Modal Analysis of Structures Loaded With Fluid Using Virtual Fluid Mass Method S.Arun Kumar Manager Ashok Leyland Limited Chennai-600103 India Arunkumar.S2@ashokleyland.com S.Sivasankaran Sr.Manager Ashok Leyland Limited Chennai-600103 India Sivasankaran.S@ashokleyland.com E.Loganathan Div. manager Ashok Leyland Limited Chennai-600103 India Loganathan.e@ashokleyland.com Abbreviations: NSM Non-Structural Mass method, VFM Virtual Fluid Mass method, CAE Computer Aided Engineering, FE Finite Element, MAC Modal Assurance Criteria. Keywords: Modal Characteristics, Structure, Fluid, NSM, VFM, Test, Frequency, MAC Correlation Abstract: Modal characteristics of a structure are critical indicators of its vibration behavior and durability performance. Established methods exist for estimating modal characteristics at concept stage using CAE tools. These are well correlated with test results [1]. In automobiles, modal characteristics of structures carrying fluid are generally calculated by representing fluid as non-structural mass (NSM) on the wetted faces of the structures. This modelling method does not account for the hydro-dynamic fluid behavior due to inertial forces of the surrounding fluid. Virtual fluid mass (VFM) modelling offers an efficient method to include hydrodynamic behavior, by accounting additional fluid forces acting on the structural surfaces in contact with the fluid. In this paper oil sump of an engine used in commercial vehicle is considered for the modal analysis. Modal frequencies and modal assurance criteria obtained in CAE by modelling oil as non-structural mass and virtual fluid mass is compared with the experimental modal analysis results. For the FE analysis, the mesh is created in Altair HyperMesh and modal analysis is performed using Altair Optistruct version 13. Measurement locations for experimental modal testing are arrived based on modal analysis using FE. Level of test result correlation with CAE results obtained using these two fluid modelling methods is assessed. It is observed that virtual fluid mass has better correlation with experimental results compared to NSM method. Introduction: Power train is the major source of noise and vibration in commercial vehicles and has significant contribution on the pass-by noise as well as in-cab noise levels. Oil sump is one of the major contributors for radiated noise from power train. This radiated noise depends on the natural frequencies and corresponding mode shapes of the oil sump. Oil sump is filled with oil and accounting its effect on dynamic behavior is crucial in designing oil sump for better reliability and noise and vibration performance. To capture the dynamic behavior it is required to model the distribution of fluid mass accurately. If fluid mass is modeled as NSM the mass of fluid gets distributed over the surface of the oilsump which is not a true assumption. VFM method allows a better method of modeling the mass distribution. FE modal analysis results of oil sump of a commercial vehicle engine using NSM and VFM methods are compared with experimental modal analysis results in terms of frequency and modal assurance criteria (MAC). 1
Process Methodology: CAE Modal analysis with NSM method Oil sump CAD model in catia format imported into Altair HyperMesh and finite element model is created (Refer figure 2 for FE model of oil sump). Figure 1: FE Model of Oil Sump A fixed boundary condition is applied to the holes connecting the oilsump with the crankcase. Virtual CAE analysis and experimental modal analysis is carried out without oil. Good correlation between test and CAE is ensured to validate the FE model and methodology used for oil sump structure without oil. The oil mass corresponding to volume of oil inside the sump when the vehicle is static and the engine turned off and oil and components are in room temperature is considered for the study. The total mass of the oil is represented as non-structural mass [NSM] in the PSHELL property card (refer Figure 2) for the surfaces wetted with oil. Figure 2: PSHELL property card in HyperMesh Bolt holes used for connecting oil sump with cylinder block is constrained in all degrees of freedom corresponding to vehicle condition. Optimum number of accelerometer locations for experimental modal test is arrived at so that all major mode shapes can be captured. Figure 3: Reduced wireframe geometry (19 points) from FE model, same locations are used for fixing accelerometers in test Experimental modal testing NSM method Based on the 19 optimum points for capturing mode shapes from FE model (refer Figure 3), accelerometer are fixed as shown in Figure 4 for experimental modal test. Structure is excited with impact hammer and FRF is extracted to arrive at the modal frequencies and mode shapes [2]. 2
Figure 4: Experimental setup with accelerometer locations Results & Discussion NSM method Experimental modal results and CAE results are compared in terms of modal frequencies and mode shapes. With NSM method, test-cae modal model correlation [3] is below the required correlation targets. i.e percentage difference in modal frequency <10% and mode shape correlation (MAC criteria) >70%. TABLE I MODAL FREQUENCIES, MAC COMPARISON BETWEEN CAE-NSM METHOD & TEST Mode CAE - NSM Method Test Frequency Difference (%) MAC (%) 1 88.2 63.4 39.1 77% 2 99.5 100.2 0.7 <50% 3 219.5 132 66.3 <40% 4 224.7 168.2 33.6 <40% 5 245.5 259.2 5.3 <40% 6 255.8 301.8 15.2 <40% 3
CAE Modal Analysis with VFM Method: Virtual Fluid Mass simulates the mass effect of an incompressible inviscid fluid in contact with a structure. It does not represent the actual mass of the fluid in terms of geometry and hence there is no mesh needed for the fluid domain. The Virtual Fluid Mass represents the full coupling between acceleration and pressure at the fluid-structure interface and this fluid is represented by a coupled mass matrix attached directly to the structural points, a dense mass matrix is generated among damp grids at the fluid-structure interface. Sloshing effects/acoustic effects and gravity effects is not accounted in the VFM method. Fluid is represented using MFLUID definition in the bulk data entry [4]. PARAM, VMOPT, 2 is used for the analysis. In this case the virtual mass is added after the eigen solution, and the computational time is not increased significantly. When PARAM, VMOPT, 2 is used, the structural dry modes are computed without adding virtual mass in the computation. Then the modes are modified based on the virtual mass matrix. We must request more modes than desired for better accuracy. A general rule-of-thumb is to double the frequency range of interest. Results & Discussion VFM Method With VFM method, Test-CAE modal model correlation is meeting the targets and shown in below table II. Figure 5 shows the bar chart comparison between CAE-NSM, CAE-VFM and test results. Mode shape comparison between CAE with VFM method and test are shown in Figure 6 & 7 for first and second mode respectively. TABLE II MODAL FREQUENCIES, MAC COMPARISON BETWEEN CAE-VFM METHOD & TEST Mode CAE VFM Method Test Frequency Difference (%) MAC (%) 1 68.5 63.4 8.0 87% 2 102.3 100.2 2.1 72% 3 134.2 132.0 1.7 68% 4 160.1 168.2 4.8 72% 5 244.4 259.2 5.7 88% 6 290.6 301.8 3.7 70% 4
Figure 5: Modal Frequencies Bar Chart Comparison 5
Figure 6: Mode shape comparison between CAE and Test First Mode Figure 7: Mode shape comparison between CAE and Test Second Mode Benefits Summary Level of test result correlation with CAE results obtained using the two fluid modeling methods NSM and VFM are assessed. It is observed that virtual fluid mass has better correlation with experimental results compared to NSM method. With the VFM feature in Optistruct, it is possible to simulate the dynamic characteristics of fluid loaded structure close to reality. With the confidence on correlation level achieved with VFM, various proposed design configurations of oil sump for new commercial vehicle program is evaluated virtually using optistruct. Challenges Consideration of oil in VFM method generates fully populated matrix and hence the computation time is significantly higher compared to NSM method. Maximum number of shell elements which can be wetted to define fluid interface is limited to 46340 (that too with PARAM, VMOPT, 2 ). This necessitates manual mesh modification to create a mesh which conforms to element count limit, mesh size/quality criteria and at the same time reasonably represent the geometrical and displacement field variations. Solving time increases tremendously when the number of wetted shell elements in the model is increased. 6
Future Plans Currently, the analysis and test is carried out for vehicle static, engine turned off condition with oil sump structure and oil at atmospheric temperature. In vehicle operating condition part of the oil will be circulating around reducing the level of oil left in the sump. The oil will be also hot during this condition which changes its density. To understand the sensitivity of such changes in the modal characteristics, DOE analysis using Altair Hyper study has to be carried out. Conclusions Oil sump behavior in vehicle static condition is simulated with NSM and VFM method and it is observed that with VFM the modal frequencies and mode shapes correlates well with test results. Validated methodology for evaluating the dynamic behavior of oil sump structures loaded with fluid using VFM arrived out using Altair HyperWorks software. The procedure can be extended for evaluating the dynamic behavior of other automotive structures loaded with fluid such as fuel tank, de-aerated tank, etc. ACKNOWLEDGEMENTS The authors would like to thank Mr.P.T.Haridas, AGM-CAE & IVT and Mr.R.Karthik for their efforts in reviewing the manuscript and continuous encouragement and motivation during the execution of this project. Also would like to thank Mr.Ganesh Prasad, Engine R&D and Mr.Paulse Aditya, NVH attributes engineering for their support in design and testing. REFERENCES [1] A Frequency Domain Correlation Technique for Model Correlation and Updating by R. Pascual, J. C. Golinval, M. Razeto [2] Modal Testing, Theory, Practice, and Application by D.J.Ewins [3] CAE Model Correlation & Design Optimization of a Laminated Steel Oil Pan by means of Acceleration and Strain Measurement on a Fired Engine by Rıfat K. Yanarocak and, Abdulkadir Çekiç [4] Altair reference documentation. [5] Practical finite element analysis by Nitin S. Gokhale, Sanjay S. Despande, Sanjeeev V. Bedekar, Dr. Anand N. Thite 7