The RLA actuator converts rotary stepper motor torque into linear thrust using a belt-driven ballscrew (or roller screw) mechanism. The conversion follows a straightforward mechanical relationship.
The thrust scalar k relates motor torque to linear force:
k = Rbelt × (2π / L) × η
Where:
- Rbelt — belt reduction ratio (driven pulley teeth / motor pulley teeth). A 2:1 ratio doubles the effective torque at the screw.
- L — screw lead (linear travel per revolution), in meters. Smaller lead = higher force multiplication but lower speed.
- η — drivetrain efficiency, typically 0.85 to 0.90 for a ball screw with belt drive.
The belt reduction stage serves two purposes: it amplifies torque delivered to the screw, and it reduces reflected load inertia back to the motor by the square of the reduction ratio. Both effects allow a moderately sized stepper motor to produce thrust levels (800 to 2,000 lbf) that would otherwise require a much larger motor.
The compliance tradeoff — honestly: A belt introduces slight mechanical compliance compared to a direct-coupled design. Under sudden load changes, the belt stretches microscopically before the screw sees the full force. For high-bandwidth servo positioning, this would be a problem. For web guiding — where correction rates are 0.5 to 2 Hz and the web sensor outer loop corrects any residual error — this compliance is inconsequential. The belt's benefits (torque amplification, inertia reduction, compact packaging) far outweigh the compliance penalty at web guiding speeds.
The actuator sizing calculator uses this equation internally, with the correct k values for each RLA model, so you do not need to calculate it manually.