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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 2003-01-3434 Correlation of Fatigue Test Results and Finite Element Analysis for a Prototype Independent Suspension Axle Housing S. S. Timoney, E. P. Timoney a
2、nd C. Lynch Timoney Technology Ltd. Reprinted From: Vehicle Dynamics, Braking, Steering and Suspensions (SP1814) 2003 SAE International Truck and Bus Meeting and Exhibition Fort Worth, Texas November 10-12, 2003 All rights reserved. No part of this publication may be reproduced, stored in a retrieva
3、l 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 Permissions 400 Commonwealth Drive Warrendale, PA 15096-0001-USA Email: permissionssae
4、.org Fax: 724-772-4891 Tel: 724-772-4028 For multiple print copies contact: SAE Customer Service Tel: 877-606-7323 (inside USA and Canada) Tel: 724-776-4970 (outside USA) Fax: 724-776-1615 Email: CustomerServicesae.org ISBN 0-7680-1333-X Copyright 2003 SAE International Positions and opinions advanc
5、ed 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 consi
6、dered 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 USA 2003-01-3434 Correlation of Fatigue Test Results and Finite Element Analysis for a Prototype Independent Suspension A
7、xle Housing S. S. Timoney, E. P. Timoney and C. Lynch Timoney Technology Ltd. Copyright 2003 SAE International ABSTRACT This paper reports on the correlation of fatigue results with Finite Element Analysis (FEA) predictions for an axle housing designed as an integral part of an independent suspensio
8、n for an off-road truck. The axle initially failed to meet the prescribed fatigue performance criteria and a description of the failures is given. Maximum permissible stress levels were estimated for the prescribed performance. Linear FEA was used to determine the stresses in the original axle housi
9、ng that had failed the fatigue test. Analysis of the available fatigue data predicted component life that was in good agreement with the test results. Further FEA allowed the effectiveness of design modifications to be monitored, resulting in a new design having a high degree of probability of meeti
10、ng the fatigue performance criterion, without increase in weight, and at a lesser cost than repeated testing. 1 INTRODUCTION The axle-housing element in this design has multiple functionality. It houses the differential assembly, it acts as an extremely stiff structural cross member of the chassis a
11、nd it provides axle arms as anchor points for the suspension control arms. The hub-to-hub independent suspension assembly was originally designed to be fitted with twin coil springs between chassis and lower wishbone. This original design meets the fatigue performance criterion outlined in section 2
12、.1 below. The suspension was redesigned to accommodate a single hydro-pneumatic strut (hydrostrut) instead of the twin spring arrangement. The load paths through the suspension components were consequently altered. The purpose of the tests reported here was to determine if this modified design would
13、 meet the fatigue performance criterion of 300,000 cycles. Failure actually occurred after 17000 cycles. 2 FATIGUE TESTING 2.1 FATIGUE PERFORMANCE CRITERION The fatigue performance criterion for this hub-to-hub assembly is that it should survive 300,000 cycles of 2g vertical loading. Thus, for a giv
14、en vehicle, the 2g vertical load is equivalent to twice the vehicle load acting on the hub-to-hub assembly. The load varies from zero to 2g, at a frequency of 1 Hz, with a dwell period at maximum load of 0.3-0.5 s. The advantage of using a fixed frequency test rather than a random input signal to si
15、mulate the road loads is that the results can be compared to available fatigue data from materials laboratories. 2.2 TEST APPARATUS Figure 1 Schematic of load application The stub axles were replaced with mock-up stub axles having a hardened insert at the point of contact with the rigid supporting b
16、locks (Fig. 1). The inserts had a curved surface to allow the mock-up stub axle to rock slightly as the assembly is loaded and unloaded. On the test rig the hydrostruts were replaced by rigid links, which prevented the suspension from articulating. Consequently, only small deflections occurred in th
17、e suspension assembly due to compliance in the joints and material deflections in the cast components. The length of the rigid links was chosen such that the suspension was in its neutral position for the test. The cyclic vertical loading was applied to the top of the axle housing through the chassi
18、s rails. 2.3 TEST RESULTS After 17,000 cycles a crack developed in the axle housing at the junction between the central spine, which carries the two aft axle arms, and the main body of the axle housing, some distance below the through-drive boss (Fig. 2). High tensile stress levels caused this failu
19、re. The cracked axle housing was replaced with a new housing. Bracing was fitted to the axle housing to prevent the area, where the failure had occurred after 17,000 cycles, from going into tension. The test recommenced and after a further 116,000 cycles one of the axle arms failed close to the poin
20、t where it was attached to the central spine. Figure 3 shows the failed axle arm and also the bracing plate underneath the axle housing, which was used to prevent the first failure from recurring. Figure 2 Failure of central spine after 17000 cycles. Figure 3 Failure of axle arm after 116000 cycles
21、3 MATERIAL PROPERTIES The axle housing was manufactured from GH60/38/10 ductile iron. Fatigue data for this material was not readily available and so data relating to the equivalent GGG60 spheroidal-graphite iron was used instead. Treatment of this fatigue data is presented in the following section.
22、 The mechanical properties of GH60/38/10 are shown in Table 1. Ultimate Tensile Strength 588 MPa Yield Strength 373 MPa Elongation 10 % Table 1. Mechanical Properties of GH60/38/10 4 DETERMINATION OF PERMISSIBLE STRESS LEVELS Fatigue properties for GGG60 were available from Hck et al., 1. In the fol
23、lowing, the number of cycles corresponding to the knee of the S/N curve is taken as ND= 1.35 x 106(Hck et al., 1 Table 3). This corresponds to the fatigue endurance limit or infinite fatigue life. This section describes the assumptions made in applying the information available from Ref. 1 to estima
24、te the maximum permissible stresses for a life of 300,000 cycles. The Haigh diagram for GGG60, Figure 4, shows the allowable combinations of alternating stress, a, mean stress, m, and having a 50% probability of infinite life (106 cycles), for a range of stress concentration factor, Kt. Reciprocatin
25、g Loads refers to stresses which vary from -a to +a, with m= 0, whereas Pulsating Loads refers to stresses which vary from zero to +2a, with m = a. Figure 4. Haigh Diagram for GGG 60 showing the maximum permissible combinations of mean and alternating stresses for 50% probability of attaining infini
26、te life. Reproduced from Reference 1. For a stress concentration factor of 1, the maximum permissible pulsating load to give a 50% probability of infinite life has a mean stress, m, of 210 MPa and an alternating stress, a, of 210 MPa (i.e. stress varies from 0 to 420 MPa). To adjust these figures fo
27、r a 99% survival probability, reference is made to Figure 5, which relates to reciprocating loads and shows the alternating stresses corresponding to different probabilities of achieving infinite life, for a range of stress concentration factors. From Figure 5, for a stress concentration of 1, the a
28、lternating stress having 50% probability of achieving infinite life is 270 MPa, and this appears on Figure 4 at the point (m, a) = (0, 270) MPa. On Figure 5, the alternating stress having 99% probability of achieving infinite life is 220 MPa. On Figure 4, this plots as the point (m, a) = (0, 220) MP
29、a and through this point a line is drawn approximately parallel to the line for a stress concentration factor of 1 and 50% probability of attaining infinite life. This represents an estimate of all combinations of mean stress and alternating stress having 99% probability of attaining infinite life a
30、t a stress concentration of 1.The intersection of this line and the pulsating load line indicates that for m = a =160 MPa (i.e. load varying from zero to 320 MPa) the probability of attaining infinite life is 99%. Figure 5. Permissible nominal stresses for different probabilities of attaining infini
31、te life for GGG 60. Reproduced from 1. Next, the permissible stress level had to be modified to take account of the fact that a life of only 300,000 cycles was required. Again from Hck et al., 1, the allowable stress at N = 3 x 105cycles can be calculated from 1 1 Eq N N k D D a = with ND =1.35 x 10
32、6 k =8.6 These figures are from Hck et al., 1, Table 3. The figures for bending rather than axial loading were taken as more appropriate for the stress gradient in the component. The resulting value, 380 MPa, is then the estimated permissible maximum stress level, for pulsating loading, that will ha
33、ve 99% probability of achieving a life of 300,000 cycles. 5 FINITE ELEMENT ANALYSIS OF ORIGINAL AXLE HOUSING Finite element analysis (FEA) was carried out to establish the stresses in the axle housing that failed during fatigue testing, and to allow comparison of the failure sites predicted by the F
34、EA with those observed in the testing. 5.1 MODEL ASSUMPTIONS AND BOUNDARY CONDITIONS The loading is staticno account is taken of the cyclic nature of the loading. The dwell period at maximum load ensures that the stresses in the axle housing have sufficient time to reach a maximum and stabilize. The
35、 analysis is linear, insofar as there are no large deflections and the material stress-strain characteristic is linear, and does not exhibit yielding behavior. The axle housing is symmetrical about the vertical plane through the longitudinal axle housing centerline. The plane of symmetry is parallel
36、 to plane y-z in Figure 6. in the finite element model the symmetry can be used as a boundary condition, which halves the size of the model. The boundary conditions applied to the nodes on the top surface of the axle housing mounting plate constrain movements in the x-, y-, and z-directions. This mo
37、dels the rigid attachment of the axle housing to the chassis in real situations. 5.2 INPUT LOADS The vehicle for which the hydrostrut arrangement was tested has a single wheel station load of 41.54 kN. Hence the 2g load corresponding to this vehicle, which was used in the fatigue testing, was 83.08
38、kN. The forces acting in the suspension components were analyzed and the loads acting on the axle housing at the points of attachment of the upper and lower suspension control arms were calculated and are shown in Table 2. The aft axle arms supported by the central spine carry a significantly greate
39、r load because the hydrostrut is mounted on the lower control arm closer to them. FxkNFykN FzkN Load Location Fore -17.53 0 -1.95 Upper WishboneAft -17.53 0 -1.95 Fore 24.50 0 -6.60 Lower WishboneAft 21.02 0 -83.08 5.3 FEA RESULTS FEA was used to calculate the principal and von Mises stress levels w
40、ithin the casting. As can be seen at Locations A and B of Figure 6, the von Mises stress is well in excess of the permissible stress level of 380 MPa, so that failure would be expected to occur before reaching 300,000 cycles. The FEA results exhibit good qualitative correlation with the results of t
41、he fatigue testing. Location A has the highest level of stress and as such, failure would be expected to occur here first. As the loading is symmetrical two regions of high stress would exist on either side of the central spine. Crack initiation at one or other of these locations will propagate acro
42、ss the central spine leading to the failure seen in Figure 2. Figure 6. von Mises stress plot of original axle housing A prediction of the number of cycles to failure can be made from fatigue data presented in Figures 7 and 8. The FEA reports a stress of 700 MPa at Location A. This is based on a lin
43、ear analysis, which does not account for the yielding of the material. The strain at the center of Location A is assumed to be controlled by the bulk material surrounding the hotspot, which is not stressed beyond yielding and so remains in the elastic, linear region of the stress/strain plot. Figure
44、 7 shows the stress/strain curve for GGG60. It is clear that the stress can never reach 700 MPa at location A because of the plastic yielding of the material. Figure 7. Cyclic and monotonic stress-strain behaviour of GGG 60 reproduced from Reference 2. The true stress can be estimated using a Neuber
45、 plasticity correction. The following data was extracted from the Table for low cycle fatigue properties for GGG60 in the appendix of Ref. 2. E = 158 GPa K = 918 MPa n = 0.1064 f =828 MPa b = -0.0736 f = 0.3852 c = -0.6947 Figure 8. Strain-life curve for GGG 60 reproduced from Reference 2. The maxim
46、um stress calculated for Location A was 700 MPa using a linear analysis. The Neuber analysis gives a corrected maximum stress value of 497 MPa with a corresponding strain of 0.00625. The linear stress amplitude of 350 MPa gives a corrected value of 343 MPa and a strain amplitude of 0.00226. At Locat
47、ion B the maximum stress calculated was 680 MPa, giving a corrected maximum stress of 492 MPa with a strain of 0.00600, and corrected stress amplitude of 334 MPa with strain of 0.00220. Fatigue lives were then estimated with and without a Smith-Watson-Topper (SWT) mean stress correction with and wit
48、hout a surface correction factor ns = 1.316 to account for the as-cast surface, using the equation: 2.)2()2( )( /2 2/ max 2 EqNN E n cb fff b f f as + += The results for cycles to failure are summarized in Table 2. As can be seen there is reasonably good agreement of values calculated from the FEA w
49、ith the test results. Location Test Result ns = 1 no mean stress ns = 1 SWT correction ns = 1.32 SWT correction A 17000 80000 11800 1660 B 116000 112400 14400 1870 Table 3. Correlation of test results with fatigue calculation. 6 FINITE ELEMENT ANALYSIS OF REDESIGNED AXLE HOUSING The axle housing was redesigned to reduce the stresses to below the permissible stress levels. FEA was used to determine the stress levels after the shape and geometry of the axle housing were modified. The redesign was