APPLICATION ON AN UPDATED FINITE ELEMENT MODEL OF AN ENGINE IN THE AUTOMOTIVE INDUSTRY
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1 SISOM 2011 and Session of the Commission of Acoustics, Bucharest May APPLICATION ON AN UPDATED FINITE ELEMENT MODEL OF AN ENGINE IN THE AUTOMOTIVE INDUSTRY Gabriel-Petru ANTON, Mihai PAVAL, Fabien SOREL Renault Technologie Roumanie DIM / DAPEM NVH, Barba Center Sos. Pipera-Tunari, Nr. 1/VI, Voluntari, Jud. Ilfov, , Romania. s : gabriel-petru.anton@renault.com; mihai.paval@renault.com; fabien.sorel@renault.com Nowadays, due to the market concurrence in the automotive field and the high customers standards, the acoustic comfort have become the one of the most important engineering require. This paper deals with the NVH test-calculation correlation, the finite element (FE) model updating of an engine and the vibration level (low and medium frequency range) on the engine/body interface points. The main objective for this approach is to obtain the absolutes values of the vibration level (low and medium frequency range) on the interface points using an updated FE model. Experimental and theoretical analysis used for this work, have allowed us to understand the real vibratory behavior and to obtain a new FE model more closed by reality. The final updating, the test-calculation correlation results and also the operational simulation and measurements level are presented within this paper. Key words: finite element, automotive engine, NVH, modal analysis, correlation, updating, optimization. 1. INTRODUCTION The vibrations transmitted to the body car by powertrain remain the main source for low and middle frequencies. NVH numerical calculations are perform during the first steps of the development process of the powertrain. The purpose of the paper is mainly to present a general approach to validate an engine in low and medium frequency, from NVH point of view, using like example the results of calculation of an engine bracket. This process is described in the layout below (Figure 1), starting with the design conception, then the performing of the finit elements model, updating of the virtual model in according to the real model (EMA) and the calculation of the vibratory levels. Sometimes, when the customer specifications are not fulfilled, we can apply an optimization process up to reach the maximum topological potential of the part and/or the desired response. CAD design FE model UPDATING EMA VIBRATORY CALCULATION OPTIMISATION RESU LTS SPECIFICATIONS FULFILLED NOK OK Figure 1: NVH validating Flow Chart
2 69 Application on an updated finite element model of an engine in the automotive industry 2. EXPERIMENTAL MODAL ANALYSIS Experimental modal analysis is the process of determining the modal parameters (frequencies, damping factors, modal vectors and modal scaling) of a linear, time invariant system by way of an experimental approach. The modal parameters may be determined by analytical means, such as finite element analysis, and one of the common reasons for experimental modal analysis is the verification/correction of the results of the analytical approach (model updating). In order to have high quality measurements and confident results from Experimental Modal Analysis (EMA) we follow the steps presented in the Figure 2. Figure 2: Steps in performing EMA The main reason for EMA in our case is to offer experimental results for the FE model updating process. In order to perform specific measurements for EMA we are using different types of accelerometers tri-axis with high sensitivity (100 mv/g) and low weight (5 g), impact hammers with different sizes and sensitivities appropriate for various types of structures and shakers for assemblies and subassemblies. The approach for EMA performed on engines starts with measurements on single parts and after that, we test the engine base assembly. Before starting the measurements, we verify the boundary conditions of the test support (tested structure and suspensions used to achieve the free-free conditions, rigid body modes determination) and also the linearity of the structure by specific measurements. In the table 1 are presented the extracted modal parameters (frequencies, damping factors, modal vectors and modal scaling) obtained on the engine base assembly, which will be used for the updating process presented further in the paper. Table 1 Extracted modal parameters of the engine base assembly Mode Modal Frequency Modal Damping Ratio No. (Hz) (%) Deformations Bending around Z Torsion Deformation of the Cylinder Head Cover Bending around X Deformation of the Oil Pan The extracted modal base is validated by three methods: AutoMAC Matrix, statistical analysis for the Curve Fitting and visual evaluation (Figure 3).
3 Gabriel-Petru ANTON, Mihai PAVAL, Fabien SOREL 70 AutoMAC Matrix Correlation Synthesized/Measured FRF s Visual evaluation dof # Frequency Cumulative % 120% 100% 80% 60% 40% 20% 0% More Correlation % Figure 3: Modal validation methods Taking into account the validation results obtained, low values for the off-diagonal elements of the AutoMAC matrix, high values for the correlation Synthesized/Measured a/f transfer functions and physically realizable modal shapes we can conclude that the extracted modal base is valid. After the measurements on the engine base assembly the EMA process can continue by testing the peripheral elements adding gradually the exhaust system, the accessories (alternator, air conditioning compressor and steering pump) and gearbox. In further, using the results obtained by EMA, we pass to the updating of the finit elements model of the powertrain. 3. UPDATING ANALYSIS In order to perform the model updating, we use a dedicated software having an iterative model updating method based on a sensitivity formulation. where: R = R e R a ; { R} = [ S]{ ΔP} Δ (1) { Δ } { } { } { e } reference in the updating analysis and { R } responses; R is a vector of the experimental data considered like is a vector of the predicted system { Δ P} = { } { }; { P } is a vector of the updated parameter values and { P } P u P o u vector containing the initial parameter values; [S] is the sensitivity matrix given by formula: δri [ S] = Sij = (2) δpj The updated values of parameters P are obtained from (1) and (2): { P} { P } + [ G] ({ R } { R }) o e a a = (3) where: [G] is the gain matrix computed using a Bayesian estimation theory. In according to the theoretical aspects presented above we intend to decrease the frequency difference between the two models, experimental and FE, for each single part of the assembly. For this, we use the CAE special software, setting the responses in frequency and the parameters to be changed within the updating analysis. Finally, after the updating of the each single part of the assembly, we built a new base structure like FE model and we animate the results with successive iterations and correlations. For example, some final results for the base structure are presented below in the Table 2. o is a
4 71 Application on an updated finite element model of an engine in the automotive industry Table 2 Correlation test-calculation of the base structure, at the end of the updating analysis FEA Hz EMA Hz Diff. [%] MAC [%] A synthesis in MAC and Diff (difference in frequency) of the updating approach (before and after updating) on the base structure of the engine is presented in the Figure 4. MAC [%] Comparison of the engine assembly before and after the updating Diff [%] MAC before MAC after Diff before Diff after 10 0 horizontal bending torsion vertical bending Modal Shape Figure 4: Updating synthesis MODAL ANALYSIS AND VIBRATORY CALCULATION IN LOW / MEDIUM FREQUENCY Using the FE model updated we have realized a modal analysis and a vibratory calculation in low and medium frequency on the engine suspensions. The modal analysis permit us to visualize the global and local modal shapes of the engine. In Figure 5 below see three global modal shapes (horizontal bending, vertical bending and torsion). PWT Horizontal Bending PWT Vertical Bending PWT Torsion Figure 5 : Global modal shapes of PWT In order to obtain information (natural frequency, damping, stiffness and mass behavior) about the structure of the engine, it is necessary to have a driving point on the different parts. For example, the Figure 6 shows a driving point curve, in 3 directions XYZ, on the one of the three engine suspensions (on the timing side). Vertical line indicates the 1 st natural frequency of the part.
5 Gabriel-Petru ANTON, Mihai PAVAL, Fabien SOREL 72 Figure 6 : Driving point on the engine mounting bracket In order to calculate the representative vibratory levels, it is taken into account the efforts from the chamber combustion, liner cylinder and crankshaft bearings. These efforts are calculated using the cylinder pressure at the different engine speed. The vibratory calculation give us the information concerning the amplitude of the vibrations on the 3 engine suspensions, taking into account two ranges of frequency: low frequency Hz named booming noise and medium frequency divided in 250 Hz octave (timing noise) and 500 Hz octave (whirring noise). These values of amplitudes have to fulfilled the customer specifications. The main harmonic for 4 stroke engine with 4 cylinders is H2 (second order). An exemple of a tracking H2 on the engine mounting bracket is given in the Figure 7. Figure 7 Tracking H2 on the engine mounting bracket Sonogram and Peak Hold are used for medium frequency range, in order to identify the contribution of the harmonics; an example on the engine mounting bracket is given in the Figure 8. The red color indicates the highest level of vibration on the part considered on the engine. The vertical line show the first mode of the engine mounting bracket at the different values of the engine speed. Figure 8 Sonagram and Peak Hold
6 73 Application on an updated finite element model of an engine in the automotive industry At the end of our vibratory calculation, in according with the customer specifications, we consider that it is necessary to increase the 1 st natural frequency of the engine mounting bracket. So, the next step is to evaluate the geometric potential of the part using a topological optimization. 5. TOPOLOGICAL OPTIMIZATION OF THE ENGINE BRACKET 5.1 Theoretical considerations At the base of the topological optimization is the density method, also known as the SIMP method in the research community. With the density method, the material density of each element is directly used as the design variable, and varies continuously between 0 and 1; these represent the state of void and solid, respectively. The stiffness of the material is assumed to be linearly dependent on the density. The iterative procedure is based on the local approximation method to solve the optimization problem. This method determines the solution of the optimization problem using the following steps: - Analysis of the physical problem using finite elements; - Convergence test, whether or not the convergence is achieved; - Design sensitivity analysis; - Solution of an approximate optimization problem formulated using the sensitivity information; - Back to the first step (analysis). 5.2 Description of the part to be optimized Concerning the interface engine / body, two parts are taken into account like example in this paper: the engine mounting bracket and the engine bracket (see Figure 9). The optimization approach within this paper refers only the engine bracket which impact the behavior of the engine mounting bracket. The initial part has differents ribs on the interior surface, contributing at the stiffness of the part. The CAO part is meshed with tetra elements and it has a number of elements by The connections on the engine are performed by rigid elements [2]. Engine mounting bracket Figure 9 FE Model Engine bracket 5.3 Definition of the optimization problem In this case we use a topological optimization which is a mathematical technique that produces an optimized shape and material distribution for a structure within a given package space. By discretizing the domain into a finite element mesh, a dedicated software calculates material properties for each element. The mathematical algorithm alters the material distribution to optimize the user-defined objective under given constraints.
7 Gabriel-Petru ANTON, Mihai PAVAL, Fabien SOREL 74 Objective Constraints Responses - decreasing of mass of the engine mounting bracket - increasing of the natural frequency with 15% Dynamic constraints: - 1st natural frequency to be minimum 440 Hz and max 460 Hz; - 2nd natural frequency to be minimum 600 and max 1000 Hz; Static constraints: Von Misses Stress: 120 MPa. - 1 st natural frequency : 414 Hz - 2 nd natural frequency : 800 Hz - mass: kg (-15%) Performing of part to be optimized It is performed the optimization calculation starting from initial part and hasing a full volum, without ribs and keeping the connection holes. We mention the 1 st frequency of the full volum use to optimization: 449 Hz > 440 Hz. So, the main condition to start the optimization calculation is fulfiled. 5.4 Results of the optimization process The initial mass is kg and the first mode of the initial part is 396 Hz. Part full volume Part after optimization study Final part after optimization 449 Hz / kg 414 Hz 401 Hz / kg The final frequency obtained after optimization is 401Hz, under of the target (440Hz). However, we have reduced 15% from the initial mass, eliminating some material and increased the frequency of 5Hz. In this situation the objective in frequency is not still reached, showing a low topological potential of the part and imposing a new design conception. 6. CONCLUSIONS The methodology presented within this paper permit to perform the predictive calculations due to the updating of the finit elements model and the optimization phase, providing a good acoustic prestation / price ratio and avoiding at maximum the performing of the prototype and the measurements. The approach applied on the engine mounting bracket is used to calculate all the elements of the powertrain. In this way, the customer specifications are fulfilled respecting the constraints of deadline and price of the project. REFERENCES 1. SCHWARZ, J., RICHARDSON, M., Experimental Modal Analysis, CSI Reliability Week, Orlando, USA, CRAVEUR, Jean-Charles, Modelisation par elements finis, Dunod, Paris, 2008, 3 e edition.
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