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## Linear Electric Actuator (Motor Model)

This model shows how to develop a model of an uncontrolled linear actuator using datasheet parameter values. The actuator consists of a DC motor driving a 6.25:1 worm gear which in turn drives a 3mm lead screw to produce linear motion. Manufacturer data for the actuator defines the no-load linear speed (26mm/s), rated load (1000N), rated-load linear speed (19mm/s), and maximum current (5A). The maximum static force is 4000N and the rated voltage is 24V DC.

If friction and rotor damping are neglected, the DC Motor mask parameters can be calculated as follows. A no-load speed of 26mm/s is equivalent to (26/3)*6.25*60=3250rpm. The rated motor speed is (19/3)*6.25*60=2375rpm, and the rated power is 1000N*19e-3m/s=19W. To run the model based on these parameters, set the DC Motor Model parameterization parameter to By rated power, rated speed & no-load speed and remove the Friction block. The results validate the speeds for zero and 1000N load, but under-predict the maximum current and maximum static force.

For a more accurate approximation of the motor, friction effects must be included. The no-load and rated-load speed information depends on the unknown friction levels, so instead we parameterize the motor in terms of the maximum current which occurs when the rotor is locked (i.e. no back emf). Then the winding resistance is given by rated voltage divided by maximum current i.e. 24V/5A = 4.8 ohms. The torque constant is given by maximum static torque divided by the current i.e. (4000N*3e-3m/s/(2*pi*6.25))/4.8A = 0.3056Nm/A. To run the model based on these parameters, set the DC Motor Model Parameterization parameter to By equivalent circuit parameters and reinstate the Friction block. You should find that a torsional friction of 0.03Nm results in a 26mm/s no-load speed. The model also confirms rated-load speed is 19mm/s, maximum current is 5A and maximum linear force is 4000N.

Note that a limitation of this model is that the load can back drive the motor through the worm gear. A more detailed friction model would be required to prevent this.