Scribd
Upload
99 views3 pages

Problem Set 2

1. The document contains 6 problems related to electromechanical energy conversions involving translational motors, electromagnetic systems, actuators, electromagnets, and reluctance machines. Forces, fluxes, energies, currents and other parameters are calculated. 2. Problem 1 asks to find the force on a moving part of a translational motor given a current-position relationship. Problem 2 involves calculating force using energy and coenergy approaches for an electromagnetic system. 3. Problems 3-5 involve actuators, electromagnets and a moving-iron ammeter, calculating values like current, voltage, flux density, force, energy, inductance and deflection. Problem 6 examines a reluctance machine, finding rotor speeds that develop torque

Uploaded by

Yara
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
99 views3 pages

Problem Set 2

1. The document contains 6 problems related to electromechanical energy conversions involving translational motors, electromagnetic systems, actuators, electromagnets, and reluctance machines. Forces, fluxes, energies, currents and other parameters are calculated. 2. Problem 1 asks to find the force on a moving part of a translational motor given a current-position relationship. Problem 2 involves calculating force using energy and coenergy approaches for an electromagnetic system. 3. Problems 3-5 involve actuators, electromagnets and a moving-iron ammeter, calculating values like current, voltage, flux density, force, energy, inductance and deflection. Problem 6 examines a reluctance machine, finding rotor speeds that develop torque

Uploaded by

Yara
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 3

Problem Set 2 Electromechanical Energy Conversions

1. Consider a translational motor actuator with the following condition

𝑖 = 𝜆3/2 + 2.5𝜆(𝑥 − 1)2


For 0 < x < 1 m, where i is the current in the coil of the actuator. Find the force acting on the moving
part at x = 0.6 m.

2. Consider an electromagnetic system with the following condition

1.2𝑖 1/2
𝜆=
𝑔
Where g is the air gap length. If i = 2 A and g = 10 cm, find the mechanical force acting on moving part

a. By energy of the system.

b. By coenergy of the system.

3. Consider an actuator system as shown below with all dimensions are in centimeters. The magnetic
material is cast steel, with magnetization characteristics as shown below. The magnetic core and air
gap both consist of a square cross-sectional area. It consists of 500 turns with resistance of 4 Ω.

a. If gap is 1 mm, find

i. The coil current and required DC supply voltage to produce an air gap flux density of 0.5 T.

ii. The stored energy in the actuator system.

iii. The attraction force on the actuator arm.

iv. The inductance of the coil.


b. If the actuator arm is allowed to move with the air gap closed finally.

i. For zero air gap, find the flux density in the core, force on the arm and stored energy in the
actuator system.

ii. Excluding energy loss in the coil resistance, find the energy transfer between the DC source
and the actuator. Assume the arm is moved slowly. Find the direction of energy flow and how
much mechanical energy generated.

4. Consider an electromagnet lift system as shown It consists of 2500 turns with flux density in air gap
of 1.25 T. Assume the core material is ideal.

a. If gap is 10 mm, find

i. The coil current.

ii. The energy stored in the system.

iii. The force acting on the load, i.e., sheet of steel.

iv. The mass of the load, with gravity of 9.81 m/s2.

b. If gap is 2 mm, find the coil current required to lift the load.

5. Consider moving-iron ammeter as shown When current flows through the curved solenoid coil, a
curved ferromagnetic rod is pulled into the solenoid against the torque of a restraining spring with
spring constant of 0.65 x 10-3 Nm/rad. The coil consists of inductance of L = 4.5 + 18θ μH, where θ is
angle of deflection in radians, and resistance of 0.015 Ω.
a. Show the ammeter measures the rms of the current.

b. Find the deflection in degree for a current of 10 A (rms).

c. When 10 A (rms) at 60 Hz flows through the ammeter, find the voltage drop across the terminal.

6. Consider a reluctance machine as shown below. A current of 10 A (rms) at 60 Hz flows through its
stator coil. The inductance of stator winding is Lss = 0.1 – 0.3cos2θ – 0.2cos4θ H. Find

a. The values of rotor speed where the machine can develop an average torque.

b. The maximum torque and mechanical power that can be developed by the machine at each speed.

c. The maximum torque at zero speed.

Answer

1. λ2

2. – 226.3 N; – 226.3 N

3. (ai) 1.22 A; 4.88 V (aii) 0.38 J (aiii) 248.7 N (aiv) 0.512 H

(bi) 1.2 T; 1432 N; 0.9 J (bii) 1.068 J; from source to actuator; 0.548 J

4. (ai) 7.96 A (aii) 19.8 J (aiii) 1980 N (aiv) 201.6 kg (b) 3.98 A

5. (b) 79.4° (c) 0.186 V

6. (a) ±377 rad/s; ±188.5 rad/s (b) 15 Nm; 5655 W; 20 Nm; 3770 W (c) 62.5 Nm

You might also like