1)  300 turns of wire are placed around the left leg of the magnetic structure shown at the right.  The length of the air gap is 1.5 mm.  What should the magnitude of current in the wire be in order to produce a magnetic flux density of 0.5 T in the air gap?  

Assume µ = 350µ_o.

 

What is the inductance of the structure?

2)  The following information is given concerning a simple DC machine:

            B_f   = 1.45 T                                          n_a  = 55turns

            l     = 0.15 m                                         R_a   = 0.75W

            r    = 0.060 m                                       v_a   = 75 V (applied voltage)

 

The machine is rotating at 1800 RPM.

 

a)      Is this machine operating as a motor or as a generator?  Explain you conclusion.

b)      What is the current flowing into or out of the machine?

c)      How much power is the machine delivering or absorbing?

d)     At what RPM does the machine change function (motor vs. generator)?

 

 

3)  A field_winding DC motor is to be started from rest.  The motor parameters are:

            R_a  = 0.60 W                                         L_a  = 4.5 mH

            k_E   = 0.55 V/(rad/s)                              k_T   = 0.55 Nm/A

            J_m  = 0.08kg×m²

This motor is driving a load with parameters:

            J_L   = 0.14 kg×m²Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  T_L  = 4 Nm

The motor current must not exceed 10 A. 

 

a)  Calculate and plot both the voltage v_a, which must be applied to bring this motor-load combination to a steady-state-speed of 2000 RPM as quickly as possible, and the speed, as a function of time.  Neglect the effect of L_a.  How long (in seconds) does it take to bring the motor-load combination to steady-state?

b)  While the motor is driving the load at a steady-state speed of 2000 RPM, the field coil current is changed so that B_f is reduced to 75% of the value in part a while the armature voltage, v_a, remains constant.  Calculate the new steady-state speed.

 

4) A DC motor with the following parameters:

            R_a  = 0.3 W                                           L_a  = 4.5 mH

            k_E   = 0.6 V/(rad/s)                                k_T   = 0.6 Nm/A

            J_m  = 0.04kg×m²

is supplied by a switch-mode DC-DC converter that has a DC-bus voltage of 120 V.  The switching frequency, f_s = 30 kHz and a duty cycle range of 0.10 £d_A£ 0.90.  The motor is driving a load with the following properties:

            J_L   = 0.08 kg×m²Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  T_L  = 7.5 Nm

a)      When the motor is driving the load, what range of steady-state motor speeds (in RPM) can the switch-mode converter achieve?

b)      At 900 RPM (driving the load), what is the duty cycle of the DC-DC converter?

c)      What is the peak-to-peak ripple in the armature current under the conditions of part b?

d)   What is the peak-to-peak ripple in the motor speed under the conditions of part b?

 

5)  A DC motor with the following parameters:

            R_a  = 0.75 W                                         L_a  = 3.5 mH

            k_E   = 0.8 V/(rad/s)                                k_T   = 0.8 Nm/A

            J_m  = 0.07kg×m²

Is driving a load described by:

            J_L  = 0.09 kg×m^{2                                             Â}  T_L  = 0.028wNm(linear with w)

 

a)  What voltage, v_a, must be applied to keep the motor-load combination running at a constant 350 rad/s?  What is the electrical power consumption at that speed?  What is the mechanical power being delivered to the load?

 

b)  The motor-load combination is to be stopped as quickly as possible from its steady-state speed of 350 rad/s.  The motor current must not exceed 15 A.  Calculate and plot the voltage, v_a, which must be applied to stop this motor- load combination (and keep it stopped).  How long (in seconds) does it take to stop the motor-load combination?