Bevel Gears Formula

Question 1

Cutting or Root Angle

Answer 1

ω= y - δ

where:
ω= cutting angle
y= pitch angle
δ= dedendum angle

Question 2

Face Angle

Answer 2

β= y - α

where:
β= face angle
y= pitch angle
α= addendum angle

Question 3

Dedendum angle

Answer 3

δ= tan-1 (d/ L)

where:
δ= dedendum angle
L= length of cone
d= dedendum

Question 4

Addendum Angle

Answer 4

α= tan-1 (a/ L)

where:
α= addendum angle
L= length of cone
a= addendum

Question 5

Pitch Angles

Answer 5

Yp=tan-1 (Np/ Ng)
Yp= tan-1 (Rp/ Rg)

Yg= tan-1 (Ng/ Np)
Yg= tan-1 (Rg/ Rp)

Where:
Np= number of teeth in pinion
Ng= number of teeth in gear
Rp= radius of pinion
Rg= radius of gear
Yg= pitch angle of gear
Yp= pitch angle of pinion

Question 6

Face Width

Answer 6

b ≤ L / 3

where:
b= face width
L= length of cone

Question 7

Length of Cone

Answer 7

L= √Rp^2 + Rg^2

where:
L= length of cone
Rp= pinion radius
Rg= gear radius

Question 8

Beam Fatigue Strength

Answer 8

Fs= SbY (L- b) / Pd L

where:
Fs= Beam fatigue strength
S= endurance stress
b= face width
L= length of cone
Y= Lewis form factor
Pd= diametral pitch

Question 9

Dynamic Load

Answer 9

Fd= Ft (600 + Vm) / 600

where:
Fd= dynamic load
Ft= transmitted load
Vm= pitch line velocity

Question 10

Checking for Failure Based on Fatigue

Answer 10

Fs ≥ Fd
where:
Fs= beam fatigue strength
Fd= dynamic load