Indicator Lights

Indicator lights, often referred to as pilot lights, provide a visual indication of a circuit's operating condition. An indicator light may be wired to turn on for any predetermined condition. Indicator lights are available in round designs with 16 mm, 22 mm, or 30 mm mounting diameters as well as in square designs.

Figure 4.19: Different types of push buttons switch

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5.1 Electro-mechanical energy conversion

Energy is converted to electrical form because of the advantages listed in the introductory part of the note. It is seldom available or used in electrical form, but converted into electrical form at the input to a system and back to non-electrical form at the output of a system. A typical example is the processing of energy from and hydro generating plant. It is converted into electrical form at the power plant. Transmitted through transmission lines and distribution lines, and converted to mechanical energy in an electric motor are the point use.

A second example is in the conversion of the energy in sound pressure waves, and the transmission in electrical form from the taker to the listener in a telephone system. Few more energy conversion principles will be mentioned.

5.1.1 Major energy coversion principles

Energy conversion between electrical and non- electrical forms includes (i) Electrochemical eg battery

(ii) Electrothermal eg. Thermocouple (iii) Photo electrical eg photo cell

5.2 Energy coversion

itself. If the displacable part of the machine moves under force and does work, this can only be at the expense of the field energy of the permanent magnet, which must decrease. Such an

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arrangement has obvious limitations. It may also be inconvenient a permanent magnet”

lifting magnet, for example would not e capable of releasing its load. Where the magnetic affected by the movement is produced by a current circuit, changes of field energy have to be supplied electrically from a source. This implies the appearance in the circuit of an electromotive force e, which, with the current I, represents the delivery or absorption by the source of energy at the rate ei consider the elementary system of fig 2.1 A sources of voltage is connected to a device (e.g a secondary battery or a machine) in which the energy-conversion process results in the appearance of an e.f.m.

The effective resistance of the circuit is represented by R. if current flows into the circuit form the positive terminal of the source, and the input power p = Vi Rl + el, has the direction as shown at (a). However¸ if e >, the current reverses and we can now call it –e. the power input from the now p = v (-i) = Rl² + e (-l), which is negative, i.e it is an output from the device into the source, as at (b). to illustrate this simple but fundamental point, suppose that v = 10v d.c nad R = 1-2. then if e = 8vd.c.

The current o = v-e = 10-8 =2A R 1

And the source provides an input power p = 10 x 2 = 20w The converting device accepts 8 x 2 W as a motor And power loss due to plissipation = 1 x RT² = 4W Conversely, if e 12V, The current again is 10 -12 -2A (I.e reversed) The device produces 12 x 2 = 24 W as a generator of which RT² 2² x 1 = 4W is dissipated in R, and 10 x 20W is delivery as an output to the source. In the case of the electromagnetic machine, the relationship between the emf and the magnetic field is obtained from the faraday induction law (which had been mentioned in 1.1)

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5.3 Linked energy systems

An electromechanical machine forms a coverting link between an electrical energy system ( such as a main power –supply network) and a mechanical one (such as a prime- mover or a train). In action a machine is not an isolated things, but has a behavious strongly influenced by its terminal systems. A relay, for instance, will be affected if its operating battery becomes discharged; a loudspeaker will behave very differently it enclosed in an evacuated vessels with the air loading thus removed; a hydro electric generator, suddenly short-circuited, will react severely on the turbine and pipe-line.

A machine can, of course, be studies initially in isolation, but the engineering interest begins in fact when the complete linked system is considered. Again, the steady-state behavious is informative up to a point, but operation in responses to change – i.e, the transient responses is fro move important and fundamental.

Fig 2.1 Electro–mechanical linked energy system

System analysis can be complicated. Fig 2.2 shows diagrammatically a typical electric supply system feeding a mechanical load through an electromechanical machine. In some cases we might simplify the analysis by assuming, say, that the terminal voltage and frequency of the machine were constant. This is good enough if the machine is a small contactor but if it is a 25MW motor the effects of its behaviour reach for back through even an extensive supply system. Methods are available for evaluating such a complex for any

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given stimulus, such as the occurrence of a transmission- line fault or starting of a large motor.

5.4 Energy storage

We now consider how a flux is established and energy is stored in simple toroidal magnetic Circuit of cross sectional area A, path length L, and of material of constant permeability u, The flux is to be established by a current i, in a uniformly wound coil of N-turns. In order To concentrate on energy storage we neglect the coil resistance. With i initially zero, let a Voltage V, be applied to the coil terminals, what happen thereafter depends on Faraday’s Law of electromagnetic induction.

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5.5 Energy balance

Fig: 2.1 Electromechanical machine conventions

A machine accepts energy in a variety of forms from its attached terminal systems. By conversion we take energy input as positive, so that an output is regarded as a negative input.

The machine internally electrical energy- mechanical energy is a motor mechanical energy to electrical energy is a generator converts some energy, stores some, and dissipates the rest:

these energies are positive if they increase with time. As the prime object of a machine is conversion to useful output, one of the terminal inputs will normally be negative. Recalling the principle of conservation of energy which states that energy is neither created nor destroyed and combining it with the laws of electric and magnetic fields, electric circuits and Newtonian mechanics, the energy balance can be expressed as:-

Total terminal energy input internal energy + Dissipation 2.1 for an electromechanical machine using a magnetic field as the means of conversion, the balance can be stated in more specific terms as electrical energy input + mechanical energy input

= stored magnetic –field energy + stored mechanical energy + Dissipation

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Reckoned from an initial condition of zero energy, w = o.A comparable relation must apply to energy changes dw, and also to energy rate dw/dt i.e to power, P. in corresponding symbols these relations are total energy w_f + w_s + w 2.2(a)

Energy change dwe + dwm = dwf + dws + dw 2.2(b) Energy rate P_e + p_m = dw_f + dw_s + p 2.2(c)

dt dt

The rates of change of stored field energy wf and stored mechanical energy, w_s, are left in differential form because there is always a practical limit to storage. A magnetic field can not grow in strength indefinitely when ferromagnetic materials is employed; and if the kinetic energy in a flywheel is continually increased, the speed must rise and the wheel may burst under centrifugal force.

We shall now examine the electromechanical machine in more detail with fig 2.3. The machine links an electric source of voltages supplying a current; and a mechanical sources represented by a bar moving to positive directions, thus both vi and f_mu are inputs ( The mechanical source could alternatively be a shaft rotated at angular speed wr by a tongue mm to give an input power m_nw_r ). The electrical end of the machine is precisely that of fig 2.1 (a), with opposing v. the mechanical end has the magnetically developed force fe opposing fm > fm it can reverse speed w so that the mechanical system is driven and absorbs a mechanical output.

The behavior can now be summarized. With the machine operating in the steady state as a motor, the applied voltage u drive +I against e to give a total electrical power input pe = u(+e), of which the part ei is converted. The outcome of conversion is the force fe which drives the bar against fm to develop the mechanical input pm = fm (-u) which, being

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negative, is actually an output. With the machine as a generator; the bar is driven at speed u by the force fm to provide the mechanical input pm = fm ( +u), as a result which e now exceeds u and reverse the current to provide the negative electrical input (i.e output (i.e output) pe = u (-i) the sum of the inputs (pe +pm) must be rate of rise of internal energy storage plus the rate of energy dissipation.

A real electromagnetic machine has fairly obvious points of attachment (e.g the electrical terminals and the shaft) by which it is connected to the electrical and mechanical sources to form a link between them. But it is very to concentrate source to from link between them.

But it is very convenient attention on the conversion region enclosed by the chain- dotted line in fig 2.3, for it contains only the essential quantities e and i,. U and fe. Various losses, and the mechanical storage, are excluded so that attention can be directed on to the physical process if useful energy conversion by electromagnetic means outside the conversion region we can account for conduction and core losses associated with the electrical end and represented rough by the resistance R in fig 2.3, and friction and similar losses on the mechanical side. It is to be noted that the externally applied force fm is not necessarily equal to –fe because there may be force-absorbing components of inertial and elasticity in the mechanical working parts of the machine itself, as well as internal friction.

The machine has new been reduced to an analyzable form. Its behaviors under specified conditions involves the forces and movement of the mechanical parts, the voltages and current at the electrical terminals and processes of energy conversion and storage and dissipation going on inside. Evaluation is based on the well-established principles and laws summarized in the following table.

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Part of system Quantities Principles

Electrical Voltage, current Faraday-Lenz and Kirchhoff laws

5.5.1 Block diagram for energy balance equation

The energy balance equation is given by equation 2.2 as electrical energy input mechanical energy input

= stored magnetic-=field energy + stored mechanical energy + dissipation The dissipation (energy lossess) arise from three main causes

(ii) Part of electrical energy is converted directly to heat in the resistance of current path.

(ii) Part of mechanical energy developed with the device is absorbed in friction ad windage and converted to heat.

(iii) Part of the energy absorbed by the coupling field is converted to heat in magnetic core losses (for magnetic coupling ) or dielectric loss) for electric coupling).

if we associate the various losses with the corresponding energies, equation 2.2 be written as Electrical energy mechanical energy increase in energy stored

Input minus = Output plus friction + in the coupling field Resistance losess and windage losses plus associated losses

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Equation 2.3 is obtained ( for a motor) with the mechanical energy transferred to the R.H.S of the equality sign and neglecting the energy mechanical stored energy ( for a machine without a flywheel and neglecting the mass of the shaft). If there is a flywheel, the stored mechanical energy is 1/2mu2 or ½ mr2w2

Where m = mass of flywheel

V = linear velocity of rotating wheel w = angular velocity of rotating wheel r = radius of flywheel

Equation 2.3 may be represented in the form of a block diagram as shown in fig 2.4 Fig 2.4 General representation of electromagnetic energy conversion. Fro a generator action, the positions of the electrical system and that or the mechanical system will be interchanged.

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5.6 Magnetic field energy and forces

In order to be able to analyse mathematically the electromechanical system that is completely described by the energy balance equation, we need to be able to determine qualitatively the energy of the magnetic field and the associated force.

5.6.1 Magnetic field

A magnetic field is a region of space in which certain physical effects occurs in particular the development of mechanical force. A pictorial model of the field can be made by drawing closed loops of magnetic flux, such that their direction and spacing at any point are a measure of the flux density. The magnetic circuit in the present context is composed partly of ferromagnetic material such as iron, and partly of an airgap. The iron serves to “guide” the flux in a desired path; the airgap is necessary to make useful magnetic effects readily accessible.

The lines in a flux plot have no real existence. In a given region a magnetic field may change direction, become weaker in some place and stronger in others.

5.6.2 Magnetic circuit n/a

Engineers look upon magnetic flux (Weber) as produced by electric current. A current I develops around any path that links it a magneto motive force (M.M.F) F = I (ampere). The effect of a current can be multiplied. By coiling the electric circuit into N turns so that around a path linking all N turns the m.m.f is N times as great, giving F =- ampere- turn.

The m.m.f is distributed along the path, to give along a path element of length dx the magnetic field intensity h (ampere-turn/ metre). The summation of Hdx around a single loop closed with F i.e F = Hdx = m.m.d.

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At any point, H gives rise to a flux density B = NH (tesla or Weber/m²) our Henry/meter]

Flux summation of the flux density over the area available to the flux path given the total

Where s = the total reluctance (ampere-turn per weber]

And = 1/s = total permeance [ weber per ampere-turn]

For a path- length x of materials of absolute permeability U, and having a uniform cross- sectional area A over which the density B is everywhere the same, the mmf f require = N x x

= Hx…………..2.8 If, however the parts are in parallel and share the flux

F = fx =fy =fz and

For fields in ferromagnetic materials U is very much greater, and the relative permeability Nr

=u =Uo 4 /107 1/80000

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Which means that H = Ub = 800000B

For field ferromagnetic materials U is very much greater, Ad the relative permeability Ur = U

Uo

Since, usually Ur is large, then it is convenient ( it simplies analysis) to assume that the whole mmf is required for the excitation of the air gap i.e the whole of the field energy is stored in the air-gap

5.7 Magnetic field energy

With the assumption that the magnetic filed energy is concentrated within the air gap. It becomes easy to calculated the magnetic field energy.

A magnet attract on iron bar. If the iron bar is light enough and the magnet filed is enough, the bar will be seen to move up to get attached to the magnet. The movement of the bar signifies that work is done, since the iron bar has mass and covered some distance

(work done = force x distance). This means that the space that the file occupies (the field region) can demonstrated or has on attribute of force. And hence, the filed region must process some energy. If can be easily noticed that the force is strong when the air gap is short but rapidly diminishes as the air gap length is increased.

5.8 Maxwell stress

Fig 2.5 maxwell forces

Maxwell formulated the concept that the forces is transmitted across the gap between a pair of magnetized surface as a result of two stresses. If at a point in the gap the flux density is B and the corresponding field intensity is H =B/U,. then there is a tensile stress of magnitude

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1.2 BH along the direction of a flux line and a compressive stress ½ BH along all directions at right angles to a flux line.

Fig 2.5 shows two iron bars forming part of magnetic circuit when, as at (a), the polar surfaces are close together, the flux is mainly concentrated between the surfaces. The density B is large, and so therefore is H, and ½ BH represented a strong tensile force of attraction between the faces. Not all the flux is useful; some, of the leakage flux, exists at the sides of each bar. Flux crossing the boundary between air and a high permeable materials must enter or leave the boundary between air and a high permeable materials must enter or leave the boundary almost at right angles, so that the tensile stress due to faces. All the comprehensive stresses balance out by symmetry.

In case (b), the greater reluctance of the long air gap reduces the total flux, the useful flux density of the pole faces is smaller while the leakage flux is much greater hence the forces of attraction between the pole faces is much less than in case (a)

In most practical applications, the air gap is small enough to enable us assumes a uniform flux density over the polar area. i.e in the air gap.

.

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5.9 ENERGY DENSITY

The Maxwell stress concept is another way of saying that the energy to the value

½ BH is stored in a unity cube of the space occupied by = magnetic, thus ½ BH is the energy density [weber (metre²) x (amper/metre] = volt –second x ampere/cubic metre

= Joule /cubic metre.

Fig 2.6 magnetic energy.

Consider an air gap, initially unmagnetized. Apply a magnetic force to the gap, an increase of H from zero causes the flux density B = μoH to increase proportionately, Fig 2.6(o). The energy (m³ is [HdB, and for and values Bi and H1 the final energy density (shaded area) is clearly ½ B1H1 . The some summation applies to a filed set up by in a ferromagnetic matter, with similar result Fig. 2.6 (b0, if the permeability U is constant; but for the same and density B1 a much smaller magnetizing force Hii is need and much less energy is stored.

If the ferromagnetic materials is subjected to saturation, the stored energy is as shown in Fig 2.6(c0 and is calculated by piece-wise approximation to composite area of DOAD plus area of trapezium AB,CD.

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5.10 FARADAY- LENZ LAW

When the flux 4 associated with an electric increase in time at by amount d4, an emf, e = de/dt appears in the circuit. The minus sign implies that the direction of the emf is such that a current produced by it in the circuit opposes the change d4.

Flux-linkage 4 (weber- turn] is the product of a magnetic flux and the number of turns through which it passes in the same direction. Since the current is proportional the flux,

then flux likage Ų = NQ

Since we are neglecting the coil resistance, then around the electric circuit loop formed by the voltage source and the N turns of coil on the toroid, the KVL gives

u = +Dq/DT =-E. 2.17

The instantaneous electric power input to the coil P =vi = (dw/dt)i

The total energy required to establish from zero a flux Q1 and a linkage Q1, (corresponding to a current mmf F₁ =Ni) is

Wf = (^t pdt = (⁴ idQ =(^Q fdQ

Since the core of the toroid has constant permeability.

Which is represented by the shaded area in Fig, 2. 6 (d). this magnetically stored energy can be assumed to be uniformly distributed through the active volume Al of the core. Then because

Q₁ = Q_IN =NB,A and Nli =Fi =H il The energy density = ½ 4ili/Al =1/2 Bi Hi

The total magnetic energy can be stated in several ways [f =1/24I =1/2QF =1/2Q²S =1/2 F²S =1/2Q / 1/2F² =1/2Li²]

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Also, since Q BA and F =Hl and H =B/U Then wf =1/2 QF =1/2 BAHL =1/2AL

U But al = volume

Wf = Vol. B²

2U

Any expression for the energy of the field wf in equation 2.32 and 2.23 may be employed depending on the parameters given.

5.11 ENERGY CONVERSION

Fig. 2.7 Energy change with position

Fig 2.7 (a) shows airgap region and existing coil of a magnetic circuit, the ferromagnetic

Fig 2.7 (a) shows airgap region and existing coil of a magnetic circuit, the ferromagnetic

In document EEC 233 Theory (Page 49-75)