Chapter 8, Problem 1P

A power screw is 25 mm in diameter and has a thread pitch of 5 mm.

1. (a)   Find the thread depth, the thread width, the mean and root diameters, and the lead, provided square threads are used.
2. (b)   Repeat part (a) for Acme threads.

To determine

The thread depth for square threads.

The thread width for square threads.

The mean diameter for square threads.

The root diameter for square threads.

The lead provided for square threads.

Answer to Problem 1P

The thread depth for square threads is $2.5\text{mm}$.

The thread width for square threads is $2.5\text{mm}$.

The mean diameter for square threads is $22.5\text{mm}$.

The root diameter for square threads is $20\text{mm}$.

The lead provided for square threads is $5\text{mm}$.

Explanation of Solution

The Figure (1) shows the free body diagram square thread.

Figure (1)

Write the expression for the mean diameter.

$d_m=d-\left(\frac{p}{4}+\frac{p}{4}\right)$ (I)

Here, the mean diameter is $d_m$, the diameter of the thread is $d$ and the pitch is $p$

Write the expression for the root diameter.

$d_r=d-p$ (II)

Here, the root diameter is $d_r$.

Write the expression for the lead of the square threads.

$l=p$ (III)

Here, the lead is $l$.

Conclusion:

From Figure (1), obtain the thread depth of the square thread as, $2.5\text{mm}$.

Thus, the thread depth for square threads is $2.5\text{mm}$.

From Figure (1), obtain the width of the square thread as, $2.5\text{mm}$.

Thus, the thread width for square threads is $2.5\text{mm}$.

Substitute $25\text{mm}$ for $d$ and $5\text{mm}$ for $p$ in Equation (I).

$\begin{array}{c}{d}_m=\left(25\text{mm}\right)-\left[\frac{\left(5\text{mm}\right)}{4}+\frac{\left(5\text{mm}\right)}{4}\right]\\ =25\text{mm}-1.25\text{mm}-1.25\text{mm}\\ =22.5\text{mm}\end{array}$

Thus, the mean diameter for square threads is $22.5\text{mm}$.

Substitute $25\text{mm}$ for $d$ and $5\text{mm}$ for $p$ in Equation (I).

$\begin{array}{c}{d}_r=\left(25\text{mm}\right)-\left(5\text{mm}\right)\\ =20\text{mm}\end{array}$

Thus, the root diameter for square threads is $20\text{mm}$.

Substitute $5\text{mm}$ for $p$ in Equation (III).

$l=5\text{mm}$

Thus, the lead provided for square threads is $5\text{mm}$.

To determine

The thread depth for Acme threads.

The thread width for Acme threads.

The mean diameter for Acme threads.

The root diameter for Acme threads.

The lead provided for Acme threads.

Answer to Problem 1P

The thread depth for Acme threads is $2.5\text{mm}$.

The thread width for Acme threads is $2.5\text{mm}$.

The mean diameter for Acme threads is $22.5\text{mm}$.

The root diameter for Acme threads is $20\text{mm}$.

The lead provided for Acme threads is $5\text{mm}$.

Explanation of Solution

The Figure (2) shows the free body diagram Acme thread.

Figure (2)

Write the expression for the mean diameter.

$d_m=d-\left(\frac{p}{4}+\frac{p}{4}\right)$ (IV)

Write the expression for the root diameter.

$d_r=d-p$ (V)

Write the expression for the lead of the Acme threads.

$l=p$ (VI)

Conclusion:

From Figure (2) obtain the thread depth of the Acme thread as, $2.5\text{mm}$.

Thus, the thread depth for Acme threads is $2.5\text{mm}$.

From Figure (2) obtain the width of the Acme thread as, $2.5\text{mm}$.

Thus, the thread width for Acme threads is $2.5\text{mm}$.

Substitute $25\text{mm}$ for $d$ and $5\text{mm}$ for $p$ in Equation (IV).

$\begin{array}{c}{d}_m=\left(25\text{mm}\right)-\left[\frac{\left(5\text{mm}\right)}{4}+\frac{\left(5\text{mm}\right)}{4}\right]\\ =25\text{mm}-1.25\text{mm}-1.25\text{mm}\\ =22.5\text{mm}\end{array}$

Thus, the mean diameter for Acme threads is $22.5\text{mm}$.

Substitute $25\text{mm}$ for $d$ and $5\text{mm}$ for $p$ in Equation (V).

$\begin{array}{c}{d}_r=\left(25\text{mm}\right)-\left(5\text{mm}\right)\\ =20\text{mm}\end{array}$

Thus, the root diameter for Acme threads is $20\text{mm}$.

Substitute $5\text{mm}$ for $p$ in Equation (VI).

$l=5\text{mm}$

Thus, the lead provided for Acme threads is $5\text{mm}$.