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8/18/2019 Investmech - T&M Seat Response Reconstruction
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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
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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
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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
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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
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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)
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
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Non-linear time and state dependant
modelling
6
∑ = − 4 + 1 − 3= , ̈,
∑ = 1 + 4 − 11 − 3= , ̈,
∑ = 1 + + 3 + 4 = ̈
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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
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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
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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
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Strain gauges & accelerometers
10
Instrumentation to record
acceleration input and
response of crew seatStrain gauges to
measure suspension
force
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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
13
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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 − 1 + − 2 +⋯+ − = 1 + − 1 +⋯+ − + 1 +() • The function solves the & coefficients•
(
) is external noise
– Simulation: Response=idsim(Input,th)
14
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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
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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 ̈
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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
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
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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
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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
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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
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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
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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]
D i s p l a c e m e n t [ m ]
0 1 2 3 4 5 6 7 8 9 10-0.04
-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]
D i s p l a c e m e n 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]
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]
D i s p l a c e m e n t [ m ]
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]
D i s p l a c e m e n t [ m ]
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
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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
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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: 2.197
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
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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]
A c c e l e r a t i o n [ m / s 2 ]
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
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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]
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]
A c c e l e r a t i o n [ m / s 2 ]
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
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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
28