shigley Example 7-4

Machine Design: Shafts

Example 7-2

Oct 19th 2015

1. Perform free body diagram analysis to get reaction forces at the bearings.

2. Torque in the shaft between the gears

3. Shear Moment Diagrams

4. Total Moments

A G I J K B

5. Real Work Begins!

A G I J K B

Which dimensions?D4, D5, D6, D7

Locate critical areas and start with them

• Mm=Ta=o; Tm, Ma->

• Select Material: Sut, Se’->Se

• Assume a safe kb to find Se

• Use table 7-1 for the critical area selected:

At ‘I’

• r/d = 0.1

• Kt = 1.7; Kts = 1.5

• Kf=Kt, Kfs=Kts

• Material: Sut-> Se

• Use DE Goodman criterion of eq. 7-8 for ‘d’

• Select a standard size below the value of ‘d’ found = dreal

Why a standard size below the value of ‘d’ found:

Next: Use dreal as ‘d’

• Find -> D (D/d=1.2 (Any value between 1.5-1.02) Fig A-15-7) ‘D’ (D4) & ‘d’ (D5) (Selected D/d)

• Find ‘r’ (d*0.1) -> now you have r/d, and D\d Kt,kts

• Kt (A-15-9), q(6-20)-> Kf,

• Kts(Table A-15-8), q(6-21)-> Kfs,

• find Kb using ‘d’ Se

• Goodman Criterion for ‘n’

• N yielding

• If n>1.5, the selected d is fine for that critical area (‘I’ in this case).

• Now check ‘n’ at other critical locations using that ‘d’.– If all the value of n for all the critical locations is greater than 1.5,

select that diameter ‘d’

– Else change the material with one having greater strength or increase the diameter and perform calculations again.

• von Mises stresses for rotating round, solid shafts

• Goodman Criterion for ‘n’

• Or directly using:

• N yielding

Quick summary For ‘I’ :

• r/d = 0.1

• Kt = 1.7; Kts = 1.5

• Kf=Kt, Kfs=Kts

• Use DE Goodman criterion of eq. 7-8 for ‘d’

• Select a standard size below the value of ‘d’ found

• -> D (D/d=1.2 (Any value between 1.5-1.02) Fig A-15-7) ‘D’ (D4) & ‘d’ (D5) (Selected D/d)

• Find ‘r’ (d*0.1) -> now you have r/d, and D\d Kt,kts

• Kt (A-15-9), q(6-20)-> Kf, Kts(Table A-15-8), q(6-21)-> Kfs,

• find Kb using ‘d’ Se

• Goodman Criterion for ‘n’ and n yielding

• Check n at other locations using newly found and select a value of d with n>1.5 at all critical locations.

• In this way find all the required diameters.

Kt

q (Kt) bending

Kts

q (Kts) torsion