Effect of Surface Slope on Shear Angle in Metal Cutting

1970 ◽  
Vol 92 (1) ◽  
pp. 115-118 ◽  
Author(s):  
G. Boothroyd
Keyword(s):  
Metal Cutting ◽  
Chip Thickness ◽  
Shear Angle ◽  
Rate Of Change ◽  
Cutting Condition ◽  
Surface Slope ◽  
Undeformed Chip Thickness ◽  
Work Surface ◽  
Machine Tool Chatter ◽  
Effect Of Surface

The effect of the work surface slope, or the rate of change of undeformed chip thickness, on the shear angle in metal cutting is studied experimentally. It is shown that the results of previous analyses only apply to one specific cutting condition and cannot generally be used in studies of machine tool chatter.

Machine Tool Chatter: Effect of Surface Slope on Machining Forces During Wave Removing

1974 ◽  
Vol 96 (4) ◽  
pp. 1202-1206 ◽  
Author(s):  
J. F. Sarnicola ◽  
G. Boothroyd
Keyword(s):  
Chip Thickness ◽  
Rate Of Change ◽  
Surface Slope ◽  
Phase Component ◽  
Undeformed Chip Thickness ◽  
Machining Forces ◽  
Work Surface ◽  
Tool Force ◽  
Machine Tool Chatter ◽  
Effect Of Surface

The effect of work surface slope (rate of change of undeformed chip thickness) on machining forces has been measured. The results of these experiments are used to develop equations for the cutting and thrust components of the resultant tool force during wave removing. It is found that the work surface slope effect gives rise to a significant out-of-phase component of the oscillating tool force which should not be neglected in stability analyses.

Shear Angle Relationship With Variable Undeformed Chip Thickness

1974 ◽  
Vol 96 (4) ◽  
pp. 1272-1276 ◽  
Author(s):  
G. S. Kainth ◽  
R. C. Gupta
Keyword(s):  
Metal Cutting ◽  
Chip Thickness ◽  
Present Theory ◽  
Rake Angle ◽  
Shear Angle ◽  
Surface Slope ◽  
Undeformed Chip Thickness ◽  
Orthogonal Metal Cutting ◽  
Effect Of Surface ◽  
Good Agreement

Effect of surface slope of the workpiece on shear angle has been considered by applying Hill’s [1] deformation criteria to the triangular shear zone in orthogonal metal-cutting process with variable undeformed chip thickness. It is shown that the variation of the shear angle with the surface slope δ can be written in the form φ = φ0 + Cδ where “C” is not a constant but depends upon steady state shear angle φ0, surface slope δ, and rake angle α. It is also shown that the present theory is in good agreement with the experimental results of Boothroyd [2].

Machining Forces: Some Effects of Removing a Wavy Surface

1966 ◽  
Vol 8 (2) ◽  
pp. 129-140 ◽  
Author(s):  
P. W. Wallace ◽  
C. Andrew
Keyword(s):  
Chip Thickness ◽  
Shear Plane ◽  
Shear Angle ◽  
Surface Slope ◽  
Experimental Conditions ◽  
Undeformed Chip Thickness ◽  
Cutting Force Components ◽  
The Mean ◽  
Force Components ◽  
Made In

Previous work has shown that during the removal of a surface waveform oscillating cutting force components arise which may have a phase difference with respect to the oscillating component of undeformed chip thickness; it has also shown that the shear angle is affected by the slopes of the surface waveform. However, no attempt to predict the oscillating force behaviour from the geometry of cutting has been reported. The present work attempts to achieve such a prediction by means of an analysis of the phase and magnitude of the oscillating force components acting in two directions; in the directions of the mean shear plane and of the tool rake face. In the analysis it is assumed that the shear angle oscillates in phase with and proportionally to the surface slope, and that the curvature of the chip varies with the undeformed chip thickness. An experimental technique for cutting with variable undeformed chip thickness is described, together with a method for recording and measuring the oscillating components of force and undeformed chip thickness. Experimental results are presented which show the assumptions made in the analysis to be substantially valid; the predicted oscillating forces are shown to be in adequate agreement with experiment over a range of experimental conditions. It is shown that the oscillation of the shear angle is primarily dependent on the surface slope and that the frictional force behaviour is consistent with the characteristics of the two regions of friction, sticking and sliding, as found in work on cutting with constant undeformed chip thickness.

Cutting Dynamics in Machine Tool Chatter: Contribution to Machine-Tool Chatter Research—3

1965 ◽  
Vol 87 (4) ◽  
pp. 464-470 ◽  
Author(s):  
R. L. Kegg
Keyword(s):  
Machine Tool ◽  
Metal Cutting ◽  
Chip Thickness ◽  
Cutting Process ◽  
Dynamic Force ◽  
General Technique ◽  
Cross Sensitivity ◽  
Machine Tool Chatter ◽  
Measuring Techniques ◽  
Tool Chatter

This is one of four papers presented simultaneously on the general subject of chatter. This work is concerned with finding a representation of the dynamic metal-cutting process which is suitable for use in a linear closed-loop theory of stability of the system composed of the machine tool structure, the cutting process, and their means of combining. Measuring techniques for experimentally determining this behavior are discussed and some problems in the dynamic measurement of forces are explored. It is found that it is not at all sufficient to simply build a dynamometer whose lowest natural frequency is well beyond the range of interest. It is also shown that dynamic cross sensitivity can far exceed static cross sensitivity so that a more general technique for data correction developed in the present work must be used to calibrate dynamic force data. Results obtained to date with an oscillating tool and a flat uncut surface show that some phase, increasing with frequency, is always present between the dynamic cutting forces and the oscillatory uncut chip thickness. This phase is different for the two components of the resultant cutting force. It is felt that two mechanisms, both associated with the tool clearance flank, can explain most of the dynamic cutting effects found in testing.

Dynamics of the Metal-Cutting Process

1965 ◽  
Vol 87 (4) ◽  
pp. 429-441 ◽  
Author(s):  
Paul Albrecht
Keyword(s):  
Dynamic Response ◽  
Cutting Forces ◽  
Metal Cutting ◽  
Dynamic Properties ◽  
Chip Thickness ◽  
Cutting Process ◽  
Uncut Chip Thickness ◽  
Work Surface ◽  
Experimental Approaches ◽  
Inertia Forces

An investigation into the dynamics of the metal-cutting process has been carried out using analytical and experimental approaches. An exploratory analysis into the dynamic behavior of the cutting process revealed such dynamic properties as a loop response of the cutting forces caused by the waviness of the work surface. This finding indicates the possibility of unstable behavior of the cutting process in itself. It was possible to describe analytically the phase between the force response and fluctuations of uncut chip thickness for the case of a wavy work surface. Effects of the magnitude of the shear angle as well as of its fluctuations have been studied which make it possible to correlate the instability within the cutting process to the properties of the work material. Apart from the configuration of the cutting process, its physical properties, such as inertia forces in chip formation, have been introduced into the analysis because inertia forces, negligible at steady state, may grow significant if cutting conditions are fluctuating at higher frequencies. An experimental setup has been devised and built featuring a special design of a tool dynamometer particularly suitable for the measurement of dynamic response of the cutting forces. In the setup, a cutting tool activated by a hydraulic shaker is controlled in an average position by a feedback loop mechanism. This setup makes it possible to obtain a record of the dynamic response of cutting forces caused by the fluctuation of uncut chip thickness produced by an oscillating tool in the frequency range up to about 400 cps.

Nonlinear Stability Analysis of Chatter in Metal Cutting

1974 ◽  
Vol 96 (2) ◽  
pp. 670-675 ◽  
Author(s):  
N. Saravanja-Fabris ◽  
A. F. D’Souza
Keyword(s):  
Stability Analysis ◽  
Nonlinear Theory ◽  
Metal Cutting ◽  
Experimental Studies ◽  
Chip Thickness ◽  
Nonlinear Stability Analysis ◽  
Machine Tool Chatter ◽  
Stability Chart ◽  
Production Problems ◽  
Cutting Speeds

The occurrence of machine-tool chatter is usually undesirable as it gives rise to severe production problems. The existing theoretical and experimental studies on dynamic cutting indicate that the chip thickness and forces in cutting are related by a nonlinear equation. But the existing studies on chatter stability employ a linear relationship between these variables. In this paper, a relationship is developed between the chip thickness and forces in cutting under dynamic conditions. This relationship is based on existing experimental results and it exhibits active hysteresis. Hence, the oscillations in chip thickness lead the oscillations in cutting forces for all frequencies. A nonlinear theory is developed based on the describing function approach. An example is given of computing a stability chart giving the width of cut, frequency of chatter, and critical cutting speeds for regenerative chatter. In contrast to the linear stability analysis, the nonlinear theory can better explain the experimentally observed phenomena as well as give better correlation with the theoretical analysis of dynamic cutting.

Metal Cutting Dynamics With Reference to Primary Chatter

1976 ◽  
Vol 98 (1) ◽  
pp. 258-264 ◽  
Author(s):  
Richard J. Szakovits ◽  
A. F. D’Souza
Keyword(s):  
Function Method ◽  
Metal Cutting ◽  
Orthogonal Cutting ◽  
Chip Thickness ◽  
Limit Cycle Oscillation ◽  
Describing Function ◽  
Undeformed Chip Thickness ◽  
Describing Function Method ◽  
Cycle Oscillation ◽  
The Relationship

Identification of metal cutting dynamics is important for predicting the occurrence of chatter. An experimental investigation was conducted to study the relationship between the oscillations in the undeformed chip thickness and the oscillations in the thrust and cutting forces in orthogonal cutting during wave producing or a simulation of primary chatter. The relationship exhibits hysterisis which changes from passive to active as the frequency is increased; it is also a function of the amplitude of oscillations in the undeformed chip thickness. The objective was to relate the experimental results to the development of a nonlinear theory of analysis of chatter as a limit cycle oscillation by the describing function method.

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