Machine Tool Chatter and Surface Quality in Milling Processes

2004 ◽  
Author(s):  
Tama´s Insperger ◽  
Janez Gradisek ◽  
Martin Kalveram ◽  
Ga´bor Ste´pa´n ◽  
Klaus Weinert ◽  
...  
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Periodic Motion ◽  
Milling Process ◽  
Location Error ◽  
Surface Location Error ◽  
Stability Chart ◽  
Stable Periodic ◽  
Surface Location ◽  
Delay Differential

Two degree of freedom model of milling process is investigated. The governing equation of motion is decomposed into two parts: an ordinary differential equation describing the stable periodic motion of the tool and a delay-differential equation describing chatter. Stability chart is derived by using semi-discretization method for the delay-differential equation corresponding to the chatter motion. The stable periodic motion of the tool and the associated surface location error are obtained by a conventional solution technique of ordinary differential equations. Stability chart and surface location error are determined for milling process. It is shown that at spindle speeds, where high depths of cut are available through stable machining, the surface location error is large. The phase portrait of the tool is also analyzed for different spindle speeds. Theoretical predictions are qualitatively confirmed by experiments.

Machine Tool Chatter and Surface Location Error in Milling Processes

2006 ◽  
Vol 128 (4) ◽  
pp. 913-920 ◽  
Author(s):  
Tamás Insperger ◽  
Janez Gradišek ◽  
Martin Kalveram ◽  
Gábor Stépán ◽  
Klaus Winert ◽  
...  
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
High Speed ◽  
Dominant Frequency ◽  
Free Motion ◽  
Solution Technique ◽  
Location Error ◽  
Surface Location Error ◽  
Surface Location ◽  
Delay Differential

A two degree of freedom model of the milling process is investigated. The governing equation of motion is decomposed into two parts: an ordinary differential equation describing the periodic chatter-free motion of the tool and a delay-differential equation describing chatter. The stability chart is derived by using the semi-discretization method for the delay-differential equation corresponding to the chatter motion. The periodic chatter-free motion of the tool and the associated surface location error (SLE) are obtained by a conventional solution technique of ordinary differential equations. It is shown that the SLE is large at the spindle speeds where the ratio of the dominant frequency of the tool and the tooth passing frequency is an integer. This phenomenon is explained by the large amplitude of the periodic chatter-free motion of the tool at these resonant spindle speeds. It is shown that large stable depths of cut with a small SLE can still be attained close to the resonant spindle speeds by using the SLE diagrams associated with stability charts. The results are confirmed experimentally on a high-speed milling center.

Assessment of Friction Behavior with Surface Location Error Analysis in Milling Process

2019 ◽  
Vol 823 ◽  
pp. 129-134
Author(s):  
N.A. Rafan ◽  
Siti Nur Madihah Ab Rashid ◽  
Z. Jamaludin
Keyword(s):  
Manufacturing Industry ◽  
Milling Process ◽  
Work Piece ◽  
Location Error ◽  
Friction Behavior ◽  
Error Location ◽  
Surface Location Error ◽  
Highly Nonlinear ◽  
Important Quality ◽  
Surface Location

Accurate roundness or circularity measurement is essential to obtain correct functioning of assemblies, making roundness an important quality control parameter in manufacturing industry. Since circular motion while milling a circular work piece leads to quadrant glitches, a phenomenon familiar with existence of highly nonlinear friction behavior, roundness measurement was conducted to investigate this surface location error due to feed rate of the moving work table. This paper presents friction behavior on a milling process circular work piece in line resulted from identified surface error location (SLE).

Chatter stability and surface location error predictions in milling with mode coupling and process damping

2017 ◽  
Vol 233 (3) ◽  
pp. 686-698 ◽  
Author(s):  
Zhongyun Li ◽  
Shanglei Jiang ◽  
Yuwen Sun
Keyword(s):  
Dynamic Model ◽  
Mode Coupling ◽  
Vital Role ◽  
Milling Process ◽  
Location Error ◽  
Process Damping ◽  
Stability Lobes ◽  
Surface Location Error ◽  
Surface Location ◽  
Extended Dynamic

Together with machining chatter, surface location error induced by forced vibration may also inhibit productivity and affect workpiece surface quality in milling process. Addressing these issues needs the combined consideration of stability lobes diagram and surface location error predictions. However, mode coupling and process damping are seldom taken into consideration. In this article, an extended dynamic milling model including mode coupling and process damping is first built based on classical 2-degree-of-freedom dynamic model with regeneration. Then, a second-order semi-discretization method is proposed to simultaneously predict the stability lobes diagram and surface location error by solving this extended dynamic model. The rate of convergence of the proposed method is also investigated. Finally, a series of experiments are conducted to verify the veracity of the extended dynamic model. The modal parameters including direct and cross terms are identified by impact experiments. Via experimental verification, the experimental results show a good correlation with the predicted stability lobes diagram and surface location error based on the extended dynamic model. Also, the effects of mode coupling and process damping are revealed. Mode coupling increases the whole stability region; however, process damping plays a vital role in stability improvement mainly at low spindle speeds.

Simultaneous Stability and Surface Location Error Predictions in Milling

2004 ◽  
Vol 127 (3) ◽  
pp. 446-453 ◽  
Author(s):  
Brian P. Mann ◽  
Keith A. Young ◽  
Tony L. Schmitz ◽  
David N. Dilley
Keyword(s):  
A Priori ◽  
Milling Process ◽  
Flip Bifurcation ◽  
Location Error ◽  
Element Analysis ◽  
Milling Stability ◽  
Surface Location Error ◽  
Solution Convergence ◽  
Surface Location ◽  
Stability And Accuracy

Optimizing the milling process requires a priori knowledge of many process variables. However, the ability to include both milling stability and accuracy information is limited because current methods do not provide simultaneous milling stability and accuracy predictions. The method described within this paper, called Temporal Finite Element Analysis (TFEA), provides an approach for simultaneous prediction of milling stability and surface location error. This paper details the application of this approach to a multiple mode system in two orthogonal directions. The TFEA method forms an approximate analytical solution by dividing the time in the cut into a finite number of elements. The approximate solution is then matched with the exact solution for free vibration to obtain a discrete linear map. The formulated dynamic map is then used to determine stability, steady-state surface location error, and to reconstruct the time series for a stable cutting process. Solution convergence is evaluated by simply increasing the number of elements and through comparisons with numerical integration. Analytical predictions are compared to several different milling experiments. An interesting period two behavior, which was originally believed to be a flip bifurcation, was observed during experiment. However, evidence is presented to show this behavior can be attributed to runout in the cutter teeth.

State Dependent Regenerative Delay in Milling Processes

2005 ◽  
Author(s):  
Ta´mas Insperger ◽  
Ga´bor Ste´pa´n ◽  
Ferenc Hartung ◽  
Janos Turi
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Delay Differential Equation ◽  
Linear Equations ◽  
Additional Term ◽  
Milling Process ◽  
Constant Time ◽  
State Dependency ◽  
State Dependent ◽  
Delay Differential

Traditional models of regenerative machine tool chatter use constant time delays assuming that the period between two subsequent cuts is a constant determined definitely by the spindle speed. These models result in delay-differential equations with constant time delay. If the vibrations of the tool relative to the workpiece are also included in the surface regeneration model, then the resulted time delay is not constant, but it depends on the actual and a delayed position of the tool. In this case, the governing equation is a delay-differential equation with state dependent time delay. Equations with state dependent delays can not be linearized in the traditional sense, but there exists linear equations that can be associated to them. This way, the local behavior of the system with state dependent delays can be investigated. In this study, a two degree of freedom model is presented for milling process. A thorough modeling of the regeneration effect results in the governing delay-differential equation with state dependent time delay. It is shown through the linearization of the nonlinear equation that an additional term arises in the linearized equation of motion due to the state-dependency of the time delay.

Stability of the Damped Mathieu Equation With Time Delay

2003 ◽  
Vol 125 (2) ◽  
pp. 166-171 ◽  
Author(s):  
T. Insperger ◽  
G. Ste´pa´n
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Delay Differential Equation ◽  
Mathieu Equation ◽  
Important Class ◽  
System Parameters ◽  
Oscillatory Systems ◽  
Stability Chart ◽  
The Stability ◽  
Delay Differential

In the space of the system parameters, the stability charts are determined for the delayed and damped Mathieu equation defined as x¨t+κx˙t+δ+ε cos txt=bxt−2π. This stability chart makes the connection between the Strutt-Ince chart of the damped Mathieu equation and the Hsu-Bhatt-Vyshnegradskii chart of the autonomous second order delay-differential equation. The combined charts describe the intriguing stability properties of an important class of delayed oscillatory systems subjected to parametric excitation.

Fold Bifurcation in the State-Dependent Delay Model of Milling: Analytical and Numerical Solutions

2011 ◽  
Author(s):  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Delay Differential Equation ◽  
Milling Process ◽  
The State ◽  
Delay Model ◽  
State Dependent ◽  
Fold Bifurcation ◽  
State Dependent Delay ◽  
Delay Differential

The standard models of the milling process describe the surface regeneration effect by a delay-differential equation with constant time delay. In this study, an improved two degree of freedom model is presented for milling process where the regenerative effect is described by an improved state dependent time delay model. The model contains exact nonlinear screen functions describing the entrance and exit positions of the cutting edges of the milling tool. This model is valid in case of large amplitude forced vibrations close to the near-resonant spindle speeds. The periodic motions of this nonlinear system are calculated by a shooting method. The stability calculation is based on the linearization of the state-dependent delay differential equation around these periodic solutions by means of the semi-discretization method. The results are validated by an advanced numerical time domain simulation where the chip thickness is calculated by means of Boolean algebra.

scholarly journals Prediction of surface location error in milling considering the effects of uncertain factors

2017 ◽  
Vol 8 (2) ◽  
pp. 385-392
Author(s):  
Xianzhen Huang ◽  
Fangjun Jia ◽  
Yimin Zhang ◽  
Jinhua Lian
Keyword(s):  
Dimensional Accuracy ◽  
Cutting Parameters ◽  
Milling Process ◽  
Machining Accuracy ◽  
Location Error ◽  
Estimation Errors ◽  
Surface Location Error ◽  
Surface Location ◽  
Artificial Neural Network Ann ◽  
Mcs Method

Abstract. Machining accuracy of a milled surface is influenced by process dynamics. Surface location error (SLE) in milling determines final dimensional accuracy of the finished surface. Therefore, it is critical to predict, control, and minimize SLE. In traditional methods, the effects of uncertain factors are usually ignored during prediction of SLE, and this would tend to generate estimation errors. In order to solve this problem, this paper presents methods for probabilistic analysis of SLE in milling. A dynamic model for milling process is built to determine relationship between SLE and cutting parameters using full-discretization method (FDM). Monte-Carlo simulation (MCS) method and artificial neural network (ANN) based MCS method are proposed for predicting reliability of the milling process. Finally, a numerical example is used to evaluate the accuracy and efficiency of the proposed method.

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