Various computer simulations are run to show the effect of rougher edge geometry on cutting forces and on chatter stability. The workpiece material is A17075 with cutting pressure and edge force coefficients: K1c=810 Mpa, K1e=23Nlmm, Krc=238 Mpa, K,,, =3 l N/mm. The cutter is a six fluted endmill with a 19.05mm radius, and 30 degree helix.
For cutting force predictions, two typical cutting conditions are simulated. Figure 4 (A) shows a heavier roughing cut resulting in an uncut chip thickness of over 0.5mm on parts of the cutting edge. Cutting forces in the Y direction are reduced by about 30%. Figure 4 (B) shows a flank milling cut. Due to the large depth of cut, small feed rate, and small radial immersion of flank milling operations, the cutting forces generated using a regular endmill are predominantly edge forces. In this example, the rougher endmill reduces cutting forces in the Y direction by about 70%.
KINEMATICS AND DYNAMICS OF ROUGHING END MILLS 137 The effect of rougher edge geometry on cutting forces is best demonstrated in Figure 5 (A) and Figure 5 (C), where average force is plotted against the feed per tooth for a slotting cut and for a smaller immersion down-milling cut. Note that the uncut chip thickness for regular cutters is s, sin </J, while for a roughing endmill, the actual chip load may be higher by a factor of N . When using roughing endmills with very small feed rates relative to the edge wave amplitude, a , there is almost no overlap in chip load between flutes. Hence, the edge forces are one N'h of that of a regular cutter. As the chip thickness increases, this effect is reduced until s, sin¢ increases beyond the edge wave height, where the effect of the serrated edge geometry is completely lost. In most practical cutting conditions, this effect remains very significant.
The experimental average force measurements are also shown. They are generally in good agreement with the predictions. For regular edge cutters, at small feed rates, the decrease in force measured can be attributed to runout. With some flutes having less contact with the workpiece, the edge forces will decrease as runout increases relative to the feed rate.
For the roughing endmill, on the other hand, runout has less of an impact on the cutting forces, particularly with smaller feed rates. When there is little overlap between serrated flutes, runout will not cause the chip load to change significantly. In practice, this is another reason for using roughing endmills in large depth, low feed flank milling cuts, where runout is high because of the large length to diameter ratio of the cutter, and where cutter breakage is a limitation due to high radial cutting forces.
Figure 5 (B) and Figure 5 (0) show sample X and Y forces for each case above, again comparing very well with simulated results.
In Figure 6 (A), the chatter stability lobes are plotted for a six fluted roughing endmill at half immersion down-milling with different feed rates. Here, the dynamics are modelled as a single dominant spindle mode in each ofX and Y directions, with stiffitess: k = I.4x 106 m/N, natural frequency wn = 660 Hz, and a damping ratio of t; = 0.04 .
With decreasing feed, the overlap between flutes decreases and the stability lobes approach those of a single flute cutter. The baseline of stability is almost six times higher and the lobes six times closer together. As the feed rate increases, the stability lobes approach those of the regular cutter.
Figure 6 (B) shows experimental versus simulated chatter limits for both a regular edge and a twelve pitch roughing endmill. The dynamics of the cutter in the X and Y directions were measured by experimental modal analysis. There is good agreement between the two, clearly showing the large increase in stability when using the roughing endmill. The discrepancy that exists for the rougher endmill may, in part, be attributed to runout. While a small amount of runout will not affect stability for regular endmills, runout on roughing endmills can alter the amount of overlap between flutes, which affects the regeneration effect and the chatter stability limit.
138
Average Forces - Slotting
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Average Forces - Rougher Down Millino
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Figure 5. Simulation and experimental cutting forces for Al7075, '!. inch carbide endmill, 30 degree helix; (A) Average forces in X and Y directions for regular and rougher endmills for slotting, a=6.25mm, (B) cutting forces of a slotting cut with a 12 pitch rougher endmill, a=6.35mm, feed per tooth=0.025 mm, (C) average cutting forces for a down-milling cut, a=l2.7mm, width of cut=4mm, (D) cutting forces for a down-milling cut, a=l2.7mm, width of cut=4mm, feed per tooth=0.05mm
KINEMATICS AND DYNAMICS OF ROUGHING END MILLS
Chatter Stability Lobes
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139
Figure 6. (A) simulated stability limit for a 6 fluted regular and rougher endmill with edge wavelength of2.lmm (12 waves/inch), feeds per tooth from S 1=0.01 mm to S 1 =0.2mm, half immersion down-milling, (B) Simulated versus experimental chatter stability limits for slotting with regular and roughing endmills, feed per tooth=0.08 mm, Al7075, carbide l inch diameter 6 fluted endmill, 30 degree helix.
140 M. L. CAMPOMANES
CONCLUSIONS
A milling kinematics model is presented to describe the unique chip geometry for roughing endmills. The reduced edge contact resulting from using roughing endmills is the main mechanism responsible for the decrease in cutting forces and increase in chatter stability.
Generally, both lower cutting forces and larger increases in stability with the roughing endmill will result with more flutes, lower feedrates, smaller radial immersions, and larger amplitude of the sinusoidal edge serration. Roughing endmills also decrease the effect of runout on cutting forces. This is an important factor in deep flank milling cuts, where higher peak forces due to runout can cause cutter breakage.
These trends are supported by the presented simulation results and experimental cutting tests, and with trends observed in practice at Pratt & Whitney Canada in the flank milling of integrally bladed rotors.
REFERENCES
I. Tlusty, J., Ismail, F., and Zaton, W. "Use of Special Milling Cutters Against Chatter", NAMRC 11, University of Wisconsin, SME, pp. 408-415.
2. Slavicek, J., "The Effect of Irregular Tooth Pitch on Stability of Milling'', Proceedings of the 6th MTDR Conference, 1965, Pergamon Press, London, pp. 15-22.
3. Vanherck, P., "Increasing Milling Machine Productivity by Use of Cutters with Non-Constant Cutting Edge Pitch", 8th MTDR Conference, Manchester, 1967, pp. 94 7-960.
4. Budak, E., Altintas, Y., and Armarego, E.J.A., "Prediction of Milling Force Coefficients from Orthogonal Cutting Data", Transactions of ASME Journal of Engineering Industry, Vol 118, 1996, pp 216-223.
5. Budak, E., and Altintas, Y., 1998, "Analytical Prediction of Chatter Stability in Milling, Part I: General Formulation", Trans. ASME, J. of Dynamic Systems, Measurement, and Control, Vol. 120, pp 22-36.
6. Martellotti, M.E., An Analysis of the Milling Process, Part II: Down Milling". Transactions of the ASME, Vol.
67, pp 233-251.
7. Campomanes, M., and Altintas, Y. "An Improved Time Domain Simulation for Dynamic Milling at Small Radial Immersions and Large Depths of Cut'', submitted: ASME, 200 I.