Noise, Vibration and Harshness

Noise, vibration and harshness

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AIM

• Introduce the basic concepts and importance of vibration theory to vehicle design

• Consider the role of the designer in vibration control

• Demonstrate methods for the control of vibration to help the elimination of noise and harshness

• Indicate methods by which the designer can control vibration and noise to create an equitable driving environment

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Basic concepts

• Vibration sources are characterized by their time and frequency domain characteristics

• Categorized principally as – Periodic –

• originate from the power unit, ancillaries or transmission • simplest form of periodic disturbance is harmonic • In the time domain this is represented by a sinusoid and in

the frequency domain by a single line spectrum

– Random disturbances • from terrain inputs to wheels • only statistical representations are possible • commonly represented by its power spectrum

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Basic concepts

• All mass-elastic systems have natural frequencies – For linear system these frequencies are constant

• related only to the mass and stiffness distribution

– Non-linear effects require special treatment

• A few of the lower order frequencies are of interest because the higher ones are more highly damped.

• For one frequency, a system vibrates in a particular way, depicted by the relative amplitude and phase at various locations - mode of vibration

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Reason for vibration analysis

• Lightly damped structures can produce high levels of vibration from low level sources if frequency components in the disturbance are close to one of the system’s natural frequencies.

• This means that well designed and manufactured sub-systems, which produce low level disturbing forces, can still create problems when assembled on a vehicle.

• In order to avoid these problems, at the design stage it is necessary to model the system accurately and analyze its response to anticipated disturbances

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Approach to vibration analysis

• Develop a mathematical model of the system and formulate the equations of motion

• Analyze the free vibration characteristics (natural frequencies and modes)

• Analyze the forced vibration response to prescribed disturbances and

• Investigate methods for controlling undesirable vibration levels if they arise

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Mathematical models

• Provide the basis of all vibration studies at the design stage. • Represent the dynamics of a system by one or more differential equations. • Distributed-parameter approach - distributed mass and elasticity of some

very simple components such as uniform shafts and plates by partial differential equations. – not generally possible to represent typical engineering systems (which tend to

be more complicated) in this way.

• Lumped-parameter approach - a set of discrete mass, elastic and damping elements, resulting in one or more ordinary differential equations. – Masses are concentrated at discrete points and are connected together by

mass less elastic and damping elements. – The number of elements used dictates the accuracy of the model – To have just sufficient elements for natural vibration modes and frequencies

while avoiding unnecessary computing effort.

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Mathematical models

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Formulation of System

• Equations of motion determined by applying Newton’s second law to each free-body

• For complicated geometry, the equations can be formulated by energy methods

Figure from Smith,2002

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System characteristics

• Equation of motion

mx˙˙ + cx˙ + kx = F(t ).

• Characteristics taken at free vibration [F(t) =0]

• x = X cos (ωnt – φ) – no damping

• Similar formulation of a SDOF system to obtain response as given by graph

A(w) =

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Multi Degree of freedom

*M+,x˙˙- + *K+,x- = ,0-

Assuming {x} = {A} est

([M]s2 + [K]){A} = {0}

The non-trivial solution of these is the characteristic equation (or frequency determinant)

Set of roots si2 = – λ = –ω2

λi is the i-th eigenvalue and ωi the i-th natural frequency -

λ*M]{u} = [K]{u}

It is solved using standard procedures used for vibration problems

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Multi Degree of Freedom

• Viscous Damping – In (stable) lightly damped systems the frequency

determinant is | [M]s2+ [C]s + [K] | = 0

– For an n-DOF system this produces n complex conjugate roots having negative real parts

– providing information about the frequency and damping associated with each mode of vibration

– Damping must be considered in the analysis of response of the system when one or more components of a periodic excitation is at or near to one of the system’s natural frequencies

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• Forced-damped vibration (harmonic) – Many of the features of harmonic response analysis of

SDOF systems extend to MDOF ones, e.g.: • When subjected to harmonic excitation an MDOF system

vibrates at the same frequency as the excitation.

• The displacement amplitudes at each of the degrees of freedom are dependent on the frequency of excitation and

• The dynamic displacement at each DOF lags behind the excitation

– The frequency response functions (and hence the frequency responses) are complex if damping is included in the analysis.

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• Forced damped vibration (random excitation) – Random excitation arises particularly from terrain inputs

and is important in the analysis and design of vehicle suspensions.

– Form of excitation is non-deterministic in that its instantaneous value cannot be predicted at some time in the future.

– Some properties of random functions which can be described statistically.

– The mean or mean square value can be determined by averaging and the frequency content can be determined from methods based on the Fourier transform (Newlands, 1975).

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Vibration control

• Control at source

• Engine firing and reciprocating unbalance combine to produce a complex source of vibration which varies with engine operating conditions

• Reciprocating unbalance arises at each cylinder because of the fluctuating inertia force associated with the mass at each piston

• no such thing as ‘perfect balance’

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Vibration isolation

• k* = k(1 + ηi)

– where k is the dynamic stiffness and

– η the loss factor

mx˙˙ + k(1 + i)x =

mer2 sin wt = F f (t )

Up to 1.4

SDOF vibration isolation model and free-body diagram


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Tuned absorbers

• useful for reducing vibration levels in those systems in which an excitation frequency is close to or coincides with a natural frequency of the system

• The principles of undamped and damped tuned absorbers can be understood by outlining first the analysis of the damped absorber

• Undamped absorber as a special case


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Tuned absorbers

For C = 0 ( undamped) [ideally k2-m2w2=0 ie w1= w2]


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Tuned absorbers A1 = K *X1 / F

A2 = K *X2 / F

• Dimensionless numbers

• With damping – Wider operating range

– Reduced fatigue of absorber spring

Un damped Damped Figure from Smith,2002

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Untuned viscous dampers • Devices consist of

– an inertia (seismic) mass

– which is coupled to the original system via some form of damping medium (usually silicone fluid)

• Not tuned for particular resonance

• At infinite damping both masses move together as one

Models for analyzing the untuned viscous damper

Response of an untuned viscous damper (m = 1.0) Figure from Smith,2002

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Engine Isolation

• Fluctuating torque at the crankshaft • Shaking forces and moments • additional dynamic inertial loads arising from vehicle maneuvering and

terrain inputs to the wheels • The primary components of engine vibration at idling are integer multiples

of engine speed – Idle speeds for four cylinder engines range from 8–20 Hz producing dominant

frequency components in the range from 16–40 Hz. – Since the primary bending mode of passenger cars can be less than 20 Hz it is

obvious that it is easy to excite body resonance at idle if engine isolation is not carefully designed

• The problem – isolate the chassis from the excitations and – restrain the engine against excessive movement due to the engine torque

• Select appropriate mounts and position them correctly

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Formulation of the vibration equations

• Denoting the position of the i-th mount attachment point relative to the powertrain in the equilibrium position as r

• ri 0 (in chassis coordinates) and the translation and rotation of the powertrain relative to the chassis axes as rG and Θ, the deflection of the mount is given by

dci = ri – ri0

• ρi is the location of the mount attachment point relative to the powertrain axes


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• The ‘elastic’ potential energy for a set of mounts typically having orthogonal complex stiffness components represented by the diagonal stiffness matrix [km]i is

• For chassis

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Is a non-diagonal matrix

Kinetic energy of the system is

{h}G is the momentum denoted by

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• [M], the symmetrical mass/inertia matrix, is of the form

• Lagragne’s Equations

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Mount requirements and types

• a low spring rate and high damping during idling and

• a high spring rate and low damping for high speeds, manoeuvring and when traversing rough terrains.

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Mounting types [1/4]

Simple rubber engine mounts

– These are the least costly and least effective forms of mount and clearly do not meet all the conflicting requirements.

– They do not provide the high levels of damping required at idling speeds.

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Hydro-elastic mounts – These generally contain two elastic reservoirs filled with a

hydraulic fluid. – Some also contain a gas filled reservoir. – This type of mount exploits the feature of mass-augmented

dynamic damping which is a form of tuned vibration absorber. – In operation there is relative motion across the damper which

produces flexure of the rubber component and transfer of fluid between chambers, thereby inducing a change in mount transmissibility.

– This type of mount has become common in recent years and some examples are given in the literature (Kim et al., 1992; Muller et al., 1996).

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Semi-active mounts – The operation of these mounts is dependent on modifying the

magnitude of the forces transmitted through coupling devices. – They may be implemented via low-bandwidth low power

actuators which are suited to open-loop control. – Some forms of hydraulic semi-active (adaptive) mount use low

powered actuators to induce changes in mount properties by modifying the hydraulic parameters within the mount.

– The actuators may then be on–off (adaptive) or continously variable (semi-active) types.

– Considerable effort has been devoted to this type of technology in recent years. Some examples are given in Morishita et al. (1992) and Kim et al. (1993).

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Active mounts – This type of mount requires control of both the magnitude

and direction of the actuator force used to adjust the coupling device.

– High-speed actuators and sensors require having an operating bandwidth to match the frequency spectrum of the disturbance.

– Power consumption is generally high in order to satisfy the response criteria.

– Active vibration control is typically implemented by closed-loop control.

– An example of active engine mount modelling and performance is given by Miller et al. (1995).

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Engine mounting system for a four-cylinder diesel engine

• It comprises two mass carrying mounts (one a hydramount, the other a hydrabush, both passive mounts) and two torque reacting tie bars.

• The hydramount is linked to the power unit by an aluminium bridge bracket.

• Both tie bars have a small bush at the power unit end and a large bush at the body end

A torque axis engine mounting system (courtesy of Rover Group Ltd)


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Engine Mounts

• level isolation for passenger cars.

• The modern car designs have a trend for lighter car bodies and more power-intensive engines.

• Such a weight reduction and increased power requirements often have adverse effects on vibratory behavior, greatly increasing the vibration and noise level

From Yunhe Yu, 2001

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Elastomeric mounts

• Since 1930s • represented by familiar Voigt model • compact, cost-effective and

maintenance free. • Bonded elastomeric mounts are

known to provide more consistent performance and longer life

• Dynamic stiffness of an elastomeric mount will be greater at higher frequencies due to damping

• Desirable : – specific nonlinear characteristics to

obtain constant natural frequency in a broad weight-load range

– use of materials with high internal damping

– materials with highly amplitude-dependent damping and stiffness

From Yunhe Yu, 2001

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Passive hydraulic mounts

• All hydraulic mounts reported in the literature are conceptually similar but differ in detailed structural design

• An elastomeric mount capable of supporting the load and acting as a piston to pump the liquid into the button chamber.

• Two separate chambers for fluid transfer.

• An orifice or inertia track to generate damping.

• A fluid medium • Sealing between chamber and the

outside. • Decoupler to permit low amplitude

by-pass of the damping.

From Yunhe Yu, 2001

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Passive hydraulic mounts

• Dynamic stiffness of hydraulic mount with simple orifice or inertia track is greater than that of a comparable elastomeric mount

• Hydraulic mounts greatly increase damping at low frequencies, they also degrade isolation performance at higher frequencies

• A de-coupler functions as amplitude limited floating piston.

• It makes hydraulic mount amplitude-dependent at low amplitude displacement

From Yunhe Yu, 2001

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Semi-active and active Engine mounts

• Semi-active control mechanism

• Hydraulic type • Electro-rheological (ER) fluids -

increase damping at resonance and reduce the transmissibility for shock excitation

• Theory : One degree sky-hook system and used for increasing the damping during the low frequency shock excitation

• Mainly to improve the system performance at the low frequency range

From Yunhe Yu, 2001

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Active engine mounts

• Counteracting dynamic force created by one or more actuators to suppress transmission of system disturbance force

• Passive mounts used to support engine in event of an actuator failure

• Classical- hydraulic mount, and an electromagnetic actuator to isolate high frequency vibration

• Servo-hydraulic • Piezo-actuators -high-speed

response, but displacement very small and requires suitable mechanism to increase amplitude

Model for active elastomeric mount

Model for active hydraulic mount From Yunhe Yu, 2001

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Active engine mounts

• The active mount stiffness is equivalent to the stiffness of the passive mount at every frequency except where engine vibration occurs

• At the disturbance frequency, a tonal controller commands the mount to be very soft

• Active hydraulic mounts achieve adequate damping at engine bounce frequency and have very low dynamic stiffness at higher frequency

• considered to be the next generation of engine mounts

Dynamic stiffness of hydraulic active mount

Dynamic stiffness of an active elastomeric mount

From Yunhe Yu, 2001

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Crankshaft damping

• Torsional dynamics of crankshafts dependent on the distribution of their mass and elasticity and the excitations arising from the torque/cylinder

• Because the torque contains a number of harmonic components and engine speed is variable there is a tendency to excite a large number of Torsional resonances as illustrated by the waterfall plot (Torsional amplitude plotted as a function frequency for a range of engine speeds)

Waterfall plot for a multi-cylinder engine (courtesy of Simpson International (UK) Ltd)


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Determination of the mass-elastic model

Mass-elastic model and first torsion mode of a six cylinder engine

Modal analysis of the mass-elastic model

Equivalent model based on first mode of the mass-elastic model


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Fundamentals of acoustics

General sound propagation • In an automotive context this is the surrounding air or the vehicle

body structure, giving rise to the term structure-borne sound. • Produces a propagating (travelling) wave which has a characteristic

velocity c, the velocity of sound in air. • At some arbitrary point on the path, the air undergoes pressure

fluctuations which are superimposed on the ambient pressure. • A sound source vibrating at a frequency f, produces sound at this

frequency. • The distance between pressure peaks is constant and known as the

wavelength λ. • This is related to c and f by the equation:

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Fundamentals of acoustics

Plane wave propagation

• Wave motion are most easily understood by considering the propagation of a plane wave

Table from Smith,2002

Elastic deformation

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Plane wave propagation

Specific acoustic impedance, Z

• The impedance which a propagating medium offers to the flow of acoustic energy is called the acoustic impedance.

• It is defined as the ratio of acoustic pressure p to the velocity of propagation u. It can be shown (Reynolds, 1981) that

Acoustic intensity, I • This is defined as the time

averaged rate of transport of acoustic energy by a wave per unit area

• normal to the wavefront. It is given by Reynolds (1981)

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Spherical wave propagation, acoustic near and far fields

• Spherical waves more closely approximate true source waves, but approximate to plane waves at large distances from a source.

• It may be shown (Reynolds, 1981) that the wave equation in spherical coordinates is

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General solution is

• At large distances from the source (kr >> 1 or r >>

λ/2π), z → ρc. [k – wave number = w/c; z – impedance] • Then pressure and particle velocity are in phase and we

are in what is called the acoustic far field where spherical wave-fronts approximate to those of plane waves and pressure and velocity are in phase.

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• At distances close to the source (kr << 1 or r << λ/2π), z → iρckr. Then pressure and velocity are 90° out of phase and we are in what is called the acoustic near field.

• The transition from near to far field is in reality a gradual one, but is normally assumed to take place in the vicinity of λ/2 π.

• For a harmonic wave at 1 kHz (λ ≈ 1 kHz), r = 50 mm; while at 20 Hz; r = 2.5 m.

• The far field/near field transition has important implications for microphone positioning in sound level measurements

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Acoustic quantities expressed in decibel form

Sound Power, Intensity and Pressure levels

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Acoustic quantities expressed in decibel form

• When it is noted that the threshold of hearing corresponds to a sound pressure level of 0 dB it may be shown (Reynolds, 1981) that for normal temperature and pressure (101.3 kPa and 20 °C). LW, LI and Lp are related as follows

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Effects of reflecting surfaces on sound propagation

• When an incident wave strikes a reflecting surface the wave is reflected backwards towards the source.

• In the vicinity of the reflecting surface the incident and reflected waves interact to produce what is known as a reverberant field

Sound pressure level as a function of distance from a simple spherical source


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Effects of reflecting surfaces on sound propagation

• If the sound source is next to a hard reflecting surface, four idealized cases -- – whole space radiation – when there are no reflecting surfaces, i.e. the

source is in free space, – half-space radiation – when the source is positioned at the centre of a

flat hard (reflecting) surface – quarter space radiation – when the source is positioned at the

intersection of two flat hard surfaces which are perpendicular to one another

– eighth space radiation – when the source is positioned at the intersection of three flat perpendicular hard surfaces. In each case there is an increase in acoustic intensity.

• The effect can be described by the directivity index DI in terms of the directivity factor Q.

DI = 10 log10 Q dB

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Human response to sound

• The frequency range extends from 20 Hz to 20 kHz and the SPL extends from the threshold of hearing at the lowest boundary to the threshold of feeling (pain) at the highest

• Human ear is most sensitive between 500 Hz and 5 kHz and is insensitive to sounds below 100 Hz The audible range


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Sound measurement

Sound level meters • The most basic instrument

for sound measurement is a sound level meter comprising a microphone, r.m.s. detector with fast and slow time constants.

• A-weighting network to enable measurements to be made which relate to human response to noise, leading to so called A weighted noise levels LpA, expressed in dB(A). The A-weighting curve

Because of the frequency sensitivity of the human ear, the A-weighting network has the form shown in Figure


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Frequency analysers

• Since the frequency spectrum of noise is closely related to the origins of its production, frequency analysis is a powerful tool for identifying noise sources and enables the effectiveness of noise control measures to be assessed

• Narrow band frequency analyzers are a necessity.

• Simultaneous filtering in multiple narrow band filters

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Drive-by noise tests (ISO 362, 1981)

• The procedure is to accelerate the vehicle in a prescribed way and in a prescribed gear past a microphone set up at a height of 1.2 m above a hard reflecting surface and 7.5 m from the path of the vehicle

• When the vehicle reaches A the throttle should be opened fully and maintained in this position until the rear of the vehicle reaches B

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Noise from stationary vehicles

• Vehicles in the vicinity of the exhaust silencer (ISO 5130, 1978)

• Engine running at 75% of the speed at which it develops maximum power

• For these measurements, the exhaust outlet and microphone are in the same horizontal plane with the microphone 500 mm from the exhaust outlet and at an axis of 45° to it.

• The background noise level is also measured and the maximum difference between the vehicle noise and the background noise is then compared with vehicle’s specified noise level

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Interior Noise

• No legal requirements

• Assessed by experienced assesors

• Ad Hoc Criterion like Articulation Index used

• 200 Hz to 16kHz split into 16 bands

• SPL is measured in each band

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Interior noise in vehicles

• Articulation index ( by Greaves)

Where,

• A0 = SPL for zero intelligibility of conversation

• A100 = SPL for 100% intelligibility

• Wf = weighting factor for each third octave band

• Overall AI is measured by adding together 16 different indices

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Engine noise

• Engine noise originates from both the combustion process and mechanical forces associated with engine dynamics

• Noise control: – Controlling pressure variations

– Piston slap – mass of piston, gudgeon pin design, offset

– Noise shields

– Crankshaft – spoked, damper

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Transmission noise

• Misalignment of shafts, single tooth incorrectly cut or damaged.

fs1, fs2 = ftm ± fss

fss – shaft speed frequency

• Correct standard tooth profiles

– to account for tooth elasticity effects – But gear teeth are subjected to variable loading, – it is impossible to correct for all eventualities

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INTAKE NOISE

• Generated by interruption of airflow at inlet valves

• Transmitted via air cleaner

• Radiated by air duct

• Noise of 10-15 dB

• Turbo charger compressor noise also radiated from the air duct – At blade passing frequency (also higher harmonics)

– Typically 2-4 kHz

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EXHAUST NOISE

• Produced by release of gases as exhaust valves open and close

• F = engine speed /60 * number of cyls / 2

• Vary with engine load (upto 15 dB)

• Turbo charging reduces engine and exhaust noise (because of better combustion)

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Attenuation of intake and exhaust noise

• Devices which minimize flow of sound waves

– Allow gas flow

– Called acoustic filters

• Two types

– Dissipative (absorb acoustic energy)

– Reactive (by intereference)

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Intake and exhaust noise

• Dissipative silencers – absorptive material which

absorbs acoustic energy from the gas flow

– Produces attenuation at f>500Hz

• Reactive silencers – when the sound in a pipe or duct

encounters a discontinuity in the cross-section,

– some of the acoustic energy is reflected back

– creating destructive interference

– Suitable for attenuating low frequency noise

– Causes pressure loss


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The Helmholtz resonator

• Incorporated in the air filter

• Produces low frequency resonance, and

• Attenuation at higher frequencies

2

c Af

LV

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Catalytic Convertors

• Fitted immediately after exhaust manifold – For quick heating needed for their functioning

• Have an acoustic attenuation effect – Gas passes through narrow ceramic pipes – Attenuation as well as dispersion

• Silencers downstream of catalytic convertors • Have an acoustic resonant frequency

– Tuned to avoid exciting structural frequencies

• Hence, Often have a double skin and insulation AND • Isolated from vehicle body by suspending it from

flexible systems

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Intake and exhaust noise

• The following are some of the devices used to overcome specific silencer tuning problems. – The Helmholtz resonator – a through-flow resonator

which amplifies sound at its resonant frequency, but attenuates it outside this range.

– Circumferential pipe perforations – create many small sound sources resulting in a broadband filtering effect due to increased local turbulence.

– Venturi nozzles – designed to have flow velocities below the speed of sound, they are used to attenuate low frequency sound.

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Aerodynamic noise

• For road vehicles this can be broken down into three noise generating components: – Boundary layer distributed over the vehicle body

• Boundary layer noise tends to be random in character

• Absorbent materials

– Edge effects • noise level higher than boundary layer noise

• Caused by vortices formed at edges

– Vortex shedding (large vortices roll up and break into smaller ones)

– at various locations on the vehicle body and also at cooling fans

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• Minimizing Aerodynamic noise – minimizing protrusions from the body surface, making the body

surface smooth and continuous and ensuring that gaps around apertures such as doors are well sealed.

– Vortices produced at windscreen pillars • very little which can be done to improve as aerodynamics at A-pillar

contradicts visibility requirements

– Wing mirrors and wheel trims also cause vortices

– where S is the Strouhal Number (based on geometry), U is speed of air, d – obstruction dia

– f = 640 Hz, for d=10 at 70mph – inlet and outlet apertures are carefully sited and designed

• Should not generate noise and noise from engine compartment should not be transmitted to the occupant

SUf

d

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Noise from the cooling fan Blades shed helical trailing vortices Result in periodic pressure fluctuations when they strike obstacles fan rotors are made with unevenly spaced blades and with an odd numbers of blades

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Tire noise

• Two sources of noise – Tread pattern excited noise (affected by tire design) – Road surface excited noise

• Tire designers reduce tire noise • Chassis designers reduce transmission to occupant • The mechanism of tire noise generation is due to an

energy release when a small block of tread is released from the trailing edge of the tire footprint and returns to its undeformed position. – Tread patterns designed to control frequencies – Models of tires with structural dynamic characteristics and

the air contained within them are used at the design stage.

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Brake noise

• Mechanism of noise generation in disc and drum brakes is still not fully understood – Complex system of linkages – Elements of large area held in contact with hydraulic /

friction loading

• Ad hoc / empirical solutions often used – For low frequency drum brake noise

• Add either a single mass or a combined mass and a visco-elastic layer applied at anti-nodes of the drum back plate (Fieldhouse et al., 1996).

– At higher frequencies • a redistribution of drum mass to eliminate some of the specific

back plate vibration modes.

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Noise, Vibration and Harshness