Governing Equations of the Shear Angle Oscillation in Dynamic Orthogonal Cutting

1986 ◽  
Vol 108 (4) ◽  
pp. 280-287 ◽  
Author(s):  
D. William Wu
Keyword(s):  
Orthogonal Cutting ◽  
Shear Plane ◽  
Shear Angle ◽  
Governing Equations ◽  
Line Field ◽  
Angle Variation ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Transfer Behavior ◽  
Good Agreement

Chatter is a complex physical process in machining. One of the practical ways of modeling its transfer behavior is to derive the force functions theoretically from the substance of steady state cutting. This often requires a knowledge about the shear angle variation during the process. This paper presents a new method of modeling the angular oscillation in dynamic orthogonal cutting. The system governing equations were derived based on the work-hardening slip-line field theory in cutting mechanics by taking into account the changes of stress conditions on both the shear plane and the tool-chip interface. The result of a simulation study conducted for a wide range of cutting conditions has shown a very good agreement between the theoretical predictions and the existing experimental evidence.

scholarly journals Experimental investigation of the shear angle variation during orthogonal cutting

2018 ◽  
Vol 5 (13) ◽  
pp. 26495-26500 ◽  
Author(s):  
Szabolcs Berezvai ◽  
Tamas G. Molnar ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Experimental Investigation ◽  
Orthogonal Cutting ◽  
Shear Angle ◽  
Angle Variation

Crystal anisotropy-dependent shear angle variation in orthogonal cutting of single crystalline copper

2020 ◽  
Vol 63 ◽  
pp. 41-48 ◽  
Author(s):  
Zhanfeng Wang ◽  
Junjie Zhang ◽  
Zongwei Xu ◽  
Jianguo Zhang ◽  
Guo Li ◽  
...  
Keyword(s):  
Orthogonal Cutting ◽  
Shear Angle ◽  
Angle Variation ◽  
Single Crystalline ◽  
Crystal Anisotropy

scholarly journals Prediction of Vibration Behavior of Micro-Circular Disks at Low Reynolds Number Regime

2018 ◽  
Vol 09 (04) ◽  
pp. 1850005 ◽  
Author(s):  
Adil El Baroudi ◽  
Fulgence Razafimahery
Keyword(s):  
Analytical Procedure ◽  
Outer Boundary ◽  
Theoretical Method ◽  
Gap Effect ◽  
Governing Equations ◽  
Structure Interaction ◽  
Finite Element Software ◽  
Wide Range ◽  
Circular Disks ◽  
Good Agreement

In the current study, a theoretical method is developed to predict the vibrational behavior of micro-circular disks filled with viscous fluids and numerical results are presented to validate the model. Vibrations with two outer boundary conditions, rigid and deformable vessel, are studied. The coupled governing equations of both rigid and deformable vessel vibration are solved by the analytical procedure, taking fluid–structure interaction into account. The fluid gap effect on the coupled eigenfrequencies is also considered. The frequency spectrum plots of the first several eigenfrequencies are presented in a wide range of fluid gap and elasticity ratio. The correctness of results is demonstrated using a commercial finite element software. It is shown that the obtained results through the proposed method reveal very good agreement with the numerical solution.

Steady Compressible Flow through a Single Row of Radial Holes in the Wall of a Pipeline

1970 ◽  
Vol 12 (4) ◽  
pp. 248-258 ◽  
Author(s):  
G. H. Trengrouse
Keyword(s):  
Discharge Coefficient ◽  
Pressure Change ◽  
Single Row ◽  
One Dimensional ◽  
Discharge Coefficients ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Flow Through ◽  
Flow Theories ◽  
Good Agreement

Measured values of discharge coefficient for air flow through a single row of radial holes in the wall of a pipeline are reported, together with the values of pipe Mach numbers in the immediate vicinity of the holes. A wide range of pressure and area ratios are considered, the flow through the holes being either into or out of the pipe. It is shown that the effects on the measured values of both the pressure level at discharge from the holes and the air temperature are negligible. The agreement between the pressure change in the pipeline due to the holes, obtained experimentally, and that predicted by simple, one-dimensional flow theories is generally unsatisfactory. However, theoretical predictions of the jet efflux angles based on two-dimensional, incompressible, non-viscous flow arguments are in good agreement with those measured, but discrepancies do arise in the prediction of discharge coefficients.

Force and Moment Measurements of Supercavitating Hydrofoils of Finite Span With Comparison to Theory

1975 ◽  
Vol 97 (4) ◽  
pp. 453-462
Author(s):  
P. Leehey ◽  
T. S. Stellinger
Keyword(s):  
Aspect Ratio ◽  
Asymptotic Expansions ◽  
Cavity Length ◽  
Large Aspect Ratio ◽  
Drag Coefficients ◽  
Finite Span ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Lift And Drag ◽  
Good Agreement

Measurements were made of lift, drag, and moment coefficients, and cavity length for aspect ratio 3 and 5 supercavitating hydrofoils of elliptical planform. These measurements are compared with theoretical predictions obtained from matching asymptotic expansions for large aspect ratio. Good agreement was obtained for lift and drag coefficients for angles of attack from 10 deg to 15 deg and for a wide range of cavity lengths. Theoretical moment coefficients were too large indicating the need for lifting surface corrections.

scholarly journals NUMERICAL ANALYSIS OF THE NATURAL CONVECTION IN HORIZONTAL ANNULI AT LOW AND MODERATE Ra

2006 ◽  
Vol 5 (2) ◽  
pp. 58
Author(s):  
E. L. M. Padilla ◽  
R. Campregher ◽  
A. Silveira-Neto
Keyword(s):  
Natural Convection ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Governing Equations ◽  
Concentric Cylinders ◽  
Wide Range ◽  
Horizontal Annuli ◽  
Rayleigh Numbers ◽  
The Heat Transfer Coefficient ◽  
Good Agreement

The natural convection at low and moderate Rayleigh numbers (Ra) incylindrical horizontal annuli with imposed temperatures in both surfaces isnumerically studied. This flow inside concentric cylinders classic configuration has a wide range of practical and technological applications, which justifies its growing studies efforts. In this work, the governing equations are discretized by the volume finite technique over a staggered grid, with second-order accuracy in space and time. The flow pattern is presented by several Rayleigh numbers, with an analysis of the heat transfer coefficient and flow properties. Furthermore, a three-dimensional field is shown at a moderate Ra number. The results showed a good agreement with the experimental data.

Stiffness and Bond Strength of Rubber-Filled Hinges

1993 ◽  
Vol 66 (5) ◽  
pp. 733-741 ◽  
Author(s):  
A. N. Gent ◽  
Y-W. Chang
Keyword(s):  
Finite Element Analysis ◽  
Bond Strength ◽  
Direct Analysis ◽  
Test Method ◽  
Bond Rupture ◽  
Experimental Measurements ◽  
Element Analysis ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Good Agreement

Abstract The stiffness of rubber-filled hinges for small rotations of the hinge plates has been determined by finite element analysis (FEA). The rubber is assumed to be linearly elastic and virtually incompressible, and the hinge is assumed to be long enough for the rubber to be in a state of plane strain, i.e., prevented from any displacement parallel to the hinge. Results have been obtained for hinges of a wide range of unstrained angle, ranging from 5° up to 360°. The calculated stiffnesses for long hinges vary by over four orders of magnitude over this range. For small angles, an approximate solution has been obtained by direct analysis—it is in good agreement with the FEA solution for hinge angles up to about 40°. Experimental measurements on several rubber-filled hinges are also reported. The measured rotational stiffnesses are in satisfactory agreement with theoretical predictions. Because a rubber-filled hinge constitutes a possible test method for bond strength, conditions are derived for bond rupture as a hinge is strained open.

Dynamic Behavior of Spherical Friction Dampers and Its Implication to Damper Contact Stiffness

2006 ◽  
Vol 129 (2) ◽  
pp. 511-521 ◽  
Author(s):  
K-H. Koh ◽  
J. H. Griffin
Keyword(s):  
Contact Stiffness ◽  
Friction Damper ◽  
Test Fixture ◽  
Friction Dampers ◽  
Vibratory Response ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Vibrating Systems ◽  
Good Agreement ◽  
Mindlin’S Theory

A model that predicts the quasi-static behavior of a friction damper that has spherical contacts was developed using Mindlin’s theory. The model was integrated into a dynamic analysis that predicts the vibratory response of frictionally damped blades. The analytical approach was corroborated through a set of benchmark experiments using a blades/damper test fixture. There was good agreement between the theoretical predictions of amplitude and the values that were measured experimentally over a wide range of test conditions. It is concluded that it is possible to predict the vibratory response of frictionally damped vibrating systems using continuum mechanics, provided that the contact geometry is clearly defined and the local nonlinear contact is correctly taken into account.

Modeling of Tool Forces for Worn Tools: Flank Wear Effects

1996 ◽  
Vol 118 (3) ◽  
pp. 359-366 ◽  
Author(s):  
S. Elanayar ◽  
Y. C. Shin
Keyword(s):  
Flank Wear ◽  
General Procedure ◽  
Three Dimensional ◽  
Shear Plane ◽  
Workpiece Material ◽  
Ceramic Tools ◽  
Indentation Force ◽  
Normal Forces ◽  
Theoretical Predictions ◽  
Good Agreement

A general procedure for the separation of ploughing forces from shearing forces on the shear plane is outlined. The first part of the paper deals with the experimental separation of these forces using the predictive machining theory developed by Oxley. The forces are decomposed by first separating the shear forces from the total forces and then employing an iterative procedure to calculate the normal forces on the shear plane. All analysis is conducted for three dimensional cutting. The second part of the paper develops a procedure to model the ploughing forces by accounting for the change in geometry with flank wear. The procedure uses the indentation models along with values of tool and workpiece material constants to determine the indentation force. Models for the indentation depth are developed from a few designed experiments and the predictions by the established models are then compared with experimental results obtained for different cutting conditions. The theoretical predictions of the ploughing forces agree closely with results of the experiments. Additional analysis using ceramic tools also show reasonably good agreement between predictions and experimental measurements.

Sign in / Sign up

Export Citation Format

Share Document