# Modal Analysis on an Exhaust Manifold to define a Catalyst FE-model

Faurecia Exhaust Systems AB develops and manufactures exhaust manifolds for the car industry. In the developing process the FE-models are one of the main tools and they are becoming more and more important in the automotive development. In the tough competition between the manufacturers, the demands for fast development require good FE-models both from the manufacturers and their subcontractors.The main goal of this thesis is to update an existing FE-model of a close coupled exhaust manifold and look at the catalyst to investigate the behavior of the catalytic converter and suggest a way to model the monolith.The thesis combines analytical calculations with experimental measurements. By the use of modal theory, an analytical model is updated to resemble the experimental data…

Contents

Notation
1  Introduction
1.1  Background
1.2  Purpose and aim
1.3  Approach
2  Theoretical background
2.1  Frequency Response Function (FRF)
2.2  Modal Theory
2.3  Modal theory in practice
2.4  Mounting of the test object
2.5  Excitation
2.6  Data quality assessment
2.7  Selection of reference point
2.8  Selection of response point
2.9  The coherence function
2.10  Direct modal comparison
2.11  The modal assurance criterion (MAC)
2.12  AutoMAC
2.13  Coordinate modal assurance criterion (CoMAC)
2.14  Frequency Difference (FreqDiff)
2.15  Change of basis matrix (S-matrix)
2.16  Damping
2.17  Parameters used to update the FE-model
3  Experimental test
3.1  Measurement preparation
3.2  Point selection
3.3  Data quality assessment
3.3.1   Coherence
3.3.2   Reciprocity
3.3.3   Linearity
3.3.4   Quality check of measuring points
3.3.5   Validity check of the S-matrix
3.4  Results
3.5  Equipment & The measurement set-up
4  Mode shapes
5  Model updating
5.1  Initial Model vs. Exhaust manifold
5.2  Updating the manifold without the monolith
5.3  Model with updated welds vs. Exhaust manifold
5.4  Updating the manifold with the monolith
6  Verification
6.1  The empty canning
6.2  The canning with added weight
6.3  The canning with added weight and stiffness
7  Results
7.1  Initial Model vs. Exhaust manifold
7.2  Updating the manifold without the monolith.
7.3  Model with updated welds and added mass vs. Exhaust manifold
with monolith
7.4  Updated analytical model vs. Exhaust manifold with monolith
8  Conclusion
9  Reference

Author: Björn Zettervall, Henrik Ekholm

Source: Blekinge Institute of Technology