Master Thesis at SKF:
Lateral force estimation acting at
a vehicle wheel using a hub
bearing unit equipped with strain
gauges and Eddy-current sensors
By: John den Engelse
Date: 19 – 6 - 2013
Challenge the future
1
Presentation overview
• Introduction
• Research goals
• Strain gauge measurements
• Eddy-current sensor measurements
• Field- / validation measurements
• BETSY calibration method
• Conclusions
Challenge the future
2
1
Introduction
Challenge the future
3
Introduction: Load Sensing Bearing (LSB)
• Why would we like to measure forces?
• Monitoring the mechanical loads of a bearing.
• Control the active safety systems in vehicles like the ABS
(longitudinal force) and ESC (lateral force).
• Measure the vertical load in, for instance, trucks.
Challenge the future
4
Introduction – Research goals – Strain gauge measurements – Eddy-current sensors measurements – Field- / validation measurements - …
Introduction: Load Sensing Bearing (LSB)
• How?  A load sensing hub bearing unit instrumented with:
• 6 strain gauges: deformation of the bearing outer ring.
• 2 Eddy-current sensors: tilting movement of the ABS-ring.
Challenge the future
5
Introduction – Research goals – Strain gauge measurements – Eddy-current sensors measurements – Field- / validation measurements - …
2
Research goals
Challenge the future
6
Research goals
1)
Lateral force estimation, acting at a vehicle wheel, using
strain gauges and Eddy-current sensors.
2)
Calibration of the load sensing bearing using the
Bearing Test System (BETSY)
Challenge the future
7
Introduction – Research goals – Strain gauge measurements – Eddy-current sensors measurements – Field- / validation measurements - …
3
Strain gauge measurements
Challenge the future
8
Strain gauge measurements
• The strain gauges measure the deformation of the bearing
outer ring at six places along the circumference.
• The deformation provides information about the loads
acting on the bearing.
Challenge the future
9
Introduction – Research goals – Strain gauge measurements – Eddy-current sensors measurements – Field- / validation measurements - …
Strain gauge measurements
• So what happens?
Challenge the future
10
Introduction – Research goals – Strain gauge measurements – Eddy-current sensors measurements – Field- / validation measurements - …
Warning
The following slide features a mathematical trick
performed by a professional
and under the supervision of a professional.
Accordingly, the TU Delft and the students
must insist that no one attempt to
recreate of re-enact any trick or
activity performed on this slide.
Strain gauge measurements: MLRA
• Multivariate Linear Regression Analysis (MLRA): The output is
assumed to be a linear combination of the input and higher order
terms of the input.
• For one single dimension:
Fy  0  1  0 2  ...  n n  
• For multi input multi output
1 
 
 Fy    Fy   2 
      
 Fz    Fz  ... 
 
 n 
 
     F   (  
T
T 1
)
The entries of F have dimensions [1 x N ] with N the number of samples
The entries of  have dimensions [1 x (6n  1)] with n the order the polynomial
The entries of  have dimensions [(6n  1) x N] with n the order the polynomial
Challenge the future
12
Introduction – Research goals – Strain gauge measurements – Eddy-current sensors measurements – Field- / validation measurements - …
Strain gauge measurements: MLRA
1) Absolute value problem
2) Difference in sensitivity for Fy < 0 N and Fy > 0 N
3) Difference in response for 0 Hz < f < 1 Hz and 1 Hz < f < 10 Hz
Challenge the future
13
Introduction – Research goals – Strain gauge measurements – Eddy-current sensors measurements – Field- / validation measurements - …
Strain gauge measurements: Fy
estimation block diagram
Challenge the future
14
Introduction – Research goals – Strain gauge measurements – Eddy-current sensors measurements – Field- / validation measurements - …
4
Eddy-current sensor
measurements
Challenge the future
15
Eddy-current sensor measurement
• Why (inductive) Eddy-current sensor measurements?
•
The strain gauges are subject to the absolute value
problem.
•
Strain measurements are subject to low frequent thermal
influences.
Challenge the future
16
Introduction – Research goals – Strain gauge measurements – Eddy-current sensors measurements – Field- / validation measurements - …
Eddy-current sensor measurement
• ABS-ring integrated in the seal of the bearing. 48 holes and
48 spokes.
• The tilting movement of the ABS-ring gives an estimate of the
lateral force Fy acting on the bearing.
Challenge the future
17
Introduction – Research goals – Strain gauge measurements – Eddy-current sensors measurements – Field- / validation measurements - …
Eddy-current sensor measurement
• Two Eddy-current sensors are mounted into the knuckle.
Challenge the future
18
Introduction – Research goals – Strain gauge measurements – Eddy-current sensors measurements – Field- / validation measurements - …
Eddy-current sensor measurement:
Signal
• The change in the lower values provides the information
about Fy
Eddy-current sensor signals BETSY: BMW+0005
8
Bottom sensor
Top sensor
7
6
Signal [V]
5
4
3
2
1
0
35
35.005
35.015
35.01
35.02
35.025
Time [s]
Challenge the future
19
Introduction – Research goals – Strain gauge measurements – Eddy-current sensors measurements – Field- / validation measurements - …
Eddy-current measurement: Low value
algorithm
Discontinious
output
Sensor signal [V]
• Algorithm to retrieve these lower values.
• Based signal derivative
• Maximum change per time sample ∆ymax
• An initial condition y0 (the equilibrium value)
Eddy-current sensor - low value algorithm
• The wheel speed
8
Algorithm input
Unfiltered algorithm output
6
4
2
0
35
35.005
35.01
35.015
35.02
Time [s]
Eddy-current sensor - low value algorithm
35.025
Continuous
output
Sensor signal [V]
8
Algorithm input
Filtered algorithm output
6
4
2
0
35
35.005
35.01
35.015
35.02
35.025
Time [s]
Challenge the future
20
Introduction – Research goals – Strain gauge measurements – Eddy-current sensors measurements – Field- / validation measurements - …
5
Field measurements
Challenge the future
21
Field measurements
• The LSB equipment has been built in a BMW E60 and tests
have been performed at the test track at SKF
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
22
Field measurements
• Movie: Circle run at 30 km/h
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
23
Field measurements
• A Kistler VELOS force measuring wheel is used as reference
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
24
Fy [N]
Fy [N]
0
0
Field measurements: Tilt vs Fy
-1000
-2000
-1000
-2000
-3000
• Eddy-current sensor measurement.
-3000
force• Data
approximated
by nth order polynomials
is approximated by a 2nd and a 6th order polynomial:
-100
-50
0
50
100
-100
-50
Tilt [m]
left 20 kmph
Accuracy vs extrapolation characteristics
left 30 kmph
right 20 kmph
right 30 kmph
N
Order
2, RMS
error
= 260.8957
Order
fit =fit5,=RMS
error
= 171.4631
Fy [N]
Fy [N]
10001000
Fy [N]
Fy [N]
10001000
-1000-1000
0
Tilt [m]
right 10, 20 and 30
0
-1000-1000
-2000-2000
-2000-2000
-3000-3000
-3000-3000
-100 -100
100
Order
3, RMS
error
= 192.1875
N
Order
fit =fit6,=RMS
error
= 161.7996
20002000
0
50
left 10, 20 and 30 kmph
20002000
0
0
-50 -50
0
0
50
[m]
TiltTilt
[m]
50
100 100
-100 -100
-50 -50
0
0
50
50
100 100
[m]
TiltTilt
[m]
Challenge the future
25
Order
fit measurements
= 5, RMS –error
171.4631
Order
fit =method
6, RMS
error = 161.7996
…– Eddy-current
sensors
Field- =
/ validation
measurements – BETSY
calibration
- Conclusions
Field measurements
• Strain measurement
Fy vs straingauge 1
Strain [m/m]
300
1
2
3
4
200
100
400
Strain [m/m]
Test
Test
Test
Test
400
0
-4000
300
200
100
0
-3000
-2000
-1000
0
1000
2000
3000
-4000
Lateral force [N]
Fy vs straingauge 3
Challenge the future
]
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
26
]
400
400
Field measurements : Fy estimation
• Two force estimation algorithms. Both for an in-situ calibration
and a BETSY calibration.
1) Using 4 MLRA on the strain gauges and use the Eddy-
current sensors for the determination of the direction.
2) Using both the Eddy-current sensors and the strain
gauges for the force estimation.
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
27
Field measurements : Algorithm 1
• Using 4 MLRA on the strain gauges and use the Eddy-current
sensors for the determination of the direction.
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
28
Field measurements: Algorithm 2
• Using both the Eddy-current sensors and the strain gauges
for the force estimation
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
29
Field measurements : Fy estimation,
result
• Estimated force vs time for both algorithms.
Lateral force estimation: In-situ calibration
2000
Measured force
Estimated force by 2 LMRAs and tilt
Estimated force by four LMRAs
1500
1000
500
Fy [N]
0
-500
-1000
-1500
-2000
-2500
-3000
0
10
20
30
40
50
60
Time [s]
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
30
Field measurements : Fy estimation,
result
• Estimated force vs measured force for both algorithms.
Lateral force estimation: in situ calibration
2000
1500
Estimated force by 2 LMRAs and tilt
Estimated force by four LMRAs
Ideal
Estimated force [N]
1000
500
0
-500
-1000
-1500
-2000
-2500
-3000
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
Measured force [N]
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
31
Field measurements : Fy estimation,
result
• Estimation errors
Frequency content
0 Hz - 10 Hz
0 Hz - 10 Hz
Method
Algorithm 1
Algorithm 2
RMS Error [N] Error [%]
232,00
20,09
216,82
18,78
Frequency content
Method
MLRA
Tilt 2nd order
Tilt 6th order
RMS Error [N]
188,82
229,84
174,47
Method
MLRA
RMS Error [N] Error [%]
130,89
141,82
0 Hz - 1 Hz
Frequency content
1 Hz - 10 Hz
Error [%]
16,46
20,04
15,21
In-situ calibration
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
32
6
BETSY calibration
Challenge the future
33
Strain gauge measurements: BETSY
• What is BETSY and why do we want to use it?
• The Bearing Test System is a 5 Degree of Freedom (DoF)
system, where forces and moments are applied in 5 DoF
by hydraulic actuators.
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
34
200
0
Strain [m/m
400
Strain [m/m]
Strain [m/m
600
400
600
400
BETSY calibration: strain
200
0
-200
-8000 -200 -6000
-4000
-2000
0
2000
200
0
-200
-8000
4000
-6000
-4000
-2000
0
2000
4000
2000
4000
urg and BETSY: Lateral force Fy versus strain
-8000
-2000
0
Lateral force [N]
2000
Fy vs straingauge 4
800
BETSY
0
-6000
-4000
-4000
-2000
-2000
0
0
2000
Lateral forceFy[N]
[N]
600
-2000
200
400
200
•
εvehicle = c1 ∙ Fy + c2
0
0
Fy [N]
0
-200
straingauge
3
-8000
-200
-8000
•
 BETSY
Fy [N]
0
-2000
0
-200
-8000
-6000
2000
-4000
-2000
0
Lateral force [N]
800
0
-8000
0
Fy vs straingauge 2
200
Fy vs straingauge 6
-4000
 BETSY-2000- c4 0 vehicle 2000
-c
600 2
Fy ,Lateral


Fy
[N]
test
force [N]
c3
c1
•
-2000
2000
-4000
400
200
-6000
-6000
600
600
εBETSY
= c3 ∙ F400
y + c4
-200
4000
Strain [m/m]
400
Strain [m/m]
Strain [m/m]
800
600
Fy vs straingauge
6
Fy vs straingauge
5
400
2000
4000
Strain [m/m]
-200
-200
-8000
-8000
-6000
Strain [m/m]
0
600
Strain [m/m]
Papenburg
400
straingauge
200 1
200
Lateral force [N]
600
Strain [m/m]
Strain [m/m]
400
-4000
Fy [N]
Fy vs straingauge
3
Fy vs straingauge
4
800
600
-6000
-6000
-4000
200
0
2000
Fy [N]
Fy vs straingauge 4
0
-200
-8000
-2000
-6000
-4000
-2000
0
2000
4000
Lateral force [N]
400
c3   vehicle - c3  c2 200

 c4  cA   vehicle  cB
0
c1
2000
-200
-8000
-6000
-4000
Challenge
-2000 the future 035
Fy [N]
2000
BETSY calibration: Eddy-current
sensors
Tilt versus Fy for BETSY and field measurements at SKF: 2nd order
2000
BETSY
Field measurements SKF
1000
Fy [N]
0
Good! 
-1000
-2000
-3000
-4000
-100
-80
-60
-40
-20
0
20
Tilt [ m]
40
60
80
100
Challenge the future
36
Field measurements : Fy estimation,
result
• Estimated Fy vs time for both algorithms
Lateral force estimation: In-situ calibration
2000
Estimated force by four LMRAs
Estimated force by 2 LMRAs and tilt
Measured force
1500
1000
500
Fy [N]
0
-500
-1000
-1500
-2000
-2500
-3000
-3500
0
10
20
30
40
50
60
Time [s]
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
37
Field measurements : Fy estimation,
result
• Estimated Fy vs measured Fy for both algorithms.
Lateral force estimation: in situ calibration
2000
1500
Estimated force by four LMRAs
Estimated force by 2 LMRAs and tilt
Ideal
1000
Estimated force [N]
500
0
-500
-1000
-1500
-2000
-2500
-3000
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
Measured force [N]
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
38
Field measurements : Fy estimation,
result
• Estimation errors using a BETSY calibration
Frequency content
0 Hz - 10 Hz
0 Hz - 10 Hz
Method
Algorithm 1
Algorithm 2
RMS Error [N] Error [%]
335,29
29,04
374,55
32,44
Frequency content Method
MLRA
Tilt 2nd order
0 Hz - 1 Hz
Tilt 6th order
RMS Error [N]
191,44
261,23
342,64
Frequency content
1 Hz - 10 Hz
RMS Error [N] Error [%]
265,34
287,49
Method
MLRA
Error [%]
16,69
22,78
29,88
• So we can use BETSY for calibration?
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
39
Reproducibility: strain
BETSY: Reproducibility
• Reproducibility is necessary
for calibration of a whole
production line of LSBTest run 1
Test run 2
Test run 3
Linear fitlines
Fy vs straingauge 2
400
Strain [m/m]
Strain [m/m]
Fy vs straingauge 1
300
200
100
0
400
300
200
100
0
-5000
-4000 for
-3000the
-2000field
-1000 measurements
0
1000
2000
-6000
-5000
-4000at -3000
-2000and
-1000 Papenburg
0
1000
2000
Fy -6000
vs strain
performed
SKF
Papenburg
Lateral force [N]
Not good!

Fy vs straingauge 4
SKF
Linear fitlines
Fy vs straingauge 2
600
600
400
400
Strain [[m/m]
Strain
m/m]
Strain [[m/m]
Strain
m/m]
Lateral force [N]
Fy vs
vs straingauge
Fy
straingauge3 1
400
300
200
200
100
0
0
-200
-6000
-8000
-5000
-6000-4000
-3000
-4000
-2000
-2000
-1000
0
0
1000
2000
400
300
200
200
100
0
0
-200
-6000
-8000
2000
4000
Lateral
force[N]
[N]
Lateral force
-2000
-2000
-1000 0
0
1000
2000
Fy
Fyvs
vs straingauge
straingauge 64
600
400
400
in [[
m/m]
m/m]
n
in [[
m/m]
m/m]
n
Fy
straingauge5 3
Fy vs straingauge
300
-3000
-4000
Lateral
force[N]
[N]
Lateral force
600
400
-5000
-6000 -4000
400
300
Challenge the future
200 sensors measurements – Field- / validation measurements – BETSY
200 calibration method - Conclusions
200
200
…– Eddy-current
40
2000
4000
Reproducibility: Eddy-current
sensors
• Reproducibility is necessary for calibration of a whole
production line of LSB
Tilt versus Fy for BETSY
4000
BETSY2011
NEW
2012
BETSY OLD
2000
Fy [N]
0
Good! 
-2000
-4000
-6000
-8000
-150
-100
-50
0
50
Tilt [ m]
100
150
200
250
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
41
7
Conclusions
Challenge the future
42
Conclusions: lateral force estimation
• In the semi-static frequency range the strain gauges as well as the
Eddy-current sensors can be used for force estimation with errors
ranging from 15 % - 20 %.
•
In the dynamic frequency range the lateral force is not correlated with
the strain and ABS-ring deflection.
• Regarding the Eddy-current sensors BETSY can be used for calibration.
• Regarding the strain gauges sensors BETSY cannot be used for
calibration.
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
43
Questions?
Thank you for your attention !
Challenge the future
44
Backup slides
Challenge the future
45
Introduction: Load Sensing Bearing
• What forces act on a vehicle?
• 3 forces:
• Fx = longitudinal force
• Fy = lateral force
• Fz = vertical force
• 3 moments:
• Mx = moment around the x-axis
• My = moment around the y-axis
• Mz = moment around the z-axis
Challenge the future
46
Strain gauge measurements: Applied
loads
• Cycle consisting of 24 load steps.
• Load steps with 10 seconds of duration.
4
• Between each load step
•
Combinations of static
and dynamic forces are
applied.
Betsy: 24 load cases with superpositioned noise
Fy [N]
Fz [N]
Mx [Nm]
0.8
0.6
Force [N], Moment [Nm]
a 10 seconds interval
of running without load
is inserted.
1
x 10
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
100
200
300
400
Time [s]
500
Challenge the future
600
47
700
Strain gauge measurements: Signal
conditioning process
•
•
•
•
•
Filtering
Static offset and drift
Inverted signal strain gauge 3
No-load intervals
Scaling to physical dimensions
Unconditioned strain signals
Conditioned strain signals
2
Strain 1
Strain 2
Strain 3
Strain 4
Strain 5
Strain 5
1.5
Strain 1
Strain 2
Strain 3
Strain 4
Strain 5
Strain 5
350
300
1
Strain [m/m]
Strain signal [V]
400
0.5
0
250
200
150
100
-0.5
-1
50
0
0
100
200
300
Time [s]
400
500
600
0
1
2
3
4
5
6
Time [samples]
7
8
9
10
4
x 10
Challenge the future
48
Fy vs straingauge 2
400
200
0
-200
-8000
800
400
BETSY calibration
300
200
100
0
• BETSY
Lateral force [N]
Lateral force [N]
-6000
-6000
-5000
-4000
-4000
-2000
-3000
-2000
0
-1000
2000
0
4000
1000
Strain [m/m]
600
Strain [m/m]
Strain [m/m]
800
-200
-8000
800
Strain [m/m]
urg
600
400
200
0
Strain [m/m]
BETSY
300
200
Fy vs straingauge 2
600
100
-2000
0
2000
4000
2000
4000
Lateral force [N]
600
400
200
0
0
400
-6000-6000-5000
200
-4000
-4000
-3000
-2000
-2000 0 -1000
0
2000
1000
4000
400
-200
-8000
300
-6000
-4000
0
force Fy versus strain
2000
Papenburg
-4000
-3000
-2000
-2000
0
-1000
LateralLateral
force force
[N] [N]
BETSY
0
2000
-4000
-2000
Fy [N]
Fy vs straingauge 6
400
200
Eddy-current
1000
4000
2000
600
0
-6000
0
800
Fy vs straingauge 4
-4000
-2000
Fy vs straingauge 6
-2000
0
400
-4000
Lateral force [N]
600
100
600
-6000
LateralLateral
force force
[N] [N]
200
-200
-8000
-200
-8000
2000
Fy vs straingauge
6
Fy vs straingauge
5
0
-200
-6000
-8000
traingauge
1 -5000
200 -6000
in [m/m]
-4000
400
• BETSY
and field
and
BETSY:
Fy [N]Lateral
…–
-2000
-6000
Fy vs straingauge 4
0
400
Strain [m/m]
0
0
800
Strain [m/m]
200
Strain [m/m] Strain [m/m]
Strain [m/m]
Strain [m/m]
Strain [m/m]
400
200
• Field
800
enburg
400
-200
-8000
2000
vs straingauge
Fy vs straingauge
4
Lateral force FyFy
versus3 strain
600
600
600
400
• Some differences are present
200
0
-200
-8000
-2000
0 2
Fy-4000
vs straingauge
Lateral
force [N]
• How can we
compensate
for
-6000
2000
4000
those differences.
2000
200
0
Challenge the future
-200
sensors
measurements
– Field- / validation measurements
– BETSY
Conclusions
0
2000
-8000
-6000 calibration
-4000method --2000
0
49
2000
BETSY calibration
By describing both sides of the V-shape by a 1st order polynomial
two coefficients, Ca and Cb, can be derived for both positive and
negative Fy to transform te one to the other. (So 4 coefficients in
total).
BETSY
εright,BETSY = c1,right ∙ Fy,right + c2,right
Εleft,BETSY = c1,left ∙ Fy,left + c2,left
Field
εright,Field = c3,right ∙ Fy,right + c4,right
Εleft,field = c3,left ∙ Fy,left + c4,left
Fy ,right 
 BETSY 
 right , BETSY - c2
c1
c1    vehicle - c4 
c3

 right , field - c4
 c2 
c3
c1   vehicle - c1  c4
 c2  cA,right   vehicle  cB ,right
c3
Challenge the future
50
ce Fy versus strain including linear fits
eft cornering
00
00
Linear fitlines
Fy vs straingauge 2
Strain [m/m]
800
600
400
• By describing both sides of the V-shape by a 1st order polynomial
4000
200
two coefficients, Ca and Cb, can be derived for both positive and
negative Fy to transform
te[N]one to the other. (So 4 coefficients in
Lateral force
Fy vs straingauge 4
total).
0
-200
-8000
-6000
-4000
-2000
0
2000
4000
-6000
-4000
-2000
0
2000
4000
Strain [m/m]
800
600
400
200
0
-200
-8000
4000
Lateral force [N]
εright = c1,right ∙ Fy,rightFy+vsc2,right
straingauge 6 εleft = c1,left ∙ Fy,left + c2,left
800
Strain [m/m]
00
BETSY calibration
Right cornering
600
Fy ,test 
4000
400
 BETSY - c2
c1
200
0
 vehicle - c4
c1    vehicle - c4 
-200
-8000
 BETSY 

-6000
c1   vehicle - c1  c4

c

 c2  cA,right   vehicle  cB ,right
Lateral force
2 [N]
c3
-4000
c3
c3
-2000
0
2000
4000
Challenge the future
51
BETSY calibration: Eddy-current
sensors
Tilt versus Fy for BETSY and field measurements at SKF: 6th order
2000
BETSY
Field measurements SKF
1000
Fy [N]
0
-1000
-2000
-3000
-4000
-100
-80
-60
-40
-20
0
20
Tilt [ m]
40
60
80
100
Challenge the future
52
Estimation errors distributions
0.03
0.03
0.0250.025
0.025
0.025
0.020.02
0.02
0.02
Probability
Probability
0.030.03
Probability
Probability
Probability
densitydistribution
distributionerror:
error: 22 LMRAs
LMRAs and
error:
4 LMRAs
Probability
density
and tilt
tilt Probability
Probabilitydensity
densitydistribution
distribution
error:
4 LMRAs
0.0150.015
0.015
0.015
0.010.01
0.01
0.01
0.0050.005
0.005
0.005
0
0
-2000
-2000 -1500
-1500
-1000
-1000
-500
-500
Error
Error[N]
[N]
00
500
500
1000
1000
00
-2000
-2000
-1500
-1500
-1000
-1000
-500-500
0
0
500 500 1000 1000
Error
Error
[N][N]
Challenge the future
53
Summary: lateral force estimation
• Fy estimation summary:
Calibration
In-situ
BETSY
Strain
16.5 %
16.7 %*
0 Hz – 1 Hz
Tilt 2nd order fit
20.0 %
22.8 %
Tilt 6th order fit
15.2 %
29.9 %
Challenge the future
…– Eddy-current sensors measurements – Field- / validation measurements – BETSY calibration method - Conclusions
54
Recommendations
• Errors obtained with estimation using the Eddy-current sensor are
mainly caused by the rubber seal and low value algorithm.
• This research focused on Fy. Next: Fx, Fz
• Online testing
• Excite with higher amount of dynamic forces
Challenge the future
55
Questions?
Thank you for your
attention !
Challenge the future
56
Questions?
Thank you for your
attention !
Challenge the future
57