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Electrical Linear Actuator Calculations

Electrical linear actuators are available in various forms but the two most common technologies are ball screw and belt drive. Ball screw actuators tend to have lower linear speeds but can produce higher forces than the belt drive versions. The main factors for sizing of a linear drive are required force, required speed and required lifetime. Other factors include positioning accuracy, required acceleration, radial and torsional loadings and load inertia. The performance of a particular drive for each of these parameters is available from the manufacturer's data. Some drives are supplied with an integral motor but many are just the mechanical assembly to which a suitable motor needs to be fitted. The required input torque and speed can be calculated using the formulae below which can then be used to determine the size of the motor from the motor manufacturer's speed/torque curves.

Screw Actuators

Torque (Nm) = Force (N) x Pitch (mm)
(2000 x π x system efficiency factor)

RPM =Required linear speed (m/s) x 60000
Pitch (mm)

The system efficiency factor depends on the design of the actuator. It is typically 0.9 for a ball screw but can be as low as 0.4 for a standard lead screw.

Belt Actuators

Torque (Nm) =Force (N) x Pulley Radius (mm)

RPM =Required linear speed (m/s) x 30000
(π x Pulley Radius (mm))

These formulae assume direct connection of the motor to the actuator drive input. The ratio and efficiency of any intermediate gearing or drive belt arrangement also needs to be factored in.

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