Page 61 - Mechanical Engineer's Data Handbook

50 MECHANICAL ENGINEER’S DATA HANDBOOK

x = radial displacement P, = axial force to give interference fit
E = Young’s modulus a = coefficient of linear expansion of inner or outer
L =length cylinder
At = temperature difference between cylinders
ohmex=- ~ (r’z (at inner radius)
(rb-ra)
urmax=p (at inner radius)

3 3
pra (rb + 2ra) (1 - 1
x a =-[ 2(rt-r:) +
E

Contact pressure

Hoop stresses

Inner cylinder:
1.8.2 Shrink fit of cylinders Q,= -pK, at ra
pb= -pK3 at rb
Two hollow cylindrical parts may be connected to- Outer cylinder:
gether by shrinking or press-fitting where a contact o~b=pK, at rb
pressure is produced. In the case ofa hub on a shaft this u,=pK, at r,
eliminates the need for a key. Formulae are given for
the resulting stresses, axial fitting force and the result- where: K, = l/[(rc/rb)2 - 13; K, = (rc/rb)2 + 1.
ing torque capacity in the case of a shaft. (rc/rb)z - ’
Symbols used:
ra = inner radius of inner cylinder ( = 0 for solid shaft)
rb = outer radius of inner cylinder
rb=inner radius of outer cylinder pa = 2pnrbLp; T= Parb.
r, = outer radius of outer cylinder
x = interference between inner and outer cylinders
L = length of outer cylinder Thermal shrinkage
Ei, E, = Young’s modulus of inner and outer cylinders
vi, v, = Poisson’s ratio of inner and outer cylinders
p = radial pressure between cylinders If the outer cylinder is heated or the inner cylinder is
cooled by At, then:
p = coefficient of friction between cylinders
T= torque capacity of system x = 2arbAt