Random vibration analysis and fatigue life evaluation of auxiliary heater bracket Arshad Khan, Devashish Sarkar, Reshad Ahmar and Hitenkumar Patel Larsen and Toubro Integrated Engineering Services, INDIA Abstract: CAE has been an important tool in the process of automotive product development. Chassis mounted components on the truck are subjected to random excitations from the road during their life cycle. While designing the components, it should be ensured that the component should sustain the random vibration loads for the life cycle of the vehicle. These random vibration loads are also responsible for the fatigue failure of the component. The object of this study was to predict the fatigue life cycle of a chassis mounted component, an Auxiliary Heater Bracket concept which was, in actual scenario, subjected to random vibration excitations from the road. The weld fatigue life was also calculated in this exercise. It was estimate that the bracket concept was not able to sustain infinite life in the 1 level of confidence. A redesign of the Auxiliary Heater Bracket was suggested to achieve infinite fatigue life. There is a requirement about the bracket that it must endure infinite life in 1 and 2 level of confidence. Infinite life cycle in the FEA simulation was achieved for the modified bracket. Random Vibration Analysis was performed on the bracket model in Abaqus and response was calculated up to 130 Hz. RMS stresses were used for the fatigue life cycle calculations and the fatigue life cycle was determined from the Basquin's relation. Abaqus was very helpful in completing this life cycle simulation. Python scripting was used to post process huge amount of data in generating the RMS stresses. Keywords: Fatigue, Auxiliary heater bracket, Abaqus, Random Vibration Fatigue, PSD, Weld Fatigue, Basquin s Relation, PYTHON scripting, CAE 1. Introduction The auxiliary heater bracket mounted on the chassis cross member along with several other components on truck is subjected to loads due to the engine operations and vehicle road conditions. These loads are typically random in nature. It is very important to predict the fatigue life of the components for getting an optimized design for these components. This application forms a specialized analysis domain which can be referred as random vibration fatigue analysis. In a compressed design cycle, most of the FEA is done on the various engine and chassis mounted components using simplified load representations. This is in the form of applying fixed inertia loads on the components as per relevant industry standards and calculating the natural frequencies. In this paper, we may observe that with the help of Abaqus, the loads and boundary conditions were simulated close to the real environment. This was achieved in a very small time frame, thus not impacting the design life cycle. SIMULIA India Regional Users Meeting 11 Page 1 of 12
2. Finite Element Model The auxiliary heater bracket is mounted on the cross member of the rail chassis. The components which were directly attached the bracket are considered in the simulation. Figure 1shows the geometry considered for the analysis. We can see the Auxiliary Heater Bracket mounted on the cross member. Figure 1 Auxiliary Heater Bracket Assembly The finite element model is shown in the Figure 2. Figure 2 FE Model SIMULIA India Regional Users Meeting 11 Page 2 of 12
All the sheet metal parts including Auxiliary heater bracket were assigned steel material. Linear elastic material properties were considered for the analysis. Auxiliary heater bracket was meshed with hexahedral elements (C3D8I), whereas all other sheet metal components were meshed with shell elements. Bolted joints have been simulated with rigid and beam connection. Density of pump and pipes mounted on auxiliary heater bracket were adjusted to achieve a total mass of the assembly. 3. Simulation 3.1 Loads and Boundary Condition The FE model was created in Altair Hypermesh. The necessary connections in terms of bolted joints were modeled. Loading history was derived from the mission tests in the forms of accelerations load history in all the Cartesian directions at certain locations on the chassis. This load data was converted to the PSD amplitude data in the form of PSD accelerations vs. frequency components. One of the locations for this data acquisition is as shown in Figure 3. The data collected from the road test data has to be increased by 1.3 to take into account the pot-hole effect. This corresponded to 1.69 times increases in the PSD amplitude. From the loading scenario, it was clear that this was a case of base excitation. A deck was prepared in Abaqus for modeling this scenario. Figure 3 Data acquisition point and Boundary condition Location SIMULIA India Regional Users Meeting 11 Page 3 of 12
The PSD data used in the simulation is as shown in the Figure 4. Figure 4 PSD input for analysis in G2/Hz The node at PSD application point was connected with chassis cross member thru rigid elements and fixed in all degrees of freedom as shown in Figure 3. 3.2 Random response analysis Existing Bracket Random Vibration Response analysis was performed using acceleration spectrum density curve. Response was obtained up to 130 Hz (First mode of Bracket was 13.59 Hz). Equivalent RMS Stress was used for the fatigue life calculation. Structural damping ratio of 2% has been considered for the analysis. The first mode for the natural frequency extraction is shown in Figure 5. We can observe from the Figure 5 that the bracket is bending in X-directions about Y-axis. Figure 6 shows the Response of bracket at node number 33939 for PSD excitation. It can be observed from the Figure 6 that the bracket response is high at first natural frequency i.e. 13.59 Hz. In Abaqus/VIEWER we have a limitation of getting only component stresses for the PSD stresses. A python script was used to generate the equivalent stresses from the component stresses. The python script used for these calculations can be referred in the Appendix SIMULIA India Regional Users Meeting 11 Page 4 of 12
Figure 5 First natural frequency of assembly Figure 6 Equivalent Stress PSD distribution against frequency SIMULIA India Regional Users Meeting 11 Page 5 of 12
Figure 7 PSD and RMS Stresses Figure 7 shows the distribution of 1σ stress against frequency. PSD Stresses (OR any response) is taken as a qualitative measure of response due to PSD base excitation. However Equivalent RMS Stresses (1 stress) are used for Fatigue Cycle evaluation corresponding to the PSD excitation. Square root of area under the PSD Stress (MPa 2 /Hz) curve gives the RMS Stress (MPa). As the area under the PSD stress curve increases the RMS value also increases, as can be observed from the PSD curve Figure 7. When the PSD Stress response is zero or negligible, the RMS value becomes constant as it does not add up to the area. 1 stress plot for the bracket can be seen in the Figure 8. Figure 8 1σ Stress Plot of the bracket SIMULIA India Regional Users Meeting 11 Page 6 of 12
3.3 Fatigue Life Calculation Existing Bracket Equivalent RMS Stress is used for the fatigue life calculation. By using Gaussian distribution, 1σ values occur 68.3% of the time, 2σ values occur 27.1% of the time in addition to the 1σ time and 3σ values occur 4.33% of the time in addition to the 1σ and 2σ time. It has been found in various literatures and forums that basically random broadband signal with linear model (Irrespective of distribution) is assumed to have a Gaussian nature of stresses. Nonlinear model can be a Non-Gaussian phenomenon. Fatigue Life is determined from the following Basquin's relation: Where, N B ) ( e N = Number of cycles. B = Constant specific for each curve. σ e = Alternating Stress. m m = Slope of S-N curve. Weld imperfection effects has been considered in the base material SN curve (fatigue strength curve) according to International institute of welding, therefore the endurance limit has been reduced to 83.25 MPa. Random Vibration Analysis on the Auxiliary Heater brackets for the given acceleration spectrum density suggests that the bracket experience a very high 1σ stress (1082.5 MPa), which is much higher than the endurance limit of material (83.25 MPa), this suggest that bracket will not endure infinite life in 1σ level of confidence. Figure 9 shows the SN curve used for fatigue cycle calculations. Figure 9 SN curve SIMULIA India Regional Users Meeting 11 Page 7 of 12
3.4 Modified Concept Figure 10 shows the modified concept to achieve the desired life of the bracket. Figure 10: Modified Bracket 3.5 Random response analysis-modified Bracket The first natural frequency of the bracket was improved by adding the rear stiffener as shown in Figure 11. The first mode of Bracket is 26.5 Hz. Structural damping ratio of 2% had been considered for the analysis. Figure 12 shows the Response of bracket at node number 26278 for PSD excitation. It can be observed from Figure 12 the bracket response is high at first natural frequency i.e. 26.5 Hz. Figure 13 shows the distribution of 1σ stress against frequency. SIMULIA India Regional Users Meeting 11 Page 8 of 12
Figure 11 First natural frequency of assembly Figure 12 Equivalent Stress PSD distribution against frequency SIMULIA India Regional Users Meeting 11 Page 9 of 12
Figure 13 PSD and RMS Stresses 1 stress plot for the bracket can be seen in the Figure 14. Figure 14 1σ Stress Plot of the bracket SIMULIA India Regional Users Meeting 11 Page 10 of 12
3.6 Fatigue Life Calculation-Modified Bracket Random Vibration Analysis on the Auxiliary Heater brackets for the given acceleration spectrum density suggests that 1σ stress induced in the bracket is 42.0 MPa, which is almost half of the endurance limit of material (83.25 MPa), this suggest that bracket will endure infinite life in 1σ and 2σ level of confidence. 4. Conclusion The original concept of the bracket was not able to sustain infinite life in the 1 level of confidence. A redesign of the Auxiliary Heater Bracket was suggested to achieve infinite fatigue life in 1 and 2 sigma level of confidence. Infinite life cycle in the FEA simulation was achieved for the modified bracket. Abaqus proved to be an efficient tool in modeling the random vibration environment. 5. References Following references were taken while execution of this project: 1. Abaqus Version 6.9 Documentation, Abaqus 6.9-1. 6. Acknowledgement We are grateful to our colleagues Dr. PK Roy, Mr. Sridharababu Inala and Mr. Sohel Ujjaini to helping us in executing this project and preparing this paper. SIMULIA India Regional Users Meeting 11 Page 11 of 12
7. Appendix Figure 15 Sample Python script for RMS stress calculation SIMULIA India Regional Users Meeting 11 Page 12 of 12