Structural and Multidisciplinary Optimization https://doi.org/10.1007/s00158-020-02496-5 RESEARCH PAPER Misalignment topology optimization with manufacturing constraints Simon Bauduin 1 · Pablo Alarcon 1 · Eduardo Fernandez 1 · Pierre Duysinx 1 Received: 30 August 2019 / Revised: 30 November 2019 / Accepted: 7 January 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract 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 man- ufacturability of the optimized solution. Subsequently a 3D test case further highlights the usefulness of this contribution. Keywords Density-based · Topology optimization · Misalignment · Manufacturing constraints 1 Introduction Optimization design aims at the minimization of a perfor- mance indicator while satisfying various constraints. Since the introduction of Bendsøe and Kikuchi (1988), topology optimization is based on compliance formulation. The for- mulation provides interesting solutions as the deformations are globally controlled by reaching the most rigid struc- ture under the specified load case. Further works have Responsible Editor: YoonYoung Kim  Simon Bauduin s.bauduin@uliege.be Pablo Alarcon palarcon@uliege.be Eduardo Fernandez efsanchez@uliege.be Pierre Duysinx p.duysinx@uliege.be 1 Department of Aerospace and Mechanical Engineering, University of Li` ege, 4000 Li` ege, Belgium improved the practicality of density-based topology opti- mization method. Firstly, the work of Bendsøe (1989) intro- duces a material model for porous microstructure known nowadays as the solid isotropic material with penalization (SIMP). This model answers to critics stating that optimized structures solutions depict a porous behaviour impossi- ble to manufacture. Subsequently the physical meaning of the SIMP model was validated by Bendsøe and Sigmund (1999) and used broadly by the optimization community (see Sigmund and Maut 2013, for a review). With the arrival of additive manufacturing, the domain of fabrication is under considerable interest for the topology optimization community. As pointed out by Thompson et al. (2016), additive manufacturing introduces the means to manufacture parts obtained by topology optimization. As this article focuses on mechanical components, the printing technologies considered are all based on metallic additive manufacturing, such as selective laser melting (SLM) and electron beam melting (EBM) with their powder bed configuration, direct metal deposition (DMD) of filaments and others. Metallic additive manufacturing has specific design constraints that need to be taken into consideration for good printing results. Through the printing process, the deposition of metal layers, high thermal gradients