From a07f63de81c43a67736ce94b071b0ea53b7890ff Mon Sep 17 00:00:00 2001 From: Alvie Rahman Date: Thu, 30 Mar 2023 11:35:23 +0100 Subject: [PATCH] mmme2051 notes on dc motors --- .../dc_motors.md | 57 ++++++++++++++++++ .../images/dc_motor.png | Bin 0 -> 1050 bytes ...ot-2023-03-30T11:18:31,204273426+01:00.png | Bin 0 -> 41851 bytes ...ot-2023-03-30T11:30:38,394462585+01:00.png | Bin 0 -> 14311 bytes ...ot-2023-03-30T11:33:14,679355133+01:00.png | Bin 0 -> 31632 bytes .../Exercise Sheet 12 - DC Motors.pdf | Bin 0 -> 77817 bytes 6 files changed, 57 insertions(+) create mode 100755 uni/mmme/2051_electromechanical_devices/dc_motors.md create mode 100644 uni/mmme/2051_electromechanical_devices/images/dc_motor.png create mode 100644 uni/mmme/2051_electromechanical_devices/images/vimscrot-2023-03-30T11:18:31,204273426+01:00.png create mode 100644 uni/mmme/2051_electromechanical_devices/images/vimscrot-2023-03-30T11:30:38,394462585+01:00.png create mode 100644 uni/mmme/2051_electromechanical_devices/images/vimscrot-2023-03-30T11:33:14,679355133+01:00.png create mode 100644 uni/mmme/2051_electromechanical_devices/seminar_worksheets/Exercise Sheet 12 - DC Motors.pdf diff --git a/uni/mmme/2051_electromechanical_devices/dc_motors.md b/uni/mmme/2051_electromechanical_devices/dc_motors.md new file mode 100755 index 0000000..be79626 --- /dev/null +++ b/uni/mmme/2051_electromechanical_devices/dc_motors.md @@ -0,0 +1,57 @@ +--- +author: Akbar Rahman +date: \today +title: MMME2051 // DC Motors +tags: [ dc_motors, motors ] +uuid: b8313ef8-ef1e-486d-8031-52c39ac88751 +lecture_slides: [ ./lecture_slides/MMME2051EMD_Lecture9.pdf ] +lecture_notes: [] +exercise_sheets: [ ./seminar_worksheets/Exercise Sheet 12 - DC Motors.pdf ] +--- + +Relevant lecture slides are 15-26. +Two worked examples can be found in the lecture slides 24-26. + +In a simple DC motor, the stator is either a permanent magnet or a coil with a +current flowing through it. +Both create a constant magnetic field. + +![](./images/dc_motor.png) + +The rotor is just a coil with current flowing through it by a (different) DC power supply: + +![](./images/vimscrot-2023-03-30T11:18:31,204273426+01:00.png) + +Note the commutator and brushes. +This flips the current direction inside the coil, flipping the direction of the induced magnetic field, +and therefore flipping the direction of the resultant force. + +The split in the commutator is placed such that the current flips just as the force would. +This is [visualised in this video (timestamped to 50s)](https://youtu.be/LAtPHANEfQo?t=50). + +# Torque, $T$ + +$$T = rBIl = KI$$ + +using $F = BIl$ and $T = rF$, where $B$ is magnetic field strength, $I$ is current flowing through coil, $l$ is length +of coil in the magnetic field, +$K$ is a constant which varies with motor designs, and $I$ is the current through the motor. + +# Back EMF, $E_b$ + +$$ E_b = Bvl = K\omega $$ + +where $B$ is magnetic field strength, $v$ is linear velocity, $l$ is length of coil in field, +$K$ is a constant defined by the motor, and $\omega$ is angular velocity. + +# Relating Voltage to Motor Performance + +There are two equations which govern the motor's performance: + +$$V_\text{in} = E_b + IR$$ + +\begin{equation} \label{eqn_torquespeed} +V_\text{in} = K\omega + \frac{T}{K}R +\end{equation} + +![Equation \ref{eqn_torquespeed} can be plotted to show how speed varies with load. Plotting multiple voltage also show how speed varies with coltages.](./images/vimscrot-2023-03-30T11:33:14,679355133+01:00.png) diff --git a/uni/mmme/2051_electromechanical_devices/images/dc_motor.png b/uni/mmme/2051_electromechanical_devices/images/dc_motor.png new file mode 100644 index 0000000000000000000000000000000000000000..7b2c0d76a6bd2bc460f7562715e0934fd92f6e58 GIT binary patch literal 1050 zcmV+#1m*jQP)I_T0Rh(i{aMi4F05^z;)x`@yY zMJRMJLQ0pqIruNwr7j&TbP#`Rp|ubML0Um*YcMflf^9S=xyk*$!_~ZPHRpZblhd0t z@BP4m8=mCJ=brnV=OnoS{!|F?cMlEdtM>jaW}fVS#gdc7l9R=flf{ygMNZD)0KR<# zN+saqN8r}2%g=fI*of!z!2SCs$^pRj>&EbUfk@@bDq<<%{unYz*-GYfcNOs<}b|c=pWbX>PZ1c@>~;LA-eb zeE47-2ZO+a2Q{ZuC-?n3@bsxMdjN3fPR%LR?ya#H@ZyECbm}+$SFeCipOmChFZcN~ zFgK?pm0UwAm4Mf;jmG=_J)rA<$4KDiOQYtTPM}-{zJ66A`xDleY5|s%Ll>bB7Qu zb5&3f6UvERXa)`a6Iesb)qG>r?RFy=45G8M6E>R-nxqsOLDjcgq(dg;v z;nC3%HBI9Mx~@~xG#(rraAage`1t%m`KQ}iwD}sxQi_&t^HD|Zm0RU%bXPBR#$I8kI0AOcl2jk=8m^;5Y zmrAA3+S-a@QGM5}ddA^!xH5C`c$`a1OPrXPV0(M}zp1m|ds%%xANTh5F4dW?>x@RD 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