Acoustics-An An Overview. Lecture 1. Vibro-Acoustics. What? Why? How? Lecture 1

Transcription

1 Vibro-Acoustics Acoustics-An An Overview 1 Vibro-Acoustics What? Why? How? 2

2 Linear Non-Linear Force Motion Arbitrary motion Harmonic Motion Mechanical Vibrations Sound (Acoustics) 3 Our heart beat, our lungs oscillate, we hear because our ear drum vibrates Vibration even makes us snore!! The light waves which permit us to see & sound waves through which we hear entail vibration We cannot even say Vibration without vibration of larynges, vocal cord We move by oscillating our legs We limit out discussion to MECHANICAL VIBRATION & Noise i.e. Vibration & Acoustics of Dynamic Systems What is a Dynamic System??? Any System that contain Mass and Elasticity. 4

3 Friend Conveyors, Hoppers, Compactors, Pneumatic Drills, etc. Opening of a cork from a wine bottle Washing Machine Mechanical Shakers, Mixers, Sieves, Sorters, etc. Musical Instruments Clocks, Watches Medical Field Massagers, etc. Foe RESONANCE RESONANCE RESONANCE Tacoma Narrows Bridge Similar problems in machine tools, vehicles, turbines, pumps, compressors, buildings, aircraft & spacecraft systems Excessive vibration leads to loosening on parts, noise & eventual failure Effects of vibration on human body: Discomfort, Fatigue, Loss of Efficiency Sound quality in products 5 Vibro-Acoustic Design Considerations Acoustic Criteria Noise: Hearing Damage, Annoyance Speech Intelligibility, Enjoyment of Music Sound Quality: Perception & Judgment of Product/Process Quality Warning Signals: Use of sound to determine safety Use of Sound for Diagnostics & Health Monitoring Vibration & Dynamic Design Criteria Localized Damage, Fatigue, Human Discomfort Roughness or Harshness of Operation & Environment Use of Vibration for Diagnostics & Health Monitoring Structural Integrity & Crashworthiness 6

4 Automotive Noise & Vibration Acoustic Response (drivers ear) Vibration Response (steering column) Powertrain Forces Road Inputs (forces) Aerodynamic Forces 7 Building Blocks: m, c, k The fundamental building blocks of a physical system that undergoes dynamic behavior are; m Mass elements, m Energy dissipation elements (dampers), c Energy storage elements (springs), k 8

5 Real Structures (m, c, and k) 9 Basic System (SDOF) F(t) m X(t) applied force k ground c m X Applying Newton's Law: X Forces = mass * acceleration spring damping force spring force + damping force + applied force = mass * acceleration 1

6 Free Vibration Response.15 damped free vibration.1.5 amplitude time - seconds Given an initial state of energy and no applied force, an exponentially decaying harmonic motion will result. This motion is characteristic of the physical properties (M,C,K) of the system. 11 k m ground Fundamental Properties c X(t) Natural Frequency ωn = Natural Frequency (Hz) f n K M ωn = 2 π Damping Ratio ζ = 2 C KM Damped Natural Frequency ω d = 1 ζ 2 ω n 12

7 Free Vibration Response.15 damped free vibration amplitude The free response of the system can be described in terms of the fundamental properties time - seconds x(t) = e ζω nt ( Asin( ω t + Θ) ) d Forced Response k X(t) m c ground F(t) F(t) = Fcos(2πft) Amplitude of Force F Steady State Response x(t) = X cos(2πft + Φ) Displacement - X time X time 14

8 Forced Response 1 1 X F 1 X F = [( K Mω ) + ( Cω) ] fn Freq Φ = tan 1 Cω K Mω 2 Φ degrees f n Freq Effect of Damping on Forced Response X F 1 2 zeta(ζ) 1% 2% 5% 1 1 1% 2% 5% Freq Φ zeta(ζ) 1% 2% 5% 1% 2% 5% Freq. 16

9 Regions of the FRF 1 Frequency Response Function Log-Magnitude 1-1 damping controlled region mass controlled region stiffness controlled region Frequency Hz -5 Phase Frequency Hz 17 Total Response.6 X(t) steady state.4.2 X(t) transient time - seconds.1.8 SDOF total response time - seconds 18

10 k2 m2 c2 k3 m3 c3 Real Structures p(t) m1 k1 c1 mode 1 p(t) p(t) mode 2 mode Mode Shapes mode mode mode 3 6 2

11 Source - Path - Receiver Concept Source Path Receiver Sources: Engine, transmission, transfer case, prop-shaft,rotating components, chain drives, wind, pumps, road surface, etc. Paths: Structure-borne or airborne Receiver: Operators ear, steering column, seat, passengers ear/seat, passby observers. 21 Source, Path, Receiver Characteristics Source: Depends on the definition of the analysis Apparent source of energy, e.g. Electric motor Vector Quantity, e.g. rotating unbalance, acoustic energy Characterized by forces, moments, volume-velocities Operating System, e.g. IC engine, washing machine, AC compressor 22

12 Sources and Paths 23 Characterizing Sources What is the best way to characterize NVH sources? Time Domain? Frequency Domain? Order Domain? What are these different domains? 24

13 Characterizing Sources What do we want to learn about a system to characterize it? Amplitude? Frequency? Damping? Natural Frequencies? What are significant contributors to response? Intricate details about different contributors? 25 Time Domain Characterization What is the time domain? RESONANCES Simply digitized signal from a transducer. 26

14 Time Domain Characterization What can we learn from the time domain? Sometimes when an event occurs Transients Lightly damped resonances Peak amplitude of overall signal Excellent for Sound Quality playback! Basis for frequency and order domain data! 27 Frequency Domain Characterization What is the frequency domain? Fourier transform of digitized time domain data. What good is it? Decomposes time domain signals into individual frequency components. Does this help? YES! - remember each source produces different frequencies!! 28

15 Frequency Domain Characterization ORDERS - RADIAL LINES RESONANCES - VERTICAL LINES 29 Order Domain Characterization What is the order domain? Order domain is when data are Fourier transformed relative to the shaft position instead of time. What good is it? Energy of an order is not smeared across the spectrum. Orders appears as vertical lines on colormaps! 3

16 Source, Path, Receiver Characteristics Source, Path, Receiver Characteristics Path: Capable of transmitting energy from the source to the receiver Any media, steel, rubber, plastic, fluids, gases Directionality may be important, (X,Y,Z, Θx, Θy, Θz) Compliant Paths characterized by complex stiffness Characteristics described by Frequency Response Functions. Examples include: engine mounts, body mounts, bolted joints, springs, shock absorbers, air, water, any structural member 31 Paths of Interest Paths of Interest Air-borne paths Receiver Substructure Source Substructure Structure borne paths 32

17 Air-borne vs. Structure-borne Structure-borne Path Tire/road interface energy travels through the structure of the vehicle to the steering column. Air-borne Path Tire/road interface energy travels through the air and leaks into the cabin through a small hole in the door seal. 33 Source, Path, Receiver Characteristics Receiver: Responds to energy flowing through the paths Human or Human-structure interface Structural components Directionality may be important, (X,Y,Z, Θx, Θy, Θz) Can be affected by multiple paths at the same time Examples include: drivers right ear, steering column, seat, conversation in the house, Floor, cabinet, isolated hardware 34 17

18 Automotive Receivers Energy from the sources travels through both structure-borne and air-borne paths to the receivers Driver s Ear Mirrors Steering Column Seat Track Accelerator pedal 35 Driver s Ear Characterization of the NVH energy received at the Drivers Ear is done with a measurement of the Sound Pressure Level. 36