T–79
SECTION 22 CENTER DISTANCE FORMULAS
22.1 Nomenclature And Basic Equations
Figure 40 illustrates the notation involved.
The following nomenclature is used:
C
=
Center Distance (in)
L
=
Belt Length (in) = p
×
NB
p
=
Pitch of Belt (in)
NB =
Number of Teeth on belt = L/p
N1
=
Number of Teeth (grooves) on larger pulley
N2
=
Number of Teeth (grooves) on smaller pulley
f
=
One half angle of wrap on smaller pulley (radians)
q
=
p/2 – f = angle between straight portion of belt and line of centers (radians)
R1
=
Pitch Radius of larger pulley (in) = (N1) p/2p
R2
=
Pitch Radius of smaller pulley (in) = (N2) p/2p
p
=
3.14159 (ratio of circumference to diameter of circle)
Figure 40 Belt Geometry
The basic equation for the determination of center distance is:
2C sinf = L – p (R1 + R2) – (p – 2f) (R1 – R2)
(22-1)
where C cosf = R1 – R2
(22-2)
These equations can be combined in different ways to yield various equations for the
determination of center distance. We have found the formulations, which follow, useful.
22.2 Exact Center Distance Determination – Unequal Pulleys
The exact equation is as follows:
C = (1/2)p [(NB – N1) + k(N1 – N2)]
(22-3)
1 p f
where k = (––) [tan(–– – ––) + f ]
(22-4)
p
4 2
and f is determined from:
1
(NB – N1)
(––) (tanf – f) = –––––––––– = Q (say)
(22-5)
p
(N1 – N2)