SHIGLEY'S MECH.ENGR...(LL)-PKG.>CUSTOM<
SHIGLEY'S MECH.ENGR...(LL)-PKG.>CUSTOM<
10th Edition
ISBN: 9781260028379
Author: BUDYNAS
Publisher: MCG/CREATE
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Textbook Question
Chapter 10, Problem 1P

Within the range of recommended values of the spring index, C, determine the maximum and minimum percentage difference between the Bergsträsser factor, KB, and the Wahl factor, KW.

Expert Solution & Answer
Check Mark
To determine

The maximum percentage difference between Bergstrasser factor and Wahl factor.

The minimum percentage difference between Bergstrasser factor, KB and Wahl factor, KW.

Answer to Problem 1P

The maximum percentage difference between KB and KW is 1.36.

The minimum percentage difference between KB and KW is 0.741.

Explanation of Solution

Write the expression for Bergstrasser factor.

KB=4C+24C3 (I)

Here, Bergstrasser factor is KB and the spring index is C.

Write the expression for Wahl factor KW.

KW=4C14C4+0.615C (II)

Here, the Wahl factor is KW.

Write the expression for the minimum percentage difference between KB and KW.

Min=(KWKBKW)×100 (III)

Write the expression for Maximum percentage difference between KB and KW.

Max=(KWKBKW)×100 (IV)

Conclusion:

Substitute 12 for C in Equation (I).

KB=4×12+24×123=5045=1.1111

Substitute 12 for C in Equation (II).

KW=4×1214×124+0.61512=4744+0.05125=1.068+0.05125=1.1194

Substitute 1.1111 for KB and 1.1194 for KW in Equation (III).

Min=(1.11941.11111.1194)×100=0.0083×1001.1194=0.741%

Thus, the minimum percentage difference between KB and KW is 0.741.

Substitute 4 for C in the Equation (I)

KB=4×4+24×43=1813=1.3846

Substitute 4 for C in the Equation (II).

KW=4×414×44+0.6154=1512+0.1537=1.25+0.1537=1.4037

Substitute 1.3846 for KB and 1.4037 for KC in the Equation (IV).

Max=(1.40371.38461.4037)×100=0.0191×1001.4037=1.36

Thus, the maximum percentage difference between KB and KW is 1.36

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Chapter 10 Solutions

SHIGLEY'S MECH.ENGR...(LL)-PKG.>CUSTOM<

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