shigley example 7-4

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Machine Design: Shafts Example 7-2 Oct 19 th 2015

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Page 1: shigley Example 7-4

Machine Design: Shafts

Example 7-2

Oct 19th 2015

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

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2. Torque in the shaft between the gears

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3. Shear Moment Diagrams

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4. Total Moments

A G I J K B

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5. Real Work Begins!

A G I J K B

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Which dimensions?D4, D5, D6, D7

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Locate critical areas and start with them

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• 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:

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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

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

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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.

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• von Mises stresses for rotating round, solid shafts

• Goodman Criterion for ‘n’

• Or directly using:

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• N yielding

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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.

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Kt

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q (Kt) bending

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Kts

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q (Kts) torsion

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