# Spur gear calculation tips

Getting your spur gear calculations right is essential to make the most out of these kinds of devices, which are the most used to accomplish large gear ratios, medium speeds and low speeds.

They are essential for a number of mechanical and electromechanical transmission mechanisms and motion control. In this article we will show you how to properly perform this calculation with the purpose of helping you design gears for your projects.

## What is a spur gear?

Spur gears have their teeth mounted on parallel axes, which makes them very useful when your goal is to transfer a motion from one shaft to another that is near and parallel.

In addition to being very reliable, spur gears stand out because they produce no axial thrust, precisely due to the fact that the teeth are parallel to their axis. This means that ball bearings can be used for the gears’ shafts.

Spur gears transfer their motion from one shaft to another that is near and parallel

### Parts of a spur gear

The various parts that we can find in a spur gear are:

• Teeth. The gear’s teeth are the ones in charge of generating the thrust, which means that they transmit power from the driver shaft to the driven shaft. A well-defined profile is considered when manufacturing and designing them.
• Circles. These include the pitch circle (R), along which all teeth mate; the root circle (Ri), which crosses the dedendum, and is where the dedendum ends, and the outside circle (R3), which is the outer boundary of the gear. The dedendum is the part of the tooth that lies between the pitch circle and the root circle.

### Types of straight toothed gears

We can find straight toothed gears both in parallel, cylindrical gears and in perpendicular, bevel gears.

In the former case – parallel straight-toothed gears – these are the simplest types of gears, with a high capability of transmitting power through the shaft. They are especially used for slow and medium speeds, because at these speeds little noise is generated.

In the case of perpendicular bevel gears, a force is transmitted between shafts that are oblique to each other and intersect along one same plane, almost always in a straight angle. They have somewhat fallen into disuse (they were mostly used to reduce speeds of shafts at a 90-degree angle), among other reasons because they generate more noise than other types of gears.

You may be interested: Tips to keep in mind when buying gears

### Spur gear applications and uses

Spur gears are very common in several sectors:

They are widespread in applications that require slow motions and where the noise that they may generate in fast motions is of no consequence, such as in security or vending systems.

Other uses of straight-toothed gears are:

• Printing and serigraphic machines
• Machines used to treat materials such as PVC, metal or wood
• Industrial conveyor belts
• Food handling devices
• Packaging and labeling machines
• Renewable energy and robotics
• Etc.

## How to perform straight gear calculations step by step

Below we will see how to perform calculations for spur gears and the steps you need to take to do it correctly, as well as the variables that you must consider:

First, you need to define a series of concepts to perform the spur gear calculations:

• The number of teeth (z). This value is: z = d/m
• Module (m). Ratio between the pitch circle in millimeters and the number of teeth. Anglo-Saxon countries use the “Diametral Pitch” instead, which is inversely proportional to the module. The value of the module is determined by calculating the material resistance in relation to the force to be transmitted and the gear ratio. Two mating gears must have the same module: m = d/z
• Pitch Diameter (d) is the diameter of the pitch circle; its value is: d = m x z
• Outside Diameter (de) is the diameter of the outside circle; its value is: de = m (z + 2);    de = d + 2m
• Root Diameter (df) is the diameter of the root circle; its value is: df = m (z – 2.5)  or df = de – 2h
• Center Distance (dc) is the distance between the shafts of the gear and the pinion; its value is:  dc = (D + d) / 2, where “D” corresponds to the pitch diameter of the gear and “d” to the pitch diameter of the pinion

The concepts used for spur gear calculations are: number of teeth; module; pitch, outer and root diameter, and center distance

As for the tooth dimensions, we will need to know that:

• h =  Tooth depth;  h = 2,25 x m.
• Pc = Circular Pitch. This is the length of the arc on the pitch circle composed of two homologous points of two consecutive teeth; Pc = πx m.
• B= Tooth thickness;  B=10 . m

Standard modules are classified as follows: modules 1 through 4 vary by 0.25; modules 4 through 7 vary by 0.5; modules 7 through 12 vary by 1; and lastly, modules 12 through 20 vary by 2.

When using inches instead of centimeters as a unit of length, in order to perform the calculations for spur gears we will need to define the ‘diametral pitch’, which is equivalent to the number of teeth per inch located along the pitch diameter. The ratio between the diametral pitch and the module is m= 25.4/Pt.

## How to design straight-tooth gears

In order to design straight-tooth gears you need to identify three concepts:

• The input speed of the pinion np
• The target output speed for the gear pair nG
• The power to be transmitted P

Once the type of material to be used to manufacture the gears has been chosen, you need to specify the type of driver and the driven machine as the overload factor Ko.

The main factor will be what is called the expected load value. The proposed diametral pitch value (the nameplate power is Pdis=KoP) will have to be defined next.

The next step is to calculate the contact stress of the teeth of both the pinion and the gear in the form of the bending stress. For this, you will need to calculate:

• The pitch line velocity
• Geometry factor
• Quality number

A contact stress on the pinion that is not too excessive will lead to a longer service life for the device.

The design process may require for the spur gear calculation process to be performed several times until the most optimal design is found

## Conclusions for an adequate gear calculation

Spur gears stand out due to their ability to transmit a large amount of power, and they are widespread in various sectors because of:

• Their reliability
• Their efficiency when compared to helical gears of the same size
• Because they allow for a gear ratio that is both stable and constant

In addition, simpler processes are used for the calculation, design and manufacturing of spur gears when compared to other types of gears, which means that projects that specifically require the use of these types of gears will be able to quickly obtain them.

CLR has a track record of several decades manufacturing precision gear motors and components that can be adapted to small spaces, always with the highest quality.

CLR, a company that bases its projects on engineering, quality and production, offers integral actuator solutions to every company, which makes it the perfect partner that will give you the best results in the least amount of time.

Do you want to make your project come true? Get in touch with us and we will assist you!

### 1 thought on “Spur gear calculation tips”

1. Very useful message

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