Helical interpolation
Helical interpolation is the superposition of a circular interpolation (plane of 1st and 2nd main axis) and a linear motion in the 3rd main axis. The resulting helical motion is executed at constant pitch. The pitch is programmed by the third parameter of the circular interpolation depending on the selected plane.
Syntax example for G17 plane:
G02 | G03 X<expr> Y<expr> Z<expr> I<expr> J<expr> | R<expr> K<expr> |
G02 | G03 | Circular interpolation CW / CCW |
X<expr> Y<expr> | Target point in XY plane in [mm, inch] |
Z<expr> | Target point on helical axis perpendicular to XY plane in [mm, inch] |
I<expr> J <expr> | Position of circle centre point of interpolation in XY plane (I in X, J in Y) in [mm, inch], according to G161/G162 |
R<expr> | Radius of interpolated circle (alternative to I,J) |
K<expr> | Pitch of helix in Z (value always without sign) in [mm, inch] |
Syntax according to selected interpolation plane:
Plane | Interpolation | Target point | Target point | Centre point | Pitch |
G17 | G02/G03 | X..Y.. | Z.. | I..J../R | K |
G18 | G02/G03 | Z..X.. | Y.. | K..I../R | J |
G19 | G02/G03 | Y..Z.. | X.. | J..K../R | I |
It is not necessary to define the pitch so that the helix reaches the programmed target point exactly. In this case, the NC kernel calculates a "corrected" pitch taking into consideration the fixed points for start and target points. The corrected pitch approximates to the programmed pitch as closely as possible.
In this case, the helix target point is first calculated based on the programmed pitch. If the calculated target point differs from the programmed target point, correction is required. The criteria for correction is the distance between the programmed target point and the calculated target point viewed in the direction of rotation.
If the distance is less than or equal to π(180°), the target point of the helix is shifted in the opposite direction of rotation towards the programmed target point, i.e. the pitch is increased.
If it is greater than π(180°), the target point of the helix is shifted in the direction of rotation, i.e. the pitch is reduced.
Example
Principal correction of a helix clockwise (G02) (1st case)
The target point calculated using the programmed pitch P_{prog} is within the range of 180° after the programmed target point (viewed clockwise).
Correction takes place by reducing the pitch P_{corr} .
Example
Principal correction of a helix clockwise (G02) (2nd case)
The target point calculated using the programmed pitch P_{prog} is within the range of 180° ahead of the programmed target point (viewed clockwise).
Correction takes place by reducing the pitch P_{corr} .
Programing Example
Helical interpolation in the XY plane clockwise
The following helix is travelled:
Starting point a: X-10 Y0 Z0
Target point b: X0 Y-10 Z-20
Helix centre point I, J: Zero point
Helix pitch K: variable
:
N10 G17 G90 X-10 Y0 Z0 F500 G161
N20 G02 X0 Y-10 Z-20 I0 J0 K..
:
Minimum rotation: ¾ → pitch K=26.66
Pitch K ≥ 26.66:
The helix from a to b is generally executed in ¾ rotation because the correction is limited to the maximum possible pitch K = 26.66.
Pitch K < 26.666:
Programmed | Helix rotations from | Corrected |
17.5 | ¾ | 26.66 |
16 | 1¾ | 11.4 |
15 | 1¾ | 11.4 |
12.5 | 1¾ | 11.4 |
10 | 1¾ | 11.4 |
7.5 | 2¾ | 7.27 |
5 | 3¾ | 5.33 |
2.5 | 7¾ | 2.58 |
2 | 9¾ | 2.05 |
1 | 19¾ | 1.01 |