Spur gears are commonly used to change the speed of applications such as conveyors, engines, and gear pumps. They have teeth that are uniformly spaced around the external surface. The teeth are parallel to the gear axis, and the gear is made to mesh with another spur gear on a parallel shaft.

Teeth are an important part of a spur gear. They enable it to interlock with another gear and deliver rotational motion and torque. As a result, effective power transmission from one shaft to another takes place. In this post, we’ll explain exactly how to calculate the number of teeth in spur gear.

Design of Spur Gear Teeth

Spur gear teeth have a straight-line orientation. They are parallel to the coplanar shafts. The profile of the contact surface of the teeth in a spur gear is an involute curve, which is the path that the end of a string takes when it unwinds from a cylinder.

This profile of a spur gear teeth transmits power between two gear teeth. It maximizes rolling and minimizes sliding. Due to an involute curve, the spur gear teeth deliver radial force.

Radial forces are perpendicular to the gear axis. This contrasts with helical, bevel, and spiral bevel gears. They give both radial and axial forces.

Spur Gear Teeth Calculation

To learn how to calculate the number of teeth in spur gear, use the following steps.

1. Understand the Key Terminology Used in the Gear Teeth Calculation Formula

The gear teeth calculation formula uses a number of terms. Understanding each one is important to finding the number of teeth in a spur gear.

Pitch Circle Diameter (PCD)

The pitch circle is an imaginary circle where two gears in mesh roll against each other. The pitch circle diameter is the diameter of this circle. Think of it as the diameter of the gear at the core of the gear tooth. The operating pitch circles of meshing gears are tangent to each other.

Module (m)

The module represents the size of a gear. It is the reference diameter of the gear divided by the number of teeth.

Module = (Reference Diameter (d)) / (Number of Teeth (N))

Diametral Pitch (P)

Diametral pitch is the teeth in for every inch of pitch diameter. It shows the size and shape of a gear’s teeth. To calculate it, divide the number of teeth by the pitch diameter.

D = N / P

Addendum and Dedendum

The addendum is the gear tooth’s height above the pitch circle. Think of it as the radial distance from the pitch circle to the top of the tooth. Dedendum is the depth of the gear tooth from the pitch circle to its bottom.

Pressure Angle

It is the angle between the line of action and a line perpendicular to the line of centers. Typically, it is 20°1. Less common values are 14.5° and 25°

Circular Pitch (p)

It is the distance along the pitch circle from a point on one tooth to the corresponding point on the tooth at the side.

2. Use Major Gear Teeth Calculation Formulas

Now, you must use the following formulas to calculate the number of teeth:

1. Relationship between PCD, module, and number of teeth

The relationship between pitch circle diameter, module, and number of teeth is reflected through the following formula:

d = m*z, where

1. d is the reference diameter (pitch circle diameter)
2. m is the module
3. z is the number of teeth

m = d / z, where m is the module, d is the pitch diameter, and z is the number of teeth

2. Calculate the Number of Teeth

N = P * D, where

1. N is the number of teeth
2. P is the diametral pitch
3. D is the pitch diameter

N = (π * D) / p, where

1. N is the number of teeth
2. D is the pitch diameter
3. p is the circular pitch

3. Alternative formula using diametral pitch

Another formula to use diametral pitch is:

P = N / D, where

1. D is the diametral pitch
2. N is the number of teeth
3. P is the pitch diameter

P = π / p, where P is the diametral pitch, and p is the circular pitch

3. Find the desired gear ratio and its impact on the number of teeth

The gear ratio shows how much an output gear is sped up or slowed down or the amount of torque lost or gained in a system. To find out the gear ratio, use these steps:

1. Identify the driving and the driven gear
2. Count the number of teeth on these gears
3. Divide teeth on the driven gear by the number of teeth on the driving gear

If the driven gear teeth equals 30 and the drive gear equals 5, the calculation is 30/5, and the gear ratio is 6:1.

Changing the number of teeth on a spur gear will directly alter the gear ratio. A wider ratio delivers greater torque but at the expense of speed.

4. Decide the Pitch Circle Diameter

The pitch circle diameter is important to know the size and spacing of the spur gear’s teeth so you can calculate gear meshing, the center distance between mating gears, and the gear design accurately.

The PCD is related to module (m) and number of teeth (z) using this formula:

PCD = m * z

You will need to iterate between PCD, module, and number of teeth to find the desirable combination.

5. Select a Module or Diametral Pitch (imperial) Based on Design Requirements

The module indicates how large or small a spur gear is. It is directly related to the number of teeth in a spur gear. To find it out, divide the ratio of the gear’s pitch or reference diameter by the number of teeth.

If using the metric module, preferred module sizes are:

• 25
• 5
• 2
• 5
• 3
• 4
• 5
• 6
• 8
• 10

If using diametral pitch, higher numbers mean finer teeth.

6. Calculate the Number of Teeth in the Spur Gear

After knowing the gear ratio, choosing either the module or diametral pitch, and knowing the PCD, compute the number of teeth in a spur gear as follows:

1. If Using Module: Number of Teeth (z) = PCD / Module (m)
2. If Using Diametral Pitch: Number of Teeth (N) = Diametral Pitch (P) * PCD

You can find out the number of teeth for both the driving and driven gears with the same module or diametral pitch.

Practical Example to Calculate the Number of Teeth in a Spur Gear

Let’s say you have a spur gear with:

Pitch Diameter (D) = 10 inches

Diametral Pitch (P) = 8 teeth per inch

To find the number of teeth (N), we will use this formula:

N = P * D

In this example, N = 8 teeth/inch multiplied by 10 inches

N = 80 teeth

Therefore, the spur gear has 80 teeth.

What’s the Effect of Changing the Number of Teeth on a Spur Gear?

The pitch diameter of a spur gear increases with an increase in the number of teeth. Its opposite is also true. A higher gear ratio means that there are more teeth on the driven gear and fewer teeth on the driving gear. A higher gear ratio results in:

1. Decreased speed: The driven gear rotates slower than the driving gear.
2. Higher torque: The driven gear gets a higher turning force.

For example, a large gear driving a smaller gear will cause a smaller gear to spin more rapidly but with less force.

Conclusion

Now you know how to calculate the number of teeth in spur gear. Use the stepwise instructions to calculate teeth for better machinery performance. If you want to learn more about spur gear or want them for your application, feel free to contact Exim Engineering. As an authorized distributor of industrial power transmission products and components in southern California, we stock Industrial gearboxes from leading brands. Let us know how we can help you.

Frequently Asked Questions

1. What is the formula for gear teeth calculation?

The gear teeth calculation formula using a module (m), which is the ratio of the pitch diameter (d) to the number of teeth (z) of gear, is z = d divided by m.

2. How many teeth are in a spur gear?

Usually, spur gears have six to 48 teeth per inch. Ideally, the spur gear should not have less than 18 teeth so that the tooth profile is not disturbed during machining.

3. What is the gear tooth thickness formula?

Gear tooth thickness can be determined by measuring the chordal tooth thickness, which is measuring the thickness at the reference circle through a tooth caliper referenced from the gear’s tip diameter. The gear tooth thickness formula using diametral pitch is 1.5708 ÷ diametral pitch.

4. What is the contact ratio of meshing gears, and why is it important?

The contact ratio of a gear indicates the number of teeth contacting one another during the meshing process. A lower contact ratio means that the tooth is exposed to a higher load, which means that it cannot operate quietly.