ComputerAided_Design_Engineering_amp_Manufactur.pdf

Usually, maximum and minimum speed constraints are imposed by the machine tool. However, in
the case of carbide and ceramic tools, certain minimum cutting speeds need to be maintained to avoid
the failure of these cutting tools due to burring formation or micro-chipping. Hence, the minimum
speed constraint is determined as the larger of the values of minimum cutting speed from machine
tool and minimum cutting speed due to cutting tool (V min). Thus, the speed constraint can be expressed
as
max �DN ⎧ min ⎫ �DNmax ⎨------------------ , Vmin ⎩ 1000
⎬�
v � -------------------
1000
⎭
The maximum feed constraint for the cutting tool (f tmax) is set per the recommendations given by the
cutting tool manufacturer (Widia, 1989). According to these recommendations, f tmax should not exceed
0.4–0.5 times the insert corner radius for triangular inserts and 0.6–0.7 times the corner nose radius for
square inserts. The minimum feed constraint value is set to the smallest feed rate available on the machine
tool. This constraint checks the feed rate during finishing operation from becoming too small. Thus the
feed constraints can be expressed as
fmin � f � min{ fmin, ft max}
The maximum depth of cut constraint has relevance in roughing operations, while the minimum depth
of cut constraint should be considered in finishing operations. The maximum limit on depth of cut due
to cutting tool (d t max) is set to half the cutting edge length for inserts with included angle of 55° or 60°
and for inserts with included angle of 80°–100°, d t max is set to two-thirds of the cutting edge length
(Widia, 1989). Minimum limit on depth of cut (d min) is set to 0.5 mm for finishing operations, and 1 mm
or depth of pocket, whichever is lower, for roughing operations. The depth of cut constraints can thus
be expressed as
dmin � d� dmax Another important constraint in case of multipass machining is total depth constraint. The sum of
depths of cut in individual passes, both roughing and finishing, must be equal to the total depth of
material to be removed.
m
�d i
i�1
�
dt This constraint may not be relevant if equal depths of cut are used for all passes.
Solution Methodology
In the case of multipass optimization, the parameters to be determined are the number of passes, cutting
speed, feed, and depth of cut to be used in each pass. As the number of passes is not known a priori, the
number of variables becomes unknown. This makes a complex problem to solve.
When the total depth of material has to be removed in more than one pass and there is surface finish
or diametral tolerance or both specified on the machined surface, the machining of this pocket needs
both roughing and finishing passes. As the governing constraints for rough and finish turning operations
are different, these two operations are treated separately.
If rigorous optimization has to be carried out for each individual pass, the solution obtained will be
computationally expensive. In any case, the cost of employing different depths of cut does not appear to