Vis Madhavan

Extension of Oxley’s Analysis of Machining to Use Different Material Models

The aim of the present work is to extend the applicability of Oxleys analysis of machining to a broader class of materials beyond the carbon steels used by Oxley and co-workers. The Johnson-Cook material model, history dependent power law material model and the Mechanical Threshold Stress (MTS) model are used to represent the mechanical properties of the material being machined as a function of strain, strain rate and temperature. A few changes are introduced into Oxleys analysis to improve the consistency between the various assumptions. A new approach has been introduced to calculate the pressure variation along the alpha slip lines in the primary shear zone including the effects of both the strain gradient and the thermal gradient along the beta lines. This approach also has the added advantage of ensuring force equilibrium of the primary shear zone in a macroscopic sense. The temperature at the middle of the primary shear zone is calculated by integrating the plastic work thereby eliminating the unknown constant η. Rather than calculating the shear force from the material properties corresponding to the strain, strain rate and temperature of the material at the middle of the shear zone, the shear force is calculated in a consistent manner using the energy dissipated in the primary shear zone. The thickness of the primary and secondary shear zones, the heat partition at the primary shear zone, the temperature distribution along the tool-chip interface and the shear plane angle are all calculated using Oxleys original approach. The only constant used to fine tune the model is the ratio of the average temperature to the maximum temperature at the tool-chip interface (ψ). The performance of the model has been studied by comparing its predictions with experimental data for 1020 and 1045 steels, for aluminum alloys 2024-T3, 6061-T6 and 6082-T6, and for copper. It is found that the model accurately reproduces the dependence of the cutting forces and chip thickness as a function of undeformed chip thickness and cutting speed and accurately estimates the temperature in the primary and secondary shear zones.

Upper bound analysis of oblique cutting with nose radius tools

Abstract A generalized upper bound model for calculating the chip flow angle in oblique cutting using flat-faced nose radius tools is described. The projection of the uncut chip area on the rake face is divided into a number of elements parallel to an assumed chip flow direction. The length of each of these elements is used to find the length of the corresponding element on the shear surface using the ratio of the shear velocity to the chip velocity. The area of each element is found as the cross product of the length and its width along the cutting edge. Summing up the area of the elements along the shear surface, the total shear surface area is obtained. The friction area is calculated using the similarity between orthogonal and oblique cutting in the ‘equivalent’ plane that includes both the cutting velocity and chip velocity. The cutting power is obtained by summing the shear power and the friction power. The actual chip flow angle and chip velocity are obtained by minimizing the cutting power with respect to both these variables. The shape of the curved shear surface, the chip cross section and the cutting force obtained from this model are presented.

Upper bound analysis of oblique cutting: improved method of calculating the friction area

This paper describes further development of the upper bound analysis of oblique cutting with nose radius tools described previously by Adibi-Sedeh et al. [1] by incorporation of an improved method for calculating the friction area at the chip-tool interface. Previously, the friction area was obtained from the shear surface area assuming that the ratio of these areas is the same as in orthogonal machining. Our results showed that this led to overestimation of the effect of friction on the chip flow angle, thereby resulting in smaller changes in the chip flow angle with inclination angle as compared to experimental data. In the new approach, the chip-tool contact length is obtained from the length of the shear surface assuming that the ratio of the lengths is the same as in orthogonal machining and the friction area is calculated using this length. The chip flow angle predicted using the new approach shows much better agreement with experimental data. In particular, the dependence of the chip flow angle on the inclination angle is accurately reproduced. Upper bound analysis of oblique cutting using this new model for the friction area provides an elegant explanation for the relative influence of the normal and equivalent rake angles on the cutting force.

The Effect of Surface Tilt on Nanoindentation Results

The effect of surface tilt on results of nanoindentation tests is studied for Berkovich, cube corner and conical indenters. The true projected areas are calculated as a function of tilt angle and orientation using the exact three dimensional geometry of each indenter. The true area is compared with the area when there is no tilt and the resulting error in hardness and modulus are discussed. It is found that the error increases with increasing tilt angle, and magnitude of the error increases as the equivalent cone angle of the indenter increases.Copyright

Investigation of the Transition From Plane Strain to Plane Stress in Orthogonal Metal Cutting

It is widely known that in practical orthogonal machining experiments, interior sections of the deforming material undergo plane strain deformation whereas material near the side faces of the workpiece undergoes plane stress deformation. This study is aimed at investigating the plane strain to plane stress transition using 3D coupled thermo-mechanical finite element analysis of orthogonal machining. The temperature, stress, strain and strain-rate distributions along different planes of the workpiece are analyzed to obtain estimates of the fraction of material undergoing plane strain deformation for different widths of cut. While it is found that the deformation in the mid-section of the workpiece is close to that observed in 2D plane strain simulations, the deformation along the side faces is quite different from that observed in 2D plane stress simulations, due to the constraint imposed upon the material along the sides by the material in the middle. Though the chip thickness along the sides is smaller than the chip thickness in the middle, the strain, strain-rate, and temperature fields along the side face and mid-section are quite similar. This study confirms that accurate maps of temperature, strain and strain-rate in plane strain deformation can be obtained by observing the side faces. It is found that for the cutting conditions used, a width to depth-of-cut ratio of twenty (not ten, as is commonly assumed) results in a close approximation to plane strain deformation through more than 90% of the width of the work material. For a width to depth-of-cut ratio of ten, significant deviations are observed in the stresses, with respect to their corresponding values in plane strain. Recommendations for the width of cut to depth of cut ratio to be used in experiments for other cutting conditions can be developed based upon similar studies.Copyright

An image-splitting-optic for dual-wavelength imaging

Dual-wavelength imaging is used in several scientific and practical applications. One of the most common applications is dual-wavelength thermography which has many advantages over single wavelength thermal imaging. Optical imagesplitters can be used to turn any imaging equipment into a dual-wavelength imaging system. In this paper, a new design of an image-splitting optic, for use in dual-wavelength imaging, is presented. The new design evades the limitations encountered with the basic image-splitter design where images can be captured at higher resolutions and frame rates. The new design also facilitates the adjustment of the image magnification. With very minor changes in the optical components, the image-splitter can be used in different thermal imaging techniques such as Infrared (IR) imaging and Laser Induced Fluorescence (LIF) imaging or any other technique that utilizes dual-wavelength imaging. Furthermore, with some modifications in the optical path, the image splitter can be used for imaging

A novel multichannel nonintensified ultra-high-speed camera using multiwavelength illumination

Multi-channel gated-intensified cameras are commonly used for capturing images at ultra-high frame rates. However, the image intensifier reduces the image resolution to such an extent that the images are often unsuitable for applications requiring high quality images, such as digital image correlation. We report on the development of a new type of non-intensified multi-channel camera system that permits recording of image sequences at ultra-high frame rates at the native resolution afforded by the imaging optics and the cameras used. This camera system is based upon the use of short duration light pulses of different wavelengths for illumination of the target and the use of wavelength selective elements in the imaging system to route each particular wavelength of light to a particular camera. A prototype of this camera system comprising four dual-frame cameras synchronized with four dual-cavity lasers producing laser pulses of four different wavelengths is described. The camera is built around a stereo microscope such that it can capture image sequences usable for 2D or 3D digital image correlation. The camera described herein is capable of capturing images at frame rates exceeding 100 MHz. The camera was used for capturing microscopic images of the chip-workpiece interface area during high speed machining. Digital image correlation was performed on the obtained images to map the shear strain rate in the primary-shear-zone during high speed machining.

A hybrid model for analysis of 3-D machining operations

Abstract This paper describes the development of a physically based model for the analysis of commonly encountered 3-D machining processes using arbitrarily oriented cutting tools. This model consists of two modules, a generalized upper bound analysis module capable of handling any given cutting edge geometry, and a 2-D machining analysis module capable of using a wide range of constitutive equations to handle most commonly machined materials. The upper bound module is used for prediction of the chip flow angle and is followed by application of the extended Oxleys analysis of machining (Adibi-Sedeh, Madhavan, and Bahr 2003a) in the equivalent plane to obtain two components of the cutting force in the plane. The out-of-plane component is calculated by applying the constraint that the resultant cutting force should not have any component along the rake face in a direction perpendicular to the chip flow direction. The performance of the hybrid model is validated through extensive comparison with experimental data for different operations and materials.