1. Methods of Attaching Components to a Shaft
Keys: squared, tapered, ….
Set screws: with or without heads
Pins: straight, tapered, split, …
Snap rings
Splines
Press or Shrink fits
Ken Youssefi
Mechanical Engineering Dept.

2. Mechanical Engineering Dept.
Keys
Hub
Shaft
Ken Youssefi
Mechanical Engineering Dept.

3. Mechanical Engineering Dept.
Keys
ANSI standard
w = d/2, L = 2d L w
Ken Youssefi
Mechanical Engineering Dept.

4. Mechanical Engineering Dept.
Pins
Pins and Keys could be used as a mechanical fuse, they shear off to protect the drive train.
Pins and keys weaken the shaft and create stress concentration.
ANSI standard
d = D / 10
Torque capacity
τxy = Force / shear area = (Torque)(radius) / 2(πd 2/4) = Ssy (shear strength)
T = πd 2 D Ssy / 4
Ken Youssefi
Mechanical Engineering Dept.

5. Mechanical Engineering Dept.
Set Screws
ANSI standard
d = D/8 + 5/16
D = shaft diameter
d = set screw diameter
F = 2500 ( d ) 2.31
Maximum safe holding force
Use safety factor of 2.5
Ken Youssefi
Mechanical Engineering Dept.

6. Retaining (Snap) Rings
Snap rings are used to prevent the axial motion of mating concentric components such as gear hubs and shafts.
Material; SAE spring steel, beryllium copper alloy 25, stainless steel, or aluminum.
Refer to catalog for size and groove dimensions.
Ken Youssefi
Mechanical Engineering Dept.

7. Mechanical Engineering Dept.
Splines
Splines may be considered as using multiple keys, integral with the shaft. Best way to transmit large torque.
See ANSI or SAE standards for dimensions
τxy = Force / (shear area /4), SAE assumption that only 25% of teeth are actually sharing the load at any one time.
τxy = 4F / A = (4T) / (rp A) = (8T) / (dp A) = (16T ) / (πdp2 l) = Ssy
l = spline length
rp = pitch radius ,
Ssy = yield strength in shear
T = Ssy (πdp2 l) / 16
Ken Youssefi
Mechanical Engineering Dept.

8. Mechanical Engineering Dept.
Press or Shrink Fits
Interference Fit – shaft diameter is slightly larger than hub diameter. Inexpensive and semi-permanent connection.
Allowance always equals smallest hole minus largest shaft.
Ken Youssefi
Mechanical Engineering Dept.

9. Mechanical Engineering Dept.
Press or Shrink Fits
Ken Youssefi
Mechanical Engineering Dept.

10. Mechanical Engineering Dept.
Press or Shrink Fits
When two cylindrical parts are assembled by shrinking or press-fitting one part on another, contact pressure is created between the two parts. Thick-walled cylindrical pressure vessel equations are used to derive the equation relating the contact pressure to the interference.
δ = p R / E [(2R2 (ro2 – ri2) / (ro2 – R2)(R2 –ri2)]
δ = radial interference , p = contact pressure
Ken Youssefi
Mechanical Engineering Dept.

11. Mechanical Engineering Dept.
Press or Shrink Fits
Example
Class FN3 is used to press fit a hub onto a shaft. Determine the torque that can be transmitted. The shaft diameter is 2.0 in. and hub diameter is 3.0 in. and has a length l = 2 in.
2.0
Hole =
Shaft =
FN3 fit R
3.0
2.0 ro
shaft
Min diametral interference = =.0013
Max diametral interference = = .0032
hub
δmax = radial interference = .0032/2 = .0016, tightest fit
δmin = radial interference = .0013/2 = , loosest fit
p = contact pressure, R = contact radius = 1.0 in., ro = hub radius = 1.5, ri = shaft inside radius = 0, and δ = radial interference
Ken Youssefi
Mechanical Engineering Dept.

12. Mechanical Engineering Dept.
Press or Shrink Fits
δ = p R / E [(2R2 (ro2 – ri2) / (ro2 – R2)(R2 –ri2)]
pmax = 13,333 psi and pmin = 5417 psi
Torque capacity
μ = coefficient of friction, steel on steel (dry)  .15
μF = friction force between the outside surface of the shaft and the inside surface of the hub
F = (contact pressure)(contact area)
Torque = (μ F) R, F = p (2πRl)
Torque = (μ p 2πRl) R = (.15)(5417)(2π)(1)(2)(1) = 10,210 lb-in
hp = T ω / = (10210)(1800)/63000 = 290
Ken Youssefi
Mechanical Engineering Dept.

13. Various Methods of Attaching Components to a Shaft
Ken Youssefi
Mechanical Engineering Dept.