WHAT IS PCD (PITCH CIRCLE DIAMETER)?

How to Calculate PCD (Pitch Circle Diameter)?

PCD is the short form of Pitch Circle Diameter; the Pitch Circle Diameter (PCD) is the diameter of that circle that passes through the center of all the bolt holes or wheel bolts or wheel rim holes or studs.  The best example is Flanges, there are multiple holes in the Flanges, the circle through the center of these holes is known as the pitch circle, and the diameter of this circle is known as Pitch Circle Diameter, in short PCD. Look at the figures and find the PCD of different stud arrangement circles.

Studs: the definition of a stud is “a large-headed piece of metal that pierces and projects from a surface, especially for decoration”, shown in the figure as different forms of stud arrangement, such as 3 studs means 3 holes; 4 stud means 4 holes; 5 stud means 5 series of holes and so on.  

Pitch circle: The transverse section of the pitch cylinder is normal to the axis.

Pitch, Circular: The distance measuring along the pitch circle between the centers of two adjacent teeth (holes) on a plane at right angles to the axis of rotation.

The easiest way to calculate the PCD for different numbers of studs is as follows:

Fig: PCD of Different Numbers of Studs

For calculation hole to hole, distance H is an important calculation. Distance H may be the hole’s center to center or the same side to side. R is the diameter of the pitch circle.

As per circle and triangle theory, the total angle of the circle= 360^o total angle of the triangle =180^o

Example-1:

For 3 studs, PCD= 258mm, what would be the hole distance?

360^o /number of holes

= 360^o /3 =120 ^o , half of 120^o is 60^o.

Using Sin rules in the triangle,

SIN = Perpendicular/Hypotenuse= (H/2)/R= H/2R= H/D (Diameter or PCD)

Or, SIN = H/PCD

Or, Sin60^o=H/258

Or, H= 258x Sin60^o= 223.45mm, hole-to-hole distance.

Similarly, for 8 holes:

360^o /8 =45^o, half is (45^o/2)

Sin (45^o/2) = H/258

Or, hole to hole distance, H= 258x Sin (45^o/2) =98.73mm;

So, the common formula is,

Hole to hole distance, H= Sin [(360^o/hole number)/2]*PCD

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How does Measure the Pitch Circle Diameter of the Gear?

In order to design, build and discuss gear drive systems it is necessary to understand the terminology and concepts associated with gear systems. Good designers and engineers have experience and knowledge and the ability to communicate their thoughts and ideas clearly with others. The students and teachers who participate in this unit will learn the gear terms and concepts necessary to design, draw and build gear drive systems, and improve their “Gear literacy”. 

Fig: Pitch Circle Diameter of a Gear Tooth

Module
The length in mm of the pitch circle diameter per tooth.
MOD = PCD / N

Number of Teeth
The number of teeth on the gear.
N = PCD / MOD

Pitch Circle Diameter
The diameter of the pitch circle.
PCD = N x MOD

Outside Diameter
The outside diameter of the gear.
OD = (N + 2) x MOD

Center Distance
The distance between the axes of two gears in mesh.
C = PCD(g) + PCD(p)
                      2
Circular Pitch
The distance between adjacent teeth was measured along the arc at the pitch circle diameter.
CP = pi x MOD

Circular Tooth Thickness
The width of a tooth is measured along the arc at the pitch circle diameter.
CTT = CP / 2

Addendum
The height of the tooth above the pitch circle diameter.
A = MOD

Dedendum
The depth of the tooth below the pitch circle diameter.
D = H - A

Whole Depth
The total depth of the space between adjacent teeth.
Finer than 1.25 MOD:
H = 2.4 x MOD

1.25 MOD and coarser:
H = 2.25 x MOD

If you are interested to know more details about the PCD calculation of gear tooth, you may read the full article or even download the pdf file for free from the link below:

PCD-Pitch Circle Diameter Calculation of Gear Tooth

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How to Calculate the PCD (Pitch Circle Diameter) of a Flange?

The PCD of a flange is one of the most critical dimensions. Now we will try to make it easy to find the PCD (Pitch Circle Diameter) of a flange in our daily work.

PCD (Pitch Circle Diameter) is the diameter of a circle that goes through each of the bolt holes. Let's see the 8 holes flange in figure below:

Fig: PCD Calculation of a Flange

Sometimes it’s hard to measure the PCD of a butterfly valve or a flange that’s installed in the pipework. Realizing your requirement at a crucial time, we brought some handy tips to find the PCD calculation of flange having different numbers of holes. 

As accurately as you can, measure two adjacent holes using a vernier scale and calculate the PCD; then calculate for-

4 holes: multiply by 1.414

8 holes: multiply by 2.613

12 holes: multiply by 3.864

16 holes: multiply by 5.126


Example:
This 150mm flange has 8 holes and measures 90mm.

PCD = 90 x 2.613 = 235mm

How to Calculate the Pitch Circle Diameter of a Bolt Thread?

Another difficulty to measure the PCD- the Pitch Circle Diameter of a bolt or wire thread. Here we brought you some easy and simple ways to calculate the bolt thread PCD.

Major Diameter: Given On Print (if it is a machine screw #0-14 SEE NOTE 1A).
Pitch: 1/number of threads per inch.
Flat: pitch/8.
Compound Movement: .75(pitch).
Single Thread Height: .75(pitch) (cosine 30 degrees).
Pitch Diameter: major diameter - single thread height.
Minor Diameter: major diameter - 2 (single thread height).
Vertex Diameter: major diameter - 1.75(pitch) (cosine 30 degrees).
Best Wire Size (BWS): pitch (tangent 30 degrees).
Measurement Over Wires (MOW): vertex diameter + 3 (best wire size).
Lead: equals pitch if the thread is a single lead.
Pitch Circumference: Pi (pitch diameter).
Lead Angle (Also Called Helix Angle): arc tangent of lead/pitch circumference.
NOTE 1A: Machine Screw Major Diameter: [machine screw# (0.013”)] +0.060”.
Major Diameter of a #10 Screw = [10 (0.013”)] + 0.060” or 0.1900”
EXAMPLE ¾ - 10 UNC BOLT:
Major Dia = 0.750”
Pitch = 1/10” OR 0.1000”
Flat = 0.0100/8 OR 0.0125”
Compound Movement = .75(0.01000”) or 0.0750”
Single Thread Height = .75(0.1000”)(cos 30 deg) or 0.06495”
Pitch Diameter = 0.7500”- 0.06495” or 0.6850”
Minor Diameter = 0.7500”- 2(0.06495”) or 0.6201”
Vertex Diameter = 0.7500”- 1.75(0.1000”)(cos 30 deg) or 0.5985”
BWS= 0.1000” (tan 30 deg) or 0.0577”
MOW= vertex dia + 3(0.0577”) or 0.7716”
Lead is a single lead or 0.1000”
Pitch Circumference = Pi(0.6850”) or 2.1520”
Helix Angle = arc tan 0.1000”/2.1520” or 2.66053 deg [2 deg, 39 min, 38 sec)
NOTE: Helix Angle has to be calculated if you are going to grind threads. The reason is that if the grinding
the wheel head is not rotated to the same as the lead angle the thread will have either a drunken lead or a
zero lead, both of which are unacceptable.

Must Remember When Cutting Threads on a Lathe.

Even Pitch Threads 2, 4, 6...Etc: use any line on the threading dial.
Odd Pitch Threads 3, 5, 7….Etc: use any numbered line on the chasing dial.
½ Pitch Threads 11½: use #1 or #3.

• Compound rest is always swung to the idle side of the tool.
• The tool must have the correct thread angle.
• The tool must be sharp.
• The tool must be square to the surface being threaded.
• The tool must be in the center.
• The compound rest is used to cut the thread to the correct depth.
• The cross slide is used to maintain a zero point on the “x” axis.

How to Calculate Cord Length of 8 Holes Flange?

To calculate the cord length of an 8-hole flange, you need to know the diameter of the flange and the distance between the centers of two adjacent holes.

Here's the step-by-step process to calculate the cord length:

• Measure the diameter (D) of the flange. It is the distance across the widest point of the circular flange.

• Measure the distance (C) between the centers of two adjacent holes. This is the distance from the center of one hole to the center of the hole next to it.

• Calculate the radius (r) of the flange by dividing the diameter (D) by 2. The formula is r = D/2.

• Calculate the angular distance (θ) between two adjacent holes using the formula: θ = 360° / number of holes. In this case, the number of holes is 8, so θ = 360° / 8 = 45°.

• Calculate the length of the cord (L) connecting two adjacent holes using the formula: L = 2 * r * sin(θ/2). Here, sin is the trigonometric function for calculating the sine of an angle.

• Substitute the values into the formula: L = 2 * r * sin(45°/2).

• Calculate the cord length by substituting the value of the radius (r) into the formula: L = 2 * (D/2) * sin(45°/2).

• Simplify the formula: L = D * sin(22.5°).

• Calculate the cord length using a scientific calculator or a trigonometric table by taking the sine of 22.5 degrees (sin(22.5°)).

• Multiply the result by the diameter (D) to obtain the cord length.

For example, if the diameter of the flange is 10 inches:

L = 10 * sin(22.5°)

Using a calculator, sin(22.5°) is approximately 0.3827.

L = 10 * 0.3827 = 3.827 inches

Therefore, the cord length of the 8-hole flange with a diameter of 10 inches is approximately 3.827 inches.