Page 154 - Marks Calculation for Machine Design

P1: Rakesh
January 4, 2005
14:16
Brown˙C03
Brown.cls
136
STRENGTH OF MACHINES
If the inner shaft is solid, meaning the inside radius (r i ) is zero, then Eq. (3.14) for the
interface pressure (p) simplifies to the expression in Eq. (3.15).
2
Eδ R
p = 1 − (3.15)
2R r o
U.S. Customary SI/Metric
Example 6. Calculate the interface pressure Example 6. Calculate the interface pressure
(p) for a solid shaft and collar assembly, with (p) for a solid shaft and collar assembly, with
both parts steel, where both parts steel, where
δ = 0.0005 in δ = 0.001 cm = 0.00001 m
R = 2in R = 5cm = 0.05 m
r o = 3in r o = 8cm = 0.08 m
2
6
2
9
E = 30 × 10 lb/in (steel) E = 207 × 10 N/m (steel)
solution solution
Step 1. Substitute the radial interface (δ), Step 1. Substitute the radial interface (δ),
interface radius (R), outside radius (r o ) of interface radius (R), outside radius (r o ) of
the collar, and the modulus of elasticity (E) in the collar, and the modulus of elasticity (E) in
Eq. (3.15) to give Eq. (3.15) to give

2 2
Eδ R Eδ R

p = 1 − p = 1 −
2 R r o 2R r o
2
6
2
9
(30 × 10 lb/in )(0.0005 in) (207 × 10 N/m )(0.00001 m)
= =
2 (2in) 2 (0.05 m)
2 2
2in 0.05 m

× 1 − × 1 −
3in 0.08 m
15,000 lb/in 2,070,000 N/m
= (1 − 0.44) = (1 − 0.39)
4in 0.1m
2
2
= (3,750 lb/in )(0.56) = (20,700,000 N/m )(0.61)
2
2
= 2,100 lb/in = 2.1 kpsi = 12,627,000 N/m = 12.6MPa
Fit Terminology. When the radial interference (δ) and interface radius (R) is known, as
in Example 1, the interface pressure (p) can be calculated from either Eq. (3.13), (3.14),
or (3.15) depending on whether the collar and shaft are made of the same material, and
depending on whether the shaft is solid or hollow.
The radial interference (δ) and the interface radius (R) are actually determined from
interference fits established by ANSI (American National Standards Institute) standards.
There are ANSI standards for both the U.S. customary and metric systems of units.
As the interference (δ) is associated with the changes in the radial dimensions, it can be
expressed in terms of the outside diameter d shaft of the shaft and the inside diameter D hole
of the collar given in Eq. (3.16).
1
δ = (d shaft − D hole ) = δ c + |δ s | (3.16)
2
By convention, uppercase letters are used for the dimensions of the hole in the collar,
whereas lowercase letters are used for the dimensions of the shaft. Also, the radial increase