DC MACHINES (17CA02301) - Crectirupati
LECTURE NOTESONDC MACHINES(17CA02301)2018 – 2019II B. Tech I Semester (CREC-R17)Mr. K.Raju, Assistant ProfessorCHADALAWADA RAMANAMMA ENGINEERING COLLEGE(AUTONOMOUS)Chadalawada Nagar, Renigunta Road, Tirupati – 517 506Department of Electrical and Electronics EngineeringJAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY ANANTAPUR
DC MACHINESIII Semester: EEECourse CodeCategory17CA02301CoreContact Classes: 34Hours / WeekCreditsLTPC22-3Tutorial Classes: 34Practical Classes: NilMaximumMarksTotaCIA SEEl3070100Total Classes: 68OBJECTIVES:To make the students learn about:I. The constructional features of DC machines and different types of winding employed inDC machinesII. The phenomena of armature reaction and commutationIII. Characteristics of generators and parallel operation of generatorsIV. Methods for speed control of DC motors and applications of DC motorsV.Various types of losses that occur in DC machines and how to calculate efficiencyVI. Testing of DC motorsPRINCIPLES OF ELECTROMECHANICAL ENERGYUNIT-IClasses: 12CONVERSIONSources of dc Supply- Electromechanical Energy Conversion – Forces and Torque In MagneticField Systems – Energy Balance – Energy and Force in a Singly Excited Magnetic Field System,Determination of Magnetic Force - Co-Energy – Multi Excited Magnetic Field Systems.UNIT-IIClasses: 14D.C. GENERATORS –ID.C. Generators – Principle of Operation – Constructional Features – Armature Windings – Lapand Wave Windings – Simplex and Multiplex Windings – Use of Laminated Armature – E. M.FEquation– Numerical Problems – Parallel Paths-Armature Reaction – Cross Magnetizing andDe-Magnetizing AT/Pole – Compensating Winding – Commutation – Reactance Voltage –Methods of Improving Commutation.UNIT-III D.C GENERATORS – IIClasses: 14Methods of Excitation – Separately Excited and Self Excited Generators – Build-Up of E.M.F Critical Field Resistance and Critical Speed - Causes for Failure to Self-Excite and RemedialMeasures-Load Characteristics of Shunt, Series and Compound Generators – Parallel Operationof D.C Series Generators – Use of Equalizer Bar and Cross Connection of Field Windings –Load Sharing- Applications of DC generators.UNIT-IVD.C. MOTORSClasses: 14D.C Motors – Principle of Operation – Back E.M.F.– Circuit Model – Torque Equation –Characteristics and Application of Shunt, Series and Compound Motors – Armature Reaction
and Commutation.Speed Control of D.C. Motors: Armature Voltage and Field Flux ControlMethods. Ward-Leonard System–Braking of D.C Motors – Permanent Magnet D.C Motor(PMDC). Motor Starters (3 Point and 4 Point Starters) – Protective Devices-Calculation ofStarter Steps for D.C Shunt Motors.UNIT-VTESTING OF DC MACHINESClasses: 14Losses – Constant & Variable Losses – Calculation of Efficiency – Condition for MaximumEfficiency. Methods of Testing – Direct, Indirect – Brake Test – Swinburne’s Test –Hopkinson’s Test – Field’s Test – Retardation Test- Applications of DC Motors.Text Books:1. Electric Machines by I.J. Nagrath & D.P. Kothari, Tata Mc Graw – Hill Publishers, 3rdEdition, 2004.2. Electrical Machines – P.S. Bimbhra., Khanna Publishers, 2011.Reference Books:1. Performance and Design of D.C Machines – by Clayton & Hancock, BPB Publishers, 2004.2. Electrical Machines -S.K. Battacharya, TMH Edn Pvt. Ltd., 3rd Edition, 2009.3. Electric Machinary – A. E. Fitzgerald, C. Kingsley and S. Umans, Mc Graw-Hill Companies,5th Editon, 2003.4. Electrical Machines – M.V Deshpande, Wheeler Publishing, 2004.5. Electromechanics – I - Kamakshaiah S., Overseas Publishers Pvt. Ltd, 3rd Edition, 2004.Web w.freevideolectures.comhttps://www.ustudy.in › Electrical Machineshttps://www.freeengineeringbooks.comE-Text Books:1. https://www.textbooksonline.tn.nic.in2. https://www.freeengineeringbooks.com3. m4. https://www.books.google.co.inCourse Outcomes: At the end of course, the student will be able to Understand the construction and principle of working of DC Machines Diagonise the failure of DC generator to build up voltage Understand the gross torque and useful torque developed by DC motor Understand the suitable methods and conditions for obtaining the required speed of DCmotor Understand the Calculations of losses and efficiency of DC generators and motors Over view of Applications of DC Machines.
UNIT-IUNIT IPRINCIPLES OF ELECTROMECHANICALPRINCIPLES OF ENERGY CONVERSIONPrinciples of ElectromechanicalELECTROMECHANICALENERGY CONVERSIONEnergy ConversionTopics to cover:1) Introduction4) Force and Torque Calculation from2) EMF in Electromechanical Systems3) Force and Torque on a ConductorEnergy and Coenergy5) Model of Electromechanical SystemsIntroductionFor energy conversion between electrical and mechanical forms, electromechanicaldevices are developed. In general, electromechanical energy conversion devices can bedivided into three categories:(1) Transducers (for measurement and control)These devices transform the signals of different forms. Examples are microphones,pickups, and speakers.(2) Force producing devices (linear motion devices)These type of devices produce forces mostly for linear motion drives, such as relays,solenoids (linear actuators), and electromagnets.(3) Continuous energy conversion equipmentThese devices operate in rotating mode. A device would be known as a generator ifit convert mechanical energy into electrical energy, or as a motor if it does the otherway around (from electrical to mechanical).Since the permeability of ferromagnetic materials are much larger than the permittivity ofdielectric materials, it is more advantageous to use electromagnetic field as the medium forelectromechanical energy conversion. As illustrated in the following diagram, anelectromechanical system consists of an electrical subsystem (electric circuits such aswindings), a magnetic subsystem (magnetic field in the magnetic cores and airgaps), and amechanical subsystem (mechanically movable parts such as a plunger in a linear actuator anda rotor in a rotating electrical machine). Voltages and currents are used to describe the
Principle of Electromechanical Energy Conversionstate of the electrical subsystem and they are governed by the basic circuital laws: Ohm'slaw, KCL and KVL. The state of the mechanical subsystem can be described in terms ofpositions, velocities, and accelerations, and is governed by the Newton's laws. The magneticsubsystem or magnetic field fits between the electrical and mechanical subsystems and actingas a "ferry" in energy transform and conversion. The field quantities such as magnetic flux,flux density, and field strength, are governed by the Maxwell's equations. When coupled withan electric circuit, the magnetic flux interacting with the current in the circuit would producea force or torque on a mechanically movable part. On the other hand, the movement of themoving part will could variation of the magnetic flux linking the electric circuit and inducean electromotive force (emf) in the circuit. The product of the torque and speed (themechanical power) equals the active component of the product of the emf and current.Therefore, the electrical energy and the mechanical energy are inter-converted via themagnetic field.Concept map of electromechanical system modelingIn this chapter, the methods for determining the induced emf in an electrical circuit andforce/torque experienced by a movable part will be discussed. The general concept ofelectromechanical system modeling will also be illustrated by a singly excited rotatingsystem.2
Principle of Electromechanical Energy ConversionInduced emf in Electromechanical SystemsThe diagram below shows a conductor of length l placed in a uniform magnetic field offlux density B. When the conductor moves at a speed v, the induced emf in the conductor canbe determined bye lv BThe direction of the emf can be determined by the "right hand rule" for crossproducts. In a coil of N turns, the induced emf can be calculated bye d dtwhere is the flux linkage of the coil and the minus sign indicates that the induced currentopposes the variation of the field. It makes no difference whether the variation of the fluxlinkage is a result of the field variation or coil movement.In practice, it would convenient if we treat the emf as a voltage. The above express canthen be rewritten ase d L di i dLdx dt dt dx dtif the system is magnetically linear, i.e. the self inductance is independent of the current. Itshould be noted that the self inductance is a function of the displacement x since there is amoving part in the system.Example:Calculate the open circuit voltage between the brushes on a Faraday's disc as shownschematically in the diagram below. rShaftr2r1BrushesvBSN 3SN
Principle of Electromechanical Energy ConversionSolution:Choose a small line segment of length dr at position r (r 1 r r2)from the center of the discbetween the brushes. The induced emf in this elemental length is thende Bvdr B r rdrwhere v r r. Therefore,rr22r2e de B r rdr r B2r1r r Br2 r22121Example:Sketch L(x) and calculate the induced emf in the excitation coil for a linear actuatorshown below.A singly excited linear actuatorSolution:and2L x NRg x 2gRg x o d x l N 2 l d x L x 2 goe d L di i dL dxdtdtdx dt2di N lo L x dt i 2 g v4
Principle of Electromechanical Energy ConversionL(x)L(0)OdXInductance vs. displacementIf i Idc,2 N le I dcIf i Imsin t,v2g2 N2loe o2g Im I m N l d x I m cos t vI m sin t2o2g o N l2 g d x cos t v sin t 2v oN l 2 d x 2 v 2cos t arctan 2g d x Force and Torque on a Current Carrying ConductorThe force on a moving particle of electric charge q in a magnetic field is given by theLorentz's force law:F q v B The force acting on a current carrying conductor can be directly derived fromthe equation as F I Cdl Bwhere C is the contour of the conductor. For a homogeneous conductor of length l carryingcurrent I in a uniform magnetic field, the above expression can be reduced toF I l B In a rotating system, the torque about an axis can be calculated byT r Fwhere r is the radius vector from the axis towards the conductor.5
Principle of Electromechanical Energy ConversionExample:Calculate the torque produced by the Faraday's disc if a dc current I dc flows fromthe positive terminal to the negative terminal as shown below.TShaftr2r1BrushesIBSNSN Solution:Choose a small segment of length dr at position r (r1 r r2) between the brushes. Theforce generated by this segment isdF Idrr Baz IBdra where a is the unit vector in direction. The corresponding torque isdT r dF IBrdra zTherefore,22r ra IB2 zr22T dT IBrdra z1r1Force and Torque Calculation from Energy and CoenergyA Singly Excited Linear ActuatorConsider a singly excited linear actuator as shown below. The winding resistance is R. Ata certain time instant t, we record that the terminal voltage applied to the excitation windingis v, the excitation winding current i, the position of the movable plunger x, and the forceacting on the plunger F with the reference direction chosen in the positive direction of the xaxis, as shown in the diagram. After a time interval dt, we notice that the plunger has6
Principle of Electromechanical Energy Conversionmoved for a distance dx under the action of the forceF. The mechanical done by the force acting on theplunger during this time interval is thusdWm FdxThe amount of electrical energy that has beentransferred into the magnetic field and converted intothe mechanical work during this time interval can becalculated by subtracting the power loss dissipated intheA singly excited linear actuatorwinding resistance from the total power fed intothe excitation winding as2dW dW dW vidt Ri dteBecausee d v Ridtfwe can writemfemdW dW dW eidt Fdx id FdxFrom the above equation, we know that the energy stored in the magnetic field is a functionof the flux linkage of the excitation winding and the position of the plunger. Mathematically,we can also writedWfW , x f ,xW ,x d f dx xTherefore, by comparing the above two equations, we concludei Wf , x Wf , x andF xFrom the knowledge of electromagnetics, the energy stored in a magnetic field can beexpressed as Wf , x i , x d 0For a magnetically linear (with a constant permeability or a straight line magnetization curvesuch that the inductance of the coil is independent of the excitation current) system, theabove expression becomes7
Principle of Electromechanical Energy Conversion21 Wf , x 2 L x and the force acting on the plunger is then21 dL x Wf , x 2 L x xF 1 dL x 2 idx2dxIn the diagram below, it is shown that the magnetic energy is equivalent to the areaabove the magnetization or -i curve. Mathematically, if we define the area underneath themagnetization curve as the coenergy (which does not exist physically), i.e. Wf ' i, x i Wf , x we can obtaindWf ' i, x di id dWf , x di Fdx W ' i, x W ' i, x f ifdi x'Wf ( i, x )dxTherefore, andF ( , i)Wf ( , x)OiEnergy and coenergy Wf ' i, x i Wf ' i, x xFrom the above diagram, the coenergy or the area underneath the magnetizationcurve can be calculated byi Wf ' i, x i, x di0For a magnetically linear system, the above expression becomes12Wf ' i, x 2 i L x and the force acting on the plunger is thenF Wf ' i, x x 12i2dL x dxExample:Calculate the force acting on the plunger of a linear actuator discussed in this section.8
Principle of Electromechanical Energy Conversion RgNiRg(c)A singly excited linear actuatorSolution:Assume the permeability of the magnetic core of the actuator is infinite, and hence the systemcan be treated as magnetically linear. From the equivalent magnetic circuit of the actuatorshown in figure (c) above, one can readily find the self inductance of the excitation windingasNL x 22 Rg2 o N l d x 2gTherefore, the force acting on the plunger isF 1 i 2 dL x 2dx o l4g Ni 2The minus sign of the force indicates that the direction of the force is to reduce thedisplacement so as to reduce the reluctance of the air gaps. Since this force is caused by thevariation of magnetic reluctance of the magnetic circuit, it is known as the reluctance force.Singly Excited Rotating ActuatorThe singly excited linear actuator mentioned above becomes a singly excited rotatingactuator if the linearly movable plunger is replaced by a rotor, as illustrated in the diagrambelow. Through a derivation similar to that for a singly excited linear actuator, one canreadily obtain that the torque acting on the rotor can be expressed as the negative partialderivative of the energy stored in the magnetic field against the angular displacement or asthe positive partial derivative of the coenergy against the angular displacement, assummarized in the following table.9
Principle of Electromechanical Energy ConversionA singly excited rotating actuatorTable: Torque in a singly excited rotating actuatorEnergyCoenergydWf id Td dWf ' di Td In general, i Wf , i , d Wf ' i, i, di0 Wf , i Wf , T 0 Wf ' i, iT Wf ' i, If the permeability is a constant,1 2W , fT 1 2 1Wf ' i, 2 i L 2 L 2dL L d 1 dL 1dL 2d i22T i22 d Doubly Excited Rotating ActuatorThe general principle for force and torque calculation discussed above is equallyapplicable to multi-excited systems. Consider a doubly excited rotating actuator shownschematically in the diagram below as an example. The differential energy and coenergyfunctions can be derived as following:dWf dWe dWm where dWe e1i1dt e2 i2 dt10
Principle of Electromechanical Energy ConversionA doubly excited actuatore d 1 ,1 dtandHence,e d 22dtdWm Td dWf 1 , 2 , i1d 1 i2 d 2 Td Wf 1 , 2 , and Wf 1 , 2 , d 1 1 W f 1 , 2 , d d 2 2 dWf ' i1 ,i2 , d i1 1 i2 2 Wf 1 , 2 , 1di1 2 di2 Td Wf ' i1 ,i2 , i1 Wf ' i1 ,i2 , di1 Wf ' i1 ,i2 , d i2Therefore, comparing the corresponding differential terms, we obtainT orT Wf 1 , 2 , Wf ' i1 ,i2 , 11di2
Principle of Electromechanical Energy ConversionFor magnetically linear systems, currents and flux linkages can be related by constantinductances as following 1 L11 L12 i1 2 L 2221 2 or i1 11 12 1 2 2122 2 2where L12 L21, 11 L22/ , 12 21 L12/ , 22 L11/ , and L11L22 L12 . Themagnetic energy and coenergy can then be expressed as22 1Wf 1 , 2 , 1 12 1 211 122 222and11Wf ' i1 ,i2 , 2 L i 2 2 L i 2 L i i11 122 2respectively, and it can be shown that they are equal.12 1 2Therefore, the torque acting on the rotor can be calculated as Wf 1 , 2 , T 1 i212dL 11 1 Wf ' i1 ,i2 , 2i22dL22 i i dL12 1 2 Because of the salient (not round) structure of the rotor, the self inductance of the stator is afunction of the rotor position and the first term on the right hand side of the above torqueexpression is nonzero for that dL11/d 0. Similarly, the second term on the right hand sideof the above torque express is nonzero because of the salient structure of the stator.Therefore, these two terms are known as the reluctance torque component. The last term inthe torque expression, however, is only related to the relative position of the stator and rotorand is independent of the shape of the stator and rotor poles.Model of Electromechanical SystemsTo illustrate the general principle for modeling of an electromechanical system, we stilluse the doubly excited rotating actuator discussed above as an example. For convenience, weplot it here again. As discussed in the introduction, the mathematical model of anelectromechanical system consists of circuit equations for the electrical subsystem and force12
Principle of Electromechanical Energy ConversionA doubly excited actuatoror torque balance equations for the mechanical subsystem, whereas the interactions betweenthe two subsystems via the magnetic field can be expressed in terms of the emf's and theelectromagnetic force or torque. Thus, for the doubly excited rotating actuator, we can writedd 12 v R i 1 R i 111dt1111dtanddidi1 i11 d L2 i dL12 d d dtdt12 dt1111 dt1 d 2dL di dL L dii L R r ri 2 d d dtdtv R i d 2 R i d 21 22 dtdt2222dLdidLdi2 i222 d R i L 1 i 12 d L2 212 dt1 d dt22dtd dtdidL12 dL22 L1 Ldi2 ri1 R2 r 2d d 12 dt22 dt d rT Tload J dtwhere Ri LdL11121 11121122r d dtis the angular speed of the rotor, Tload the load torque, and J the inertia of the rotor andthe mechanical load which is coupled to the rotor shaft.The above equations are nonlinear differential equations which can only be solvednumerically. In the format of state equations, the above equations can be rewritten as13
Principle of Electromechanical Energy Conversiondidtdi2and1 1R L11dL 1 1 dL 12dtd 22d r 1 T 1 TJdtJ loadd 11d r i 1 1 R22 i r11 dL 12L11 2d dL 22d i2r L di11dtL11L di12 r12Li2 12221dt v11v222 dtrTogether with the specified initial conditions (the state of the system at time zero in terms of the state variables): i , ii1t 0102 i , t 020r , , and t 0r0t 00the above state equations can be used to simulate the dynamic performance of the doubly excited rotatingactuator.Following the same rule, we can derive the state equation model of any electromechanicalsystems.
UNIT-IIUNIT-IIUNIT-IID.C.D.C GENERATORS-IDC GENERATORGENERATORS-IThe electrical machines deals with the energy transfer either from mechanical toelectrical form
DC MACHINES (17CA02301) 2018 – 2019 II B. Tech I Semester (CREC-R17) . Tirupati – 517 506 Department of Electrical and Electronics Engineering JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY ANANTAPUR . DC MACHINES III Semester: EEE Course Code Category Hours / Week Credits Maximum . Electrical Machines – M.V Deshpande, Wheeler Publishing .
Tools and machines Worksheet 6.1 Simple machines 1. Complete the sentences. tools one two Simple machines have one or two parts. Simple machines are called tools. 2. Write the names of these simple machines. 3. Match. pulley wheel and axle lever wedge screw inclined plane screw lever pulley inclined plane wedge wheel and axle .
answer questions 2.1 - 2.13 Note: You are studying only simple machines in this course. The other category of machines is compound machines, which are made up of two or more simple machines working together. Cars and dishwashers are examples of compound machines. Note: Ask your instructor for a copy of the worksheet, Classes of Levers, to .
distance needed to do work. Simple machines do not change the amount of work done 2) Identify examples of simple machines in everyday objects. 3) Identify simple machines within complex machines. 4) Choose appropriate simple machines to solve a mechanical problem. 5) a) Define engineering design as the process of creating
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simple machines closely and learn how machines can multiply and alter forces. Investigations for Chapter 4 Machines can make us much stronger than we normally are. In this Investigation, you will design and build several block and tackle machines from ropes and pulleys. Your machines will produce up to six times as much force as you apply. As .
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