Investigation of Period-Doubling Islands in Milling With Simultaneously Engaged Helical Flutes

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Firas A. Khasawneh ◽  
Oleg A. Bobrenkov ◽  
Brian P. Mann ◽  
Eric A. Butcher
Keyword(s):  
State Space ◽  
Period Doubling ◽  
Helix Angle ◽  
Milling Process ◽  
Collocation Methods ◽  
Depth Of Cut ◽  
Stability Behavior ◽  
The Stability ◽  
Step Over ◽  
High Depth

This paper investigates the stability of a milling process with simultaneously engaged flutes using the state-space TFEA and Chebyshev collocation methods. In contrast to prior works, multiple flute engagement due to both the high depth of cut and high step-over distance are considered. A particular outcome of this study is the demonstration of a different stability behavior in comparison to prior works. To elaborate, period-doubling regions are shown to appear at relatively high radial immersions when multiple flutes with either a zero or nonzero helix angle are simultaneously cutting. We also demonstrate stability differences that arise due to the parity in the number of flutes, especially at full radial immersion. In addition, we study other features induced by helical tools such as the waviness of the Hopf lobes, the sensitivity of the period-doubling islands to the radial immersion, as along with the orientation of the islands with respect to the Hopf lobes.

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 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.

scholarly journals Stability Prediction of Milling Process with Variable Pitch Cutter

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Gang Jin ◽  
Qichang Zhang ◽  
Shuying Hao ◽  
Qizhi Xie
Keyword(s):  
Helix Angle ◽  
Milling Process ◽  
Depth Of Cut ◽  
Force Model ◽  
Stable Limit ◽  
Variable Pitch ◽  
Tool Geometries ◽  
Piecewise Continuous ◽  
The Stability ◽  
New Phenomena

The use of variable pitch cutter is a known means to increase the stable limit depth of cut by disrupting the regenerative effect. In this paper, an improved semidiscretization algorithm is presented to predict the stability lobes for variable pitch cutters. Modeling efforts develop a straightforward analytical integral force model that can cover any case of piecewise continuous cutting regions regarding the helix angle. The proposed approach has been verified with the comparisons with prior works, time domain simulations, and cutting tests. In addition, the method is also applied to examine the effect of the tool geometries on the stability trends for variable pitch milling. Some new phenomena for certain combinations of parameters are shown and explained.

Stability of Up- and Down-Milling Using Chebyshev Collocation Method

2005 ◽  
Author(s):  
Eric A. Butcher ◽  
Praveen Nindujarla ◽  
Ed Bueler
Keyword(s):  
Cutting Force ◽  
Monodromy Matrix ◽  
Period Doubling ◽  
Milling Process ◽  
Depth Of Cut ◽  
Approximation Technique ◽  
Stability Properties ◽  
Chebyshev Collocation ◽  
Collocation Points ◽  
The Stability

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 like milling are modeled by delay-differential equations (DDEs) 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 representation of the solution at their extremum points, the Chebyshev collocation points. The stability properties are determined by the eigenvalues of the approximate monodromy matrix which maps function values at the collocation points from one interval to the next. We check the results for convergence by varying the number of Chebyshev collocation points and by simulation of the transient response via the DDE23 MATLAB routine. The milling model used here was derived by Insperger et al. [14]. Here, the specific cutting force profiles, stability charts, and chatter frequency diagrams are produced for up-milling and down-milling cases for one and four cutting teeth and 25 to 100 % immersion levels. The unstable regions due to both secondary Hopf and flip (period-doubling) bifurcations are found which agree with the previous results found by other techniques. An in-depth investigation in the vicinity of the critical immersion ratio for down-milling (where the average cutting force changes sign) and its implication for stability is presented.

Study on the stability for non-uniform helix angle tools in the milling process

2020 ◽  
Vol 37 (8) ◽  
pp. 387-393
Author(s):  
Qiang Guo ◽  
Ming-Yang Zhang ◽  
Yuan-Shin Lee ◽  
Zhi-Bo Yang ◽  
Yan Jiang ◽  
...  
Keyword(s):  
Helix Angle ◽  
Milling Process ◽  
The Stability

scholarly journals Stability Analysis of Milling Process with Multiple Delays

2020 ◽  
Vol 10 (10) ◽  
pp. 3646 ◽  
Author(s):  
Yonggang Mei ◽  
Rong Mo ◽  
Huibin Sun ◽  
Bingbing He ◽  
Kun Bu
Keyword(s):  
Stability Limit ◽  
Helix Angle ◽  
Milling Process ◽  
Machining Process ◽  
Multiple Delays ◽  
Calculation Time ◽  
Discretization Algorithm ◽  
Cutting Chatter ◽  
Regeneration Effect ◽  
The Stability

Cutting chatter is extremely harmful to the machining process, and it is of great significance to eliminate chatter through analyzing the stability of the machining process. In this work, the stability of the milling process with multiple delays is investigated. Considering the regeneration effect, the dynamics of the milling process with variable pitch cutter is modeled as periodic coefficients delayed differential equations (DDEs) with multiple delays. An adaptive variable-step numerical integration method (AVSNIM) considering the effect of the helix angle is developed firstly, which can discretize the cutting period accurately, thereby improving the calculation accuracy of the stability limit of the milling process. The accuracy and efficiency of the AVSNIM are verified through a benchmark milling model. Subsequently, a novel spindle speed-dependent discretization algorithm is proposed, which is combined with the AVSNIM to further reduce the calculation time of the stability lobes diagram (SLD). The simulation experiment results demonstrate that the proposed algorithm can effectively reduce the calculation time.

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.

Stability prediction of milling process with variable pitch and variable helix cutters

2013 ◽  
Vol 228 (2) ◽  
pp. 281-293 ◽  
Author(s):  
Gang Jin ◽  
Qichang Zhang ◽  
Shuying Hao ◽  
Qizhi Xie
Keyword(s):  
Helix Angle ◽  
Milling Process ◽  
Force Model ◽  
Stability Prediction ◽  
Chatter Vibration ◽  
Variable Pitch ◽  
Tool Geometries ◽  
Variable Helix ◽  
Piecewise Continuous ◽  
The Stability

The use of variable pitch or helix cutters is a known means to prevent chatter vibration during milling. In this article, an alternative method based on an improved semi-discretization method is proposed to predict the stability of variable pitch or variable helix milling. In order to consider the effect of distributed system delays attributed to helix variation, the average delays were calculated for each flute after the engaged cutting flutes were divided into a finite number of axial elements. Meanwhile, a straightforward integral force model, which can consider the piecewise continuous regions of the cutting that describe the helix angle is used to determine the cutting force. Through comparisons with prior works, time-domain simulations, and cutting tests, the proposed approach was verified. In addition, the method was applied to examine the effect of tool geometries on stability trends. Several phenomena for certain combinations of pitch and helix angles are shown and explained.

scholarly journals Stability Analysis of Milling Process with Variable Spindle Speed and Pitch Angle considering Helix Angle and Process Phase Difference

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Gang Jin ◽  
Haotian Jiang ◽  
Jianxin Han ◽  
Zhanjie Li ◽  
Hua Li ◽  
...  
Keyword(s):  
Phase Difference ◽  
Pitch Angle ◽  
High Speed ◽  
Helix Angle ◽  
Stability Domain ◽  
Milling Process ◽  
Spindle Speed ◽  
The Stability ◽  
The Time Domain ◽  
Milling Chatter

Suppression of milling chatter by disrupting regenerative effect is a well-known method to obtain higher cutting stability domain. In this paper, a dynamic model of the milling process with variable spindle speed and pitch angle considering helix angle and process phase difference is presented. Then, an updated semidiscretization method is applied to obtain the stability chart. After the effectiveness of the proposed method is confirmed by comparisons with the previously published works and the time-domain simulations, lots of analyses are conducted to deeply evaluate the influence of the helix angle, the process phase difference, and feed per tooth on milling stability. Results show that the change of helix angle can result in significant stability discrepancies for both high-speed and low-speed regions. Though the process phase difference has the randomness and immeasurability in the practical application, it has an important influence on the stability and will result in a periodic evolution of the stability with a period π. Also, its recommended values are given for the practical milling process.

Active Chatter Suppression in Low Immersion Intermittent Milling Process

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
Le Cao ◽  
Tao Huang ◽  
Da-Ming Shi ◽  
Xiao-Ming Zhang ◽  
Han Ding
Keyword(s):  
Period Doubling ◽  
Milling Process ◽  
Period Doubling Bifurcation ◽  
First Order ◽  
Chatter Suppression ◽  
Stability And Stabilization ◽  
Piecewise Model ◽  
Full Immersion ◽  
The Stability ◽  
Time Invariant

Abstract Chatter in low immersion milling behaves differently from that in full immersion milling, mainly because of the non-negligible time-variant dynamics and the occurrence of period doubling bifurcation. The intermittent and time-variant characteristics make the active chatter suppression based on Lyaponov theorem a non-trivial problem. The main challenges lie in how to deal with the time-variant directional coefficient and how to construct a suitable Lyaponov function so as to alleviate the conservation, as well as the saturation of the controller. Generally, the Lyaponov stability of time-invariant dynamics is more tractable. Hence, in our paper, a first-order piecewise model is proposed to approximate the low immersion milling system as two time-invariant sub-ones that are cyclically switched. To alleviate the conservation, a novel piecewise Lyaponov function is constructed to determine the stability of each subsystem independently. The inequality conditions for determining the stability and stabilization are derived. The validity of the proposed stabilization algorithm to suppress both the hopf and period doubling bifurcation, as well as to reduce the conservation of the controller parameters have been verified.

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