PSpice Application Notes

APPLICATION NOTE 2 The basic equation which describes the mechanical system is: Ttotal = J·d 2θ/dt 2 Where, Ttotal is the total torque, including friction, applied to the motor shaft from all sources (g.cm) J is the mechanical system moment of inertia (g.m.sec 2 ) θ is the motor angle shaft (radians) Ttotal can also be expressed as: Ttotal = 2ߨJdS/dt Where, S is the shaft speed (rev/sec) represented by the equation: S = Cd߭/dt You can implement the equation for Ttotal expressed in terms of S by modeling torque as a current and the moment of inertia, 2ߨJ, as a capacitor. This gives the shaft speed as the voltage across the capacitor. Modeling torque as a current and moment of inertia as a capacitor is convenient because you can model any additional mechanical system moment of inertia as an additional capacitor in parallel with the first one. Also, you can add various torque and drag forces as parallel current sources making the model easier to use in a system. You can use the equation for the shaft speed again on the circuit equation for a capacitor to give the shaft angle as the voltage across a capacitor which has a current equal to the shaft speed applied to it. Here is a PSpice sub-circuit for the motor's mechanical system: .subckt motor_mech shaft_speed shaft_angle + params: + J= .30 ; moment of inertia of rotor (g*cm*sec*sec) + twopi = {2 * 3.141596} Cmotor shaft_speed 0 {J*twopi} ; Inertia Gintegrate 0 shaft_angle_intg VALUE = {V(shaft_speed)} Cintegrate 0 shaft_angle_intg {1/twopi} IC=0.0 Rdummy2 0 shaft_angle_intg 1e12 ; (otherwise floating) Ecopy shaft_angle 0 VALUE = {V(shaft_angle_intg)} ; Copy the voltage Rdummy3 shaft_angle 0 1 ; Make sure there is a load .ends To use the model, apply a current proportional to the shaft torque between nodes SHAFT_SPEED and 0 (1 amp = 1 g.cm). The voltage on SHAFT_SPEED will correspond to the shaft speed (1 volt = 1 rev/sec), and the voltage on SHAFT_ANGLE will be the shaft angle (1 volt = 1 radian). You now need to model the mechanical losses of the motor. The simplest are the linear losses, damping and eddy current losses. They are described by the equation: Tdamping = 2ߨ(B · S) B is the damping and eddy current losses (g·cm·sec/rad) S is the shaft speed (rev/sec)

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