Chapter 46, Problem 63A

To determine

(a)

The values of pitch diameter.

Answer to Problem 63A

  $25mm$

Explanation of Solution

Given information:

  $\text{Module}(m)=2.5mm;\text{No of teeth }(T)=10$

Calculation:

Pitch diameter $(D)$ is given by,

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

Using above formula,

  $\begin{array}{l}\text{Pitch Diameter(}D\text{)}=mT\\ \Rightarrow \text{Pitch Diameter(}D\text{)}=2.5\times 10\text{ mm}\\ \Rightarrow \text{Pitch Diameter(}D\text{)}=25\text{ mm}\text{.}\end{array}$

Hence, pitch diameter of given spur gear will be $25$ mm.

To determine

(b)

The values of circular pitch of given metric spur gear.

Answer to Problem 63A

  $7.854mm$

Explanation of Solution

Given information:

  $\text{Module}(m)=2.5mm;\text{No of teeth }(T)=10$

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,

  $\begin{array}{l}\text{Circular pitch (}{P}_c\text{)}=\pi m\\ \Rightarrow \text{Circular pitch (}{P}_c\text{)}=3.14\times 2.5\text{ mm}\\ \Rightarrow \text{Circular pitch (}{P}_c\text{)}=7.854\text{ mm}\text{.}\end{array}$

Hence, circular pitch of given spur gear will be $7.854$ mm.

To determine

(c)

The values of outside diameter of given metric spur gear.

Answer to Problem 63A

  $30mm$

Explanation of Solution

Given information:

  $\text{Module}(m)=2.5mm;\text{No of teeth }(T)=10$

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,

  $\begin{array}{l}\text{Outside diamter (}{D}_0\text{)}=D+2m\\ \Rightarrow \text{Outside diamter (}{D}_0\text{)}=25+2\times 2.5\text{ mm}\\ \Rightarrow \text{Outside diamter (}{D}_0\text{)}=30\text{ mm}\text{.}\end{array}$

Hence, outside diameter of given spur gear will be $30$ mm.

To determine

(d)

The values of addendum of given metric spur gear.

Answer to Problem 63A

  $2.5mm$

Explanation of Solution

Given information:

  $\text{Module}(m)=2.5mm;\text{No of teeth }(T)=10$

Calculation:

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

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

Using above formula,

  $\begin{array}{l}\text{Addendum(}a)=1.00m=1.00\times 2.5\text{ mm}\\ \Rightarrow \text{Addendum(}a)=2.50\text{ mm}\end{array}$

Hence, addendum of given spur gear will be $2.5$ mm.

To determine

(e)

The values of working depth of given metric spur gear.

Answer to Problem 63A

  $5mm$

Explanation of Solution

Given information:

  $\text{Module}(m)=2.5mm;\text{No of teeth }(T)=10$

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,

  $\begin{array}{l}\text{Working depth (}w)=2m\\ \Rightarrow \text{Working depth (}w)=2\times 2.5\text{ mm}\\ \Rightarrow \text{Working depth (}w)=5\text{ mm}\end{array}$

Hence, working depth of given spur gear will be $5$ mm

To determine

(f)

The tooth thickness depth of given metric spur gear.

Answer to Problem 63A

  $3.917mm$

Explanation of Solution

Given information:

  $\text{Module}(m)=2.5mm;\text{No of teeth }(T)=10$

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,

  $\begin{array}{l}\text{Tooth thickness (}t)=\frac{P_c}{2}\\ \Rightarrow \text{Tooth thickness (}t)=\frac{7.854}{2}\text{ mm}\\ \Rightarrow \text{Tooth thickness (}t)=3.917\text{ mm}\end{array}$

Hence, tooth thickness of given spur gear will be $3.917$ mm.