Answer Happy

1.Provide the measured values in Tables 1 and 2.
2. Plot the measured values of speed and current, and plot the line that fits them. Find the value of a and & for the line (either manually or using Matlab/Octave). What is the values of a and b?
3. Find the armature resistance. Show your calculations and compare it to the measured value.
commutator segments, however because brushes constantly switches from on segment to another, sparks appear at the brushes and this causes deterioration of the brushes and the need for constant maintenance especially for large motors. Bearings Page (2/6) Run-away condition in DC motors The relation between the rotation speed and the flux inside a DC motor can be derived as follows: Enduced VM-IM RM=kw ⇒@= (VM-IM RM) ko Which means that as the magnetic flux decreases, the speed of the motor increases. When the flux is produced by a field circuit, if the current in becomes zero (for example due to cut in the wire) the motor will run at a very high speed, this situation is called run-away motor and should be avoided. Speed control in DC motors The main advantage of DC machines is the linear relationship between the main voltage and the speed of the machine, which means that the speed is easily controlled by changing the applied voltage. Another way to control the speed of the motor is by changing field current. Linear least squares fit Linear least squares fit is a way to find the best line that fits some data x₁,x₂,...,xx, and y₁.₁. Y If the line that fit the data is expressed as y=ax+b, then: N NΣxy-Ex₁. i=1 i=1 i=1 a= N N NΣX²-(Σx)² i=1 i=1 N Σy-a Σx i=1 i=1 b= N Using Matlab (or gnu Octave) to find linear least squares fit Let's say that we have the points XX=[2,4,5,7], YY = [18, 17, 14, 13] and we want to find the coefficients a and b of the line y=ax+b that best fit the data, then the following can could be used: 20 XX= [2,4,5,7] % defining the x values YY [18, 17, 14, 13] % defining the y values 15 coef = polyfit (XX, YY,1) % finding the coefficients a coef (1) 10 b = coef (2) % To plot the data and the line that fit them x= [0:10] % define x for the line. 10 y = ax + b % define y for the line plot(x,y,XX, YY, 'or', 'Marker FaceColor', 'r') % plotting the line and the values it fits ylim ( [0,22]) % set limits for y axis Speed-Current characteristic In this experiment, the speed-current characteristic of the DC motor will be found by applying different loads to the motor and measuring the speed and the current at each load. Then the best line y=ax+b that fits the data is found as described before. Page (3/6) At no-load (i.e. current =0) the speed is maximum, and it will decrease as current increases. By finding the value of the speed at no-load no, which equals to b, the speed n is evaluated as follows: 2πη Einduced=VM-IRM=-IRM+VM, Enduced=kw > 00= 60 =-IRM+VM k$2лn 60 -60 RM 60 V Armature

Table 1: Measured resistance values for motor armature and field circuits. Armature resistance(0) Field Resistance (2) 583 Table 2: Measured values for armature current and motor speed (in RPM) Current (IM) (A) 1.48 3.65 Speed (n) (rpm) 2918 2868