Worm Gears Formula

Question 1

Worm Diameter

Answer 1

Dw= Nt/ Pdn^sinλ
or
Dw= C^0.875 / 2.2

Where:
Dw= worm diameter
Nt= number of threads
Pdn= normal diametral pitch
C= center distance
λ= lead angle

Question 2

Gear Diameter

Answer 2

Dg= Nt/ Pdn^sinλ

Where:
Dg= gear diameter
Nt= number of teeth in gears
Pdn= normal diametral pitch
λ= lead angle

Question 3

Outside Diameter of Worm

Answer 3

Dwo= Dw+ 2a

Where:
Dwo= outside diameter of worm
Dw= worm diameter
a= addendum

Question 4

Center Distance Between Shafts

Answer 4

C= Dw+ Dg/ 2

Where:
Dg= gear diameter
Dw= worm diaemete
C= center distance

Question 5

Lead angle

Answer 5

λ= tan-1 (L/πDw)
or
λ= tan-1 (Nt/ Ng) (Dg/ Dw)

Where:
L= lead
Dw= worm diameter
λ= lead angle
Dg= gear diameter
Ng= number of teeth in gear
Nt= number of threads

Question 6

Face Width

Answer 6

b= 1/2 Dwo

where:
b= face width
Dwo= outside diameter of worm

Question 7

Pitch Line Velocity

Answer 7

Vg= π Dg ng
or
Vw= π Dw nw

where:
Vg= pitch line velocity
Dg= gear diameter
ng= rotative speed of gear
Vw= pitch line velocity of worm
Dw= worm diameter
nw= rotative speed of worm

Question 8

Efficiency

Answer 8

e= tan λ (cos θn - f tan λ / cos θn tan λ+ f ) x 100

Where:
e= efficiency
f= coefficient of friction
λ= lead angle
θn= pressure angle

Question 9

Torque of Worm

Answer 9

T= Ft (Dw/ 2)= P/ 2πn

where:
T= torque
P=power
n= rotative speed
Ft= tangential force on worm

Question 10

Sliding Velocity

Answer 10

Vs= Vw/ cos λ

Where:
Vs= sliding velocity
Vw= worm velocity
λ= lead angle