Electromechanical Automation

Nicolas Giovanangeli (11378344)

Electromechanical AutomationLab 1: EM Energy ConservationNicolas Giovanangeli, 11378344 Lab Group B

Table of ContentsAim2Abstract2Materials3Pre Lab4Results/Measurements10Discussion12Conclusion13References13

Aim

To measure the magnetic flux and torque in a singly excited electromagnetic system. To calculate the flux and torque and compare with measurement. To be familiar with Op-Amp circuits and to use it in a fluxmeter.

AbstractA 2-pole variable reluctance rotating machine is used as a singly excited electromagnetic system. Calculations of flux variations with rotor angle, based on the machine dimensions and excitation, are used to study the variation in stored energy and hence the machine torque. Flux and torque measurements are performed and the calculated performance is compared with measured performance. The variation of the coil self-inductance with rotor position is also noted. In general an electromechanical system has an electrical part, a mechanical part and a control part. The electrical part may be electrostatic or electromagnetic; the latter will be considered here. In general, an electromagnetic device will have several coils, an electromagnetic circuit with a moving part, and/or permanent magnets. To form an electrical model we need: The resistance of each coil (at the operating temperature) The self inductance or self flux linkage of each coil and its variation with position of the moving part and with the coil current The mutual inductance or mutual flux linkage between all coils and the variation with moving part position and coil currents The induced voltage in each coil due to motion of the permanent magnets relative to the coils To simplify the example, we consider a system with one excited winding (formed of two coils in series) on a 2-pole solid iron stator, and a moving 2-pole solid iron rotor. This is a singly excited variable reluctance machine. (There are coils on the rotor, but these are not used in this experiment.)

Materials Lybotec 2-pole rotating machine. The machine has 2-pole salient pole stator with a rated coil current of 2 A, and 2-pole salient pole rotor, shown below. The rotor coils are not used in this lab.

Shaft locker Shaft encoder Shaft encoder counter Commutator-mounted torque arm Salter 10N spring balance Fluxmeter (electronic integrator) Reversing switch Connecting leads with retractable shrouds on the plugs

Note: The spring balance for force measurement may be calibrated in gram weight. (1 g wt = 9.8 10-3 newton). Torque = force radius, its SI unit is newton-metre, Nm.

Pre Lab

i. Use the BH curves, shown above, to determine the maximum permeability of cast iron forming the magnetic path.

ii. Assuming no fringing and that the iron parts have the permeability calculated above, sketch the magnetic equivalent circuit and derive ideal expressions for the flux linking the stator winding for the rotor angles of to , where is the angle of the rotor when aligned with the stator poles. The dimensions of the machine are given in below.

iii. Plot the flux variation with rotor angle over to range for current I=1.5A DC (75% of its rated value).

iv. From the analytic expression calculated in (ii) for the flux, derive an expression for the derivative of the flux with respect to rotor angle over 0o to 76o.

v. From the flux derivative, determine and plot the restoring torque for I=1.5A DC, over the range of rotor angles from -76o to +76o. Note that , the restoring torque will take a negative value and vice versa.

vi. On a graph paper, sketch flux and torque variation with rotor position over a range, making sensible assumptions as to machine symmetry.

vii. How would the torque differ if 1.5A AC was used instead of 1.5A DC?

viii. How could a unidirectional torque be produced for?

Results/MeasurementsFlux/Rotor angle measured results

Rotor angle(deg)Voltage output for a rotor angle (V)Initial fluxmeter reading (I < 0)(mWb)Final fluxmeter reading (I > 0)(mWb)Coil Flux amplitude(mWb)

04.20.068.808.74

54.20.068.758.69

104.470.068.578.51

154.70.058.188.13

204.920.058.088.03

305.250.057.757.70

405.580.056.866.81

506.250.055.505.45

606.360.055.165.11

707.150.053.543.49

757.30.053.063.01

807.50.042.832.79

-53.40.058.568.51

-103.130.058.418.36

-152.90.058.168.11

-202.80.058.098.04

-302.50.047.507.46

-402.240.047.257.21

-501.690.045.965.92

-601.470.045.085.04

-701.030.044.554.51

-750.580.043.973.93

-800.250.043.153.11

Rotor Angle (degrees)

Torque/Rotor angle measured results (Torque arm radius = 160mm = 0.16m)

Rotor angle(deg)Voltage output for a rotor angle (V)Spring balance force (F)Torque(T = F*r)(N m)

00.13500

50.471-0.16

100.691.5-0.24

150.912-0.32

201.583-0.48

301.912.8-0.448

402.14.1-0.656

502.574.2-0.656

602.694.4-0.656

703.354.4-0.656

753.84.4-0.656

804.024.4-0.656

-50.1710.16

-100.471.50.24

-150.3620.32

-200.252.80.448

-300.0283.10.496

-40-0.33.80.608

-50-0.754.50.72

-60-1.34.50.72

-70-1.54.50.72

-75-1.974.50.72

-80-2.44.70.752

DiscussionAfter analysing the results we can see there is a strong correlation between the theory and acquired practical data/graphs.(1) Magnetic Flux vs. Rotor AngleThe lab results confirmed that an increase in the rotor angle leads to a decrease in magnetic flux. Logically, this was to be expected as the more the rotor rotates, the less exposed the rotor face would be to the magnetic flux lines of the stator. This is evident in the graph displaying the result; at 0o there is maximum exposure between the rotor and stator cross sectional area, hence maximum magnetic flux. Moreover, as the rotor moves in either direction, the rotor becomes less exposed to the magnetic field of the stator; hence the magnetic flux on the rotor from the stator decreases. This continues until the rotor ends are nearly out of the stators magnetic field, where the magnetic flux is proven to be at minimum. However, the magnetic flux didnt reach zero at 80o as expected theoretically. There would have been two main reasons as to why this occurred: The angles used contained human error as they were estimated based on an approximation of how much the rotor needed to be turned to achieve a target angle. In the calculations, we assume a closed system; disregarding the fringing effect. This effect exists in a practical sense and would of provided a magnetic flux, even though the rotor had just left the direct magnetic field/straight magnetic flux lines.

(2) Torque vs. Rotor AngleThe torque created opposes the direction of motion, as it is a restoration torque. This is why as the rotor increases in the positive sense; the torque will increase in the negative/opposing sense, and vice versa. The torque we create will be equal to the restoration torque (but in the opposite direction) when the rotor is stationary/in equilibrium (as were measuring forces). The lab results confirm that by increasing the rotor angle, the torque increases in the opposite sense (i.e. you more force apply to get the rotor to turn anticlockwise would result in a larger restoration torque acting clockwise). This is a result of an increase of the rotor angle causing a decrease in magnetic flux, therefore increasing torque to preserve the conservation of energy. The electrical energy input is equal to the sum of the magnetic stored energy and mechanical energy output. If the magnetic flux decreases, there will be a decrease in magnetic stored energy; thus, a force is exerted (creating torque), increasing mechanical energy to balance the energy in the system. However, there is a noticeable difference in the predicted results from the theoretical side and the actual practical results. This difference being in theory, the restoration has a step from just before zero to just after zero degrees; it jumps between values as the rotor begins to rotate in either direction. The results show no step but instead a gradual rise in the restoration torque as the rotor angle rises in the corresponding direction. Human error was to blame as it was assumed that when the rotor was at 0o there will be zero torque, therefore we can move on to testing the next angle. However, we didnt test the angle just before zero and just after zero like in the theoretical graph. As a result, we would have missed how a certain force/torque needs to be reached before the rotor can begin moving.ConclusionBy comparing the acquired data from this lab against the derived theoretical equations, there is proof of a strong relationship between the rotor angle, magnetic flux and torque. There is a strong enough correlation between the magnetic flux and rotor angle to conclude that the magnetic flux is inversely proportional to the rotor angle. In addition, results have demonstrated how the restoration torque is proportional to the rotor angle. Furthermore, by proving these two relationships, we have demonstrated how a decrease in magnetic flux will result in an increase in torque to satisfy the conservation of energy.References Lab 1: EM Energy Conservation Notes Chapter 3: Electromechanical Energy Conservation Lecture slides Tutorial 2: Problem 52