Chapter 11, Problem 8A

To determine

(a)

The working depths, clearance and tooth thickness.

Answer to Problem 8A

Working depth $=0.2499$ inches.

Clearance $=0.0198$ inches.

Tool thickness $=\text{0}\text{.1983}$ inches.

Explanation of Solution

Given information:

Circular pitch of a gear is given as $0.3925$ inches.

Also, below formula is given for a gear-

Working depth $=0.6366\times \text{Circular pitch}$

Clearance $=0.05\times \text{Circular pitch}$

Tool thickness $=0.5\times \text{Circular pitch}$

Calculation:

As per given information, circular pitch $=0.3925$ inches.

From the given formula,

Working depth $=0.6366\times \text{Circular pitch}$

i.e. Working depth $=0.6366\times 0.3925$ inches.

  $\Rightarrow$ Working depth $=0.2498665$ inches.

  $\Rightarrow$ Working depth $=0.2499$ inches {Rounding off to $4$ decimal places}

Similarly,

Clearance $=0.05\times \text{Circular pitch}$

i.e. Clearance $=0.05\times 0.3965=0.0198$ inches

Also, tool thickness $=0.5\times \text{Circular pitch}$

i.e. tool thickness $=0.5\times \text{0}\text{.3965}=\text{0}\text{.1983}$ inches.

Thus, working depth $=0.2499$ inches.

Clearance $=0.0198$ inches.

Tool thickness $=\text{0}\text{.1983}$ inches.

To determine

(b)

The working depths, clearance and tooth thickness.

Answer to Problem 8A

Working depth $=0.1007$ inches.

Clearance $=0.0079$ inches.

Tool thickness $=\text{0}\text{.0791}$ inches.

Explanation of Solution

Given information:

Circular pitch of a gear is given as $0.1582$ inches.

Also, below formula is given for a gear-

Working depth $=0.6366\times \text{Circular pitch}$

Clearance $=0.05\times \text{Circular pitch}$

Tool thickness $=0.5\times \text{Circular pitch}$

Calculation:

As per given information, circular pitch $=$ $0.1582$ inches.

From the given formula,

Working depth $=0.6366\times \text{Circular pitch}$

i.e. Working depth $=0.6366\times 0.1582$ inches.

  $\Rightarrow$ Working depth $=0.10071012$ inches.

  $\Rightarrow$ Working depth $=0.1007$ inches {Rounding off to $4$ decimal places}

Similarly,

Clearance $=0.05\times \text{Circular pitch}$

i.e. Clearance $=0.05\times 0.1582=0.0079$ inches

Also, tool thickness $=0.5\times \text{Circular pitch}$

i.e. tool thickness $=0.5\times 0.1582=\text{0}\text{.0791}$ inches.

Thus, working depth $=0.1007$ inches.

Clearance $=0.0079$ inches.

Tool thickness $=\text{0}\text{.0791}$ inches.

To determine

(c)

The working depths, clearance and tooth thickness.

Answer to Problem 8A

Working depth $=0.5137$ inches.

Clearance $=0.0403$ inches.

Tool thickness $=\text{0}\text{.4035}$ inches.

Explanation of Solution

Given information:

Circular pitch of a gear is given as $0.8069$ inches.

Also, below formula is given for a gear-

Working depth $=0.6366\times \text{Circular pitch}$

Clearance $=0.05\times \text{Circular pitch}$

Tool thickness $=0.5\times \text{Circular pitch}$

Calculation:

As per given information, circular pitch $=$ $0.8069$ inches.

From the given formula,

Working depth $=0.6366\times \text{Circular pitch}$

i.e. Working depth $=0.6366\times 0.8069$ inches.

  $\Rightarrow$ Working depth $=0.51367254$ inches.

  $\Rightarrow$ Working depth $=0.5137$ inches {Rounding off to $4$ decimal places}

Similarly,

Clearance $=0.05\times \text{Circular pitch}$

i.e. Clearance $=0.05\times 0.8069=0.0403$ inches

Also, tool thickness $=0.5\times \text{Circular pitch}$

i.e. tool thickness $=0.5\times 0.8069=\text{0}\text{.4035}$ inches.

Thus, working depth $=0.5137$ inches.

Clearance $=0.0403$ inches.

Tool thickness $=\text{0}\text{.4035}$ inches.

To determine

(d)

The working depths, clearance and tooth thickness.

Answer to Problem 8A

Working depth $=0.7880$ inches.

Clearance $=0.0619$ inches.

Tool thickness $=\text{0}\text{.6189}$ inches.

Explanation of Solution

Given information:

Circular pitch of a gear is given as $1.2378$ inches.

Also, below formula is given for a gear-

Working depth $=0.6366\times \text{Circular pitch}$

Clearance $=0.05\times \text{Circular pitch}$

Tool thickness $=0.5\times \text{Circular pitch}$

Calculation:

As per given information, circular pitch $=$ $1.2378$ inches.

From the given formula,

Working depth $=0.6366\times \text{Circular pitch}$

i.e. Working depth $=0.6366\times 1.2378$ inches.

  $\Rightarrow$ Working depth $=0.78798348$ inches.

  $\Rightarrow$ Working depth $=0.7880$ inches {Rounding off to $4$ decimal places}

Similarly,

Clearance $=0.05\times \text{Circular pitch}$

i.e. Clearance $=0.05\times 1.2378=0.0619$ inches

Also, tool thickness $=0.5\times \text{Circular pitch}$

i.e. tool thickness $=0.5\times 1.2378=\text{0}\text{.6189}$ inches.

Thus, working depth $=0.7880$ inches.

Clearance $=0.0619$ inches.

Tool thickness $=\text{0}\text{.6189}$ inches.

To determine

(e)

The working depths, clearance and tooth thickness.

Answer to Problem 8A

Working depth $=1.0412$ inches.

Clearance $=0.0797$ inches.

Tool thickness $=\text{0}\text{.7966}$ inches.

Explanation of Solution

Given information:

Circular pitch of a gear is given as $1.5931$ inches.

Also, below formula is given for a gear-

Working depth $=0.6366\times \text{Circular pitch}$

Clearance $=0.05\times \text{Circular pitch}$

Tool thickness $=0.5\times \text{Circular pitch}$

Calculation:

As per given information, circular pitch $=$ $1.5931$ inches.

From the given formula,

Working depth $=0.6366\times \text{Circular pitch}$

i.e. Working depth $=0.6366\times 1.5931$ inches.

  $\Rightarrow$ Working depth $=1.01416746$ inches.

  $\Rightarrow$ Working depth $=1.0412$ inches {Rounding off to $4$ decimal places}

Similarly,

Clearance $=0.05\times \text{Circular pitch}$

i.e. Clearance $=0.05\times 1.5931=0.0797$ inches

Also, tool thickness $=0.5\times \text{Circular pitch}$

i.e. tool thickness $=0.5\times 1.5931=\text{0}\text{.7966}$ inches.

Thus, working depth $=1.0412$ inches.

Clearance $=0.0797$ inches.

Tool thickness $=\text{0}\text{.7966}$ inches.