vibration and noise - university of...

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