Chapter 48, Problem 64A

To determine

(a)

The pitch diameter of the spur gear.

Answer to Problem 64A

The pitch diameter is 60 mm.

Explanation of Solution

Given:

Module (m) = 3.75mm

Number of teeth = 16

Concept Used:

  $\mathrm{mod}ule=\frac{pitchdiameter}{numberofteeth}$

Calculation:

  $\begin{array}{l}\mathrm{mod}ule(m)=\frac{pitchdiameter(D)}{numberofteeth(N)}\\ pitchdiameter=mN\\ pitchdiameter=3.75\times 16mm\\ pitchdiameter=60mm\end{array}$

Conclusion:

The pitch diameter is 60 mm.

To determine

(b)

The circular pitch of the spur gear.

Answer to Problem 64A

The circular pitch is 11.781 mm.

Explanation of Solution

Given:

Module (m) = 3.75 mm

Number of teeth = 16

Concept Used:

  $\begin{array}{l}Forspurgear,\\ Circularpitch(P_C)=\frac{3.1416\times Pitchdiameter(D)}{Numberofteeth(N)}\end{array}$

Calculation:

  $\begin{array}{l}Forspurgear,\\ Circularpitch(P_C)=\frac{3.1416D}{N}\\ P_C=\frac{3.1416\times 60}{16}\\ P_C=11.781mm\end{array}$

Conclusion:

The circular pitch is 11.781 mm.

To determine

(c)

The outside diameter of the spur gear.

Answer to Problem 64A

The outside diameter is 67.5 mm.

Explanation of Solution

Given:

Module (m) = 3.75 mm

Number of teeth = 16

Concept Used:

  $\begin{array}{l}Pitch(P)=\frac{Numberofteeth(N)}{Pitchdiameter(D)}\\ Outsidediameter(D_o)=\frac{N+2}{P}\end{array}$

Calculation:

  $\begin{array}{l}Pitch(P)=\frac{Numberofteeth(N)}{Pitchdiameter(D)}\\ P=\frac{16}{60}\\ P=0.2666\\ Outsidediameter(D_o)=\frac{N+2}{P}\\ D_o=\frac{16+2}{0.2666}\\ D_o=67.5mm\end{array}$

Conclusion:

The outside diameter is 67.5 mm.

To determine

(d)

The addendum of the spur gear.

Answer to Problem 64A

The addendum is 3.75 mm.

Explanation of Solution

Given:

Module (m) = 3.75 mm

Number of teeth = 16

Concept Used:

  $addendum=0.3183\times Circularpitch(P_C)$

Calculation:

  $\begin{array}{l}addendum(a)=0.3183P_C\\ a=0.3183\times 11.781mm\\ a=3.75mm\end{array}$

Conclusion:

The addendum is 3.75 mm.

To determine

(e)

The working depth of the spur gear.

Answer to Problem 64A

The working depth is 7.518 mm.

Explanation of Solution

Given:

Module (m) = 3.75 mm

Number of teeth = 16

Concept Used:

  $\begin{array}{l}Foraspurgear,\\ Workingdepth(WD)=\frac{2.000}{Pitchofthegear(P)}\end{array}$

Calculation:

  $\begin{array}{l}Foraspurgear,\\ Workingdepth(WD)=\frac{2.000}{Pitchofthegear(P)}\\ WD=\frac{2}{0.266}\\ WD=7.518mm\end{array}$

Conclusion:

The working depth is 7.518 mm.

To determine

(f)

The tooth thickness of the spur gear.

Answer to Problem 64A

The thickness of the tooth is 5.9 mm.

Explanation of Solution

Given:

Module (m) = 3.75 mm

Number of teeth = 16

Concept Used:

  $\begin{array}{l}Foraspurgear,\\ Thicknessofatooth(T)=\frac{1.5708}{Pitchofthegear(P)}\\ \end{array}$

Calculation:

  $\begin{array}{l}Foraspurgear,\\ Thicknessofatooth(T)=\frac{1.5708}{Pitchofthegear(P)}\\ T=\frac{1.5708}{0.266}\\ T=5.9mm\\ \end{array}$

Conclusion:

The thickness of the tooth is 5.9 mm.