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1、400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-5760 Web: www.sae.org SAE TECHNICAL PAPER SERIES 2006-01-1255 Automotive Axle Simulation and Correlation Yuejun E. Lee, Sree Sreedhar, D. Marla and C. Pawlicki Visteon Corporation Reprinted From: Load Simulat
2、ion & Analysis in Automotive Engineering (SP-2038) 2006 SAE World Congress Detroit, Michigan April 3-6, 2006 The Engineering Meetings Board has approved this paper for publication. It has successfully completed SAEs peer review process under the supervision of the session organizer. This process req
3、uires a minimum of three (3) reviews by industry experts. 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
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5、utside USA) Fax:724-776-0790 Email:CustomerServicesae.org ISSN 0148-7191 Copyright 2006 SAE International Positions 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 b
6、y 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 to Secretary, Engineering Meetings Board, SAE. Printed in USA 2006-01-
7、1255 Automotive Axle Simulation and Correlation Yuejun E. Lee, Sree Sreedhar, D. Marla and C. Pawlicki Visteon Corporation Copyright 2006 SAE International ABSTRACT Up to date, computer aided engineering (CAE) has been used in improvement of design quality and reduction of cost and delivery time. Al
8、though it has been widely accepted as a standard product development tool by the engineering community, CAE still faces many challenges in improving simulation process efficiency through process integration and automation, and simulation accuracy by analytical model/physical testing correlation. CAE
9、 engineers are constantly improving the accuracy of their analytical models through test correlation to deliver higher confidence for their analysis result. Although laboratory testing has provided an effective way to accelerate product development, analytical simulation of the lab test has been use
10、d frequently to further reduce the development cost and time throughout many industries. This paper presents a case study of CAE correlation of a finite element (FE) model of an automotive beam axle assembly in a laboratory test environment. A simplified boundary constraint model using springs was p
11、roposed for axle vertical bending test. Both strain and displacement measurements were adopted as the targets in the correlation. Maximum shear strain contours of the correlated models were compared to the test measurement. The analytical model update process was automated by applying optimization t
12、echniques. Good correlation results have been achieved. It proves that linear CAE simulation can accurately model the axle vertical bending lab test for stress and strain analysis. Certain correlation process issues related to data selection and finite element modeling are discussed and guidelines a
13、re recommended. The correlation process can be applied in other similar applications of the real world. INTRODUCTION For years, automotive suppliers have heavily relied on the key life laboratory testing as compared to proving ground testing to validate their designs in their product development pro
14、cess. The main reason for this is that they have no easy access to prototype vehicles for testing their products during the early development stage. Another reason is the higher cost of proving ground testing as compared to laboratory testing. Additionally, laboratory test environment is relatively
15、easy to control and provides opportunities for accelerating tests to reduce the development time. As the increase of todays market competition, automotive suppliers are constantly challenged to quickly bring innovations to the market as well as to minimize the development cost for all products in or
16、der to survive in the competition. Among other efforts, reducing hardware test and increasing the use of up-front CAE analyses become ever critical through the product development process. It drives engineers to create accurate analytical models through test correlation and knowledge reuse. A lot of
17、 research works have been cited in the field of CAE model correlation 1-2. In the previous study 1, a simple automotive control arm was used to investigate certain critical correlation issues including measurement selection, boundary condition model, FE model reduction as well as correlation tools a
18、nd methods. The preliminary study proved that a simple spring model could be used to simulate general rigid boundary connections in the lab test. The work has also identified a general correlation process and certain guidelines for FE modeling. By applying the previously obtained knowledge, the curr
19、ent research focused on how to apply the correlation process to a complicated automotive component, i.e., an automotive axle assembly. To further improve correlation confidence, a new Visteon patented strain measuring technology was used to obtain full field strain distribution for CAE model correla
20、tion and update. Through selective use of strain and/or displacement measurements, three correlation strategies were studied. The optimization technique was applied in search for the optimal boundary spring stiffness values that lead to the minimum difference between CAE results and physical testing
21、 measurements. The case study proved again that linear spring elements could be used to simulate the test fixture boundary condition of a complicated assembly to achieve good test correlation. The correlated test fixture model will improve accuracy of up-front CAE analysis for future product develop
22、ment. EXPERIMENTAL TEST AND MEASUREMENT Laboratory axle vertical bending testing has been used in the product development for durability validation. In this study, the test was performed in a test laboratory where the loading and the mounting fixtures were used to replicate the service conditions of
23、 the tested assembly. The complete laboratory test setup is shown in Fig.1. Figure 1: Laboratory axle vertical bending test setup The tested beam axle assembly was mounted on two test fixtures, which allow free rotation about the vertical axis (perpendicular to the ground) at their centers. One of t
24、he fixtures also allows same free vertical rotation at the grounded test bed. Those free rotational degrees of freedom (DOF) were used to simulate real vehicle wheel/tire reactions. At two suspension spring seats (marked by arrows in the picture), two pneumatic actuators were used to simultaneously
25、apply bending loads. The actuators were rigidly connected to the suspension seats through specially designed mounting fixtures that allow the same free vertical rotation like the mounting fixtures in the vehicle. Three different load levels of 1000 lb, 2000lb and 3000 lb were applied incrementally a
26、t two suspension seats. To investigate various CAE correlation strategies, both strain and displacement measurement data were acquired at each load level. The studied correlation strategies included the displacement correlation, strain correlation and strain/displacement correlation. The maximum she
27、ar strain field of the external surface of the axle housing was measured by Visteons new strain measuring technology. This technology is able to measure full in-plane strain field data and its maximum principle direction on the surface of the tested axle housing. Furthermore, four displacement dial
28、indicators were used to get the displacement values at four specified locations on both the axle housing and the housing tubes. To minimize the errors caused by possible tip sliding of the dial indicators, the measurement positions and the directions was carefully selected. All test data were acquir
29、ed through several repeated runs for test repeatability checking. Though strain data can be recovered at all locations within the measurement area by the new strain measuring tool, only limited locations were selected in the CAE correlation in order to simplify the analytical correlation process by
30、optimization technique. The recovered maximum shear strain locations are shown in Fig.2. The recovered strain data was then filtered through a data screening process to eliminate potential bad test data primarily due to the measuring system noise errors of 50 micro-strain. The finally selected data
31、points are plotted in Fig.3. The displacement data is plotted in the Fig.4. The displacement data of dial 2 showed significant nonlinear behavior and was then removed from the final correlation. Additionally, only mechanical strain readings due to actuator load application were reported. Figure 2: M
32、aximum shear strain recovery location points Actuator Vertical Bending Deflection Test D.I # 4 D.I # 3 D.I # 1 & 2 Vertical Bending Measurement 0 50 100 150 200 250 0100020003000 Suspension Spring Seat Load (lb) Maximum in-plan shear Strain 17 18 21 28 29 38 40 37 1 24 Figure 3: Vertical Bending Max
33、imum Shear Strain Measurement Vertical Bending Measurement 0.0000 0.0400 0.0800 0.1200 0.1600 0.2000 0100020003000 Suspension Spring Seat Load (LB) Deflection (in.) D.I.#1 (in.) D.I.#2 (in.) D.I.#3 (in.) D.I.#4 (in.) Figure 4: Vertical Bending Displacement Measurement FE MODEL AND CORRELATION METHOD
34、 The FE model of the complete beam axle assembly (Fig.5) was created following the CAE modeling guide 3-4. To eliminate the geometry errors due to manufacturing process, the axle housing CAD model was built by reverse engineering technique using Steinbichler equipment. The reverse engineered CAD axl
35、e housing was then meshed with second order tetrahedral elements. A layer of thin shell elements was coated onto the solid elements of the axle housing to recover the maximum shear strain on the external housing surface. As a result, the surface maximum shear strain value could be calculated at the
36、locations where the strain measurements were recovered experimentally (Fig. 2). The simple spring model was adopted from the previous research work 1 for modeling the test boundary constraints. The five rigid constraints of each mounting fixtures were modeled by five zero length spring elements resp
37、ectively. For the fixture that had the pivoting joint at the grounded test bed, a rigid bar element was used to connect the fixture center and the ground center. The pivot end of the rigid bar element was then restrained by only five single point constraints (SPC) and the unconstrained rotational DO
38、F allowed for the pivoting movement. For the center nodes of the two suspension seats where the loads are applied, only axial and vertical rotational DOFs are set to be free and the rest four DOFs were restrained through grounded springs respectively. The complete FE model including loading and boun
39、dary conditions is shown in Fig.5. There are about 200,000 elements and 300,000 nodes in the axle FE model. The test mounting fixture contains total 18 spring elements and one rigid element. Those 18 spring elements were selected as design variables in the analytical correlation process using optimi
40、zation technique. To simulate the rigid connection of the fixtures of the baseline model, very large stiffness values were used for all 18 mounting fixture springs (Table 5). Since over 90 percent of the FE model is not changed during the analytical correlation process, it provides a good opportunit
41、y for reducing assembly FE model to reduce analysis CPU time through FE model condensation. Therefore, only the DOFs that represent the locations of load, measurement responses as well as design variables are kept explicitly in the final condensed optimization model. This model reduction technique l
42、ed to more than 90 percent reduction of the optimization computing time. Figure 5: FE model of axle assembly The optimization process for CAE correlation generally involves the following steps: select design and response parameters define the optimization problem, which includes setting the bounds o
43、f design parameters, defining the objective function and the constraints select the optimization algorithm monitor and post-process the results The correlation objective is to find the proper test boundary constraint by matching as close as possible strain and/or displacement of the FE model with co
44、rresponding physical test measurements. Therefore, those 18 boundary spring elements described before were selected as design variables and their stiffness were automatically adjusted during the optimization searching process. Among all the measurement locations, only 10 locations for strain and 3 l
45、ocations for displacement were selected as final matching target response by a dada screening process. Different combinations of strain and/or displacement measurements were used as targets for matching the FE results for different correlation strategies Force comparisons. Three selected correlation
46、 or matching strategies are listed in the following: displacement measurement matching strain measurement matching both displacement and strain measurements matching Minimizing the difference between the calculated FE responses and the experimental measurements at the selected locations is set as op
47、timization objective function. A general matching algorithm provided by GENESIS software was used. For more details about the algorithm, please refer to GENESIS users manual 5. The algorithm basically minimizes the difference between the calculated and the targeted (or measured) responses at the spe
48、cified locations. RESULTS AND DISCUSSION Comparisons of measurements vs. calculated responses of the baseline model and the correlated models by the three different strategies are shown in Tables 1-4. Discussions of the correlation results as well as research findings are summarized in the following
49、, Among all three matching strategies, the matching for both displacement and strain at the same time provides the best over-all correlation result with the smallest difference percentages for all strain and displacement measurements. The displacement measurement matching shows larger difference percentages of the strain targets while the strain measurement matching has larger difference percentages for displacement targets. Comparing to the baseline model, all three types of matching show over-all improvement of the target differen
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