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 61A
To determine

(a)

The pitch diameter of the spur gear.

Expert Solution
Check Mark

Answer to Problem 61A

The pitch diameter is 117 mm.

Explanation of Solution

Given:

Module (m) = 6.5mm

Number of teeth = 18

Concept Used:

  module=pitchdiameternumberofteeth

Calculation:

  module(m)=pitchdiameter(D)numberofteeth(N)pitchdiameter=mNpitchdiameter=18×6.5mmpitchdiameter=117mm

Conclusion:

The pitch diameter is 117 mm.

To determine

(b)

The circular pitch of the spur gear.

Expert Solution
Check Mark

Answer to Problem 61A

The circular pitch is 20.4204 mm.

Explanation of Solution

Given:

Module (m) = 6.5mm

Number of teeth = 18

Concept Used:

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

Calculation:

  Forspurgear,Circularpitch(PC)=3.1416DNPC=3.1416×11718PC=20.4204mm

Conclusion:

The circular pitch is 20.4204 mm.

To determine

(c)

The outside diameter of the spur gear.

Expert Solution
Check Mark

Answer to Problem 61A

The outside diameter is 130 mm.

Explanation of Solution

Given:

Module (m) = 6.5mm

Number of teeth = 18

Concept Used:

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

Calculation:

  Pitch(P)=Numberofteeth(N)Pitchdiameter(D)P=18117P=0.1538Outsidediameter(Do)=N+2PDo=18+20.1538Do=130mm

Conclusion:

The outside diameter is 130 mm.

To determine

(d)

The addendum of the spur gear.

Expert Solution
Check Mark

Answer to Problem 61A

The addendum is 6.5 mm.

Explanation of Solution

Given:

Module (m) = 6.5mm

Number of teeth = 18

Concept Used:

  addendum=0.3183×Circularpitch(PC)

Calculation:

  addendum(a)=0.3183PCa=0.3183×20.4204mma=6.5mm

Conclusion:

The addendum is 6.5 mm.

To determine

(e)

The working depth of the spur gear.

Expert Solution
Check Mark

Answer to Problem 61A

The working depth is 13 mm.

Explanation of Solution

Given:

Module (m) = 6.5mm

Number of teeth = 18

Concept Used:

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

Calculation:

  Foraspurgear,Workingdepth(WD)=2.000Pitchofthegear(P)WD=20.1538WD=13mm

Conclusion:

The working depth is 13 mm.

To determine

(f)

The tooth thickness of the spur gear.

Expert Solution
Check Mark

Answer to Problem 61A

The thickness of the tooth is 10.21 mm.

Explanation of Solution

Given:

Module (m) = 6.5mm

Number of teeth = 18

Concept Used:

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

Calculation:

  Foraspurgear,Thicknessofatooth(T)=1.5708Pitchofthegear(P)T=1.57080.1538T=10.21mm

Conclusion:

The thickness of the tooth is 10.21 mm.

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Chapter 48 Solutions

EBK MATHEMATICS FOR MACHINE TECHNOLOGY

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