Uncoupling Development Time from the Size of a Library of AM Parts Through Complexity Reduction and Modeling of Topology Optimization Results

Abstract

Additive manufacturing (AM) framework enables the customization of geometries regardless of the number of parts to manufacture. Hence, the right product can be provided to the right customer. However, traditional optimization methods, used to improve performance and mass, are usually non-parametric. Therefore, the process flow shall be repeated even if all parts in a library display similar functions and overall geometry. As such, the relation between development time and the number of parts to design is linear. Hence, one cannot afford to generate large libraries using these approaches.

In this paper, we propose an alternative solution for structural design, inspired by Knowledge Based Engineering. First, topology optimization is used to emulate a prior knowledge of optimal geometry. As this result is nonparametric, it is approximated using low complexity elements such as shells and beams. Then, batch optimization is run to model the optimal geometry in function of the load case. Finally, the ready to print part is reconstructed using traditional parametric CAD software.

We benchmarked our methodology with the Design for AM (DfAM) of a library of chassis components. Thanks to the selective complexity reduction, the computation time is reduced significantly compared to traditional approaches. Furthermore, the parametrization of the part and the modeling of its behavior rationalize the design of families of parts. Indeed, most activities are only executed once.

In this manner, our methodology uncouples the development time from the number of load cases allowing to design for AM entire libraries of similar part.

1 Introduction

The development of Additive Manufacturing (AM) has opened the door to a new design freedom: its layered approach enables the manufacturing of intricate and freeform parts without increasing the manufacturing complexity and cost [1]. This revolution has led to the emergence of new design tools such as topology optimization (TO) [2]. These tools are quite efficient to generate complex structural parts, impossible to manufacture before [3]. However, the process to transform optimization results into a ready to print geometry is tedious and time-consuming. Furthermore, this final geometry is nonparametric. Hence, it leads to a linear relation between development time and the number of parts to design. In this context, one cannot afford to generate large libraries using these approaches.

In this paper, we propose an alternative methodology¹ aiming to decouple the development time from the number of designs in a product library². We focus on libraries where parts perform the same function, but where the load-cases vary or where each part fosters different performances. Even if we focus on structural applications in this paper, these foundations and concepts can be applied to other domains of engineering.

The novelty of this methodology does not lie in the tools used but comes from a selective reduction of complexity. We use the raw results of topology optimization to build a representative reduced model using shell and beam elements. Then a batch optimization is set up to model the optimal design parameters within the product family. Finally, traditional CAD software are used to reconstruct the parametrized part which includes all required manufacturing features.

To illustrate our demarch, we apply our methodology to the Design for AM of a library of chassis components for the automotive industry.

2 Context and Use-Case Description

MANUELA, Additive Manufacturing using Metal Pilot Line, is an European Union’s Horizon 2020 Research and Innovation Program (grant Agreement no. 820774) [5]. It aims to benchmark and promote AM in Europe. In the context of series production, this is almost impossible to compare the capabilities and cost of AM with traditional manufacturing technologies. Indeed, processes, design methodologies and logistics have been built on traditional manufacturing specificities. Hence, a consortium of AM experts has been gathered to rethink and implement an AM optimized development cycle, from design to manufacturing, including validations.

The automotive industry is incredibly competitive. This degree of competition pushes manufacturers to streamline manufacturing processes. As such, small series often share common components to save on the cost of molds. This results in parts being oversized for most. As such, Renault Trucks investigates AM as an alternative to casting. Indeed, even for low volumes, AM allows to customize parts on clients’ demand and thus rationalizes vehicles’ weight, CO2 emissions and resource consumptions. MANUELA’s business use-case PARCO aims to design a series of customized truck’s spring anchorage. The design shall not only be conducted for one specific truck, but for an entire range of vehicles. The actual line of trucks has four payload capacities and five structural interfaces (same size and position but different thickness of the chassis). Therefore, a total of twenty load cases shall be considered. The time allocated to this project does not allow us to design these parts separately. Hence, we developed this methodology to tackle this restriction.

3 Design Process Methodology

Knowledge-Based Engineering (KBE) is a research topic which focusses on the structure of algorithms/processes to capture design intent and automatizes ill-structured processes using heuristics [6, 7]. These design rules are built on prior experience in solving a particular problem [8].

Our approach, inspired by KBE approach is composed on five main concepts: identification, interpretation, batch optimization, modeling, and reconstruction (see Fig. 1). The following chapters present each of these steps. In parallel, we illustrate our approach with the PARCO use-case.

Fig. 1.

Flow chart of the proposed methodology. Highlights of the five main concepts: identification, interpretation, batch optimization, modeling, and reconstruction. Illustration with the PARCO use case.

3.1 Identification: Initial Guess on Geometry

The first step of this methodology aims to propose an initial guess on the geometry. Such activity lays into the category of “creative design” based on the taxonomy of Sriram and al [9]. This is one of the most complicated classes of KBE problems which by construction need experience.

We propose to use topology optimization to provide the optimal material distribution within a structural part. This result can then be used to emulate a prior knowledge of the optimal structural architecture. Note that this step can be skipped if this knowledge is already available.

Topology optimization is a constrained optimization method which distributes material within a design space (Solid Isotropic Material with Penalization method [2]). Its most common formulation minimizes the overall compliance while keeping the mean density under a user-provided value. The density, $\eta \in [{\eta }_{min},1]$ attributed to each FEM elements alters locally the stiffness, through the Young modulus, (SIMP model of degree $n$: $E\left(\eta \right)={E}_{0}\cdot {\eta }^{n}$) and the material density (linear model: $\rho \left(\eta \right)={\rho }_{0}\cdot \eta$).

$$\underset{\eta }{\mathrm{min}}\left\{{U}^{T}\cdot K\left(\eta \right)\cdot U\right\} , s.t. \left\{\begin{array}{c}\overline{\eta }<{\overline{\eta }}_{obj}\\ K\left(\eta \right)\cdot U=F\\ 0<{\eta }_{min}<{\eta }_{i}<1\end{array}\right.$$

(1)

Where, $U$ and $K$ is the generalized displacement and stiffness matrices, respectively. $\overline{\eta }$ is the integral of the design density ($\eta$), it allows to constrain the amount of material distributed by the algorithm (the user provides this limit through ${\overline{\eta }}_{obj}$).

In our methodology, the whole available envelope must be considered as design space. If important interfaces are identified, (e.g., screws wall, important surface of contact) these regions can be defined as non-design space where the density, $\eta$, will be kept at 1 by the optimizer.

Since topology optimization used a gradient-based approach, the number of elements have a major impact on the computation time. At that stage, we are only seeking a guess on geometry. Hence, to stay coherent with the philosophy of this methodology, a relatively coarse mesh can be used.

The selection of the load case has a significant impact on the solution: it drives the topology optimization. Two approaches can be considered: median or extreme load cases. We recommend using the median values which leads, intuitively, to an overall lower mass (in term of 2-norm on the whole library). However, if the stress level is critical, for the highest load cases, choosing extreme values may be more relevant.

In PARCO, we used the formulation proposed in Eq. 1. We selected an objective volume fraction, ${\overline{\eta }}_{obj}$, of 0.3 and a median load case. Furthermore, PARCO’s requirements impose a minimum stiffness. Therefore, we added a total of 6 constraints on the displacement of the interface with the spring shackle. Note that we do not consider manufacturing constraints during the topology optimization. Indeed, it may complexify the model simplification in the next step. The design space used in PARCO and the TO raw results are presented in Fig. 2.

Fig. 2.

Design space, and result of the topology optimization for the median load case of PARCO.

3.2 Interpretation and Simplification of the Initial Guess

Traditional AM design methodologies use smoothing or polyNURBS approximation to interpret the result of TO. Such solutions are usually not parametrizable. Hence, this single solution cannot be adapted to withstand other load cases. The second step of our methodology bypasses this limitation. The main objective is to reduce our problem complexity to mainstream and accelerate parametric analysis. In the context of structural design, shells and beams can often approximate the result of TO. Furthermore, such low-dimensional elements highlight possible design parameters through shells and beams thicknesses.

In the use-case PARCO, we indeed used only shells and beams (see Fig. 3). In Solidworks, we generate the shells manually from the initial envelope used for the TO of step 1. Then, we import and mesh these surfaces in Altair Hypermesh. A beam element is added to mimic TO results (represented as a blue line in Fig. 3). We group these elements into 5 components whose properties will drive shells’ and beams’ thicknesses during the next step.

If we decided to put aside manufacturing constraints before, we deem relevant to consider them during the simplification process. Printing orientation shall be defined, and manufacturing features must be identified. For example, the shape of most surfaces has been adapted to allow a supportless printing of PARCO. However, one shell was perpendicular to the building plate and required the integration of non-sacrificial supports. Since the impact of these structures has been considered negligible on the operational performance, we decided to not implement them yet to keep the model as simple as possible.

Fig. 3.

Illustration of our interpretation of the TO results using shell and beam elements.

3.3 Batch Analysis on Simplified Model

The third step generates the data required to model the system. We introduced design parameters in the previous section. If a batch optimization can be built on design parameters presented in the previous section, we think this highly inefficient in the context of product design. Instead, the designs generation can be formulated as a finite number of optimization where design parameters are the optimization variables. We introduce “external parameters” to differentiate elements in the batch. The interpretation of these external parameters depends on the objective of the design family. We identified four potential interpretations of external parameters based on the objective of the library (this list is not exhaustive). The Fig. 4 presents a decision flow chart to identify the adequate interpretation.

Fig. 4.

Flow chart to identify batch construction scheme (interpretation of external parameters) based on the objective of the series.

• 1. One performance shall be optimized (typ. Mass) for a range of load cases. In that configuration, the load cases are parametrized through the external parameters. The objective of the batch analysis is then to find an optimal set of design parameters for each load case.

• 2. Multiple performances shall be optimized for a range of load cases, and their relative importance is known. This problem can be reduced to case 1 using the derived cost function defined as the weighted sum of all performances.

• 3. Multiple performances shall be optimized for a single load case, but their relative importance (weights) is unknown. In that case, it is not possible to identify an optimal solution as in the first two approaches. Indeed, improving one performance will have a negative effect on the others. In multi-objective optimization, this is the definition of the Pareto front: no solution is dominated by another. The objective of the batch is thus to find the Pareto front and identify its corresponding design parameters. The simplest solution is to reduce the problem to a simple optimization under constraints: if we have $m$ different performances to optimize, we create $m-1$ external parameters. These external parameters are then used to set equality constraints on $m-1$ parameters while the last one is being optimized. For a model with $n$ design parameters, the multi-objective is optimization is thus simplified into:

  $$\underset{{p}_{\mathit{design}}}{\mathrm{min}}\left\{per{f}_{1}\right\} ,\mathrm{ s}.\mathrm{t}. \left\{\begin{array}{c}{lb}_{i}<{p}_{design, i}<u{b}_{i}, i=1, \dots ,n\\ {p}_{external, j}={\lambda }_{j}, j=2,\dots , m\\ \dots \end{array}\right.$$

  (2)

  Where, $l{b}_{i}$ and $u{b}_{i}$ are respectively the lower and upper bounds of the i-th design parameter. In this formulation, the set $\langle {\lambda }_{1} ,\dots , {\lambda }_{m-1}\rangle$ varies for each instance of the series.

• 4. Multiple performances shall be optimized for a range of load cases, but their relative importance is unknown. In that case, the objective of the batch is to find the Pareto front for each load case. Therefore, we first apply approach three to reduce the multi-objectives optimization problem and use this formulation as input of the first approach. It leads to a total of $m+k-1$ external parameters, where $k$ is the number of parameters required to control the use cases.

In all approaches, the batch is thus a succession of simple optimizations under constraints. Each run represents one specific combination of external parameters. If the behavior of the system’s is a priori known, we recommend reducing the number of combinations using a design of experiment approach. However, if this information is unknown – as it is often the case - a full box evaluation will lead to a batch’s size of:

$${len}_{batch}=\prod_{i=1}^{n}{k}_{i}$$

(3)

Where, ${k}_{i}$ is the number evaluation of the i-th external parameter, and $n$ the number of external parameters.

Note that additional probes can be defined to constrain the optimization. They can be any output of the FE simulation such as displacements of important nodes, maximum stress, or strain. It does not increase the size of the batch but may influence the optimization time.

In PARCO, our design problem lays in the first scenario. Therefore, we define two external parameters: the first to parametrize the front axle load of the truck (loads’ magnitude) and the second to control the thickness of the chassis (which is interfaced in the model). Then, we identify eight outputs: six displacement/rotation of the interface with the spring shackle, the maximum stress, and the total mass. Limits on compliance and safety factor are given by the requirements of the part. Therefore, we minimize the mass while keeping both displacements/rotations and maximum stress below the imposed limits.

We implemented this batch using the in-build module of Altair HyperStudy and limited the number of iterations of the optimizer to fifty. We run a full box on four truck weight and five chassis thickness. The result of this batch simulation is thus a list of twenty sets of optimal design parameters and their corresponding masses (one for each external parameters couple).

3.4 Modeling

The fourth step aims to model the relation between design and external parameters. Given the external parameters, the model shall provide the corresponding optimal design parameters. This modeling step reduces the number of simulations required. Indeed, for any intermediate load cases, optimal design parameters can then be extrapolated.

The selection of the adequate model shall be based on both the evolution of the parameters and their interactions. Therefore, we invite the reader to identify the best identification or approximation method for her/his application.

In PARCO, the need for modeling is limited: the sizes of trucks are normalized, and we evaluated all combinations during the batch optimization. Therefore, all optimal parameters are already known. However, we can use any approximation approach to model the optimal shell thicknesses in function of external parameters (see Fig. 5). Hence, if a new truck is being developed or if the chassis thickness varies, optimal designs can be extrapolated without the need of further computation.

Fig. 5.

Global (left) and local (right) cubic approximation of the optimal back skin thickness (cyan surface in Fig. 3) in function of truck’s front axle load (FAL) and chassis thickness (interface). All values have been normalized to protect intellectual property.

3.5 Reconstruction

The last step of this method is the reconstruction and parametrization of the geometry. As mentioned earlier, usual AM workflows reconstruct the geometry (e.g., solution of the topology optimization) using polyNURBS surfaces. However, free-shape geometries cannot be parametrized in general. Thus, we propose to come back to more traditional CAD approaches where design parameters can be used as input of the construction. The interpretation step already provides the skeleton of the geometry: the surfaces used for the batch processing can easily be extruded. The length of the extrusion is provided by the model generated during step 4.

Manufacturing features such as non-sacrificial supports or reference surfaces can be integrated at that stage. In general, such structure will have only limited impact on the stress distribution in the part. However, we propose to validate the final design – at least one in the library– through traditional FE analysis.

A total of four modifications/features have been introduced in PARCO (see Fig. 6):

• 1. The beam has been replaced by a shell to facilitate manufacturing and improve symmetry.

• 2. A thin structure has been used as a non-sacrificial support for the central shell.

• 3. A total of four reference surfaces have been added to clamp the part during post-machining operations.

• 4. The back shell has been opened – where stress was minimum – to prevent issues during part’s removal from the build plate.

Fig. 6.

Reconstruction of the geometry based on the shell representation of the optimized part. Additional features have been introduced to ensure support-less manufacturing and rationalize post-manufacturing operations.

4 Results and Discussions

4.1 PARCO Library Performances

As mentioned in Sect. 2, the main objective of PARCO was to investigate if AM can be used as an alternative to traditional manufacturing for serial demand.

The first interesting consideration is the print-on demand capability of AM. Indeed, we mentioned that trucks often share standard parts which are thus oversized for the smallest vehicles in the range. With no need for expensive molds, AM can thus offer a great alternative to customize such small series. Our methodology enables users to foster the full customization potential of AM. Indeed, it provides a design framework to customize a whole family of parts with almost no additional effort, nor time.

In the PARCO use-case, we optimized the mass of a family of spring anchorage while keeping their stiffness and yield safety factor within admissible bounds. We were able to reduce the mass by approximately 40% for the whole library. As an example, the printed demonstrator shown in Fig. 8, (optimized for a low front axial load and an intermediate interface thickness) weights 6.25 kg while its casted counterpart was above 10.5 kg.

It is important to notice that the design freedom is not the only leverage we used to reach these performances. Indeed, we tend to forget that the range of material available is dictated by the manufacturing processes. During PARCO, we used the EOS 20MnCr5 powder. This alloy displays a higher yield strength than usual cast steels. Hence, the walls can be thinner – leading to a higher stress in the part – without negative impact on factors of safety.

We shared the performances of our final library in Fig. 7.

4.2 Development Time

The mechanical performances of our methodology cannot be benchmarked with our use-case PARCO, the material properties of AM and cast alloys being too different. In any case, our methodology is not exclusive to one optimization scheme – which dictates the outcome –, thus, it would be pointless to compare the results. However, our methodology stands out from traditional approaches because it uncouples the development time from the number of – similar – parts to design. This behavior is achieved through two main strategies: the minimization of computation’s impact on the development time and the extrapolation of new solutions.

The model simplification step drastically reduces the computation time. Indeed, we estimated that direct implementation of TO would take multiple hours for each load case (in the case of PARCO). Using our simplified model, the optimization takes at most 8.5 min (maximum 50 evaluations and evaluation’s duration <10 s). To optimize the full box (20 external parameters sets) of PARCO, the actual elapsed time did not exceed 1.75 h. As such, the time spent running the analysis becomes almost negligible with respect to other tasks, such as the setup of the model or the parametric reconstruction.

Furthermore, we decided to optimize the full box. However, most behaviors in structural mechanics are smooth (at least C3 continuous). It is therefore possible to extrapolate the design parameters of the entire library from a limited number of solutions. Design of experiment can be used to define the optimal batch size: in our use-case, only nine load cases would have been enough to capture the quadratic behavior of design parameters. Hence, the performance of our methodology revolves around its modeling step.

Fig. 7.

Performances for the optimized bracket family in function of truck’s front axle load (FAL) and chassis thickness (interface): mass [kg] (top), normalized displacement of the spring interfaced [-] (bottom left) and yield safety factor [-] (bottom right).

In algorithm analysis, the complexity is given as the order of magnitude of the number of operations required in the worst-case scenario (in function of the number of input’s size). Following this definition, the combination of these strategies allows us to reach an almost constant complexity with respect to the final number of parts in the library. Indeed, most operations are only performed once, and the length of batch analysis can be uncorrelated from the library thanks to the modeling step. We estimated that using our methodology, increasing the series size from 5 to 20 will only lead to a 7% increase in term of development time (see Table 1).

4.3 Limitations

This methodology has been developed based on two fundamental assumptions: the design space is the same and the overall optimal geometry is similar for the whole design family. If the first condition is not verified, this method cannot be implemented as is. In the best-case scenario, the interfaces are the same and the method (applied to the smallest envelope) will provide poor solutions for the larger envelopes: the stiffness (second moment of inertia) varies with the cube of the distance from neutral axis. In the worst case, where the interfaces are different, alternative strategies (such as scaling and parametric meshing) shall be implemented. The second condition is less critical. Indeed, this methodology provides feasible but sub-optimal solutions. Note that any non-convex optimization algorithm, such as topology optimization, provides only a local optimum.

Furthermore, the performance of this method depends on the manual interpretation of step 2. Indeed, changing the reduced model will obviously impact the optimization results. For example, we assumed in PARCO that the non-sacrificial supports are negligible regarding mechanical performances. However, if this assumption were found to be incorrect, it is certain that the result of the batch optimization would have provided better (lighter) geometries by implementing them into our finite element model.

Finally, systematic parametrization may be problematic if a wide range of design parameters are considered. Indeed, some operations, such as Boolean operations or chamfers, are complex to handle using explicit modeling. Hence, it is essential to constrain the range of design parameters during the batch optimization.

Table 1. Estimation of the development time (in working days) of traditional AM and proposed design methodologies for series of 1, 5 and 20 elements.Footnote

A working day, denoted as “d” in Table 1, corresponds to 8.25 h of work for a trained engineer.

4.4 Further Discussion

In this paper, we apply our methodology to the optimization of a library of parts. However, someone may be interested in studying the impact of design parameters on performances (e.g., effective stiffness). In that case, the batch may be defined on design parameters (in addition to external ones) and the optimization replaced by traditional simulation. Step 2 is still interesting under these circumstances since reducing the model complexity will drastically reduce the computation time.

The objective of MANUELA is to benchmark and promote AM in Europe. To highlight AM capabilities, we were asked to approximate our parametric CAD using polyNURBS (see Fig. 8). Unfortunately, this operation is against the philosophy of this methodology since we lose the flexibility of the design. In retrospect, we realized that most AM parts found in the literature display free-shape geometries. However, the rationale behind this design decision is not stated in general. In contradiction with observation, we found no study which investigates the benefits of free-form geometries (compared to parametrizable constructions). This raises the question of the reason behind this trend. A meta-analysis on AM product development would be crucial to identify the logic behind the free-form trend: Is free-form used in an objective of optimization? Is it due to training and popular AM tools? Is freeform a marketing option to promote AM? Or do we use free-form geometries only because we can?

Fig. 8.

Final CAD of PARCO (left) and printed part (right).

On a more philosophical note, this methodology invites the reader to question the concept of complexity and technological capability. Is a blind consumption of technology always beneficial? – We are here referring to the use of optimization methods and freeform shapes. However, the reconsideration of what really matters can lead to a more appropriate and more desirable conception of our fundamentals. – The selective reduction of complexity, implemented in this methodology, demonstrates that some level of temperance can be profitable (and required) to rationalize our development processes.

5 Conclusion

In this paper, we propose a KBE methodology as an alternative to design a family of parts. This approach is based on five main concepts: identification, interpretation, batch optimization, modeling, and reconstruction.

In the context of structural mechanics, we propose to use topology optimization to emulate a prior knowledge of the optimal architecture. A parametric reduced model is then generated from these results. For a predefined set of load cases, optimal design parameters are computed during the batch optimization step. These values are used to model the relation between external parameters (inputs of the model) and optimal design parameters (outputs). Finally, the parametrized part is reconstructed with traditional CAD software and manufacturing features are integrated.

We benchmarked our methodology with the DfAM of a library of truck’s spring anchorage. Based on prior experience, we estimated to 5.5 working days the development time required to design a similar part using traditional DfAM approaches. Since these approaches are non-parametrizable, we cannot extrapolate a new solution. Hence, there is a linear dependence between the development time and the number of parts in the library. Using our methodology, most operations are only run once, and the computation time has been drastically reduced. Hence, development time and number of parts to design are uncoupled. As such, we developed the optimized library of twenty parts in only 14.5 days and solutions for additional load cases can be generated in a matter of minutes.

The novelty of our method comes from the selective reduction of complexity and the modeling of the optimization batch’s results. Indeed, a blind use of traditional design approach (topology optimization) confines designers in a narrow and rigid environment. Alternative angles of approach emerge by moving away from free-shape approximation. Hence, our methodology highlights that some level of temperance can be profitable (and required) to rationalize the development processes for the design of parts’ libraries.