- 1 - Department of Mechanical and Aeronautical Engineering. Vibration and Noise 320

Transcription

1 - 1 - Department of Mechanical and Aeronautical Engineering Vibration and Noise 320

2 - 2 - Copyright OVERVIEW AND APPROACH Vibration and Noise 320 focuses on the motion of systems in which the elastic deformation of the system is important (in contrast to Dynamics 210 where the motion of the system is large in comparison to its elastic deformation). Such systems are widespread and do not only form the basis of fundamental human activities such as speech, but is of importance on almost every terrain of mechanical engineering. Very often vibration and noise are undesirable and must be reduced to acceptable levels. Examples of this are the vibration and noise in automotive applications, the flutter of aircraft wings and vibration of turbine blades. In other cases vibration and noise may be usefully applied, for example the use of vibration feeders in coal plants and vibration monitoring for the early identification of system problems. The impact of vibration and noise on man and his environment is an aspect of increasing importance and is finding its way into standards and legislation. Examples of this are noise in the work place, aircraft noise in the vicinity of airports and the effects of hand-held machinery on operators. To understand and control these systems and their effects, you must be able to: Formulate dynamic models of typical mechanical systems (single and multi-degree of freedom systems). Discrete models are emphasised because of their utilitarian value. A limited exposure to continuum models is however also necessary - especially in the light of the increasing importance of sound and noise. Formulate the governing equations for typical inputs. Find solutions for the governing equations under steady and transient conditions. For this purpose the use of computer techniques are emphasised. Standard numerical solutions from the mathematics are used for this purpose and the focus here is not on the algorithms. Interpret en use results for design purposes. Specify sensible experiments to determine system behaviour, based on sufficient understanding of the measuring process. In all engineering disciplines the ability to work in groups is of paramount importance. Therefore, as a secondary purpose with this module, we want to contribute and develop your ability in this regard. The module further serves to prepare you for the Control Systems 410 module.

3 - 3 - ORGANISATION DEPARTMENTAL STUDY GUIDE This study guide is a crucial part of the general study guide of the Department. In the study guide of the Department, information is given on the mission and vision of the department, general administration and regulations (professionalism and integrity, course related information and formal communication, workshop use and safety, plagiarism, class representative duties, sick test and sick exam guidelines, vacation work, appeal process and adjustment of marks, university regulations, frequently asked questions), ECSA outcomes and ECSA exit level outcomes, ECSA knowledge area, CDIO, new curriculum and assessment of cognitive levels. It is expected that you are very familiar with the content of the Departmental Study Guide. It is available in English and Afrikaans on the Department s website. English 12(1).pdf Afrikaans pdf Take note of the specific instructions in the above study guide on: a. Safety b. Plagiarism c. What to do if you were sick (very important)? d. Appeal process on the adjustment of marks LECTURERS AND COMMUNICATION Lecturers: Name Office Telephone Lecturers Prof PS Heyns (PSH) 10-7 Eng stephan.heyns@up.ac.za Mr KP Grimsehl (KPG) Eng karl.grimsehl@up.ac.za Secretary TBA 10-8 Eng Instructors TBA Mr Grimsehl coordinates the module, handle the admin and marks.

4 - 4 - Consultation hours: By appointment. You are encouraged to arrange appointments with the lecturers by . You can also arrange appointments with Prof Heyns through Mrs Calder at tel Notice board: The official notice board for this module is the MVR320 ClickUP Announcements. For some practicals arrangements we will use the notice board in the passage at the workshops. Post-box: All assignments and practical reports must be posted in the post-box marked: MVR320. MATERIAL Textbooks: Rao,S.S. Mechanical vibrations. 5th edition in SI units. Pearson. Study guide: This guide has been carefully compiled to assist you to work independently and structured. The document is however subject to changes by announcement in class or on ClickUP. ClickUP: The ClickUP site is very actively used in this module and it is expected of students to consult it daily. Powerpoint Slides are continuously updated and the date of the last update is displayed to assist you. The Announcements functionality is used as the primary mechanism of formal communication. LEARNING ACTIVITIES Lectures: 3 lectures per week for 12 weeks. Through the semester you are expected to spend about two hours of preparation for every hour lecture time on this module. You are further expected to attend lectures regularly and be ready to participate in class discussions at any time. Group work: Modern teaching in engineering emphasises the ability of students to function in groups. For this module you will be grouped in groups of 6 (not less than 5 and not more than 7). These groups will work together in the practicals and assignment. For all group work only one consolidated report must be submitted. To prevent individual students from taking a free ride, students must however indicate the contribution of each student to the assignment and marks will be scaled accordingly. Computer work: Much of the work in this module is computationally intensive. Since you can, however, not develop a good feel for this subject without doing the computations, convenient access to a computer is necessary. You are expected to have a good working knowledge of OCTAVE or MATLAB. We are in the process of switching over to OCTAVE because it is free, which will empower students by allowing continued use of OCTAVE after completion of their studies. The package can be

5 - 5 - downloaded from the UP server at: Some material on the web is still in MATLAB and will gradually be transferred to OCTAVE. The working of problems as indicated in the study guide is of the utmost importance to master this work. You are expected to do your problems regularly. However you do not have to submit them. Solutions to underlined problems are posted on the web page. You may compare your solutions to these after you have tried them yourself. Solutions to the other problems will not be provided to give you an opportunity to get accustomed to doing problems without knowing the answers. You are however encouraged to discuss the problems and your solutions with your group members. Tutorial classes: Two tutorial classes will be presented, one before each test. It is the responsibility of the student representatives to determine an appropriate date and time in consultation with the lecturer. Practicals: There are 3 compulsory practicals, namely: (1) Photogrammetry and vibrations date TBA (2) Modal analysis date TBA (3) Vibration monitoring date TBA Comprehensive consolidated group reports must be submitted on practicals (1) and (2). A brief report on practical (3) will suffice. The content and presentation of reports will be evaluated. See p.17 for further information on practicals. Reports must be typed and should linguistically be of a high standard. The standard cover page on which you sign a statement regarding plagiarism must be attached to all homework that is handed in for assessment in this module. The Cover Page for MVR320 reports can be found on the Module Admin page op ClickUP. Assignment: Each group must submit one assignment, which will be graded. The assignment will comprise a practical problem with an open end and will be posted on the ClickUP site. The assignment must be submitted strictly in accordance with the specified due date. Only one consolidated group effort must be submitted in the Module post box. The due date is as follows: Assignment Date TBA Tests and examinations: Tests and examinations will all be closed book. The prescribed formula page that is posted on the ClickUP site (see Module Admin page) will be attached to all tests and examination papers. It is your responsibility to familiarise yourself with the meaning of everything that appears on the formula page, before tests and exams. No questions relating to the formula page will be answered during tests or exams. All assessment events will concentrate on problem solving. There will be only one sick test for both semester tests. This will take place during October and will cover all the work up to that stage.

6 - 6 - Use of calculators: The departmental policy on the use of calculators for closed book modules is applicable. For more info see the departmental website. Assessment marks: Semester marks are calculated as follows: Test 1 37 % Test 2 38 % Assignment 10 % Practicals 15 % The final mark is calculated as follows: Semester mark: 50 % Exam mark 50 % To pass this module, the candidate must obtain a final mark of at least 50%, participate in all practicals and obtain a sub-minimum average of 50% for the practicals and the assignment together. No marks will be carried over from one year to the next. Candidates repeating the module must also redo the practicals.

7 - 7 - STUDY MODULE STRUCTURE The module is comprised of the following study themes: VIBRATION AND NOISE 320 INTRODUCTION TO VIBRATION SINGLE DEGREE OF FREEDOM SYSTEMS Free vibration Harmonic excitation General forcing Discuss Test 1 MULTIDEGREE OF FREEDOM SYTEMS VIBRATION CONTROL Discuss Test 2 VIBRATION MEASUREMENT & MONITORING CONTINUUM SYSTEMS TECHNICAL ACOUSTICS Lecturer (lectures) Planned date PSH (4) 21, 22, 22 & 28 July KPG (3) 29, 29 July, 4 August KPG (4) 5, 5, 11, 12 August KPG (2) 12, 25 August KPG (1) 26 August KPG (4) 26 August, 1, 2, 2 September PSH (7) 4, 4, 15, 16, 16, 22 Sep 13 Oct PSH (1) 14 October PSH (3) 14, 20, 21 October KPG (2) 21 & 27 October PSH (4) 28, 28 October, 3, 4 Nov For each study unit fundamental concepts are identified. You must be able to explain each of these concepts properly and illustrate where applicable. For each study unit clear learning outcomes are identified. These outcomes form the basis of all assessment in this module. In the study of the learning outcomes it is critical to note the cognitive domain in which each of these outcomes must be mastered.

8 - 8 - STUDY THEME 1: INTRODUCTION TO VIBRATION 4 lectures Module overview Why Vibration and Noise? Basic concepts of vibration Classification of vibration Vibration analysis procedure Spring elements Mass (inertia) elements Damping elements Harmonic motion Study guide Rao bedded Rao 1.4 Rao 1.5 Rao 1.6 Rao 1.7 Rao 1.8 Rao 1.9 Rao 1.10 degree of freedom, generalised co-ordinate, discrete and continuum systems, free vibration, forced vibration, linear vibration, non-linear vibration, deterministic vibration, random vibration, modelling elements (spring, mass, damper), series and parallel connection of modelling elements, equivalent mass and stiffness, viscous damping, Coulomb-damping, material damping, harmonic motion, periodic motion, amplitude, oscillation period, frequency, natural frequency, phase angle, beating, octave, decibel. 1. Explain the effect of vibration on the human body with reference to hand-arm vibration and wholebody vibration. 2. Explain why the Tacoma Narrows bridge failed. 3. Construct discrete dynamic models of real physical systems. 4. Evaluate the applicability of models for real physical systems. 5. Classify vibration phenomena. 6. Implement the typical vibration analysis procedure in the solution of vibration problems. 7. Explain the modelling assumptions for mass, spring and damping elements. 8. Explain and compute the energy flow in a system comprised of a mass, spring and damper. 9. Construct equivalent single degree of freedom models for typical mechanical systems. 10. Describe harmonic motion in terms of complex numbers. Do the following problems from Rao: 1.1, 1.4, 1.5, 1.7, 1.11, 1.24 (see front page of Rao for formulae), 1.28, 1.38, 1.49, 1.50, 1.54 (also calculate k eq ), (check your answers with OCTAVE), 1.87 (plot the time response with OCTAVE), Solutions to underlined problems are posted on the ClickUP site (Sample Problems).

9 - 9 - STUDY THEME 2: FREE VIBRATION OF SDOFs 3 lectures Introduction Undamped translational system Undamped torsional system Rayleigh s energy-method Free vibration with viscous damping Stability conditions Rao 2.1 Rao 2.2 Rao 2.3 Rao 2.5 Rao to plus Rao 2.11 undamped system, damped system, free vibration, D'Alembert's principle, principle of conservation of energy, static equilibrium, characteristic equation, eigenvalues, harmonic oscillator, stability, Rayleigh's energy method, critical damping constant, damping ratio, underdamped system, critically damped system, overdamped system, logarithmic decrement. 1. Formulate the equation of motion for a single degree of freedom system by means of Newton's second law, D'Alembert's principle, and Rayleigh's energy method. 2. Explain in broad terms how the development of an expression for the solution for the equation of motion may be done (eq and eq. 2.70). 3. Explain the nature of the roots of the characteristic equation of a damped system and discuss the physical implications thereof. 4. Calculate the natural frequency of a typical single degree of freedom system. 5. Calculate the free vibration response of a typical single degree of freedom system. 6. Demonstrate stability and instability by means of an example. 7. Determine the damping of a system by means of the logarithmic decrement. 8. Evaluate the level of damping in typical SDOFs by looking at its free vibration. Do the following problems from Rao: 2.5, 2.7, 2.12, 2.24, 2.25, 2.29, 2.71, 2.99 (demonstrate graphically with OCTAVE), (demonstrate graphically with OCTAVE), 2.109, Solutions to the underlined problems are posted on the ClickUP site.

10 STUDY THEME 3: HARMONIC EXCITATION 4 lectures Introduction Equation of motion Response of undamped system under harmonic force Response of damped system under harmonic force Response of damped system under F(t)=e i t Response of damped system under harmonic motion at the base Rao 3.1 Rao 3.2 Rao 3.3 Rao 3.4 Rau 3.5 Rao 3.6 harmonic response, transient response, magnification factor, resonance, beating, quality factor, half power points, bandwidth, complex frequency response, displacement transmissibility, force transmissibility. 1. Explain the steady response of a single degree of freedom system under the influence of a harmonic force (at different frequencies) with specific reference to magnification factor and phase angle. 2. Compute the steady and transient response of a single degree of freedom system subjected to a harmonic force. 3. Explain the steady response of a single degree of freedom system under the influence of harmonic motion of the base (at different frequencies) with specific reference to displacement transmissibility and phase angle. 4. Compute the steady and transient response of a single degree of freedom system subjected to harmonic base motion. Do the following problems from Rao: 3.30, 3.34, 3.35, 3.41, 3.52, 3.55 (first do through analysis - then by systematically varying the speed and plotting the corresponding amplitudes in OCTAVE), 3.64, 3.67, 3.103,

11 STUDY THEME 4: GENERAL FORCING 2 lectures Introduction Non-periodic excitation Runge Kutta numerical integration Response under a general periodic force (only second order systems) Rao 4.1 Notes on ClickUP under Study Material Rao 4.2 Rao 1.11 Fourier-series expansion, Gibbs phenomenon, frequency spectrum. 1. Explain the use and application of the Fourier-series expansion for the analysis of systems with periodic excitation. 2. Compute a Fourier series expansion of a periodic force input and use it in the computation of the response of a single degree of freedom system. 3. Compute the response of a system excited by a general force function by using Runge Kutta integration in OCTAVE. Do the following problems from Rao: 4.5, 4.8, 4.94, 4.95 Also use OCTAVE ode45.m or equivalent for 4.62 and Compare the computed responses. Investigate the effect of increased damping.

12 STUDY THEME 5: MULTIDEGREE OF FREEDOM SYSTEMS 4 lectures Introduction Modelling of continuous systems as MDOF systems Using Newton's second law to derive EoM Torsional systems Eigenvalue problem Solution of the eigenproblem Co-ordinate coupling Rao 6.1 Rao 6.2 Rao 6.3 Rao 5.4 Rao 6.9 Rao 6.10 Rao 5.5 characteristic equation, fundamental frequency, dynamic matrix, standard form of the eigenvalue problem, static and dynamic coupling. 1. Construct a discrete multidegree of freedom model of a physical system. 2. Formulate equations of motion for a discrete multidegree of freedom system. 3. Solve the eigenproblem for a simple system (2 or 3 degrees of freedom) by using hand methods. Do the same for larger systems by using eig.m in OCTAVE. 4. Generalise the numerical solution method that you studied as part of the work on SDOFs, for MDOFs. You will be assessed on this as part of the compulsory assignment. Do the following problems from Rao: 5.4 (verify with eig.m), 5.5, 5.12 (verify with eig.m), 5.24, 5.37, 5.40, 5.53 (do with ode45.m), 5.57, 6.65, 6.68, 5.90, Additional Problem.

13 STUDY THEME 6: VIBRATION CONTROL 7 lectures Introduction Vibration criteria Reduction of vibration at the source Balancing of rotating machines Whirling of rotating shafts Balancing of reciprocating machines Control of vibration Control of natural frequencies Introduction of damping Vibration isolation Vibration absorbers Rao 9.1 Rao 9.2 Rao 9.3 Rao Rao 9.5 Rao 9.6 Rao 9.7 Rao 9.8 Rao 9.9 Rao 9.10 single-plane balancing, multi-plane balancing, reciprocating machines, critical speed, loss factor, vibration isolation, transmissibility, isolator, shock isolation, shock spectrum, active vibration control, vibration absorber. 1. Explain what a vibration severity chart is and show how it is used for the evaluation of vibration levels. 2. Balance purely rotating machines using single-plane and two-plane balancing techniques. 3. Compute the response of an elastic shaft on bearings. 4. Balance a reciprocating machine. 5. Evaluate the use of different techniques to control vibration for typical applications. 6. Develop vibration control strategies for typical mechanical problems. 7. Compute the properties of vibration isolators. 8. Design vibration absorbers for machinery exposed to tonal excitation. Do the following problems from Rao: 9.3, 9.6, 9.10, 9.11, 9.13, 9.15, 9.16, 9.17, 9.23, 9.24, 9.25, 9.26, 9.27, 9.29, 9.32, 9.39, 9.63, 9.69, 9.74 Write an OCTAVE program to do single-plane and two-plane balancing and apply to problems 9.3 and 9.13.

14 STUDY THEME 7: VIBRATION AND SOUND MEASUREMENT 3 lectures Introduction Transducers, measuring instruments and exciters Signal analysis Dynamic testing of machines and structures Experimental modal analysis Machine condition monitoring and diagnosis Rao 10.1 Rao 10.2 to 10.5 Rao 10.6 Rao 10.7 Rao to Rao 10.9 strain gauge, displacement transducer, velocity transducer, accelerometer, vibration pickup, vibrometer, velometers, phase and amplitude distortion, Frahm and Fullarton tachometer, vibration exciters, FFT, time windows, anti-aliasing, spectrum analyser, filters, operational deflection modes, modal analysis, Bode diagram, Argand diagram, Nyquist diagram, defect frequency, condition based maintenance, time domain analysis, frequency domain analysis. 1. Select appropriate motion sensors for practical problems and evaluate their strong and weak points. 2. Calculate the characteristics of accelerometers and velocity transducers. 3. Calculate the accuracy with which transducers with specified characteristics measure vibration over a specific frequency band. 4. Specify accelerometers for typical tests. 5. Evaluate the use of various time and frequency domain techniques for condition monitoring. Do the following problems from Rao: 10.2, 10.9, 10.14, 10.18, 10.20, 10.24, 10.25, 10.27,

15 STUDY THEME 8: CONTINUUM SYSTEMS 2 lectures Introduction Transverse vibration of a string Longitudinal vibration of a bar Torsional vibration of a rod Rao 8.1 Rao 8.2 Rao 8.3 Rao 8.4 partial differential equation, mode shape, natural frequency, node, boundary condition. 1. Describe the difference between continuous and discrete systems. 2. Formulate boundary conditions for the vibration of strings, bars and rods and discuss the influence thereof on the natural frequencies of the system. 3. Compute the natural frequencies and positions of the nodes for: The transverse vibration of a string with both ends fixed The longitudinal vibration of a bar The torsional vibration of a rod by using standard results. 4. Sketch the mode shapes for the cases mentioned above. 5. Discuss the effect of axial forces on the natural frequencies of beams. 6. Derive the PDE to be solved for the natural frequencies and mode shapes for: The longitudinal vibration of a rod. The torsional vibration of a bar. Do the following problems from Rao: 8.1, 8.2, 8.3, 8.4, 8.6, 8.10

16 STUDY THEME 9: TECHNICAL ACOUSTICS 4 lectures Sound waves Sound levels, decibels and spectra (Octave analysis) Sound directions Sound measurement Noise and man Noise and legislation Noise control Technical Acoustics Notes on ClickUP Study Material Also take cognisance of the WHO Guidelines on Community Noise decibel, sound intensity, sound power, sound pressure, sound level, sound directions, absorption, reflection, transmissibility, sound isolation, acoustics, noise levels, weighting functions, correlated and uncorrelated sources. 1. Explain the effects of noise on human hearing. Explain which legislation is applicable for the evaluation of noise levels, and explain the implications thereof for practising engineers. 2. Compute the total noise at a particular point caused by various noise sources. 3. Compute the total noise at a specific point caused by various noise sources, as well as the relative importance of the sources. 4. Design appropriate noise control systems. See problems on ClickUP under Study Material

17 PRACTICALS ARRANGEMENTS GENERAL ARRANGEMENTS FOR PRACTICALS General a) All practicals will take place in the Sasol Laboratory for Structural Mechanics and will take about one-and-a-half hours. b) Groups must make their own reservations for a suitable time. c) Unprepared groups may be declined permission to proceed with the practical. d) Every group must do all three practicals. e) Every student must be present and participate in each practical. f) A sub-minimum of 50% for practicals and the assignment is required for entrance to the exam. g) No student will be exempted from practicals. h) Students must strictly observe the safety rules in the labs (including clothing and closed shoes.) Technical Information Study the slide show: Measurement in the Sasol Lab before you do the Practicals. Reports a) Document your findings thoroughly for pracs (1) and (2). Your report must typically include the following: Purpose (detailed) Instrumentation Approach Results Conclusion and evaluation (Particularly important! Devote sufficient attention to the critical discussion and evaluation of your results.) b) Post a group report in the post-box within one academic week after completion of practical (test weeks do not count as academic weeks for this purpose). c) Each report must have a standard cover page that can be obtained from the ClickUP Module Admin page. d) All reports must be typed. Enquiries The following members of staff are finally responsible for practicals: 1. Photogrammetry and vibrations Prof PS Heyns and TA 2. Modal analysis Prof PS Heyns and TA 3. Vibration monitoring Prof PS Heyns and TA