On the Cause of Regenerative Chatter Due to Workpiece Deflection

1974 ◽  
Vol 96 (1) ◽  
pp. 179-186 ◽  
Author(s):  
S. Kato ◽  
E. Marui
Keyword(s):  
Differential Equation ◽  
Experimental Results ◽  
Phase Lag ◽  
Chatter Vibration ◽  
Transient Vibration ◽  
Regenerative Chatter ◽  
Work Surface ◽  
Chatter Vibrations

The cause and the mechanism of regenerative chatter vibrations due to the deflection of workpiece occurring in machining metals are investigated experimentally. The regenerative chatter vibration is induced by the phase lag of the undulations in successive cutting. This means that small undulations initially produced on a work surface by the transient vibration of the workpiece become larger and the undulations extend over the whole work surface because a given amount of energy is available for exciting or maintaining the vibration owing to the phase lag of successive undulations. Then, a differential equation of chatter vibration is introduced based on the experimental results, and some remarks on the properties of chatter vibration are given.

Chatter Vibration in Drilling

1988 ◽  
Vol 110 (4) ◽  
pp. 309-314 ◽  
Author(s):  
S. Ema ◽  
H. Fujii ◽  
E. Marui
Keyword(s):  
Natural Frequency ◽  
Cutting Parameters ◽  
Experimental Results ◽  
Chatter Vibration ◽  
Additional Mass ◽  
Regenerative Chatter ◽  
Drill Point ◽  
The Stability

Chatter vibration of long drills has been investigated using several drills with different overhang lengths and special drills with different pieces of additional mass. The frequency, amplitude, initiation boundary, and unstable range of chatter vibration were measured at various cutting parameters. The experimental results showed that the vibration is a regenerative chatter and its frequency is equal to the bending natural frequency of the drill when the drill point is supported in a machined hole. Based upon the experimental results, the stability of chatter vibration was discussed. It was clarified that unstable ranges appear only when the chatter frequency in one workpiece rotation is an odd number.

The Mechanism of Chatter Vibration in a Spindle-Workpiece System: Part 1—Properties of Self-Excited Chatter Vibration in Spindle-Workpiece System

1988 ◽  
Vol 110 (3) ◽  
pp. 236-241 ◽  
Author(s):  
E. Marui ◽  
S. Kato ◽  
M. Hashimoto ◽  
T. Yamada
Keyword(s):  
Cutting Force ◽  
Energy Supply ◽  
Phase Lag ◽  
Chatter Vibration ◽  
Regenerative Chatter ◽  
Phase Lags ◽  
System Part ◽  
Cutting Operation ◽  
Dynamic Rigidity ◽  
Chatter Marks

The elimination of chatter vibration is important to improve cutting accuracy and to improve productivity of the cutting operation. In this study, the characteristics of the primary and regenerative chatter vibration occurring in the spindle-workpiece system are investigated experimentally using six spindle-workpiece systems having different vibratory properties. The vibratory locus of the spindle-workpiece system is found. The phase lag between the cutting force and chatter displacement and the phase lag between the successive chatter marks are obtained quantitatively. These phase lags are closely related to the energy supply. The chatter vibration hardly grows up in the spindle-workpiece system having large dynamic rigidity.

Approximated Solutions for Axisymmetric Wrinkled Inflated Membranes

2015 ◽  
Vol 82 (11) ◽  
Author(s):  
Riccardo Barsotti
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Finite Element ◽  
Nonlinear Ordinary Differential Equation ◽  
Experimental Results ◽  
Limit Case ◽  
Reasonable Approximation ◽  
Constituent Material ◽  
Actual Solution ◽  
Wrinkled Membrane

The axisymmetric inflation problem for a wrinkled membrane is solved by means of a simple nonlinear ordinary differential equation. The solution is illustrated in full details. Both the free and constrained cases are addressed, in the limit case where the membrane is fully wrinkled. In the constrained inflation problem, no slippage is allowed between the membrane and the constraining surfaces. It is shown that an actual membrane can in no way reach the fully wrinkled configuration during free inflation, regardless of the membrane's initial configuration and constituent material. The fully wrinkled solution is compared to some finite element results obtained by means of an expressly developed iterative–incremental procedure. When the values of the inflating pressure and length of the meridian lie within a suitable applicability range, the fully wrinkled solution may represent a reasonable approximation of the actual solution. A comparison with some numerical and experimental results available in the literature is illustrated.

Suppression of regenerative chatter vibration in simultaneous double-sided milling of flexible plates by speed difference

CIRP Annals ◽  
2010 ◽  
Vol 59 (1) ◽  
pp. 387-390 ◽  
Author(s):  
E. Shamoto ◽  
T. Mori ◽  
K. Nishimura ◽  
T. Hiramatsu ◽  
Y. Kurata
Keyword(s):  
Chatter Vibration ◽  
Regenerative Chatter ◽  
Speed Difference ◽  
Flexible Plates

Design and Fabrication of the Superabrasive Grinding Wheel with Phyllotactic Pattern

2012 ◽  
Vol 472-475 ◽  
pp. 2354-2360 ◽  
Author(s):  
Yu Shan Lu ◽  
Cheng Yi Zhao ◽  
Jun Wang ◽  
Yan He ◽  
Zhi Hui Kou
Keyword(s):  
Experimental Results ◽  
Grinding Wheel ◽  
Wheel Surface ◽  
Work Surface ◽  
Phyllotactic Pattern ◽  
Uv Lithography ◽  
Working Surface ◽  
Abrasive Grain ◽  
Grinding Performance ◽  
Cluster Pattern

In order to achieve the controllability of the abrasive arrangement on the working surface of grinding wheel,a new kind of the superabrasive grinding wheel, which has defined abrasive grain cluster pattern, has been designed based on the phyllotaxis theory of biology, and fabricated with UV lithography method and electroplating technology. The analytical results indicate that the phyllotactic parameters influence on the abrasive arrangement configuration on the work surface of the superabrasive grinding wheel, so as to improve grinding performance of the grinding wheel, increasing the diameter of phyllotactic abrasive grain cluster and decreasing phyllotactic coefficient can increases the abrasive grain density of the surperabrasive grinding wheel surface. Electroplating experimental results show that the reasonable electroplating processes can reduce the faults of defined abrasive arrangement on the superabrasive grinding wheel surface.

Dynamic Behavior of a Thin-Walled Cylindrical Workpiece During the Turning Process, Part 1: Cutting Process Simulation

2002 ◽  
Vol 124 (3) ◽  
pp. 562-568 ◽  
Author(s):  
K. Mehdi ◽  
J.-F. Rigal ◽  
D. Play
Keyword(s):  
Dynamic Behavior ◽  
Process Simulation ◽  
Point Of View ◽  
Cutting Process ◽  
Natural Phenomenon ◽  
Chatter Vibration ◽  
Turning Process ◽  
Chatter Vibrations ◽  
Cylindrical Workpiece ◽  
Thin Walled

From a practical point of view, in machining applications, chatter vibration constitutes a major problem during the cutting process. It is becoming increasingly difficult to suppress chatter during cutting at high speeds. Many investigators have regarded chatter vibrations as a “natural” phenomenon during the cutting process and a part of the process itself. In classical machining operations with thick-walled workpieces chatter vibrations occur when the cutting depth exceeds stability limits dependent on the machine tool. On the other hand, in the case of thin-walled cylindrical workpieces, chatter vibration problems are not so simple to formulate. The main purpose of this study is to qualify the dynamic behavior of a thin-walled workpiece during the turning process. It contains two parts: the cutting process simulation and the definition of experimental stability criteria. In the first part, a numerical model, which simulates the turning process of thin-walled cylindrical workpieces, is proposed. This model also permits obtaining workpiece responses to excitation generated by cutting forces. Finally, the stability of the process is discussed.

Regenerative Chatter Vibration Occurring in Turning With Different Side Cutting Edge Angles

1995 ◽  
Vol 117 (4) ◽  
pp. 551-558 ◽  
Author(s):  
E. Marui ◽  
M. Hashimoto ◽  
S. Kato
Keyword(s):  
Energy Supply ◽  
Cutting Tool ◽  
Cutting Tools ◽  
Cutting Edge ◽  
The Other ◽  
Chatter Vibration ◽  
Regenerative Chatter ◽  
Edge Angle ◽  
Regenerative Effect ◽  
Two Factors

This paper deals with the regenerative chatter vibration occurring in cutting tools with different side cutting edge angles. The occurrence of regenerative chatter vibration of the cutting tool is influenced by two factors, which are closely related to the vibratory energy supply or consumption. One factor is the interference effect between the tool flank and the workpiece. Of course, this factor exists in the primary chatter, too. The other is the regenerative effect. The influence of both factors on the regenerative chatter vibration of cutting tools with different side cutting edge angles is examined experimentally. The vibratory energy supply is simulated, considering the dynamic cutting process. As a result, the property of the regenerative chatter vibration and the influence of the side cutting edge angle on the regenerative chatter vibration are clarified.

scholarly journals Numerical Method for Fuel Distribution Downstream of the Emulsifying Channel Injector

1985 ◽  
Author(s):  
Liu Bing ◽  
Wang Hong-Ji
Keyword(s):  
Differential Equation ◽  
Numerical Method ◽  
Calculation Model ◽  
Experimental Results ◽  
Two Dimensional ◽  
Physical Processes ◽  
Mixture Formation ◽  
Fuel Distribution ◽  
Good Agreement

Based upon experimental results, the physical processes of fuel-air mixture formation downstream of the emulsifying channel injector (ECI) have been studied and a calculation model for predicting fuel distribution downstream of ECI has been proposed in this paper. The two-dimensional differential equation of diffusion is solved by numerical method and the fuel distribution downstream of ECI is calculated. The calculated values are in good agreement with the experimental results.

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