Answer Happy

(a) In reference to Figure 1, show how load parameters: moment of inertia J,, viscous friction D, and fixed load torque T are referred to the motor shaft across a reduction gear box. The reduction gear ratio is given by, a, where a < 1. @ Current Controller Ve 4Q converter V₂ DC Servo Motor Jm. Da Gear (01/0m = a) Ⓒm Figure 1 (b) For the drive of Figure 1, the following load parameters are given: 00% Gear ratio, a = 1/9; Jm=0.08 kg-m²; D = 0.15 Nm/rad/sec, J = 7 kg-m²; D₁ = 5.0 Nm/rad/sec; and Tz = fixed load torque = 20 Nm. Parameters of the separately excited DC motor of Figure 1 are: 1₂ Write the torque balance equation of the system, using all quantities referred to the motor shaft. R₂ = 0.62; L₂=0H; Kr=K=1.8 Nm/A (or V/rad/sec), Larated = 30A and Com, rated = 1300 rev/min. (c) Sketch the motor and load torque-speed characteristics for several input voltage V, to the armature and hence comment on the stability of the operating speed of the drive for small disturbances in V, and load torque. (d) Find the total developed torque TM and the armature current Ia, when the motor drives the load of part (b) at a constant speed of 1000 rev/min. What is the input voltage V₂ for this condition of operation? Calculate the no-load speed of the motor. Note: no-load condition implies that all friction and load toque could be assumed to be zero. (e) Find the maximum allowable control voltage v. at start from standstill if the maximum armature current is to be limited to twice the rated value. Assume that the converter gain is 50V per volt of the control voltage v. (i. e., the converter voltage gain = 50).