For an ideal motor driving a cable drum through reduction ratio R, drum speed is nd = nm/R. To produce selected no-slip carriage speed v, the required drum pitch circumference is C = 12v/nd inches per revolution and equivalent pitch diameter is D = C/Ï€.
Where actuator force enters the Sawmill Feed Mechanism design
When sawmill feed mechanism is driven by a linear actuator, the actuator force changes through the travel as the geometry changes. A comfortable static force number at one position can still leave the actuator overloaded near the start or end of stroke.
For rack-and-pinion motion, actuator comparison should include backlash, rack guidance, and whether the actuator will push the rack directly or drive through a secondary linkage.
A senior review would normally separate the required output force from the actuator force. Output force belongs to the mechanism; actuator force belongs to the installed geometry. Confusing those two numbers is one of the most common causes of undersized linear actuators.
- Calculate actuator force at the worst bracket angle, not just at mid-stroke.
- Check stroke, retracted length, and extended length against the mechanism envelope.
- Confirm the structure can accept the higher loads created by a stronger actuator.
For a FIRGELLI actuator application, run the FIRGELLI actuator force calculator, then compare available stroke, force, and mounting envelope in the FIRGELLI linear actuator range. If the goal is to replace an existing unit, use the linear actuator replacement finder before assuming the new actuator is a direct fit.
Ideal Reducer–Drum Carriage-Feed Model
Size an equivalent cable-drum pitch diameter for selected motor speed, reduction and ideal no-slip carriage feed.
Equation Used
- The reducer ratio is exact and the drum is directly keyed to its output.
- The cable does not slip or stretch and winds at a constant effective pitch diameter.
- The selected carriage feed is steady and is not a recommendation.
- Load, acceleration, reversal, cable buildup, torque, power, strength and safety are excluded.
The equivalent pitch diameter is not necessarily the drum outside diameter.
Connected motor, reducer, drum and carriage
The animation shows a motor shaft feeding an ideal reducer, a keyed output drum winding a cable, and a carriage translating on rails. Motor phase advances R times the drum phase; the presentation resets after one drum revolution.
This is an ideal pitch-line model. Cable layering, groove geometry, slip, stretch, reversal and acceleration are excluded.
What the calculator determines
Select motor speed, reduction ratio and desired carriage feed. The calculator returns drum speed, repeats the selected feed, calculates required pitch circumference and reports the equivalent pitch diameter.
It does not select a saw feed, motor, reducer, drum, cable, brake or carriage and does not calculate cutting load, torque, power, traction, strength or safe speed.
Ideal no-slip sizing identities
nd = nm/R. With v in ft/min, C = 12v/nd in/rev and D = C/π. Equivalently, v = ndπD/12.
Selected-input example
At 1,750 rpm motor speed, 30:1 reduction and 132 ft/min selected feed, drum speed is about 58.33 rpm. Required pitch circumference is about 27.15 in/rev and equivalent pitch diameter is about 8.64 in.
Scope and correction boundary
The former limit-margin output merely measured distance from the slider endpoints of 50 and 300 ft/min; it was not an engineering limit. It is replaced with equivalent pitch diameter.
Unsupported bite recommendations, performance limits, named-machine claims, loads, tolerances, materials, failure diagnoses and the fabricated worked example are removed. Actual design requires measured loads and manufacturer data.
Questions
Is pitch diameter the outside drum diameter?
Not necessarily. It is the effective cable pitch-line diameter.
Does selected feed mean recommended saw feed?
No. It is a kinematic target only.
Does the model include cable buildup?
No. Effective diameter is assumed constant.
Can this size the drive?
No. Torque, power, braking, traction, structure and safety are excluded.
Technical references
- NIST Special Publication 811 — SI and accepted unit notation.
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