Project # 2 - Slides

Shaft Design


Step # 1 - Determine the conceptual shape/design of each of the two shafts

  1. Draft a rough sketch (top view) of the shafts with the gears mating with each other
  2. Determine the lengths of the various sections of each shaft by:
    1. Considering the face width of the pinion and the gear
    2. Considering approximate hub widths the gears
    3. Considering values for the air gaps
    4. Considering a width of the bearings that may be used
  3. Determine the distances between all the load/reaction locations
  4. Assume that both shafts lie on the same horizontal plane


 Step # 2 - Select Materials for the Shafts

Assume the basic shaft diameters and make a first trial material selection for each shaft

Hint: For strength based designs, shafts having diameters less than 3.5" are usually made from a cold drawn steel in order to resist fatigue


For D 3.5" Cold Drawn (CD) Material - better surface finish and easily machinable

For D 3.5" Hot Rolled (HR) or preferably Quenched & Treated (Q&T) - generally rough surface but low cost




Step # 3 - Select safety factors for the design of each shaft

Basic Rules:


Safety Factor



For ductile materials where a high level of confidence exists in the loads, material properties and operating conditions


For brittle materials where a high level of confidence exists and operating conditions are well known


For ductile materials with some doubt about the adequacy of material properties data, loads or the stress analysis


For uncertain conditions about same combination of material properties, loads and the stress analysis



Step # 4 - Calculate the torques and sketch torque diagrams for each shaft

Using the following equation, calculate the torque of each shaft:



P is power in HP

n is speed in rpm

Draw the torque diagrams based upon the torque values



Step # 5 - Determine the tangential and normal forces on each of the gears

wpe2.jpg (6141 bytes)


Tangential Force:

Wt = T/(D/2) compute for G1, P2 and G2

Radial Force:

Wr = Wt (Tan F ) compute for G1, P2 and G2

Where: F (Pressure angle) is 20

T is torque

D is gear pitch diameter


Step # 6 - Perform a complete force analysis for each shaft and draw force diagrams showing all forces acting on the shaft and compute the bearing reactions at the bearing seat locations


Resultant reaction at any point is given by:

R=square root(Ry2+Rz2)

wpe1.jpg (1406 bytes)

Step # 7 - Draw shear force and bending moment diagrams for the shafts, both in the vertical and horizontal planes and draw the resultant bending moment diagrams


Do the following for each shaft:

  1. Draw SFD & BMD in the vertical direction (y-axis)
  2. Draw SFD & BMD in the horizontal direction (z-axis)
  3. Draw RBMD on graph paper, to scale with a sketch of the shaft at the top



Step # 8 - Determine the basic shaft diameters using static analyses and rough assumptions

Do the following for each shaft:

  1. Using the torque and RBMD diagrams, perform static analyses to determine the static diameters of the different sections of the shaft
  2. Where static analyses are not possible or are unnecessary, assume diameters based upon the diameters of the adjacent sections


 Step # 9 - Determine the shaft diameters using fatigue analyses

Do the following for each shaft:

  1. Determine critical points by first identifying the stress concentration locations
  2. Perform fatigue analyses at each critical (fatigue) location to determine the fatigue diameters of the shaft
  3. Summarize the preliminary shaft diameters from the static and fatigue analyses