DOCSLIB.ORG

Analysis of Induction Motor Torque

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

ANALYSIS OF INDUCTION MOTOR TORQUE DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of the Ohio State University By Sakae Yamamura, B. E., M. S. The Ohio State University 1953 Approved by; Adviserv^ TABLE OF CONTENTS Page Chapter I. Introduction. 1 Chapter II. The Principle of the Analyzer. 6 Chapter III. The Component Parts of the Analyzer. 12 1. Homopolar generator. 12 2. Amplifiers. 15 3* Power supplies. 20 4. Differentiating circuit. 23 5. Frequency response of the analyzer. 27 6. Cathod-ray scope. 31 7. Adjustments of the complete set. 33 Chapter IV. Results Obtained. 38 1. Three-phase induction motor; 220 V, 1/4 HP, 4 poles, 60-cycle. 38 2. Single-phase operation of the three-phase Induction motor; 220 V, l/A HP, 4 poles, 60-cycle. 45 3. Three-phase induction motor; 220 V, 1/8 HP, 4 poles, 60—cycle. 48 4- Single-phase induction motor; 115 V, 1/6 HP, 4 poles, 60-cycle. 53 5. Shaded-pole motor; 115 V, 1/12 HP, 6 poles, 60-cycle. 58 Chapter V. Consideration of Steady States. 63 1. Three-phase induction motor. 63 2. Single-phase induction motor; 115 V, 1/6 HP, 4 poles, 60—cycle. 66 -i- A 0 U 8 6 1 Page 3. Consideration of braking torque of the three-phase induction motor; 220 V, 1/4 HP, 4 pOles, 60-cycle. 75 (a). Friction and windage. 79 (b). Iron loss try fundamental magnetic flux. 80 (c). Saturation of iron. 83 (d). Skin effect. 88 (e). Space harmonics of air gap magnetic flux. 92 (f). Iron loss due to zigzag leakage flux. 95 (g). Some additional considerations of the extraordinary braking torque. 99 4- Single-phase operation of the three-phase induction motor; 220 V, 1/4 HP, 4 poles, 60-cycle. 103 Chapter VI. Tr*isient Torque of Three-phase Induction Motors* 108 1. Differential equations of unbalanced two-phase induction motors. 109 2. Transient phenomena of a balanced two-phase induction motor. 112 3. Solution of the transient phenomena of the three-phase induction motor (220 V, 1/4 HP, 4 poles, 60-cycle) by the electronic analog computer. 126 Chapter VII. Conclusion and Acknowledgments. 133 Appendix I. Some experiments about the tooth-pulsation loss due to zigzag leakage flux. 135 -11- Page Appendix II. Derivation of the equivalent two-phase induction motor for a three-phase induction motor. 140 Appendix III. Solution of transient phenomena of a balanced three-phase induction motor by the ReeveB Analog Computer. 14-9 Bibliography. 159 Autobiography. 160 -iii- CHAPTER I IKTRODUCTIOli Speed-torque characteristics sre among the most important characteristics of induction motors. They enable us to judge, when the ■peed-torque curve of the load is also known, whether a motor under consideration can start and carry expeoted loads successfully or not. Here, we take the speed-torque characteristics to mean generally any relation between motor speed and motor torque. Usually they mean the relation between motor speed and time-average torque at steady state. But there are many aspects of speed-torque characteristics, as we shall see in this dissertation; and not all of these have been thoroughly investigated, mainly because they are difficult to determine experi­ mentally or to compute. In order to measure torque at any given speed with a dynamometer, the induction motor under test must be kept at constant speed under a certain load. This is difficult for certain speed ranges, although not impossible. Labor and cost involved in such measurements are prohibitively high in some oases, When attempts are made to oaloulate the torque, computations do not give accurate results for wide range of speed. This is probably due to variation of machine constants used in these computations. The machine constants are usually obtained from no load test and locked rotor test, or by calculations from formulas and design data. Because of magnetic saturation of the iron, these values are usually satisfactory for current up to or a little higher than rated current. Hence, for lower 2 speed, torque computed from these machine constants is different from the measured torque due to magnetic saturation by larger current. Several attemptshave been made to correct the machine con­ stants for magnetic saturation. But they are not accurate and are often awkward to use for practical purposes. Deep slot-oage motors or double-cate motors are of great practical importance, but the speed-torque curves involving deep slot or double cage effect are very difficult to oompute. It will be shown in Article 3 of Chapter V that stray load loss has a great influence on torque, sometimes doubling or tripling the torque that would be developed without it. But so far practioally no attempt has been made to com­ pute stray load loss. From the above considerations we can see the need for devices which will enable us to obtain the speed-torque characteristics of in­ duction motors with more accuracy and ease. In order to meet the need, many attempts have been made.^®^^^®^ The principles underly­ ing these attempts are about the same, and the devices developed by these investigations may be called speed-torque analyzers. These analyzers trace out speed-torque curves on an oscilloscope while the motors under test are accelerated from standstill to no load speed. Hence, speed-torque curves are determined with much less labor than by the other methods, such as the dynamometer method or computation. But in spite of their adequacy for certain purposes, these analyzers are not accurate enough and cannot indioate some of the fine details of the speed-torque curve. In the following section we shall briefly explain the main reasons why they are not satisfactory, if more details 5 of the speed-torque curve are desired. f 3 } Z. Set o'- J uses an ordinary d-c generator as a tachometer. In order to obtain instantaneous torque# the output voltage from the d-c generator is differentiated by a C-R series oirouit. But an ordinary d-c generator has commutation ripple or noise in its output voltage. Generally, when any voltage is differentiated# high frequency componente of the voltage become more pronounced, ^ence# in the torque signal the commutation noise becomes more predominant due to its high frequencies qnd masks the details of the speed-torque curves. YJhen the commutation noise is fil­ tered out# the higher harmonic components of the frequency spectrum of the speed-torque curves are also filtered out. Details of the curves are thus lost and the curves obtained do not give a complete or true picture. H. Kondo^) uses a vacuum tube osoillator to measure instantaneous torque. The frequency of the oscillator is controlled by slight change of capacitance resulting from the twist of the motor shaft by the torque transmitted. Due to meohanic&l transient phenomena of the motor shaft# frequency change of the oscillator does not always represent the true instantaneous torque# and error is introduced thereby# especially for rapidly changing portions of the curve. S. Chang^5^ uses a square wave generator consisting of a circular disc with evenly distributed slots on its periphery. Square wave voltage is generated photo-electrically and its frequency is proportional to instantaneous motor speed. By taking average value of the sequence of square waves by a filter# d-c voltage# which is proportional to motor speed# is obtained. But the filter# which takes the average value of the sequence of square wave voltages# suppresses the higher harmonics of the signal as well. Hence, curves obtained by Chang's analyzer are distorted and not accurate. In the present research a homopolar generator is used as a tachometer instead of an ordinary d-c generator. In a homopolar generator the electromotive force induced in a single oonductor is d-c while it is a-o in an ordinary d-c generator. So the commutator is not required for a homopolar generator. Thus, its output voltage does not contain any com­ mutation ripple or noise and is pure d-c voltage at any constant speed. It mig^it seem strange that a homopolar generator has not been used as a tachometer in previous analysers, but this can be explained by the fact that it introduces a new difficulty. A homopolar generator is inherently a lew voltage device. Its output voltage is therefore too low for indicators of the type such as an electromagnetic oscillograph or a oathode-ray oscillograph, as long as the generator size remains within practical dimensions. Hence, a high-gain d-c amplifier is needed to produce enough deflection on an indicator. As is well known, a stable high-gain d-c amplifier is difficult to build. This is the reason afcy a homopolar generator has not been used successfully thus far. But proper design of the homopolar generator and the d-c ampli­ fiers, which will be explained in Chapter III, has resulted in the construction of a satisfactory speed-torque analyzer. This analyzer reveals on its cathode-ray scope such details of speed-torque curves as switching transient torque, pulsating torque of single-phase induction motors, eto. In Chapters II and III of this dissertation the principle and the structure of the analyzer will be explained. The various interesting 5 results obtained "with it will be given in Chapter IV. This analyzer revealed many features of speed-torque curves which had not been obtained by the dynamometer method or by the analyzer developed heretofore. Some of the curvos are quite different from the familiar one. In order to show that these new curves give a satis­ factory representation of the actual speed-torque curves, they will be compared with measured or calculated values in Chapters V and VI.
Recommended publications
  • Motion Projectile Motion,And Straight Linemotion, Differences Between the Similaritiesand 2 CHAPTER 2 Acceleration Make Thefollowing As Youreadthe ●

    Motion Projectile Motion,And Straight Linemotion, Differences Between the Similaritiesand 2 CHAPTER 2 Acceleration Make Thefollowing As Youreadthe ●

    026_039_Ch02_RE_896315.qxd 3/23/10 5:08 PM Page 36 User-040 113:GO00492:GPS_Reading_Essentials_SE%0:XXXXXXXXXXXXX_SE:Application_File chapter 2 Motion section ●3 Acceleration What You’ll Learn Before You Read ■ how acceleration, time, and velocity are related Describe what happens to the speed of a bicycle as it goes ■ the different ways an uphill and downhill. object can accelerate ■ how to calculate acceleration ■ the similarities and differences between straight line motion, projectile motion, and circular motion Read to Learn Study Coach Outlining As you read the Velocity and Acceleration section, make an outline of the important information in A car sitting at a stoplight is not moving. When the light each paragraph. turns green, the driver presses the gas pedal and the car starts moving. The car moves faster and faster. Speed is the rate of change of position. Acceleration is the rate of change of velocity. When the velocity of an object changes, the object is accelerating. Remember that velocity is a measure that includes both speed and direction. Because of this, a change in velocity can be either a change in how fast something is moving or a change in the direction it is moving. Acceleration means that an object changes it speed, its direction, or both. How are speeding up and slowing down described? ●D Construct a Venn When you think of something accelerating, you probably Diagram Make the following trifold Foldable to compare and think of it as speeding up. But an object that is slowing down contrast the characteristics of is also accelerating. Remember that acceleration is a change in acceleration, speed, and velocity.
  • Frames of Reference

    Frames of Reference

    Galilean Relativity 1 m/s 3 m/s Q. What is the women velocity? A. With respect to whom? Frames of Reference: A frame of reference is a set of coordinates (for example x, y & z axes) with respect to whom any physical quantity can be determined. Inertial Frames of Reference: - The inertia of a body is the resistance of changing its state of motion. - Uniformly moving reference frames (e.g. those considered at 'rest' or moving with constant velocity in a straight line) are called inertial reference frames. - Special relativity deals only with physics viewed from inertial reference frames. - If we can neglect the effect of the earth’s rotations, a frame of reference fixed in the earth is an inertial reference frame. Galilean Coordinate Transformations: For simplicity: - Let coordinates in both references equal at (t = 0 ). - Use Cartesian coordinate systems. t1 = t2 = 0 t1 = t2 At ( t1 = t2 ) Galilean Coordinate Transformations are: x2= x 1 − vt 1 x1= x 2+ vt 2 or y2= y 1 y1= y 2 z2= z 1 z1= z 2 Recall v is constant, differentiation of above equations gives Galilean velocity Transformations: dx dx dx dx 2 =1 − v 1 =2 − v dt 2 dt 1 dt 1 dt 2 dy dy dy dy 2 = 1 1 = 2 dt dt dt dt 2 1 1 2 dz dz dz dz 2 = 1 1 = 2 and dt2 dt 1 dt 1 dt 2 or v x1= v x 2 + v v x2 =v x1 − v and Similarly, Galilean acceleration Transformations: a2= a 1 Physics before Relativity Classical physics was developed between about 1650 and 1900 based on: * Idealized mechanical models that can be subjected to mathematical analysis and tested against observation.
  • Sri Venkateswara College of Engineering and Technology Department of Electrical & Electronics Engineering EE 6504-Electrical

    Sri Venkateswara College of Engineering and Technology Department of Electrical & Electronics Engineering EE 6504-Electrical

    Sri Venkateswara College of Engineering and Technology Department of Electrical & Electronics Engineering EE 6504-Electrical Machines-II UNIT-I 1. Why a 3-phase synchronous motor will always run at synchronous speed? Because of the magnetic coupling between the stator poles and rotor poles the motor runs exactly at synchronous speed. 2. What are the two classification synchronous machines? The classification synchronous machines are: i. Cylindrical rotor type ii. Salient pole rotor type 3. What are the essential features of synchronous machine? i. The rotor speed is synchronous with stator rotating field. ii. Varying its field current can easily vary the speed. iii. It is used for constant speed operation. 4. Mention the methods of starting of 3-phase synchronous motor. a. A D.C motor coupled to the synchronous motor shaft. b. A small induction motor coupled to its shaft.(pony method) c. Using damper windings –started as a squirrel cage induction motor. 5. What are the principal advantages of rotating field system type of construction of synchronous machines? · Form Stationary connection between external circuit and system of conditions enable the machine to handle large amount of volt-ampere as high as 500 MVA. · The relatively small amount of power required for field system can be easily supplied to the rotating field system via slip rings and brushes. · More space is available in the stator part of the machine for providing more insulation to the system of conductors. · Insulation to stationary system of conductors is not subjected to mechanical stresses due to centrifugal action. · Stationary system of conductors can easily be braced to prevent deformation.
  • Direct Torque Control of Induction Motors

    Direct Torque Control of Induction Motors

    DIRECT TORQUE CONTROL FOR INDUCTION MOTOR DRIVES MAIN FEATURES OF DTC · Decoupled control of torque and flux · Absence of mechanical transducers · Current regulator, PWM pulse generation, PI control of flux and torque and co-ordinate transformation are not required · Very simple control scheme and low computational time · Reduced parameter sensitivity BLOCK DIAGRAM OF DTC SCHEME + _ s* s j s + Djs _ Voltage Vector s * T + j s DT Selection _ T S S S s Stator a b c Torque j s s E Flux vs 2 Estimator Estimator 3 s is 2 i b i a 3 Induction Motor In principle the DTC method selects one of the six nonzero and two zero voltage vectors of the inverter on the basis of the instantaneous errors in torque and stator flux magnitude. MAIN TOPICS Þ Space vector representation Þ Fundamental concept of DTC Þ Rotor flux reference Þ Voltage vector selection criteria Þ Amplitude of flux and torque hysteresis band Þ Direct self control (DSC) Þ SVM applied to DTC Þ Flux estimation at low speed Þ Sensitivity to parameter variations and current sensor offsets Þ Conclusions INVERTER OUTPUT VOLTAGE VECTORS I Sw1 Sw3 Sw5 E a b c Sw2 Sw4 Sw6 Voltage-source inverter (VSI) For each possible switching configuration, the output voltages can be represented in terms of space vectors, according to the following equation æ 2p 4p ö s 2 j j v = ç v + v e 3 + v e 3 ÷ s ç a b c ÷ 3 è ø where va, vb and vc are phase voltages.
  • The Fundamentals of Ac Electric Induction Motor Design and Application

    The Fundamentals of Ac Electric Induction Motor Design and Application

    THE FUNDAMENTALS OF AC ELECTRIC INDUCTION MOTOR DESIGN AND APPLICATION by Edward J. Thornton Electrical Consultant E. I. du Pont de Nemours Houston, Texas and J. Kirk Armintor Senior Account Sales Engineer Rockwell Automation The Woodlands, Texas Edward J. (Ed) Thornton is an Electrical Electrical Mechanical Consultant in the Electrical Technology Coupling System Field System Consulting Group in Engineering at DuPont, in Houston, Texas. His specialty is the design, operation, and maintenance of electric power distribution systems and large motor installations. He has 20 years E , I T , w of consulting experience with DuPont. Mr. Thornton received his B.S. degree Figure 1. Block Representation of Energy Conversion for Motors. (Electrical Engineering, 1978) from Virginia Polytechnic Institute and State University. The coupling magnetic field is key to the operation of electrical He is a registered Professional Engineer in the State of Texas. apparatus such as induction motors. The fundamental laws associated with the relationship between electricity and magnetism were derived from experiments conducted by several key scientists J. Kirk Armintor is a Senior Account in the 1800s. Sales Engineer in the Rockwell Automation Houston District Office, in The Woodlands, Basic Design and Theory of Operation Texas. He has 32 years’ experience with The alternating current (AC) induction motor is one of the most motor applications in the petroleum, rugged and most widely used machines in industry. There are two chemical, paper, and pipeline industries. major components of an AC induction motor. The stationary or He has authored technical papers on motor static component is the stator. The rotating component is the rotor.
  • Chapter 3 Motion in Two and Three Dimensions

    Chapter 3 Motion in Two and Three Dimensions

    Chapter 3 Motion in Two and Three Dimensions 3.1 The Important Stuff 3.1.1 Position In three dimensions, the location of a particle is specified by its location vector, r: r = xi + yj + zk (3.1) If during a time interval ∆t the position vector of the particle changes from r1 to r2, the displacement ∆r for that time interval is ∆r = r1 − r2 (3.2) = (x2 − x1)i +(y2 − y1)j +(z2 − z1)k (3.3) 3.1.2 Velocity If a particle moves through a displacement ∆r in a time interval ∆t then its average velocity for that interval is ∆r ∆x ∆y ∆z v = = i + j + k (3.4) ∆t ∆t ∆t ∆t As before, a more interesting quantity is the instantaneous velocity v, which is the limit of the average velocity when we shrink the time interval ∆t to zero. It is the time derivative of the position vector r: dr v = (3.5) dt d = (xi + yj + zk) (3.6) dt dx dy dz = i + j + k (3.7) dt dt dt can be written: v = vxi + vyj + vzk (3.8) 51 52 CHAPTER 3. MOTION IN TWO AND THREE DIMENSIONS where dx dy dz v = v = v = (3.9) x dt y dt z dt The instantaneous velocity v of a particle is always tangent to the path of the particle. 3.1.3 Acceleration If a particle’s velocity changes by ∆v in a time period ∆t, the average acceleration a for that period is ∆v ∆v ∆v ∆v a = = x i + y j + z k (3.10) ∆t ∆t ∆t ∆t but a much more interesting quantity is the result of shrinking the period ∆t to zero, which gives us the instantaneous acceleration, a.
  • Abstract Controlling Ac Motor Using Arduino

    Abstract Controlling Ac Motor Using Arduino

    ABSTRACT CONTROLLING AC MOTOR USING ARDUINO MICROCONTROLLER Nithesh Reddy Nannuri, M.S. Department of Electrical Engineering Northern Illinois University, 2014 Donald S Zinger, Director Space vector modulation (SVM) is a technique used for generating alternating current waveforms to control pulse width modulation signals (PWM). It provides better results of PWM signals compared to other techniques. CORDIC algorithm calculates hyperbolic and trigonometric functions of sine, cosine, magnitude and phase using bit shift, addition and multiplication operations. This thesis implements SVM with Arduino microcontroller using CORDIC algorithm. This algorithm is used to calculate the PWM timing signals which are used to control the motor. Comparison of the time taken to calculate sinusoidal signal using Arduino and CORDIC algorithm was also done. NORTHERN ILLINOIS UNIVERSITY DEKALB, ILLINOIS DECEMBER 2014 CONTROLLING AC MOTOR USING ARDUINO MICROCONTROLLER BY NITHESH REDDY NANNURI ©2014 Nithesh Reddy Nannuri A THESIS SUBMITTED TO THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE MASTER OF SCIENCE DEPARTMENT OF ELECTRICAL ENGINEERING Thesis Director: Dr. Donald S Zinger ACKNOWLEDGEMENTS I would like to express my sincere gratitude to Dr. Donald S. Zinger for his continuous support and guidance in this thesis work as well as throughout my graduate study. I would like to thank Dr. Martin Kocanda and Dr. Peng-Yung Woo for serving as members of my thesis committee. I would like to thank my family for their unconditional love, continuous support, enduring patience and inspiring words. Finally, I would like to thank my friends and everyone who has directly or indirectly helped me for their cooperation in completing the thesis.
  • Electric Motors

    Electric Motors

    SPECIFICATION GUIDE ELECTRIC MOTORS Motors | Automation | Energy | Transmission & Distribution | Coatings www.weg.net Specification of Electric Motors WEG, which began in 1961 as a small factory of electric motors, has become a leading global supplier of electronic products for different segments. The search for excellence has resulted in the diversification of the business, adding to the electric motors products which provide from power generation to more efficient means of use. This diversification has been a solid foundation for the growth of the company which, for offering more complete solutions, currently serves its customers in a dedicated manner. Even after more than 50 years of history and continued growth, electric motors remain one of WEG’s main products. Aligned with the market, WEG develops its portfolio of products always thinking about the special features of each application. In order to provide the basis for the success of WEG Motors, this simple and objective guide was created to help those who buy, sell and work with such equipment. It brings important information for the operation of various types of motors. Enjoy your reading. Specification of Electric Motors 3 www.weg.net Table of Contents 1. Fundamental Concepts ......................................6 4. Acceleration Characteristics ..........................25 1.1 Electric Motors ...................................................6 4.1 Torque ..............................................................25 1.2 Basic Concepts ..................................................7
  • Exploring Robotics Joel Kammet Supplemental Notes on Gear Ratios

    Exploring Robotics Joel Kammet Supplemental Notes on Gear Ratios

    CORC 3303 – Exploring Robotics Joel Kammet Supplemental notes on gear ratios, torque and speed Vocabulary SI (Système International d'Unités) – the metric system force torque axis moment arm acceleration gear ratio newton – Si unit of force meter – SI unit of distance newton-meter – SI unit of torque Torque Torque is a measure of the tendency of a force to rotate an object about some axis. A torque is meaningful only in relation to a particular axis, so we speak of the torque about the motor shaft, the torque about the axle, and so on. In order to produce torque, the force must act at some distance from the axis or pivot point. For example, a force applied at the end of a wrench handle to turn a nut around a screw located in the jaw at the other end of the wrench produces a torque about the screw. Similarly, a force applied at the circumference of a gear attached to an axle produces a torque about the axle. The perpendicular distance d from the line of force to the axis is called the moment arm. In the following diagram, the circle represents a gear of radius d. The dot in the center represents the axle (A). A force F is applied at the edge of the gear, tangentially. F d A Diagram 1 In this example, the radius of the gear is the moment arm. The force is acting along a tangent to the gear, so it is perpendicular to the radius. The amount of torque at A about the gear axle is defined as = F×d 1 We use the Greek letter Tau ( ) to represent torque.
  • Improvement of Electromagnetic Railgun Barrel Performance and Lifetime By

    Improvement of Electromagnetic Railgun Barrel Performance and Lifetime By

    IMPROVEMENT OF ELECTROMAGNETIC RAILGUN BARREL PERFORMANCE AND LIFETIME BY METHOD OF INTERFACES AND AUGMENTED PROJECTILES A Thesis Presented to the Faculty of California Polytechnic State University San Luis Obispo In Partial Fulfillment of the Requirements for the Degree Master of Science in Aerospace Engineering by Aleksey Pavlov June 2013 c 2013 Aleksey Pavlov ALL RIGHTS RESERVED ii COMMITTEE MEMBERSHIP TITLE: Improvement of Electromagnetic Rail- gun Barrel Performance and Lifetime by Method of Interfaces and Augmented Pro- jectiles AUTHOR: Aleksey Pavlov DATE SUBMITTED: June 2013 COMMITTEE CHAIR: Kira Abercromby, Ph.D., Associate Professor, Aerospace Engineering COMMITTEE MEMBER: Eric Mehiel, Ph.D., Associate Professor, Aerospace Engineering COMMITTEE MEMBER: Vladimir Prodanov, Ph.D., Assistant Professor, Electrical Engineering COMMITTEE MEMBER: Thomas Guttierez, Ph.D., Associate Professor, Physics iii Abstract Improvement of Electromagnetic Railgun Barrel Performance and Lifetime by Method of Interfaces and Augmented Projectiles Aleksey Pavlov Several methods of increasing railgun barrel performance and lifetime are investigated. These include two different barrel-projectile interface coatings: a solid graphite coating and a liquid eutectic indium-gallium alloy coating. These coatings are characterized and their usability in a railgun application is evaluated. A new type of projectile, in which the electrical conductivity varies as a function of position in order to condition current flow, is proposed and simulated with FEA software. The graphite coating was found to measurably reduce the forces of friction inside the bore but was so thin that it did not improve contact. The added contact resistance of the graphite was measured and gauged to not be problematic on larger scale railguns. The liquid metal was found to greatly improve contact and not introduce extra resistance but its hazardous nature and tremendous cost detracted from its usability.
  • Rotation: Moment of Inertia and Torque

    Rotation: Moment of Inertia and Torque

    Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn that where the force is applied and how the force is applied is just as important as how much force is applied when we want to make something rotate. This tutorial discusses the dynamics of an object rotating about a fixed axis and introduces the concepts of torque and moment of inertia. These concepts allows us to get a better understanding of why pushing a door towards its hinges is not very a very effective way to make it open, why using a longer wrench makes it easier to loosen a tight bolt, etc. This module begins by looking at the kinetic energy of rotation and by defining a quantity known as the moment of inertia which is the rotational analog of mass. Then it proceeds to discuss the quantity called torque which is the rotational analog of force and is the physical quantity that is required to changed an object's state of rotational motion. Moment of Inertia Kinetic Energy of Rotation Consider a rigid object rotating about a fixed axis at a certain angular velocity. Since every particle in the object is moving, every particle has kinetic energy. To find the total kinetic energy related to the rotation of the body, the sum of the kinetic energy of every particle due to the rotational motion is taken. The total kinetic energy can be expressed as ..
  • Electrical Machines-II 2015-16(ODD)

    Electrical Machines-II 2015-16(ODD)

    A Course Material on Electrical Machines-II 2015-16(ODD) By Mrs. M.Latha Assistant Professor DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING SASURIE COLLEGE OF ENGINEERING VIJAYAMANGALAM – 638 056 QUALITY CERTIFICATE This is to certify that the e-course material Subject Code : EE6504 Subject : Electrical Machines -II Class : III YEAR EEE Being prepared by me and it meets the knowledge requirement of the university curriculum. Signature of the Author Name: M.Latha Designation: AP This is to certify that the course material being prepared by Mrs.M.Latha is of adequate quality. She has referred more than five books among them minimum one is from aboard author. Signature of HD Name: SEAL Syllabus EE6504 Electrical Machines -II UNIT I SYNCHRONOUS GENERATOR Constructional details – Types of rotors –winding factors- emf equation – Synchronous reactance –Armature reaction – Phasor diagrams of non salient pole synchronous generator connected to infinite bus--Synchronizing and parallel operation – Synchronizing torque -Change of excitation and mechanical input- Voltage regulation – EMF, MMF, ZPF and A.S.A methods – steady state power angle characteristics– Two reaction theory –slip test -short circuit transients - Capability Curves UNIT II SYNCHRONOUS MOTOR Principle of operation – Torque equation – Operation on infinite bus bars - V and Inverted V curves – Power input and power developed equations – Starting methods – Current loci for constant power input, constant excitation and constant power developed-Hunting – natural frequency of oscillations – damper windings- synchronous condenser. UNIT III THREE PHASE INDUCTION MOTOR Constructional details – Types of rotors –- Principle of operation – Slip –cogging and crawling- Equivalent circuit – Torque-Slip characteristics - Condition for maximum torque – Losses and efficiency – Load test - No load and blocked rotor tests - Circle diagram – Separation of losses – Double cage induction motors –Induction generators – Synchronous induction motor.