Optimization of Castings and Forgings at AUDI AG (published in Simulation 2003-02)

OPTIMIZATION OF CASTINGS AND FORGINGS AT AUDI AG Thomas Binder and Peter Hougardy, Audi AG, D-85045 Ingolstadt Peter Haffner, Audi AG, D-74172 Neckarsulm (authorized translation of an article published in „Simulation – Das Fachmagazin für FEM, CFD und MKS“, issue 02/2003)

1. Introduction The automobile industry today is confronted with radical changes in competitive conditions. In addition to globalisation and a reduction in development time, individual customer-orientated product development has a great influence on the competitive situation. Customer orientation is not only especially bound to the increasing complexity of products available, but increasing demands pertaining to product quality also play a large role. This, however, should not influence or have a negative outcome on the efficiency of development methods, and as a result has lead to a growth in the necessity of simulation tools that can be applied as early as possible in the operating chain. Topology and shape optimization have become the most important development tools used by the Audi AG in the last few years. The following sections describe both methods in detail and show several examples.

2. Possibilities and limits of topology optimization The classic development process is one in which simulations (CAE) begin after a CAD draft has been completed. First information received from the simulation usually comes so late that the design phase of a part can hardly be influenced and has a negative impact on the development and efficiency of the component in question. Topology optimization is brought into play at this point in time in the development chain. Already in the design phase, information is provided regarding loads and optimal weight of the component geometry in the design space available (Fig. 2.1). In this way, design decisions can be made based on more detailed knowledge. Furthermore, the first CAD draft is of very high quality which has a positive impact on the development process. Figure 2.2 shows the procedure undertaken in topology optimization. For example, at the start of optimization a CAD model of the design space is made. After mesh-building has been completed with a CAE pre-processor, the important boundary conditions are defined. Load marking and the saving of the analysis model is decisive for the design Fig. 2.1: Changing the development process using topology optimization suggestion determined. The subsequent transfer of the force flow framework in a production-relevant construction is the job of the designer and calculator working in close collaboration. The CAD draft that results then undergoes several analysis loops. OptiStruct and TOSCA are used as software tools for topology optimization. Both offer the possibility of determining the direction of deformation which has solved a time-weary problem in the optimization of castings and forgings. In addition, it is also possible to smooth the optimized structure and to transfer this in STL- or IGES format in a CAD system. Problems can also arise in the shaping of castings where a minimum as well as a maximum strength is to be maintained. At present, a “max. member size“ cannot be specified in contrast to a “min. member size” with OptiStruct. The result of a topological optimization in spite of smoothing is not a finished design, only a design suggestion. The potential hidden in the design suggestion can only be used when an experienced designer carries out the transfer. Three examples of different complexity using topology optimization with AUDI are described in detail below.

Fig. 2.2: Procedure followed in topology optimization

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Optimization of Castings and Forgings at AUDI AG (published in Simulation 2003-02)

2.1 Topology optimization of an engine support for the V6 FSI Motor of the A8 The engine support is often used to show the many uses of topology optimization in the development of components for the engine mount system (Fig. 2.1.1). Usually aluminium castings are used and the starting point for the optimization is the existing design space based on a DMU-investigation (Fig. 2.1.2). The design space model is then meshed and boundary conditions and material data are defined for the FE calculation. The maximum engine mount forces are specified as the load. In addition to the rigidity demands, a lower maximum permissible value is to be maintained for the first natural frequency in topology optimization in order to fulfil the acoustic demands. The results of optimization with TOSCA and OptiStruct can be compared in Fig. 2.1.2 below. The design model is hollow. Another characteristic are the recesses (“arches“) between the screws of the engine block which contain strong struts. In general, when comparing TOSCA – OptiStruct the results are very similar. It takes very little to shift from a TOSCA inputdeck to OptiStruct and vice

Fig. 2.1.1: View of components of the power-plant suspension system for the a V8 motor of the Audi A8

versa and often both solutions are determined. Which result is better suited for the final decision depends on the problem at hand. In this example, preference is given to the TOSCA results. The optimized structure is automatically smoothed and transferred as a IGES file in the CAD system (Fig. 2.1.3). Data reduction takes place here and the basis for a new design is available in the CAD system. A pure visual transfer in the form of plots has proven to be unreliable. Based on this design suggestion, a new support could be constructed (Fig. 2.1.4). Some struts in the area of the bolt position were strengthened and wall strengths could be partly reduced. The optimized support was re-calculated and the demands of rigidity and natural frequency were met. Figure 2.1.4 compares a previous model created without topology optimization and shows that the first natural frequency of the new support is over 30 % when weight has been reduced by 20 %. These contradictory demands (weight reduction – improvement in acoustics) can hardly be met without the use of topology optimization. In the development of castings for the engine mount system, topology optimization has proven to be a successful method in standardizing design needs.

Fig. 2.1.3: Comparison of design space model and smoothed result obtained with topology optimization

Fig. 2.1.2: Design space model in DMU and results of topology optimization with TOSCA (left) and OptiStruct (right)

Fig. 2.1.4: A designed support based upon the design suggestion compared with a reference support

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Optimization of Castings and Forgings at AUDI AG (published in Simulation 2003-02)

2.2 Auxiliary bracket of the R4 FSI motor The auxiliary bracket is a very complex part found in the stress field of the chassis-motor and is used to mount six components (generator, air compressor, intake manifold, idler pulley, pump, belt tensioner) onto the engine block. Due to the stress found in these parts, a high-quality topology is necessary. Base for the calculations is a bench tested and compared aggregate model of acoustic analysis which links a very fine meshed design space model of the bracket (Fig. 2.2.1). The loads of the auxiliary bracket are obtained from test stand calculations, in which the calculation model was marked with point load applications and coupling of RBE elements. The first optimization results produced a force flow framework which could only be transferred to a production-relevant design after many geometric changes were made due to several undercuts. The new structure showed no advantage with regards to weight or manufacturing costs when compared with the serial production. The project was stopped soon after because the specification of deformation directions was not possible at the Fig..2.2.1: Design space model with boundary conditions time of optimization. In another topological optimization, the serial structure of the bracket was used as an initial model instead of the usual design space model. In this way, a geometry could be specified that provided an unexpected large weight reduction of 20 % and made a cost reduction possible even though the demands were maintained (Figures 2.2.2 and 2.2.3). At this stage, the evaluation of the natural frequency of the optimized design was very important. This should not change when compared with serial configurations in order to avoid problems of vibration engineering. The results here showed that the component stresses could not only be maintained at the same level but also that the stiffness could be increased at the same time. Furthermore, the use of less material caused a reduction in weight and manufacturing costs.

Fig. 2.2.2: Steps taken from a serial component to a designed casting with the use of topology optimization

Fig. 2.2.3: Comparison of cost and weight

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Optimization of Castings and Forgings at AUDI AG (published in Simulation 2003-02)

2.3 Crankshaft bearing cap The design space of the crankshaft bearing cap is similar to the auxiliary bracket in that it is rather restricted geometrically. The component stress is much more complex however. In addition to assembly forces, shear forces act with the temperature cycles in the engine on the material assembly joint cover/engine block (GG/AL). The complex stresses from the crank assembly also come into play (Fig. 2.3.1). The program AVL Excite is used to determine these forces and calculate the heterogeneous bearing load distribution. Using the bearing load as the optimization input (dependant on the engine geometry, combustion pressure etc.) an influencing variable is a decisive factor on the results of topology optimization. Another optimization parameter is the target volume and the relationship between the bolt force and the main bearing force. A parameter variation produced two different geometrical concepts. The low proportion of the bolt prestress to the main bearing force with a larger target volume produced bond bridges between the bearing bracket and the sleeves. In addition, a lower target volume combined with a larger proportion of the bolt prestress to the main bearing force produced the shape of an I-Profile on the rear side of the bearing (Fig. 2.3.2). The final analysis from both optimization results derived from the three designs showed a clear advantage for variation 3 (Fig. 2.3.3). Variation 2.3.3 created a symbiosis of the geometrical concept and produced a weight reduction of 22 % compared with the serial design. The life span analysis showed that the optimized bearing cap had the same stiffness as the serial design.

Fig. 2.3.1: Design space model with boundary conditions

Fig. 2.3.2: Conversion of Topology optimization results

Fig. 2.3.3: Results of stiffness calculations

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Optimization of Castings and Forgings at AUDI AG (published in Simulation 2003-02)

3. Possibilities and limits of shape optimization In comparison to topology optimization which is a very important tool used at the start of product development to achieve a global design, shape optimization is used to determine the final design of an object. The results of shape optimization are based on a given geometry. The component has already been described geometrically in detail and not as in topology optimization, as a design space with the relevant boundary conditions. A design suggestion taken from a topological optimization can be used for further processing in shape optimization. Shape optimization means the displacement of surface nodes in the design area of the FE model with the aim of reducing stress peaks in areas of high stress gradients. This method results in an even stress distribution in the critical areas of the component. If each node of the design area can be moved by the optimizer, this is known as nonparametric optimization which is part of the TOSCA package. For shape optimization to be successful, a FE model with a high quality mesh fineness should be used. Only the surface nodes of the mesh are moved. For the layers under the surface, a mesh smoothing takes place, i.e. the nodes are tightened in order to avoid strong distortions of the inner elements. All demands and boundary conditions can be made on the component and all features of the FE solver to be used are available. TOSCA for example, can use both solvers NASTRAN and ABAQUS which opens the doors to the world of non-linearity. For example, contact between components of force transmission can be more effectively represented and taken into consideration for the optimization. For example, an optimization target can be that the minimization of the effective stress can be chosen at the same time as the weight of the component is minimized. The advantages of this are: the optimization problem can be easily defined; it is not necessary to produce Shape Basis vectors; growth and shrinkage is possible (weight reduction potential) The disadvantages are: growth movement on one node A always occurs because of the stress found on this node, i.e. minimization of stress and node displacement occurs together. Optimization at point X by a distinct change at point Y (notch stress reduction) is sometimes desirable but not possible at this present time.

3.1 Shape optimization of the stabiliser bar link for the front axle of the A8 The stabiliser coupling link, a forging, joins the supporting arm to the stabiliser bar with rubber bearings on the front axle of the new Audi A8 (Fig. 3.1.1). Due to changes made to the front axle, the design of the coupling link used to date did no longer meet the stiffness requirements. The problem was plain to see in tests and simulations (see Fig. 3.1.2). During simulation it was enough for symmetrical purposes when only a quarter of the coupling link was calculated. Based on the proportion of the absolved load alternations and the number of load alternations requested, it could be determined from the test results while taking the Woehler curve into consideration, that the stress at the point of fracture could be reduced by at least 25 %. In addition, the given geometry was to be changed as little as possible.

Fig. 3.1.1: Partial view of the front axle of the A8 in a test of the stabiliser coupling element

to the surface and to the stresses present. This resulted in freeform geometry and a stress reduction of 30 % at the critical areas. This improvement could be based on the stress-optimal shape achieved. As a comparison, Figure 3.1.3 illustrates the maximum design space possible restricted by a radius R24. Using this method, stress reduction would have been only 18 %. This clearly showed the difference in results between a stress-optimal shape and a simple radius. In the most critical areas, the optimized shape showed locally a much bigger radius than R24 and the radius gradually declined at the point under least stress.

This problem was tackled by shape optimization with TOSCA. The area to be changed was restricted to the area around the fracture. A given surface derived from freedom of motion investigations was used as a growth restriction (see Fig. 3.1.3.). Design shrinkage was to be avoided in the less-stressed areas in order to minimize the changes on the given geometry. During optimization, each node of the design area could move as normal

Fig. 3.1.2: Position of the fracture in the intermediate stage of test and simulation

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Optimization of Castings and Forgings at AUDI AG (published in Simulation 2003-02)

Recalculation with Pro/Mechanica showed once again the difference between the initial geometry and the optimized design (see Fig. 3.1.4). The optimized geometry was transferred as a bevelled surface to a CAD system and the coupling link was adjusted accordingly. The improved coupling link successfully completed the stiffness tests and was assembled in the new A8. This simple example is typical for similar examples and uses that have the aim of reducing local notch stresses by changing the actual stress at the point of the stress. The standard achieved through stress reduction is approximately 15 % to 40 % depending on the type of component. A weight reduction can also occur when combined with shrinkage in geometry in the areas under low stress.

Fig. 3.1.3: Definition of the optimization area and the results of shape optimization

Fig. 3.1.4: Comparison of initial geometry and optimized coupling element

3.2 Shape optimization of the towing eye of the Audi A8 The towing attachment of an automobile lies in concealment, well hidden behind the screen and the disguised covering cup and where careful scrutiny is required to find the piece when needed. The technical standard of today is the screw-in towing eye made of high-quality, stabile steel forging (Fig. 3.2.1). This kind of eye can be screwed into the screw socket of the main chassis beam or onto the bumper bar and can be used either on the rear or the front of the car. When the vehicle is towed, enormous stress is put on the chassis via the towing eye. When using a tow bar, tensile and compressive stresses occur. As the loads occur lengthwise and at an angle, a great test spectrum is required (Fig. 3.2.2) to ensure that the chassis and the towing eye can carry the weight without any hint of deformation. The test loads are based on the total weight of the vehicle. The new Audi A8 is a vehicle designed with an Aluminium Space Frame (ASF), different screw lengths in the rear and front of the vehicle have been introduced as a new towing eye method that contains two threads (Patent Nr. 101 53 032.3-21).

Load directions 0°, +30°, -30° Tensile-compressive stress test 0°, +5°, -5° Load directions +70°, -70° Tensile stress test only – > a total of 24 load cases

Fig. 3.2.1: Example of a screw-in towing eye based upon the technical standards which are present today

Fig. 3.2.2: Test load cases

In this way it is possible to compensate for different screw lengths with the same towing eye. Figure 3.2.3 depicts this principle with a screwed-in eye in the front of a vehicle. The long cantilever is supported by a guide bushing. When towing a load from the rear, a shorter cantilever with a larger nominal diameter can be used with the previously designed second thread found at the front. A relatively long shaft remained that was under tensile, compressive and bending stress. The first FE analysis of the eye under a 30° inclined load clearly showed plastic deformation in the shaft. The relatively long eye shaft was really a problem area. In the stress analysis, the design suggestion showed a very red shaft having stresses of more than 30 % over the yield stress (Fig. 3.2.4). The steep gradient, clear to be seen in the forked area was a problem that could not be solved at this point in time to make this part a serial component.

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Optimization of Castings and Forgings at AUDI AG (published in Simulation 2003-02)

Fig. 3.2.3: Method depicting screw-in towing eye in the front of the vehicle

Fig. 3.2.4: Design suggestion of a towing eye with inclined compressive stress (stress illustration based on von Mises)

A new design of the shaft and fork was necessary that allowed the stresses of external loads to be distributed evenly over the whole geometry. Parallel, a stress reduction of about 30 % was necessary hand-in-hand with a minimum weight requirement for the part. There was little room for trial and error in the time needed to find a solution. A virtual design based on a numerical optimization system was the only choice at. The numerical optimization of the towing eye was the last step, however, of the simulation process. More important was the chassis design with these load cases. The FE model with the relevant components is shown in Fig. 3.2.5. Figure 3.2.6 illustrates the arrangements of these parts in the front of the vehicle. Stress analytical observations of components in a chassis are usually evaluated with ABAQUS because the boundary conditions are usually dominated by non-linearities. For example: material properties in regards to the register of possible local plastifications, mainly to guarantee a “leakage prior to fracture“ criterion of improper stresses, as well as contact non-linearities as in components of forcetransmission in order to depict the force flow line.

Fig. 3.2.5: FE model of the relevant parts

Fig. 3.2.6: Arrangement of components in the front of the vehicle

Using a tow load case as an example, the behaviour of the chassis was observed using an ideal eye in the form of a rigid beam element. In this phase, the working principle of the new towing eye was designed (Fig. 3.2.7 to 3.2.10) and the chassis was designed according to the demands of the tow load case. It was necessary to go away from method A of the standard eye to avoid the problem of local plastification in the area of force application. A new method, B, gave much stress relief to the critical area in the front but also resulted in an increased stress on the bolt connection in the main chassis beam (Fig. 3.2.10). The conformance of the bolt joint between the front longitudinal support and the connection on the demands of the tow test was carried out with the help of a detailed ABAQUS substructure model. The cutting load is determined in the complete model (Fig. 3.2.5) and used as boundary conditions on the sub model. The bolt stresses and the effect of friction and contact were tested and analysed in detail with this pure solid model (Fig. 3.2.11).

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Optimization of Castings and Forgings at AUDI AG (published in Simulation 2003-02)

Fig. 3.2.7: Method A, short towing eye under angled pressure load (illustrating the max. plastic strains)

Fig. 3.2.8: Method B, long towing eye under angled pressure load (illustrating max. plastic strains)

Fig. 3.2.9: Method A, short towing eye under angled tensile load (illustrating max. plastic strains)

Fig. 3.2.10: Method B, long towing eye under angled tensile load (illustrating max. plastic strains)

The slipping of the bolt joint (Fig. 3.2.12) could be stopped in the FE model by increasing the tightening torque and using a different sized bolt. As friction was a tricky subject in simulation and it was difficult to quantify the actual proportion of this, the main chassis beam and the bolt connection were verified in the testing of the components. In this way, the actual status and design suggestion were checked from the FE calculations. Confirmation of the calculation results strongly confirms the acceptance of the FE analysis with critical observation of the tester. Design of a suitable chassis brought great interest to the towing eye. A design suggestion was subjected to test loads in a simple model (Fig. 3.2.13).

Fig. 3.2.11: Substructure model of the bolt connection of the main chassis beam

Fig. 3.2.12: Simulation results for the bolt connection (Stress illustration based upon v.Mises theory)

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Optimization of Castings and Forgings at AUDI AG (published in Simulation 2003-02)

The model of the eye is made up of approximately 200,000 tetrahedrons of the sort C3D10. At the rear of the screw-in bolt thread a firm clamping was defined in the FE model. Support was determined using the space-fixed guide bushing with help of the contact boundary conditions with specified tolerance intervals between the towing eye and the guide bushing. The result of the basic analysis was positive as already described and shown in Fig. 3.2.4. The optimization system TOSCA supports the FE system ABAQUS and was chosen as the optimization solution of the weak eye shaft. As a geometrical draft which fulfilled all design specifications and constraints already existing, it was useful to work with TOSCA SHAPE and to leave Fig. 3.2.13: FE model of the towing eye start geometry for shape optimization using the design of the shaft and forked area to TOSCA SHAPE the optimizer. At first the optimization problem did not look too difficult, but more problems were seen as more detail was used as in the previous example with the boundary conditions. The cross-sectional area of the eye shaft was to have been in the shape of a circle. However, when a towing force was applied, a preferential direction appeared at each perimeter which lead to a more or less strong ellipticity. In order to avoid this undesired change in shape, synthetic handles were necessary. TOSCA offers the possibility of linking node groups with certain dependencies. In the case of the tow shaft, the dependency was that all nodes on the surface could only be moved in a certain direction in uniform and this was in a radial direction to the longitudinal axle. This constraint was made using the radial LINK SHAPES and the card GROUP AUTO DEF to be specified in the parameter FILE. To generate radial LINK SHAPES properly, it was necessary to place the nodes in the shaft area in a rotationally symmetrical arrangement (Fig. 3.2.14). The PARENT node group was defined along a line as shown in Fig. 3.2.14. Using this group, the GROUP AUTO DEF command could be generated which was responsible for a radial displacement of the single PARENT nodes along the longitudinal axle of the shaft area. Each node of the PARENT group was automatically delegated the respective circumferential node by the use of an automatic node capturing function and a tolerance specification in the command GROUP AUTO DEF. These ring segments received the same radial displacement in the course of the later optimization process. In this way, a rotational symmetrical cross-section could be achieved while maintaining a minimum volume at the same time. In addition to the shaft area which had the complex boundary conditions as just described, a second free shape design area was necessary for the forked area (Fig. 3.2.15).

Fig. 3.2.14: Shaft design area with complex boundary conditions

Fig. 3.2.15: Dividing the optimization model into two design areas

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Optimization of Castings and Forgings at AUDI AG (published in Simulation 2003-02)

The basic ABAQUS model was analysed in four STEP´s per computing run. Restricting it to the four major load cases was to help control the complete time needed for optimization with TOSCA. A modified INPUT deck was produced from each computing run which built the basis for the next optimization loop. The aim of the towing eye optimization for a stress reduction based on values lower than the yield point while at the same time having a minimum component weight, was concluded after approximately 17 iterations. The computing time took approximately 40 hours with restrictions on contact non-linearities and limiting the run to four load cases. The results clearly showed a changed geometry. The radius at the shaft end had changed from a circular shape to an ellipsoid (Fig. 3.2.16). The thickend shaft showed a constant degree of taper with a coordinated graduation that is similar to the branch of a tree (Fig. 3.2.17 and 3.2.18). The boundary between the design areas showed a messy graduation that was smoothed afterwards. The quality of the optimization results was dependant on the degree of mesh fineness. This can be clearly seen in the case of optimization of radial transition as in the rear of the shaft (Fig. 3.2.16 and 3.2.14). Compared with the basic edge length of about 1.5mm Fig. 3.2.16: Rear transition areas of the towing eye shown before and after shape the element edge length in the area of optimization (stress illustration based v.Mises theory) the radius is only about 0.5mm. In the v.MISES illustration it is clear to see how the stresses in the optimized component were evenly distributed over the fork and eye shaft (Fig. 3.2.19). Steep gradients as in the initial draft have completely disappeared. The newly designed towing eye geometry was then analysed in all load cases and proved to be useful, at least on screen. The geometry calculated with TOSCA SHAPE was transferred directly into CAD data after the transition from shaft to fork was lightly smoothed (Fig. 3.2.18) and has been used today as the serial solution in the new Audi A8 (Fig. 3.2.21). The resulting steel forging achieved from this optimization is depicted in Figure 3.2.20.

Fig. 3.2.17: Transition area between shaft and fork shown before and after shape optimization (stress illustration based on v.Mises theory)

Fig. 3.2.19: Comparison between initial geometry and results of shape optimization

Fig. 3.2.18: Forked area from shape optimization and transfer to manufactured component

Fig. 3.2.20: Towing eye of the Audi A8 based on the geometrical specifications and optimized with TOSCA SHAPE

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Optimization of Castings and Forgings at AUDI AG (published in Simulation 2003-02)

4. Summary The examples here clearly show that topology optimization is a very useful tool in the development process. Already in the conception phase of a project important information can be gained regarding the optimal use of a given design space. Furthermore, topology optimization aids in finding new solutions and increases the product quality for the following classical development process. Instead of having a “packaged“ design area, it is useful to use an existing structure as an initial model for optimization. The knowledge of an experienced designer is still necessary in order to use the design suggestion from topology optimization as a production-relevant and cost-efficient design. Shape optimization has established itself as an effective method in detail design. Local stress reduction of 30 % and more can be achieved and the optimized contours are free-form surfaces which approach tangential interweaving merging radii. Both methods have now been used by Audi as standard methods in the development of castings and forgings.

Fig. 3.2.21: The new Audi A8

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