2007-01-1653_Reliability-based Test Track Schedule Development for a Vehicle Suspension System
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SAE TECHNICALPAPER SERIES2007-01-1653Reliability-based Test TrackSchedule Development for aVehicle Suspension SystemSalman Haq and Yung-Li LeeStress Lab & Durability Development, DaimlerChryslerJerry L. Larsen and Marvin FrinkleT est Schedule Development & T est Management, DaimlerChryslerBindu AkkalaLMS of North AmericaReprinted From: Reliability and Robust Design in Automotive Engineering, 2007(SP-2119)2007 World CongressDetroit, MichiganApril 16-19, 2007By mandate of the Engineering Meetings Board, this paper has been approved for SAE publication upon completion of a peer review process by a minimum of three (3) industry experts under the supervision of the session organizer.All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE.For permission and licensing requests contact:SAE Permissions400 Commonwealth DriveWarrendale, PA 15096-0001-USAEmail: permissions@Fax: 724-776-3036Tel: 724-772-4028For multiple print copies contact:SAE Customer ServiceTel: 877-606-7323 (inside USA and Canada)Tel: 724-776-4970 (outside USA)Fax: 724-776-0790Email: CustomerService@ISSN 0148-7191Copyright © 2007 SAE InternationalPositions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely responsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published in SAE Transactions.Persons wishing to submit papers to be considered for presentation or publication by SAE should send the manuscript or a 300 word abstract of a proposed manuscript to: Secretary, Engineering Meetings Board, SAE. Printed in USAABSTRACTA process for establishing an accelerated proving ground durability schedule for a vehicle suspension system, based on real customer roads, was developedin this work. The available road load data for a specific chassis design was acquired by using a test vehicle that was equipped to measure the front and rear spindle loads, wheel–to-body displacements, and body mount loads. The test target representing the customer usage consists of a combination of 5 tracks of public roads located in Michigan, adding up to 100 miles, and is based upon a previous work by Ferris, J.B. and Larsen, J.L. [2]. It was then extrapolated to a target customer equivalent mileage of 150,000 miles with an assigned extrapolation factor for each public road. A repeat value for each of seven test tracks at the Chelsea Proving Grounds was generated using state-of-the-art optimization techniques to match the weighted, rainflow cycle histograms from the road load data channels,. These repeat values represent how many total passes of each event would need to be combined to duplicate spindle loads and wheel-to-body displacements during 150,000 miles of public road usage for the 95th percentile customer.INTRODUCTIONOne of the most challenging tasks for an automotive company is to design a compact and light-weight vehicle with the highest quality and reliability, while maintaining the speed-to-market criterion. The vehicle development time window is shrinking and leaves no room for lengthy field tests to validate vehicle reliability. For example, to meet a 150,000 mile design life target, it would take about one-year of vehicle field tests at an average of 500 miles a day. Therefore, an accelerated test track schedule representing a specific 150,000 mile user profile was developed.An accelerated test track schedule development for a vehicle chassis and suspension system was presented. In this study, the load data from the accelerated test track schedules would accumulate the same damaging effect as a targeted customer usage profile of 150,000 miles, based on the 100 miles of acquired road load data. Extrapolation of rainflow cycle histogram for each load data employing kernel methods, first proposed by Dre E ler et al [1], was adopted in our study. In the extrapolation process, the damage potential at the target miles was obtained by using the nonparametric probability density function that was applied to the damage contained in the 100 miles. Further, with the optimization technique, the accelerated test track schedule would be determined by matching the damage potential of the targeted rainflow matrix to the targeted customer usage profile. This results in reducing significant test length from 150,000 miles to less than 24,000 miles.The following sections describe the step-by-step methodologies for establishing a reliability-based test track schedule for a vehicle chassis/suspension system.TARGET PUBLIC ROAD TYPESThe durability test target was derived based on work by Ferris and Larsen [2]and consists ofA)roughness values2007-01-1653Reliability-based Test Track Schedule Developmentfor a Vehicle Suspension SystemSalman Haq and Yung-Li LeeStress Lab & Durability Development, DaimlerChryslerJerry L. Larsen and Marvin FrinkleTest Schedule Development & Test Management, DaimlerChryslerBindu AkkalaLMS of North America Copyright © 2007 SAE InternationalB)total distancesfor the following defined road types:Type 1 – Interstate highway road with multi-lanes where the vehicle speed exceeds 45 mphType 2 – Minor arterials with multi-lanes where the vehicle speed exceeds 45 mphType 3 – City road interrupted traffic with a minimum vehicle speed of 40 mphType 4 – Residential roads with the maximum vehicle speed of 40 mphType 5 - Unpaved road with the vehicle speed less than 40 mphTarget roads for types (1-5) were either chosen from existing road measurement libraries or sought out as needed to match cumulative distribution function (cdf) as calculated by Ferris and Larsen [2].Similar to the CARLOS-standard [4], the overall distance (150,000 miles) was appointed to the road types in Table 1. Table 1 – Distance-distribution of public road typesRoad Type ID% Target MilesMeasured Miles1 Highway 30102 Minor arterials 29103 City road 23104 Residential road 14105 Unpaved road460MEASUREMENT OF DATAThe test vehicle was instrumented by wheel force transducers for the 3-dimensional spindle forces at each wheel, by vertical force transducers for each body mount, and by rotational variable differential transducers (RVDTs) for front upper control arm angles and linear variable differential transducers (LVDTs) for displacement of rear shock absorbers.Data acquisitions were performed on the above mentioned target road types, altogether adding up to 100 miles. An extrapolation technique is required to predict the long-term loads on the target miles based on the short-term measured data on the 100 miles.A test track represented a mix of seven major different events on the Chelsea proving ground was selected. Data acquisitions were again conducted on the seven test tracks, from which the number of repeats for each test track would be estimated by an optimization technique resulting similar loading characteristics between the target roads and the test tracks.RAINFLOW CYCLE EXTRAPOLATIONThe purpose of the rainflow cycle extrapolation is to predict the rainflow cycle matrix for 150,000 miles based on a load measurement of 100 miles. For fatigue assessment,it was assumed that each channel of acquired data was statistically independent. The popular rainflow cycle counting technique could then be applied to each channel of data. The extrapolation factor for each road type was determined by the ratio of target miles to the measured miles. The state-of-the-art cycle extrapolation technique developed by Dre E ler et al [1] was adopted in this work.Readers were referred to the textbook by Lee et al. [5] for details.Figure 2 showed two rainflow matrices that were represented by a from-to format, where the number of cycles in each bin is depicted by a different color or a larger size. The left and the right figures are the cycle counting results from a short-term measurement and a long-term extrapolation, respectively. The left rainflow matrix was equivalent to a two-dimensional probability density function that was obtained by dividing the number of cycles in each bin of the matrix by the total number of cycles. To any number of total cycles, a new rainflow matrix could then be constructed by randomly inserting the cycles in each bin based on their probability of occurrence within the bin and around its neighborhood bins, described as the elliptic bandwidth in Figure 2.Figure 2 – Illustration of a rainflow cycle extrapolation techniqueAn adaptive variable bandwidth was selected to account for variability of the centered cycles in the boundary.AsAfter Extrapolated to Number of Cyclesshown in Equation (1), the kernel estimator, K , was used to convert the discrete probability density distribution into a continuous probability density function.¦ »»¼º««¬ª¸¸¹·¨¨©§O O O n i i i i i i h Y y h X x K h n y x f 12,11),( (1)where n, is the total number of cycles in the rainflowmatrix, K is the kernel estimator corresponding to X i and Y i , h and O i are the kernel and adaptive bandwidths.Figure 3 depicted the two-dimensional cumulative exceedance histograms for the five road types after extrapolations.Figure 3 – Example of the cumulative exceedance histograms for the five target road typesTARGET RAINFLOW MATRIXThe final target rainflow cycle matrix for each channel of data at 150,000 miles was then obtained by superposition of the extrapolated rainflow cycle matrices based on the five road types. Figure 4 showed an example of the formation of the target rainflow matrix.Figure 5 also illustrated the target cumulative exceedance histogram for the same channel of data.Figure 4 - Formation of the target rainflow matrixFigure 5 – Example of the target cumulative exceedance histogramTEST TRACK SCHEDULE DEVELOPMENTA rainflow matrix optimization technique developed by LMS [5] was used in our work to determine the number of repeats for each test track so that the loading and fatigue characteristics of the test tracks (RFH i ) matched with those of the target public roads (RFH T ). For durability testing, the difference in damage content (RFH T - RFH i ) was of interest. Both the so-called “global” and “partial” damage values were considered in the optimization process. The “global” damage values were calculated directly from each RFH T and RFH i with the assumption that the fatigue damage was calculated on a given pseudo S-N curve defined by a slope of -0.2 and the fatigue strength coefficient of 108. The partial damage values were calculated for each of cluster of the bin in the whole rainflow matrix. This would result in an optimal solution because it took into account the shape of the rainflow histogram.A scale factor defined the weight of the corresponding load variable relative to the other variables duringoptimization. The scale factors (4, 2, and 1) for verticalTargetType1Type2Type3Type4Type5Customer ProfileTargetType1Type2Type3Type4Type5Customer Profile(4), longitudinal (2), and lateral (1)loads were assigned in our work. Figure 6 showed the optimized schedules (repeats) for the seven test tracks and the target road matrices. The final optimization results for one of the channels of loads were validated in Figure 7which displays this in terms of global and partial damage values in the target rainflow matrix. A factor of two damage ratio was considered a reasonably good correlation. The global damage values with respective to the target values for all the acquired channels were also listed in Table 2.Figure 6 – Schematic illustration of the optimized schedules for the seven test tracks and the target road matricesFigure 7 – Global and partial damage optimization in the target rainflow matrix.Table 2 – Global damage percentages relative to the target matrix for all the channelsRFWFT-Long 146LFWFT-Lat 44RFWFT-Lat 62LFWFT-Vert 88RFWFT-Vert 103LRWFT-Long115RRWFT-Long 147LRWFT-Lat 193RRWFT-Lat104LF Body Mount89RF Body Mount 104LR Body Mount 193RR Body Mount 191LF LCA Angle 122RF LCA Angle 177LR Shock 122RR Shock177CONCLUSIONSThis paper presents a methodology to develop reliability-based test track schedule for a vehicle suspension and chassis system. The methodology includes (1) definitions of the target customer road types using the International Roughness Index (IRI), (2) short-term measurement of the suspension/ chassis data using load and displacement transducers, (3) long-term rainflow cycle extrapolation of the measured data, (4) final accelerated track schedule development using a rainflow matrix optimization technique. This methodology results in reducing significant test length from 150,000 miles to less than 24,000 miles.Global & Partial Histogram Optimization using Histogram ClustersRelative Damage in PercentageAbsolute DamageTargetEvent 7 x Weight, W7PG EventsEvent 1 x Weight, W1Event 6 x Weight, W6Event 2 x Weight, W2Event 3 x Weight, W3Event 4 x Weight, W4Event 5 x Weight, W5Channel IDDamage % relative to TargetLFWFT-Long 78rainflow cycle counting and extrapolation, damage calculation, and schedule optimization.The authors also thank the following persons for their significant contributions to the road profile measurement and data acquisitions: Prof. John B. Ferris of Virginia Technology, Mike Temkin of DaimlerChrysler, Chris Williams of DaimlerChrysler, and Bob Weir of DaimlerChrysler.REFERENCES1.Dre E ler, K ., Grunder, B., Hack, M., and K ottgen, V.B., “Extrapolation of Rainflow Matrices”, SAE No. 960569, 1996.2.Ferris, J.B. and Larsen, J.L., “Establishing ChassisReliability Testing Targets Based on Road Roughness,” International Journal of Materials and Product Technology, Vol. 17, Nos. 5/6, 2002, pp. 453-461.3.Sayers, M.W., “On the Calculation of International Roughness Index from Longitudinal Road Profile,” Transportation Research Record 1501, 1995, pp. 1-12.4.Sch utz, D., Klatschke, H., Steinhilber, H., Heuler, P., Sch utz, W., Standard Load Sequences for Car Wheel Suspension Components: Car Loading Standard (CARLOS), LBF-Report No. FB-191, 1990.5.Lee, Y.L., Pan, J., R. Hathaway, and M. Barkey, Fatigue Testing and Analysis: Theory and Practice, Elsevier Inc., 2005.6./06 7HF:DUH 8VHU 0DQXDO 9ROXPH ,9 0DWKHPDWLFDO , LMS International -Durability Technologies Division, 1999.CONTACTYung-Li Lee, Stress Lab & Durability Development, DaimlerChrysler, 800 Chrysler Drive, CIMS 484-05-20, Auburn Hills, MI 48326; email: YL2@ACKNOWLEDGEMENTSThe authors appreciated the technical support from LMS North America. The fatigue software (LMS-TecWare) was used for acquired data reduction,。
