BEEE 104 Lecture Slides 3 (1).pdf

Electromechanical Energy Conversion and Transformers Electromechanical Energy Conversion 12/07/2024 Prepared by C. K. Dzah 1 Electromechanical Energy Conversion and Transformers 12/07/2024 Prepared by C. K. Dzah 2 Electromechanical Energy Conversion and Tra...

Electromechanical Energy Conversion and Transformers Electromechanical Energy Conversion 12/07/2024 Prepared by C. K. Dzah 1 Electromechanical Energy Conversion and Transformers 12/07/2024 Prepared by C. K. Dzah 2 Electromechanical Energy Conversion and Transformers LEARNING OUTCOME To know the three main classifications of electromechanical energy conversion devices To understand and apply Lorentz’s force law to determine force and torque in magnetic field To be able to calculate the generated voltage in a magnetic systems To understand the principle of induction in electrical machine To know the two types of mechanical force developed by electromagnetic system 12/07/2024 Prepared by C. K. Dzah 3 Electromechanical Energy Conversion and Transformers Introduction The conversion of electrical energy into mechanical energy is called electromechanical energy conversion. It is based on the principles of conservation of energy and involves an interchange of energy between an electrical and mechanical systems through a coupling field 12/07/2024 Prepared by C. K. Dzah 4 Electromechanical Energy Conversion and Transformers Any electromechanical system consists of the following components: 1.Electrical System 2.Mechanical System 3.Coupling Field 12/07/2024 Prepared by C. K. Dzah 5 Electromechanical Energy Conversion and Transformers Basic Electromechanical Energy Conversion Devices FORCE TRANSDUCERS PRODUCING DEVICES CONTINUOUS ENERGY CONVERSION DEVICES 12/07/2024 Prepared by C. K. Dzah 6 Electromechanical Energy Conversion and Transformers Transducers They convert electrical energy to mechanical energy and vice-versa. These conversion devices are used for measurement, control and alarm indicators. They operate under linear input-output conditions for relatively small signals. Example:- Microphones, Loudspeakers etc 12/07/2024 Prepared by C. K. Dzah 7 Electromechanical Energy Conversion and Transformers One Another Form of Form of Energy Energy 12/07/2024 Prepared by C. K. Dzah 8 Electromechanical Energy Conversion and Transformers Force Producing Devices These conversion devices are used for producing force or torque. They have limited mechanical motion. Example:- Relays, Solenoids etc 12/07/2024 Prepared by C. K. Dzah 9 Electromechanical Energy Conversion and Transformers 12/07/2024 Prepared by C. K. Dzah 10 Electromechanical Energy Conversion and Transformers 12/07/2024 Prepared by C. K. Dzah 11 Electromechanical Energy Conversion and Transformers Continuous Energy Conversion Devices These devices continuously convert electrical energy into mechanical energy and vice-versa. They are used for generation and utilisation of energy in bulk quantities. Example:- Motors and Generators 12/07/2024 Prepared by C. K. Dzah 12 Electromechanical Energy Conversion and Transformers MOTOR Electrical Mechanical Energy Energy GENERATOR 12/07/2024 Prepared by C. K. Dzah 13 Electromechanical Energy Conversion and Transformers Forces and Torques in Magnetic Fields Lorentz force, the force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B. The entire electromagnetic force F on the charged particle is called the Lorentz force and it is given by F = qE + qv × B. 12/07/2024 Prepared by C. K. Dzah 14 Electromechanical Energy Conversion and Transformers F = q E + qv  B Electric Magnetic force force According to Lorentz’s force law, in pure magnetic field systems, the force on a moving particle of charge q is indicated by the vector product; F =q v  B ( ) 12/07/2024 Prepared by C. K. Dzah 15 Electromechanical Energy Conversion and Transformers where v is the velocity in m/s of the particle of charge q moving in a magnetic field density of B Tesla. 12/07/2024 Prepared by C. K. Dzah 16 Electromechanical Energy Conversion and Transformers 12/07/2024 Prepared by C. K. Dzah 17 Electromechanical Energy Conversion and Transformers Force Between Two Parallel Current Carrying Conductors when a current-carrying conductor is brought near another current-carrying conductor, a magnetic force is experienced between the wires. two parallel wires of length l separated by a distance d currents iA and iB flowing in opposite directions in these parallel wires 12/07/2024 Prepared by C. K. Dzah 18 Electromechanical Energy Conversion and Transformers Magnetic field due to conductor B is given by IB H= 2 d Force acting on conductor A, F = BIAl Where B is the flux density of the field due to conductor B Force, F = o r H  I A  l 12/07/2024 Prepared by C. K. Dzah 19 Electromechanical Energy Conversion and Transformers The force exerted on iA will be in an outward direction with a magnitude of iB i AiB l F = Bil sin  = i A  o  l = o N 2 d 2 d 12/07/2024 Prepared by C. K. Dzah 20 Electromechanical Energy Conversion and Transformers Magnetic Field due to Current Carrying Conductor The forces between two parallel currents are of two types: Attractive: When current is flowing in the same direction in both wires then attractive force is exerted. Repulsive: When current is flowing in the opposite direction in both wires then repulsive force is exerted. 12/07/2024 Prepared by C. K. Dzah 21 Electromechanical Energy Conversion and Transformers 12/07/2024 Prepared by C. K. Dzah 22 Electromechanical Energy Conversion and Transformers Considering two parallel current-carrying wires, separated by a distance ‘d’, such that one of the wires is carrying current I1 and the other is carrying I2. We can say that wire 2 experiences the same magnetic field at every point along its length due to wire 1. Using the Right-Hand Thumb rule we can determine the direction of magnetic force. The magnitude of the field due to the first conductor can be calculated using Ampere’s Circuital Law, 12/07/2024 Prepared by C. K. Dzah 23 Electromechanical Energy Conversion and Transformers Ampere’s Circuital Law states that; the line integral of magnetic field around a closed path is equal to the product of the magnetic permeability of that space and the total current through the area bounded by that path. The force on a segment of length L of wire 2 due to wire 1 can be given as, F21 = I2LB1 = (μ0I1I2 / 2πd) L 12/07/2024 Prepared by C. K. Dzah 24 Electromechanical Energy Conversion and Transformers Similarly, we can calculate the force exerted by wire 2 on wire 1. We see that wire 1 experiences the same force due to wire 2 but the direction is opposite. Thus, F12 = -F21 Also, the currents flowing in the same direction make the wires attract each other and that flowing in the opposite direction makes the wires repel each other. We can find the magnitude of the force acting per unit length by the formula, 12/07/2024 Prepared by C. K. Dzah 25 Electromechanical Energy Conversion and Transformers Fba = μ0IaIb / (2πd) where, d is the distance between two conducor Ia is the current in wire 1 Ib is the current in wire 2 12/07/2024 Prepared by C. K. Dzah 26 Electromechanical Energy Conversion and Transformers Example 1: Two current-carrying wires of equal length are parallel to one another and spaced 4.8 m apart, producing a force of 1.5 10-4 N per unit length. What will be the force per unit length on the wire if the current in both wires is doubled and the distance between the wires is halved? 12/07/2024 Prepared by C. K. Dzah 27 Electromechanical Energy Conversion and Transformers Force per unit length on both wires fab = fba = f = 1.5 × 10-4 N distance (d) = 4.8m The force per unit length on wires is given as, fab = fba = f = μ0IaIb / 2πd (1) when the current in both wires is doubled, I’a = 2Ia I’b = 2Ib Distance between the wires is halved, d’ = d/2 12/07/2024 Prepared by C. K. Dzah 28 Electromechanical Energy Conversion and Transformers equation (1) can be written as, f’ab = f’ba = f’ = μ0I’aI’b / 2πd’ f’ = 2 × (μ0×2Ia×2Ib / 2πd) f’ = 8 × (μ0×Ia×Ib / 2πd) f’ = 8f f’ = 8 × 1.5 × 10-4 N f’ = 12 × 10-4 N 12/07/2024 Prepared by C. K. Dzah 29 Electromechanical Energy Conversion and Transformers Example 2: Two very long wires are placed parallel to each other and separated by a distance 3m apart. If the current in both the wires is 6A, then the force per unit length on both wires will be Solution Current in both the wires Ia = Ib = 6A distance (d) = 3m The force per unit length is given as, fab = fba = f = μ0IaIb / 2πd —(1) from equation (1), 12/07/2024 Prepared by C. K. Dzah 30 Electromechanical Energy Conversion and Transformers f = (μ0×6×6) / (2π×3) f = (6μ0/π) × (4/4) f = 24μ0 / 4π —(2) f = 24 × 10-7 N 12/07/2024 Prepared by C. K. Dzah 31 Electromechanical Energy Conversion and Transformers Force Between Two Current-Carrying Wires 12/07/2024 Prepared by C. K. Dzah 32 Electromechanical Energy Conversion and Transformers Example 3 The two conductors are 2 cm apart, and both carry 2000 A of current in opposite directions as shown in the figure above. What is the force on each conductor if both wires are 1 m long? Solution i1i2l −7 2000  2000  1 F = o = 4  10  = 40 N 2 d 2  0.02 12/07/2024 Prepared by C. K. Dzah 33 Electromechanical Energy Conversion and Transformers Example 4: If 8 A of current flows in the first wire, 11 A of current flows in the second wire. The distance between two wires is 15 m and find the magnetic force between the two wires. 12/07/2024 Prepared by C. K. Dzah 34 Electromechanical Energy Conversion and Transformers Solution Given that Current in the first wire Ia = 8 A Current in the second wire Ib = 11 A Distance between two wires d = 15 m F/L = μ0 × Ia × Ib /(2πd) = 4π x 10-7 × 8 × 11/(2π × 15) = 176 × 10-7/15 =11.733 × 10-7 N Therefore, the magnetic force between two wires is 11.733 × 10-7 N. 12/07/2024 Prepared by C. K. Dzah 35 Electromechanical Energy Conversion and Transformers Magnetic flux lines without current flowing Magnetic flux lines with current flowing 12/07/2024 Prepared by C. K. Dzah 36 Electromechanical Energy Conversion and Transformers Magnetically Induced EMFs (Voltages) A very important effect of a magnetic field on an electric circuit is that when the flux linking the circuit changes, an emf is induced. This effect is described by Faraday’s Law, which state that; the magnitude of emf ( or voltage) is directly proportional to the rate of change of flux linkages or to the product of number of turns and rate of change of flux linking the coil 12/07/2024 Prepared by C. K. Dzah 37 Electromechanical Energy Conversion and Transformers d d e=N = dt dt The direction of induced emf is governed by Len’s law which states that; the direction of induced emf or voltage is such that the current produced by it sets up a magnetic field opposing the flux change. The minus (-) sign required just to indicate the phenomenon explained by Lenz’s law. 12/07/2024 Prepared by C. K. Dzah 38 Electromechanical Energy Conversion and Transformers Generated Voltage in Magnetic systems 12/07/2024 Prepared by C. K. Dzah 39 Electromechanical Energy Conversion and Transformers Voltage Induced on a Moving Conductor 12/07/2024 Prepared by C. K. Dzah 40 Electromechanical Energy Conversion and Transformers 12/07/2024 Prepared by C. K. Dzah 41 Electromechanical Energy Conversion and Transformers The straight wire PQ is moving at constant velocity at right angles to a uniform magnetic field, directed into the plane of the page. Wires PS and QR are fixed and continue to make contact with the moving wire. As PQ moves to the right, the flux linkage in the circuit SPQR reduces since the area reduces and a voltage is induced between S and R. 12/07/2024 Prepared by C. K. Dzah 42 Electromechanical Energy Conversion and Transformers A voltmeter may be connected between S and R and this then measures the open circuit voltage induced between the ends of the moving wire, but does not allow current to flow around the circuit. 12/07/2024 Prepared by C. K. Dzah 43 Electromechanical Energy Conversion and Transformers 12/07/2024 Prepared by C. K. Dzah 44 Electromechanical Energy Conversion and Transformers Principle of Induction in electrical machine Principle of Induction: Is the essential production of an e.m.f by magnetic means via an interlinked electrical and magnetic circuits. If flux is made to change, an e.m.f is induced in the electric circuit 12/07/2024 Prepared by C. K. Dzah 45 Electromechanical Energy Conversion and Transformers 12/07/2024 Prepared by C. K. Dzah 46 Electromechanical Energy Conversion and Transformers The induction motor is an A.C electrical machine that converts electrical energy into mechanical energy. The core here acts as a medium for carrying and concentrating the magnetic flux generated by the coil during operation. 12/07/2024 Prepared by C. K. Dzah 47 Electromechanical Energy Conversion and Transformers According to Ohms law, the current in a conductor is directly proportional to terminal voltage, According to Lenz’s law, ‘A conductor carrying a current will generate a magnetic field around its surface. A magnetic field will be generated by each loop in both coils. This entire flux will appear on the iron core as the coil was wound on the core body. 12/07/2024 Prepared by C. K. Dzah 48 Electromechanical Energy Conversion and Transformers During the positive cycle of the AC power source, the current in both windings increases gradually from zero to maximum and then gradually goes back from maximum to zero. 12/07/2024 Prepared by C. K. Dzah 49 Electromechanical Energy Conversion and Transformers During the negative cycle of the sinusoidal voltage, the positive voltage at point ‘B’ will gradually goes from zero to maximum and then comes back to zero. 12/07/2024 Prepared by C. K. Dzah 50 Electromechanical Energy Conversion and Transformers A constantly changing magnetic field is the most basic and important requirement for electromagnetic induction. This is the principle of Faraday's law of electromagnetic induction. 12/07/2024 Prepared by C. K. Dzah 51 Electromechanical Energy Conversion and Transformers Since the law is universal, the conductor loop of the rotor must also generate a magnetic field because the current is flowing through it as a result of electromagnetic induction. If we call the magnetic field generated by stator windings and iron core setup as Main flux or Stator flux. Then we can call the magnetic field generated by the conductor loop of the rotor as Rotor flux. 12/07/2024 Prepared by C. K. Dzah 52 Electromechanical Energy Conversion and Transformers Because of the interaction between Main flux and the Rotor flux a force gets experienced by the rotor. This force tries to oppose the EMF induced into the rotor by adjusting the position of the rotor. Hence we will experience a movement in the shaft position at this time. Now the magnetic field keeps changing because of alternating voltage the force also keeps adjusting the rotor position continuously without stop. 12/07/2024 Prepared by C. K. Dzah 53 Electromechanical Energy Conversion and Transformers So the rotor keeps rotating because of alternating voltage and thereby we have mechanical output at the shaft or the axis of the rotor. Have seen how because of Electromagnetic induction into the rotor we have mechanical output at the shaft. So the name given for this setup is called Induction Motor. 12/07/2024 Prepared by C. K. Dzah 54 Electromechanical Energy Conversion and Transformers 12/07/2024 Prepared by C. K. Dzah 55 Electromechanical Energy Conversion and Transformers Applications of Single Phase Induction motors Electric fans in the home Drilling machines Pumps Grinders Toys Vacuum cleaner Exhaust fans Compressors and electric shavers 12/07/2024 Prepared by C. K. Dzah 56 Electromechanical Energy Conversion and Transformers Applications of Three Phase Induction motors Small scale, Medium-scale and large scale industries. Lifts Cranes Driving lathe machines Oil extracting mills Robotic arms Conveyers belt system Heavy crushers 12/07/2024 Prepared by C. K. Dzah 57 Electromechanical Energy Conversion and Transformers Force Developed in an Electromagnetic System An electromagnetic system can develop a mechanical force in two ways: 1. By alignment 2. By interaction 12/07/2024 Prepared by C. K. Dzah 58 Electromechanical Energy Conversion and Transformers Force of Alignment 12/07/2024 Prepared by C. K. Dzah 59 Electromechanical Energy Conversion and Transformers Reluctance motor utilises force of alignment 12/07/2024 Prepared by C. K. Dzah 60 Electromechanical Energy Conversion and Transformers Force of Interaction 12/07/2024 Prepared by C. K. Dzah 61 Electromechanical Energy Conversion and Transformers 12/07/2024 Prepared by C. K. Dzah 62 Electromechanical Energy Conversion and Transformers 12/07/2024 Prepared by C. K. Dzah 63