EBK MATHEMATICS FOR MACHINE TECHNOLOGY
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
8th Edition
ISBN: 9781337798396
Author: SMITH
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Chapter 48, Problem 62A
To determine

(a)

The pitch diameter of the spur gear.

Expert Solution
Check Mark

Answer to Problem 62A

The pitch diameter is 216 mm.

Explanation of Solution

Given:

Module (m) = 9 mm

Number of teeth = 24

Concept Used:

  module=pitchdiameternumberofteeth

Calculation:

  module(m)=pitchdiameter(D)numberofteeth(N)pitchdiameter=mNpitchdiameter=9×24mmpitchdiameter=216mm

Conclusion:

The pitch diameter is 216 mm.

To determine

(b)

The circular pitch of the spur gear.

Expert Solution
Check Mark

Answer to Problem 62A

The circular pitch is 28.2744 mm.

Explanation of Solution

Given:

Module (m) = 9 mm

Number of teeth = 24

Concept Used:

  Forspurgear,Circularpitch(PC)=3.1416×Pitchdiameter(D)Numberofteeth(N)

Calculation:

  Forspurgear,Circularpitch(PC)=3.1416DNPC=3.1416×21624PC=28.2744mm

Conclusion:

The circular pitch is 28.2744 mm.

To determine

(c)

The outside diameter of the spur gear.

Expert Solution
Check Mark

Answer to Problem 62A

The outside diameter is 234 mm.

Explanation of Solution

Given:

Module (m) = 9 mm

Number of teeth = 24

Concept Used:

  Pitch(P)=Numberofteeth(N)Pitchdiameter(D)Outsidediameter(Do)=N+2P

Calculation:

  Pitch(P)=Numberofteeth(N)Pitchdiameter(D)P=24216P=0.111Outsidediameter(Do)=N+2PDo=24+20.111Do=234mm

Conclusion:

The outside diameter is 234 mm.

To determine

(d)

The addendum of the spur gear.

Expert Solution
Check Mark

Answer to Problem 62A

The addendum is 9 mm.

Explanation of Solution

Given:

Module (m) = 9 mm

Number of teeth = 24

Concept Used:

  addendum=0.3183×Circularpitch(PC)

Calculation:

  addendum(a)=0.3183PCa=0.3183×28.2744mma=9mm

Conclusion:

The addendum is 9 mm.

To determine

(e)

The working depth of the spur gear.

Expert Solution
Check Mark

Answer to Problem 62A

The working depth is 18 mm.

Explanation of Solution

Given:

Module (m) = 9 mm

Number of teeth = 24

Concept Used:

  Foraspurgear,Workingdepth(WD)=2.000Pitchofthegear(P)

Calculation:

  Foraspurgear,Workingdepth(WD)=2.000Pitchofthegear(P)WD=20.111WD=18mm

Conclusion:

The working depth is 18 mm.

To determine

(f)

The tooth thickness of the spur gear.

Expert Solution
Check Mark

Answer to Problem 62A

The thickness of the tooth is 14.15 mm.

Explanation of Solution

Given:

Module (m) = 9 mm

Number of teeth = 24

Concept Used:

  Foraspurgear,Thicknessofatooth(T)=1.5708Pitchofthegear(P)

Calculation:

  Foraspurgear,Thicknessofatooth(T)=1.5708Pitchofthegear(P)T=1.57080.111T=14.15mm

Conclusion:

The thickness of the tooth is 14.15 mm.

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Chapter 48 Solutions

EBK MATHEMATICS FOR MACHINE TECHNOLOGY

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