In deformation type A, due to decreasing variation in stock being removed, the error diminishes with subsequent cuts. However, errors of type B depend, according to equation 7.27, almost entirely on the force used in the last cut only.<br>In the operation ii. with feed accomplished by extending the spindle, one has to take in to account the cutting forces. Calculations give Fr = 1560 N and Ff = 90 N for roughing and finishing, respectively. The form error due to the variation of flexibility ∆c will be, after the roughing cut, δr = 0.05 mm and after the finishing cut δ f = 0.003 mm. A comparison of results using methods a) and b) shows that the type B error is larger than the type A error by a factor of 2 after the first cut and 30 after the second cut. In general, however, it may be stated that, with the exception of grinding, the errors due to the cutting force deformations are negligible in most metal cutting operations if one roughing and one finishing cut are taken. This is generally valid if errors of type B are avoided.<br>A special case is multi-tooth machining, end milling for ex- ample. In end milling the tool itself is rather flexible and cutting stiffness is rather high because of the usually large axial depth of cut. For example, for a 19.05 mm (3/4 inch) diameter cutter 63 mm (3.5 inch) long and an axial depth of cut 40 mm (or 1.6 inch), with tool stiffness of about 15,000 N/mm and cutting stiffness in steel of 40,000 N/mm, we find μ = 2.67 and i = 0.73. The improvement of the error in one pass would be merely 0.73 times.<br>The “copying ratio” i (improvement factor of form error) is very high – as high as in internal grinding. After two passes the im- provement is still only 0.53, after three passes 0.4, etc. Actually, the cutting force has a periodic component of frequency anywhere be- tween 30 and 1000 Hz. Consequently, the “dynamic” value of μ may be as much as 5 times higher, resulting in an i value of up to 0.96.<br>However, in end milling the relationship between the cutting force, the deflection, and the error of the machined surface is very special and the rather straightforward deliberations based on the<br>47<br>above values of i do not apply. Figure 7.19, from Tlusty , is a sim-<br>plified picture of cutters shown with straight teeth. The end mill and its shaft and support are flexible. In up-milling, cases a) and c), the end mill deflects mostly towards the workpiece. Every tooth starts with a very small force at Point A and reaches the maximum force at point B. Every tooth generates the final surface while at point A. In
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