![]() This back EMF not only reduces the height of the initial current inrush but in the steady-state means that the current draw is significantly lower than the motor terminal resistance alone would permit. The faster the motor turns, the greater the back EMF in the coils. This is observed as the gradient of the initial current inrush (the greater the inductance, the lower the rate of change, the shallower the gradient).Īfter the voltage is applied the motor begins to turn. ![]() The coil inductance opposes this change and generates a voltage proportional to dI/dt which is known as back EMF. This change in voltage causes a change of current in the circuit. After some time, a DC voltage is applied (V_drive = 3V). Modelling The Transition To Steady State BehaviourĪssume initially that the motor is unpowered (V_drive = 0V). It is therefore clear that in our model the inductance L_inertia is the electrical equivalent variable of the moment of inertia of the rotor. The mechanical equivalent for which is (I now represents the moment of inertia):□=□×□=□×□□□□ The voltage dropped across the motor is given (remember, here I is current):□=–□□□□□ What does the inductor represent? L_inertia limits the current in the mechanical circuit when there is a change in voltage V_torque. It does, however, clearly illustrate the role of friction as an energy sink in the mechanical system which acts to reduce the speed of the motor. This is a simple model of viscous friction (see more in the conclusion), and does not fully convey the complexities of friction in DC motors. In other words, it represents velocity-dependent friction. This acts to reduce the rotor torque, and it has a velocity-dependent loss. The voltage dropped over R_loss depends on the current, as per Ohm’s law:□=□×□ So what limits the speed of the rotor? Anything in the mechanical circuit which limits the current, such as the resistor R_loss. The resulting speed of the rotor, ω, is represented by the current in the mechanical circuit. Torque is represented as the voltage V_torque in the mechanical equivalent circuit. The rotor torque in a DC motor is determined by the current through the coils and the torque constant, Kτ. Pay careful attention to whether you’re working with the electrical or the mechanical parameters to avoid mistakes. Important Note: We can see from the above that the Current and the Moment of Inertia share the same symbol, I. Mechanical Equivalentdescription, symbol, unitĬoefficient of viscous friction, μ, Electrical Variabledescription, symbol, unit The table below outlines the variables in the mechanical circuit. Justification For The Mechanical Equivalent Circuit The back EMF voltage source depends on the current sensed by V_Sense_2. These do not alter the behaviour of the circuit and are simply used to provide convenient current measurements. Note the two 0V voltage sources, V_sense_1 and V_sense_2. ![]() Basic Electrical and Mechanical Equivalent of a DC MotorĬurrent-dependent voltage sources are used to communicate information between the electrical and mechanical equivalent circuits. The SPICE engine doesn’t explicitly support mechanical models, however, it is facilitated by the use of electrical equivalent circuits. W, therefore, need a mechanical system model in order to calculate the speed of the motor. The back EMF voltage source is dependent on the speed of the motor and the torque constant Kτ. ![]()
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