SAE 2005-01-3565

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SAE Commercial Vehicle Engineering ConferenceNovember 1-3, 2005

Development of Accelerated Development of Accelerated Durability Tests for Commercial Durability Tests for Commercial

Vehicle Suspension ComponentsVehicle Suspension Components

R. Ledesma, L. Jenaway, Y. Wang, S. ShihR. Ledesma, L. Jenaway, Y. Wang, S. ShihAdvanced EngineeringAdvanced Engineering

Commercial Vehicle SystemsCommercial Vehicle Systems

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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

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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

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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)

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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 States Road 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%

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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)

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Rainflow MatricesRainflow Matrices

• Characterize the fatigue damage potential of the spindle forces by generating rainflow matrices for each force component

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tuple of Rainflow-MatricesFxr

Fyr

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Fxl

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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

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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

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Fx

Fy

Fz

+

+

+

=

=

=

RFM-Fx

RFM-Fy

RFM-Fz

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Customer Duty Profile (Target RFM)Customer Duty Profile (Target RFM)

customer1%

special test

track

Superposition10 %

25 %

65 % target

ExtrapolationRepeat Factors

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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?

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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

optimaltrack mixing target

Select proving ground events such that the target matrices representing the customer duty cycle are reproduced

MultidimensionalOptimization Problem

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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 trackover target absolute valuesclusters

Partial Pseudo-Damage

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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

GravelAltern. BumpsA.Bumps to Emb. Rocks

Quality Check: Global Damage

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Comparison of Target and PG Rainflow Comparison of Target and PG Rainflow MatricesMatrices

Quality Check: Shape of Rainflow Matrices

Good Agreement in Range Pair Histograms

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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

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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 96.76The damage quotient of the 3. channel after filtering is 98.94The damage quotient of the 5. channel after filtering is 99.85The damage quotient of the 2. channel after filtering is 99.47The damage quotient of the 4. channel after filtering is 99.54The damage quotient of the 6. channel after filtering is 99.4429. direction has minimum damage quotient of 89.65

Original Signal

Fatigue-edited Signal

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Accelerated Test Schedule: Range Pair Accelerated Test Schedule: Range Pair HistogramsHistograms

FxFy

FzComparison between PG and accelerated durability rig test: high amplitude cycles are kept 100%

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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

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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

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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

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Defining the Single-Axis Component Defining 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

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Example: Specification for a Single-Axis, Example: Specification for a Single-Axis, Constant-Amplitude, Component Durability Constant-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

01

23

45

0 2 4 6 8 10

Log of Cumulative Counts

Lo

g o

f L

oad

A

mp

litu

de

Field Duty Cycle Reference Load-Life Curve

Proving Ground Schedule

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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

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