In the context of lattice-based design and manufacturing, the problem of physical realization of density maps into lattices of a particular family is central. Density maps are prescribed by design optimization algorithms, which seek to fulfill structural demands on a workpiece, while saving material. These density maps cannot be directly manufactured since local graded densities cannot be achieved using the bulk solid material. Because of this reason, existing topology optimization approaches bias the local voxel relative density to either 0 (void) or 1 (filled). Additive manufacturing opens possibilities to produce graded density individuals belonging to different lattice families. However, voxel-level sampled boundary representations of the individuals produce rough and possibly disconnected shells. In response to this limitation, this article uses sub-voxel sampling (largely unexploited in the literature) to generate lattices of graded densities. This sub-voxel sampling eliminates the risk of shell disconnections and renders better surface continuity. The manuscript devises a function to produce Schwarz cells that materialize a given relative density. This article illustrates a correlation of continuity against stress concentration by simulating C 0 and C 1 inter-lattice continuity. The implemented algorithm produces implicit functions and thus lattice designs which are suitable for metal additive manufacturing and able to achieve the target material savings. The resulting workpieces, produced by outsource manufacturers, are presented. Additional work is required in the modeling of the mechanical response (stress/strain/deformation) and response of large lattice sets (with arbitrary geometry and topology) under working loads.

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In the context of generation of lubrication flows, gear pumps are widely used, with gerotor-type pumps being specially popular, given their low cost, high compactness, and reliability. The design process of gerotor pumps requires the simulation of the fluid dynamics phenomena that characterize the fluid displacement by the pump. Designers and researchers mainly rely on these methods: (i) computational fluid dynamics (CFD) and (ii) lumped parameter models. CFD methods are accurate in predicting the behavior of the pump, at the expense of large computing resources and time. On the other hand, Lumped Parameter models are fast and they do not require CFD software, at the expense of diminished accuracy. Usually, Lumped Parameter fluid simulation is mounted on specialized black-box visual programming platforms. The resulting pressures and flow rates are then fed to the design software. In response to the current status, this manuscript reports a virtual prototype to be used in the context of a Digital Twin tool. Our approach: (1) integrates pump design, fast approximate simulation, and result visualization processes, (2) does not require an external numerical solver platforms for the approximate model, (3) allows for the fast simulation of gerotor performance using sensor data to feed the simulation model, and (4) compares simulated data vs. imported gerotor operational data. Our results show good agreement between our prediction and CFD-based simulations of the actual pump. Future work is required in predicting rotor micro-movements and cavitation effects, as well as further integration of the physical pump with the software tool.

Lattice-based workpieces contain patterned repetition of individuals of a basic topology (Schwarz, ortho-walls, gyroid, etc.) with each individual having distinct geometric grading. In the context of the design, analysis and manufacturing of lattice workpieces, the problem of rapidly assessing the mechanical behavior of large domains is relevant for pre-evaluation of designs. In this realm, two approaches can be identified: (1) numerical simulations which usually bring accuracy but limit the size of the domains that can be studied due to intractable data sizes, and (2) material homogenization strategies that sacrifice precision to favor efficiency and allow for simulations of large domains. Material homogenization synthesizes diluted material properties in a lattice, according to the volume occupancy factor of such a lattice. Preliminary publications show that material homogenization is reasonable in predicting displacements, but is not in predicting stresses (highly sensitive to local geometry). As a response to such shortcomings, this paper presents a methodology that systematically uses design of experiments (DOE) to produce simple mathematical expressions (meta-models) that relate the stress–strain behavior of the lattice domain and the displacements of the homogeneous domain. The implementation in this paper estimates the von Mises stress in large Schwarz primitive lattice domains under compressive loads. The results of our experiments show that (1) material homogenization can efficiently and accurately approximate the displacements field, even in complex lattice domains, and (2) material homogenization and DOE can produce rough estimations of the von Mises stress in large domains (more than 100 cells). The errors in the von Mises stress estimations reach 42 % for domains of up to 24 cells. This result means that coarse stress–strain estimations may be possible in lattice domains by combining DOE and homogenized material properties. This option is not suitable for precise stress prediction in sensitive contexts wherein high accuracy is needed. Future work is required to refine the meta-models to improve the accuracies of the estimations.