EngOpt 2008 - International Conference on Engineering Optimization Rio de Janeiro, Brazil, 01-05 June 2008. Optimization to Reduce Automobile Cabin Noise Harold Thomas, Dilip Mandal, and Narayanan Pagaldipti Altair Engineering, Inc., Irvine, California, USA, thomas@altair.com 1. Abstract It is very important for automobile manufacturers to design automobiles with low levels of powertrain and road noise in the passenger compartment. In general, the more luxurious the car is, there is lower the noise level in the passenger compartment. Noise is generated from the tires, engine, transmission, and exhaust system and transmitted through the body structure to the air in the passenger compartment. Coupled structure-fluid (air) frequency response analysis is used to determine the sound levels at the driver s and passenger s ears at different driving speeds and engine speeds. The passenger compartment noise can be reduced by correct sizing of structural components such as suspension bushings and dampers, motor mounts, exhaust system hangers, etc., as well as by applying sound absorbing materials to the metal structures of the automobile. In addition, the structural design itself can be modified to change vibration load paths to reduce the noise levels. These design decisions are usually made by trial and error. In this work we look at applying optimization design concepts to the reduction of the noise level in the passenger cabin. Topology Optimization as well as sizing and material optimization can be used to reduce the sound levels to specified levels at different frequencies. In addition, we present sub-structuring techniques to reduce the optimization run time. With these techniques, the nondesign portion of the structure does not have to be reanalyzed during the design iterations. The use of sub-structuring techniques is required because a single coupled structure-fluid frequency response analysis of a typical automobile finite element model containing over 10 million DOF can take many hours on a modern computer. 2. Keywords: Acoustic, Optimization, Automobile, Noise, NVH 3. Introduction In order to increase passenger comfort it is important to reduce the sound level in the passenger compartment of the automobile. This can be achieved by changing the structure of the automobile to modify vibration transmission paths, by changing the structure in order to move resonant frequencies and harmonics, by changing the damping characteristics of bushings and dampers in the suspension and drive train, and by adding damping materials or coatings to the structural components. While these physical modifications can be made and their effect on the cabin noised measured by test equipment, this trial and error approach is expensive and time consuming. 3.1 Finite Element Analysis and Optimization It is far more efficient to build a virtual model of the automobile using finite elements and then using finite element analysis to perform virtual testing. While a trial and error approach using the virtual model is less expensive and faster than trial and error on the real structure, the time can be reduced even further using optimization techniques. In addition, optimization provides a very good design, rather that a design that is just acceptable. In this work, the RADIOSS software from Altair Engineering [1] is used to perform the finite element analysis and optimization. 3.2 Scope of this Work In this work, the system equations required to determine the sound level in the passenger compartment are presented. This involves performing frequency response on a combined fluid-structure model of the automobile. In this case, the fluid is the air in the passenger compartment. In addition, optimization of structural components is performed in order to minimize sound levels in the fluid. Examples are given that show the benefit of applying optimization techniques on virtual finite element models in order to come up with superior designs. 4. Acoustic Analysis Acoustic analysis is performed to model sound propagation inside a structural cavity filled with air. In this work, both the structure and air are modeled with finite element meshes. These meshes can be separate and do not have to match on the boundary between the air and the structure. In fact, in real world meshes used by the automobile industry, the meshes do not match due to the level of detail of the structural meshes. It is not reasonable to spend the modeling time required to create a mesh of the air cavity with this level of detail. Therefore, the size of the finite elements in the air cavity can be 2-5 times larger than those used in the structural mesh. Because of the size of the sound wavelength, large elements can be used without any loss of accuracy. 4.1 Overview The interaction between the structure and the air domain happens at the interface between the structural and fluid meshes. The acoustic analysis can be done by either direct or modal frequency response analysis. The analysis computes the response of both the structural and fluid domains. The responses in the structural domain are the displacements and rotations at structural grid points. In the fluid domain, the responses are the pressures at the fluid grid points. The accelerations on the structural grids at the interface excite the pressure on the fluid domain and conversely, the pressures on the fluid grids at the interface excite the structural domain. Hence the problem is coupled and the motions of structural DOF and fluid DOF are solved simultaneously. The structure is loaded
by sinusoidal forces and/or enforced displacements, velocities, and accelerations at an excitation frequency Ω. Many types of damping (viscous, material, structural, and modal) are supported in the structural domain. In the fluid domain, the types of damping supported are material, fluid and modal. 4.2 Analysis of the Fluid The fluid analysis is based on inviscid flow with linear pressure-density relation as: 1 P + u& = 0 (1) ρ and the continuity equation would be: P + β. u = 0 (2) where P and u are the pressure of the fluid domain and displacement of the structural domain. β and ρ are the compressibility and the density of the fluid domain respectively. When the above equations are combined, the governing equation of the fluid domain becomes: P&& 1 2 P = 0 (3) β ρ 4.3 Coupled Analysis After finite element discretization, the assembly of equations of the fluid domain would be as follows: M pp & + BpP& + K pp Au& = S p (4) Where M p, B p, K p, and S p, are the mass matrix, damping matrix, stiffness matrix and source vector respectively of the fluid part. The gradient of pressure on the interface is going to be influenced by the acceleration of the structural grids. The A matrix represents the interface matrix and ü is the acceleration of the structural grids at the interface between the fluid and structure. The interface matrix is determined by the geometric relationship between the faces of the fluid elements on the surface of the fluid mesh and the structural grids on the wetted surface of the structural mesh. The structural equation can be also written as: T M su& + Bsu& + Ksu& + A P = Ss (5) where P is the pressure at the interface fluid grids. Therefore the combined fluid structure interface equation is: M T s 0 u&& Bs 0 u& K s A u Ss + + = A M p P && 0 Bp P & (6) 0 K p P S p The above equations are solved simultaneously for the unknowns in the structural and the fluid domains, either by direct frequency response or modal frequency response. For modal frequency response, eigenvalue analysis is performed separately for both the structural and fluid domains. 5. Basic Example The first example will be used to explain the modeling techniques and aspects of structural-acoustic analysis and optimization. A simplified version of an automobile is shown in Figure 1. Figure 1. Simplified Automobile
5.1 Basic Example Finite Element Model The automobile body is modeled by the six faces of the hexahedron. Each face is meshed with 2D triangular elements. The air cavity is meshed with 3D tetrahedral elements. There are 1362 triangular elements and 3941 tetrahedral elements. Young s modulus of 1000.0, Poisson s ratio of 0.33, and density of 7.96E-10 is used for the structural material. For the air, a Bulk Modulus of 1.2E-13 and a density of 3.4E05 are used. The structure is 630 units wide, 950 units tall, with base and top dimensions of 1900 and 1320 units respectively. Note that for this example the wetted surface of the structural mesh matches with the surface of the fluid mesh. A rigid element on the front face of the structure is used to apply the loading due to engine vibrations. The sound pressure level will be measured at fluid grid 18906, which represents the location of the driver s ear. The engine vibrations will cause the structural mesh to vibrate, which will in turn cause sound pressure levels in the air mesh. An example of the sound pressure field is shown in Figure 2. Figure 2. Sound Pressure Levels The analysis is performed using coupled fluid-structure modal frequency response with the engine loaded applied from 0.0 to 200.0 Hz. The modes up to 300 Hz for both the fluid and structure are used to build the modal space. In addition, the structural modal space is augmented by a residual flexibility vector generated by applying the dynamic engine load as a static load. The resulting static deformed shape is used to augment modal space after it has been orthonormalized with respect to the natural mode shapes. 5.2 Basic Example Optimization Problem In this example, the six design variables control the thickness of each side of the hexahedron. The initial thickness is 1.3 and the thicknesses can range from 0.1 to 3.0. The objective is to minimize the mass of the structure while keeping the magnitude of the sound level at the driver s ear below 5.0E-07. The initial design has a mass of 0.00661 and the maximum sound lever is at 12.4E-05 at 44 Hz. 5.3 Basic Example Optimization Results The design optimization converges in 14 iterations with the sound level at the driver s ear being reduced from a maximum of 12.4E-05 at 44 Hz to 4.8E-05 at 47 Hz. The percentage of the maximum constraint violation of the sound level at the driver s ear is shown in Figure 3.
Figure 3. Maximum Constraint Violation (%) The mass of the structure is reduced from 0.00661 to 0.00626. The objective function history is shown in Figure 4. Figure 4. Objective Function History Finally, the sound level spectrums at the driver s ear for the initial and final designs are shown in the figures below.
Figure 5. Sound Spectrum of the Initial Design Figure 6. Sound Spectrum of the Final Design 6. Taurus Model This example consists of a public doming full vehicle model of a Taurus sedan. The trimmed body model is shown in Figure 7 and the air cavities in the passenger compartment and trunk are shown in Figure 8.
Figure 7. Taurus Trimmed Body Figure 8. Taurus Air Cavities 6.1 Taurus Finite Element Model For this model, the structural and Fluid meshes do not match. In this case, an automated search algorithm is used to generate the mesh coupling matrix [A] between the fluid and structural meshes. A unit force load is applied at various points (suspension, power train, body and exhaust attachments) in X, Y and Z directions. Velocity output is requested at each excitation point and also at tactile locations on the steering column and seat track would produce the point mobility plots or V/F plots. The pressure level at the ear locations of each occupant is converted to decibels gives the A/F or Sound Pressure Level (SPL) curves 6.2 Taurus Structural Optimization A frequency response gauge optimization using RADIOSS was used to reduce the point mobility. The results of this optimization are shown in Figure 9. The red curve represents the original model and the blue curve is the response of the optimized model. Figure 9. Taurus Point Mobility
6.3 Taurus Panel Participation A panel contribution analysis was setup for the different color component panels shown in Figure. 10 below to identify which panels contribute the most to the acoustic response at the driver s ear. Figure 10. Taurus Panel Definition 6.4 Taurus Acoustic Optimization Gauge and topography (bead pattern) optimization were performed on the critical panels to improve the acoustic response. The cumulative effect is shown below in Figure 11. Figure 11. Taurus Acoustic Optimization Result 7. Conclusions In this work it is shown that the sound levels at in a fluid surrounded by a structure can be reduced by making modifications to the structure. Coupled fluid-structure modal frequency response is performed using the finite element method in order to determine the sound levels at the driver s ear in an automobile. Modern gradient based optimization techniques are used to reduce the maximum sound level to an acceptable limit while simultaneously reducing the mass of the structure.
8. Future Work The computational requirements for couple fluid-structure analysis and optimization can be quite large. This is principally due to the large number of structural degrees of freedom, as well as the large number of structural modes, and finally, the large number of excitation frequencies. The computation burden can be reduced by reducing the number of degrees of freedom in the model. These degrees of freedom can be reduced by using dynamic Component Mode Synthesis (CMS) Super Elements (SE). Non-design portions of the structural model can be replaced by CMS SE s in order to reduce the computational time. Since only small portions of the structure are designed at any one time, the computational burden per analysis can be reduced from hours to minutes. Following papers will show acoustic response optimization of full vehicle models in which most of the structural DOF are replaced by CMS SE s. 9. References 1. RADIOSS Version 9.0 User s Manual, Altair Engineering, 2008.