![]() The voltage fed back into the circuit, as a result of the motion of wires in a magnetic field is called the back electromotive force, or vBEMf, and can be determined from the equation, VaEmf(t) = NK90, (2) where N is the gear ratio of the planetary gearbox, Kg is the motor speed coefficient, and å, is the rotational velocity of the motor pinion gear. Here, the constants Ra and La represent the armature resistance and inductance, and the variables ia(t), and va(t) represent the motor current draw and the applied voltage respectively. ![]() DC Motor Current By using Kirchhoffs Voltage Law on the circuit diagram in Figure 11, Raia(t) + La “aO + VBEMF(t) = v4(t) (1) dt La Ra Keha Gearbox v,(t) = K,ôÔm Im %3D Pinion Gear Вт DC Motor Rack Figure 11: DC motor schematic diagram relating applied voltage to position of the motor pinion gear, 8, i. ![]() Mathematical Modeling Please complete the modeling of the dynamics.
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