Strength Calculations For Spur Gears With Calculators

Here, you can find out detailed information on how to design successful spur gear pairs in terms of strength. The fundamental principle is very easy. There is a formula that is generally used in gear stress and strength analysis. But, engineering considerations are very important.

How The Stresses Are Calculated For Spur Gears?

Machine Elements in Mechanical Design (What’s New in Trades & Technology)

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In the strength design of spur gears, one kind of stress is considered for spur gear teeth. It is bending stress resulting from the tangential force acting on spur gear teeth from another mate. This stress must be calculated and compared with the gear material’s strength values to ensure the safety of the gear system.

In general, Lewis Equation is used to calculate final bending stress acting teeth. But, the place where bending stress is calculated is important. For Lewis Equation, bending stress must be calculated according to tooth root of tooth form. 

You know that there is a radius beneath the root of spur gear teeth. So, this is a very critical point to calculate gear stresses.

Bending Stress Calculator For Spur Gear Mates

Bending Stress Calculator For Spur Gear Mates

The use of the calculator above is very simple. You just need to enter the required values into brackets and click on the ‘Calculate!’ button to see ‘Bending Stress’. If you want to make another calculation, just click on the ‘Reset’ button then re-enter all values again. All the required values are explained below.

Tangential Force

Power is transmitted between spur gear teeth through tangential force. The calculation of tangential force is very simple. You can find out the tangential force calculation from here.

Diametral Pitch

You can calculate the tangential force for an individual gear by using the calculators in this link.

This is also a very important parameter for all gear types. Take a look at the article here to understand the diametral pitch and metric module.

Face Width Of Tooth

Illustration of face width(Image Source:

The total thickness of teeth set on a gear. This is a very important parameter because the bending stress will be calculated along this width.

Overload Factor

The overload factor is the multiplication factor of load on gear teeth. This factor is bigger than 1 if there are vibrational or variational working conditions. Generally, the overload factor is selected from catalogs, according to the machinery and working characteristics of the gear set.

You can enter a 1 to overload factor value if you have smoothly working machinery.

Size Factor

According to the size of the gear, you can select a size factor. You can find a reference below to select the proper size factor for your system.

Size factor selection(Image Source: Robert L. Mott: Machine Elements In Mechanical Design).

Load Distribution Factor

This is the hardest factor to specify for a gear system. This factor originated because of lots of kinds of sources. Elastic deformations of different elements in the machinery, misalignments of shafts, thermal distortions, and gear teeth inaccuracies can be the reason for the non-uniform distribution of load.

To calculate the load distribution factor, you need to specify two values before that;

If which is pinion proportion factor and Cma mesh alignment factor. You can roughly specify these two values from the graphs below.

Cpf graph(Image Source: Robert L. Mott: Machine Elements In Mechanical Design).
Cma graph(Image Source: Robert L. Mott: Machine Elements In Mechanical Design).

But we are sharing this information for giving a reference to you. You can use another source. This information is also sourced from American Gear Manufacturers Assoc.

Load Distribution Factor Calculator

Enter the Cpf and Cma factors inside the brackets then hit the ‘Calculate!’ button to see Km.

Rim Thickness Factor

Rim thickness is also a very important factor. It is important because the stress concentration place can change into the rim of gear if the thickness of the rim is low.

Rim thickness illustration(Image Source:

You can calculate the rim thickness factor by using the calculator below.

Rim Thickness Factor Calculator

You just need to enter the rim thickness and depth of gear tooth values to find out the rim thickness factor.

You just need to enter the rim thickness and depth of gear tooth values to find out the rim thickness factor.

Dynamic Factor

For dynamic loadings, this factor is also included. There is a bunch of consideration to define this factor.

  • If the used gears are produced with average quality toolings, which is also the most general type, you can find the dynamic factor by using curves 5, 6, or 7.
  • If the accuracies of tooth profiles are increased with the additional grinding or other kinds of methods, 8, 9, 10, and 11 can be used.
  • Qualities below 5 are generally not used in high velocities.
Representative curve to select Kv(Image Source: Robert L. Mott: Machine Elements In Mechanical Design).

Geometry Factor

You can select a proper geometry factor for your gear. But we provided data for only a pressure angle of 20.

Geometry factor chart(Image Source: Robert L. Mott: Machine Elements In Mechanical Design).


With the guide above you can make accurate bending stress calculations for your spur gear system. And these calculations are valid for individual gears.

Mechanicalland does not accept any responsibility for the calculations made by a user with calculators. A good engineer must check the calculations every time.

Take a look at the other engineering calculators available in Mechanicalland!

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