Topology optimization of mechanical components fabricated by additive manufacturing for a Shell Eco Marathon vehicle

Since 2004, a team of students and researchers of University of Liege takes part to the Shell Eco Marathon race with a lightweight electric vehicle. The goal of this pedagogical project is to design, fabricate and operate a vehicle exhibiting the least energy consumption. A key factor to reduce the energy consumption is to minimize the vehicle mass. Besides the body structure made of CRFP, engineers have also to focus on the weight reduction of any mechanical parts of the powertrain, transmission and of rolling gear. The combination of topology optimization with additive manufacturing techniques allows to propose innovative designs exhibiting a high performance to weight ratio. Topology optimized designs are often characterized by a high geometrical complexity that is not possible to manufacture without 3D printing. This work presents the CAE design methodology that was developed to combine topology and shape optimization with 3d printing manufacturing. Novel developments both in shape and topology optimization have also been realized for the specific character of these components. The design methodology is illustrated with several applications of components of our new Eco Marathon prototype. They include a support for electric traction motors and different torque arms of the steering mechanism to be implemented in the new 2017 vehicle. The presentation is going to show the different design steps from the specifications and the formulation of the design problem to the 3D-printing of the parts: the topology optimization, interpretation and CAD reconstruction, shape optimization and detailed finite element verification of the solution. The optimization is performed thanks to the commercial software NX-TOPOL and the final CAD design is reconstructed in the CATIA environment software after a smoothing procedure in the NX-CAD environment. We show that the final design can be 3D-printed and a comparison with a design produced using traditional design approach is provided.INOXYPE

Topology optimization in OpenFOAM: how to define the maximum inverse permeability to consider manufacturing constraint

Topology optimization in OpenFOAM: how to define the maximum inverse permeability to consider manufacturing constraint Proton-Exchange Membrane Fuel Cells (PEMFC) are systems that directly convert chemicals into electricity by means of an electro-chemical reaction between hydrogen and oxygen. Following the concerns related to climate change, Hydrogen PEMFC are a promising option to contribute to a decarbonized society. Nevertheless, to rival the Internal Combustion Engine (ICE), PEMFC shall decrease their manufacturing cost, increase their lifetime and their efficiency, among others. The INOXYPEM research project explores new designs of bipolar plates made of stamped coated steel. This work aims at increasing the efficiency of PEMFC by defining the channel network layout of bipolar plates using Fluid Flow Topology Optimization (FFTO) techniques, while simultaneously accounting for the manufacturing restrictions of the sheet metal forming process. We developed an in-house design environment that couples fluid simulations from OpenFOAM with Optimization Algorithms. The flow is simulated using the Incompressible Navier Stokes equations in steady-state condition. These equations are combined with Darcy’s law by means of a Brinkman penalization, resulting in a density-based method to perform the Topology Optimization. Our research addresses two of the main difficulties found in the topology optimization for fluid-based problems: Firstly, the vast majority of the related publications is performed using the finite element method (76% of all publications), whilst the number of publications that use the finite volume method (the preferred for computational fluid dynamics) reach a surprisingly low level of use of only 7% (the other 16% goes to the lattice Boltzmann method and 1% to particle-based methods). Our research is developed using the finite volume method with a continuous adjoint formulation for the sensitivity analysis. Secondly, when solving the modified Navier-Stokes equations, it’s necessary to define a maximum value for the inverse permeability that comes from the Brinkman penalization, which is the design variable in the problem (0 in the fluid zones and a large value in solid zone). This large value should be big enough to correctly penalize the velocity inside the solid regions, but not too big in order to avoid numerical problems. It’s common practice to either define a really big number by intuition or to define a value based on the Darcy number. However, when using the Darcy number, numerical simulations have shown that this method leads to highly-problem-dependent designs. Thus, our research proposes a new way of defining the maximum value of the inverse permeability based on the Reynolds number, principally because this is the main dimensionless number when working with the Incompressible Navier Stokes equations in steady-state condition. In summary, our in-house developed solver performs the minimization of the total pressure loss considering constraints over the volume. In order to reflect manufacturing restrictions of the steel forming process, constraints on the maximum size of the channels and the separation between them are also implemented. The main contributions brings closer the world of the topology optimization to the computational fluid dynamics by considering the nature of the working fluid (using the Reynolds number to define the inverse permeability) and also by using the finite volume method

Imposing Manufacturing Constraints in Topological Optimization of 2D Fuel Cell flow problems using OpenFOAM

INOXYPE

Imposing Manufacturing Constraints in Topological Optimization of 2D Fuel Cell flow problems using OpenFOAM

peer reviewedINOXYPE

Misalignment topology optimization with manufacturing constraints

This work aims at introducing misalignment response in the design of mechanical transmission components using topology optimization. Misalignment considerations can be of high importance for various industrial applications as in gearbox or differential, where aligned axes are to be ensured during the usage of the part. Nevertheless, to the authors’ knowledge, no work so far implements such response in a topology optimization framework. In this contribution, misalignment between two spatial vectors is evaluated in various ways using trigonometry and vector functions. The misalignment is formulated through the spatial displacements of the constituent nodes of the objective vectors. The authors choose a formulation among other and implement the later in a 2D topology framework for further investigation on test cases. Issues such as material disconnection, non-discrete solutions or lack of engineering meaning are tackled along this work by the introduction of constraints and parametric studies. A performance test is achieved on a simplified gearbox transmission system to assess the performance between designs with or without misalignment considerations.Manufacturing constraints are introduced to improve the manufacturability of the optimized solution. Subsequently a 3D test case further highlights the usefulness of this contribution

Critical Plane approach for fatigue resistance using stress-based topology optimization

Fatigue is responsible for almost 80% of the overall breakages in mechanical components (Oest(2017)). Such a failure phenomenon must be prevented as soon as the early stage of design. Since the seminal works by Augut Wöhler, see Schültz(1996), the literature counts various methods able to prevent fatigue failure (Schijve(2003)). In the automotive industry, the components undergo a high number of cycles leading to consider the stresses as variables into the fatigue criteria. Topology optimization has become a valuable tool used to propose preliminary designs as attested by several commercial software on the market. Combining fatigue design with a stress-based topology optimization procedure is therefore natural. In this work, the coupling of the Dang Van criterion (Dang Van et al(1989), Dang Van(2010)) within a topology optimization code is investigated to provide fatigue resistant layouts. The choice of the Dang Van criterion is encouraged by its wide usage in the automotive industry (Koutiri(2011)). The former is based on the concept of critical plane in the vicinity of which plastic yielding occurs. With the hypothesis of reaching the elastic shakedown state, the criterion establishes that crack initiation is prevented if the microscopic stress state remains below a prescribed threshold. Following the framework proposed by Dang Van (Dang Van(1989)), the fatigue failure procedure is introduced into a density-based topology optimization code embedding stress constraints. The first step of the procedure is to construct the microscopic stress using a regular finite element analysis and evaluate a damage value in the sense of Dang Van. A sub-optimization routine is necessary to solve a min-max problem in order to find the residual stress tensor to construct the microscopic stresses (Mandel et al(1977), Bernasconi(2002)). This sub-optimization might be time consuming and must be dealt with care. In a second step, this work shows how the fatigue resistance procedure is implemented into a density-based topology optimization using stress constraints and in particular how the sensitivity analysis is performed using the adjoint approach (Tortorelli and Michaleris(1994)). The optimization process is carried out with the Method of Moving Assymptotes (Svanberg(1987)) along the qp-relaxation (Bruggi(2008)) to overcome the singularity phenomenon of the stress constraints. The proposed optimization framework is evaluated in terms of its numerical performances and is compared to classical results obtained by a regular stress-based topology optimization on several benchmarks

Constraints Aggregation in Topology Optimization

A vast amount of the methods that address local design requirements introduce a wide set of constraints within the optimization problem. This local formulation calls for the use of aggregation functions in order to avoid the computational burden on the optimizer. This step of collecting the constraints within a few representative ones seems as a simple implementation detail coming at the final stage of the formulation. Therefore it is often neglected in the discussion. However if this aggregation step is not well treated the success of the whole method may be compromised, and in many cases the simplest part of the constraint becomes time-consuming or even, the hardest point of the formulation. Aggregation functions are built to be smooth and differentiable approximations of the max function. In addition their sensitivity information should be smooth in order to be used in efficient continuous optimization algorithms. They have also to catch accurately the most critical constraints to mimic the locally constrained problem. The classical application is in the field of stress constraints, where a large amount of contributions have been made on the subject. Most of the research contributes with new aggregation techniques, which are adapted to the context of topology optimization with stress constraints. However, to tailor high quality global manufacturing constraints, we need to make further progress in the understanding of the aggregation functions when used in the topology optimization. To this end, we perform a deep theoretical investigation and a quantitative numerical assessment of the behavior of these functions when being used in different formulations of manufacturing and mechanical constraints. Specifically, we focus the study on p-mean and p–norm functions within the framework of density methods. We include in the analysis methods to introduce: i) maximum size control, ii) minimum gap between solid members, iii) minimum size, iii) overhang control for additive manufacturing and iv) stress constraints. Some important observations obtained from this study are: p-norm depends on the amount of data that is being aggregated, making it more unstable under mesh refinement. On the other hand, p-mean is less dependent on mesh modifications but it is likely to produce results that do not satisfy every local constraint. In addition, by looking at the sensitivities it is possible to have an insight of the nonlinearity of a method.Aero+ Projec

An aggregation strategy of maximum size constraints in density-based topology optimization

The maximum size constraint restricts the amount of material within a test region in each point of the design domain, leading to a highly constrained problem. In this work, the local constraints are gathered into a single one using aggregation functions. The challenge of this task is presented in detail, as well as the proposed strategy to address it. The latter is validated on different test problems as the compliance minimization, the minimum thermal compliance, and the compliant mechanism design. These are implemented in the MATLAB software for 2D design domains. As final validation, a 3D compliance minimization problem is also shown. The study includes two well-known aggregation functions, p-mean and p-norm. The comparison of these functions allows a deeper understanding about their behavior. For example, it is shown that they are strongly dependent on the distribution and amount of data. In addition, a new test region is proposed for the maximum size constraint which, in 2D, is a ring instead of a circle around the element under analysis. This slightly change reduces the introduction of holes in the optimized designs, which can contribute to improve manufacturability of maximum size–constrained components.Aero

OVERHANGING CONSTRAINTS IN ADDITIVE MANUFACTURINGUSING TWODIFFERENT TOOLS

As the manufacturing methods undergo huge evolution thanks to the emergence of additive manufacturing techniques, the interest of a coupling with the topology optimization problem is highly demanded by industries (such as automotive and aerospace). The challenges are still numerous around such coupling and this work focuses on the overhanging problem related to the metalic additive manufacturing technics(LBM and EBM). To tackle the problem various research directions are investigated and compared to another

Development of a Topological Optimization framework for 2D problems using OpenFOAM

INOXYPE