Workshop Calculation: Gears, Screw Threads, Tapers and Fits
Gears, screw threads, tapers and fits
This domain tests gear ratios and module calculations, thread pitch and lead, taper dimensions and the classification of fits. These are common setting and assembly calculations in fitting and machining work.
Core rules
- Gear ratio = driven teeth/driver teeth = driver speed/driven speed. A larger driven gear reduces speed and increases torque.
- Module m = pitch circle diameter/T, where T is the number of teeth. Outside diameter for a standard spur gear = m(T + 2). Circular pitch = πm.
- Thread pitch is the axial distance between corresponding crests. Lead = pitch × number of thread starts.
- Taper: (D − d)/L gives taper per unit length; the half-angle satisfies tan α = (D − d)/(2L).
- Fits: clearance fit has a gap; interference fit has shaft larger than hole; transition fit may be either.
Worked example
A spur gear has module m = 2.5 mm and T = 40 teeth. Pitch circle diameter = mT = 2.5 × 40 = 100 mm. Outside diameter = m(T + 2) = 2.5 × 42 = 105 mm. If a 40-tooth driver at 800 rpm drives an 80-tooth gear, ratio = 80/40 = 2:1 reduction, so driven speed = 800 × 40/80 = 400 rpm. The reasoning is to use teeth for the ratio and module for the geometry.
Traps
- Reversing the gear ratio and getting an increase instead of a reduction.
- Confusing pitch circle diameter with outside diameter.
- Using thread lead as pitch when the thread has multiple starts.
- Giving taper per side when the question asks for included taper.
- Mixing clearance and interference fit definitions.