FANUC G34 variable-lead threading: axial acceleration at constant spindle speed
Using the F and K definitions for 0i-F lathe G34, build an ideal lead model based on spindle revolutions. It explains feed-axis acceleration at constant spindle speed and why an increment per revolution is not an increment per millimetre.
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A feed axis that keeps accelerating while spindle speed remains constant does not necessarily indicate a threading-synchronization fault. For a thread with increasing lead, the distance travelled per revolution grows, so axial velocity naturally increases.
F describes initial lead; K describes change per revolution
The FANUC 0i-F lathe operator's manual B-64604EN-1/01, §3.3, pages 27–28 (public mirror of the original manual) defines G34 F as longitudinal lead at the starting point and K as the lead increment or decrement per spindle revolution. This article concerns 0i-F lathes equipped with the function. G34 is not confused with ordinary constant-lead G32 or feed per minute.
Use spindle revolutions as the independent variable
In this original design model, n is the cumulative number of spindle revolutions from the start. Initial lead is L₀=2 mm/rev and lead increases by K=0.25 mm/rev each revolution. Idealize the change as the continuous linear relation L(n)=2+0.25n. The model uses the manual's meaning of change per revolution; it does not claim to reproduce the CNC's internal discrete interpolation algorithm.
| Cumulative spindle revolutions n | Local lead in the model | Axial velocity at spindle speed 600 r/min |
|---|---|---|
| 0 | 2 mm/rev | 1200 mm/min |
| 4 | 3 mm/rev | 1800 mm/min |
| 8 | 4 mm/rev | 2400 mm/min |
Velocity is local lead multiplied by rotational speed. Spindle speed 600 r/min is 10 rev/s. In the model, axial velocity increases each second by 0.25×10²=25 mm/s, giving constant axial acceleration of 25 mm/s². Constant spindle speed does not imply constant feed-axis velocity.
Change per revolution and change per millimetre describe different threads
In this continuous model, axial distance is s(n)=2n+0.125n². Thus 4 revolutions correspond to 10 mm, and 8 revolutions to 24 mm. The latter 4 revolutions travel 4 mm farther than the first 4. Multiplying initial lead by total revolutions does not calculate the whole travel.
If K is incorrectly taken to mean an increase of 0.25 mm/rev for every 1 mm of travel, the lead follows a different law. The preceding revolution, endpoint-lead and velocity calculations would no longer apply. When checking drawing requirements, first establish whether change is defined against angle, revolutions or axial position, then convert accordingly.
Negative K cannot be extended indefinitely either
In the cited edition, K outside its range, a changed lead above the maximum, or a negative lead triggers PS0313. A decreasing lead must therefore be checked throughout the specified range, not merely by confirming a positive initial F. A mathematical result close to zero lead is not presented here as a guarantee of machinability.
The example ignores spindle acceleration, following error and entry/exit transitions, and provides no directly executable cutting program. Its purpose is to explain the velocity demand caused by variable lead. Final checks must use the drawing's lead function and the particular system's limits. Related resources are in the OPTION section.