General engineering analysis

Case Study

Faster Vibration Analysis of Automotive Exhaust Systems

Mechanical vibrations of vehicle exhaust systems can cause both cabin noise and structural durability concerns. To reduce the time taken to assess new exhaust systems Arvin Exhaust R&D, based in Warton, England commissioned FEA Ltd's consultancy department to produce the Arvin Modal Analysis Program (AMAP) as an extension to LUSAS Analyst which already in use. By using AMAP the vibrational behaviour of proposed new exhaust systems can be evaluated more rapidly than by manual modelling or other previous automated methods giving man-time reductions of around 50%.

Because dynamics modelling requires highly idealised representations of complex sub-assemblies, a different approach is required to that used for component level analysis meaning that direct transfer of full 3D CAD models is not useful. Instead, a partially automated 'top down' approach is adopted, where AMAP provides a strict framework for model creation and verification, analysis set-up and post-processing. This imposes discipline and consistency on the analysis process. In addition, for dynamic analyses of this type it is essential that the complete exhaust assembly is modelled - including a representation of the engine and manifold. This is because dynamic excitation is predominantly comprised of unbalanced forces within the engine, and forced vibration response calculations are only possible if the vibration source is included in the model.

To model an exhaust system the coordinates of all pipe and muffler centrelines are defined, either by using forms within AMAP or by importing centreline data from a CADDS V model, via an intermediate ASCII file. Once done, individual sections of centreline which make up a pipe run or muffler can be selected graphically with AMAP providing a form to allow tube diameter, thickness and bend radius to be entered.

Muffler boxes are located in a similar manner to pipe runs. Because these components can be very complex internally with the configuration being application-specific, and with the degree of structural connection between baffles, tubes, end plates and casing varying considerably with either "lock-seam" or "clam shell" construction, less automatic modelling procedures are used. However, significant modelling aids are still provided by AMAP. On-screen forms are used to define muffler tube or baffle size, perforation pattern, packing density, end plate details etc. Connections between muffler components are modelled using springs, so that flexible, articulated or sliding connections can be defined. Definition of these springs is assisted by a very useful "exploded view" facility, which separates the muffler components on the screen so that springs may be inserted graphically. AMAP automatically defines and assigns all mass and stiffness property data to the model based on data entered by the designer. 'Trace lines', another useful feature, are provided to indicate outlines of muffler and converter boxes where a 'wire-frame' as opposed to a 'shell model' idealisation is used.

In addition to pipe runs and mufflers, catalytic converters, exhaust manifolds; rigid-mass representations of engine/transmission assemblies including compliant mounts and exhaust system hangers can be individually defined and added to the model. In transversely mounted engines a "hinge" between the engine and exhaust system is also required to de-couple "torque wind" movements of the engine. Both knuckle and bellows type de-couplers have a marked effect on the dynamic response of the exhaust system, and so careful modelling is required. Beam elements with axial, bending and shear flexibility are used to represent bellows type connections, with spring elements being used for knuckle joints.

Careful checking is especially important for dynamic analysis models. Incorrect representation of mass or stiffness is likely to have more influence on dynamic response predictions than a similar error in a static analysis. Considerable effort was made in the development of AMAP to assist the task of checking the model. Throughout the creation of the model, AMAP tracks and controls numbering of property data, so that when the model is complete an annotated table of properties can be requested. The program also creates plots showing properties assigned to all the features in the model. The table and plots together form a complete description of the model, allowing comprehensive checking. Further checking data is provided by the LUSAS analysis run, which lists total mass and centre of gravity of all materials in the model. Since each component is assigned a different material, masses of individual mufflers etc. can be readily checked.

LUSAS provides a number of different eigensolvers for natural frequency analysis. AMAP automatically selects the solver that has been proved most effective for exhaust system models. Once the eigenvalue analysis has been performed, AMAP produces a complete set of annotated mode shape plots. On-screen mode shape animations are also generated for interactive viewing. LUSAS results processing features include tools for interactive dynamic response calculation, using previously calculated mass normalised eigenmodes. This facility is invoked by AMAP to automatically generate frequency response functions for critical response positions, such as chassis attachment points.

Frequency response graph for selected nodes

For modal analysis it is very important that the analytical model represents the true behaviour of the physical system under investigation. To achieve this, Arvin Exhaust use LMS modal test software to measure and extract mode shapes and frequencies of selected prototype systems for comparison with AMAP/LUSAS predictions. The LUSAS-test correlation process is assisted by the LMS-export facility within the LUSAS results processing features which provides mesh and mode shape data in CADA-X format. Many of the modelling techniques and rules in AMAP evolved as a result of LUSAS-test correlation, and it is expected that this process will continue for the foreseeable future.

"Our evaluation of proposed new exhaust systems can now be performed at least twice as fast as previous methods with greater accuracy also being achieved."

Ian Rutherford, CAE Team Leader, Arvin Exhaust R&D


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