**2. Research Background**

#### *2.1. Manufacturing Processes for Multi-Material Parts*

The hybridization of semi-finished parts is a widely discussed and promising topic for raising the performance of structural components. In order to create a composite of different metallic materials, different methods are researched and applied in the industrial environment.

In explosive welding, two plate-shaped workpieces are joined together by a controlled explosion. The workpieces are welded at the joint surfaces without heat input by applying an abrupt force caused by the pressure wave generated by the detonation of explosives, preferably without filler metal [31,32]. Another family of production processes that is used to create hybrid semi-finished materials is additive manufacturing [33]. Different from this is a relatively new approach that combines two different materials in laser powder bed fusion processes [34]. All of these approaches have in common that an inter-metallic joining zone between both materials occurs.

With the hybrid forging developed by the Leiber company, non-plate shaped semi-finished products of steel and aluminum alloys can also be joined together. This approach does not aim at an inter-metallic bonding of both materials [35]. In e.g., hybrid compound forging, this is different since a material joint is created using a soldering material [36].

In the CRC 1153 of Leibniz University Hannover, various process chains for the production of multi-material and formed solid components are being researched. The materials used are mainly aluminum (EN AW 6082) and steel alloys (20MnCr5, 41Cr4). The general process chain can be seen in Figure 1.

**Figure 1.** General tailored forming process chain, according to [2].

In the first step, a so-called hybrid semi-finished product is produced. Two mono-material semi-finished products are joined together by friction welding [37,38], ultrasonic-assisted laser beam welding [39], deposition welding [40] or composite rod extrusion (LACE (LACE = Lateral Angular Co-Extrusion) process) [41]. The hybrid semi-finished product is then shaped in a forming process. Here, cross wedge rolling [42], impact extrusion [43] and drop forging [40] are investigated. Both materials are formed during the process step and thus form an intermetallic compound. The process differs here, for example, from hybrid forging, in which the materials are not joined before forming and only one material is formed. In the end, heat treatment processes follow in order to be able to influence the component's mechanical properties [44] and the component is finished by machining [19]. The manufacturing process relevant for this article consists of the process steps friction welding, impact extrusion and machining. As the heat treatment processes only influence the component properties, but not the geometric shape, these are not considered.

Rotary friction welding is suitable for welding different materials that cannot be joined by other welding processes [45]. For friction welding of hybrid components, various investigations have been carried out in the CRC 1153 in which the strengths of steel–steel alloy combinations have been analyzed [46], also in comparison to US laser beam welding [45]. In addition, the strengths of steel–aluminum alloy combinations at different temperatures have been investigated [47]. Furthermore, it has been explored how different geometries (different cone angles in the semi-finished steel product), properties of the surfaces and temperatures also affect the strength of the composite [37].

Impact extrusion is a metal forming process in which a semi-finished workpiece is pressed through a die to obtain a product with a smaller cross-sectional area. These are differentiated according to the direction of material flow and the geometry of the formed product. The process used here is called forward rod extrusion [48]. In connection with extrusion, SFB 1153 has developed heating strategies for inhomogeneous heating, since the required forming temperature is different for each material. In addition, it is investigated how the shape and strength of the joining zone can be influenced by impact extrusion so that the strength of the composite is increased. The first concepts for impact extrusion and inhomogeneous heating by induction can be found in [2,49]. In Goldstein et al. 2017 the simulative results of heating are validated by experimental tests on steel–aluminum semi-finished products (20MnCr5, EN AW 6082) [48]. Based on these results, the joining zone geometries and properties of manufactured components are investigated in [18], which are then optimized in [43] by adjustments in the forming process. In addition, it has been shown that forming can improve the strength of the joining zone of components (41Cr4, C22.8) produced by US laser beam welding [50].

Besides pure shaping, machining is used to manipulate the properties of the surfaces of hybrid components [51,52]. However, these aspects are not ye<sup>t</sup> relevant for the current state of the CAEE. Behrens et al. 2019 illustrate the entire product development and manufacturing process from the

creation of the joining zone geometry, joining, forming and heat treatment to the finished machined component [11]. Figure 2 illustrates the manufacturing process.

**Figure 2.** Process chain for the production of a hybrid shaft by tailored forming [11].

#### *2.2. Computer-Aided Engineering Environments*

The development of technical products follows well-known process models that are either of a sequential or networked nature [53]. As an example, the process according to Pahl and Beitz divides the development process into four phases which are task clarification, concept determination, embodiment design and detailed design [54]. Another example is Suh's approach of Axiomatic Design where customer requirements are translated into functional requirements, design parameters and process variables for manufacturing [12]. The translation is achieved with design matrices and is thus strictly formalized [14]. Usually, the processes allow iterations and zig-zagging through the phases, as requirements are sharpened and new knowledge is created continuously while the design team converges the solution space against the final design [55].

In modern product development, independently from the process, the application of software tools for synthesis and analysis of design artefacts is state of the art for many disciplines [56]. Beside these, such computer-aided engineering environments (CAEE) comprise product data managemen<sup>t</sup> and collaboration support systems that allow for coordination of large teams as well as formalizing and communicating knowledge between all relevant stakeholders [15,57]. A very central tool for mechanical engineering is still the computer-aided design (CAD) system for defining e.g., product shape and production information [58,59]. Over time, these CAD systems have developed from tools for 2D line drawing to powerful parametric 3D design systems where a designer is able to modify his parts and assemblies simply by changing values of e.g., dimensions for lengths and adding or deleting features [60]. Hereby, it has to be considered that only a part of the product's characteristics may be modeled directly, like geometry, material, or surface quality. e.g., stress distribution is a resulting property that is influenced by the characteristics and thus modeled indirectly which leads to synthesis-analysis loops during development [61].

Two lines of development stand representative for the progress in CAEE implementation. First, knowledge-based engineering and design systems use formal, explicit knowledge that has been integrated into the according to synthesis and analysis systems [62–66]. As an example, knowledge-based CAD uses dimensioning formulae, design rules, spreadsheet integration and intelligent templates to automate routine design tasks [67,68]. Exemplary works from this line of development describe CAEE for fixture design [30,69,70], automotive and aircraft engineering [67,71] or mechanical and plant engineering [20,72–74]. In Sauthoff 2017, the automatic configuration and optimization of structural components from automotive engineering are proposed, integrating a knowledge-based design system and an evolutionary optimization algorithm [75]. All of these works have in common that a more or less closed solution space of predetermined designs is modeled. The resulting artefact description is usually of high quality and corresponds to detailed design.

As the second line of development, computational design synthesis systems rely on a more informal and implicit formulation of knowledge in order to design an artefact [59]. Their aim is more to capture the laws-of-creation of how a design artefact is developed. The consequence is that computational design systems commonly deliver more abstract artefact descriptions which have to be reengineered e.g. into parametric CAD [76]. An example of this is 3D topology optimization that considers manufacturing restrictions [6]. Other works from this line include the synthesis of additively manufactured parts using object-oriented programming, CAD and parametric optimization [21] or the design and optimization of mechanical engineering parts using CAD and multi-agent systems [27].

#### **3. Computer-Aided Engineering Environment for Tailored Forming Parts**

In order to design a tailored forming part, both lines of development make a contribution. The determination of the material distribution is more subject to computational design synthesis as laws-of-creation, therefore, may be formulated, independently from distinct geometry. Especially the design of the joining zone necessitates a formal representation that considers the restrictions of the later manufacturing processes precisely. Thus we propose a CAEE that uses both approaches for the respecting phases of the development of tailored forming parts.

The basic structure of the CAEE is shown in Figure 3. It essentially consists of four different areas. Three of the areas represent the product development process and provide tools for potential determination (1), for the creation of the rough design (2), and for the generation of the embodiment design or elaboration (3). The fourth area is the knowledge base (4), in which the expertise required for development is stored. The focus of this paper is on the areas (2), (3) and partly (4). Further information on area (1) can be found in [5,77] and is not part of this paper.

Opmized Tailored Forming component

**Figure 3.** Structure of the computer-aided engineering environment (CAEE) for tailored forming.

#### *3.1. Rough Design by Interfacial Zone Evolutionary Optimization*

The Interfacial Zone Evolutionary Optimization (IZEO), developed in [78], is a method able to deal with the specific challenges of the present study since it can solve general multi-material problems that have the presence of strong manufacturing restrictions. As recommended in [79], taking these restrictions into account in an early phase of the design process avoids the loss of the optimized properties when these are applied later.

The working principle of IZEO can be visualized in Figure 4. This method is based on evolutionary optimization algorithms, such as the Bidirectional Evolutionary Structure Optimization (BESO) [80], where the domain is discretized into elements and the material of the elements are changed iteratively, following a sensitivity function. The primary difference in IZEO is how these changes occur, which is limited to the interfacial zone between the different materials.

**Figure 4.** Model representation of the interfacial evolutionary process [81].

This strategy allows the implementation of a variety of manufacturing restrictions [81]. Following the theory proposed in [79], each manufacturing technique can be modeled as a combination of geometric constraints, as shown in Figure 5. IZEO follows the same principle, allowing the designer to apply different constraints at the same time.

**Figure 5.** Relationship between geometric constraints and manufacturing techniques [79].

The constraints shown in Figure 5 can be also serialized in the simulation, which works as a prioritization from the first one applied until the last one. This is in accordance with typical manufacturing process-chains, where many restrictions are applied in different stages of the process. For multi-material processes, this also allows different constraints for the connections between the materials and the component body. This way, with the inclusion of all necessary geometric constraints, a general approach can be implemented to attend to the specific challenges inherent to a manufacturing process and generate optimized conceptual designs.

In the current study, the implementation of IZEO was extended for a 3D environment, differently from previous works. This was implemented in the FE-software Abaqus, using its scripting capabilities in Python. Therefore, the full IZEO program was implemented with Python, using the solving capabilities of the FE-software. In this case, the implementation of the manufacturing restrictions described in [81] was made following the same concepts, but considering the third dimension and a higher degree-of-freedom to control them. Table 1 presents the implemented geometric constraints and the respective control parameters.



It can be observed that with the inclusion of the control parameters, the implementation of geometric constraints adds new degrees of freedom to the generation of optimized solutions. Naturally, these restrictions will be selected according to the chosen manufacturing process. Ideally, the optimization should be performed several times with a variation of these constraints, in order to find the most suitable geometry and manufacturing process at the same time. In this case, not only the control parameters (radius, points and vectors), would be varied, but also different combinations of the constraints, simulating different process chains. Since the current study is focused on tailored forming, only the constraints related to the proposed process are here investigated.

#### *3.2. Detailed Design Using the Generative Parametric Design Approach*

A CAD-centric KBE environment was proposed by Sauthoff for the automatic configuration and optimization of structural components in mechanical engineering [75]. It combines a CAD modeling strategy called generative parametric design approach (GDPA) with knowledge integration and an evolutionary optimization algorithm. In order to achieve the necessary flexibility, the CAD model of a structural component is divided into several design zones which are linked by a common skeleton (Figure 6a). For each design zone, independent CAD models are implemented as so-called design elements that reflect parts of the structural component and may be understood as generic parametric templates (Figure 6b). In such a design element, all relevant design knowledge, like dimensioning, design rules or manufacturing restrictions, are stored [65]. The top-level assembly of the component is implemented in such a way that adjacent design zones communicate with each other and exchange interface parameters. The design elements can be replaced with other design elements that are also approved for the design zone, as required. When now a control parameter of the skeleton or general requirements for the structural component change, this is propagated through all design elements that check themselves for consistency, technical correctness and violation of restrictions. The result is that highly flexible models are created which can be rebuilt without errors even after topological

changes [82]. If a sufficient library of generic and task-specific design elements exists, a large solution space of structural components like vehicle chassis or bodies, is available [83].

**Figure 6.** Generative parametric design approach (GPDA) model of a connection rod: (**a**) skeleton and interfaces, (**b**) computer-aided design (CAD) model, according to [84].

Due to the flexible model structure, it is possible to optimize the shape of the GPDA models in automated synthesis-analysis loops. According to Sauthoff, the CAD system is coupled with an FE system via an optimization program, the so-called Opti-Toolbox. The Opti-Toolbox generates several component variants on the basis of e.g., evolutionary algorithms by automatically adjusting the parameters in the GPDA model and exchanging design elements. These are then analyzed in the FE system and the results are evaluated by the Opti-Toolbox. If the requirements are not met, further component variants are generated. This loop is repeated until the requirements are met [75]. Figure 7 shows the schematic structure of the GPDA engineering environment.

**Figure 7.** Schematic structure of the GPDA engineering Environment [83].

#### **4. Implementation for Shaft-Like Tailored Forming Parts**

A hybrid demonstrator shaft developed in CRC 1153 is used as an application example. The shaft is manufactured by the above-described manufacturing processes of friction welding, impact extrusion and machining. The material combination under consideration and 41Cr4 and EN AW-6082, whose properties are given in Table 2. The objective function is to generate a component that is as light as possible with sufficient strength.


**Table 2.** Material properties.

Figure 8 shows the load and boundary conditions considered in this example. Furthermore, the represented geometry describes the boundaries of the domain in which the optimization is allowed to take place. The absolute values for force and torque were set to generate a global safety factor of 1 when the shaft is completely made of steel and the proportion between them was set to generate 15% of maximal stress through the bending and the rest through the torsion.

**Figure 8.** Domain with load and boundary conditions of the shaft for the 3D optimization.

#### *4.1. Expansion of Geometric Constraints*

With the geometric constraints described in Table 1 and the idea of a combination of constraints from Figure 5, a grea<sup>t</sup> variety of processes can already be simulated. However, for the current application, two constraints were added: rotational symmetry and radial growth.

Rotational symmetry is self-explained, being related to components that are subjected to processes such as rolling or turning. Two control parameters are necessary: initial and final coordinates of the symmetry line. In the case of multi-materials, this constraint can be applied not only to the component body as a whole, but also separately to the connection between the two materials. IZEO allows these possible configurations, as presented in Figure 9. This restriction was implemented using the same principle of planar symmetry presented in [81], where the sensitivity of all elements present in the rotational curve are averaged.

**Figure 9.** Rotational symmetry applied to: (**a**) joining zone only; (**b**) component body only; (**c**) both joining zone and component body.

Radial growth is a special constraint present in tailored forming. In the manufacturing of rotational symmetric components, the possible processes do not allow the presence of the softer material inside the harder material. Due to thermal properties, the harder material always flows inside the softer material. This translates to the optimization method as a special type of "unidirectional growth" constraint, where the direction is not linear, but radial coming from outside, similar to what is seen

in a turning machine (Figure 10). Therefore, the same as rotational symmetry, the initial and final coordinates of the center-line are required as control parameters.

**Figure 10.** Rotational symmetric components with joining zone constrained by: (**a**) radial growth only; (**b**) radial and unidirectional growth.

This radial growth is not only important because of the thermal effects of the multi-material connection, but it also describes the main restriction involved in the manufacture of shafts during turning in a mono-material approach.

#### *4.2. IZEO and Robust Design for Tailored Forming*

The model described was submitted to IZEO with the following constraints: minimum member size (3 mm), unidirectional growth (same direction of the aluminum in the friction welding), rotational symmetry and radial growth (aligned to the axis of the shaft). Since the outer geometry of the shaft should remain unchangeable and the addition of aluminum will tend to reduce the strength of the shaft, it was set as the objective function a safety factor of 50% the value for a shaft made entirely of steel. The last interactions are presented in Figure 11.

During implementation, it became clear that design and manufacturing process development need to be aligned towards a common objective. The information exchange between the two fields is commonly of a sequential nature. Thus, an additional information exchange platform for continuous improvement was created to prevent from losing the knowledge acquired in past interactions.

For that purpose, the use of Knowledge-Based Engineering (KBE) tools are necessary for the creation of this common interface between design and manufacturing processes, and for the operationalization of both, as proposed in [85]. Therefore, an adaptation of a case-based reasoning (CBR) cycle was proposed, where the decision-making process is supported by a unified information managemen<sup>t</sup> system. This method makes use of parametric models to analyze the information generated on both sides, compare them and sugges<sup>t</sup> innovative design solutions based on new specifications and previous experiences. The topology optimization result will serve as the first input in the construction of this parametric model. Thereby, both design and manufacturing research can be performed in parallel, exchanging information in a continuous way and enhancing the system with its use.

**Figure 11.** Optimization evolution for the tailored forming shaft model with IZEO.

With the results obtained with IZEO, a parametric model of the joining zone was constructed for the submission in the adapted CBR. With different parametric models and parameters, a large number of variations were simulated. Figure 12 shows a graph where the two objectives are set at both axes and every variation is represented as a point in the space. A Pareto front of optimal solutions can be easily recognized, where the simulations close to this curve are considered optimal solutions.

**Figure 12.** Plot of every parametric simulation over safety factor and weight, where a Pareto front is observed.

With the completion of the CBR cycle, the best candidates for manufacturing can be selected and submitted to the process chain of tailored forming. In this way, the process learns on every cycle while more optimized solutions are being generated.

For validation purposes, various joining zone geometries were examined in test bench trials, e.g., on the torsion test bench, and compared with the simulation results. Subsequently, the parameters were adjusted so that the simulation provides an adequate representation of the manufactured components [6].

## *4.3. Intermediate Results*

The comparison with a mono-material shaft cannot be straightforward executed, since multi-materials are intrinsically connected to more requirements, but it serves to show the potential of the technology for lightweight. This potential, however, is also connected to some of the geometric restrictions imposed, such as the allowable size of the component. Figure 13 makes a

comparison between the multi-material design achieved and an equivalent mono-material shaft with the same requirements for strength and wear, considering a life-span of 1 billion cycles.

**Figure 13.** Shaft design for same requirements, where a reduction of 11% in weight is seen for the multi-material shaft (**a**) in comparison to the mono-material one (**b**).

#### *4.4. GPDA for Tailored Forming*

In the GPDA implementation for tailored forming, the design elements are carriers of the knowledge that gives the design its shape. In addition, a design catalog [86,87] of the CAEE controls the GPDA models and serves as a superordinate knowledge base. Depending on the application and load case, the knowledge in the catalog determines which skeleton and which design elements should form the basis for the development of the tailored forming component. The more knowledge is available in concrete form, the better the selected starting point and the lower the effort required for subsequent optimization. The design catalog does not consist of a single catalog, but of a general main catalog that refers to concrete detail catalogs. The connection of the catalogs is shown in Figure 14.

**Figure 14.** Structure of design catalogs.

Different component types and the corresponding general application and load cases are defined in the main catalog. It shows how a tailored forming implementation for conventional mono-material parts can look like, e.g., by showing the general material distribution according to IZEO. The main catalog also provides the skeleton and thus the basic structure for the GPDA model. For each case in the main catalog, there is a detailed catalog in which concrete characteristics are derived from the general case. Here, concrete values have been assigned to the parameters that describe the load cases

and geometry characteristics. In addition, the resulting and relevant component properties such as max. deformation or stress are also stored.

The structure of the GPDA model of the shaft is shown in Figure 15 The skeleton consists of an axis on which the interface geometries are defined. Along the axis, there is a design zone between the interfaces in which the design elements are attached. The design elements are defined in such a way that they represent exactly one shaft step. The leading diameter of each design element is defined by the interface geometry of the skeleton.

**Figure 15.** Skeleton (**a**) and CAD model (**b**) of tailored foming shafts.

The design elements contain the concrete knowledge of geometry and take into account the manufacturing restrictions and design guidelines. Figure 16 shows, for example, how the relief grooves required on a shaft are implemented in the model. The dimensions of the relief grooves depend directly on the leading diameter of the shaft shoulder and are described according to DIN 509 in Table 3 [88]. Furthermore, the shape of the relief grooves can vary depending on the application. In the case of a relief groove of type F, the definition goes beyond the limits of the design element, so that the geometry in the adjacent element must adapt accordingly. For this case, parameters are already stored in the adjacent design element, which are then filled accordingly via the skeleton. These parameters are suppressed for relief grooves of the type E that do not extend beyond the design zone.

**Table 3.** Relief groove parameters for shafts according to DIN 509 [88].


**Figure 16.** Parameters for a relief groove (type F) that extends over two design elements (DE1 and DE2).

*4.5. Application Example of the GPDA: Model Adaptation in Case of Changes in Boundary Conditions*

In the GPDA a load case of the shaft is considered as an example, where *F* = 5.5 kN and *T* = 40 Nm. For this load case, the joining zone position from the results of IZEO (Figure 11, result 5) and the shape from the results of CBR are used. In the GPDA model, the joining zone position is the distance from the left shaft end to the center of the joining zone area (*P* = 73 mm; Figure 17a). As can be seen in Figure 17b, the v. Mises stress does not exceed the yield strength of 280 MPa of the aluminum alloy in the relief groove under consideration, with an assumed safety factor of 1.

**Figure 17.** (**a**) Joining zone position and (**b**) resulting v. Mises stresses (max. 278.9 *Nmm*2 ) at *F* = 5.5 kN and *T* = 40 Nm.

If the force is increased at a constant torsional moment, the yield strength is exceeded. Figure 18 shows the case at *F* = 8 kN. To reduce the stresses, the position or geometry of the joining zone must now be adjusted. It is not possible to increase the diameter of the shaft on which the relief groove lies, because the bearing size is determined by the external connection dimensions.

**Figure 18.** Exceeded yield strength (max. 363.07 *N mm*<sup>2</sup> ) at a joining zone position of *P* = 73 mm at *F* = 8 kN and *T* = 40 Nm.

Therefore, the position of the joining zone is shifted 10 mm to the right to *P* = 83 mm in the following. The yield strength of the aluminum alloy is no longer exceeded in the undercut. Figure 19 shows the new joining zone position (a) and the resulting stresses (b).

**Figure 19.** (**a**) Joining zone position (**b**) and resulting stresses (max. 375.39 *N mm*<sup>2</sup> ) at *F* = 8 kN and *T* = 40Nm.

Table 4 summarizes the individual results. By increasing the proportion of steel alloy in the component, the weight of the shaft increases from 245.61 g to 264.05 g.

**Table 4.** v. Mises Stress in the relief groove at different forces.


In this case that the GPDA offers the possibility to move the joining zone over the boundaries of the individual design elements. This increases the proportion of steel and reduces the stresses in the undercut of the aluminum area. Because the model is designed according to the approach of the GPDA, it can be used to develop similar shafts that are exposed to similar load cases. Due to the flexible structure, which is based on the use of the design elements, parametric and topological changes can be made without much effort if they are necessary for another load case under different boundary conditions. The test bench trials required for validation are still pending.
