Digital twin-based analysis of volumetric error mapping procedures

The evaluation of the volumetric accuracy of a machine tool is an open challenge in the industry, and a wide variety of technical solutions are available in the market and at research level. All solutions have advantages and disadvantages concerning which errors can be measured, the achievable uncertainty, the ease of implementation, possibility of machine integration and automation, the equipment cost and the machine occupation time, and it is not always straightforward which option to choose for each application. The need to ensure accuracy during the whole lifetime of the machine and the availability of monitoring systems developed following the Industry 4.0 trend are pushing the development of measurement systems that can be integrated in the machine to perform semi-automatic verification procedures that can be performed frequently by the machine user to monitor the condition of the machine. Calibrated artefact based calibration and verification solutions have an advantage in this field over laser based solutions in terms of cost and feasibility of machine integration, but they need to be optimized for each machine and customer requirements to achieve the required calibration uncertainty and minimize machine occupation time.This paper introduces a digital twin-based methodology to simulate all relevant effects in an artefact-based machine tool calibration procedure, from the machine itself with its expected error ranges, to the artefact geometry and uncertainty, artefact positions in the workspace, probe uncertainty, compensation model, etc. By parameterizing all relevant variables in the design of the calibration procedure, this simulation methodology can be used to analyse the effect of each design variable on the error mapping uncertainty, which is of great help in adapting the procedure to each specific machine and user requirements. The simulation methodology and the analysis possibilities are illustrated by applying it on a 3-axis milling machine tool.     

Investigation of stress fields for non-standard sized glass plates loaded by ring-on-ring

A ring-on-ring (ROR) test is a prevailing test method for evaluating the equi-biaxial strength of glass materials. However, current ROR test standards limit the strength and size of glass to prevent a nonlinear behavior. In this study, the feasibility of ROR testing for non-standard, high-strength glass, such as tempered or ion-exchanged rectangular glass is investigated. To this end, ROR simulation based on theory and experiment is conducted for thirty non-standard glasses with widths of 100–300 mm and aspect ratios of 1.0–2.0. As a result, the maximum measurable stress was about 215.6 MPa for 100 × 200 mm glass and 481.3 MPa for 300 × 600 mm glass with a 3% deviation, which is well above the strength of regular tempered glass. The main purpose of this work is to understand the range of aspect ratio of horizontal and vertical widths of a glass plate that can be evaluated by the standard ROR test.     

Context-free grammars to detect straight segments and a novel polygonal approximation method

A new method for the polygonal approximation is presented. The method is based on the search for break points through a context-free grammar, that accepts digital straight segments with loss of information, as well as the decrease in the error committed employing the comparison of a tolerable error. We present an application of our method to different sets of objects widely used, as well as a comparison of our results with the best results reported in the literature, proving that our method achieves better values of error criteria. Besides, a new way to find polygonal approximations, with context-free grammars to recognize digital straight segments without loss of pixels, it is also addressed.     

Unreliable numbers: error and harm induced by bad design can be reduced by better design

Number entry is a ubiquitous activity and is often performed in safety- and mission-critical procedures, such as healthcare, science, finance, aviation and in many other areas. We show that Monte Carlo methods can quickly and easily compare the reliability of different number entry systems. A surprising finding is that many common, widely used systems are defective, and induce unnecessary human error. We show that Monte Carlo methods enable designers to explore the implications of normal and unexpected operator behaviour, and to design systems to be more resilient to use error. We demonstrate novel designs with improved resilience, implying that the common problems identified and the errors they induce are avoidable.     

On the performance of improved quadrature spatial modulation

Quadrature spatial modulation (QSM) utilizes the in‐phase and quadrature spatial dimensions to transmit the real and imaginary parts of a single signal symbol, respectively. The improved QSM (IQSM) transmits two signal symbols per channel use through a combination of two antennas for each of the real and imaginary parts. The main contributions of this study can be summarized as follows. First, we derive an upper bound for the error performance of the IQSM. We then design constellation sets that minimize the error performance of the IQSM for several system configurations. Second, we propose a double QSM (DQSM) that transmits the real and imaginary parts of two signal symbols through any available transmit antennas. Finally, we propose a parallel IQSM (PIQSM) that splits the antenna set into equal subsets and performs IQSM within each subset using the same two signal symbols. Simulation results demonstrate that the proposed constellations significantly outperform conventional constellations. Additionally, DQSM and PIQSM provide a performance similar to that of IQSM while requiring a smaller number of transmit antennas and outperform IQSM with the same number of transmit antennas.     

A stiffness parameter and truncation error criterion for adaptive path following in structural mechanics

We explore a truncation error criterion to steer adaptive step length refinement and coarsening in incremental-iterative path following procedures, applied to problems in large-deformation structural mechanics. Elaborating on ideas proposed by Bergan and collaborators in the 1970s, we first describe an easily computable scalar stiffness parameter whose sign and rate of change provide reliable information on the local behavior and complexity of the equilibrium path. We then derive a simple scaling law that adaptively adjusts the length of the next step based on the rate of change of the stiffness parameter at previous points on the path. We show that this scaling is equivalent to keeping a local truncation error constant in each step. We demonstrate with numerical examples that our adaptive method follows a path with a significantly reduced number of points compared to an analysis with uniform step length of the same fidelity level. A comparison with Abaqus illustrates that the truncation error criterion effectively concentrates points around the smallest-scale features of the path, which is generally not possible with automatic incrementation solely based on local convergence properties.     

Flame characteristics of premixed H2-air mixtures explosion venting in a spherical container through a duct

The explosion venting duct can effectively reduce the hazard degree of a gas explosion and conduct the venting energy to the safe area. To investigate the flame quantitative propagation law of explosion venting with a duct, the effects of hydrogen fraction and explosion venting duct length on jet flame propagation characteristics of premixed H₂-air mixtures were analyzed through experiment and simulation. The experiment results under initial conditions of room temperature and 1 atm show that when hydrogen fraction was high enough, part of the unburned hydrogen was mixed with air again to reach an ignitable concentration, resulting in the secondary combustion was easier produced and the duration of the secondary flame increased. With the increase of venting duct length, the flame front distance and propagation velocity increased. Meanwhile, the spatial distribution of pressure field and temperature field, and the propagation process and mechanism of the flame venting with a duct were analyzed using FLUENT software. The variation of the pressure wave and the pressure reflection oscillation law in the explosion venting duct was captured. Therefore, in the industrial explosion venting design with a duct, the hazard caused by the coupling of venting pressure and venting flame under different fractions should be considered comprehensively.     

M-estimator based Chinese Remainder Theorem with few remainders using a Kroenecker product based mapping vector

The Chinese Remainder Theorem (CRT) explains how to estimate an integer-valued number from the knowledge of the remainders obtained by dividing such unknown integer by co-prime integers. As an algebraic theorem, CRT is the basis for several techniques concerning data processing. For instance, considering a single-tone signal whose frequency value is above the sampling rate, the respective peak in the DFT informs the impinging frequency value modulo the sampling rate. CRT is nevertheless sensitive to errors in the remainders, and many efforts have been developed in order to improve its robustness. In this paper, we propose a technique to estimate real-valued numbers by means of CRT, employing for this goal a Kroenecker based M-Estimation (ME), specially suitable for CRT systems with low number of remainders. Since ME schemes are in general computationally expensive, we propose a mapping vector obtained via Kroenecker products which considerably reduces the computational complexity. Furthermore, our proposed technique enhances the probability of estimating an unknown number accurately even when the errors in the remainders surpass 1/4 of the greatest common divisor of all moduli. We also provide a version of the mapping vectors based on tensorial n-mode products, delivering in the end the same information of the original method. Our approach outperforms the state-of-the-art CRT methods not only in terms of percentage of successful estimations but also in terms of smaller average error.     

Development and validation of a micro-fin tubes evaporator model using R134a and R1234yf as working fluids

This paper presents a model of shell and tube evaporator with micro-fin tubes using R1234yf and R134a. The model developed for this evaporator uses the ε-NTU method to predict the evaporating pressure, the refrigerant outlet enthalpy and the outlet temperature of the secondary fluid. The model accuracy is evaluated using different two-phase flow boiling correlations for micro-fin tubes and comparing predicted and experimental data. The experimental tests were carried out for a wide range of operating conditions using R134a and R1234yf as working fluids. The predicted parameter with maximum deviations, between the predicted and experimental data, is the evaporating pressure. The correlation of Akhavan– Behabadi et al. was used to predict flow boiling heat transfer, with an error on cooling capacity prediction below 5%. Simulations, carried out with this validated model, show that the overall heat transfer coefficient of R1234yf has a maximum decrease of 10% compared with R134a.