vibration and noise - university of...
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Engine Testing and Instrumentation 1
Vibration and Noise
Engine Testing and Instrumentation 2
Majority Engines: Single or multi-cylinder in-line vertical engines
6 degrees of freedom
X
Y
Z
Engine Testing and Instrumentation 3
Engine Vibration Sources
1. Vertical oscillations on X axis due to unbalanced vertical forces
2. Rotational about Y axis due to cyclic variation in torque
3. Rotation about Z axis due to unbalanced vertical forces in different transverse planes
Engine Testing and Instrumentation 4
Combustion| Exhaust Induction |Compression
revolution 1 revolution 2
Engine Testing and Instrumentation 5
Rotating masses are balanced
Reciprocating masses cannot be balanced
Piston inertia force:
massrodconnectingmasspistonml
rrmmaf cc
___3/1_
2coscos22
2
+−
+==
θωθω
Engine Testing and Instrumentation 6
αθ
θθθ
θ
θθαθθα
θθαα
θαθωθωθ
coscos)(
sincos
sin1
coscoscos
coscossinsin
0
2222
2
lrlrx
rlr
lrl
rl
rrl
rlt cc
−−+=
−=
−
==
=
====
&&&&
&&
&&&
x
Engine Testing and Instrumentation 7
θθθθθθ
θθθθθααθθ
αθθ
θθαθθαθθαα
θαθα
θωθωθ
222
2
222
222
sin22sinsinsin
sincossinsinsin
coscos)(sin
coscoscoscoscos
sinsinsinsin
0
rlrr
lr
rlrlrlrx
lrlrxrl
rl
rrl
lrrl
t cc
−+=
−+=+=
−−+=−
==→=
=→=
===
&&
&&&&&
&&&&&
&&&
Engine Testing and Instrumentation 8
( )
( )
( )( )
( )
( ) ( )( )rln
tn
t
tn
ttrx
eirl
r
rl
rr
rlrl
rrlrr
rlrl
rrlrrrx
c
c
c
cc /
sin8
4cos1
sin
2coscos
..sin4
2sin
sin
2coscos
sinsin22sinsin2cos2
2cos
sinsin2
cossin22sin2cos22sinsin
2cossin
2/32/1
2/32/1
2222
2
222
224
222
222
222
222
2222222
22
222
222
22222
22
=
−
−+
−+=
−+
−+=
−−
+−+=
−−
−−+−
++=
ω
ω
ω
ωωω
θ
θθ
θ
θθθθ
θθ
θθθθθθθ
θθθθθθθθθθθθ
θθθθ
&&
&&&
&&
&
&&&&&
&&&&&
Engine Testing and Instrumentation 9
tn
rmforceinertiaorderSecond
trmforceinertiaorderFirst
tn
rmtrmf
t
cc
cc
cc
cc
c
ωω
ωω
ωωωω
ωθ
2cos
:___
cos:___
2coscos
2
2
22 +=
=
Vertical first and second inertia exciting forces
Engine Testing and Instrumentation 10
tn
rmtn
rmtrmtrmf
tn
rmtn
rmtrmtrm
Ttn
rmTtrmtn
rmtrmf
cc
cc
cccc
cc
cc
cccc
cc
cccc
cc
ωωωωωωωω
πωωωωπωωωω
ωωωωωωωω
2cos2coscoscos
)22cos(2cos)cos(cos
22cos
2cos2coscos
2222
2222
22
22
++−=
+++++=
++
++
+=
Vertical first and second inertia forces:2 cylinders
Engine Testing and Instrumentation 11
Engine Testing and Instrumentation 12
Vertical X Forces:
For a single cylinder engine, 1st and 2nd order forces are unbalanced
For 2,4 cylinder engine, 1st order forces are balanced, but 2nd
orders are unbalanced (worse)
Couple about Z axis:
For 2 cylinder engine, there is a 1st order couple.
For 2,4 cylinder engine, all couples are balanced
6 cylinder engines are fully balanced, known for smooth running.
Engine Testing and Instrumentation 13
Design of Engine Mountings – control of vibration
( )
( ) ( )
ratiodampingkmcCfrequencynatural
mk
C
mkc
C
kF
cmk
FX
amplitudethewheretXx
tFkxdtdxc
dtxdm
_2
_
1
2tan
21
/
sin
sin
0
2
0
02
1
2
0
22
0
222
2
2
−=−=
−
=−
=
+
−
=+−
=
−=
=++
−
ω
ωω
ωω
ωωε
ωω
ωωωω
εω
ω
c k
m
F sin ω t
Engine Testing and Instrumentation 14
Engine Testing and Instrumentation 15
Transmissibility – control of vibration
( )
( ) ( )
( ) ( ) 2
0
222
22
211
sin)(
sin
+=
+=
+==
+=
−=
ωωωω
ω
εω
ω
CF
kXk
cF
kXF
XckXFFT
bilityTransmissi
XckXF
groundthetodtransmitteForcetXtx
ntDisplacemetF
forceExciting
T
T
2
0
22
0
2
0
21
21
+
−
+
=
ωω
ωω
ωω
C
CT
cωX
kX
F
mω^2
Engine Testing and Instrumentation 16
Engine Testing and Instrumentation 17Massive foundation
Engine Testing and Instrumentation 18
Engine Testing and Instrumentation 19
Coupling the engine to the dynamometer
• Problems:• 1 Torsional vibrations• 2. Vibration of engine and dynamometer• 3. Whirling of coupling shaft
• Those problem will cause• 1. damage bearings• 2. catastrophic failure of coupling shafts
Engine Testing and Instrumentation 20
Drive shafts
Engine Testing and Instrumentation 21
Bush type torsionally resilient coupling
Engine Testing and Instrumentation 22
Drive shaft guard
Drive Shaft Containment
Firmly bolt to bed frame
Drive shaft
Containing Blocks
Safety Guard
Engine Testing and Instrumentation 23
Engine Testing and Instrumentation 24
Engine and dynamometer dynamic behaviour
Engine Testing and Instrumentation 25
Cause of torsional vibration:the dynamometer is not equivalent dynamically to the system
driven by the engine in service.
In engine test:Dynamometer has higher inertia and low damping
In Vehicle:Between engine and wheels there are clutch, and gearbox.
They have low inertia and high damping.
Engine Testing and Instrumentation 26
Single cylinder 4 stroke engine torque - crank angle curve
Engine Testing and Instrumentation 27
Periodic function f(θ) has the Fourier series
∑∑∞
=
∞
=
++=1n
n1n
n0 nbna
2af θθθ sincos)(
∫−=π
πθθ
πdf1a0 )(
∫−=π
πθθθ
πdnf1an cos)(
∫−=π
πθθθ
πdnf1bn sin)(
Engine Testing and Instrumentation 28
The Fourier series may also be written
∑∞
=
−=0n
nn tnAf )cos()( ϕωθ with φ0 = 0 and a0/2 = A0. The nth harmonic has an amplitude An =(an
2 + bn2)1/2 and phase
φn = tan-1bn/an
Engine Testing and Instrumentation 29
For single cylinder engine: The first critical speed occurs at N=1/2 th order. (half of the shaft-speed) for a 4-cylinder engine The first major critical speed is 4/2=2 th order (2 x shaft speed) Example: Engine 950 rpm, the first major critical speed (frequency) 950x2/60=31.6 Hz
Engine Testing and Instrumentation 30
Torsional vibrationNewton’s second law
bbbe
eebe
Ik
andIk
θθθ
θθθ
&&
&&
=−
=−−
)(
)(
Or
0
0
=+−
=+−
bebb
ebee
kkI
kkI
θθθ
θθθ&&
&&
Using matrix
=
−
−+
00
00
b
e
b
e
b
e
kkkk
II
θθ
θθ&&
&&
Assuming solution
tb
e
b
e ωθθ
sin
ΘΘ
=
=
ΘΘ
−−−−
00
sin2
2
tIkk
kIk
b
e
b
e ωω
ω
Engine Testing and Instrumentation 31
Generalised eigen-value/vector problem:
=
ΘΘ
−−−−
00
2
2
b
e
b
e
IkkkIkω
ω
0))((..
0
222
2
2
=−−−
=−−−−
kIkIkei
IkkkIk
be
b
e
ωω
ωω
( )
( )be
be
bebe
IIIIk
and
kIIII
+=
==+−
2
1
24
00
ω
ωωω
This the torsional vibration frequency rad/s. Or using rpm
( )be
be
IIIIkn +
=π2
60
- the resonant speed or critical speed.
Engine Testing and Instrumentation 32
Engine Testing and Instrumentation 33
Stiffness k should be chosen to ensure the critical speed is outside the normal operating range
Torsional vibration is excited by the variations in engine torque associated with the pressure cycles in the individual cylinders
Engine Testing and Instrumentation 34
Shaft whirl
The coupling shaft is usually supported at each end by a universal joint or flexible coupling. The shaft will whirl at a certain rotational speed:
couplingshalfshaftofmassMdiametershaftD
shaftoflengthL
MDE
LN
s
sw
____
__
6430 4
2
+−−−
=ππ
The whirling speed is identical with the natural frequency of transverse oscillation.The whirl will also appear at higher speeds:
,...3,2 22ww NN
Engine Testing and Instrumentation 35
Noise
• Higher-frequency vibration (100Hz+) will generate structure-borne noise
• Sound intensity
)____(/10
log20log10
/
2120
010
010
22
audibilityofthresholdloweraveragemWI
pp
IIdB
mWc
pI
−=
=
=
=ρ
Engine Testing and Instrumentation 36
Accelerometer
Engine Testing and Instrumentation 37
Noise study
Engine Testing and Instrumentation 38
Automotive anechoic test cell