Enter the torque, gear reduction ratio, lead, and efficiency into the calculator to determine the ball screw force.
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Ball Screw Force Formula
The following equation is used to calculate the ball screw force.
F = (2 π η · GRR · T) / L
- Where F is the axial force (N)
- T is the torque (N-m)
- GRR is the gear reduction ratio (dimensionless)
- L is the lead (m per revolution)
- η is the efficiency (decimal form, 0 to 1)
To calculate the ball screw force, multiply the torque by 2π, multiply by the gear reduction ratio, multiply by the efficiency (as a decimal), then divide by the lead.
What is a Ball Screw Force?
Definition:
In ball screw applications, “ball screw force” typically refers to the axial thrust force produced along the screw axis when a torque is applied to the screw or nut. This thrust is determined primarily by the applied torque, the screw lead, and the mechanical efficiency of the screw (and any gearbox between the motor and screw). Radial forces can exist due to external side loads, misalignment, and bearing/support constraints, but they are not part of the axial thrust calculation.
The axial thrust produced for a given input torque is influenced mainly by:
● The torque delivered to the screw (including any gear reduction)
● The screw lead (linear travel per revolution)
● The mechanical efficiency (affected by preload, lubrication, speed, and load)
Design features such as ball diameter, number of load circuits, and contact geometry primarily affect load ratings, stiffness, and efficiency rather than changing the basic torque-to-thrust relationship.
How to Calculate Ball Screw Force?
Example Problem:
The following example outlines the steps and information needed to calculate the Ball Screw Force.
First, determine the torque. In this example, the torque is 300 N-m.
Next, determine the gear reduction ratio. The gear reduction ratio for this problem is 2.5.
Next, determine the lead distance. In this case, the lead is .3m.
Next, determine the efficiency. This ball screw system has a 75% efficiency.
Finally, calculate the ball screw force using the formula above:
F = (2 * PI * η * GRR * T) / L
F = (300 * 2 * 3.14159 * 0.75 * 2.5) / 0.3
F = 11,781.0 N
