2012/10/18

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Strain and acceleration measurement and analysis for vehicle damper selection and

rigid body response reconstruction

Dr. Michiel Heyns Pr.Eng.T: +27 12 664-7604

C: +27 82 445-0510

mheyns@investmech.com

Introduction

• Objective:– To reduce weighted root-mean-square seat response of

the driver and crew seats to specified limit:• Limited time - only 1 month• Limited resources – only four measurement opportunities on the

Gerotek test track• Could only change damping of the vehicle suspension – only 3

days for this phase

• Needed an approach using– Analytical modelling – optimize damper characteristics– Experimental response measurements– Laboratory testing and seat characteristic refinement

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2012/10/18

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Method

3

Best damping

• Non-linear time and state dependant transient equations – solve by fixed step Fourth Order Runge-Kutta

• Response simulation with pseudo-random theoretical road profile• Measure vehicle responses• System ID and road profile reconstruction• Verify road profile accuracy by calculating responses and compare• Damping factor sensitivity analysis – optimal damping factor• Verify on the test track

Seat weighted RMS

• Select test track• Seat and seat mount response measurements• Test rig assembly• Reconstruct seat mount vibration in the laboratory• Iterative testing and seat modification to obtain required seat Weighted RMS

Vehicle layout

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The position of the centre of gravity was determined as follows:1. Horizontally – from

weights measured at rear and front wheels

2. Vertically – estimated from relative weight and CoG’s of the components

Effect of modifications on CoG determined in the same way

2012/10/18

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Tyre model

5

1 1.5 2 2.5 3 3.5 4 4.5 50.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

Displacement (mm)

Spr

ing

stiff

ness

(M

N/m

)

350 kPa 30 kN load

350 kPa 40 kN load600 kPa 30 kN load

600 kPa 40 kN load

No data at 2

This bump occursat both pressuresand 40 kN load

Used stiffness and damping coefficient10% damping factor was assumedMeasured data was usedLinear stiffness coefficient and linear damping coefficient was assumedEffect of stiction during characterization was assumed negligible

Note, in this case tyre stiffness >> suspension stiffness

Non-linear time and state dependant modelling

6

∑

, ,

∑

, ,

∑

2012/10/18

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Axle mathematical model

7

xy

z

∑ , ,

∑

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 0.2 0.4 0.6 0.8 1 1.2

Fo

rce[

N]

Velocity [m/s]

Force vs. velocity

Tension

Compression

Damper model

• Rebound/Compression force ratio = typically 1 to 3– R/C ration = 1 typical for off-road

– R/C ration = 3 typical for sport sedan vehicles

– In this case 2.33

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0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 0.2 0.4 0.6 0.8 1 1.2

Fo

rce[

N]

Velocity [m/s]

Force vs. velocity

Tension

Compression

2012/10/18

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Reference damping factor

• Use average of compression and rebound

• Damping factor for the reference vehicle 0.27

9

18500

2 360000133004

0.27

Question: What is a typical damping factor for off-road vehicles?Answer:Trade-off between ride comfort, road holding and road handling, you must compromise, cannot have allLow value at High Speed and High value at Low speedNeed more as road roughness increaseRace cars need good handling: 0.65 0.75Passenger cars maximized for ride comfort:

0.250 0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

Frequency ratio

Tra

nsm

issi

bilit

y

= 0.05

= 0.25

= 0.60

= 0.80

Strain gauges & accelerometers

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Instrumentation to record acceleration input and response of crew seat

Strain gauges to measure suspension force

2012/10/18

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Hardware used

• Accelerometers– Type: VibraSense ICP Accelerometer Model 101 and 103.

– Calibration certificate:

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Hardware used

• Strain gauges– Type: K-LY41-6/350 350 Ω Linear strain gauge

– Epoxy: X 60 Superglue

– Bridge configuration: Quarter-bridge

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2012/10/18

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Hardware used

• Data Logger:– Description: Somat eDaq-Lite

– Sampling frequency = 2,000 Hz

– Anti-aliasing: • Linear Phase

• Cut-off frequency = 667 Hz

• Output data type: 32 Bit Float

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ARX modelling

• ARX = AutoRegresive model with eXternal input

• Part of PCMatlab System Identification toolbox– Model Characterization: th=arx([Response Input],NN)

• Mathematics: 1 2 ⋯1 ⋯ 1

• The function solves the & coefficients

• is external noise

– Simulation: Response=idsim(Input,th)

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2012/10/18

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MIMO-System ID with random road profile

150 0.5 1 1.5 2 2.5

x 104

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

Correlation coefficient = 0.87

Reconstructed road input

Point

Dis

plac

emen

t [m

]

Blue - from transient analysis

Red - reconstructed

8060 8080 8100 8120 8140 8160 8180 8200 8220-0.04

-0.03

-0.02

-0.01

0

0.01

0.02Reconstructed road input

Point

Dis

plac

emen

t [m

]

Blue - from transient analysis

Red - reconstructed

ARX forward system identification was used: th= arx([y_temp u_id],NN);Check accuracy by reconstructing acceleration responses used: y_id=idsim(u_id,th);

The mode order was , , 1,1,0Reverse-inverse ARX model to reconstruct road input Correlation coefficient = 0.87

Only a slight shift in mean of signal required to give good perception of fit

Road profile reconstructed from recorded accelerations

160 1 2 3 4 5 6

x 104

-0.06

-0.04

-0.02

0

0.02

0.04

0.06Reconstructed road input from measured accelerations

Point

Dis

plac

emen

t [m

]

0 1 2 3 4 5 6

x 104

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15Reconstructed road input from measured accelerations

Point

Dis

plac

emen

t [m

]

Measured acceleration used to calculate road profiles: y_idRIm=idsim(u_idRIm,thRI);The function does not use time step or sampling frequency – time step in reconstructed data = time step of response data used, 200 Hz in this case

Calculated road profile Measured

2012/10/18

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Simulations to Weighted RMS

• Use road profile to calculate responses

• ISO 2631 running weighted RMS

• Repeat for damping magnification factor varied from 0.2 to 2.4 in steps of 0.2– That is the compression and rebound damper

characteristics were multiplied with this factor

– This will indicate in which direction to adjust the dampers

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Tips that enabled 55 simulations of 120s each in 15 hour span on ONE Dell Notebook Computer:• Read data into memory and limit disk operations to the minimum• Ensure that all computer threads are used – split algorithms if necessary• Declare result matrix sizes before starting the simulation• Limit array values used in interpolations to find instantaneous road profile displacement

and velocity

Damping factor sensitivity

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0 0.5 1 1.5 2 2.53.4

3.6

3.8

4

4.2

4.4

4.6

4.8

5Max. wrms for Road 2

Damper modification factor

Obj

ectiv

e fu

nctio

n

Results indicated an increase of 60% (factor 1.6) on damping factorDamping factor was changed to 1.6 x 0.27 = 0.43 (43%)

Response optimal point

2012/10/18

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Test rig

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Designed to give mounting points exactly as in the vehicle No natural modes in the operating

frequency range

40 kN servo-hydraulic actuator excites the

super structure

Objective – reconstruct measured seat frame acceleration

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Instrumentation to verify drive signal

0 20 40 60 80 100 120-10

-8

-6

-4

-2

0

2

4

6

8

10

Time [s]

Acc

eler

atio

n [m

/s2 ]

Acceleration in the Time domain

This is the measured acceleration, that is also the desired response of the seat frame on the servo-hydraulic actuator

2012/10/18

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Why High-pass filter – Sine wave?

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0 1 2 3 4 5 6 7 8 9 10-2

-1.5

-1

-0.5

0

0.5

1

1.5

2Sine wave

Time [s]

Acc

eler

atio

n [m

/s]

0 1 2 3 4 5 6 7 8 9 10-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Sine wave

Time [s]

Vel

ocity

[m

/s]

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5Sine wave

Times [s]

Dis

plac

emen

t [m

]

0 1 2 3 4 5 6 7 8 9 10-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Sine wave

Time [s]

Vel

ocity

[m

/s]

=

=

Note the non-zero mean

20.318

Non-zero mean causes the trend

Solution: High-pass filter signals

Servo-hydraulic actuator in displacement control →

High-pass filter effect on random signals after integration

22

0 1 2 3 4 5 6 7 8 9 10-4

-3

-2

-1

0

1

2

3

4Random wave

Time [s]

Acc

eler

atio

n [m

/s]

0 1 2 3 4 5 6 7 8 9 10-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15Random wave

Time [s]

Vel

ocity

[m

/s]

0 1 2 3 4 5 6 7 8 9 10-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1Random wave

Times [s]

Dis

plac

emen

t [m

]

0 1 2 3 4 5 6 7 8 9 10-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04Random wave - High-pass filtered

Time [s]

Vel

ocity

[m

/s]

0 1 2 3 4 5 6 7 8 9 10-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5x 10

-3 Random wave - High-pass filtered

Times [s]

Dis

plac

emen

t [m

]

d1x = filtfilt(B,A,(cumtrapz(t,d2x)));

x=filtfilt(B,A,cumtrapz(t,d1x));

d1x = cumtrapz(t,d2x);

x=cumtrapz(t,d1x);

Fs=200;HPFCutoff=1;

[B,A]=butter(8,HPFCutoff/(Fs/2),'high');

UNFILTERED FILTERED

It is essential to remove the low-frequency “drifts” from the

integrated signals

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Test rig drive signal

230 5 10 15 20 25 30 35 40 45 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency [Hz]

Am

plitu

de [

m/s

2-R

MS

]

Spectrum of recorded acceleration

Measured Acc. Spectrum RMS = 2.04

0 5 10 15 20 25 30 35 40 45 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency [Hz]

Am

plitu

de [

m/s

2 -RM

S]

FREQUENCY SPECTRUM FOR MEASURED ACC. SIGNAL VS. COMPENSATED ACC. SIGNAL

Measured Acc. Spectrum RMS = 2.04 Compensated Acc. Spectrum RMS = 2.65

Blue - Measured Acc.

Red - Compensated Acc.

0 20 40 60 80 100 120 140-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

Time [s]

Dis

plac

em

ent

[m]

Dsplacement in the Time domain

0 20 40 60 80 100 120 140-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

Time [s]

Dis

pla

cem

ent

[m]

Dsplacement in the Time domain

Red - Compensated Displacement

Blue - Recorded Displacement

Test rig (DAC – Hydraulics – Servo-valve – Inertias – AAF – ADC):• Non-linear frequency dependant responses

• Natural frequencies• Inertia in the oil supply system, etc.

• Therefore, • Solution:

• Compensate in the time or frequency domains• In this case, frequency domain is sufficient

Measured acceleration spectrum = Desired response

Drive signal

How was this done

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0 20 40 60 80 100 120 140-15

-10

-5

0

5

10

15

Time [s]

Acc

eler

atio

n [m

/s2 ]

Acceleration in the Time domain

Blue - Recorded Acc.

Red - Compensated Acc.

Measure rig Response

Iterate until: 90%

The result is an acceleration drive signal adjusted for the rig

frequency response

2012/10/18

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Reconstructed frame response

250 5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Marlin Spectrum RMS = 2.04

Rig Spectrum RMS = 2.05

X: 2.197Y: 0.7608

Frequency [Hz]

Am

plitu

de [

m/s

2 -RM

S]

FREQUENCY SPECTRUM RMS OF THE MARLIN VS. RIG

X: 6.348Y: 0.4391

Blue - Marlin

Red - RigMeasured RMS = 2.04

Rig RMS = 2.05

The objective is to have accurate reconstruction of the dominant peaks in the spectrum

Motion sickness: 0.1 – 0.5 HzHealth, comfort, perception: 0.5 Hz – 80 Hz

5 10 15 20 25 300

0.5

1

1.5

2

2.5

3Transmissibility function driver seat responce/vehicle

Frequency [Hz]

FR

F A

mpl

itude

0 0.5 1 1.5 2 2.5 30

1

2

3

4

5

6

X: 0.991Y: 5.123

X: 0.929Y: 1.995

X: 1.414Y: 1

Frequency ratio

Tra

nsm

issi

bilit

y m

agni

tude

Effect of damping on magnitude at resonance

= 0.1

= 0.3

Driver Seat32 km/h Rally Track Full

Load

Transmissibility more than 1 at f < 6 HzSeat resonatesSolution: Increase damping

5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6Spectrum RMS = 1.54

X: 1.587Y: 0.5959

Frequency [Hz]

Am

plitu

de [

m/s

2 -RM

S]

Spectrum of Driver Seat Response acceleration

5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

Spectrum RMS = 1.88

X: 1.709Y: 0.3531

Frequency [Hz]

Am

plitu

de [

m/s

2 -RM

S]

Spectrum of Driver Seat Input

250 250.5 251 251.5 252 252.5 253 253.5 254 254.5

-8

-6

-4

-2

0

2

4

6

8

10

12

Time [s]

Acc

eler

atio

n [m

/s2 ]

Paramount Run3: 32km/h Rally track (Full L)

Blue - Seat Input

Red - Seat Response

This seat filters high frequency content

2012/10/18

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0 5 10 15 20 25

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Transmissibility function crew seat responce/vehicle

Frequency [Hz]

FR

F A

mpl

itude

Crew Seat32 km/h Rally Track Full

Load

Seat response is in phase with vehicleSeat is stiff due to mounting strapsSolution: Replace straps with elastic material

250 250.5 251 251.5 252 252.5 253 253.5 254 254.5 255

-6

-4

-2

0

2

4

6

Time [s]

Acc

eler

atio

n [m

/s2 ]

Paramount Run3: 32km/h Rally track (Full Load)

Blue - Seat Input

Red - Seat Response

5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Spectrum RMS = 0.90

Frequency [Hz]

Am

plitu

de [

m/s

2 -RM

S]

Spectrum of Crew Seat Response acceleration

X: 1.343Y: 0.2884

5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Spectrum RMS = 0.97

Frequency [Hz]

Am

plitu

de [

m/s

2 -RM

S]

Spectrum of Crew Seat Input X: 1.465Y: 0.4281

Note how this seat acceleration follows that of the vehicle body over the frequency spectrum

of the time signal

Final remarks

• Servo-hydraulic test rig now used to minimise transmissibility to the seat– Adding elasticity to isolate– Seat layout design changes

• This process major contribution– Enable quick (3 Days) for damper selection for minimum

seat weighted RMS response– Test rig that enables continuous, cheap, repeatable,

reliable reconstruction of vehicle responses at the seat mounts

– Laboratory verification of seat designs to meet client objectives

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