Chapter 46, Problem 61A

To determine

(a)

The values of pitch diameter.

Answer to Problem 61A

  $D=\text{117}mm$

Explanation of Solution

Given information:

  $\begin{array}{l}\text{Module(}m\text{)}=\text{6}\text{.5 mm}\\ \text{No of teeth (}T\text{)}=\text{18}\end{array}$

Calculation:

Pitch diameter $(D)$ is given by,

  $D=mT\text{ where }m=\text{Module,}T=\text{No}\text{. of teeth}$.

Using above formula,

  $\begin{array}{l}\text{Pitch Diameter(}D\text{)}=mT\\ \Rightarrow \text{Pitch Diameter(}D\text{)}=6.5\times 18\text{ mm}\\ \Rightarrow \text{Pitch Diameter(}D\text{)}=117\text{ mm}\text{.}\end{array}$

Hence, pitch diameter of given spur gear will be $117$ mm.

To determine

(b)

The values of circular pitch of given metric spur gear.

Answer to Problem 61A

  $20.41$ mm.

Explanation of Solution

Given information:

  $\begin{array}{l}\text{Module(}m\text{)}=\text{6}\text{.5 mm}\\ \text{No of teeth (}T\text{)}=\text{18}\end{array}$

Calculation:

Circular pitch $(P_c)$ is given by,

  $P_c=\pi m\text{ where }m=\text{Module,}T=\text{No}\text{. of teeth}$.

Using above formula,

  $\begin{array}{l}\text{Circular pitch (}{P}_c\text{)}=\pi m\\ \Rightarrow \text{Circular pitch (}{P}_c\text{)}=3.14\times 6.5\text{ mm}\\ \Rightarrow \text{Circular pitch (}{P}_c\text{)}=20.41\text{ mm}\text{.}\end{array}$

Hence, circular pitch of given spur gear will be $20.41$ mm.

To determine

(c)

The values of outside diameter of given metric spur gear.

Answer to Problem 61A

  $130$ mm.

Explanation of Solution

Given information:

  $\begin{array}{l}\text{Module(}m\text{)}=\text{6}\text{.5 mm}\\ \text{No of teeth (}T\text{)}=\text{18}\end{array}$

Calculation:

Outside diameter $(D_o)$ is given by,

  $D_0=D+2m\text{ where }m=\text{Module,}D=\text{Pitch diameter}$.

From part $a$ of this exercise pitch diameter $D=$

  $117$ mm.

Using above formula,

  $\begin{array}{l}\text{Outside diamter (}{D}_0\text{)}=D+2m\\ \Rightarrow \text{Outside diamter (}{D}_0\text{)}=117+2\times 6.5\text{ mm}\\ \Rightarrow \text{Outside diamter (}{D}_0\text{)}=130\text{ mm}\text{.}\end{array}$

Hence, outside diameter of given spur gear will be $130$ mm.

To determine

(d)

The values of addendum of given metric spur gear.

Answer to Problem 61A

  $6.50$ mm.

Explanation of Solution

Given information:

  $\begin{array}{l}\text{Module(}m\text{)}=\text{6}\text{.5 mm}\\ \text{No of teeth (}T\text{)}=\text{18}\end{array}$

Calculation:

Addendum $(a)$ of a spur gear is given by,

  $a=1.00m\text{ where }m=\text{Module,}a=\text{addendum}$.

Using above formula,

  $\begin{array}{l}\text{Addendum(}a)=1.00m=1.00\times 6.5\text{ mm}\\ \Rightarrow \text{Addendum(}a)=6.50\text{ mm}\end{array}$

Hence, addendum of given spur gear will be $6.50$ mm.

To determine

(e)

The values of working depth of given metric spur gear.

Answer to Problem 61A

  $13$ mm.

Explanation of Solution

Given information:

  $\begin{array}{l}\text{Module(}m\text{)}=\text{6}\text{.5 mm}\\ \text{No of teeth (}T\text{)}=\text{18}\end{array}$

Calculation:

Working depth $(w)$ of a spur gear is given by,

  $w=2m\text{ where }m=\text{Module,}w=\text{working depth}$.

Using above formula,

  $\begin{array}{l}\text{Working depth (}w)=2m\\ \Rightarrow \text{Working depth (}w)=2\times 6.5\text{ mm}\\ \Rightarrow \text{Working depth (}w)=13\text{ mm}\end{array}$

Hence, working depth of given spur gear will be $13$ mm.

To determine

(f)

The tooth thickness depth of given metric spur gear.

Answer to Problem 61A

  $10.205$ mm.

Explanation of Solution

Given information:

  $\begin{array}{l}\text{Module(}m\text{)}=\text{6}\text{.5 mm}\\ \text{No of teeth (}T\text{)}=\text{18}\end{array}$

Calculation:

Tooth thickness $(t)$ of a spur gear is given by,

  $t=\frac{P_c}{2}\text{ where }{P}_c=\text{circular pitch,}t=\text{tooth thickness}$.

Using above formula,

  $\begin{array}{l}\text{Tooth thickness (}t)=\frac{P_c}{2}\\ \Rightarrow \text{Tooth thickness (}t)=\frac{20.41}{2}\text{ mm}\\ \Rightarrow \text{Tooth thickness (}t)=10.205\text{ mm}\end{array}$

Hence, tooth thickness of given spur gear will be $10.205$ mm.