Hans Bode
University of Wuppertal (D) Christian Guist BMW AG, Munich (D)
1 Introduction and Purpose of Research Work
The complex interrelations which determine the mechanical stability of metal catalyst supports cause high levels of time and cost investments in establishing assurances with regard to life- time predictions via experimentation. For this reason, the emphasis is shifting with regard to assurance in the direction of simulation models.
In order to be able to make precise statements using simulations, exact descriptions of the relationships concerned and known facts with regard to parameters, especially material pa- rameters, are of major importance. The method used to establish these relationships and pa- rameters will be explained in the following. The method has been validated using a reference system.
2 Construction of a Model for Lifetime
The approach here is to bring the task and technical system onto a virtual level and to construct a model. This model should be able to offer:
· Precise concept design
· Better evaluation of experimental results
· Efficient transfer of knowledge and experience to subsequent projects
· Specific error search in the case of damage etc.
The created and proposed model is shown in Figure 1 and is be explained as follows: The load profile of the component is given in the left part of the diagram, considerations with re- gard to mechanical strength of the component (stability of component) are given on the far right-hand side. A comparison between load and stability leads to the lifetime prediction based on the virtual level in the much needed very early stages of product development.
In the construction design of the model, thermal load, flow-related load and vibration-related load are considered. Taking a closer look at thermal load, hot exhaust gas flows through the catalytic converter during vehicle operation, imposing thermal loading of the metal support.
Also the catalytic reaction leads to increasing thermal loads. Speed of hot exhaust gas, pressure of gas and temperature will result in flow-related load. Unfortunately, thermal- and flow- related loads are not uniform, leading to additional loads. Acceleration and spectra of vibration will result in vibration-related load and here again, these parameters are not uniform.
Material Aspects in Automotive Catalytic Converters, Hans Bode Copyright © 2002 Wiley-VCH Verlag GmbH &Co. K aA ISBN: 3-527-30491-6G
Figure 1:Model
Influencing parameters with regard to load are type of engine and vehicle, as well as driving conditions and the geometry of the catalytic support. Parameters with regard to the mechanical strength of the component are: alloy composition, brazing – if applied, the way in which the component is shaped and eventually also welding. The parameters of the vehicle and driving conditions, considered in the research work related to lifetime prediction are: untreated exhaust gas, speed, pressure, temperature, acceleration and frequency spectrum.
For a selected reference system, values for stresses and strains of loads have to be calculated or measured and these values have to be compared with permissible stresses and strains of the component. Material data will become very important and here, not only yield and tensile strength, but also dynamic strength and deformation characteristics have to be taken into con- sideration. Special measurement techniques, such as holography for deformation characteriza- tion (strains), have to be applied. Additional details can be found in [1].
3 Reference System
The reference system (Figure 2) consists of a BMW 6-cylinder engine (left side) and an EMITEC closed coupled catalyst-system (center). Each support consists of an outer shell, often called the mantle and an inner matrix (example right side).
The matrix is composed of flat and corrugated foils. In certain areas these are brazed to- gether at their contact points. Details of this kind of support are given by [2.The matrix is also brazed to the mantle in various possible ways. Therefore, properties of foils in the “as- delivered” state and in the “brazed” state are different or in other words, the actual supports have different properties to the thin foils in the “as-delivered” state. The geometrical data of
the supports is also provided. The ferritic foil material used in the materials tests was Alu- chrom ISE (see [3]) in the “as-delivered” and in the “brazed-simulated” condition. Compo- nents composed of these foils were always temperature brazed with a Nickel-based material.
Figure 2: System of reference
In order to be able to quantitatively determine the input values for stresses and strains, these values have to be derived for the reference engine. The relationships explained in the following are valid with regard to new systems. The following groupings can be derived:
· Vibration-related load is vibration due to inertial forces and flow loads, leading to stress values, and both values can be grouped together.
· High frequency radial load is natural vibration (self vibration), leading to a value for defor- mation characteristics, i.e. strain.
· Thermal load, leading again to a value for stress.
4 Determination of Axial Load and Comparison with Mechanical Strength Stability
Flow-related load (Figure 3) has been determined by numerical simulation (CFD). Values of flow-related loads were found to be very small (in the order of less than 1 N/mm2 in the refer- ence system). Details of that calculation are given in [1].
Figure 3: Load caused by flow and vibration
The vibration-related load on the substrate in axial direction is caused by excitation by the engine, the road surface and gas pulsation. Excitation by the engine is the most extreme of these, in terms of its acceleration and frequency spectrum. It has therefore been considered as the only significant source of vibration.
The effects of this vibrational excitation have to be examined from two different points of view: Inertial forces and natural vibrations (self vibration), see Chapter 5.
If the catalytic converter is viewed as a rigid physical system, acceleration leads to the exer- tion of inertial forces mainly in an axial direction. These forces generate stress at the connect- ing points between the mantle and the matrix (Figure 3). The tension (Jload) is calculated from the inertial force and the load bearing section. The load bearing section is the sum of the foil sections that are brazed to the mantle. To compare load with stability, Jload can be used directly as can comparative stress (Iv). According to the shear stress hypotheses, the comparative stress is two times larger than the inertial load.
These values have to be compared with the strength of the foil material in the “as-brazed”
condition. Two possibilities exist for the determination of strength:
· Determination of allowable stresses due to dynamic testing and / or
· taking the yield stress as reference, divided by factor 3 for dynamic loadings [4].
Figure 4 shows the results of dynamic testing of foils in a heat-treated condition (left part) and the yield strength (static testing) as a function of temperature (right part). The heat treat- ment parameters correspond to those applied during brazing of supports.
Parameters in the dynamic material tests are given in the figure on the left-hand side. The test was not conducted up to sample breaking point but to an allowed deformation of 2% due to
the requirement of cell stability and adherence requirements of ceramic coatings placed on the supports prior to starting service life. This was the limiting factor and the diagram is therefore a modified Smith-Diagram. The reduction of yield strength due to the brazing process is sig- nificant, but the differences in allowable max. I-amplitudes are small between “brazed”
simulated samples and samples in an “as-delivered” state, i.e. the brazing parameters do not significantly influence the dynamic properties but rather the static properties.
The comparison of high frequency axial load in the reference system with the mechanical strength stability of the material is also shown in Figure 4. Values of JLoad in total (flow-related and inertial-related) are about 4 N/mm2 for the first support and they are equivalent to a com- parative stress sV of 8 N/mm2. These load values from the reference system are much lower than the maximum permissible values in the modified Smith diagram for the whole tempera- ture range. This is confirmed by using or Jpermissible as a function of temperature.
Figure 4: Comparison of load and stability
Concerning Rp0.2/u as a function of temperature, there is an intersection of allowable shear stress with load stress above 900 °C. According to experiences in service, the critical point is the area close to the mantle. However, temperature of 900 °C will not be reached in this area, so flow forces and inertial forces are not significant and will not limit the lifetime of the refer- ence products.
5 Determination of High Frequency Radial Load and Comparison with Mechanical Strength Stability
Because high frequency vibrations occur along the radial axis as well, this means that natural frequencies now have to be considered. By considering the catalytic converter as a complex spring-mass system instead of a rigid body (discussed previously), the result will be that a number of different natural frequencies occur along with corresponding deformation effects.
The following approach has been chosen for determining these deformation effects: Only one of four modes has been selected because it is considered to be most critical [1].
At the beginning of the analyses of a given engine, the frequency spectrum initiated in the catalytic converter (support) and the energy required to produce excitation of the different frequencies has to be determined. The natural frequencies of the catalytic converter and the corresponding deformation effects are determined in parallel. The deformation in form of extension- or compression- related strains, which occurs during vehicle operation, is then de- termined because the stress as a result of this deformation is difficult to calculate. Therefore, strains are used as comparative values instead of determining stresses.
Deformation can be determined in a planar manner by means of holography (Figure 5, right- hand side) as a function of frequency. The deformation-related strain values determined in this way are in the order of less than 1 mm/mm. Details are given in [1]. Figure 5, left-hand side shows determined permissible deformation values (here elongation). Brazed samples have been tested as a function of different phase relationships.
Figure 5: Comparison of load and stability
Phase relationship describes how the sinus waves are arranged. Wave crest over wave crest means 0 degrees, wave crest over wave trough means 180 degrees. Tests have been carried out at room temperature and 800 °C. These tests contained samples composed of 2 layers or 5 layers. However, 5 layers were only used at 800 °C just in order to show the tendency in me- chanical behavior. Forces and calculated stresses were applied in tests in order to reach 107 cycles. The maximum strain value was then measured. It can also be seen from Figure 5-left- hand side, that the phase has a very strong influence on mechanical strength stability. Lowest stability is given at 90 degrees and higher.
The maximum permissible strain for reaching 107 cycles is about 6 mm/mm at room tem- perature and 5 mm/mm at 800 °C. When the number of layers is increased to 5, the permissible strain to reach 107 cycles at room temperature is lower, here 4 mm/mm. Further tests at differ- ent temperatures and with other numbers of layers should be carried out.
By comparing the degree of extension-related strain expected during vehicle operation with the permissible degree of strain at room temperature for the two supports used in the reference system it has been established that natural frequencies will not lead to plastic deformations.
The investigations have been confirmed experimentally.
6 Determination of Thermal Load and Comparison with Mechanical Strength Stability
The connections between the catalytic converter and the engine and its position in the vehicle determine the distribution of flow and the boundary conditions of heat transfer. A gradient of temperature between the outer shell and inner parts of the matrix has to be considered as well as transient temperature distributions due to the transient nature of vehicle operation. In addi- tion, the maximum temperature has to be taken into account for thermal loading. The non- uniform thermal load will have an influence on a variety of properties, such as physical and mechanical properties of the support, elongation/extension of the support and oxida- tion/corrosion of the support. The resulting stresses will not be uniform.
In view of the catalytic converter’s complex geometry, the load was not modeled by means of FEM programs. A separate mathematical model has been developed just for calculating thermal stresses in order to describe the characteristic status. It contains the principal con- tributory effects. Figure 6 shows how stresses resulting from thermal load were determined.
A spiral wound support was used for the model. Sinus-shaped cells were taken as quadratic cells. The difference between outer radius Ra and inner radius Ri is the length of such a quad- ratic cell. If a temperature is applied, Ra and Ri will change, so A can be calculated (Figure 6, left-hand side). When such a segment is heated up, the outer shell (mantle) will impose pres- sure tensions on the cells. When cooled down, tensile tensions occur, starting at the point of pressure deformations which have possibly been caused previously. By simply considering the warm-up scenario, the cell is now viewed as a cylindrical container and the comparative stress can be calculated according to the given rule [5] for sV in Figure 6.
The relationship between e and pa has been established in [6] with regard to matrix struc- tures. The temperature dependence has to be taken into consideration. The relative change in the elasticity modulus is seen in Figure 6-center. In order to calculate the comparative stress it has to be multiplied by the temperature factor for the E-module as stated here. The relevant
property for the stability of the component is the yield strength of foils in the “as-brazed” con- dition. Their dependence on temperature has already been stated in Figure 4.
Figure 6: Determination of load (stress)
The comparison of load and stability is made as a function of cross section by referring to the radii in the previously given equation for the comparative stress and leads to the following prediction of deformation occurrence for an extreme thermo-shock loaded system, not the reference system. It emerged, as shown in Figure 7, that permanent deformation is to be ex- pected in the outer zone, since Rp0.2 is less than the actual comparative stress. Plastic deforma- tion occurs. The result was confirmed in experiments. Deformation caused by thermal effects is the most critical type of load on catalytic converters.
An example for a damaged matrix is given in [2]. The objective of development work is to reduce this deformation to a minimum so that no changes in the catalytic converter’s charac- teristics occur. The mathematical model now provides a tool by means of which this can be done. Figure 8 shows the relevant parameters at the critical point close to the casing for cata- lyst 1 (outer zone) of the reference system. The related values for yield strength (tension and pressure) at the critical point can be seen. Comparative stress is also shown and, with regard to the reference system, is much lower than the permissible stress. No damage is predicted. This result has been verified by actual tests with the reference system.
Figure 7: Comparison of load and stability (cross-section, extreme thermo shock loaded system)
Figure 8: Comparison of load and stability (critical point, reference system)
8 Conclusions
As has been shown, it is indeed possible in spite of the extremely complex interrelationships, to make well-founded prognoses with regard to the mechanical stability of metallic catalyst supports. The model illustrated forms the basis for this. However, additional specific material values will be required. Values taken from literature are not suitable for accurate lifetime pre- dictions.
Using this work as a basis, the influence of further parameters can be investigated, for ex- ample, the influence of lesser foil thickness and higher cell densities as well as the influence of coating composition and coating thickness. Also the changes in foil properties with time is of importance.
Due to the findings established as part of the investigations described in the above, the use of metals as catalytic supports does allow calculations about lifetime predictions and this is a major advantage when modifying or developing new supports in the shorter times now re- quired.
9 References
[1] C. Guist, Dissertation D468, Bergische Universität-GH Wuppertal, 1998
[2] H. Bode in Conference Proceedings MACC 1997 (Ed. H. Bode), Wiley VCH, 1997 [3] J. Klöwer, H. Bode, M. Brede, R. Brueck, L. Wieres, Werkstoffwoche, München, (Mate-
rials Week, Munich) Section 2, 1998
[4] K. Giek, und R., Technische Formelsammlung, (Collection of Technical Formulae) Giek Verlag, 1989
[5] AD-Merblatt B6, Zylindrische Mäntel unter äußerem Druck, (Cylindrical casings under external pressure) 1977
[6] J. Pollack, Diplomarbeit (Thesis), TU Dresden, 1996