Blade Envelopes Part II: Multiple Objectives and Inverse Design

Blade envelopes offer a set of data-driven tolerance guidelines for manufactured components based on aerodynamic analysis. In Part I of this two-part paper, a workflow for the formulation of blade envelopes is described and demonstrated. In Part II, this workflow is extended to accommodate multiple objectives. This allows engineers to prescribe manufacturing guidelines that take into account multiple performance criteria. The quality of a manufactured blade can be correlated with features derived from the distribution of primal flow quantities over the surface. We show that these distributions can be accounted for in the blade envelope using vector-valued models derived from discrete surface flow measurements. Our methods result in a set of variables that allows flexible and independent control over multiple flow characteristics and performance metrics, similar in spirit to inverse design methods. The augmentations to the blade envelope workflow presented in this paper are demonstrated on the LS89 turbine blade, focusing on the control of loss, mass flow and the isentropic Mach number distribution. Finally, we demonstrate how blade envelopes can be used to visualize invariant designs by producing a 3D render of the envelope using 3D modelling software.

The Covering Radius and a Discrete Surface Area for Non-Hollow Simplices

We explore upper bounds on the covering radius of non-hollow lattice polytopes. In particular, we conjecture a general upper bound of d/2 in dimension d, achieved by the “standard terminal simplices” and direct sums of them. We prove this conjecture up to dimension three and show it to be equivalent to the conjecture of González-Merino and Schymura (Discrete Comput. Geom. 58(3), 663–685 (2017)) that the d-th covering minimum of the standard terminal n-simplex equals d/2, for every $$n\ge d$$ n ≥ d . We also show that these two conjectures would follow from a discrete analog for lattice simplices of Hadwiger’s formula bounding the covering radius of a convex body in terms of the ratio of surface area versus volume. To this end, we introduce a new notion of discrete surface area of non-hollow simplices. We prove our discrete analog in dimension two and give strong evidence for its validity in arbitrary dimension.

Characteristics of statistical properties of deformation defects of structural metallic materials within elastic deformations

At this paper was established result of the correlations characteristics of structural parameters of low-carbon steels during periodic loading under elastic deformations. According to the results of the research, the kinetic characteristics of the influence of the load parameter on the distribution of deformation defects of the surface layer of structural materials under elastic deformations are obtained. The regularities of the influence of elastic deformations on the distribution of discrete surface properties are revealed. Linear dependences of the parameter of distribution of discrete relief properties of the deformed surface on loading are revealed. The regularities of the influence of elastic deformations on the distribution of discrete surface properties are revealed. It is established that regardless of the type of load, the surface density of deformation defects of scattered fracture accumulates in the mother to a certain state of damage, which is characterized by the current state of density of elements of deformation defects.

Three-dimensional tolerance analysis of discrete surface structures based on the torsor cluster model

Purpose The purpose of this paper is to propose a novel mathematical model to present the three-dimensional tolerance of a discrete surface and to carry out an approach to analyze the tolerance of an assembly with a discrete surface structure. A discrete surface is a special structure of a large surface base with several discrete elements mounted on it, one, which is widely used in complex electromechanical products. Design/methodology/approach The geometric features of discrete surfaces are separated and characterized by small displacement torsors according to the spatial relationship of discrete elements. The torsor cluster model is established to characterize the integral feature variation of a discrete surface by integrating the torsor model. The influence and accumulation of the assembly tolerance of a discrete surface are determined by statistical tolerance analysis based on the unified Jacobian-Torsor method. Findings The effectiveness and superiority of the proposed model in comprehensive tolerance characterization of discrete surfaces are successfully demonstrated by a case study of a phased array antenna. The tolerance is evidently and intuitively computed and expressed based on the torsor cluster model. Research limitations/implications The tolerance analysis method proposed requires much time and high computing performance for the calculation of the statistical simulation. Practical implications The torsor cluster model achieves the three-dimensional tolerance representation of the discrete surface. The tolerance analysis method based on this model predicts the accumulation of the tolerance of components before their physical assembly. Originality/value This paper proposes the torsor cluster as a novel mathematical model to interpret the tolerance of a discrete surface.

An isogeometric b-rep mortar-based mapping method for non-matching grids in fluid-structure interaction

In this study the isogeometric B-Rep mortar-based mapping method for geometry models stemming directly from Computer-Aided Design (CAD) is systematically augmented and applied to partitioned Fluid-Structure Interaction (FSI) simulations. Thus, the newly proposed methodology is applied to geometries described by their Boundary Representation (B-Rep) in terms of trimmed multipatch Non-Uniform Rational B-Spline (NURBS) discretizations as standard in modern CAD. The proposed isogeometric B-Rep mortar-based mapping method is herein extended for the transformation of fields between a B-Rep model and a low order discrete surface representation of the geometry which typically results when the Finite Volume Method (FVM) or the Finite Element Method (FEM) are employed. This enables the transformation of such fields as tractions and displacements along the FSI interface when Isogeometric B-Rep Analysis (IBRA) is used for the structural discretization and the FVM is used for the fluid discretization. The latter allows for diverse discretization schemes between the structural and the fluid Boundary Value Problem (BVP), taking into consideration the special properties of each BVP separately while the constraints along the FSI interface are satisfied in an iterative manner within partitioned FSI. The proposed methodology can be exploited in FSI problems with an IBRA structural discretization or to FSI problems with a standard FEM structural discretization in the frame of the Exact Coupling Layer (ECL) where the interface fields are smoothed using the underlying B-Rep parametrization, thus taking advantage of the smoothness that the NURBS basis functions offer. All new developments are systematically investigated and demonstrated by FSI problems with lightweight structures whereby the underlying geometric parametrizations are directly taken from real-world CAD models, thus extending IBRA into coupled problems of the FSI type.

Discrete Oxidation of a Hard Carbide Tool

Comparative investigations of the effect of discrete surface hardening by standard ion-plasma technology and discrete oxidation technology on the structure and hardness of high-speed steels are carried out. It is shown that, after hardening in the ion-plasma installation on the surface and in the thickness of the layer, droplet-shaped defects, craters and bundles are formed. Metallographic studies showed that the hardened discrete oxidation layer after repeated hardening has a dense, uniform structure. It has been established that the discrete oxidation technology allows to increase the wear resistance of a complex-profile cutting tool 2 times more, compared to a tool hardened by standard ion-plasma technology after regrinding.

Increased Wear Resistance of High-Speed Tools Due to Diffusion Discrete Oxidation

Comparative studies of the effect of discrete surface hardening by standard ion-plasma technology and discrete oxidation technology on wear resistance have been carried out. Metallographic studies have shown that discrete oxidation has a polycrystalline structure. It was found that the technology of discrete oxidation makes it possible to increase the hardness by 31% in relation to the uncoated material, and the wear resistance of the cutting tool with oxidation is 1.5-3 times higher than that of the tool hardened by the standard ion-plasma technology.