class: center, middle # EE-361 # A Brief Review of DC Machine Models ## Ozan Keysan [keysan.me](http://keysan.me) Office: C-113 <span class="meta">•</span> Tel: 210 7586 --- # Model of DC Motors <img src="https://miro.medium.com/max/700/1*5Trg0JjdKROU8tEbqWqS2w.png" alt="Drawing" style="width: 800px;"/> --- #Simplest Equivalent Circuit of a DC Machine ## A voltage source (proportional to speed) connected in series with a resistance (Armature resistance) -- <img src="http://www.electrical4u.com/images/equivalent-circuit-of-pmdc-.gif" alt="Drawing" style="width: 400px;"/> ### Under constant flux (as in permanent magnet DC machine) --- # Induced Voltage in Armature -- # \\(E\_a = K\_a \omega\_m \Phi\_{pp}\\) -- - ### \\(E\_a\\): Induced armature voltage - ### \\(K\_a\\): Armature Constant - ### \\(\omega\_m\\): Mechanical Speed (rad/s) - ### \\(\Phi\_{pp}\\): Flux per-pole --- # DC Machines -- ## Motor Action: Electrical Energy is converted to Mechanical Energy -- ## Generator Action: Mechanical Energy is converted to Electrical Energy -- ## No difference between a [DC motor and generator](http://www.youtube.com/watch?v=6kgzrXFSDwA) ## Just a mode of operating point --- # Equivalent Circuit of a DC Motor ## If the flux is generated by another coil (Field Winding) -- <img src="./images/ee361/dc_motor1.png" alt="Drawing" style="width: 700px;"/> --- # Equivalent Circuit of a DC Motor <img src="./images/ee361/dc_motor1.png" alt="Drawing" style="width: 500px;"/> ## If \\(V\_a > E\_a\\) motoring action -- ## If \\(V\_a < E\_a\\) generating action --- # Electromechanical Power <img src="./images/ee361/dc_motor1.png" alt="Drawing" style="width: 700px;"/> ### Electromechanical Power = Armature Power - Armature Losses -- ## \\(P\_{out} = V\_a I\_a - I\_a R\_a = E\_a I\_a \\) ### (for the motoring mode) --- # Torque Relations <img src="./images/ee361/dc_motor1.png" alt="Drawing" style="width: 300px;"/> ## \\(P\_{mech} = \\) -- \\( T \omega = E\_a I\_a \\) -- ## \\( T \omega = K\_a \omega \Phi\_{pp} I\_a \\) -- ## \\(T =K\_a \Phi\_{pp} I\_a \\) --- # Torque is Proportional to Current # \\(T =K\_a \Phi\_{pp} I\_a \\) --- # What happens to DC motor at start-up? -- ## Rotor speed is zero: \\(\omega =0 \\) ### Induced armature voltage: -- \\(E\_a = K\_a \omega\_m \Phi\_{pp}=0\\) -- ## Armature Current: \\(I\_a = (V\_t -E\_a)/R\_a\\) -- ## Maximum Current and Torque at Startup --- # Maximum Torque at Startup -- ## Result: Never attempt a drag race with an electric car. <img src="http://www.bangshift.com/forum/filedata/fetch?id=1042213&d=1435554776&type=full" alt="Drawing" style="width: 500px;"/> - [White zombie drag race](https://youtu.be/FtrpBJbLT9M?t=120) - [White zombie](https://youtu.be/crfEecV1YFA?t=46) - [White zombie inside](https://youtu.be/OfbPf3WExwU?t=1m25s) --- # You need to wait until EE362, but ## Electric Cars: [Tesla Model S Induction Motor](https://youtu.be/NaV7V07tEMQ?t=18s)  --- ## [Tesla vs Bugatti Veyron](https://www.youtube.com/watch?v=0IgiFcVZOuY) <img src="https://cdn.motor1.com/images/mgl/10lmw/s1/veyron-vs-teslas.jpg" alt="Drawing" style="width: 600px;"/> #### [Tesla Acceleration Reactions](https://www.youtube.com/watch?v=I5mZ1IK7SuU), [Tesla trolls muscle cars](https://www.youtube.com/watch?v=4FCb70blEMw) #### More info: [What's inside Tesla Model 3?](https://www.youtube.com/watch?v=Lj1a8rdX6DU), [Tesla Model 3's motor animation](https://www.youtube.com/watch?v=esUb7Zy5Oio), [Tesla motor assembly](https://www.youtube.com/watch?v=wvLmBfwmA04) --- # Summary - ## 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 \\) --- ## You can download this presentation from: [keysan.me/ee361](http://keysan.me/ee361)