Introduction to Machinery Principles

MODULE 1: INTRODUCTION TO MACHINERY PRINCIPLES I. ELECTRICAL MACHINES An electrical machine is a device that can convert either mechanical energy to electrical energy or electrical energy to mechanical energy. When such a device is used to convert mechanical energy to electrical energy, it is called...

MODULE 1: INTRODUCTION TO MACHINERY PRINCIPLES I. ELECTRICAL MACHINES An electrical machine is a device that can convert either mechanical energy to electrical energy or electrical energy to mechanical energy. When such a device is used to convert mechanical energy to electrical energy, it is called generator. When it converts electrical energy to mechanical energy, it is called motor. The transformer on the other hand, is an electrical device that is closely related to electrical machines. It converts electrical energy at one voltage level to ac electrical energy at another voltage level. Since transformers operate on the same principles as generators and motors, depending on the action of the magnetic field to accomplish the change in voltage level, they are usually studied together with generators and motors. II. NOTES ON UNITS AND NOTATION The design and study of electric machines and power systems are among the oldest areas of electrical engineering. Study began in the latter part of the nineteenth century. At that time, electrical units were being standardized internationally, and these units came to be universally used by engineers. Volts, amperes, ohms, watts, and similar units, which are part of the metric system of units have long been used to describe electrical quantities in machines. In 1954, a comprehensive system of units based on the metric system was adopted as an international standard. This system of units became known as the Systeme International (SI) and has been adopted throughout The SI possesses a number of remarkable features shared by no other system units: It is a decimal system. It employs many units commonly used in industry and commerce: for example, volt, ampere, kilogram, and watt. It is a coherent system that expresses with startling simplicity some of the most basic relationships in electricity, mechanics, and heat. It can be used by research scientist, the technician, the practicing engineer, and by the layman, thereby blending the theoretical and practical worlds. III. ROTATIONAL MOTION, NEWTON’S LAW, AND POWER RELATIONSHIPS Almost all electric machines rotate about an axis, called the shaft of the machine. Because of the rotational nature of the machinery, it is important to have a basic understanding of rotational motion. Each major concept of rotational motion is defined below and is related to the corresponding idea from linear motion. Angular Position, θ Refers to the orientation of a line with respect to a reference direction, often measured in radians or degrees or revolution. It describes how far an object has rotated or the angle at which it is positioned relative to a fixed axis. Angular Velocity, ω Is the rate at which an object changes its angular position. It describes how fast something is spinning or rotating. It quantifies the rate of change of angular position with respect to time. Angular Acceleration, α Measures how fast the angular velocity is changing. If an object is rotating and its speed of rotation is increasing or decreasing, it experiences angular acceleration. Torque, τ Also called the “twisting force” on an object. Torque is a measure of the rotational force applied to an object, causing it to rotate around an axis. Torque is defined as the product of the force (𝐹) applied and the perpendicular distance (𝑟) from the point of rotation (the axis) to where the force is applied. Newton’s Law of Rotation F = 𝒎𝒂 (Newton) – linear form τ = Ia (N m or lb ft) – rotational form Work, W The product of the force applied to an object and the displacement of the object in the direction of the force. W = ‫ – 𝒓𝒅 𝑭 ׬‬linear form W = Fr – constant force W = ‫ ׬‬τ 𝒅𝜽 (Joule) – rotational form W = τθ (Joule) – constant torque Power, P Defined as the amount of work done (𝑊) divided by the time (𝑡) taken to do that work. IV. MAGNETIC FIELD Four basic principles to describe how magnetic fields are used in the devices 1. A current-carrying wire produces magnetic field in the area around it. 2. A time-changing magnetic field induces a voltage in a coil of wire if it passes through that coil. 3. A current-carrying wire in the presence of a magnetic field has a force induced on it. 4. A moving wire in the presence of the magnetic field has a voltage induced in it. Production of Magnetic Field When an electric current flows through a conductor, such as a wire, it generates a magnetic field around the conductor. This phenomenon is described by Ampere’s Law Ampere’s Law Relates the magnetic field around a closed loop to the electric current passing through the loop. ∮ H⋅ dl = Inet H = magnetic field intensity produced by the current Inet dl = differential length element along the path Inet = the net current passing through the surface enclosed by the loop. B 𝒄𝒐𝒔𝜽 𝒅𝒔 = µ𝟎𝑰𝒆𝒏 B = magnetic flux density cosθ = angle between the direction of the magnetic field and the direction of the differential area ds = differential element of area µ0 = permeability of free space or magnetic constant = 4π x 10-7 Henry/meter or 4π x 10-7 Newtons/Amperes2 Ienc = enclosed current Magnetic Field Intensity, H and Magnetic Flux Density, B ❑ Magnetic Field Intensity (Magnetizing Force), H Is a measure of the ability of a magnetic field to induce magnetization in a material. It is essentially the "push" given by the electric current that creates the magnetic field. Unit : Ampere/meter ❑ Magnetic Flux Density, B Is the amount of magnetic flux passing through a unit area perpendicular to the direction of the magnetic field. It tells you how strong the magnetic field is in a given area. Unit : Tesla (T ) B=μH , B=φ/Area V. FARADAY’S LAW Faraday’s Law of electromagnetic induction states: 1. If the flux linking a loop (or turn) varies as a function of time, a voltage is induced between its terminals. 2. The value of the induced voltage is proportional to the rate of change of flux. E = induced voltage N = number of turns Δφ = change in flux inside the coil (Wb) Δt = time interval during which the flux changes (secs) Example No. 1 A coil of 2000 turns surrounds a flux of 5 mWb produced by a permanent magnet. The magnet is suddenly withdrawn causing the flux inside the coil to drop uniformly to 2 mWb in 1/10 of a second. What is the volage induced? VI. PRODUCTION OF INDUCED FORCE ON A WIRE Lorentz Force on a Conductor When a current-carrying conductor is placed in a magnetic field, it is subject to a force which we call electromagnetic force or Lorentz force. The maximum force acting on a straight conductor is given by: F = Bil F = force acting on the conductor (N) B = flux density of the field (T) I = current in the conductor (A) L = active length of the conductor (m) Example No. 3 A conductor 3m long carrying a current of 200 A is placed in a magnetic field whose density is 0.5 T. Calculate the force of the conductor if it is perpendicular to the lines of force. Voltage Induced in a Conductor It is easier to calculate the induced voltage with reference to the conductors, rather than with reference to the coil itself. In effect, whenever a conductor cuts a magnetic field, a voltage is induced across its terminals. The value of the voltage induced is given by: E = Blv E = Induced voltage B = flux density (T) L = active length of the conductor in the magnetic field (m) V = relative speed of the conductor (m/s) Example No. 2 The stationary conductors of a large generator have an active length of 2m and are cut by a field of 0.6 tesla moving at a speed of 100 m/s. Calculate the voltage induced in each conductor.