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Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently. [ABSTRACT FROM AUTHOR]

Single-point incremental forming (SPIF) has emerged as a cost-effective and rapid manufacturing method, especially suitable for small-batch production due to its minimal reliance on molds, swift production, and affordability. Nonetheless, SPIF's effectiveness is closely tied to the specific characteristics of the employed sheet materials and the intricacies of the desired shapes. Immediate experimentation with SPIF often leads to numerous product defects. Therefore, the pre-emptive use of numerical simulations to predict these defects is of paramount importance. In this study, we focus on the critical role of the forming limit curve (FLC) in SPIF simulations, specifically in anticipating product fractures. To facilitate this, we first construct the forming limit curve for Al1050 sheet material, leveraging the modified maximum force criterion (MMFC). This criterion, well-established in the field, derives FLCs based on the theory of hardening laws in sheet metal yield curves. In conjunction with the MMFC, we introduce a graphical approach that simplifies the prediction of forming limit curves at fracture (FLCF). Within the context of the SPIF method, FLCF is established through both uniaxial tensile deformation (U.T) and simultaneous uniform tensile deformation in bi-axial tensile (B.T). Subsequently, the FLCF predictions are applied in simulations and experiments focused on forming truncated cone parts. Notably, a substantial deviation in fracture height, amounting to 15.97%, is observed between simulated and experimental samples. To enhance FLCF prediction accuracy in SPIF, we propose a novel method based on simulations of truncated cone parts with variable tool radii. A FLCF is then constructed by determining major/minor strains in simulated samples. To ascertain the validity of this enhanced FLCF model, our study includes simulations and tests of truncated cone samples with varying wall angles, revealing a substantial alignment in fracture height between corresponding samples. This research contributes to the advancement of SPIF by enhancing our ability to predict and mitigate product defects, ultimately expanding the applicability of SPIF in diverse industrial contexts. [ABSTRACT FROM AUTHOR]

The armature reaction of the hybrid excitation starter generator (HESG) under load conditions will affect the distribution of the main magnetic field and the output performance. However, using the conventional field-circuit combination method to study the armature reaction has the problem of low accuracy and inaccurate influencing factors. Therefore, this paper proposed a graphical method to analyze the armature reaction and a new type of HESG with a combined-pole permanent magnet (PM) rotor and claw-pole electromagnetic rotor. The analytical formula of the voltage regulation rate under the armature reaction was derived using the graphical method. The main influencing parameters of the armature reaction magnetic field (ARMF) were analyzed, and the overall output performance was analyzed using finite element software. On this basis, comparison analyses before and after optimization and the prototype test were carried out. The results show that the direct-axis armature reaction reactance, quadrature-axis armature reaction reactance, and voltage regulation rate of the optimized HESG were significantly reduced, the output voltage range of the whole machine was wide, and the voltage regulation performance was good. [ABSTRACT FROM AUTHOR]

This paper presents timber lamella structures applied to the circular cylinder surface when all lamellae axes intersect at the nodes. To achieve the uniformity of all elements in this structure, the geometry of the structure must be carefully designed. The main methods for the research are graphical and numerical methods for geometric design and a prototype construction for a specific geometric pattern. The methods are discussed for their ease of replication, as well as the possibility of reinterpretation on other surfaces, while the prototype design and construction give insight into the process from design to execution. The combination of these methods allows for a thorough analysis of the geometry for lamella structures. The analysis shows that geometrical design must begin from the whole to the lamella, and that the number of element types in the structure depends on the disposition of the elements and the angle of the pattern. The discussion shows the advantages and limitations of the proposed methods, while the conclusions give the guidelines for the implementation of lamella structures into new design projects. [ABSTRACT FROM AUTHOR]

At gauged watersheds, the time of concentration can be estimated using rainfall-runoff data; however, at ungauged watersheds, empirical methods are used instead. Large errors in the application of empirical methods may cause inaccurate modeling of floods and unreliable structure design. In this paper, methods for calculating the time of concentration (Tc) were compared to identify the best equation for estimating Tc in ungauged watersheds of an arid region. The graphical method, based on measured data, was compared to 15 empirical methods to determine which empirical method returned the best results. The graphical method was applied to 33 rainfall-runoff events in four rural sub-watersheds located in the central parts of Hormozgan province, Iran. A ranking-based procedure was used to select the best performing empirical methods. To minimize bias and improve accuracy, the best performing empirical methods were modified by adjusting their formulas. According to the study, three empirical methods: (1) Williams, (2) Pilgrim and Mac Dermott, and (3) Arizona DOT, performed the best in the study areas. The results also showed that the modified Williams and Arizona DOT's formulas were able to estimate the time of concentration in ungauged watersheds with an error lower than 1%. [ABSTRACT FROM AUTHOR]