Predictive modal analysis

6.4 Methods for performing modal analysis

6.4.5 Predictive modal analysis

case for real structures, then the transfer function between two locations will have several single degree of freedom contributions: see Fig. 6.15. The governing equation then becomes

h

i c m

i j

i r j r

r r

r r

n ,

, ,

ω ω ω ω

( ) =

(

−

)

+

∑

= ₂ ^{Φ Φ}₂ 1

(6.28)

where r denotes the respective mode number.

springs and damping elements are most commonly used. Since these methods are described in detail in other chapters of this book, we will concentrate in this section on a comparison of experimental and predictive CAE tools, outlining how to best utilize both in developing the required refi nement of vehicle noise and vibration.

The increase in performance and confi dence for the predictive methods has changed the distribution of modal analysis work between test-based and predictive methods. Today CAE models are used to give design guid- ance on increasingly complex models, i.e. comparison of dynamic proper- ties such as the frequency response functions for complete vehicle models, and this development is being backed and accelerated by the industry. But the dynamic behavior of a full vehicle is still so complex that both methods are often used in parallel.

When fi rst CAD models of the future product become available, these are taken and, e.g., fi nite element models created. These models can then be used for forced response or modal analysis calculations. The fi rst step here is to create a grid across the substructures, components and possible cavities, the fi nite element grid, on which the equations representing the acoustic and structural motion are solved. The substructure and component models are then joined to form the complete vehicle model. At this stage the boundary and coupling conditions must be defi ned, which is an impor- tant and often diffi cult task.

For full vehicles the meshes have hundreds of thousands of elements, compared to maybe 150 measurement points in experimental investiga- tions. This high element count is necessary if the details of the structure are to be represented properly, which for the test-based analysis is given by the hardware, but they make the work of creating the model, the meshing, more time-consuming and also prolong the time required for computation. This is a serious concern since further refi nement of the grids is sometimes con- sidered necessary in order to even better represent important design details of the vehicle. Therefore a balance between the required accuracy of the model and the restrictions in time available for vehicle development is required. The fi ne distribution of elements leads to the FE model picking up more modes than a test-based model. On the one hand this is an advan- tage, since the resulting modal model is more ‘complete’ than the test-based model; on the other hand the evaluation of the FE data is more diffi cult and again time-consuming since many of the calculated modes are not important for the noise and vibration characteristics of the vehicle as expe- rienced by the passengers.

The predictive models are in general of linear type, the damping often modeled as being proportional to the mass and stiffness matrices. In reality the full vehicle exhibits non-linear behavior and this is a point of concern.

But this problem also affects the experimental modal analysis investigation,

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since the applied excitation forces during a modal test are seldom equal to the forces acting during operation. A typical example is the suspension modes of the vehicle. The piston that moves in the damper strut during on-road driving requires a minimal force to overcome the stick friction.

Modal tests seldom reach an excitation level as encountered in real vehicle operating conditions, therefore modal values are not correct in this case.

So both approaches struggle with the non-linear behavior of the object under investigation.

The assumption of damping being proportional is also not strictly appli- cable but makes solution of the fi nite element problem easier. When damping is chosen to be proportional to the mass and stiffness matrices, the equations can be solved for the undamped case fi rst and the results corrected for the effects of damping afterwards. Further simplifi cations often need to be made, i.e. one global damping value defi ned over the entire structure and frequency band of interest. Since the damping encountered in vehicles is mostly at or below 3% critical damping, this assumption does not affect the mode frequency or mode shapes very much, but it does have a strong effect on amplitudes. But it is the amplitudes that engineers have set targets for and are therefore interested in most. Here one must conclude that the prediction of absolute values today is confi ned to simple structures, and noise and vibration predictions for full vehicles are best used in an A–B comparison to give a design direction. Defi ning a correct damping is a criti- cal skill and it is here that an intensive exchange between both experimental and predictive tools is a prerequisite for success.

For practical engineering it is not suffi cient to describe only the dynamic properties of a full vehicle or its systems in the form of a modal model, but it is also important that in the case when requirements are not met, some indication of what needs to be done is given. Since FE models possess a fi ne representation of a structure they can also deliver detailed structural change proposals for the vehicle. The modal model extracted from test- based analysis is restricted to structural optimization of general mass, stiff- ness or damping changes between the rather coarse positions of the response locations. This is a clear drawback in the development of a vehicle’s dynamic properties.

In modal analysis, be it test-based or predictive, much depends on the expertise of the engineer doing the evaluation. In the test-based analysis process the evaluator decides how to analyze the data, determining the modal frequency and damping by his or her own judgment and giving the mode shapes a description. The FE engineer does not have to decide what modal frequencies to include in the modal model, but the much higher number of modes derived from the calculation must be evaluated, and also mode shape descriptions must be formulated. The mode shape description can then be used for correlation or sign-off against set mode shape targets.

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But in any case, it is a demanding task to manually order two sets of mode shapes for comparison, and one would wish to have a more automated tool to do this. There are parameters available that allow a comparison of mode shapes, be it from calculation or test. The modal scale factor, MSF, and modal assurance criterion, MAC, allow the comparison of two vectors. The MSF gives an estimate of the ratio between two vectors, the MAC a cor- relation factor describing whether the vector is orthogonal or not. Some investigations have been conducted towards the usage of these two values to automate mode shape comparisons, but unfortunately with only limited success. For full vehicle mode shapes it is still inevitable to visually inspect and agree on an individual description before commencing with the task of correlating two sets of mode shapes.

Last but not least is the fact that a model describes the design intent.

When a prototype or series hardware is fi nally built from this design, then it is certain that there will be deviations and in the case of a series produc- tion additional spread within the individual vehicles. This must be kept in mind when correlating models to experimental data, not expecting to fi nd identical properties but realizing that there will be a certain variation. Of course it would be best to investigate a number of test objects to have an idea of the variation and this has been done in single projects. Within the constraints of usual vehicle development this is impossible since suffi cient hardware is often not available for testing, and since experimental modal investigations are very resource and time demanding, so that the fi nal result will come too late for actual program application.