milling and Down-milling Operations with Variable Spindle Speed

2010 ◽  
Vol 16 (7-8) ◽  
pp. 1151-1168 ◽  
Author(s):  
Xinhua Long ◽  
B. Balachandran
Keyword(s):  
Spindle Speed ◽  
Depth Of Cut ◽  
Control Parameters ◽  
Infinite Dimensional ◽  
Dimensional Matrix ◽  
Finite Dimensional ◽  
Milling Operations ◽  
The Stability ◽  
Delay Differential ◽  
Milling Dynamics

In this article, a stability treatment is presented for up-milling and down-milling processes with a variable spindle speed (VSS). This speed variation is introduced by superimposing a sinusoidal modulation on a nominal spindle speed. The VSS milling dynamics is described by a set of delay differential equations with time varying periodic coefficients and a time delay. A semi-discretization scheme is used to discretize the system over one period, and the infinite-dimensional transition matrix is reduced to a finite-dimensional matrix over this period. The eigenvalues of this finite-dimensional matrix provide information on VSS milling stability with respect to control parameters, such as the axial depth of cut and the nominal spindle speed. The stability charts obtained for VSS milling operations are compared with those obtained for constant spindle speed milling operations, and the benefits of VSS milling operations are discussed.

scholarly journals Surface Integrity Investigation to Determine Rough Milling Effects for Assessment of Machining Allowance for Subsequent Finish Milling of Alloy 718

2021 ◽  
Vol 5 (2) ◽  
pp. 48
Author(s):  
Jonas Holmberg ◽  
Anders Wretland ◽  
Johan Berglund ◽  
Tomas Beno ◽  
Anton Milesic Karlsson
Keyword(s):  
Surface Integrity ◽  
Milling Process ◽  
Depth Of Cut ◽  
Machined Surface ◽  
Milling Operations ◽  
Milling Operation ◽  
Machining Allowance ◽  
Rough Milling

The planned material volume to be removed from a blank to create the final shape of a part is commonly referred to as allowance. Determination of machining allowance is essential and has a great impact on productivity. The objective of the present work is to use a case study to investigate how a prior rough milling operation affects the finish machined surface and, after that, to use this knowledge to design a methodology for how to assess the machining allowance for subsequent milling operations based on residual stresses. Subsequent milling operations were performed to study the final surface integrity across a milled slot. This was done by rough ceramic milling followed by finish milling in seven subsequent steps. The results show that the up-, centre and down-milling induce different stresses and impact depths. Employing the developed methodology, the depth where the directional influence of the milling process diminishes has been shown to be a suitable minimum limit for the allowance. At this depth, the plastic flow causing severe deformation is not present anymore. It was shown that the centre of the milled slot has the deepest impact depth of 500 µm, up-milling caused an intermediate impact depth of 400 µm followed by down milling with an impact depth of 300 µm. With merged envelope profiles, it was shown that the effects from rough ceramic milling are gone after 3 finish milling passes, with a total depth of cut of 150 µm.

On the Investigation of Machine Tool Chatter in the Milling Process

2007 ◽  
Author(s):  
Mahsa Moghaddas ◽  
Mohammad H. Ghaffari Saadat
Keyword(s):  
Milling Process ◽  
Depth Of Cut ◽  
Non Linear Equation ◽  
Stability And Instability ◽  
Machine Tool Chatter ◽  
Stability Chart ◽  
Periodic Delay ◽  
The Stability ◽  
Two Parameters ◽  
Delay Differential

In this paper, the chatter phenomenon is investigated through a single degree of freedom model of the milling process. In this regard, the non-linear equation of motion obtained from modeling of the milling process, which is a time-periodic delay differential equation, is simulated, and by changing the parameters: spindle speed and depth of cut, and assuming constant quantities for other parameters of the system the stable and instable points for the system are gained according to these two parameters by numerical method. In the end, the stability chart for this system is plotted and the approximate boundaries between the stability and instability regions are obtained numerically.

scholarly journals Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels

2009 ◽  
Vol 4 (3) ◽  
Author(s):  
Eric A. Butcher ◽  
Oleg A. Bobrenkov ◽  
Ed Bueler ◽  
Praveen Nindujarla
Keyword(s):  
Cutting Force ◽  
Extreme Points ◽  
Period Doubling ◽  
Milling Process ◽  
Depth Of Cut ◽  
Approximation Technique ◽  
The Stability ◽  
Delay Differential ◽  
High Degree ◽  
Period Doubling Bifurcations

In this paper the dynamic stability of the milling process is investigated through a single degree-of-freedom model by determining the regions where chatter (unstable) vibrations occur in the two-parameter space of spindle speed and depth of cut. Dynamic systems such as milling are modeled by delay-differential equations with time-periodic coefficients. A new approximation technique for studying the stability properties of such systems is presented. The approach is based on the properties of Chebyshev polynomials and a collocation expansion of the solution. The collocation points are the extreme points of a Chebyshev polynomial of high degree. Specific cutting force profiles and stability charts are presented for the up- and down-milling cases of one or two cutting teeth and various immersion levels with linear and nonlinear regenerative cutting forces. The unstable regions due to both secondary Hopf and flip (period-doubling) bifurcations are found, and an in-depth investigation of the optimal stable immersion levels for down-milling in the vicinity of where the average cutting force changes sign is presented.

Countermeasure Against Regenerative Chatter in End Milling Operations With Vibration Absorbers

2010 ◽  
Author(s):  
Y. Nakano ◽  
H. Takahara
Keyword(s):  
End Milling ◽  
Spindle Speed ◽  
The Self ◽  
Depth Of Cut ◽  
Vibration Absorbers ◽  
Regenerative Chatter ◽  
Stability Lobe ◽  
Milling Operations ◽  
Wide Range ◽  
The Stability

Chatter can result in the poor machined surface, tool wear and reduced product quality. Chatter is classified into the forced vibration and the self-excited vibration in perspective of the generation mechanism. It often happens that the self-excited chatter becomes problem practically because this causes heavy vibration. Regenerative chatter due to regenerative effect is one of the self-excited chatter and generated in the most cutting operations. Therefore, it is very important to quench or avoid regenerative chatter (hereafter, simply called chatter). It is well known that chatter can be avoided by selecting the optimal cutting conditions which are determined by using the stability lobe of chatter. The stability lobe of chatter represents the boundary between stable and unstable cuts as a function of spindle speed and depth of cut. However, it is difficult to predict the stability lobe of chatter perfectly because the prediction accuracy of it depends on the tool geometry, the vibration characteristics of the tool system and the machine tool and the material behavior of the workpiece. In contrast, it is made clear that the stability lobe of chatter has been elevated in the wide range of spindle speed by the vibration absorber in the turning operations. However, it should be noted that none of the previous work has actually applied the vibration absorbers to the rotating tool system in the machining center and examined the effect of the vibration absorbers on chatter in the end milling operations to the best of authors’ knowledge. In this paper, the effect of the vibration absorbers on regenerative chatter generated in the end milling operations is qualitatively evaluated by the stability analysis and the cutting test. It is made clear the relationship between the suppression effect of the vibration absorbers and the tuning parameters of them. It is shown that the greater improvement in the critical axial depth of cut is observed in the wide range of spindle speed by the properly tuned vibration absorbers.

AN ABSTRACT DIFFERENTIAL EQUATION ARISING FROM CELL POPULATION DYNAMICS

1995 ◽  
Vol 03 (02) ◽  
pp. 469-481
Author(s):  
OVIDE ARINO ◽  
EVA SÁNCHEZ
Keyword(s):  
Differential Equation ◽  
Population Dynamics ◽  
Cell Population ◽  
Abstract Differential Equation ◽  
Cell Population Dynamics ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
The Stability ◽  
The One ◽  
Delay Differential

We provide an analysis of the stability and bifurcation properties of the solutions of an abstract differential nonlinear equation arising from cell population dynamics. The work surveyed here stems from a remark we made with respect to these equations: that it is possible to associate to any of them a delay differential equation on an infinite dimensional vector space. Perturbation theory for nonlinear equations similar to the one known for delay differential equations on finite dimensional spaces could possibly yield the same results as for those equations.

Self-Excited Vibrations in a Delay Oscillator: Application to Milling With Simultaneously Engaged Helical Flutes

2009 ◽  
Author(s):  
Firas A. Khasawneh ◽  
Brian P. Mann ◽  
Oleg A. Bobrenkov ◽  
Eric A. Butcher
Keyword(s):  
Period Doubling ◽  
Helix Angle ◽  
Milling Process ◽  
Depth Of Cut ◽  
Frame Work ◽  
Continuous Delay ◽  
The Stability ◽  
Delay Differential ◽  
Step Over ◽  
High Depth

This paper investigates the stability of a milling process with simultaneously engaged flutes by extending the state-space temporal finite elements method. In contrast to prior works, multiple flute engagement due to both a high depth of cut and a high step-over distance are considered. A particular outcome of this study is the development of a frame work to determine the stability of periodic, piecewise continuous delay differential equations. Another major outcome is the demonstration of different stability behavior at the loss of stability in comparison to prior results. To elaborate more, period doubling regions are shown to appear at relatively high radial immersions when multiple flutes with either a zero or non-zero helix angle are simultaneously cutting.

scholarly journals Stability of Milling Process with Variable Spindle Speed Using Runge–Kutta-Based Complete Method

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Shujie Lv ◽  
Yang Zhao
Keyword(s):  
Removal Rate ◽  
Modulation Frequency ◽  
Milling Process ◽  
Spindle Speed ◽  
Calculation Time ◽  
Time Varying Delay ◽  
Speed Modulation ◽  
Runge Kutta ◽  
The Stability ◽  
Delay Differential

The variable-spindle-speed (VSS) technique is effective in preventing regenerative chatter in milling processes. However, spindle-speed-modulation parameters should be deliberately selected to augment the material removal rate. Stability-prediction algorithms of stability predicting play an important role in this respect, as they allow the prediction of stability for all ranges of a given spindle speed. The increase in calculation time in variable-spindle-speed milling, which is caused by the modulation frequency, hinders its practical use in the workshop. In this paper, a Runge–Kutta-based complete discretization method (RKCDM) is presented to predict the stability of milling with variable spindle speeds, which is described by a set of delay differential equations (DDEs) with time-periodic coefficients and time-varying delay. The convergence and calculation efficiency are compared with those of the semidiscretization method (SDM) under different testing configurations and milling conditions. Results show that RKCDM is more accurate and saves at least 50% of the calculation time of SDM. The effects of modulation parameters on the stability of VSS milling are explored through stability lobe diagrams produced from RKCDM.

scholarly journals Chatter identification in milling of Inconel 625 based on recurrence plot technique and Hilbert vibration decomposition

2018 ◽  
Vol 148 ◽  
pp. 09003 ◽  
Author(s):  
Paweł Lajmert ◽  
Rafał Rusinek ◽  
Bogdan Kruszyński
Keyword(s):  
Stability Limit ◽  
Recurrence Plot ◽  
Milling Process ◽  
Machining Process ◽  
Inconel 625 ◽  
Depth Of Cut ◽  
Force Measurements ◽  
Stability Lobe ◽  
Theoretical Finding ◽  
The Stability

In the paper a cutting stability in the milling process of nickel based alloy Inconel 625 is analysed. This problem is often considered theoretically, but the theoretical finding do not always agree with experimental results. For this reason, the paper presents different methods for instability identification during real machining process. A stability lobe diagram is created based on data obtained in impact test of an end mill. Next, the cutting tests were conducted in which the axial cutting depth of cut was gradually increased in order to find a stability limit. Finally, based on the cutting force measurements the stability estimation problem is investigated using the recurrence plot technique and Hilbert vibration decomposition method.

Dynamics and Stability of Turn-Milling Operations With Varying Time Delay in Discrete Time Domain

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Alptunc Comak ◽  
Yusuf Altintas
Keyword(s):  
Time Domain ◽  
Chip Thickness ◽  
Body Motion ◽  
Depth Of Cut ◽  
Time Varying Delay ◽  
Milling Operations ◽  
Varying Time Delay ◽  
The Stability ◽  
Five Axis ◽  
Turn Milling

Turn-milling machines are widely used in industry because of their multifunctional capabilities in producing complex parts in one setup. Both milling cutter and workpiece rotate simultaneously while the machine travels in three Cartesian directions leading to five axis kinematics with complex chip generation mechanism. This paper presents a general mathematical model to predict the chip thickness, cutting force, and chatter stability of turn milling operations. The dynamic chip thickness is modeled by considering the rigid body motion, relative vibrations between the tool and workpiece, and cutter-workpiece engagement geometry. The dynamics of the process are governed by delayed differential equations by time periodic coefficients with a time varying delay contributed by two simultaneously rotating spindles and kinematics of the machine. The stability of the system has been solved in semidiscrete time domain as a function of depth of cut, feed, tool spindle speed, and workpiece speed. The stability model has been experimentally verified in turn milling of Aluminum alloy cut with a helical cylindrical end mill.

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