# Forces on Spur Gear

### Description

**Calculation Reference**

Spur Gear Design

Transmission Design

Wear and Contact

To compute the forces on a spur gear when the power, speed, and gear pair inputs are known, you can follow these steps:

- Calculate the torque: Use the power (P) and the rotational speed (ω) of the gear to determine the torque (T) transmitted by the gear. The formula for this is:

T = P / ω

where T is the torque (in Nm), P is the power (in Watts), and ω is the rotational speed (in rad/s).

Make sure to convert the rotational speed to radians per second if it is given in RPM:

ω (rad/s) = RPM * (2 * π) / 60

- Determine the pitch diameter (D) of the gear: Using the module (m) and the number of teeth (N) for the spur gear, calculate the pitch diameter:

D = m * N

where D is the pitch diameter (in mm), m is the module (in mm), and N is the number of teeth.

- Calculate the tangential force (Ft): The tangential force is the force acting along the pitch circle of the gear and is responsible for transmitting torque. You can calculate the tangential force using the torque (T) and the pitch diameter (D):

Ft = (2 * T) / D

where Ft is the tangential force (in N), T is the torque (in Nm), and D is the pitch diameter (in mm). Make sure to convert the pitch diameter to meters for consistency in units.

- Calculate the radial force (Fr): The radial force acts perpendicular to the tangential force and is a result of the gear meshing. You can calculate the radial force using the tangential force (Ft) and the pressure angle (φ) of the gear teeth:

Fr = Ft * tan(φ)

where Fr is the radial force (in N), Ft is the tangential force (in N), and φ is the pressure angle (in radians).

- Calculate the resultant force (F): The resultant force is the combination of the tangential and radial forces acting on the gear. You can calculate the resultant force using the Pythagorean theorem:

F = sqrt(Ft^2 + Fr^2)

where F is the resultant force (in N), Ft is the tangential force (in N), and Fr is the radial force (in N).

By following these steps, you can compute the forces on a spur gear when given power, speed, and gear pair inputs.

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