Chapter 13, Problem 12A

A cross-sectional view of a bevel gear is shown in Figure 13-5. Given the diametral pitch and the number of gear teeth, determine the pitch diameter, the addendum, and thededendum. Round the answers to 4 decimal places.

To determine

(a)

The pitch diameter, addendum and dedendum of the gear.

Answer to Problem 12A

  $\begin{array}{l}PitchDiameter=11.25,\\ Addendum=0.25and,\\ Dedendum=0.289\end{array}$

Explanation of Solution

Given:

Diametral pitch $=4$

Number of teeth

  $=45$

Calculation:

The pitch diameter is calculated by the formula

  $\begin{array}{l}PitchDiameter=\frac{No.ofteeth}{Diametralpitch}\\ PitchDiameter=\frac{45}{4}\\ PitchDiameter=11.25\end{array}$

Addendum is calculated by the formula

  $\begin{array}{l}Addendum=\frac{1}{DiametralPitch}\\ Addendum=\frac{1}{4}\\ Addendum=0.25\end{array}$

And, dedendum is calculated by the formula

  $\begin{array}{l}Dedendum=\frac{1.1570}{DiametralPitch}\\ Dedendum=\frac{1.1570}{4}\\ Dedendum=0.289\end{array}$

Conclusion:

The pitch diameter, addendum and dedendum of gear are $11.25,0.25and0.289,$ respectively.

To determine

(b)

The pitch diameter, addendum and dedendum of the gear.

Answer to Problem 12A

  $\begin{array}{l}PitchDiameter=12.5,\\ Addendum=0.167and,\\ Dedendum=0.193\end{array}$

Explanation of Solution

Given:

Diametral pitch $=6$

Number of teeth $=75$

Calculation:

The pitch diameter is calculated by the formula

  $\begin{array}{l}PitchDiameter=\frac{No.ofteeth}{Diametralpitch}\\ PitchDiameter=\frac{75}{6}\\ PitchDiameter=12.5\end{array}$

Addendum is calculated by the formula

  $\begin{array}{l}Addendum=\frac{1}{DiametralPitch}\\ Addendum=\frac{1}{6}\\ Addendum=0.167\end{array}$

And, dedendum is calculated by the formula

  $\begin{array}{l}Dedendum=\frac{1.1570}{DiametralPitch}\\ Dedendum=\frac{1.1570}{6}\\ Dedendum=0.193\end{array}$

Conclusion:

The pitch diameter, addendum and dedendum of gear are $12.5,0.167and0.193,$ respectively.

To determine

(c)

The pitch diameter, addendum and dedendum of the gear.

Answer to Problem 12A

  $\begin{array}{l}PitchDiameter=5.5,\\ Addendum=0.125and,\\ Dedendum=0.145\end{array}$

Explanation of Solution

Given:

Diametral pitch $=8$

Number of teeth $=44$

Calculation:

The pitch diameter is calculated by the formula

  $\begin{array}{l}PitchDiameter=\frac{No.ofteeth}{Diametralpitch}\\ PitchDiameter=\frac{44}{8}\\ PitchDiameter=5.5\end{array}$

Addendum is calculated by the formula

  $\begin{array}{l}Addendum=\frac{1}{DiametralPitch}\\ Addendum=\frac{1}{8}\\ Addendum=0.125\end{array}$

And, dedendum is calculated by the formula

  $\begin{array}{l}Dedendum=\frac{1.1570}{DiametralPitch}\\ Dedendum=\frac{1.1570}{8}\\ Dedendum=0.145\end{array}$

Conclusion:

The pitch diameter, addendum and dedendum of gear are $5.5,0.125and0.145,$ respectively.

To determine

(d)

The pitch diameter, addendum and dedendum of the gear.

Answer to Problem 12A

  $\begin{array}{l}PitchDiameter=18,\\ Addendum=0.33and,\\ Dedendum=0.396\end{array}$

Explanation of Solution

Given:

Diametral pitch $=3$

Number of teeth $=54$

Calculation:

The pitch diameter is calculated by the formula

  $\begin{array}{l}PitchDiameter=\frac{No.ofteeth}{Diametralpitch}\\ PitchDiameter=\frac{54}{3}\\ PitchDiameter=18\end{array}$

Addendum is calculated by the formula

  $\begin{array}{l}Addendum=\frac{1}{DiametralPitch}\\ Addendum=\frac{1}{3}\\ Addendum=0.33\end{array}$

And, dedendum is calculated by the formula

  $\begin{array}{l}Dedendum=\frac{1.1570}{DiametralPitch}\\ Dedendum=\frac{1.1570}{3}\\ Dedendum=0.396\end{array}$

Conclusion:

The pitch diameter, addendum and dedendum of gear are $18,0.33and0.396,$ respectively.