# How Do You Calculate Press Fit Forces?

The forces associated with a press, or interference, fit are determined using equations and pre-established values. These equations assume that the shaft is treated as a cylinder with a uniform external pressure, and the hub is treated as a hollow cylinder with uniform internal pressure.

1. Determine the pressure generated at interface of interference fit

The equation to determine the pressure is: P = delta / ((d / E_o) * (((d_o^2 + d^2) / (d_o^2 – d^2)) + v_o) + (d / E_i) * (((d^2 + d_i^2) / (d^2 – d_i^2)) – v_i)). Delta is determined by calculating the difference between the diameters of the hub and shaft: delta = d_shaft – d_hub. D is the nominal shaft diameter, d_o is the outer diameter of the hub, d_i is the inner diameter of the shaft, v_o is Poisson’s ratio of the hub, v_i is Poisson’s ratio of the shaft, E_o is Young’s modulus of the hub and E_i is Young’s modulus of the shaft.

2. Find the normal force

In order to find the normal force, use the following equation: N = P * A. P is the pressure from the interference fit, and A is the area of contact between the shaft and hub. To find the frictional force, multiply the normal force by the coefficient of static friction, mu: F = mu * N.

3. Find the maximum torque

To find the maximum torque use the equation: T = (F * d) / 2.