Lab Report 1_EELE3314

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Lakehead University *

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3314L

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Mechanical Engineering

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Apr 3, 2024

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12

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Running head: EELE3318L LAB FOR DC MACHINES 1 EELE3318L Lab for DC Machines LAB #5 Synchronous Motor
2 EELE3318L LAB FOR DC MACHINES Results and Pre-Lab Calculations - First Order System  Calculated c(t)  4(1-e^(-t)) Calculated Tr (s)  Calculated Ts (s)  2.2 3.9 Rise time: Tr = 2.2/a = 2.2/1 = 2.2s Setting line: Ts = 3.9/a = 3.9/1 = 3.9 - Second Order System  Calculated c(t)  (1-1.05409*(e^-t)*sin(3t+1.249))u(t) Calculated ζ  Calculated wn (rad/s)  Calculated DC gain kdc  Calculated P.O. (%)  0.316227766 3.16227766 1 35.09198072 ζ term: 2 ζ wn = 2 so ζ=1/wn=1/3.16227766=0.316227766 wn term: wn^2 = 10 so wn=10^(1/2) kdc: kdc*wn^2 = 10 so kdc = 10/wn^2 Calculated P.O. (%): %OS = e^(−ζπ/√1−ζ^2) ×100 = e^(−(0.316227766* π)/√1−(0.316227766) ^2) ×100 = 35.09198072 Calculated Tr (s)  Calculated Tp (s)  Calculated Ts (s)  0.40573666 1.047197551 4 Rise time: Tr = (2.16ζ+0.60)/ωn = (2.16*0.316227766 +0.60)/(3.16227766 ) = 0.40573666 Peak time: Tp = π/(ωn(√1− 𝜁 ^2)) = π/(3.16227766 *(√1− (0.316227766 ) ^2)) =1.047197551 Settling time: Ts = 4/ζωn   = 4/(3.16227766 *0.316227766) = 4 - Procedure 1.2 Measured c(t) Measured c(t)  4(1-e^(-t)) - Procedure 1.3 Measured parameters
3 EELE3318L LAB FOR DC MACHINES Measured Tr (s)  Measured Ts (s)  2.19 3.91 - Procedure 2.4 Measured parameters Measured Tr (s)  Measured Tp (s)  Measured Ts (s)  Measured P.O. (%)  0.4259 1.0592 3.5359 35% - Procedure 2.5 Plot Pole-Zero Map Measured Poles  Measured Zeroes  -1+3i -1-3i - Procedure 2.6 Find damping factor, natural frequency, and DC gain Measured ζ  Measured wn (rad/s)  Measured DC gain kdc 0.316 3.16 1 - Procedure 2.7 Measure the influence of damping factor Required ζ  Measured ζ  Measured Tr (s)  Measured Tp (s)  Measured Ts (s)  Mea P.O 0ζ  0 NaN NaN NaN Infi 1ζ  0.316 0.4257 1.0607 3.5365 2ζ  0.632 0.6117 1.2913 1.8947 3ζ  0.948 0.9811 2.7517 1.6541 4ζ  1.264 1.4831 4.4232 2.695 5ζ  1.58 1.973 6.1253 3.5855 6ζ  1.896 2.4468 8.1132 4.4289 7ζ  2.212 2.9113 9.6826 5.2512 8ζ  2.528 3.3695 11.2209 6.0618 9ζ  2.844 3.8244 12.7402 6.8655 10ζ  3.16 4.276 14.247 7.6643 - Procedure 2.8 Measure the influence of natural frequency Required wn (rad/s)  Measured wn (rad/s)  Measured Tr (s)  Measured Tp (s)  Measured Ts (s)  Mea P.O 0.5wn  1.58 0.8518 2.1184 7.0719 1.0wn  3.16 0.4259 1.0592 3.5359 1.5wn  4.74 0.2839 0.7061 2.3573
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4 EELE3318L LAB FOR DC MACHINES 2.0wn  6.32 0.213 0.5296 1.768 2.5wn  7.91 0.1704 0.4237 1.4144 Procedure 1. Step Response of First Order System - Code for Entire Section 1
5 EELE3318L LAB FOR DC MACHINES
6 EELE3318L LAB FOR DC MACHINES 1.1 Step response of G(s) - Lines 1 through 12 give us the step-response 1.2 Finding c(t) - Lines 1 through 5 and 15 through 21, give us the c(t) equation in terms of given values of transfer function. Then in plotting the graph for c(t) step response, we find that it is identical to the step response using the step() function of the transfer function.
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7 EELE3318L LAB FOR DC MACHINES 1.3 Finding Tr and Ts - Lines 1 through 13 give us the necessary information to use the stepinfo() function, which gives us a rise time of 2.197s (approximately 2.2s) and settling time of 3.9121s (approximately 3.9s), as shown in the screenshot below.
8 EELE3318L LAB FOR DC MACHINES 1. Step Response of First Order System - Code for Entire Section 1 Code 3.3 Calculate R2 and X2 from Locked 3.9 Analyzing Figure 1 and T vs speed Characteristics for an Induction Motor vs DC motor From the torque vs speed characteristics for an induction motor, we can observe that these characteristics are essentially linear between no load and full load. This is because the rotor resistance is significantly higher than the rotor reactance in this range, so the induced torque, magnetic field in the rotor, and rotor current increase linearly with increasing speed (or slip). This can all be obtained from the equation for the torque-speed characteristics of an induction motor, given by Tind = [3*VTH^2*(R2/s)]/{wsync*[(RTH+R2/s)^2 + (XTH + X2)^2]}. From this equation we can clearly see that when the s value is very small (which it is in the linear region), it means the R2/s terms become very large and the RTH and XTH+X2 terms become
9 EELE3318L LAB FOR DC MACHINES negligible in comparison, so the equation becomes Tind = (3*VTH*s)/(R2*wsync). This equation means that the induced torque changes linearly with s (which is changed by the speed in the rotor relative to the synchronous speed), which is why this the induced torque and speed have a linear relationship in this region in Figure 1. When comparing the torque vs speed characteristics for an induction motor with that of the DC motor we can observe that the linear characteristics for the induction motor between no load and full load are different than the torque-speed characteristics of a DC motor. In a DC motor, the torque-speed characteristics should be ideally linear for a constant flux; however, in practice they are not due to the presence of an armature reaction that impacts flux. When a load is connected to a DC motor, a current flows through the armature and causes its own internal flux, which distorts the flux as the load increase. This distortion results in an increase in armature current as the load is increased, which results in a non-linear response of the speed of the machine to an increase in torque. In an induction motor there is no armature current present because it is a singly excited machine and there is only one magnetic field present. So, in this region of a small s value (between full load and no load), the linear characteristics of torque and speed are not distorted. 3. 10 Why is it not safe to run the induction motor on overload or overvoltage? You should not run an induction motor on overload because when it is on overload it draws a current that is higher than its rated value. When it is running above its rated current the stator and rotor windings can be destroyed/burn up. Even though this overheating is occurring the machine may continue to run, but it will damage components while it runs.
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10 EELE3318L LAB FOR DC MACHINES Conclusion The purpose of this lab was to study the performance of the asynchronous or induction motor. In an induction motor, a three-phase voltage is applied to the stator windings which results in the creation of a rotating magnetic field in the stator that rotates at the synchronous speed. The rotor is comprised of several bars all shorted together so that current can flow through them. The rotating magnetic field of the stator rotates relative to the rotor, which results in an induced current in the rotor, which goes through all the bars that are shorted. These induced currents result in magnetic fields in the rotor that tries to oppose the field of the stator. In accordance with Lenz’s law, the direction of rotation that would oppose the current induced by the field of the stator would be in the direction of rotation of the stator. So, in opposing this current, the rotor begins to rotate in the same direction as the stator. The rotor speeds up and rotates at a value close to the synchronous speed, but never equal to it. If the rotor were to hit the synchronous speed (a slip value of 1) the relative speed of the rotor bars and stator magnetic field would go to zero, resulting in an induced voltage and induced torque of zero; so, the rotor would slow down until it stopped rotating. The value of slip represents the speed of the rotor bars relative to the magnetic field and should never reach zero or one, as previously discussed. This value of slip is important, as it allows for the frequency and speed of the rotor to be found easily. These are the basic principles of induction motors required to understand the findings in the lab. In one portion of the experiment, the DC test, no load test, and locked rotor test were performed to obtain the equivalent circuit of the induction motor. The equivalent circuit obtained was in line with theoretical expectations, as these types of motors typically have a very high magnetizing reactance when compared to the stator and rotor reactance. Similarly, their core resistance is also much higher than the stator and rotor resistances as found in the experiment. In
11 EELE3318L LAB FOR DC MACHINES the second portion of the experiment, the impact on efficiency, power factor, and different types of power (reactive, real, and apparent) when the load of the motor was increased from no load to full load were observed. From these values the torque-speed characteristics at these various loads were also determined. In terms of the impact on efficiency, power factor, and different types of power with load, it was found that the input real power of the load increased a fair amount with an increase in load. This increase in input real power resulted in an increase in the power factor as the load was increased. Furthermore, this increase in both input and output power resulted in an increase in efficiency with an increase in load. These findings are in line with the expected theory. In terms of the slip of the rotor and frequency of the rotor, it was found that both increased with an increase in load because an increase in load resulted in a decrease in the speed of the rotor (from Pout=wm*T we see that increasing torque increases output power and decreases speed). An interesting point here is that even though the slip increased from no load to full load, these values for slip were still quite small, hitting a maximum value of 0.09389 (9.389%) at full load. This small value for slip is precisely the reason that the torque-speed characteristics of the induction motor are linear in nature between no load and full load, because the small slip results in an equation for Tind that only becomes dependent on constants and a changing value for slip, meaning that the slip (which is dependent on the rotor speed relative to the stator) and induced torque change proportionally to one another. This is shown by Tind = (3*VTH*s)/(R2*wsync). Overall, the performance of this lab was successful. The lab helped students to understand the function of induction motors and observe their operation at different loads, as well as understand how to model an equivalent circuit using obtained experimental results. In this lab it was found that the operation of an induction is very similar to that of a transformer, because the
12 EELE3318L LAB FOR DC MACHINES stator (primary winding) induces a voltage and current in the rotor (secondary winding), much like a transformer. While they are similar, one major difference between the induction motor and the transformer is that in the induction motor the speed/frequency of the stator and rotor are not equal to one another, unlike the transformer.
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