Investmech - T&M Seat Response Reconstruction

8/18/2019 Investmech - T&M Seat Response Reconstruction

1/26

Strain and acceleration measurement andanalysis for vehicle seat response

reconstruction

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

C: +27 82 445-0510

[email protected]


2/26

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 theGerotek test track

• Could only change damping of the vehicle suspension – only 3days for this phase

• Needed an approach using

– Analytical modelling – optimize damper characteristics – Experimental response measurements

– Laboratory testing and seat characteristic refinement

2


3/26

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


4/26

Vehicle layout

4

The position of the

centre of gravity was

determined as follows:

1. Horizontally – from

weights measured atrear and front wheels

2. Vertically – estimated

from relative weight

and CoG’s of the

components

Effect of modifications onCoG determined in the

same way


5/26

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)

S p r i n g s t i f f n e s s ( M N /

m )

350 kPa 30 kN load

350 kPa 40 kN load

600 kPa 30 kN load

600 kPa 40 kN load

No data at 2

This bump occurs

at both pressures

and 40 kN load

Used stiffness and damping

coefficient

10% damping factor was

assumed

Measured data was used

Linear stiffness coefficient

and linear damping

coefficient was assumed

Effect of stiction during

characterization was

assumed negligible

Note, in this case tyre

stiffness >> suspension

stiffness


6/26

Non-linear time and state dependant

modelling

6

∑ = − 4 + 1 − 3= , ̈,

∑ = 1 + 4 − 11 − 3= , ̈,

∑ = 1 + + 3 + 4 = ̈


7/26

Axle mathematical model

7

3

3

4

3 4 x 1

4

y

z

4 3

3 = 3 − 3 + 3 ̇ − 3 ̇ 4 = 4 − 4 + 4 ̇ − 4 ̇

3=

− 3

4 = + 4 ∑ = 4 − 3+ 13 − 4 = , ̈, ∑ =

3+

4 − 3 − 4 = ̈

0

2000

40006000

8000

10000

12000

14000

16000

18000

0 0.2 0.4 0.6 0.8 1 1.2

F o r c e [ N ]

Velocity [m/s]

Force vs. veloci ty

Tension

Compression


8/26

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 case150306450

= 2.33

8

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 0.2 0.4 0.6 0.8 1 1.2

F o r c e [ N

]

Velocity [m/s]

Force vs. veloci ty

Tension

Compression


9/26

Reference damping factor

• Use average of compression and rebound

• Damping factor for the reference vehicle = 0.27

9

= 18500

2 360000 ×

13300

4

= 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

all

Low value at High Speed and High value at Low

speed

Need more as road roughness increase

Race cars need good handling: = 0.65− 0.75 Passenger cars maximized for ride comfort: ≈ 0.25 0 0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

Frequency ratio

T r a n s m i s s i b

i l i t y

ξ = 0.05

ξ = 0.25

ξ = 0.60

ξ = 0.80


10/26

Strain gauges & accelerometers

10

Instrumentation to record

acceleration input and

response of crew seatStrain gauges to

measure suspension

force


11/26

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

13


12/26

ARX modelling

• ARX = AutoRegresive model with eXternal input

• Part of PCMatlab System Identification toolbox

– Model Characterization: th=arx([Response Input],NN)

• Mathematics: + 1 − 1 + − 2 +⋯+ − = 1 + − 1 +⋯+ − + 1 +() • The function solves the & coefficients•

(

) is external noise

– Simulation: Response=idsim(Input,th)

14


13/26

MIMO-System ID with random road

profile

150 0.5 1 1.5 2 2.5x 10

4

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

Correlation coefficient = 0.87

Reconstructed road input

Point

D i s p l a

c e m e n t [ m ]

Blue - from transient analysisRed - 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

D i s p l a c e m e n 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 , , = 1,1,0 Reverse-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


14/26

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

Di s pl a c e

m e nt[ 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

D i s p l a c e

m e n 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 ̈


15/26

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

17

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


16/26

Damping factor sensitivity

18

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

O b j e c t i v e f u n c t i o n

Results indicated an increase

of 60% (factor 1.6) on

damping factor

Damping factor was changed

to 1.6 x 0.27 = 0.43 (43%)

Response optimal point


17/26

Test rig

19

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


18/26

Objective – reconstruct measured seat

frame acceleration

20

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]

A c c e l e r a t i o n

[ m / s 2 ]

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


19/26

Why High-pass filter – Sine wave?

21

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]

A c c e l e r a t i o 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]

V e l o c i t y [ m / s ]

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

Sine wave

Times [s]

D i s p l a c e m e n 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

0.7

Sine wave

Time [s]

V e l o c i t y [ m / s ]�

� =

=

Note the non-zero mean

̇ = ̈2 = 0.318

Non-zero

mean causes

the trend

Solution: High-pass

filter signals

Servo-hydraulic actuator in displacement control → = ∫ ∫ ̈==0 ==0


20/26

High-pass filter effect on random

signals

22

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

-3

-2

-1

0

1

2

3

4Random wave

Time [s]

A c c e l e r a t i o 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]

V e l o c i t y

[ 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

0.1

Random wave

Times [s]


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]

V e l o c i t y [ 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

2.5 x 10

-3 Random wave - High-pass filtered

Times [s]


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


21/26

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]

A m p l i t u d e [ m / s 2 - R M

S ]

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]

A m p l i t u d e [ m / s 2 - R M 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]


Dsplacement intheTimedomain

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]


Dsplacement intheTime domain

Red- CompensatedDisplacement

Blue- RecordedDisplacement

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


22/26

How was this done

24

0 20 40 60 80 100 120 140

-15

-10

-5

0

5

10

15

Time [s]

A c c e l e r a t i o n [ m / s 2 ]

Acceleration in the Time domain

Blue - Recorded Acc.

Red - Compensated Acc.

=

Measure rig Response

=

()()

+1 = ( × )

Iterate until:()() ≥ 90%

The result is an acceleration

drive signal adjusted for the rig

frequency response


23/26

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: 2.197

Y: 0.7608

Frequency [Hz]

A m p l i t u d e [ m / s 2 - R M S ]

FREQUENCY SPECTRUM RMS OF THE MARLIN VS. RIG

X: 6.348

Y: 0.4391

Blue - Marlin

Red - RigMeasured RMS = 2.04

Rig RMS = 2.05

The objective is to haveaccurate reconstruction of

the dominant peaks in the

spectrum

Motion sickness: 0.1 – 0.5 Hz

Health, comfort, perception: 0.5 Hz – 80 Hz


24/26

5 10 15 20 25 300

0.5

1

1.5

2

2.5

3Transmissibility function driver seat responce/vehicle

Frequency [Hz]

F R F A m p l i t u d e

0 0.5 1 1.5 2 2.5 30

1

2

3

4

5

6

X: 0.991Y: 5.123

X: 0.929

Y: 1.995

X: 1.414

Y: 1

Frequency ratio

T r a n s m i s s i b i l i t y m a g n i t u d e

Effect of damping on magnitude at resonance

ξ = 0.1

ξ = 0.3

Driver Seat32 km/h Rally Track Full

Load

Transmissibility more than 1 at f < 6 Hz

Seat resonates

Solution: Increase damping

5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

Spectrum RMS = 1.54

X: 1.587

Y: 0.5959

Frequency [ Hz]

A m p l i t u d e [ m / s 2 - R M 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: 1.709

Y: 0.3531

Frequency [Hz]

A m p l i t u d e [ m / s 2 - R M 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]


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

Blue - Seat Input

Red - Seat Response

This seat filters high

frequency content

Spectrum of Crew Seat Response acc eleration Spectrum of Crew Seat InputX: 1 465


25/26

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]

F R F A m p l i t u d e

Crew Seat32 km/h Rally Track Full

Load

Seat response is in phase with vehicle

Seat is stiff due to mounting straps

Solution: 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]


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]

A m p l i t u d e [ m / s 2 - R M S ]

Spectrum of Crew Seat Response acc eleration

X: 1.343

Y: 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]

A m p l i t u d e [ m / s 2 - R M S ]

Spectrum of Crew Seat InputX: 1.465Y: 0.4281

Note how this seat

acceleration follows that

of the vehicle body over

the frequency spectrum

of the time signal


26/26

Final remarks

• Servo-hydraulic test rig now used to minimisetransmissibility 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 seatmounts

– Laboratory verification of seat designs to meet clientobjectives

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Investmech - T&M Seat Response Reconstruction

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