Computers ind. Engng Vol. 19, Nos 1-4, pp. 462-464, 1990 Printed in Great Britain. All rights reserved
0360-8352/90 $3.00 + 0.00 Copyright © 1990 Pergamon Press plc
N C P A T H P L A N N I N G : IS I T R E A L L Y P O S S I B L E ? Ravi Lakkaraju
and Dr. Shivakumar Raman
School of IndustrialEngineering The University of Oklahoma, Norman, Oklahoma
NC physical verification effort can be considerably reduced by analytical modelling of NC tool path. A computer algorithm was developed to graphically emulate the tool path while machining fiat pelygoual objects. The orientation of the cutter center line relative to the object was then varied and several configurations were generated. For each configuration the total path was evaluated and plotted. Nature of the plots showed that an analytical optimization of the path is possible. In order to make the model more rigorous, attempts am being made to include the effects of the cutter tool life on the total path.
\ Figure la. Staircase Milling strategy
INTRC)D! ICTION Time taken to produce a part has always been of major importance while considering its feasibility for mass production. This time is composed of actual production and idle times and the objective is to minimize both of these times. In view of minimizing production times, many strategies have evolved among which is tool path planning. Further, with the development of CAD, analytical modelling has been made possible, while avoiding physical modelling . Physical verification of the cutter path in an NC machine involves considereble expenditure of time, money and labor. Hence NC path verification through a CAD system reduces tedium and monotony considerably. However analytical modelling ignores several physical parameters making it unrealistic many times. Hence it is necessary to include as many physical effects as possible while maintaining ease of analysis. For NC face milling operations two major strategies exist (figures la, lb) . 1. Staircase milling (SCM) 2. Window Frame milling (WFM)
Figure lb. Window Frame Milling strategy In this paper, effort has been made to explain an analytical model for generating an optimal NC path plan taking into consideration factors like cutter diameter, cutter path overlap and orientation of cutter relative to the object. IlRII~J¢ Ev~PLANATI'(')I~ OF ALP,CIRITHM
Though evaluating a path seems to be a relatively easy task, finding the optimal path has still remained an uphill task in NC path planning research. In the case of drilling or punching operations where a finite number of holes need to be produced, the use of a travefing salesman approach can result in considerable shortening of the total path followed. This path may also turn out to be the most optimal path. Note that the drilling problem can be classified as a path independent problem. However, in milling where the entire area of the object has to be swept a travelling salesman approach, or shortest path approach cannot be easily applied. An analogy to the face milling operation is a lawn mowing process where every blade of grass is cut. Another example will be vacuum cleaning. To ensure total cutting while providing proper chip clearance the adjacent cuts have to overlap. An improper selection of overlap may cause imperfect surfaces and gouges. Past research in this area of path planning is evident in [2,3].
After reviewing relevant literature, and evaluating the different possible strategies we decided to study the staircasing strategy. We computerized our algorithm to perform fl~ desired analysis. Tbe next few paragraphs explain the procedure used. We implemented our algorithm on an IBM-PC compatible using the BASIC language. The next few paragraphs explain the procedure used. Information on the shape of the object face is given in the form of X and Y co-ordinates of vertices in a particular order. The algorithm determines the analytical parameters such as equations of the lines joining adjacent vertices. When the milling tool approaches the edge of a face during machining it is made to come out of the face just enough so as to clear the center of the tool from the object. This can be any value between 0.5 to 0.6 times its diameter. This amount of clearance will allow the chip to flow out easily and avoid formation of burrs on the edges. This clearance is termed as chip clearance. The maximum distance between the two 462
Lakkaraju and Raman: Optimal NC Path Planning
adjacent lays of the tool is equal to its diameter. However due to the geomelry of the tool end other process constraints (surface roughness, tolerances) this distance was reduced to 0.8 times the tool diameter to provide a proper overlap between adjacent cuts. This further ensures total cutting. To ensure that the tool sweeps every point on the face, the tool motion begins at the vertex having the least abscissa. The tool moves in a staircasing pattem until it reaches the vertex having the maximum abscissa. This pattern makes use of an active reference plane and a check surface to guide the tool. The tool moves parallel to the reference plane until it meets the check surface. At this time, the check plane is made the reference plane. Another plane parallel to the previous reference plane end at a distance of 0.8 times the tool diameter is made the check plane. Figure 3 shows the motion of the tool at different stages of the operation. At a u'ansit point the next adjacent plane becomes the check plane (shown in figure 4). In this fashion the tool progresses towards the point of maximum abscissa. After one complete simulation the object is rotated by a defined value. Object rotation involves recalculation of object geometry. For each simulation the distance traveled by the tool is determined as the number of basic length units (B.L.U.) moved by the tool. The number of times the tool engages and disengages is also measured for later analysis of exit and entry angles.
A]qAINRLq O!~ ALGORITHM The above algorithm was created to envelop the generic class of fiat polygonal objects. Simple experiments were then conducted on simple (convex) flat polygonal part geomelries. Part shapes were chosen with a variation in the number of sides. (experimentationwas limited to 3, 4 and 5 sided shapes to maintain ease of analysis). Sample part shapes chosen m-e showed in 5a and 5b.
X-axis Figure 5a. Sample of a 3-sided Face
X.axls Figure 5b. Sample of a 4-sided Face
Figure 2. Overlap required for a complete cut.
Rsfarence~ Plane~ ?eference Plane
PlRefersnce~ ano~ Check
A constant cutter diameter end feed rate was maintained between simulations of the same part. For each part geometry all possible cutter paths were generated. This was done by rotating the original part in increments of 5 degrees, hence varyin8 the orientation of the object relative to the cutter movement. At each orientation the distance traveled by the cutter was meastued. Plots between distance traveled end cutter path orientation with respect to the part were then developed. These are shown in figures 6a, 6b and 6c, for parts having 3, 4, and 5 sides respectively. These plots show the existence of a cyclic relationship with high and low values occuring at regular intervals. This is similar to a sinusoidal curve or any simple periodic curve. It can also he seen that the low values occur at different orientations for different shapes. It can he deduced that parameters cenlrolling the shape factor bring about the late~ shift of the curve between objects of varying shapes. This fact gives us the notion that there must exist en optimum path for every shape at a specific orientation. These results were in reasonable agreement with those obtained in .
Figure 3. Too] motion at non-transit points
o.so : Figure 4. Tool motion at transit points
Figure 6a. SCM for a 3-Sided Face
Proceedings of the 12th Annual Conference on Computers & Industrial Engineering
Plane of Engagement
~ l Plane of eengagemant
~ Exlt angle
Figure 7. Definition of Exit and Entrance angles. 0
Figure 6b. SCM for a 4-Sided Face
Figure 6c. SCM mr a 5-Sided Face It remains to be seen whether a functional relationship can be developed which can predict the most optimal strategy for any given shape. This optimal strategy should reflect purely on controllable features, viz., diameter of cutter, feed rate, overlap and cutter center line orientation to the part geometry. Thus for every particular part, a unique optimal path of cut must be determined generically. At the present time we are investigating analytical modelling techniques that will determine this unique relationship between path and associated parameters. Attempts are also being made to create shape factors (perimeter, area etc) from general purpose parameters previously mentioned. R~C~MM~NDA~ONN
Previous studies on face milling operations assume the locus of tooth tip to be circular. In reality it follows a trochoid with varying shapes [4, 5] depending upon parameters such as feed rate, spindle RPM, and diameter of cutter. Using a trochoidal path makes it easier to examine the formation and effects of entrance and exit angles during operation. Entry angle is defined as the angle between the plane of engagement and rake face of the cutting tool. The exit angle is defined as the angle between the plane of disengagement and rake face. Figure 7 shows the definition of exit and entrance angles for a zero rake tool with respect to a face milling operation. Investigations have shown that exit  and entry [7, 8] angles can cause sudden and complete failure of the tool. It remains to be seen whether a relationship can be developed between the tool path, entry and exit conditions. Also the exit and entry conditions need to be examined for the path of shortest length Such an attempt of coupling the tool life issue with the optimality issue has no evidence of any precedence. However, such an approach allows for more realistic modelling of NC verification.
Kalpakjian Serope "Manufacturing Engineering Technology," Addison Wesley Publishing Company.,Reading Massachusetts, 1989., pp 26. Wang, H., Chang, H., Wysk, R.A., Chandawarkar, A., "On the E~iciency of NC Tool Path Planning for Face Milling Operations," Transactions of the ASME, Vol. 109, November 1987, pp 370-376 Anand, S., Raman, S., and Wysk, R.A., "Vision Assisted NC Path Generation," Journal of Manufacturing Systems, Vol. 7, No. 3, March 1988, pp 233-240 Martellotti, M.E.,'An analysis of the milling Process," Transactions of the A.S.M.E., November 1941, pp 64770O Martellotti, M.E.,"An Analysis of the milling process, Part H - Down Milling," Transactions of the A.S.M.E, May 1945, pp 233-251 Pekelharing, A.J., "The Exit Failure in Interrupted Cutting," Annals of the C.I.R.P., Vol 27,1, January 1978 pp 5-10 Ktonenbetg, M., "Analysis of Initial Contact of Milling Cutters and Work in relation to Tool LO~e," Transactions of the A.S.M.E., April 1946, pp 217-228 Opitz, H., and Beckhaus,H., "Influence of Initial Contact on Tool Life when Face milling High Strength Materials," Annals of the C.I.R.P. Vol 18, 1970, pp 257-264