GROUP 5 - Principle of Motor Action, Force, Torque, and Rotation PDF

MEEN 301: DC and AC Machinery “Principle of Motor Action, Force, Torque, and Rotation” Presented by: Acquiat, Kaybee A. Duquiatan, Harold J. Helutin, Reymar B. Miralles, Jake S....

MEEN 301: DC and AC Machinery “Principle of Motor Action, Force, Torque, and Rotation” Presented by: Acquiat, Kaybee A. Duquiatan, Harold J. Helutin, Reymar B. Miralles, Jake S. Rabacio, Clark Justine S. Sarmiento, Jiro Elijah C. Villanueva, Erwin Joseph B. BSME 3-1 Presented to: Engr. Joshua A. Sismaet October 2024  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ TABLE OF CONTENTS TABLE OF CONTENTS................................................................................................................ 1 Introduction..................................................................................................................................3 Objectives of the Report:......................................................................................................... 4 Contents....................................................................................................................................... 5 Basic Principles of Motor Action:........................................................................................ 5 DC Motors: Principles of Operation.....................................................................................6 1. Construction...................................................................................................................6 2. Working Principle........................................................................................................... 7 3. Types of DC Motors....................................................................................................... 8 Applications:.......................................................................................................................9 AC Motors: Principles of Operation...................................................................................10 1.Construction..................................................................................................................10 2. Working Principle......................................................................................................... 10 3. Types of DC Motors..................................................................................................... 11 Applications:.....................................................................................................................11 Comparison of AC Motor and DC Motor:.......................................................................... 12 AC and DC Machinery: Force, Torque, and Rotation....................................................... 13 Introduction...................................................................................................................... 13 Fundamentals of Force, Torque, and Rotation in Electric Motors.................................. 14 1.Force on a Current-Carrying Conductor....................................................................... 14 Lorentz force.............................................................................................................. 15 Motor Action...............................................................................................................15 2. Torque in Electric Motors............................................................................................. 16 3. Rotation in Electric Motors........................................................................................... 17 Key Points in Motor Rotation..................................................................................... 18 DC Motors: Force, Torque, and Rotation...........................................................................19 Working Principle............................................................................................................. 19 Torque Speed Characteristics..........................................................................................21 Direction of Rotation........................................................................................................ 24 AC Motors: Force, Torque, and Rotation...........................................................................27 Induction Motor (AC Motor) Torque Production............................................................... 27 ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Synchronous.................................................................................................................... 28 Torque-Speed Characteristic of AC Motors...................................................................... 29 Induction Motors........................................................................................................... 29 Synchronous Motors.....................................................................................................29 Reversing Rotation in AC Motors.....................................................................................30 Comparison: Torque and Rotation in DC and AC Motors................................................31 Factors Influencing Torque and Rotation:.........................................................................32 Conclusion................................................................................................................................. 33 Activity:.......................................................................................................................................35 References................................................................................................................................. 41 ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 2  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Introduction This paper is concerned with the essential concepts of AC (alternating current) and DC (direct current) machinery, namely motor action, force, torque and rotation. Motors are essential for converting electrical energy to mechanical power which drives everything from home appliances to industrial machinery. The report offers a comprehensive examination of AC and DC motors, elucidating their working principles as well as benefits & uses. The discussion starts from basic laws of electromagnetic induction which actually describe the action of motors. They investigated key parameters such as generation of force in magnetic fields, production of torque, dynamics during rotation to give an integral view about how the motor behaves. This study focuses on the comparison of AC and DC machines to show performance influence by types of design as well as power source. Ultimately the study underlined how important are motors in modern industries and their part to play into technological development. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 3  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Objectives of the Report: To describe the fundamental concepts of motor action in both AC and DC machines, including electromagnetic induction and interaction between currents and magnetic fields. To investigate how force and torque are developed in motors, using mathematical expressions and physical principles. To compare the torque characteristics of AC and DC machines under different load conditions. To explore how electromagnetic forces result in continuous rotation in AC and DC motors. To analyze the role of commutators in DC motors and the impact of synchronous and asynchronous operation in AC motors. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 4  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Contents Basic Principles of Motor Action: Both DC and AC motors operate on the fundamental principle of electromagnetic induction: A current-carrying conductor placed in a magnetic field experiences a mechanical force. Fleming's Left-Hand Rule helps determine the direction of force: ❖ Thumb: Force ❖ Index finger: Magnetic field direction ❖ Middle finger: Direction of current The force acting on the conductor produces a torque that rotates the motor’s shaft. This torque enables mechanical output from electrical energy, forming the foundation of motor action. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 5  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ DC Motors: Principles of Operation 1. Construction A DC motor consists of the following key parts: Stator: Permanent magnets or field windings generating a stationary magnetic field. Rotor (Armature): Contains windings connected to a commutator. Commutator: Reverses the current direction to maintain unidirectional torque. Brushes: Transfer current between external circuits and the rotating commutator. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 6  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ 2. Working Principle When DC voltage is applied, current flows through the armature windings, which are placed in the magnetic field created by the stator. The interaction between the armature current and magnetic field produces a force on the rotor, causing it to rotate. As the rotor rotates, the commutator switches the current direction to ensure continuous torque in the same direction. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 7  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ 3. Types of DC Motors Shunt Motor: A DC shunt motor is defined as a type of DC motor where the field windings are connected in parallel to the armature winding, allowing both to receive the same voltage. Series Motor: In a series motor electric power is supplied between one end of the series field windings and one end of the armature. When voltage is applied, current flows from power supply terminals through the series winding and armature winding. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 8  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Compound Motor: A compound DC motor connects the armature and fields windings in a shunt and a series combination to give it characteristics of both a shunt and a series DC motor. Applications: DC motors are used in applications requiring variable speed and high starting torque, such as Fans, blenders, Vacuum Cleaners, Electric shavers, Hairdryers, Electric Cars, Scooters, Bikes, Forklifts, Golf carts, Trains, Trolleys (for traction motors), Electric Buses, Trams, Subway systems, Conveyor belts, Hoists, Electric cranes, Machine tools, Rolling mills, Elevators, Drills, Screwdrivers, Saws, Lawn mowers, Water pumps, and more. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 9  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ AC Motors: Principles of Operation 1.Construction An AC motor consists of the following key parts: Stator: Contains windings that produce a rotating magnetic field Rotor: Either a squirrel-cage or wound type that rotates due to the field Slip rings (for wound rotor motors): Allow current to flow into rotor windings in some types of motors 2. Working Principle In an AC motor, alternating current is applied to the stator windings, creating a rotating magnetic field. This magnetic field induces a current in the rotor, which generates a force due to electromagnetic interaction. The rotor follows the rotating magnetic field, resulting in continuous rotation. The frequency of the AC supply determines the motor’s speed. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 10  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ 3. Types of DC Motors Induction Motors: Rotor current is induced by the stator’s magnetic field without direct electrical connection. Most common type due to its simple design and robustness. Synchronous Motors: Rotor rotates in synchrony with the stator’s magnetic field. Requires additional means, like a DC exciter, to maintain synchronization. Applications: AC motors are used in industrial equipment, household appliances, and HVAC systems, where high efficiency and minimal maintenance are required. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 11  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Comparison of AC Motor and DC Motor: Feature DC Motor AC Motor Power Source Direct Current (DC) Alternating Current (AC) Speed Control Easy More complex (requires VFD) Torque High starting torque Lower starting torque Maintenance Requires more Low maintenance maintenance Application Electric vehicles, cranes Fans, pumps, industrial machinery ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 12  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ AC and DC Machinery: Force, Torque, and Rotation Introduction Electric motors however are necessary for the conversion of electrical energy to mechanical energy. One of the core functions a motor performs is producing force or torque and rotation that powers different machines and devices. The electric current and magnetic fields induce forces to the motors shafts which helps in rotating of the motor's shaft, these both happens on DC (Direct Current) as well as AC (Alternating current) machinery. In this article, we examine the fundamentals of how force (or torque) and rotation are produced in DC motors vs. AC motors Describe their characteristics Draw comparisons concerning industrial designs Provide information on various applications for them. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 13  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Fundamentals of Force, Torque, and Rotation in Electric Motors 1.Force on a Current-Carrying Conductor When a conductor carrying an electric current is placed in a magnetic field, it experiences a force. This force is a result of the interaction between the magnetic field and the electric current flowing through the conductor. The Lorentz Force Law governs this interaction, and the force is given by: F=BILsinθ Where: (F) = Force (N) (B) = Magnetic flux density (T) (I)= Current through the conductor (A) (L) = Length of the conductor in the magnetic field (m) (θ) = Angle between the field and the conductor ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 14  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ This force is the basis of motor action, causing the rotor to experience torque and rotation. Lorentz force This force, known as the Lorentz force, is essential to motor action. In electric motors, the force acts on the rotor, generating torque and initiating rotation. When the conductor is positioned perpendicular to the magnetic field (θ=90∘), the force is maximized, enhancing motor performance. Motor Action This force acting on the current-carrying conductor is the foundation of motor operation. In motors, the rotor, which is the rotating part of the motor, interacts with the stator's magnetic field. As a result, the rotor experiences a force that causes it to rotate. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 15  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ 2. Torque in Electric Motors Torque is the rotational force that enables an electric motor to turn, determining how effectively the motor can rotate its load. Torque is produced when a force is applied at a distance from the axis of rotation. Formula for Torque: T = F⋅r Where: (T) = Torque (Nm) (F) = Force (N) (r) = Radius (distance from the axis to where the force is applied) In both DC and AC motors, torque results from the electromagnetic interaction between the magnetic fields of the rotor and the stator. This electromagnetic torque drives the rotor to rotate, powering the load connected to the motor’s output shaft. The strength of the torque generated is determined by the current, the motor’s magnetic field, and the radius at which the force acts on the rotor. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 16  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ 3. Rotation in Electric Motors Rotation is the continuous circular motion of the motor's rotor caused by torque. In electric motors, rotation is achieved by maintaining a continuous interaction between the rotor's magnetic field and the stator’s magnetic field. This interaction is facilitated by the alternating or direct current supply, which creates a changing magnetic environment that consistently pushes the rotor in a circular path. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 17  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Key Points in Motor Rotation Direction of Rotation: The direction of the rotor's rotation is dictated by the orientation of the magnetic fields in the stator and rotor. In DC motors, this is controlled by switching the polarity of the current, while in AC motors, it’s managed by the alternating nature of the AC power supply. Rotational Speed: The speed of rotation depends on the frequency of the AC power supply (for AC motors), the strength of the magnetic field, and the current in the conductor. For DC motors, the speed is largely influenced by the voltage applied to the motor and the load on the shaft. Applications of Rotation: Rotation is critical in converting electrical energy to mechanical energy, which powers a vast range of applications. From driving conveyor belts to running household appliances, electric motors rely on rotational motion to deliver mechanical power efficiently. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 18  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ DC Motors: Force, Torque, and Rotation Working Principle Faraday's law of electromagnetic induction. "Whenever a current-carrying conductor is placed in a magnetic field, it experiences a force". When the current-carrying conductor is placed over a magnetic field, there will be an interaction between the magnetic field created by the current-carrying conductor and magnetic field on which the current-carrying conductor is placed, which will cause the conductor to move, i.e. when electric and magnetic field interacts, a mechanical force arise. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 19  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Faraday’s second law of electromagnetic induction states that The flux linkage is the product of the number of turns in the coil and the flux associated with the coil. Where ε is the electromotive force, Φ is the magnetic flux, t is the time, and N is the number of turns. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 20  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Torque Speed Characteristics The torque in case of a dc series motor is proportional to the square of the armature current. This relation is parabolic in nature as shown in the figure. As load increases, armature current increases and torque produced increases proportional to the square of that armature current up to a particular limitation. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 21  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Speed Equation: N = V - IaRa / Ia Hence the speed of the equation, Eb = V and can be assumed constant. So speed - armature current characteristics is rectangular hyperbola ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 22  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Torque and Speed Hence, we can write In this way as torque increases when load increases, the speed decreases. On no load, torque is very small and hence speed increases to dangerously high value. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 23  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Direction of Rotation Simply put, DC motors can turn in either direction (clockwise or counter-clockwise) and can be easily controlled by inverting the polarity of the applied voltage. DC motors can create force in either direction, but they don’t always need to switch rotation to control movement. For example, in applications like haptic feedback, the motor can use "braking" by briefly reversing the voltage. This quickly decelerates the motor until it stops, without reversing the direction. If the reversed voltage remains applied after stopping, the motor will then start rotating in the opposite direction. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 24  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ To determine the direction of the force, use Fleming’s left-hand rule. This rule shows that the force will be perpendicular to both the magnetic field and the current's direction. By positioning your left hand as shown in the image at the beginning of the article, you can align it to match the illustration. This shows us that with the current flowing through the wire “into” the computer screen will cause a force pushing left, in our model, this is equivalent to the motor turning counter-clockwise. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 25  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ This shows that in order to make the motor rotate clockwise, we must reverse the flow of current. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 26  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ AC Motors: Force, Torque, and Rotation Induction Motor (AC Motor) Torque Production In AC induction motors, the stator produces a rotating magnetic field (RMF) when AC power is applied. This rotating magnetic field induces current in the rotor windings (or bars in a squirrel-cage rotor), which creates a secondary magnetic field. The interaction between the two fields produces a force that results in torque, causing the rotor to follow the rotating field. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 27  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Synchronous Synchronous motors synchronize the rotor with the stator's rotating magnetic field, generating torque as the magnetic fields lock in phase. The speed of operation is directly related to the frequency of the electrical supply and the number of poles. The torque angle, the angle between the stator's and rotor's magnetic fields, determines the torque needed to drive the load, unlike induction motors. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 28  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Torque-Speed Characteristic of AC Motors Induction Motors Torque increases with slip (the difference between synchronous speed and rotor speed) until it reaches a peak value, after which it declines. T∝(s⋅Erotor²) Where: s = slip Erotor = rotor-induced EMF. Synchronous Motors These motors deliver constant torque, but require an external source to bring the rotor up to synchronous speed initially. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 29  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Reversing Rotation in AC Motors In three-phase AC motors, reversing two of the three supply phases changes the direction of rotation. In single-phase motors, reversing the auxiliary winding achieves the same effect. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 30  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Comparison: Torque and Rotation in DC and AC Motors ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 31  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Factors Influencing Torque and Rotation: 1. Magnetic Field Strength: Stronger magnetic fields produce higher force and torque. 2. Current Through Windings: Higher currents generate more force, increasing torque. 3. Rotor Inertia: Motors with heavy rotors may take longer to reach full speed but provide smoother operation. 4. Friction and Load: Friction or a high load reduces the effective torque available to rotate the motor’s shaft. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 32  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Conclusion AC and DC machinery work based on basic motor action, force operation, torque generation or rotational movements. The force acts in a direction perpendicular to the conductor and can be detected by putting another current-carrying wire near one with an active path. The armature current in DC motors interacts with a stationary magnetic field (the field), whereas AC motors use rotating magnetic fields produced by the stator to induce rotor currents and motion. This force results in torque, which is necessary for a continuous rotation and depends on parameters including the strength of the magnetic field, I (current) and stands between conductors with respect to the direction of B. They are also used in electric vehicles and robotics because of their ability to provide accurate speed control.DC motors have a simple design. However, AC motors are quite widely used in industrial settings being more efficient and requiring less maintenance. DC motors are best for high-torque and speed-variable use cases but when it comes to the scale of a larger setup, everything prefers AC due to how perfectly they operate. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 33  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ These two types of motors are crucial for converting electrical energy into mechanical work in many areas. As motor control technologies such as inverters and smart controllers continue to develop, the performance of these machines will increase alongside sustainability, optimizing energy efficiency in order for future technological breakthroughs. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 34  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Activity: 1. A mechanic is tightening a bolt using a wrench that is 0.4 meters long. The mechanic applies a force of 50 Newtons perpendicular to the wrench. a. What is the torque applied to the bolt? b. If the mechanic increases the force to 75 Newtons while maintaining the same distance from the pivot point, what will the new torque be? SOLUTION: a. Using the formula T=F⋅r T = (50 N)(0.4 m) = 20Nm Answer: 20 Nm b. For the new force of 75 Newtons: T = (75 N)(0.4 m) = 30Nm Answer: 30 Nm ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 35  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ 2. A straight conductor carries a current of I=5 and is placed in a uniform magnetic field B=0.3T. The length of the conductor in the magnetic field is L=0.4 m. The angle θ between the direction of the current and the magnetic field is 30∘. a. Calculate the magnetic force FFF acting on the conductor. b. If the angle θ were changed to 90∘, what would be the new magnetic force FFF acting on the conductor? SOLUTION: a. Magnetic Force at θ=30∘ The magnetic force on a current-carrying conductor in a magnetic field is given by: F=BILsinθ Substitute the values: F=(0.3 T)×(5 A)×(0.4 m)×sin30∘ Since: sin30∘=0.5: F=(0.3)×(5)×(0.4)×(0.5) ANSWER: F=0.3N ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 36  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ b. Magnetic Force at θ=90∘ If the angle θ\ is changed to 90∘, then sin90∘=1. F=(0.3 T)×(5 A)×(0.4 m)×1 ANSWER: F=0.6N 3. A solenoid with length of L=25cm has a radius of r=4 cm and 500 turns. It is placed in a region where a uniform magnetic field of magnitude 400 gauss makes an angle of 37∘ with the axis of the solenoid. Find the average induced emf if the magnetic field finally is reduced to zero in 0.2s. SOLUTION: 0 = 37° At 0.2 s L = 25 cm = 0.25 m r= 4 cm 0.04 m A = πr2 Bf = 400 G = 400 × 10^4 = 0.04 T Bf = 0 ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 37  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ Since the only changing parameter is the magnetic field B so the change in magnetic flux through each turn of the solenoid is obtained as Δϕm - (Bf-Bi) A cos 0 = (0-0.04)π(0.04)2 cos 37° = 5.1 x 10 Wb The change in total flux through the coil is ΔΦ = Νϕ1 = 0.02 The amount of induced emf is obtained using Faraday's law formula as following E= − ΔΦm/Δt = - 0.02/0.2 ANSWER E = -0.1 ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 38  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ 4. In a manufacturing plant, an induction motor is used to drive a conveyor belt that transports heavy materials. The motor's torque is crucial for ensuring smooth operation, especially when the load varies.Where: k=0.015Nm/V^2. The conveyor is running with a slip of s1​ =0.06, Rotor voltage is Erotor1 =130V. Due to a sudden increase in the load on the conveyor belt, the motor's slip increases to s2=0.08. To prevent overheating, the motor controller reduces the rotor voltage to Erotor2​=110V. Question: 1. Calculate the initial torque T1 produced by the motor before the load change. 2. Determine the new torque T2 after the slip increases and the rotor voltage decreases. 3. Assess whether the motor's torque is sufficient to handle the increased load by comparing T1 and T2. If the torque decreases by more than 10%, suggest if any adjustments are needed. SOLUTION: 1. T1=ks1E1rotor^2 =0.015 Nm/V^2 (0.06) (130V)^2 ANSWER T1= 15.21 Nm ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 39  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ 2. T2=ks2E2rotor^2 =0.015 Nm/V^2 (0.08) (110V)^2 ANSWER T2= 14.52 Nm 3. Percent change = (T2-T1/T1) x 100% = (14.52 Nm - 15.21 Nm)/ 15.21 Nm) x 100% ANSWER PERCENTAGE CHAnge = - 4.54% The torque decreases by approximately 4.54%. The motor can still handle the increased load since the decrease is less than 10% ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 40  POLYTECHNIC UNIVERSITY OF THE PHILIPPINES BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MARAGONDON, CAVITE, PHILIPPINES _________________________________________________________________________ References Fitzgerald, A. E., Kingsley, C., & Umans, S. D. (2013). Electric Machinery. McGraw-Hill. Chapman, S. J. (2012). Electric machinery fundamentals (5th ed.). McGraw-Hill Higher Education. Hacettepe University. (n.d.). EEM473: Electrical machines lecture notes. Hacettepe University Electrical and Electronics Engineering Department. Hughes, A. (2010). Electric motors and drives: Fundamentals, types, and applications (4th ed.). Elsevier. ________________________________________________________________________ MEEN 301 – AC AND DC MACHINERY 41