Faurecia Exhaust Systems - Seminar Report

Abstract

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.

The results of this thesis work include a description of an updated version of the FE-model of the exhaust manifold. It also includes one example of how to model the catalyst assembly. The model of the catalyst assembly has been validated.

The initial Finite-Element model showed relatively large differences for the first four natural frequencies, when compared to experimental data. Relatively large amplitude errors were also obtained when comparing frequency response function from the experiment and the model. An acceptable error was obtained for the natural frequencies when comparing the experimental result and the updated Finite-Element Model. The updating was mainly done by changing the mass and stiffness in the welds and the converter tube.

Introduction

Background

The dynamic analysis of the exhaust manifold is today mainly performed with a natural frequency analysis methodology. The catalyst assembly - that contains a ceramic monolith brick, a mat holding and protecting the monolith and the converter tube - is usually simplified in the FE-model for dynamic analysis. The converter tube is meshed with shell elements and the mass for the mat and monolith is distributed to the shell element by locally adjusting the density.

Purpose and aim

The aim is to update a FE-model of an exhaust manifold in order to be able to evaluate how to model a FE-model of the catalyst assembly, and analyse how this affects the result in the natural frequency analysis. The results from the analysis shall be compared to modal measurements of a real close couple exhaust manifold.

One exhaust manifold should be analysed and tested and the most suitable method for representing the catalyst in a FE-model for dynamic analysis should be presented.

Approach

The initial issue that has to be investigated is how good the simplified FE­model is. When compared with the experimental test of the exhaust manifold, some questions arise:

·                     Is the structure linear?

·                     Is it already good enough?

·                     What is good enough?

·                     What is the error before updating?

All of this has to be answered. A good way to do this is to perform a modal analysis. A range of different tools can be used for this purpose and a selection of them are used in this report, like Frequency response function (FRF), AutoMAC, MAC, CoMAC, reciprocity and direct comparison of modes. A brief explanation of these tools is included in chapter 2. For more information see literature on the subject.

When good experimental data has been collected and the data quality assessment is checked, the updating of the exhaust manifold can begin.

After the first comparison between the exhaust manifold and its FE-model the second stage is to perform a modal analysis on a manifold without the monolith and update the FE-model without the monolith. This is done to eliminate any consistent errors in the material properties to avoid compensating for these material properties faults during the evaluation of how to define the monolith.

Since the materials used in the manifold is given and known from the manufacturer, the updating is done in the welds. The connections, in form of welds, between individual parts, are difficult to predict beforehand, and hence, they are mainly responsible for the errors when comparing experimental and theoretical data. However, this assumption implicitly means that all modelling errors are accounted for by changing the physical properties of the welds and it is possible that this simplification will lead to a somewhat non-physical description of the welds true dynamic behaviour.

When having a model of an exhaust manifold, that fits the experimental data, the creation of the catalyst model can be initiated.

When the FE-model without the monolith is updated as close as possible to the manifold without the monolith, the chosen method to model a catalyst is integrated in the FE-model and correlated against the manifold with the monolith.

The last part is to verify the chosen method to model the catalyst. This is done by using only the catalyst part of the manifold and performing a new modal analysis on this. This data is then correlated against the data from the updated FE-model of the

Mounting of the test object

The mounting of the test object can be done in several possible ways, either the modal analyse is done when the structure is in its operating conditions or without its operating conditions but in a somewhat similar state.

The most common condition is called the free-free condition and simulates a free object without any boundary conditions.

To obtain an approximate free-free condition, a good way is typically to suspend the test object in elastic cords. When the test object is heavy and the suspension with the elastic cords is not enough, it is preferable to use relatively soft springs to place the test object upon, if necessary together with the elastic cords.

When making a modal analysis and the purpose is to correlate/update the result of an analytical test, the free-free condition is preferred.

Excitation

When performing a modal test, the test object has to be put in some kind of motion/vibration. To make the test object vibrate, an excitation force has to be used. A force transducer is monitoring the input signal and the accelerometers monitoring the response signal. The accelerometers and the force transducer generate the time signals used in the analysis.

Excitation can be carried out in some different ways; one way is with a shaker that transfers vibrations to the test object through the force transducer. Between the shaker and the force transducer a stinger is mounted to act as a mechanical fuse and to make sure that the force from the shaker is measured in the intended direction.

The signal feeding the shaker can either be a stepped-sine signal or a normally distributed broadband-signal. The latter has the advantages of exciting all frequency simultaneously and is therefore much faster.

Another way to cause/generate vibrations in the test object is by impact excitation. This is done by using a hammer. The hammer can be equipped with a force transducer, called an impulse hammer, or the force transducer can be separately mounted on the test object.

Data quality assessment

Before using any data from the modal test, some checks are important:

·                     Is the driving point frequency response free from inconsistency?

y Does the frequency response imaginary part only have peaks or dips in one direction?

·                     Is the structure linear?

y All nonlinear parts should be removed.

y Shaker excitation - different excitations level should not differ in amplitude in a frequency response.

y Hard to test with impact excitation.

For a system to be linear it has to be additive (2.19) and homogeneous (2.20).

Xl (r) + Xz(t) -j Yl (t) + Yz(t)

·                     Does Maxwell's reciprocity theorem hold?

y A frequency response should be equal independently which DOF, of two possible, that is chosen as response point respective excitation point.

It is also important to check the coherence to see if it is acceptable, see chapter (2.9) for more information on the coherence function.

Selection of reference point

The reference point is the point that stays fixed during the entire measurement. The reference point is the excitation point for shaker excitation and the accelerometer point for measurements with roving hammer.

When selecting a reference point it is important that all modes of interest are included. This means that the reference point cannot be located near a nodal line of any mode. To select a proper reference point, it is preferable to study a FE-model of the mode shape before the measurements to determine which point that is appropriate to use.

When selecting the reference point for a three dimensional object the directions of the mode shapes must also be taken in consideration. To get a good measurement from a three dimensional object, one can try to find a skewed reference point that make the force excite in all three directions.

The skewed response then has component in all three directions in the original coordinate system, which has to be calculated. A new coordinate system is made and the components from this are then transformed in to the original coordinate system through multiplication with a matrix made for this purpose.

Selection of response point

One of the purposes of the measurement is to get a good display of the mode shapes. The response points are the points in which the response from the structure is collected. The information can be used to describe the mode shapes of the structure.

Since it is not possible to measure everywhere on the structure, a finite number of points most be chosen. The quantity of points to measure depends on the geometry of the structure.

To get as much information as possible, the points should be chosen to give a good separation of the modes. When the measurements are done an AutoMAC matrix can be used to investigate if the points separate the mode shapes good enough,

Damping

Damping is always present in a real system and has to be calculated from the experimental data. In Abaqus  and all other FEM-software, the damping is not calculated, therefore it must be given. The given values are taken from the experimental measurement.

During the measurement on the catalyst alone, to verify the update, the damping could not be calculated with the curve-fit routines. Instead the so-called "Half-power" bandwidth method was used. This method is normally only valid for low damping, but is a good enough approximation when comparing FRFs in this case when the natural frequencies in the FRF are of greater interest and the damping is only for visualization.

Parameters used to update the FE-model

To update the analytical model the FRF is used and the aim is to fit the analytical natural frequency to the experimental natural frequency. The natural frequency depends on the stiffness and mass, see equation 

The mass, m is updated just by weighing the exhaust manifold and then change the density in the welds in the model.

The stiffness, k depends on (( which is the constant for the boundary condition and I and L that are parameters depending on the structure. E is the Young's modulus and is a material parameter. To update the stiffness, k the material parameter E is used.

The boundary condition changes the natural frequency, but the boundary conditions are the same for both the analytical model and the experimental test, the free-free condition. The rubber cord used to simulate the free-free condition in the measurement setup, has negligible stiffness compared to the exhaust manifold, this gives a good estimation of the free-free condition.

Experimental test

The measurements on the exhaust manifold are following the directives from chapter 2. A short description of the different features and results are included in this chapter. During the measurement with the shaker, the shaker was fed with a random signal. In every response point there are three DOFs corresponding to the coordinates axis. This means a total of eight response points gives a total of 24 DOFs.

The software used during the measurement was SingelCalc, Mobilyzer. The data were collected in SingleCalc and afterwards analysed in Matlab using Matlab toolbox for modal analysis.

Measurement preparation

The chosen boundary condition for the measurement was the free-free condition. In order to obtain the free-free condition the exhaust manifold were suspended in soft elastic cords attached to a steel rig. See picture 3.3.

Point selection

In these measurements a fixed accelerometer and roving hammer were used to be able to change the excitation points. Several different sets of points were tested before a set was chosen for further measurements. The chosen points are displayed in fig 3.1 and 3.2. The MAC-matrixes were used to select the best points. The MAC of the best set of points is shown in chapter 3.3.4.

Data quality assessment

The collected data has to be checked before the analysis. It is good practice to perform a data quality assessment on the collected data.

Coherence

The signal to noise ratio at the anti-resonances often gets too small, and is one possible cause for the dip in some of the coherence at the anti-resonance and should be neglected.

Below is an example of the coherence from the response point 3, DOF 7, 8 and 9.

Reciprocity

The reciprocity is checked by switching input and output points. The points are located at the ends of the inlet flange point 4 and 7, see figure 3.2. The test is performed with a modal hammer and a single axis accelerometer.

Linearity

The linearity is checked by using a shaker where two different measurements are done with different amplitudes in the input signal. If the frequency response function does not change in amplitude the exhaust manifold can be approximated as linear.

The linearity is shown below both for exhaust manifold with and without the monolith. The measurement on the exhaust manifold with the monolith was done between DOF 6 and 10 and the measurement on the exhaust manifold without the monolith was done between DOF 10 and 19.

Quality check of measuring points

It is important to secure good measurement points and that the modes are correct represented in the comparison, the tool used for this is AutoMAC. An AutoMAC is done for both the analytical and experimental data.

The AutoMAC shows the ratio of the correlation between one set of modes against itself. Full correlation results in 1. The diagonal matrix shows the correlation of each mode with itself, and should be fully correlated. On the other hand the off-diagonal is the correlation between different modes and should generate a low correlation.

Validity check of the S-matrix.

To check the S-matrix, data from response point 3 were measured in two different ways. The data was collected in the skewed coordinate system and in the reference coordinate system, see figure 3.1.

By using a distance plate the accelerometer could be placed in the reference coordinate system, see picture 3.1 and 3.2

The data measured in the skewed coordinate system were then pre-multiplied with the S-matrix. Comparison of the FRFs can be seen below:

The solid line - is the response from the accelerometer in the skewed coordinate system and the dotted line ... is the response in the reference coordinate system. The amplitude difference is due to the problem mentioned in chapter 2.15

The difference in frequency is due to the distance plate made to get the accelerometer in the reference coordinate system.

The dashed-dotted line - . - is the response for the skewed coordinate system that has been pre-multiplied with the S-matrix.

The amplitude harmonizes well between the reference coordinate system and skewed coordinate system that has been pre-multiplied with the S-matrix. This show that the S-matrix used is valid.

Results

·        The responding coherence for each measurement didn't indicate any faults in the data acquisition process.

• The reciprocity shows that Maxwell theorem is valid.

·        The FRFs in figure 3.5 and 3.6 shows that the conditions of linearity are satisfied.

·        Both MACs shows that the modes correlates and therefore correct represented.

Model updating

An FE-model of the exhaust manifold is provided from the manufacturer (Faurecia AB). The given model is modelled without comparison against experimental measurements and with simplified modelling of the monolith. The updating is done by changing the properties of the welds and canning surrounding the monolith. The accelerometers/dummies have been compensated for with lumped masses in the FE-model.

Initial Model vs. Exhaust manifold

Before updating the analytical model, the praxis is to compare the analytical and experimental data sets to obtain the necessary information whether the two data sets are close enough to each other so that a correct update is at all possible. 

The comparison is done between the initial model where the mat and monolith is modelled by distributing the mass to the canning that surrounds the monolith and the experimental data.

In order to visualise the difference between the analytical and the experimental frequency response functions, an example of the FRFs is shown in figureS .1. Direct modal comparisons between the natural frequencies are displayed in figure 5.2. The systematic deviation of the points from the ideal line indicates an error in the material properties. 

The good correlation in the MAC-matrix in figure 5.3 indicates that the analytical mode shapes corresponds well to its experimental counterparts. The low off-diagonal values indicate that the different mode shapes are non­correlated.

The correlation for each measure point is displayed in the CoMAC in figure 5.4. The correlation is good. DOF 22-24 is a slightly uncorrelated but since this is where the shaker is mounted this is not to be considered as a fault but mere disturbance.

Updating the manifold without the monolith

The first updating is done on an analytical model without compensation for mat and monolith vs. an exhaust manifold without mat and monolith. The reason for this procedure is to get an as correct model as possible to start with.

Since the material properties of the model are fixed the updating procedure is done by updating the material properties for the welds.

Weighing the exhaust manifold and comparing with the model in Abaqus, shows that the analytical model weighs 145g more than the exhaust manifold. Since modal testing is rather mass sensitive the difference in mass is compensated by changing the density of the welds in the analytical model. To get an as correct model as possible 2000 kg/nr' is chosen as density for the welds. This density is rather low for welding material but since material properties are not to be changed in this updating, and the welds are distributed over the whole structure, changing the density is acceptable.

Comparison between exhaust manifold and analytical model with correct weight shows that the exhaust manifold has systematically higher natural frequencies than the analytical model. The comparison is displayed with FRFs in figure 5.5 and direct modal comparison.

The start value of the Young's modulus of the welds in the analytical model is 22 * 1010 Pa. This is the same value as for ordinary steel. Since the resonance frequencies were too low compared to the measurements done on the exhaust manifold, the model must be stiffened up to get a better match. The analytical model is tuned in by changing the Young's modulus of the welds. The tested values are displayed in figure 5.7.

In the optimization of the analytical model, a value of E= 49* lOll Pa for the Young's modulus gives the smallest difference between the natural frequencies and this is the Young's modulus for the welds that is used in the following updating procedures.

Model with updated welds vs. Exhaust manifold

The comparison is between exhaust manifold with mat and monolith, and corresponding analytical model with updated welds. To investigate the influence from the updating of the welds, the mass of the monolith is implemented at the canning surrounding the monolith. The mass is added by increasing the density over the area.

In order to visualize the difference between the analytical model and the exhaust manifold after the update of the welds, an example of the FRF plot is shown in figure 5.10. A direct modal comparison is shown in figure 5.11.

A systematic derivation of the points from the ideal line indicates an error in the material properties . Although the error is significantly reduced, changing the properties of the welds is not enough to get a good update of the analytical model.

The correlation between experimental and analytical mode shapes is displayed in a MAC-matrix in figure 5.12.

The good correlation in the diagonal matrix indicates that the analytical mode shapes corresponds to its experimental counterparts. The low off-diagonal values indicate that the different mode shapes are non-correlated.

The correlation for each measure point is displayed in the CoMAC in figure 5.13. As can be seen the experimental and analytical DOFs correlate well. The slightly lower correlation in DOF 22-24 is most likely due to that this is where the shaker is mounted and should not to be considered as a fault but mere disturbance.

Conclusion

The aim of this work was to study the dynamic behaviour of an exhaust manifold. The experimental modal analysis on the exhaust manifold showed that the existing FE-model of the manifold had to be stiffened up to match the experimental measurements.

The initial FE-model did not have a modeled monolith. The influence from the monolith was implemented as increased density on the canning. We have proved that by compensating in this way, information about how the mounted monolith affects the exhaust manifold is left out in FE calculations.

By implementing the increased stiffness in the calculations we managed to tune in the resonance frequencies. This shows that both the physical assembly of the mat and monolith stiffen the exhaust manifold. A strong correlation between the experimental and the analytical mode shapes was also found as shown in chapter 4. However, the comparison between experimental and analytical FRFs shows relatively large amplitude errors which should be studied closer in future investigations.

A possible source of error in the updating is the limited frequency resolution in experimental measurements. This error does not affect the resonance frequencies but could influence the amplitude of the FRF, and the estimated damping. Other possible sources of error are the modelling, the assembly and the meshing of the FE-model.

We like to suggest the following topics as themes for future investigation.

·                     The welds influence on the exhaust manifold.

·                     Different ways to model the mat and monolith.

·                     Difference in weight between FE-model and physical structure.

·                     Difference in stiffness between FE-model and physical structure.