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MONASH UNIVERSITY FACULTY OF ENGINEERING Department of Mechanical & Aerospace Engineering Subject Name: Dynamics I Subject Code: MEC2401 Subject Coordinator: Associate Professor Ralph Abrahams Room 204 - BUILDING 72 Phones: Ex: 51982 Email: [email protected] 1 Syllabus & Introduction 2 Profile Associate Professor Ralph Abrahams •BE(Hons), PhD(UNSW), Pen Licence •More than 340 international journals and conference publications in Dynamics, Fracture Mechanics and Welding Technology. •Main contribution is in the areas of Aircraft structure, design of truck lifter, cranes and pressure vessels. •Also involve in calculating remaining life of Aircraft structure and component. •Development of a new rail maintenance technology by using laser cladding 3 Manual to Run the Lecture Slides It is recommended that you run the Powerpoints in slideshow mode. This enables the embedded links in the lecture. Things to look out for: 1) Any underlined words contain a link. Click on them in slideshow mode to be directed to more information about the topic and more examples. 2) The tables on slides 5 – 16 provide information on the topics which will be discussed each week and the due assessments. 3) The attendance to the weekly 2 hours practical classes/Zoom sessions are important and the tasks are required to be submitted every week for receiving feedback. The topics covered are outlined in the slides 5-16 tables. 4) There are five laboratory sessions in this unit. The labs will be running from Week 7. A written technical lab report is due in week 12. 5) The assessment tasks are outlined in slide 17. 6) The prescribed text book(s) are mentioned in slides 19 and 20. 7) Professor Abrahams’ book will be uploaded on Moodle. 8) The videos are all available in the uploaded zipfiles, and can be viewed by clicking the icons in the slideshow mode. 4 Lecture /Tutorial Week 1 Lecture Description Introduction to Dynamics. Revision on Kinematics of Particles. Rectilinear Motion. Displacement, Velocity and Acceleration. Plane Curvilinear motion, Rectagular Coordinates, Normal and Tangential Coordinates, Polar Coordinates Lectures Tutorial 1 Revision Problems 5 Lecture /Tutorial Lectures Week 2 Tutorial 2 Lecture Description Dependent Motion of Particles. Constrained Motion of Connected Particles Problems: Constant and Variable Acceleration. Curvilinear Motion: Normal and Tangential Coordinates & Dependent Motion of Two Particles 6 Lecture /Tutorial Week 3 Lectures Tutorial 3 Lecture Description Kinematics of Planar Mechanism: Relative Motion. Translation, Rotation and General Plane Motion. Absolute Motion. Relative Velocity. Problems: Relative Velocity and Acceleration 7 Revision Class Work will be on Moodle by Friday of week 3. Lecture /Tutorial Lectures Week 4 Tutorial 4 Lecture Description Velocity of a Point on a Link using Relative Velocity Method (Vector Analysis and Velocity Diagrams) Problems: Calculating Velocities Using Vector Analysis 8 Lecture /Tutorial Week 5 Lectures Tutorial 5 Lecture Description Acceleration of a Point on a Link Using Vector Analysis Problems: Relative Acceleration, Acceleration Diagram. 9 Lecture /Tutorial Week 6 LECTURE Tutorial 6 Lecture Description Forces in Mechanisms using dismemberment and D’Alembert’s Principle (Inertia Forces). Calculating Forces in Mechanisms Using Dismemberment (Subgroup and Links) Calculating Forces in Mechanisms Using Dismemberment (Subgroup and Links) Revision Class Work 1 is due on Friday of week 6. Revision Class Work 2 will be on10Moodle by Friday of week 6. Lecture /Tutorial Lecture Description Lectures Linear and angular Impulse of free particles. Week 7 Tutorial 7 Problems: Calculating Forces in Mechanisms Using Dismemberment (Subgroup and Links) 11 Lecture /Tutorial Lecture Description Angular momentum of rigid bodies. Moment and product of inertia. Lectures Week 8 Test – Time will be announced Covering Topics up to week 6 10% of total marks Tutorial 8 Problems: Impulse, angular Momentum of free particles. 12 Lecture /Tutorial Week 9 Lectures Tutorial 9 Lecture Description Balancing of Several Masses Rotating in the Same Plane and Different Planes. Problems: Calculating the Balancing Masses 13 Week 10 Lecture /Tutorial Lecture Description Lectures Balancing of Reciprocating Masses Tutorial 10 Problem: Calculating the Balancing Masses for the Reciprocating Mechanism 14 Lecture /Tutorial Week 11 Lectures Tutorial 11 Lecture Description Free Vibration, Natural Frequency, Equation of Motion Using Newton’s Law and Lagrange Equation Problems: Vibration Second Revision Class work is15due on Friday of week 11. Lecture /Tutorial Week 12 Lectures Tutorial 12 Lecture Description Equation of motion Lagragian Mechanics + Revision using Solving Previous Exam Papers 16 Assessments: Examinations Final Assessment: 60% Mid-semester Test: 10% Class Works and Online Quizzes: 20% Laboratories and Technical Report: 10% (The lab report should be submitted in the provided format) 17 Laboratories include three Experiments: 3 Lab experiments run from Week 7 to Week 9. Determining the amount and the position of the unbalanced mass in a dynamic system. Balancing of rotating masses in single plane. Balancing of rotating masses in different planes. * Two lab sessions in weeks 10 & 11 focus on verification of the theoretical calculations prior to submitting the report. 18 Dynamics Book Dynamics by Ralph Abrahams Will be available On Moodle Please Note: This book (Dynamics) is covering the whole 12 weeks of Dynamics I (MEC2401). 19 Prescribed Text: Author: Associate Professor Ralph Abrahams Title: Dynamics Publisher: The book chapters will be uploaded on Moodle, throughout the semester. MERIAM, J.L., KRAIGE, L.G.,“Engineering Mechanics”, Vol. 2, Dynamics, ninth Edition, Wiley, 2019. Hibbeler, R.C., “Engineering Mechanics”. Dynamics, 11th Edition, Prentice-Hall, 2007 20 21 You can view the video by clicking on this image! Dynamic systems include rotating or moving mass or masses. 22 Internal Combustion Engine (ICE) 23 Animation for kinematics of this mechanism will be available by pressing the play button. 24 Animation for kinematics of this reciprocating mechanism will be available by pressing the play button. 25 Toggle Mechanism Animation for kinematics of this toggle mechanism will be available by pressing the play button. This mechanism is used to drive three pistons with two cranks to provide more power . It is used for applications such as breaking rocks that requires high impact. 26 When we conduct a dynamics analysis for Industry the following points have to be considered: If the mechanical design involves rotating or moving parts, a dynamic analysis should be carried out to ensure that the system is dynamically balanced and there is no rotating/reciprocating unbalanced materials. By having the system dynamically balanced we will be able to reduce the noise & vibrations and increase the life of components, aeroplanes, etc …... Noise and vibrations can rock the dynamic systems and cause failures. By dynamic balancing, we will be able to increase the productivity and reduce losses caused by vibrations and noise. 27 Caterpillar D7G Gear Box Failure Investigation performed by me on a gear that failed as a result of being overloaded. Future lectures will contain more information on this analysis, which may be similar to the dynamic analysis you will perform in the future as Mechanical and/or Aerospace Engineers. SEM of Failure Surfaces 28 Chevrolet Corvette Cars Driving shaft Optimisation of a driving shaft was designed by me with the aim to reduce the weight of this component and increase the speed. 29 DSA Structural Tube Cross Section Viewed from the rear looking forward in vehicle 63.5mm arc shown in red must be maintained for shifter linkage clearance. Black outline represent maximum section envelope for the extrusion. Z 127 mm Y X Prop Shaft Center Line Blue outline represent minimum section envelope for the extrusion. 127 mm GM Confidential 30 Optimised Cross Section of the Driving Shaft 31 Dynamic analysis involves kinematics and kinetics studies of the system. Dynamic analysis Kinematics Geometrical aspects Of motion kinetics 2D&3D analysis of ( Displacement, velocity, acceleration) 2D&3D Analysis of Forces, Torques, Couples, Power, Balancing of Rotating Materials, Noise and Vibrations 32 Kinematics Equations of Motion Constant acceleration V V0 at 1 2 S V0 t at 2 2 2 V V0 2as 33 Equation of Motion Variable acceleration VdV adS dS V dt dV a dt 34 CURVILINEAR MOTION Tangential acceleration Total Acceleration vt wr A a Radial acceleration a at an ρ = Radius of curvature dVt at dt 2 Vt an a a a 2 2 t n 35 Angular Velocity and Acceleration Displacements s qr q Angular displacement r = radius of the circle or curvature of path Speeds v wr w Angular Velocity Accelerations aar a angular acceleration • Every point on the rotating object has the same angular motion • Every point on the rotating object does not have the same linear motion e.g. pulley N=RPM ( Revolutions per minute) w = N x 2π/60 = rad/sec 36 Normal and Tangential Components an v2 v wr dv dwr at ar dt dt dw a Angular Accelerati on dt •Tangential component of acceleration reflects change of speed and normal component reflects change of direction. • Tangential component may be positive or negative. Normal component always points toward centre of path curvature. 37 38 Dependent motion The motion of one particle depends entirely on the motion of the other 39 Cable 1 B= 4Kg Cable 2 A= 6KG 40 Relative Velocity of Two particles Moving in Straight Lines v A vB v AB 41 v A vB v AB A B o VA VA VB a VAB b VB 42 Relative Velocity of Rigid Bodies The general plane motion of a rigid body can be described as a combination of translation and rotation. To view these “component” motions separately we will use a relative-motion analysis involving two sets of coordinate axes. The position vector rA specifies the location of the “base point” A, and the relative-position vector rB/A locates point B with respect to point A. By vector addition, the position of B is then rB =rA + rB/A 43 drB =drA + drB/A drB drA drB / A dt dt dt VB =VA + VB/A differentiate with respect to time aB = aA+ aB/A 44 Velocity in mechanism This year we will study the velocity in mechanism by applying the relative velocity method using the relative velocity equation: vA = vB + vA/B 1-Vector Analysis 2- Velocity Diagram 45 Studying the velocity, acceleration, displacement of the planar mechanism we can design the cutting stroke and the returning stroke. By inspecting, the cutting stroke takes more time than the return stroke. 46 Shaper Mechanism Animation for kinematics of this Shaper mechanism will be available by pressing the play button. 47 Animation for kinematics of this Toggle mechanism will be available by pressing the play button. Toggle Mechanism 48 Animation for kinematics of this Toggle mechanism will be available by pressing the play button. Toggle Mechanism 49 Forces In Mechanisms Forces, torques, and NA powers transmitted from link to link need to be calculated to design the dimensions and the materials of the links and joints. Also we need to check that the system is dynamically balanced to avoid forced vibration and noise. A 3 300 2 W3 G2 W2 F Fi2 T2 NB 4 Fi4 B W4 50 Linear motion D’Alambert’s Principle SF = ma -- For Dynamic equilibrium SF =0 ---- For Static equilibrium SFx=max SFy=may Rotational motion T T i Ia Τ = Torque I = Moment of Inertia α = Angular acceleration 51 Dynamic equilibrium The equation ΣF=ma can be written as ΣF-ma=0 This is the most important equation in Dynamics analysis (D’ Alambert’s Equation) Free Body Diagram (F.B.D.) Free Body Diagrams are always required for the Kinetics analysis The excavator’s arm ABC is considered as a single rigid body. Its mass is 1200 kg and the moment of inertia about its centre of mass is IG=3600 kg-m2. if point A is stationary, the angular velocity of the arm is zero, and the angular acceleration is 1.0 rad/s2 counter clockwise, what force does the vertical hydraulic cylinder exert on the arm at B? The distance from A to the centre of mass is = (3.4) (3) 4.53 m rG / A 2 2 at a r 1 4.53 4.53m / s 2 an w 2 r 0 since ω 0 ω=0 α Ti at G an 54 ω=0 Taking moment about A MA 0 Static Case α Ti at G an 1.7FB 3.4mg TA TA I Aa Dynamic Case Fit mat ma r 1200(1 4.53) 5436 N Fi n man m w 2 r 0 since ω 0 1.7 FB 3.4 1200 9.81 3600 a mr 2a Ti Fin 3600 1 1200 4.53 1 2 solving FB 40146 N 40.146 kN Fit mg FB 55 Balancing of Rotating Masses 56 57 Rolling Contact Fatigue & Wear as a result of Dynamic Unbalanced Load 58 In Balancing of Rotating Masses We will be studying the following: Balancing of a single rotating mass by a single mass rotating in the same plane. Balancing of different masses rotating in a single plane. Balancing of different masses rotating in different planes. 59 Balancing of a single rotating mass by a single mass rotating in the same plane. m1 Disturbing mass r1 r1 Axis of Rotation r2 r2 m2 Balancing mass Centrifugal force due to mass FC m .w 2 .r 60 Balancing of Several Masses Rotating in the Same Plane c FC3 FC2 FC2 m2 d FC4 FC1 r2 b θ2 FC1 e r1 θ1 θ3 a r3 m4 FC4 m3 FC3 61 Balancing of different masses rotating in Different planes. 62 Crankshaft balancer Crankshaft Balancing Video is available by pressing the play button. 63 Balancing of Reciprocating Masses to eliminate the shaking force and a shaking couple, Hammer Blow Reciprocating Mechanism 64 65 66 Natural Frequency of Free and Longitudinal Vibrations Using Newton Law and Lagrange Mechanics 67 Final EXAMINATION (60%) The exam will cover major classworks, weekly classwork problems, and lecture examples. The uploaded Dynamics Text Book should be enough to revise for your exam. 68