Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Textbook Question
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Chapter 12, Problem 10A

A section of a spur gear is shown in Figure 12−3. Given the circular pitches for various gear sizes, determine the working depths, clearances, and tooth thicknesses. Round the answers to 4 decimal places.

   Working depth = 0.6366 × Circular pitch Clearance = 0.05 × Circular pitch Tooth thickness = 0.5 × Circular pitch

Chapter 12, Problem 10A, A section of a spur gear is shown in Figure 123. Given the circular pitches for various gear sizes, , example  1

Chapter 12, Problem 10A, A section of a spur gear is shown in Figure 123. Given the circular pitches for various gear sizes, , example  2

Expert Solution
Check Mark
To determine

(a)

The working depth, clearances and tooth thickness of the spur gear.

Answer to Problem 10A

  WorkingDepth=0.2499in.Clearance=0.0196in.ToothThickness=0.1963in.

Explanation of Solution

Given:

Circular pitch c=0.3925in.

Calculation:

The working depth is calculated by the formula

  Workingdepth=0.6366×circularpitchWorkingdepth=0.6366×0.3925Workingdepth=0.2499in.

Clearance is calculated by the formula

  Clearance=0.05×circularpitchClearance=0.05×0.3925Clearnce=0.0196in.

And, tooth thickness is calculated by the formula

  Tooththickness=0.5×circularpitchTooththickness=0.5×0.3925Tooththickness=0.1963in.

Conclusion:

The working depth, clearance and tooth thickness of gear is 0.2499in.,0.0196in.and0.1963in., respectively.

Expert Solution
Check Mark
To determine

(b)

The working depth, clearances and tooth thickness of the spur gear.

Answer to Problem 10A

  WorkingDepth=0.1007in.Clearance=0.0079in.ToothThickness=0.0791in.

Explanation of Solution

Given:

Circular pitch c=0.1582in.

Calculation:

The working depth is calculated by the formula

  Workingdepth=0.6366×circularpitchWorkingdepth=0.6366×0.1582Workingdepth=0.1007in.

Clearance is calculated by the formula

  Clearance=0.05×circularpitchClearance=0.05×0.1582Clearnce=0.0079in.

And, tooth thickness is calculated by the formula

  Tooththickness=0.5×circularpitchTooththickness=0.5×0.1582Tooththickness=0.0791in.

Conclusion:

The working depth, clearance and tooth thickness of gear is 0.1007in.,0.0079in.and0.0791in., respectively.

Expert Solution
Check Mark
To determine

(c)

The working depth, clearances and tooth thickness of the spur gear.

Answer to Problem 10A

  WorkingDepth=0.5138in.Clearance=0.0403in.ToothThickness=0.4035in.

Explanation of Solution

Given:

Circular pitch c=0.8069in.

Calculation:

The working depth is calculated by the formula

  Workingdepth=0.6366×circularpitchWorkingdepth=0.6366×0.8069Workingdepth=0.5138in.

Clearance is calculated by the formula

  Clearance=0.05×circularpitchClearance=0.05×0.8069Clearnce=0.0403in.

And, tooth thickness is calculated by the formula

  Tooththickness=0.5×circularpitchTooththickness=0.5×0.8069Tooththickness=0.4035in.

Conclusion:

The working depth, clearance and tooth thickness of gear is 0.5138in.,0.0403in.and0.4035in., respectively.

Expert Solution
Check Mark
To determine

(d)

The working depth, clearances and tooth thickness of the spur gear.

Answer to Problem 10A

  WorkingDepth=0.7880in.Clearance=0.0619in.ToothThickness=0.6189in.

Explanation of Solution

Given:

Circular pitch c=1.2378in.

Calculation:

The working depth is calculated by the formula

  Workingdepth=0.6366×circularpitchWorkingdepth=0.6366×1.2378Workingdepth=0.7880in.

Clearance is calculated by the formula

  Clearance=0.05×circularpitchClearance=0.05×1.2378Clearnce=0.0619in.

And, tooth thickness is calculated by the formula

  Tooththickness=0.5×circularpitchTooththickness=0.5×1.2378Tooththickness=0.6189in.

Conclusion:

The working depth, clearance and tooth thickness of gear is 0.7880in.,0.0619in.and0.6189in., respectively.

Expert Solution
Check Mark
To determine

(e)

The working depth, clearances and tooth thickness of the spur gear.

Answer to Problem 10A

  WorkingDepth=1.0142in.Clearance=0.0798in.ToothThickness=0.7966in.

Explanation of Solution

Given:

Circular pitch c=1.5931in.

Calculation:

The working depth is calculated by the formula

  Workingdepth=0.6366×circularpitchWorkingdepth=0.6366×1.5931Workingdepth=1.0142in.

Clearance is calculated by the formula

  Clearance=0.05×circularpitchClearance=0.05×1.5931Clearnce=0.0798in.

And, tooth thickness is calculated by the formula

  Tooththickness=0.5×circularpitchTooththickness=0.5×1.5931Tooththickness=0.7966in.

Conclusion:

The working depth, clearance and tooth thickness of gear is 1.0142in.,0.0798in.and0.7966in., respectively.

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