Archive for April 7th, 2016
Some equations relevant to indentations produced by a filament drive gear:
For reference, the smaller indentations are 0.25 mm deep and 1.3 mm across the bottom.
- d = filament (a.k.a. circle) diameter
- r = filament radius
- m = chord depth (inward from circle)
- c = chord length
- Θ = angle across chord from circle center, degrees
- A = chord area (a.k.a. indentation face area)
The length of the chord at the bottom of the indentation, perpendicular to the filament axis:
c = 2 sqrt(2mr - m2)
The chord angle:
Θ = 2 arcsin(c/2r)
The chord area, which would be the indentation face if it were perpendicular, which it isn’t:
A = (r2 / 2) x ((πΘ / 180) - sin(Θ))
If you measured Θ in radians, the π/180 factor would Go Away.
Some doodles showing that reducing the indentation from 0.25 to 0.15 reduces the chord area by a factor of two:
The implication being that you must maintain fairly constant force on the drive bearing against the filament to prevent stripping the indentations.