Siemens SINUMERIK 840D sl Programming Manual page 248

Special motion commands
4.5 Polynomial interpolation (POLY, POLYPATH, PO, PL)
Description
The equation used to express the polynomial function is generally as follows:
In the controller, polynomials up to a maximum of the 5th degree can be programmed:
By assigning concrete values to these coefficients, it is possible to generate various curve
shapes such as line, parabola and power functions.
A straight line is generated using a
The following still applies:
It is possible to program polynomials without the polynomial interpolation having been
activated using the G command
interpolated, but instead, all of the programmed end points of the axis are linearly
approached (
activating polynomial interpolation in the part program (
Special feature: Denominator polynomial
Command
geometry axes (without specifying an axis name), i.e. the motion of the geometry axes is
then interpolated as the quotient of two polynomials.
With this programming option, it is possible to represent shapes such as conics (circle,
ellipse, parabola, hyperbola) exactly.
Example:
Program code
POLY G90 X10 Y0 F100
PO[X]=(0,–10) PO[Y]=(10) PO[]=(2,1)
The constant coefficient (a
programmed end point is independent of
248
f(p)= a + a p + a p +. . . + a
2
0 1 2
with: a : Constant coefficients
n
p: Parameter
f(p)= a + a p + a p + a
2
0 1 2
f(p) = a + a p
0 1
a Axis position at the end of the preceding block
0:
p = PL
a = (x - a - a *p - a *p
2
1 E 0 2 3
). The programmed polynomials are only moved as such after explicitly
G1
can be used to program a common denominator polynomial for the
PO[]=(...)
) of the denominator polynomial is always assumed to be 1. The
0
p
n
n
p + a p + a p
3 4 5
3 4 5
= a = a = a = 0:
2 3 4 5
)/p
3
. In this case, the programmed polynomials are not
POLY
Comment
; Geometry axes traverse linearly to
position X10 Y0.
; Geometry axes traverse along the
quadrant to X0 Y10.
/ .
G90 G91
Programming Manual, 03/2013, 6FC5398-2BP40-3BA1
).
POLY
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