# Calculation of hoop stress on a gear tooth

• k.udhay
In summary, gear teeth experience stresses at the root due to bending and shear caused by contact force from the meshing tooth. The stress model for hoop stress is not applicable to analyzing gear teeth. However, gear teeth in rolling contact have a contact angle that results in two force components, one of which cancels the root stress due to bending. For internally cut gears, there may be a small peripheral stress analogous to hoop stress, but its magnitude is attenuated by the contact angle.

#### k.udhay

Hi,

I have done hoop stress calculation on thin walled pipes. But, will gear tooth also go under hoop stress when loaded? Can somebody explain the procedure to calculate that pl.? Thanks.

Gear teeth experience stresses at the root due to contact force from the meshing tooth. The stresses are due to bending and shear on the tooth. The hoop stress model is not applicable to analyzing gear teeth.

1 person
Gear teeth are in rolling contact with a specified tooth face contact angle. That angle results in two force components, one a peripheral torque, and a smaller one tending to push the gears apart. To push the gears apart requires that the teeth are pressed onto their wheel which cancels some of the root stress due to bending. There appears to be no stress equivalent to hoop stress in spur gears.

The same is not true for internal or some epicyclic gear systems where the force of tooth contact tends to expand the internally toothed gear. In that situation the outside of the internally cut gear will have a peripheral stress. That is analogous to hoop stress, but it's magnitude is small, being only the torque attenuated by the sine of a typical 14° to 20° contact angle.

1 person

## What is hoop stress and why is it important in the calculation of gear tooth strength?

Hoop stress is the stress or force applied to the circumference of a cylindrical object, such as a gear tooth. In the calculation of gear tooth strength, hoop stress is important because it determines the maximum amount of force a gear tooth can withstand without breaking.

## How is hoop stress calculated on a gear tooth?

Hoop stress on a gear tooth can be calculated using the formula: σ = (F*D)/(2*t*b), where σ is the hoop stress, F is the applied force, D is the pitch diameter of the gear, t is the tooth thickness, and b is the face width of the gear.

## What factors can affect the calculation of hoop stress on a gear tooth?

There are several factors that can affect the calculation of hoop stress on a gear tooth, including the material properties of the gear, the applied force, the pitch diameter, the tooth thickness, and the face width of the gear. Other factors such as temperature, lubrication, and surface finish can also impact the hoop stress calculation.

## What is the maximum allowable hoop stress for a gear tooth?

The maximum allowable hoop stress for a gear tooth is typically determined by the material properties of the gear and the desired safety factor. In general, the maximum allowable hoop stress should be lower than the yield strength of the gear material to ensure the gear tooth does not permanently deform or fail under load.

## How can hoop stress be minimized on a gear tooth?

Hoop stress can be minimized on a gear tooth by selecting a material with high strength and hardness, ensuring proper lubrication, and optimizing the design of the gear tooth to distribute the load evenly. Additionally, reducing the applied force or increasing the pitch diameter, tooth thickness, and face width can also help to minimize hoop stress on a gear tooth.