No abstract

This paper presents the analytical modeling of chip load and chip volume distribution in milling processes in the presence of cutter runout. The understanding of chip load kinematics has a strong bearing on the prediction of milling forces, on the assessment of resulting surface finish and tool vibration, and on the identification of runout for multi-toothed machining process monitoring and control. In this study a chip thickness expression is analytically established in terms of the number of flutes, the cutter offset location and the ratio of offset magnitude to feed per tooth. The effects of runout geometry, feed rate, and depths of cut on the overall chip generating action is discussed through the illustration of cutting regions and chip load maps. Explicit solutions for the entry and exit angles are formulated in the context of milling parameters and configuration. Experimental measurement of the resulting chip volumes from machining with an offset cutter is compared to an analytical model formulated from the chip thickness expression. Additionally, an average chip thickness prediction, based on the chip volume model in combination with the entry/exit angle solutions, is compared to data reported in the literature for validity assessment.

This paper extends analytical modeling of the milling process to include process damping effects. Two cutting mechanisms (shearing and plowing mechanisms) and two process damping effects (directional and magnitude effects) are included. The directional effect is related to vibration energy dissipation due to directional variation of cutter/workpiece relative motion. The magnitude effect is associated with change in force magnitude due to variation of rake angle and clearance angle. Process damping is summarized as containing these separate components; direction-shearing, direction-plowing, magnitude-shearing and magnitude-plowing. The total force model including the process damping effect is obtained through convolution integration of the local forces. The analytical nature of this model makes it possible to determine unknown process damping coefficients from measured vibration signal during milling. The effects of cutting conditions (cutting speed, feed, axial and radial depths of cut) on process damping are systematically examined. It is shown that total process damping increases with increasing feed, axial and radial depths of cut, but decreases with increasing cutting velocity. Predictions based on the analytical model are verified by experiment. Results show that plowing mechanism contributes more to the total damping effect than the shearing mechanism, and magnitude-plowing effect has by far the greatest influence on total damping.

For a generalized helical end mill, this paper presents a frequency domain force model considering the ploughing as well as the shearing mechanisms. The differential chip load and the corresponding cutting forces are first formulated through differential geometry for a general helical cutting edge. The differential cutting force is assumed to be a linear function of the chip load with a proportional shearing force and a constant ploughing force. The total milling force in the angle domain is subsequently composed through convolution integration and analyzed by Fourier analysis. The frequency domain model has the parameters of a general milling process all integrated in a single framework with their roles clearly defined so that Fourier coefficients of the milling force can be obtained for any analytically definable helical cutter. Applications are illustrated for three common helical cutters: the cylindrical, taper, and ball end mills. Furthermore, as an inverse application, a linear algebraic equation is formulated for the identification of six cutting constants from the average forces of two slot milling tests. Demonstration and verification of the milling force model as well as the identification of cutting constants are carried out through experiments with three types of milling cutters.

This paper investigated the scribing process characteristics of the hard and brittle materials including single crystal silicon, STV glass, and sapphire substrate. Under various cutting angles, major process characteristics are examined including the groove geometry, specific cutting energy, and critical depth of cut at the onset of ductile-to-brittle cutting transition. As the cutting depth increases, groove geometry clearly reveals the ductile-to-brittle transition from the plastic deformation to a brittle fracture state. The material size effect in the ductile region as well as the transition in scribing behavior is well reflected by change in the specific cutting energy. Further, it is shown that the change of specific cutting energy as a function of the cutting depth can serve as a criterion for estimating the critical depth of cut. Such estimated critical depth of cut is confirmed by measurement from a 3D confocal microscope. The critical depths of cut for these hard materials are found to be between 0.1μm and 0.5μm depending on the materials and cutting angles.