Dimensional Inconsistency Research Articles

Partial auxetic behavior of 3D mesh fabric under compression

The 3D mesh fabric is a key component of automotive seat ventilation systems as it has good compression resistance and creates channels to provide effective circulating airflow. The dimensional inconsistency of fabric sheets by laser cutting to be integrated into car seats and their unrecoverable dimension changes in subsequent cushioning applications are challenging problems. A typical commercialized 3D mesh fabric was observed to shorten and widen under compression, showing an auxetic behavior in the length–thickness section. This counterintuitive partial auxetic behavior accounts for the dimensional variation. A full-size finite element (FE) model of the fabric was established to simulate the complex fabric deformation based on the precise geometry of a unit cell obtained by X-ray micro-computed tomography (μCT) scanning. The FE simulation reproduced the planar dimension change process of the fabric. The underlying mechanism of partial auxeticity was revealed from the global to local analysis, including fabric global deformation, unit meshes deformation and unit cell geometric structure change. It was shown that buckling of initially post-buckled spacer monofilaments drives in-plane movements of monofilament loops to cause partial auxetic behavior. The partial auxeticity weakens in the compression process due to the gradual intercontact and densification of spacer monofilaments. Different constraints on monofilament loops from adjacent unit cells and multifilament inlays make the deformation uneven in the plane of fabric. It is important to fully analyze the dimensional change, especially the partial auxetic deformation, of the 3D mesh fabric under compression for its practical applications.

NICKEL-BASED SUPERALLOYS EXPLOITATIONAL PROPERTIES RISING DUE TO THE INFLUENCE ON LATTICE PARAMETERS

Objective. It consists in establishing relationships between the chemical composition, mechanical properties, and dimensional inconsistency of crystal lattices of nickel-based superalloys. That makes it possible to reduce the volume of experimental research in the conditions of the production process and experimental developments. Research methods. The results of experimental and calculated data, formed on the basis of experimental and results taken from open sources, are given. The phase composition was determined by X-ray structural analysis using the Bragg-Brentano focusing method on a RIGAKU MINIFLEX 600 diffractometer (CoKα radiation). The experimental values were processed by the method of least squares with obtaining correlation dependencies of the “parameter-property” type and establishing mathematical equations of regression models that optimally describe these dependencies. Obtained results. It was established that with an increase in the amount of misalignment of crystal lattices, the strength of alloys decreases due to significant internal stresses. It was found that for alloys of uniform and directional crystallization, the extremum is observed at a value of 1.5...1.6 Kγ′, this is due to a decrease in the number of elements in the γ-solid solution. It is shown that the obtained dependences correspond to reality and coincide with experimental data at the level of 10 %. Scientific novelty. The value of the work lies in the fact that the dependence of the influence of alloying elements on the mechanical properties and the discrepancy in the sizes of the crystal lattices was obtained, which made it possible to determine the properties without conducting experiments. It was established that changes in the course of dependencies are closely correlated with the processes taking place in the structure of alloys. Practical value. The obtained dependencies can be used both for the development of new superalloys and for the improvement of the compositions of industrial alloys.

Comments on “Polymer compatibility,” Journal of Applied Polymer Science 17.10 (1973): 3175

AbstractThis concise note highlights certain errors, encompassing dimensional inconsistency and flaws in the expression of fundamental relationships, associated with Schneier's equation. This equation was initially published in the Journal of Applied Polymer Science [17.10 (1973): 3175] and has subsequently found application in consequent studies.

Workspace optimization of 1T2R parallel manipulators with a dimensionally homogeneous constraint-embedded Jacobian

This paper presents the workspace optimization of one-translational two-rotational (1T2R) parallel manipulators using a dimensionally homogeneous constraint-embedded Jacobian. The mixed degrees of freedom of 1T2R parallel manipulators, which cause dimensional inconsistency, make it difficult to optimize their architectural parameters. To solve this problem, a point-based approach with a shifting property, selection matrix, and constraint-embedded inverse Jacobian is proposed. A simplified formulation is provided, eliminating the complex partial differentiation required in previous approaches. The dimensional homogeneity of the proposed method was analytically proven, and its validity was confirmed by comparing it with the conventional point-based method using a 3-PRS manipulator. Furthermore, the approach was applied to an asymmetric 2-RRS/RRRU manipulator with no parasitic motion. This mechanism has a T-shape combination of limbs with different kinematic parameters, making it challenging to derive a dimensionally homogeneous Jacobian using the conventional method. Finally, optimization was performed, and the results show that the proposed method is more efficient than the conventional approach. The efficiency and simplicity of the proposed method were verified using two distinct parallel manipulators.

Dimensionality of Iterative Methods: The Adimensional Scale Invariant Steffensen (ASIS) Method

The dimensionality of parameters and variables is a fundamental issue in physics but is mostly ignored from a mathematical point of view. Difficulties arising from dimensional inconsistency are overcome by scaling analysis and, often, both concepts, dimensionality and scaling, are confused. In the particular case of iterative methods for solving nonlinear equations, dimensionality and scaling affect their robustness: While some classical methods, such as Newton’s, are adimensional and scale independent, some other iterations such as Steffensen’s are not; their convergence depends on scaling, and their evaluation needs a dimensional congruence. In this paper, we introduce the concept of an adimensional form of a function in order to study the behavior of iterative methods, thus correcting, if possible, some pathological features. From this adimensional form, we will devise an adimensional and scale invariant method based on Steffensen’s, which we will call the ASIS method.

Influence of system alloying and dimensional mismatch of crystalline lattices of g- and g'- phases on the characteristics of the strength of single-crystal nickel superalloys

Purpose of the work. Obtaining predictive regression models, by means of which, it is possible to adequately calculate the mechanical properties of monocrystalline nickel-base superalloys without conducting previous experiments.
 Methods of research. For experimental and theoretical studies of temperature performance, a working sample of alloys is formed consisting of known industrialt nickel-base superalloys for monocrystalline castings of domestic and foreign production, which due to contents of the main elements, cover a wide range of alloying. The obtained values were processed in the Microsoft Office with the least squares method, with the obtaining of the "parameter-property" correlation dependencies with the obtaining of mathematical equations of regression models (trend lines) that describe these dependencies optimally.
 Received results. The influence of alloying elements on their tendency to the formation of phases in foundry heat-resistant nickel alloys is considered. Based on the influence of elements on phase formation, the coefficient of the ratio of alloying elements Kg¢ in the alloys of this class was first developed.
 A close correlation dependence of the ratio Kg¢ with a dimensional discrepancy between the γ- and γ-phases crystalline lattice (localized) was found. It has also been shown that for multi-component nickel systems it is possible to predict with high probability misfit, which significantly affects the strength characteristics of alloys of this class.
 The regression models of correlation dependencies on dimensional inconsistency (γ / γ'-misfit) are given, which allow to predict the boundaries of short-term and long-term strength of alloys. It is shown that the magnitude of the misfit at the operating temperature should tend to zero. This will increase the structural stability by minimizing structural stresses, which has a positive effect on the strength and plastic characteristics.
 Scientific novelty. For the first time, a coefficient of the ratio of alloying elements Kg¢, which has a close correlation with the strength and dimensional discrepancy of casting nickel-base superalloys, is proposed.
 Practical value. The perspective and effective direction in solving the problem of forecasting of the main characteristics affecting the complex of service properties of alloys, both in the development of new monocrystalline nickel-base superalloys, and in the improvement of the composition of known industrial brands of this class, is shown.

Revisiting the Temkin Isotherm: Dimensional Inconsistency and Approximate Forms

The Temkin isotherm equation is increasingly being used to correlate adsorption isotherms of water contaminants. This research note shows that the Temkin isotherm as used in environmental adsorption research suffers from a fundamental flaw of dimensional inconsistency. In addition, an important but frequently overlooked issue concerns the approximate nature of the Temkin isotherm which limits its ability to fit type I isotherms: it has neither a Henry’s law limit at low loadings nor a finite saturation limit at high loadings. A different approximate Temkin isotherm, which approaches a linear isotherm at low concentrations and commences at the (0,0) origin, is shown to outperform the commonly used Temkin isotherm in terms of fitting ability and resembles the Langmuir and Freundlich isotherms in describing adsorption data without a saturation plateau. It is hoped that the material presented in this research note will lead to a better comprehension of the Temkin isotherm.

Dimensional Inconsistency Measures and Postulates in Spatio-Temporal Databases

The problem of managing spatio-temporal data arises in many applications, such as location-based services, environmental monitoring, geographic information systems, and many others. Often spatio-temporal data arising from such applications turn out to be inconsistent, i.e., representing an impossible situation in the real world. Though several inconsistency measures have been proposed to quantify in a principled way inconsistency in propositional knowledge bases, little effort has been done so far on inconsistency measures tailored for the spatio-temporal setting.
 In this paper, we define and investigate new measures that are particularly suitable for dealing with inconsistent spatio-temporal information, because they explicitly take into account the spatial and temporal dimensions, as well as the dimension concerning the identifiers of the monitored objects. Specifically, we first define natural measures that look at individual dimensions (time, space, and objects), and then propose measures based on the notion of a repair. We then analyze their behavior w.r.t. common postulates defined for classical propositional knowledge bases, and find that the latter are not suitable for spatio-temporal databases, in that the proposed inconsistency measures do not often satisfy them. In light of this, we argue that also postulates should explicitly take into account the spatial, temporal, and object dimensions and thus define “dimension-aware” counterparts of common postulates, which are indeed often satisfied by the new inconsistency measures. Finally, we study the complexity of the proposed inconsistency measures.

Improved eigenvectors for Pulliam-Chaussee diagonalized approximate-factorization algorithm

The eigensystem of the Pulliam-Chaussee diagonalized form of the approximate-factorization algorithm for the three-dimensional Euler and Navier-Stokes equations is revisited to remove an apparent dimensional inconsistency. The original set of eigenvectors in curvilinear coordinates were derived systematically and has been widely used and referenced. Although mathematically correct, the original eigenvectors for the advected modes appear dimensionally inconsistent and yield a set of matrices with large condition numbers for some flows. A new set of eigenvectors is presented that remove the inconsistency and improves the robustness of the diagonalized scheme.

Size effects on geometrical accuracy for additive manufacturing of Ti-6Al-4V ELI parts

A comprehensive investigation of the size and geometry dependency of the dimensional accuracy of direct metal laser sintering (DMLS) for Ti-6Al-4V ELI is presented. For features such as walls, squares, tubes, and rods with different sizes, the percent error significantly increases with decreasing the feature size. The polynomial function a t-b is suggested to describe this size dependency of the dimensional error where a and b are parameters depending on the geometry, material, and DMLS process parameters. This function is used to successfully predict the dimensional error in DMLS of two spinal cages. Therefore, these functions can be used to account for these errors in DMLS by design change or by adjusting DMLS scaling factors. Furthermore, the inconsistency of the DMLS-manufactured dimensions within the feature is shown to be in the same range of the dimensional inconsistency for features located at different positions on the build platform, implying that the location of the feature on the build platform has a negligible effect on the dimensional accuracy. Finally, it is shown that the error in the position accuracy of DMLS-manufactured features is negligible when the size dependency of the dimensional features is considered in the measurements.

Direct Adaptive Neural Control Design for a Class of Nonlinear Multi Input Multi Output Systems

This paper proposes a direct adaptive neural control law for a class of affine nonlinear multi-input-multi-output (MIMO) systems of the form $\dot {x}=f(x)+G(x)u$ using feedback linearization when both $f(x)$ and $G(x)$ are to be estimated. It is challenging to estimate $f(x)$ , a vector, and $G(x)$ , a matrix, to be used in synthesizing the control law, simultaneously, because of the dimensional inconsistency arising with the available neural structures, which do not have multiple layers of outputs. This problem is addressed in this paper by exploiting the power of matrix vectorization and reshaping techniques using the Kronecker product. The strategy may be visualized as equivalent to the neural structure consisting of multiple layers of outputs that result from the appropriate manipulation of matrices corresponding to the proposed estimations. The weight update laws, for both the radial basis function neural networks that estimate both $f(x)$ and $G(x)$ , are derived such that the proposed control law achieves the twin objective of the derived tracking performance as well as closed-loop system stability in the sense of Lyapunov. The ratios $\alpha $ and $\beta $ are proposed in line with the widely used concept of Rayleigh’s quotient adopted in structural dynamics to evaluate the natural frequency of a system. The simulation results obtained from the use of a twin rotor MIMO system are presented here to demonstrate the feasibility and effectiveness of the proposed control law. The superiority of this approach lies in the development of suitable control law for a MIMO system in the absence of knowledge about the nonlinearities.

Comment on Johnson’s creating dimensional stock-flow inconsistency in Binswanger’s model

ABSTRACTBinswanger (2009) constructed a model of a pure credit money economy with production to demonstrate the existence of growth imperative in such economies. This model entails a misspecification because money may disappear from the economy at the alleged minimal steady state growth rate (Gilányi 2015). Johnson (2015) attributes this inconsistency to the confusion between the stock of outstanding loans at the end of period and the flow of loans taken during the period; that he calls dimensional stock-flow inconsistency. On the grounds of this criticism he modifies some flows to eliminate the problem raised by Gilányi. Binswanger (2015) omits this criticism because it is a simple misinterpretation of his model; rather he explains the inadequacy of Johnson’s specification of flows. Doing so, he makes believe that there is still an unsettled debate on whether to treat loans as stocks or as flows in his model. This note demonstrates that both model specifications are dimensionally stock-flow consistent. Hence, Johnson’s criticism is just a narrative behind the rationale of altering flows in the model; the controversy is not on dimensional stock-flow inconsistency but on the logically coherent specification of the magnitude of flows in the model.

Comments on time-varying fractional order

The calculus of arbitrary order, known as the fractional calculus, allows for real- and complex-valued orders. Interest in time-varying order is growing in order to study transient behavior under varying environmental conditions. Popular forms currently in use suffer from fundamental flaws of dimensional inconsistency and predict physically implausible behaviors such as violation of causality and/or violation of conservation of energy. This article reviews some of the motivation behind the study of time-varying fractional order and makes suggestions as to how to overcome the flaws in the forms in current usage. A new fractional-order integral operator is proposed that may allow for modeling time-varying fractional-order systems in a dimensionally consistent and physically plausible manner. Possible experimental tests of the revised fractional-order model are proposed.

Epsilon-Trig Regularization Method for Bang-Bang Optimal Control Problems

Bang-bang control problems have numerical issues due to discontinuities in the control structure and require smoothing when using optimal control theory that relies on derivatives. Traditional smooth regularization introduces a small error into the original problem using error controls and an error parameter to enable the construction of accurate smoothed solutions. When path constraints are introduced into the problem, the traditional smooth regularization fails to bound the error controls involved. It also introduces a dimensional inconsistency related to the error parameter. Moreover, the traditional approach solves for the error controls separately, which makes the problem formulation complicated for a large number of error controls. The proposed Epsilon-Trig regularization method was developed to address these issues by using trigonometric functions to impose implicit bounds on the controls. The system of state equations is modified such that the smoothed control is expressed in sine form, and only one of the state equations contains an error control in cosine form. Since the Epsilon-Trig method has an error parameter only in one state equation, there is no dimensional inconsistency. Moreover, the Epsilon-Trig method only requires the solution to one control, which greatly simplifies the problem formulation. Its simplicity and improved capability over the traditional smooth regularization method for a wide variety of problems including the Goddard rocket problem have been discussed in this study.

WITHDRAWN: Non-Darcy mixed convection from a vertical surface in an electrically conducting non-Newtonian nanofluid

This article has been withdrawn at the request of the Editor. After publication of this manuscript as an Article in Press, the Editors of the journal became aware of some fundamental errors. The authors were given the opportunity and time to correct the equations in a revised manuscript, but the issue remained. For this reason, this article is being withdrawn. We would like to thank Professor Ioan Pop of the Faculty of Mathematics, University of Cluj, Romania for directing our attention to the dimensional inconsistency. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy .

Pseudo–Relativistic Vector Analysis of Animal Growth in Four–Dimensional Space–Time : Preliminary Report with Problem of Dimensional Inconsistency between Space and Time

Pseudo–Relativistic Vector Analysis of Animal Growth in Four–Dimensional Space–Time : Preliminary Report with Problem of Dimensional Inconsistency between Space and Time

Convex hull-based velocity transmission capability of parallel manipulators

This paper presents a convex hull-based velocity transmission capability analysis of parallel manipulators (PMs) for more accurate design and performance evaluation of PMs. The velocity transmission capability analysis based on the manipulability ellipsoid does not provide accurate information on how fast a PM can move along an arbitrary direction since the joint velocities are normalized by the two-norm (≤ 1). Therefore, for an accurate velocity transmission capability, a computationally efficient convex hull-based approach is proposed here using minimum infinity-norm solutions. Due to the calculation complexity and the dimensional inconsistency, the velocity transmission capability was analyzed separately for the translational and rotational velocity convex hulls. Moreover, for quantitative measures of the translational and rotational velocities, three performance indices (PI), i.e., local, global, and weighted PI, are proposed to visualize dexterousness of PMs. The proposed method is applied to a general 6 degrees of freedom PM to show the effectiveness of the proposed approach.

Analysis Economic Characters of Yunji Township Walnuts

Yunji township of Jiangyou city is the particular characters of drought, poverty. The party committee and government try to find a getting wealth road with industry development goal "thousands acres of walnuts". The main contributions of this paper are: 1) Proposing improved PCA model to eliminate dimensional inconsistency and the difference of magnitude. 2) Adopting improved PCA model to analysis five fine walnut characters, and comparison with traditional PCA. 3) Getting the conclusion that Xiangling walnut is the most suitable for Yunji township cultivate.

A new homogeneous manipulability measure of robot manipulators, based on power concept

Kinetostatic performance indices have been commonly used for many potential applications in robotics, i.e. optimal design purpose, trajectory planning, manipulation programming, redundancy treatment and dexterity analysis. This has been successful when the mechanism has either fully rotational or translational joints. However, in case of a mechanism having both rotational and translational degrees of freedom; performance indices, such as Jacobian matrix, manipulability or condition number, may not be used due to the dimensional inconsistency with its elements. In this paper, by means of the power concept, a new kinetostatic performance index of robot manipulators is proposed. The power has the same physical units in either translations or rotations. Therefore, we can make use of it as a homogeneous or natural performance index of manipulators. Although it has never been considered as a subject matter of kinetostatic performance criteria, exploiting the behaviour of its basic components namely, force and speed, along the mechanism was likely interesting. On the other hand, the new concept of Oriented Power was introduced, in order to formulate the quadrivector of apparent power, leading to the final homogeneous performance index, which is no longer susceptible to the physical units’ choice. The main benefits of this approach are as follows: firstly there is no need for any restriction on the kinematics’ limits; secondly, the new formalism is insensitive to joint types of mechanism, as well as it has the possibility of grouping translations and rotations of the operational space together. The new index is then both applied in a simple serial mechanism dexterity analysis, and extended to a planar parallel mechanism.

Conservation Coupling Technique for Dynamic Inlet-Engine Analyses

Ahybridmethodispresentedforunsteadyanalysisofturbineenginepropulsionsystems.Themethodisacoupled analysis of the inlet ‐engine combination, incorporating multidimensional inviscid computational e uid dynamics in the inlet with a one-dimensional dynamic turbomachinery model. The domain coupling technique consists of conservation averaging, which reconciles the dimensional inconsistency and characteristic wave propagation to provide time accuracy. The method is applied to an axisymmetric mixed compression inlet integrated with an eight-stageaxial compressoratMach 2.5 operating conditions. Analysis includes methodology verie cation, steadystate performance, and dynamic results for two different events. The results indicate that the method is capable of simulating large-amplitude dynamic behavior of coupled supersonic inlet ‐engine systems.