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Page 2

CNC
Programming
H ndbook

Second Edition

Page 264

CIRCULAR INTERPOLATION

ARC PROGRAMMING

With a full arc cutting, which means the complete 360°
motion, the R address cannot be used at all. The arc center
vectors I and J have to be applied, even on latest controls.

What if the circle is 359.999°? Well, at first, circle must
have 360°, therefore the word 'circle' is Incorrect. Even i.l
small difference of 0.00 I ° does make a difference between
a circle and an arc. Although this difference IS much more
important mathematically than for practical programming,
the distinction is very important. In circular interpolation
terms, an incomplete circle is nothing more than an arc.
Look at this arc a little differently. If a 90° arc is made, Ihe
R address can be programmed. for example:

GOl X2.0 YS.25 F12.0
G02 X3.75 Y7.0 Rl.7S

If an arc that covers exactly 1800 is programmed, {he pro-
gram will no! he much different:

GOl X2.0 YS.25 F12.0
G02 XS.5 YS.25 Rl.75

Note that the Y coordinate is the same for the arc start and
end position. The Y value In the circular motion block does
not have to be repeated, it is used here only for illustration.

Another example shows programming an arc of 270",
still using the R address. Are the following blocks correct?

GOl X10.5 Y8_625 F17.0
G02 X13.12S Y6.0 R2.625

The blocks appear to be correct The calculations, Ihe for-
mat, individual words. they all appear to be right. Yel, Ihe
program is wrong.! Its result Will be a 90° arc, not 2700 .

Study the illustration in Figure 29-} 5. It shows that there
is not just one, but fHiO mathemaUcal possibilities when the
R address is used for arcs. The solid contour is the tool path,
the dashes identify the two possible radii.

Programmers do not normally think of these mathemati-
cal alternatives, unlil they program arcs larger than ISO"
(or scrap a part). This is a similar situation to U1at of a full
circle, described earlier. Although (he I and J vectors can be
used to relnedy the problem, a different remedy may be a
preferred choice. The R address can still be used in Ihe pro-
gram, but with a negative sign for any arc thal is greater
than 180°. For arcs smaller than ]800 , the usual posili ve R
radius remains in effect. Recall from some earlier explana-
lions lhal if there is no sign with the R word (or any other
word), lhe word assumes a positive value. Compare the two
programming examples:

GOI XlO.5 Y8.625 F17.Q
G02 X13.12S Y6.0 R2.625 (90 DEGREES)

Start point /

I

\

Start point

Figure 29-15

./
j

"

./

/

j
./

End point
I

- R+

-- CONTOUR

.// _ .. _- CONTOUR

245

Sign of R address for circular cutting - onlv the center is different

The following example is identical [Q the previous onc,
except for the R address sign.

G01 X10.5 Y8.625 F17.0
G02 X13.125 Y6.0 R-2.625 (270 DEGREES)

If frequently programming arcs that cover more than
180°, establish a particular programming style. If the style
is well thought out, it will avoid the costly mistakes associ-
ated with the R address sign error.

FEEDRATE fOR CIRCULAR MOTION

In most programs, the feedrate for circular interpolation
is determined the same way as feedrale for linear inlerpola-
lion. The cutting feed rate for arcs is based on established
machining conventions. 'TIley include the work setup, ma-
terial machinabi1!ty, (001 diameter and its rigidity, program-
mer's expenence and other factor·s.

Many programmers do not consider the machined radius
when seiecring the cutting feedrate for the tool. Yet, If the
machined surface finish quality is really important, always
consider the size of every radius specified in the parr draw-
ing. Perhaps the same feedrate for linear and circular mo-
tions programmed so far may have to be adjusted - either
upward or downward.

In lathe programming, there is no reason \0 distinguish
between linear and circular lool motions, regardless of the
radius size. The tool nose radius is usually small, only aver-
aging .0313 inches (or 0.8 mm) and the equidistant tool
path IS close to the programmed tool path, taken from a
drawing. This is not the case for milling contour program-
ming, where large tool radii are normal and common.

Page 265

The arc feedrale is nol required in
gram. If cutler center tool path is close LO
1 contour, no adjustment is needed. On the band,
when a diameter cutter is used to contour a small out-

radius, a problem that affects the finish may
occur. this case, the tool center path a much

arc one in the drawing. In a
is used
shorter

In normal programming, the
arcs as well. as determined by

material. The formula for

iii? where ...

FI linear feedrate ormm/min)
r/min Spindle speed
F! = Feedrate per tooth
n Number of cutting

A linear feedrate for 1000 .0045 initooth load and
(WO culling edges, the r"""',.., .. ..,'" is 9 Using a rela-
tively large cutrer diameter, (\5.875 mm) or
larger, the linear feedrate or down for circu-

motion may be 11:. ........ """': good finish.

The elementary rule of adjustmenl for arcs is that
the normally programmed is increased for
outside arcs and decreased for inside arcs· Figure 29-16.

CUTTER

/
/

DECREASED --.-
FEEDRATE

Figure 29·16

'''' " NORMAL~ FEEDRATE
Feedrate adlil/stlTlel1lts for circular tool motion

Chapter 29

Two formulas provide to find the adjusted arc
feedrate, to the linear
Both formulas are recommended for external or
contouring only, nOT rough machining of solid material.

• Feedrate Outside Arcs

For outside arcs, ,ildjusled feed rate will be higher than
the linear calculated from Ihis formula:

~ where ...

F 0 Feedrate for outside arc
FI == Lineadeedrate
A radius on the part

radius

on linear feed rate of J 4 in/ml n, an
requires an upward adjustment a

Fe = 14 X (.375 + .25) / .375 = 23.333333

is a major incre<ls!!, to in lhe program,
r\n',Hl~'r the same example with ,75 cutter (01.5):

14 x (0.375 + 0.75) / 0.315 42.0

TPPflrnlt" changed from 14
If1crease. use prevIOus

inimin - D 3
to determine

adjustment is justified or not.

• Feedrate for inside Arcs

arcs, the adjusted will lower than
feed rate, calculated from formula:

F; "" Feedrate for arc
F, linear feed rate
R 0:: Inside radius on the

Cutter radius

Based on lhe Jinear feed rate
inch inside radius with
downward:

Fi '" 14 x (.8243 -

The result is a feedrate
will be Ihe applied fPpnrllfP

14 in/min, the feed rate for
I must be ad-

/ .8243 = 3.384932

inimin, In the program,
F address.

Page 529

Praise For The First

by Peter Smid fills the void for the intelligent reader who
1be simplistic concepts regurgitated in so many other books. " -

close to 20 books on CNC programming and oan honestly say that this is the
bas covered both basic and advanced programming techniques for both mills and

- Houston, Texas,

superb book, very well written, easy to understand, and should be on the desk of every
CNC Programmer and Production Engineer." - Nottingham, England

Extraordinarily comprehensive, this popular and authoritative reference covers just about every
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unusually comprehensive reference for machinists, programmers, engineers, and supervisors.
Filled with over one thousand illustrations, tables, fonnulas, tips, shortcuts, and practical
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