NONLINEAR STATIC AND MULTI-AXIAL FATIGUE ANALYSIS OF AUTOMOTIVE LOWER CONTROL ARM USING NEiNASTRAN Dr. J.M. Mahishi, Director Engineering MS&M Engineering Inc, Farmington Hills, MI, USA SUMMARY The Lower Control arm is the most vital component in a suspension system. It is usually a steel bracket that pivots on rubber bushings mounted to the chassis. The other end supports the lower ball joint. Significant amount of loads are transmitted through the control arm while it serves to maintain the contact between the wheel and the road and thus providing precise control of the vehicle. The finite element analysis of the control arm using NEiNASTRAN is presented. Inertia relief analysis was carried out as the measured road loads were in self equilibrium. The zone of maximum stress in most of the load cases studied is close to the left strut bush and around the lower ball joint bush. Since the stresses exceed the material yield strength, a nonlinear static analysis of the control arm was also carried out using NEiNASTRAN and the results are compared well with MSC.NASTRAN and ABAQUS analysis. Multi-axial Fatigue analysis using NEiNASTRAN and WINLIFE is discussed. 1 Background All the loads acting on the control arm are dynamic in nature. The vehicle dynamics and desired ride and handling specifications of the vehicle require that the control arm has certain stiffness. The design of control arms involves optimising for strength, stiffness and weight. Designing for some less frequent severe loads (pot holes, curb impact etc.) will lead to heavier sections. Based on years of experience, designing practice allows for occasional overloads. As a result the control arms have a limited life. A reliable fatigue analysis is required to ensure that the control arms at least survive the expected life span of the vehicle. The approach in this study is to subject the control arms with bushings to peak loads of varies operating conditions individually and perform static linear Inertia relief analysis (Ref. 1-3). For the load cases in which the stresses exceed yield strength of the material perform static non-linear analysis. Assuming that
all load cases are in sync and proportional, the fatigue life is estimated from individual load conditions using the Miner s cumulative theory. The assumption that all loads act in sync provides a safe conservative estimate. Whereas if more accurate estimate is required, the multi-axial alternating fatigue stress state can be analysed using multi-axial module in WINLIFE. 2 Lower Control Arm FEA The lower control arm is subjected to different magnitude of forces depending on the event (Table 1). In real life these events occur in varying sequence in and in varying combination. Table 1: Typical road loads. In order to develop an optimum weight, strength and stiffness of the control arm, one has to study the response of the control arm during all operational loading conditions. The concept cast steel control arm was modeled using second order 19,000 tetra elements (Figure 1). The bushings were represented by spring elements with spring rates in 3 directions.
Figure 1: Concept control arm. 3 Inertia relief analysis The forces acting on the control arm are dynamic in nature. The measured road loads are in equilibrium with the inertial forces from the sprung control arm. To solve such systems NEiNASTRAN (also MSC.NASTRAN / ABAQUS) provide a method in which the inertia forces are computed and subtracted from applied loads. In applying static inertia relief method to dynamic loading, it is assumed that the natural frequency of the system is at least twice that of the highest loading frequency. (2). The results of static inertia relief analysis are shown in Table 2.
Von Misses Stress Maj. Principal Stress NEi MSC NEi MSC 1 1g Vert 287 299 329 321 2 3g Vert 891 887 990 986 3 Curb Push off Left Leading 349 341 386 379 4 Curb Push off Left Trailing 390 382 318 311 5 Max Aft Acc 444 438 498 490 6 Max Aft Brake 238 246 216 159 7 Max Corner Left Turn 119 132 123 127 8 Max Corner Right Turn 720 720 430 429 9 Max Fore Acc 183 180 199 189 10 Max Fore Brake 495 488 557 550 11 Max Roll Left In Jounce 683 678 735 731 12 Max Roll Right In Jounce 125 127 127 131 Table 2: Results of inertia relief analysis. The NEiNASTRAN Inertia Relief Analysis required all 6 DOF to be defined at a SUPPORT point, whereas in MSC.NASTRAN only translational 1, 2 and 3 DOF could be defined at 3 SUPPORT points in combination. The stresses predicted by NEiNASTRAN are in close agreement to MSC. NASTRAN. Table 2 indicates that the stresses in 8 out of 12 load cases exceed the yield strength of the material.
Figure 2: Principal stress and location for load case 11. Figure 2 shows the Principal Stress Contour for the load case 11. The static analysis indicates that the location of the Maximum Principal Stress for 4 higher amplitude stress load cases in Table 2 occur at a corner between the ball bearing and front leg. This is a potential location of crack initiation and failure. However, as will be discussed later, the occurrence of these peak load events is less than some of the lower peak stress load events. The actual damage is cumulative effect from all load cases. It may be noted that the material experiences substantial increase in ultimate strength when subjected to high impact loading as in the case of potholes. The yield strength of the metals increases to the level of the increased dynamic ultimate strength, essentially exhibiting brittle behaviour. 4 Nonlinear analysis
The linear static inertia relief analysis shows that the stresses are above yield in 8 out of 12 load cases. It is necessary to perform nonlinear elasticplastic analysis. Static nonlinear analysis was performed on all load cases by adjusting the loads with inertia forces and constraining at bushing. Both MSC and NEi NASTRAN predict von Misses stress of 288 MPa for the load case 11. This also compares well with 287 MPa predicted by ABAQUS analysis. The efficiency of the iterative solution could not be established as the programs were running on different computer platforms and different operating systems Figure 3 shows the effective plastic strain contours for load case 11. Figure 3: Effective plastic strains. The effective stress and effective strain are plotted in Figure 4.
Figure 4: Elastic and plastic strains at the stress concentration location. The analysis predicts that there will be permanent set after unloading. 5 Fatigue Analysis In the absence of stress state during non-event, which may have some negative stress component, all maximum stresses listed in the table corresponding to different events are actually the alternative stress ranges.
Figure 5: Stress range for different load cases. The linear stress analysis shows that all load cases individually produce a limited life for the component. The stress distribution also shows that the maximum stress state occurs at the same location for some of the events. In which case, a cumulative damage theory had to be used to calculate the life. The life of the component depends on the frequency of occurrence of different events. In actual life of the component some of the events are far less frequent than the other. Figure 6 schematically shows different stress amplitudes and their corresponding expected number of cycles (ni).
Figure 6: Schematic representation of stress amplitudes and individual number of load cycles (n i ). Figure 7 shows the strain-life curve used to predict the number of cycles to failure for higher amplitude load cases. WINLIFE Basic will provide a means of estimating life N 1, N 2, N i during individual events using Normal Stress/ Strain life curves.
Figure 7: Strain-life curve for the material. The computed numbers of cycles to failure are listed in Table 3. Load Case 2N f 2 9,000 8 76,000 10 100,000 11 88,000 Table 3: Number of cycles (2N f ) to failure for 2, 8, 10 and 11 load cases. Since the load events 2, 8, 10 and 11 produce max stress state at the same location, the life is estimated using Palmer Miner Cumulative damage theory. This is assuming that the max fatigue stresses in all these load cases act in the same plane. According to Palmgren-Miner hypothesis, failure occurs when:
i nj / N j > = 1 (1) j=1 This will give the Cumulative damage life. It was not possible to include the OEM s n i values here. Even though events 2, 8, 10 and 11 produce max stress at same location, the directions of the principal planes are different. The same location will be subjected to cyclic fatigue loading in different planes simultaneously. In this case the Multi-axial Fatigue should be used. The multi-axial module of the WINLIFE can be used to compute the life in this case as explained in Reference 4. 6 Conclusions The paper presents a FEA approach to solve a dynamic low-cycle-fatigue problem using linear Inertia Relief method and nonlinear elastic-plastic analysis using NEiNASTRAN. A further automation of the approach can make use of WINLIFE multi-axial fatigue for more accurate fatigue life prediction. REFERENCES 1. MSC/NASTRAN Reference Manual 2. VELLAICHAMY, S and KESHTKAR, H - New approach to modal transient fatigue analysis, SAE 00C-136, 2000 3. VELLAICHAMY, S - Transient dynamic fatigue analysis using inertia relief approach with modal resonance augmentation, SAE 2002-01-3119, 2002 4. WILLMERDING, G, HACKH, J, and SCHNODEWIND, K - Fatigue Calculations Using WINLIFE, NAFEMS Seminar, Wiesbaden, Germany, Nov. 2000