Ball Screw Force Calculator

Formula

The formula to calculate the ball screw force (F) is:

\[ F = \frac{T \times 2 \times \pi \times GRR}{L \times E} \]

Where:

\(F\) is the force (N)
\(T\) is the torque (N-m)
\(GRR\) is the gear reduction ratio
\(L\) is the lead (m)
\(E\) is the efficiency

What is a Ball Screw Force?

A ball screw force results from combining two forces that act in opposite directions: the axial thrust and radial thrust. The axial thrust is created by the torque applied to the nut while rotating. This force acts axially and is usually transmitted through the balls themselves. Since a ball screw rotates, a centrifugal effect causes the balls to move towards the outside edge of the nut. This radial thrust creates a second force that acts on the nut flange, which results in a friction force between the nut and support bearings.

Both types of forces are influenced by several factors:

The hardness of the balls
The diameter (or lead) of the screw
The number of balls used in each load zone
The number of load zones in the housing
The number of supports or contact points in each row

Example Calculation

Let's assume the following values:

Torque (T) = 10 N-m
Gear Reduction Ratio (GRR) = 2
Lead (L) = 0.01 m
Efficiency (E) = 0.9

Using the formula:

\[ F = \frac{10 \times 2 \times \pi \times 2}{0.01 \times 0.9} \approx 13962.6 \, \text{N} \]

The Ball Screw Force is approximately 13962.6 N.