Analytical prediction of chatter stability for modulated turning

2021 ◽  
pp. 103739
Author(s):  
Soohyun Nam ◽  
Bora Eren ◽  
Takehiro Hayasaka ◽  
Burak Sencer ◽  
Eiji Shamoto
Keyword(s):  
Analytical Prediction ◽  
Chatter Stability

Analytical Prediction of Chatter Stability in Milling—Part I: General Formulation

1998 ◽  
Vol 120 (1) ◽  
pp. 22-30 ◽  
Author(s):  
E. Budak ◽  
Y. Altintas¸
Keyword(s):  
Stability Limit ◽  
Axial Direction ◽  
Analytical Relation ◽  
Analytical Prediction ◽  
Stability Prediction ◽  
Chatter Stability ◽  
Radial Depth ◽  
Milling Forces ◽  
Chatter Stability Prediction ◽  
Equations With Delay

A new analytical method of chatter stability prediction in milling is presented. A general formulation for the dynamic milling system is developed by modeling the cutter and workpiece as multi-degree-of-freedom structures. The dynamic interaction between the milling cutter and workpiece is modeled considering the varying dynamics in the axial direction. The dynamic milling forces are governed by a system of periodic differential equations with delay whose stability analysis leads to an analytical relation for chatter stability limit in milling. The model can be used to determine the chatter free axial and radial depth of cuts without resorting to time domain simulations.

scholarly journals Analytical Prediction of Part Dynamics for Machining Stability Analysis

2010 ◽  
Vol 4 (3) ◽  
pp. 259-267 ◽  
Author(s):  
Salih Alan ◽  
◽  
Erhan Budak ◽  
H. Nevzat Özgüven ◽  
Keyword(s):  
Material Removal ◽  
Structural Modification ◽  
Analytical Procedure ◽  
Computer Code ◽  
Analytical Prediction ◽  
Chatter Stability ◽  
Efficient Tool ◽  
Stability Analyses ◽  
Modification Method ◽  
Free Material

An analytical procedure is developed to predict workpiece dynamics in a complete machining cycle in order to obtain frequency response functions (FRF), which are needed in chatter stability analyses. For this purpose, a structural modification method that is an efficient tool for updating FRFs is used. The mass removed by machining is considered to be a structural modification in order to determine the FRFs at different stages of the process. The method is implemented in a computer code and demonstrated on different geometries. The predictions are compared and verified by FEA. Predicted FRFs are used in chatter stability analyses, and the effect of part dynamics on stability is studied. Different cutting strategies are compared for increased chatter-free material removal rates considering part dynamics.

Analytical prediction of chatter stability in turning of low-stiffness pure iron parts by nosed tool

2018 ◽  
Vol 102 (5-8) ◽  
pp. 1227-1237 ◽  
Author(s):  
Shanglei Jiang ◽  
Shuyang Yan ◽  
Yong Liu ◽  
Chunzheng Duan ◽  
Jinting Xu ◽  
...  
Keyword(s):  
Pure Iron ◽  
Analytical Prediction ◽  
Chatter Stability ◽  
Low Stiffness

Analytical Stability Prediction and Design of Variable Pitch Cutters

1999 ◽  
Vol 121 (2) ◽  
pp. 173-178 ◽  
Author(s):  
Y. Altıntas¸ ◽  
S. Engin ◽  
E. Budak
Keyword(s):  
Time Delay ◽  
Depth Of Cut ◽  
Analytical Prediction ◽  
Time Varying ◽  
Chatter Stability ◽  
Variable Pitch ◽  
Analytical Stability ◽  
The Stability ◽  
Time Invariant ◽  
Regenerative Phase

An analytical prediction of stability lobes for milling cutters with variable pitch angles is presented. The method requires cutting constants, number of teeth, and transfer function of cutter mounted on the machine tool as inputs to a chatter stability expression. The stability is formulated by transforming time varying directional cutting constants into time invariant constants. Constant regenerative time delay in uniform cutters is transformed into nonuniform multiple regenerative time delay for variable pitch cutters. The chatter free axial depth of cut is solved from the eigenvalues of stability expression, whereas the spindle speed is identified from regenerative phase delays. The proposed technique has been verified with extensive cutting tests and time domain simulations. The practical use of the analytical solution is demonstrated by an optimal tooth spacing design application which increases the chatter free depth of cuts significantly.

Analytical Prediction of Chatter Stability in Milling—Part II: Application of the General Formulation to Common Milling Systems

1998 ◽  
Vol 120 (1) ◽  
pp. 31-36 ◽  
Author(s):  
E. Budak ◽  
Y. Altintas¸
Keyword(s):  
Numerical Solutions ◽  
Degree Of Freedom ◽  
Analytical Prediction ◽  
Chatter Stability ◽  
Peripheral Milling ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Chatter Prediction ◽  
Milling Chatter ◽  
Two Degree Of Freedom

The general formulation for the milling chatter prediction developed in Part I of the paper is applied to common milling systems. Three cases are considered: a workpiece with single-degree-of-freedom, a face milling cutter with two-degree-of-freedom, and peripheral milling of a cantilevered thin web. The general milling stability formulation is further simplified for the less complicated models. For each case, an analytical expression which explicitly relate the chatter limit to the milling conditions and tool-workpiece dynamics are derived. The analytical predictions are compared with numerical and time domain solutions proposed by previous research. It is shown that the proposed method can accurately predict the chatter limits in milling and thus eliminates the time consuming numerical solutions.

ANALYTICAL PREDICTION OF THE EXIT FLOW OF CAVITATING ORIFICES

1997 ◽  
Vol 7 (6) ◽  
pp. 603-616 ◽  
Author(s):  
David P. Schmidt ◽  
Michael L. Corradini
Keyword(s):  
Analytical Prediction
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