Wave-based substructuring and modal projection provide simulation accuracy in a fraction of the time
Mitsubishi Motor Corp. and LMS engineers have teamed up to deploy analysis procedures that reduce the time required to simulate the automotive noise, vibration and harshness (NVH) performance of a car body to as little as one-hundredth of the time previously required.
Conventional full-body finite element models that are normally used to evaluate body NVH prior take so long to solve that relatively few design alternatives can be considered. The new wave-based substructuring (WBS) and modal projection method reduce the size of the finite element model in order to reduce simulation solution time while providing accuracy that is essentially equivalent to a full finite element model.
Vehicle manufacturers are redesigning existing models and launching new variants at an unprecedented pace. Since the vast majority of these vehicles are built on common platforms, body engineering is nearly always on the critical path of the car development process. Other important design and development issues, such as crash, structural rigidity, and production feasibility, can and usually are addressed early in the development process with computer simulation. But the size and complexity of vehicle body models makes them much more challenging to simulate for NVH performance than other vehicle system and component models. Hundreds of thousands of finite element nodes are typically required to provide accurate simulations of fully trimmed body models. With current high-end computing systems it typically takes on the order of 24 hours to perform a single analysis iteration.
OPTIMIZING BODY NVH EARLY IN THE DEVELOPMENT
The problem is that engineers need to evaluate hundreds of different body design alternatives to optimize body performance from an interior acoustics and comfort standpoint. These simulations typically need to be performed within the space of a few weeks in order to provide information promptly enough to be useful during the early stages of the development process. It isn't possible to perform these simulations that quickly using conventional finite element analysis methods, which means that automotive OEMs today are generally forced to address critical NVH issues late in the development process. The problem with this approach is that relatively little design flexibility is available at this late stage and most of the available options, such as adding tuned absorbers, are quite expensive. Late-stage troubleshooting also runs the risk of delaying the vehicle introduction.
Wave-based substructuring connects body components. Mitsubishi Motors worked with consultants from LMS Engineering Services to establish new approaches that increase the speed with which body NVH can be simulated while maintaining the accuracy of full finite element models. Wave-based substructuring is a new method that was developed to assemble the structural model of the full body as a compilation of the reduced FE models of individual parts.
The basic idea of the WBS method is to express the deformation of the coupling interface in the form of basis functions called waves. Connections that are normally defined in terms of the interface degrees of freedom (dof) are replaced by connections between waves that impose the continuity of the displacements and forces. Representing the connections by waves, which are analogous to mode shapes, makes it possible to reduce the computational workload by limiting the analysis to only the lower-order waves, which represent nearly all of the potential deformations. The number of interface dofs is reduced from the number of connections to the number of waves, which substantially reduces the computational workload.
According to the companies, a key advantage of the WBS approach is that it enables additional reductions in compute time by replacing components whose modification is not under consideration with modal reduction techniques while maintaining a full finite element model for parts that are subject to modifications. The full body finite element model is first used to generate the set of waves that are then utilized to build a modal reduced model of the components. This provides substantial reductions in computational time with a minimum effect on accuracy.
WAVE-BASED SUBSTRUCTURING SUPPORTS EARLY BODY NVH OPTIMIZATION
The WBS method is ideal for NVH optimization of body panels that are assembled together with spot welds, according to Misubishi and LMS. The following example shows how engineers from the companies validated the WBS approach on an existing model vehicle.
The cowl top area was identified as an important contributor to booming noise using an earlier full body analysis. The challenge was that trying many alternative cowl top designs using full body finite element analysis would have taken too long to have a positive impact on the design process. So LMS consultants divided the body into two substructures, the cowl top panels and the remainder. Since no design modifications were to be considered outside the cowl top panel, the remainder of the body was simplified using modal reduction. The substructures were connected with spot welds and also with glue at the windshield interface. Nearly 1000 coupling dofs in the original model were replaced by about 250 waves.
A comparison of the vibro-acoustic response of the full finite element and reduced WBS models showed very good correlation. LMS engineers then took advantage of the ability of the WBS model to evaluate new design modifications in a very short time. The actual calculation time using the WBS model was benchmarked as 50 times faster compared to the traditional FE model. They evaluated the effect of adding reinforcement bars and brackets, thickness and material changes, and various combinations of modifications. These modifications were selected through a weak spot detection analysis in which the critical peaks in the response are traced back to their root cause in terms of panel contribution, modal contribution, etc. They identified a modification that combined thickness changes, both increases and decreases, with the addition of reinforcements. It reduced the vibro-acoustic response in the front seat below the design target over the entire frequency range being evaluated. Then they ran a full finite element model of their proposed modifications and verified the accuracy of the WBS predictions.
The efficiency of WBS also opens the door to automatic shape optimization. The geometric changes can be applied directly to the meshed parts of the virtual assembly using the morphing tools of LMS Virtual.Lab. An alternate approach involves linking some of the meshed panels to parameterized computer aided design (CAD) data. After any changes in the parameters, the meshes are automatically updated and replaced in the WBS assembly.
MODAL PROJECTION OPTIMIZES DESIGN PARAMETERS
The second approach, modal projection of design modifications, is used for the optimization of vehicle NVH performance for small modifications, typically during the refinement phase of the development cycle. Design parameters, such as thicknesses or material properties of components such as subframes or body panels, as well as local geometry modifications can be considered.
The body areas whose modification is expected to have the most impact on NVH are identified from a weak spot detection analysis and a set of nominal modifications is defined. Each nominal modification is projected in the modal domain and its effect on the system response can be quickly determined. Scaling factors are assigned to each modification and can be used as design parameters in an automated optimization process. This process aims at improving the vibro-acoustic performance of the assembly for different load cases such as road noise, booming nose, and can also be used directly on the frequency response function between input points and target points inside the passenger compartment.
An example of the modal projection approach is provided by an application where the goal was to optimize the body noise transfer function (BNTF) between the vertical input of the engine head mount and interior noise as measured by front and rear center microphones. Using weak spot detection with full body finite element analysis, a particular set of body panels was identified. The thickness of these body panels was optimized while limiting the maximum change to +/- 15 percent. The optimization procedure substantially reduced the BNTF. A new analysis with the full body finite element model verified the predictions provided by modal projection.
REDUCING SIMULATION TIME — MAINTAINING SIMULATION ACCURACY
The two procedures described here, WBS and modal projection, substantially reduce the time required for engineers to optimize body NVH performance prior to prototyping. Both approaches reduce the size of the finite element model in order to reduce simulation solution time while providing accuracy that is essentially equivalent to a full finite element model. The modal projection method is very well suited for optimizing components using design changes that can be represented as changes of finite element model parameters, such as material properties or shell thickness, and small modifications of the local geometry. The WBS method allows consideration of more complex changes by using wave functions to couple a finite element model of the component under consideration with reduced modal models of the parts that remain constant. Speed increases up to a factor of 100 can be achieved with both of these methods, making it practical for NVH engineers to optimize body NVH early in the design phase.
For more information, contact LMS North America, 1050 Wilshire Blvd., Suite 250, Troy, MI 48084, (248) 952-5664, fax (248) 952-1610, e-mail info@lmsna.com or info@lms.be, Web site: www.lmsintl.com.
Figure 1:
Wave based substructuring — tailgate
Figure 2:
Full model vs. reduced WBS
Figure 3:
Final results from modification and optimization analyses
Figure 4:
Shape optimization from CAD data
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