1. 1
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Development of AcceleratedDevelopment of Accelerated
Durability Tests for CommercialDurability Tests for Commercial
Vehicle Suspension ComponentsVehicle Suspension Components
R. Ledesma, L. Jenaway, Y. Wang, S. ShihR. Ledesma, L. Jenaway, Y. Wang, S. Shih
Advanced EngineeringAdvanced Engineering
Commercial Vehicle SystemsCommercial Vehicle Systems

2. 2
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
ObjectiveObjective
• The objective of this study is to design accelerated
durability tests for the components of a commercial
vehicle suspension system
• Requirements for the durability test:
• should have a well-defined correlation with customer usage
• accelerated in order to reproduce the desired amount of fatigue
damage in a reasonable amount of time
• must be able to reproduce failure modes that are expected in
the field

3. 3
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
StrategyStrategy
• Development of spindle load spectra for a targeted
customer usage, based on a limited set of field data
• Development of a proving ground testing schedule,
based on a given set of proving ground events, that
results in a well-defined correlation of spindle load
spectra, between the targeted customer duty cycle and
the proving grounds
• Development of a multi-axis, accelerated durability test
in the laboratory that simulates the proving ground tests
in a compressed time frame, while at the same time
duplicating the failure modes observed at the proving
grounds

4. 4
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Duty Cycle DeterminationDuty Cycle Determination
• For accelerated durability testing purposes, the
product’s duty profile is a function of three variables
• roughness of the specific roads where the vehicle is anticipated
to operate
• the number of miles covered in the product’s warranty
• loading condition of the vehicle (percent of time the vehicle is
fully laden)

5. 5
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Duty Cycle DeterminationDuty Cycle Determination
• Obtain a road profile classification map of the national highway
system from the Federal Highway Administration
• Assume that each road in the intended area of operation has an
equal chance of being traversed by the vehicle
• Example of vehicle service environment (road profiles) by vocation
National Interstate Midwestern StatesRoad Roughness
Classification % miles % miles
smooth roads 83 996,000 75 600,000
secondary paved roads 13 156,000 17 136,000
degraded paved roads 4 48,000 5 40,000
gravel/inner city roads 3 24,000
total service miles 1,200,000 800,000
% fully laden 65% 65%

6. 6
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Mule Vehicle Data AcquisitionMule Vehicle Data Acquisition
• Drive a mule vehicle on public roads and measure
spindle loads that are representative for each type of
road surface
• Mule vehicle is operated under normal driving
conditions, usually following the allowable speed limits
• Also measure spindle loads corresponding to special
discrete events such as curb strikes, railroad crossings,
panic straight-line braking, braking while turning, and
parking lot steering
• For each measured public road event or discrete event,
perform rainflow counting on each of the spindle force
components (longitudinal, lateral, and vertical directions)

7. 7
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Rainflow MatricesRainflow Matrices
• Characterize the fatigue damage potential of the spindle forces by
generating rainflow matrices for each force component
2 4 6 8 10 12 14 16 18 20
to
2
4
6
8
10
12
14
16
18
20
from
-36.98 -18.71 -0.44 17.83 36.10
[Grad]
-36.98
-27.85
-18.71
-9.58
-0.44
8.69
17.83
26.96
36.10
45.23
[Grad]
Cycles
<= 0
<= 1
<= 3
<= 5
<= 10
<= 17
<= 31
<= 56
<= 100
<= 178
<= 318
2 4 6 8 10 12 14 16 18 20
to
2
4
6
8
10
12
14
16
18
20
from
-58.50 -32.11 -5.72 20.66 47.05
[Nm]
-58.50
-45.31
-32.11
-18.92
-5.72
7.47
20.66
33.86
47.05
60.25
[Nm]
Cycles
<= 0
<= 1
<= 3
<= 6
<= 11
<= 21
<= 39
<= 73
<= 136
<= 252
<= 466
2 4 6 8 10 12 14 16 18 20
to
2
4
6
8
10
12
14
16
18
20
from
-15.78 -8.60 -1.42 5.75 12.93
[kN]
-15.78
-12.19
-8.60
-5.01
-1.42
2.16
5.75
9.34
12.93
16.52
[kN]
Cycles
<= 0
<= 1
<= 3
<= 6
<= 12
<= 22
<= 41
<= 77
<= 144
<= 269
<= 502
2 4 6 8 10 12 14 16 18 20
to
2
4
6
8
10
12
14
16
18
20
from
-35.56 -16.90 1.75 20.41 39.07
[kN]
-35.56
-26.23
-16.90
-7.57
1.75
11.08
20.41
29.74
39.07
48.39
[kN]
Cycles
<= 0
<= 1
<= 3
<= 6
<= 12
<= 22
<= 42
<= 80
<= 150
<= 281
<= 527
tuple of
Rainflow-
MatricesFxr
Fyr
Fzr
Fxl
Fyl

8. 8
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Extrapolation of Rainflow MatricesExtrapolation of Rainflow Matrices
• After collecting samples of spindle load data for each type of road
surface, perform statistical extrapolation in order to generate
spindle loads that correspond to the required number of miles for
each type of road surface
-4
-2
0
2
4
-4
-2
0
2
400.511.52
rel.Häufigkeiten
kernel shape

9. 9
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Superposition of Rainflow MatricesSuperposition of Rainflow Matrices
• After rainflow extrapolation is completed, perform rainflow
superposition on each spindle load channel to generate the target
rainflow matrix that corresponds to the expected mix of road
surfaces
• In addition, rainflow matrices corresponding to special events such
as curb strikes and railroad crossing events may be added
8 16 24 32 40 48 56 64 72 80 88 96
to
8
16
24
32
40
48
56
64
72
80
88
96
from
-44.81 -27.02 -9.23 8.56 26.36 44.15
[Grad]
-44.81
-35.92
-27.02
-18.12
-9.23
-0.33
8.56
17.46
26.36
35.25
44.15
53.05
[Grad]
Cycles
<= 0
<= 3
<= 14
<= 55
<= 210
<= 801
<= 3050
<= 11618
<= 44246
<= 168504
<= 641720
8 16 24 32 40 48 56 64 72 80 88 96
to
8
16
24
32
40
48
56
64
72
80
88
96
from
-46.75 -29.15 -11.55 6.05 23.65 41.25
[kN]
-46.75
-37.95
-29.15
-20.35
-11.55
-2.75
6.05
14.85
23.65
32.45
41.25
50.05
[kN]
Cycles
<= 0
<= 1
<= 2
<= 4
<= 8
<= 13
<= 22
<= 38
<= 64
<= 108
<= 182
8 16 24 32 40 48 56 64 72 80 88 96
to
8
16
24
32
40
48
56
64
72
80
88
96
from
-46.75 -29.15 -11.55 6.05 23.65 41.25
[kN]
-46.75
-37.95
-29.15
-20.35
-11.55
-2.75
6.05
14.85
23.65
32.45
41.25
50.05
[kN]
Cycles
<= 0
<= 1
<= 2
<= 5
<= 8
<= 14
<= 25
<= 44
<= 75
<= 129
<= 223
8 16 24 32 40 48 56 64 72 80 88 96
to
8
16
24
32
40
48
56
64
72
80
88
96
from
-44.81 -27.02 -9.23 8.57 26.36 44.15
[Grad]
-44.81
-35.91
-27.02
-18.12
-9.23
-0.33
8.57
17.46
26.36
35.25
44.15
53.05
[Grad]
Cycles
<= 0
<= 1
<= 2
<= 4
<= 6
<= 10
<= 17
<= 27
<= 43
<= 70
<= 113
8 16 24 32 40 48 56 64 72 80 88 96
to
8
16
24
32
40
48
56
64
72
80
88
96
from
-46.75 -29.15 -11.55 6.05 23.65 41.25
[kN]
-46.75
-37.95
-29.15
-20.35
-11.55
-2.75
6.05
14.85
23.65
32.45
41.25
50.05
[kN]
Cycles
<= 0
<= 1
<= 3
<= 5
<= 10
<= 19
<= 35
<= 64
<= 117
<= 212
<= 386
8 16 24 32 40 48 56 64 72 80 88 96
to
8
16
24
32
40
48
56
64
72
80
88
96
from
-46.75 -29.15 -11.55 6.05 23.65 41.25
[kN]
-46.75
-37.95
-29.15
-20.35
-11.55
-2.75
6.05
14.85
23.65
32.45
41.25
50.05
[kN]
Cycles
<= 0
<= 1
<= 3
<= 5
<= 10
<= 19
<= 35
<= 64
<= 116
<= 211
<= 384
8 16 24 32 40 48 56 64 72 80 88 96
to
8
16
24
32
40
48
56
64
72
80
88
96
from
-44.81 -27.02 -9.23 8.57 26.36 44.15
[Grad]
-44.81
-35.91
-27.02
-18.12
-9.23
-0.33
8.57
17.46
26.36
35.25
44.15
53.05
[Grad]
Cycles
<= 0
<= 1
<= 2
<= 4
<= 8
<= 14
<= 23
<= 40
<= 68
<= 116
<= 198
8 16 24 32 40 48 56 64 72 80 88 96
to
8
16
24
32
40
48
56
64
72
80
88
96
from
-46.75 -29.15 -11.55 6.05 23.65 41.25
[kN]
-46.75
-37.95
-29.15
-20.35
-11.55
-2.75
6.05
14.85
23.65
32.45
41.25
50.05
[kN]
Cycles
<= 0
<= 4
<= 16
<= 65
<= 265
<= 1069
<= 4317
<= 17420
<= 70293
<= 283648
<= 1144576
8 16 24 32 40 48 56 64 72 80 88 96
to
8
16
24
32
40
48
56
64
72
80
88
96
from
-46.75 -29.15 -11.55 6.05 23.65 41.25
[kN]
-46.75
-37.95
-29.15
-20.35
-11.55
-2.75
6.05
14.85
23.65
32.45
41.25
50.05
[kN]
Cycles
<= 0
<= 4
<= 16
<= 65
<= 265
<= 1070
<= 4319
<= 17431
<= 70345
<= 283882
<= 1145628
Fx
Fy
Fz
+
+
+
=
=
=
RFM-Fx
RFM-Fy
RFM-Fz

10. 10
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Customer Duty Profile (Target RFM)Customer Duty Profile (Target RFM)
customer
1%
special test
track
Superposition
10 %
25 %
65 % target
Extrapolation
Repeat Factors

11. 11
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Proving Ground Test Schedule DeterminationProving Ground Test Schedule Determination
• The goal is to prescribe combinations of proving ground
segments and vehicle speeds such that the combination
of these proving ground events result in a good match
between the target rainflow matrices and the rainflow
matrices associated with the proving ground test, for all
of the spindle load channels
• An exercise in multi-objective optimization: how many
repeats of each of the candidate pairs of vehicle speed
and proving ground road segment will result in the best
match between the target rainflow matrices and proving
ground rainflow matrices?

12. 12
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Proving Ground Test Schedule DeterminationProving Ground Test Schedule Determination
test track D
test track C
test track B
test track A
special test III
special test II
special test I
mixed trackΣ ? * track j
optimal
track mixing target
Select proving ground events
such that the target matrices
representing the customer duty
cycle are reproduced
Multidimensional
Optimization Problem

13. 13
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Optimizing the PG Test ScheduleOptimizing the PG Test Schedule
• Partial pseudo-damage approach: approximating of the shape of
the rainflow histogram
• Take sub-matrices of the RFM into account (clusters)
• Consider not only the total damage, but also the shape of the RFM
ratio mixed track
over target
absolute values
clusters
Partial
Pseudo-
Damage

14. 14
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Example: Optimized PG Test ScheduleExample: Optimized PG Test Schedule
• 7 out of 76 candidate PG events
can represent customer usage
• PG runtime: 1200 hrs (assuming
no downtime)
• All load channels accumulate 64-
137% of target pseudo-damage
Belgian Blocks
Gravel to Bumps
Forest
Altern. Bumps
Gravel
Altern. Bumps
A.Bumps to Emb. Rocks
Quality Check: Global Damage

15. 15
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Comparison of Target and PG RainflowComparison of Target and PG Rainflow
MatricesMatrices
Quality Check: Shape of Rainflow Matrices
Good Agreement in Range Pair Histograms

16. 16
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Accelerated Durability Rig Test ScheduleAccelerated Durability Rig Test Schedule
• The goal is to design a multi-axis, accelerated durability
test in the laboratory such that the test simulates the
proving ground tests in a compressed time frame, while
at the same time duplicating the failure modes observed
at the proving grounds
• Strategy: use time-domain fatigue editing techniques in
order to preserve the proper phasing between multiple
loads that act on the suspension system
• Construct a pseudo-damage time history associated
with each of the spindle load channels. The pseudo-
damage time histories are then lined up to identify time
intervals at which there is little pseudo-damage across
all spindle load channels

17. 17
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Example: Multi-Axis Rig Test ScheduleExample: Multi-Axis Rig Test Schedule
• Reduce testing time by 60% relative to the proving ground test,
provided that the servo-hydraulic actuators have adequate capacity
• Retain 90% of the pseudo-damage associated with the original time
history
Method:Time-Domain Fatigue Editing:
The damage quotient of the 1. channel after filtering is 96.76
The damage quotient of the 3. channel after filtering is 98.94
The damage quotient of the 5. channel after filtering is 99.85
The damage quotient of the 2. channel after filtering is 99.47
The damage quotient of the 4. channel after filtering is 99.54
The damage quotient of the 6. channel after filtering is 99.44
29. direction has minimum damage quotient of 89.65
Original Signal
Fatigue-edited
Signal

18. 18
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Accelerated Test Schedule: Range PairAccelerated Test Schedule: Range Pair
HistogramsHistograms
Fx
Fy
FzComparison between PG
and accelerated durability
rig test: high amplitude
cycles are kept 100%

19. 19
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Accelerated Test Schedule: Frequency SpectraAccelerated Test Schedule: Frequency Spectra
Fx Fy
FzComparison between PG
and accelerated durability
rig test: frequency content
over 30 Hz is reduced

20. 20
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Controlling the Multi-Axis RigControlling the Multi-Axis Rig
• Use RPC-Pro to control a multi-
input, multi-output nonlinear
system
• Requires an iterative process
• calculate the frequency
response of the test rig
• invert the frequency response
functions
• convolve the inverse FRF’s
with the desired response
signals
• predict a correction to the
inputs to minimize the error
between the desired response
and the actual response from
the test rig

21. 21
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Simplified Single-Axis Component TestSimplified Single-Axis Component Test
• Possible only when the state of stress at the critical
locations can be considered as uni-axial state of stress,
and the geometry of the component results in stresses
at the critical locations that heavily depend only on one
input force component
• Single-axis rig test will address only one failure mode
• A series of single-axis rig tests can be performed on the
same test specimen in order to arrive at a
comprehensive design verification test that deals with
multiple failure modes

22. 22
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Defining the Single-Axis ComponentDefining the Single-Axis Component
TestTest• Using multi-body dynamics, estimate the loads acting on the
component when the measured spindle loads are applied
• Perform a finite element stress analysis to obtain the time history of
strains and stresses in the component
• Perform a fatigue life prediction to determine the critical locations
and critical planes
• Identify the direction of the input force that will produce the specified
principal stress and critical plane orientation
• Perform a rainflow cycle counting of the resultant force, projected
along the critical direction
• Use the “cumulative exceedance plot” procedure to determine the
block cycle loading schedule for the single-axis rig test

23. 23
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
Example: Specification for a Single-Axis,Example: Specification for a Single-Axis,
Constant-Amplitude, Component DurabilityConstant-Amplitude, Component Durability
TestTest
• Equivalent vertical spindle load
• Mean value = 1.0G
• Alternating load = 0.6G
• Number of cycles: 132,000
LHS Spindle Vertical Force
0
1
2
3
4
5
0 2 4 6 8 10
Log of Cumulative Counts
LogofLoad
Amplitude
Field Duty Cycle Reference Load-Life Curve
Proving Ground Schedule

24. 24
SAE Commercial Vehicle Engineering Conference
November 1-3, 2005
ConclusionConclusion
• Customer usage profile was established, based on a
limited set of field data
• An optimized proving ground test schedule was derived
using commercial software
• Test schedules for the multi-axis, accelerated durability
rig test were determined, allowing us to simulate the
proving ground tests in a compressed time frame, while
at the same time duplicating the failure modes observed
at the proving grounds
• In some cases, simplified single-axis, single-component
tests can be developed