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.

   $\begin{array}{l}\text{Working depth}=0.6366\times \text{Circular pitch}\\ \text{Clearance}=0.05\times \text{Circular pitch}\\ \text{Tooth thickness}=0.5\times \text{Circular pitch}\end{array}$

To determine

(a)

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

Answer to Problem 10A

  $\begin{array}{l}WorkingDepth=0.2499in.\\ Clearance=0.0196in.\\ ToothThickness=0.1963in.\end{array}$

Explanation of Solution

Given:

Circular pitch $c=0.3925in.$

Calculation:

The working depth is calculated by the formula

  $\begin{array}{l}Workingdepth=0.6366\times circularpitch\\ Workingdepth=0.6366\times 0.3925\\ Workingdepth=0.2499in.\end{array}$

Clearance is calculated by the formula

  $\begin{array}{l}Clearance=0.05\times circularpitch\\ Clearance=0.05\times 0.3925\\ Clearnce=0.0196in.\end{array}$

And, tooth thickness is calculated by the formula

  $\begin{array}{l}Tooththickness=0.5\times circularpitch\\ Tooththickness=0.5\times 0.3925\\ Tooththickness=0.1963in.\end{array}$

Conclusion:

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

To determine

(b)

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

Answer to Problem 10A

  $\begin{array}{l}WorkingDepth=0.1007in.\\ Clearance=0.0079in.\\ ToothThickness=0.0791in.\end{array}$

Explanation of Solution

Given:

Circular pitch $c=0.1582in.$

Calculation:

The working depth is calculated by the formula

  $\begin{array}{l}Workingdepth=0.6366\times circularpitch\\ Workingdepth=0.6366\times 0.1582\\ Workingdepth=0.1007in.\end{array}$

Clearance is calculated by the formula

  $\begin{array}{l}Clearance=0.05\times circularpitch\\ Clearance=0.05\times 0.1582\\ Clearnce=0.0079in.\end{array}$

And, tooth thickness is calculated by the formula

  $\begin{array}{l}Tooththickness=0.5\times circularpitch\\ Tooththickness=0.5\times 0.1582\\ Tooththickness=0.0791in.\end{array}$

Conclusion:

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

To determine

(c)

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

Answer to Problem 10A

  $\begin{array}{l}WorkingDepth=0.5138in.\\ Clearance=0.0403in.\\ ToothThickness=0.4035in.\end{array}$

Explanation of Solution

Given:

Circular pitch $c=0.8069in.$

Calculation:

The working depth is calculated by the formula

  $\begin{array}{l}Workingdepth=0.6366\times circularpitch\\ Workingdepth=0.6366\times 0.8069\\ Workingdepth=0.5138in.\end{array}$

Clearance is calculated by the formula

  $\begin{array}{l}Clearance=0.05\times circularpitch\\ Clearance=0.05\times 0.8069\\ Clearnce=0.0403in.\end{array}$

And, tooth thickness is calculated by the formula

  $\begin{array}{l}Tooththickness=0.5\times circularpitch\\ Tooththickness=0.5\times 0.8069\\ Tooththickness=0.4035in.\end{array}$

Conclusion:

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

To determine

(d)

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

Answer to Problem 10A

  $\begin{array}{l}WorkingDepth=0.7880in.\\ Clearance=0.0619in.\\ ToothThickness=0.6189in.\end{array}$

Explanation of Solution

Given:

Circular pitch $c=1.2378in.$

Calculation:

The working depth is calculated by the formula

  $\begin{array}{l}Workingdepth=0.6366\times circularpitch\\ Workingdepth=0.6366\times 1.2378\\ Workingdepth=0.7880in.\end{array}$

Clearance is calculated by the formula

  $\begin{array}{l}Clearance=0.05\times circularpitch\\ Clearance=0.05\times 1.2378\\ Clearnce=0.0619in.\end{array}$

And, tooth thickness is calculated by the formula

  $\begin{array}{l}Tooththickness=0.5\times circularpitch\\ Tooththickness=0.5\times 1.2378\\ Tooththickness=0.6189in.\end{array}$

Conclusion:

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

To determine

(e)

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

Answer to Problem 10A

  $\begin{array}{l}WorkingDepth=1.0142in.\\ Clearance=0.0798in.\\ ToothThickness=0.7966in.\end{array}$

Explanation of Solution

Given:

Circular pitch $c=1.5931in.$

Calculation:

The working depth is calculated by the formula

  $\begin{array}{l}Workingdepth=0.6366\times circularpitch\\ Workingdepth=0.6366\times 1.5931\\ Workingdepth=1.0142in.\end{array}$

Clearance is calculated by the formula

  $\begin{array}{l}Clearance=0.05\times circularpitch\\ Clearance=0.05\times 1.5931\\ Clearnce=0.0798in.\end{array}$

And, tooth thickness is calculated by the formula

  $\begin{array}{l}Tooththickness=0.5\times circularpitch\\ Tooththickness=0.5\times 1.5931\\ Tooththickness=0.7966in.\end{array}$

Conclusion:

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