class: center, middle # EE-361 # DC Machine Problems ## Ozan Keysan [ozan.keysan.me](http://ozan.keysan.me) Office: C-113 <span class="meta">•</span> Tel: 210 7586 --- # DC-Machine Equations - ## Induced Voltage Proportional to Speed ## \\(E\_a = K\_a \omega\_m \Phi\_{pp}\\) -- - ## Torque Proportional to Armature Current ## \\(T =K\_a \Phi\_{pp} I\_a \\) --- # DC Machine Types ## Different ways to connect field winding ### - Seperately Excited ### - Shunt Excited ### - Series Excited ### - Compound Machines --- # Ex-1: ## A 10 kW DC Shunt motor connected to 200 V supply and driving a load with the following characteristics. -- ## \\(P_l = k n^2 = 3.9\;10^{-3} n^2\\) (n: speed in rpm) -- ## Friction losses of the motor are constant and equal to 250 W. -- ## Field winding is \\(40\; \Omega\\), --- ## a) Calculate the motor speed if the motor is supplying rated power from its shaft at steady state. --- ## b) Determine the armature current and armature resistance of the motor at rated load. ## Magnetization characteristics obtained at 1500 rpm are as follows: ## <table> <tr> <th>Ea(V) </th> <th>153.7 </th> <th>161.8 </th> <th>164.8 </th> <th>170.2 </th> <th>175 </th> <th>178.3 </th> </tr> <tr> <td>Ia(A)</td> <td>2</td> <td>3</td> <td>3.3</td> <td>4</td> <td>5</td> <td>6</td> </tr> </table> --- ## c) Calculate the total current drawn from the terminals and motor efficiency <!-- d) If the shaft speed is measured as 1700 rpm, when the armature current is 54.8 A; ## i) Calculate the generated voltage (neglect armature reaction), ## ii)Calculate the generated voltage with armature reaction (refer to magnetization curve), ## iii) Calculate the extra field current supplied to compensate the armature reactance --> --- # Ex-2: ## Consider two identical DC machies having an armature resistance \\(R_a = 0.2 \Omega \\) and a field winding resistance of \\(R_f = 120 \Omega \\). -- ## One of the machines is used as a shunt motor to drive the other as a separately excited generator. --- ## The shunt motor draws 6 kW from a constant voltage source \\(V\_t = 120 V\\). The excitation currents of both machines are equal and the rotational loss is constant \\(P\_{rot}=200 W\\) per machine. -- ## a) Draw the complete circuit diagram. -- ## b) Calculate the induced voltage and efficiency of the motor. --- ## c) Assuming the induced voltage of the generator is 110.2 V, Find the armature current, output power, and efficiency of the generator. -- ## d) Complete the power flow diagram of the system, and calculate the overall efficiency. --- # 2015 Final Exam, Q4 -- ## Consider a separately-excited DC motor. -- ## Assume that Ra=0.5 Ω; friction is neglected. -- ## a) Calculate induced armature emf, Ea, by assuming that the motor runs at the no-load speed of 1500 rpm when Vt=220V --- ## b) If now a constant-torque mechanical load of TL=100 Nm is coupled to the shaft of the motor and field current If is as in (a), calculate: -- - ## New value of Vt to drive the load at the same speed (1500 rpm) -- - ## Armature current, Ia -- - ## Electromechanical torque, Te , and Mechanical power output, Po. --- ### Suppose now that Vt is suddenly reduced to 200 V, while the motor is operating in the steady-state as defined previously. If you need, you may assume that Ka φ=1.4. Calculate or explain followings **just after the terminal voltage reduction**. -- - ## Direction and magnitude of Ia -- - ## Direction of power flow in the armature circuit -- - ## Gross mechanical output power -- - ## Operation modes of the dc machine and the dc motor / load combination -- - ## Explain the response of the dc machine/load --- ## (Not in the exam) -- ## Plot the variations of current, torque, speed and induced voltage from voltage reduction until to the new steady state operating point. --- # Ex: -- ## A separately excited DC motor is operating as a crane-hoist. -- ## Its field excitation is kept constant. \\(R_a = 0.5 \Omega \\), \\(I_a= 100 A\\). -- ## Crane drum radius = 0.1 m, and the motor lifts a 100 kg mass. --- ## a) Find the applied armature voltage (Vt) in order to rise (ascend) the load at a constant speed of 5 m/s. -- ## b) Now, assume the motor lowers (descends) the load at constant speed (which is called overhauling). Find the speed at which the DC machine can overhaul the load by assuming Vt is kept constant (note that either the direction of If or Vt should be reversed to run the motor in the other direction). --- # [SOLUTIONS](../files/361_final_recitation_2017.pdf) # [Final Exam Solutions](../files/ee361_Solved_DC_machines_3.pdf) --- ## You can download this presentation from: [keysan.me/ee361](http://keysan.me/ee361)