ACOUSTIC SIMULATION OF AN AUTOMOTIVE POWER STEERING COLUMN SYSTEM USING THE NOVEL H- MATRIX BEM SOLVER

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1 The 21 st International Congress on Sound and Vibration July, 2014, Beijing/China ACOUSTIC SIMULATION OF AN AUTOMOTIVE POWER STEERING COLUMN SYSTEM USING THE NOVEL H- MATRIX BEM SOLVER Martin Meyer, Jan van Gemmeren Department of Advanced Research and Development, ThyssenKrupp Presta, Essanestrasse 10, FL-9492 Eschen, Liechtenstein Mark Boyle, Koen De Langhe LMS, A Siemens Business, Leuven, Belgium mark.boyle@lmsintl.com This study investigates the application of numerical acoustic simulation tools to optimize the sound of an automotive power steering column at the product design. While numerical acoustics is widely used in car interior design it is also applicable to mechanical component design. Acoustic optimization in the automotive industry is often conducted late in the late development process and therefore expensive. To bring costs down and improve the acoustic behavior of electric systems, acoustic simulation can be used. The subject of this study is a steering column with motorised adjustment for driver comfort and access. These movements are the source of noise emissions in close proximity to the driver so optimisation of noise control early in the product process is essential. The Finite Element Method (FEM) is used for the dynamic structural model of the steering column which is then used as boundary conditions for Boundary Element Model (BEM) analysis of the acoustic radiation. Traditionally BEM has had a practical upper frequency limit of about due to computation times. In this study a new Hierarchical Matrix BEM solver is used which is computationally much more efficient than standard BEM allowing simulation at higher frequencies. The paper demonstrates the added value of the novel Hierarchical-Matrix BEM solver to provide accurate simulations faster than standard BEM solvers for such industrial applications. 1. Introduction 1.1 MOTIVATION The priority of vehicle acoustics has risen in relevance corresponding to the development trends in lightweight and electro mobility. The acoustic emissions from electrically powered systems are of growing interest due to their replacement of the combustion engine and hydraulic power systems. Comfort within the passenger compartment and in particular electrical power adjustment systems such as the power steering column have to be considered carefully by the development engineers. Beside the core functions like the transmission of steering torque and the absorption of crash forces the steering column can hold a function for a variable adjustment of the steering wheel posi- ICSV21, Beijing, China, July

2 tion in vertical (rake/tilt) and horizontal (telescope) direction. In power steering columns, as shown in Fig. 1, these functions are provided by electric motors and the transmission of the rotation into the adjustment displacement through special gear set. New comfort features are provided for easyentry and memory function, where the steering column operates automatically during while the driver is already sitting inside the vehicle. It is important to understand the acoustic response from these mechanisms. Figure 1. ThyssenKrupp Presta, power steering column. In this study the acoustic emissions spectra are dominated by the contributions from the electric motors and the gear set. This can easily be recognized from the discrete harmonic orders of the motor rotational frequency which are clearly visible in the airborne sound spectra of any adjustment cycle as shown in Fig. 2. Figure 2. Campbell plot power steering column of adjustment. In the automotive industry, there is an increasing demand for reduced development period and prototype testing. Thus acoustic analysis occurs later in the development process with the possible consequences of increased change costs and a constrained degree of freedom for modifications. Using LMS Virtual.Lab numerical modelling software it is possible to integrate the acoustic engineering into an earlier stage of the product development process. 1.2 Capability of Numerical Tools The use of virtual development tools gives the opportunity to test different operational parameters by the application of different boundary conditions in the automotive engineering process. ICSV21, Beijing, China, July

3 The finite element method (FEM) is widely used in many engineering fields such as fluid dynamic or structural dynamic computation. Numerical acoustic simulations are frequently used for vehicle interior acoustics while applications of acoustic simulation for electro-mechanical systems like the power steering column are less common. Numerical acoustics allows the development of smart and highly integrated functional solutions and thus the reduction of cost. This is supported by the requirement of a complete reproduction of the system for an effective acoustic simulation. The analysis of the subcomponents and the complete system predicts potential on acoustic problems at an earlier stage in the design process. This allows possible solutions to be tested, making it easier to find efficient solutions. Subsequent costs and mass-intensive secondary countermeasures can progressively be avoided. Beside the design, the experimental testing can explicitly be improved with the aid of acoustic simulation. Virtual testing can replace experimental testing in parts, and also the process of experimental testing can be optimized with the integration of preceding virtual steps. Thus the efficiency of Noise Vibration and Harshness (NVH) testing procedures can be increased by the determination of feasible measurement positions from virtual simulation (PreTest). To reach this point the entire workflow of an electric power steering column acoustic simulation must be controllable. In this regard the correct setup of the acoustic radiation model represents the greatest challenge beside the formulation of structural parameter and the model interface and boundary conditions. 2. Simulating Acoustic Radiation of Power Steering Column To determine the acoustic properties of a power steering column virtually, two different modelling techniques are needed; namely a FEM dynamic structural model, shown in Fig. 3 a) and a BEM (Boundary Element Method) acoustics radiation model shown in Fig. 3 b). The first step in the modelling process is to generate a FEM structural mesh. In generating the FEM structural dynamical analysis it is essential to have accurate information on the material models, contacts, joints and constraints. In order to have confidence in the FEM structural dynamic analysis validation can be achieved by comparing structural dynamic test data and simulated data. The LMS Virtual.Lab Correlation suite can be used to easily compare the Modal Assurance Criterion (MAC), which is a technique for comparing mode shapes. It determines quantitatively the orthogonality of the measured and computed spectra of modes. Using the test data the FEM structural dynamical analysis can be updated to achieve a greater level of accuracy. The next step is to simulate operating conditions of the power steering column motor gear set system along with the alternating forces and torques from magnetic field computation of the motor. From this FEM structural dynamical analysis the degrees of freedom (displacements) can be calculated on the surface mesh using a harmonic response analysis. ICSV21, Beijing, China, July

4 Figure 3. Data Transfer; a) FEA Structural Mesh, b) BEM Acoustic Wrapper mesh. The next step is to create the acoustic radiation model. For this type of noise simulation problem the Boundary Element Method is the preferred technique for acoustic modelling. The benefit of BEM has been that modelling requires only a model (mesh) of the boundary of the acoustic domain which is comprised of the radiating surface and the scattering surface. By using the wrapper mesher available LMS Virtual.Lab Acoustics it is easy to create an acoustic boundary mesh based on the FE Structural dynamic mesh. The acoustic boundary mesh (18619 nodes) is well within the six elements per wavelength rule which is used for creating the acoustic mesh of the minimum required density 1. Once the acoustic boundary mesh is created the calculated degrees of freedom data on the surface of the FE Structural dynamic can be mapped to the acoustic boundary mesh, process shown in Fig. 3. This mapped data is the boundary conditions for the BEM acoustics response analysis. A limitation of BEM models has been that the simulation time increases exponentially with model size and frequency. Recently this constraint has been reduced through the introduction of Fast Multipole Expansion techniques 2,3. Another more recent technique is the Hierarchical Matrix method, which is an efficient framework for large-scale fully populated matrices 4, 5, typically seen in BEM problems 6. This novel solver technology available in LMS Virtual.Lab Acoustics is widely applicable to the study of medium to large acoustic radiation and scattering problems. The solver is able to efficiently solve such problems by automatically using recursive matrix storage and compression architecture based on low rank approximation 4-6. Thus H-Matrix BEM can easily solve models in the range of 10k to 200k nodes at frequencies of up to 10 khz with reduced memory requirements and with computation times that can be 100 times faster than standard BEM 7. With a direct solver approach H-Matrix BEM can compute multi-load cases efficiently and scales well with multiprocessor and multi-threading capabilities. ICSV21, Beijing, China, July

5 Figure 4. Computation times with different BEM methods. For the steering column model using conventional IBEM, the computation time is 17 minutes per frequency step but with the Hierarchical Matrix BEM solver the computation time can be reduced to approximately 1 minute. A typical comparison of the three different BEM techniques considered in this study 7 is illustrated in Fig Results and Discussion 3.1 Simulation v Measurement The acoustic field response is illustrated in Fig. 5 a). The acoustic power predictions from the BEM model are compared with laboratory measurement results. The good correlation between measurement and simulation can be found across the frequency range shown in Fig. 5b). Simulation Measurement Figure 5. a)acoustic field response, b) Comparison simulation measurement. 3.2 Development process An initial technical feasibility of the application of acoustic simulation is important first step in the development. The second step is the integration of the new method into the development process whereas mainly three phases of the product development process (PDP) are concerned: 1) Acquisition; 2) Testing and Design development; 3) Design release. 1) Risk evaluation is essential element of the acquisition phase. This can be achieved through an improved coordination of customer requirements with initial concept designs with the application of acoustic simulation. Also concepts can be specified to ICSV21, Beijing, China, July

6 meet these requirements at an early stage of a project. The interface between supplier and customer responsibilities can be defined at the acquisition phase. 2) Acoustic simulation is a powerful tool for supporting the testing and design development phase. Investigations can be carried out with the LMS Virtual.Lab suite and thus the costs of prototype testing are reduced. Savings are also achieved through shorter development becomes shorter times. Product test optimization is provided with the PreTest method. It is also possible simulate and test different design parameters and even automate optimization. 3) The number of physical prototypes for design release can be reduced. Further development of the design interface and acoustic simulation could facilitate virtual design release in future. This can be accomplished with post processed experimental verification with reduced effort and cost. The process of the acoustic development works according to the V-model shown in Figure 6. This illustrates the effect of frontloading, where acoustic development at an early stage contributes to earlier completion of the Noise Vibration and Harshness (NVH) process. Figure 6. ThyssenKrupp Presta (TKP) V-process NVH development. The first input of acoustic simulation, using LMS Virtual.Lab occurs at the functional design level where different design concepts are investigated. This process is then carried through the system design level followed by the component level and finishes in the opposite direction with vehicle testing. The design stage is strictly virtual allowing for collaboration between the system engineering supplier and the sub-supplier. 3.3 Interface to customer and supplier The investigation of the acoustic properties of steering columns as an independent unit is only useful in the first phase of the design process. The boundary conditions for a specific vehicle are required for final design validation. It is necessary to define this interface technically so than the steering column can be tested in its working environment and it requires collaboration between first and second tier suppliers and OEMs. Sharing knowledge requires all parties to have a joint responsibility for using such innovative technology. Electrical drives from a first tier supplier are sub-components of power steering columns. These interfaces have to be defined to allow the sub-component geometry and loading forces of the motors to the steering column model. This can be achieved through the use of encrypted superelements and as such they are a black box for users. These super-elements contain all the information necessary to the steering column. The OEM can similarly use the steering column model with the vehicle interior model and compute the sound pressure at any point inside the vehicle. This interface can then provide the ICSV21, Beijing, China, July

7 boundary conditions for the steering column as forces or sound pressures produced by the component level simulation. These interfaces are essential for the accuracy of the results, thus it requires all development partners to share the responsibilities for these interfaces. 4. Conclusions Acoustic Simulation facilitates design development at an earlier stage in the product design process. Design concepts can be simulated and tested virtually which reduces the time and expense of conventional prototype testing. It is also possible to exchange component and product data in the form of super-elements or as set of boundary conditions which avoids the need to disclose the complete component design. Special attention is necessary for correct meshing and the definition of the interfaces. In this study, the convergence in power transmission was used to assess the mesh quality and to avoid irregular frequencies. This produced a very fine mesh and thus to large calculation time when using conventional BEM. However, the computation time can be reduced dramatically by using the LMS Virtual.Lab Acoustics H-Matrix method solvers. The interface has an important role in providing both accurate design simulation and design validation. In the future it will be important to define these interfaces with the development partners and to discuss the responsibilities. REFERENCES Marburg S., Six boundary elements per wavelength. Is that enough?, J Comput Acoust 11, 25 51, (2002). Fischer, M., The Fast Multipole Boundary Element Method and its Application to Structure- Acoustic Field Interaction. PhD thesis, Universität Stuttgart, Germany, (2004). Marburg, S.; Wu, T. W.: Treating the Phenomenon of Irregular Frequencies. S. Marburg (Hg.); B. Nolte (Hg.) Computational acoustics of noise propagation in fluids. Finite and boundary element methods. Chap. 15, Springer, Berlin Heidelberg, pp , (2008). W. Hackbusch. A sparse matrix arithmetic based on H-matrices. Part I: introduction to H-matrices. Computing, 62(2):89 108, (1999). W. Hackbusch and B. Khoromskij. A sparse H-matrix arithmetic. Part II: applications to multidimensional problems. Computing, 64(1):21 47, (2000). M. Bebendorf. Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems, volume 63 of Lecture Notes in Computational Science and Engineering (LNCSE). Springer- Verlag, ISBN , (2008). LMS Numerical Acoustics Theoretical Manual (2014) ICSV21, Beijing, China, July