Linear Actuator Force Calculator

Calculate the force output of a linear actuator based on motor torque, lead screw pitch, and efficiency for mechanical design applications.

LINEAR FORCE OUTPUT
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Force (N)
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Force (lbf)
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Force (kgf)
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Efficiency
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What Is a Linear Actuator?

A linear actuator converts rotational motion from a motor into linear (straight-line) motion using a lead screw or ball screw mechanism. The force output depends on the motor torque, the screw pitch (distance traveled per revolution), and the mechanical efficiency of the screw thread. Linear actuators are essential in robotics, CNC machines, automotive systems, and industrial automation.

The mechanical advantage comes from the screw principle: a smaller pitch means more force but slower linear speed, while a larger pitch gives faster movement with less force. Ball screw actuators have higher efficiency (85-95%) compared to acme lead screws (30-80%) due to rolling rather than sliding contact.

Force Calculation Formula

F = 2π T η / p

Where F is the linear force (N), T is motor torque (N·m), η is efficiency (0-1), and p is lead screw pitch (m/rev).

Actuator Types

TypeEfficiencyForce RangeSpeed
Acme Lead Screw30-70%10-50,000 NSlow-Medium
Ball Screw85-95%100-500,000 NMedium-Fast
Belt Drive85-95%10-5,000 NFast
PneumaticN/A50-100,000 NVery Fast

Frequently Asked Questions

What determines actuator efficiency?

Efficiency depends on the thread type, lead angle, friction coefficient, and lubrication. Acme (trapezoidal) threads have sliding contact resulting in 30-70% efficiency. Ball screws use recirculating ball bearings for 85-95% efficiency. Proper lubrication and preload adjustment are critical for maintaining efficiency over the actuator's lifetime.

How do I choose between lead screw and ball screw?

Choose lead screws for low-cost, low-duty-cycle applications where self-locking (backdriving prevention) is desired. Choose ball screws for high efficiency, high precision, long life, and high-speed applications. Ball screws are typically 5-10x more expensive but last much longer under continuous use.

What is the backdrive force?

Backdrive force is the axial load that can cause the screw to rotate (i.e., the load pushes back through the actuator). Lead screws with low lead angles are self-locking and resist backdriving, while ball screws generally are not self-locking and require a brake or holding mechanism.