There is a type of thread called power transmission or high strength, its main feature is the profile of the tooth and its pitch, its main advantage: the low wear, strength and durability. Between this type of threads the most common is the Square Thread.

It is called a **Square Thread** because the profile of the screw thread is a perfect square.

To avoid making screws of small diameter and big pitches or on the contrary, screws of big diameter and small pitches, this relation has been normalized or standardized and it was established that to keep a proportion between the diameter of the screw and the pitch, the latter is calculated based on the screw, and the formula to find the pitch is the following:

**P = 0.2D**

Where: P is the screw pitch and D is the outside diameter of the square threaded screw.

Example:

What is the correct pitch (P) for a square thread screw with an outside diameter (D) of 35 mm.?

Then we proceed to find the pitch by using the formula:

**P = 0.2D****P **= 0.2(35)**P** = 7 mm

The correct pitch (P) for the square screw is: **7 mm**.

Now, if we have the pitch and we want to know the diameter of the screw, then from the previous formula we must have the diameter (D), like this:

**D = P/0.2**

Let’s apply the above data to check if it is correct:

What diameter (D) should I turn the screw with if I need the pitch (P) to be of 7 mm.?

**D = P/0.2****D** = 7/0.2**D** = 35 mm

The correct diameter (D) is 35 mm.

## Tooth profile data of the Square Thread:

**D**, the outside diameter of the screw, is equal to **P/0.2****P**, is the pitch of the screw, is equal to **0.2D****e**, is the thickness of the thread, in the screw is equal to **0.5P****h**, is the height of the thread, in the screw it is equal to **0.5P****d**, is the inside diameter of the screw or bottom diameter, it is equal to **D-2h**

It is also necessary to take into consideration the existing backlash between the screw and the nut, this is necessary for the nut to enter the screw:

**D’** is the diameter to turning the nut, it is equal to **d+ 0.125P****e’** is the thickness of the span of the nut, it is equal to **e + 0.05 to 0.1**

**Application examples of screw and nut with square thread:**

Calculate all necessary elements to produce the screw and nut with **square thread** in a material with a diameter of 25 mm

**SCREW:**

**D** = 25 mm.

**P = 0.2(D)****P** = 0.2(25)**P** = 5 mm

**e = 0.5(P)****e** = 0.5(5)**e** = 2.5 mm

**h = 0.5(P)****h** = 0.5(P)**h** = 2.5 mm

**d = D – 2(h)****d** = 25 – 2(2.5)**d** = 25 – 5**d** = 20 mm

**NUT:**

**D’ = d + 0.125(P)****D’** = 20 + 0.125(5)**D’** = 20+0.625**D’** = 20.625 mm

**e’ = e + 0.05****e’** = 2.5+0.07**e’** = 2.57

It is also necessary to calculate the angle of inclination of the threading cutting tool.

In the figure you can see 2 types of cutting tool when cutting the screw fillet.

**cutting tool 1: performs the finishing cut.cutting tool 2: performs the roughing cut.**

In this way, the two cutting tools have an angle α that allows the cutting tool not to damage the fillet of the screw when it passes through it. To calculate this angle we will take into consideration the following:

Calculate the medium diameter of the screw (Md)**Md = (D+d)/2**

Find the angle α of the thread’s helix like this:

If the thread is a single start, the following formula is used:**Tan α = P/(πMd)**

If the threading is of multiple start (n):**Tan α = (Pn)/(πMd)**

**Examples:**

Calculate the angle of the cutting tool so that it does not damage the fillet of a single start screw, pitch 5 mm, outside diameter 25 mm and inside diameter of the screw 20 mm.

Then:**Md = (D+d)/2****Md** = (25+20)/2**Md** = 45/2**Md** = 22.5 mm

**Tan α = P/(πMd)****Tan α** = 5/(3.1416(22.5))**Tan α** = 5/(70.686)**Tan α** = 0.07073536848**α** = tan ¯¹ (0.07073536848)**α** = 4.04609**α** = 4° 2’ 45.92’’

Now let’s assume that the screw is a two start screw, then:**Tan α =(Pn)/(πMd)****Tan α** = 5(2)/(3.1416(22.5))**Tan α** = 10/(70,686)**Tan α** = 0.141470729**α** = tan ¯¹ (0.141470729)**α** = 8.052240379**α** = 8° 3’ 8’

With these formulas and this example, it is easy to calculate the Screw and Square Nut of one or multiple start thread

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You may also be interested in: **Conversion Between Millimeters and Inches**.

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