Gears Flashcards
Module
m = p / n (= d / n)
Face width
ba = x m
where x = 9~15
Circular tooth thickness
ctt = 1/2 p
Outside tip diam.
da = dp/g + 2m
Cicular pitch with m
p = pi m
Centre distance
a = 1/2 (dg + dp)
Tangential comp. force
Ft = F (cos α)
What is α
Pressure angle
Normal comp. force is aka
Separating
Separating force
Fs = Ft (tan α)
Relationship of rpm and rad/s
N1 / N2 = ω1 / ω2 (same way round)
Relationship of rpms and diams.
N1 / N2 = d2 / d1 (flipped)
Relationship of rpm and num. of teeth
N1 / N2 = z2 / z1 (flipped)
Relationship of rad/s and num. of teeth
ω1 / ω2 = z2 / z1 (flipped)
Power transmitted with torque
P1 = T1 ω1
Power transmitted with torque, with efficiency
P1 = η T1 ω1
Torque with Ft, with diam. or rad.
T1 = 1/2 (Ft d1) = Ft r1
Transmitted load
Wt = P / V
Pitch line velocity
V = 1/2 d ω
Transmitted load using overload factor
Wt = (P / V) * (O.L. factor)
Velocity factor
Where to find this
Kv = (x + V) / x
Formula sheet
x in velocity factor eqs for a milled cut gears
6.1 (formula sheet)
x in velocity factor eqs for a cast gears
3.05 (formula sheet)
Lewis Eqs
on formula sheet
σ = Ft / (ba m Y)
What to do to Lewis eqs if you have a velocity factor
formula sheet
σ = (Kv Ft) / (ba m Y)
Y in Lewis eqs
Lewis form factor
Contact ratio eqs
= [ (rgo^2 - rgb^2)^1/2 + (rpo^2 - rpb^2)^1/2 - a sinΦ ] / (pi m cosΦ)
