Engineering Calculators

Spur Gear Teeth Geometry Calculators And Explanations

Because of the complex teeth geometries of spur gears, diameter calculations, teeth geometry calculations a bit complex. In here, we explain all the calculations related to the gear-teeth relations.

Spur gear teeth features(Source Of Image: Robert L. Mott- Machine Elements For Mechanical Design).

Explanation Of Addendum, Dedendum And Clearance Of Spur Gears

Designing of the construction of a machinery, all the geometrical features must be calculated. Contacting of pinion and gears must be calculated in detail to obtain required construction. There are bunch of terms related to these calculations;

  • Addendum(a) Of Spur Gears: The distance between pitch circle and the outermost section of gear tooth.
  • Dedendum(b) Of Spur Gears: The distance between pitch circle and the bottom of the tooth space.
  • Clearance(c) Between Spur Gears: At assembled gears, clearance defines the space between outermost section of first spur gear, and bottom of tooth space of second spur gear.
Illustration that shows the three definitions above(Source Of Image: Machine Elements In Mechanical Design- Robert L. Mott).

You can use the calculator below to calculate Addendum, Dedendum and Clearance of a spur gear, if you know diametric pitch or metric module;

The use of calculator above to calculate addendum, dedendum and clearance values for spur gear mates is very easy. Select the required information from list which you know; diametral pitch or metric module. Do not forget that the unit of diametral pitch is inches and metric module is milimeters.

Enter the required value then click on ‘Calculate!’ button. To make an another calculation, click on ‘Reset’ button then re-enter the values.

Calculation Of Outside Diameter Of A Spur Gear

Outside diameter of a spur gear is very important constructional value. It is generally referred as ‘Da’. If you know metric module or diametric pitch and number of teeth of your spur gear, you can use the calculator below to calculate outside diameter.

Just like calculator before this, you need to select the information you have baout your spur gear mates; metric module or diametral pitch…

Outside diameter calculated via diametral pitch formula is like below. Check your calculations with this formula;

Metric module outside diamater formula;

The diameter of a spur gear is calculated as extraction of two dedendum values from calculated outside diameter. This value is called as ‘D’.

Calculation Of Other Constructional Values Of Spur Gear Tooth

  • Working Depth Calculation: Working depth is calculated as multiplying addendum with 2.
  • Tooth Thickness Calculation: You can calculate the tooth tickness value of mating spur gears by using this equation; pi/(2*Pa). Pa is the diametral pitch of spur gear.
  • Root Diameter Calculation: If you extract two dedendums from diameter of spur gear, you will find out root diameter value.
  • Whole Depth Value: Whole depth is the summation of addendum and dedendum of a spur gear.

Center Distance Calculation Of Mating Spur Gears With Calculators

Maybe center distance calculation is most important aspect of spur gear mates. Exact calculation of center distance is very important in terms of the construction of other elements inside machinery such as shafts etc.

If you know the number of teeths of pinion and gear mates, and diametral pitch or metric module, you can easily calculate the center distance value between mating gears.

Center distance formula via diametral pitch;

Center distance formula via metric module;


Conclusion For Spur Gear Geometrical Calculators

These calculators can be very useful when you are making spur gear construction design.

All the responsibility of calculations made in Mechanical Base calculators are about the users of calculators. Calculators are prepeared based on very reliable sources.

You can take a look at other engineering calculators avaliable in Mechanical Base!

You can also use MB-Unit Converter tool to convert your unit sets to another sets of units.

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