Ken Youssefi Mechanical Engineering Dept. 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

KeysHub

Shaft

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Keys

ANSI standard

w = d/2, L = 2dLw

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Pins

ANSI standard

d = D / 10

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.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

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 1060-1090 spring steel, beryllium copper alloy 25, stainless steel, or aluminum.

Refer to catalog for size and groove dimensions.

Ken Youssefi Mechanical Engineering Dept. 7

SplinesSplines 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

T = Ssy (πdp2 l) / 16

l = spline length

rp = pitch radius , Ssy = yield strength in shear

Ken Youssefi Mechanical Engineering Dept. 8

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

Press or Shrink Fits

Ken Youssefi Mechanical Engineering Dept. 10

Press or Shrink FitsWhen 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 – ri

2) / (ro2 – R2)(R2 –ri

2)]

δ = radial interference , p = contact pressure

Ken Youssefi Mechanical Engineering Dept. 11

Press or Shrink FitsExampleClass 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.

δmax = radial interference = .0032/2 = .0016, tightest fit

δmin = radial interference = .0013/2 = .00065, 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

2.03.0R

ro

2.0

Hole = 2.0000 + .0012+ .0000

Shaft = 2.0000 + .0032+ .0025

FN3 fit

Min diametral interference = .0025 - .0012 =.0013

Max diametral interference = .0032 - .0000 = .0032 hubshaft

Ken Youssefi Mechanical Engineering Dept. 12

Press or Shrink Fits

Torque capacity

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 / 63000 = (10210)(1800)/63000 = 290

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)

pmax = 13,333 psi and pmin = 5417 psi

δ = p R / E [(2R2 (ro2 – ri

2) / (ro2 – R2)(R2 –ri

2)]

Ken Youssefi Mechanical Engineering Dept. 13

Various Methods of Attaching Components to a Shaft