Factors which influence gear tooth bending stresses

gear tooth bending stresses

Modern gear design must consider different factors which can have an impact on it other than the one included in the Lewis equation as:

  1. Pitch line velocity: Greater the linear velocity of the gear teeth is and greater is the impact of successive teeth as they come into contact. These impacts are caused by the impossibility to design a absolute perfect tooth profile since deflections are inevitable.
  2. Manufacturing accuracy: this has a great impact on loading. Moreover, it determines whether teeth share the load when pairs of teeth are theoretically in contact.
  3. Contact ratio: for gears with 1<G<2, the transmitted load is divided by two teeth pairs each time a contact occurs. It is important to take into consideration that there are two loading conditions:
    • Part of the load at the tooth tip
    • The whole load at the point of highest single tooth contact.
  4. Stress concentration
  5. Degree of shock loading
  6. Accuracy and rigidity of mounting
  7. Inertia moment of the gears and attached rotating members: Momentary angular accelerations and decelerations of rotating members are caused by small tooth errors. With large inertia, rotating members tend to resist acceleration, causing large momentary tooth loads. It is possible to reduce the harmful inertia effect using the torsional elasticity.

Moreover, the gear tooth bending fatigue issue needs an evaluation of the following points:

  • Fluctuating stresses in the tooth fillet
  • Fatigue strength of the material          

Gear-bending strength calculations are commonly based on the assumption that the tooth-bending fatigue strength has a normal distribution with one standard deviation being about 8 percent of the nominal endurance limit.

Gear nomenclature


Gears are special devices which transmit rotary motion from one shaft to another. They can have external or internal teeth and can be shaped in different forms according to their axis position such as:

  • Intersection axes: bevel gears
  • Parallel axes: helical gears
  • Non-intersecting: worm gears

In order to have a greater understanding of gear production and finishing process it is important to know the nomenclature of gears and all related terms. Below we have tried to offer a synthetic overview of the main parts and the nomenclature of the gears.

Let’s discover the nomenclature of the gear

gears nomenclature

There are four circles to keep in mind:

  • Addendum circle: The outer circle touching the outermost points of the teeth
  • Pitch circle: The imaginary rolling circle produced during rotation by mating gears
  • Base circle or root circle: The circle from which the involute tooth profile is developed
  • Dedendum circle: The circle touching the bottom of the tooth profile

Other main parts of the tooth profile:

  • Addendum: The radial distance for which the tooth profile is extended outward beyond the pitch circle from the pitch circle
  • Dedendum: The radial distance for which the tooth profile is extended inward from the pitch circle from the pitch circle
  • Pitch Point: The point of tangency of two gear Pitch Circles, through the Line of Centers.
  • Line of Action: A line tangent to the Base Circles of mating gears, through the Pitch Point and thus the path of tooth contact.
  • Pressure Angle: The angle formed between the Line of Action and a line tangent to the Pitch Point.
  • Tooth Thickness: The thickness of the gear tooth measured along the Pitch Circle.
  • Circular Pitch: The length of the arc along the Pitch Circle between corresponding points of adjacent teeth.
  • Face Width: The width of gear tooth measured axially.
  • Tooth Face: The mating surface of a gear tooth between the addendum circle and the pitch circle.
  • Tooth Flank: The mating surface of a gear tooth measured between the pitch circle and the base circle.
  • Backlash: Amount of clearance between mated gear teeth.