Basic Geometric Parameters Research Articles

The Quasi-Static Response of Moored Floating Structures Based on Minimization of Mechanical Energy

It is essential to design a reasonable mooring line length that ensures quasi-static responses of moored floating structures are within an acceptable level, and that reduces the cost of mooring lines in the overall project. Quasi-static responses include the equilibrium position and the line tension of a moored floating structure (also called the mean value in a dynamic response), etc. The quasi-static responses derived by the classic catenary equation cannot present mooring–seabed interaction and hydrodynamic effects on a mooring line. While a commercial program can predict reasonable quasi-static responses, costly modeling is required. This motivated us to propose a new method for predicting quasi-static responses that minimizes the mechanical energy of the whole system based on basic geometric parameters, and that is easy to implement. In this study, the mechanical energy of moored floating structures is assumed to be the sum of gravitational–buoyancy potential energy, kinetic energy induced by drag forces, and spring potential energy derived by line tension. We introduce fundamental theoretical background for the development of the proposed method. We investigate the effect of quasi-static actions on mooring response, comparing the proposed method’s results with those from the catenary equation and ABAQUS software. The study reveals the shortcomings of the catenary equation in offshore applications. We also compare quasi-static responses derived by the AQWA numerical package with the results calculated from the proposed method for an 8 MW WindFloat 2 type of platform. Good agreement was drawn between the proposed method and AQWA. The proposed method proves more timesaving than AQWA in terms of modeling of mooring lines and floaters, and more accurate than the catenary equation, and can be used effectively in the early design phase of dimension mooring lengths for moored floating structures.

Determination of the shear failure areas of rock joints using a laser scanning technique and artificial intelligence algorithms

Two artificial intelligence models-backpropagation neural network (BPNN) and support vector machines (SVM)-were created to investigate the effects of mesostructure characteristics on the shear mechanical behaviors of rock joints. This was achieved through learning training samples for the evaluation of the five basic geometrical parameters sensitivity (i.e., slope angle, horizontal orientation, elevation difference, curvature, and aperture distribution), and for determination of the shear failure regions when rock joints were subjected to low-normal and shear loads. First, the digital elevation models (DEMs) of rock joints were produced through point clouds collected using a laser scanning system. Five geometrical parameters were specified as the inputs for the artificial intelligence models, and an approach was developed to calculate the 3D aperture distribution using a point cloud registration algorithm. Shear failure regions were considered as the outputs, which were extracted from images taken after direct shear testing via the global threshold algorithm. Secondly, BPNN and SVM models were employed in order to establish relationships between the geometrical parameters and shear failure areas by machine learning on training samples. Thirdly, the information value (IV) algorithm was used to verify the two trained models. Results showed that the BPNN and SVM models made acceptable determinations of the shear failure areas, which corresponded to the real situation. The predictions from the BPNN and SVM models were more accurate than those from the IV algorithm. Furthermore, shear failure regions depended primarily on the aperture distribution of rock joints during the shearing process, followed by horizontal orientation, elevation difference, and then the slope angle. The effect of parameter curvature on shear failure was less than the other four parameters.

Rock joint detection from borehole imaging logs based on grey-level co-occurrence matrix and Canny edge detector

Rock joints play an important role in characterizing the rock mass quality for geomechanical design and stability analysis. An approach was developed to detect and characterize rock joints from images collected by a borehole imaging system. A grey-level co-occurrence matrix was employed to locate the joint regions, allowing more focused and effective detection processing, followed by extractions of the upper and lower edges of rock joints using the Canny algorithm. Four basic geometric parameters of rock joints (orientation, depth, aperture and core length) were determined based on the fitting of sinusoids to joint edges. Furthermore, the joint density was determined based on the geometric parameters. To calibrate the proposed approach, a borehole on the site of the planned Rumei hydropower station at Lantsang River was selected as a case study. Orientation of rock joints with gentle dip angles, which was determined from borehole imaging logs, corresponded to the measurements in three horizontal tunnels. Additionally, both joint density and pressure-wave velocity revealed that jointed rock mass was observed at depths from 100 to 120 m, and intact rock mass was present at depths of 150–170 m, indicating the good performance of the proposed method.

Анализ условий бесконтактного движения эксцентриковых механизмов свободного хода

Freewheel mechanisms are used in kinematic chains of technical systems of a various functionality. When such mechanisms freewheeling, it is necessary to ensure that there is no contact of their working elements to reduce friction losses and wear. At the same time, it is necessary to ensure the minimum value of the idling angle affecting the accuracy and response time of the kinematic chain in which the mechanism is installed. The task of analyzing and determining the geometric conditions allowing ensuring a radial gap between the working elements of the eccentric freewheel mechanisms with free-running engagement has been set. To solve this problem, a design scheme is proposed and a mathematical model describing the relationship between the geometrical parameters of the mechanism is obtained. The nature of the influence of the basic geometric parameters (eccentricity, radial clearance, modulus, etc.) on the value of the idling angle is established. It is shown that when designing, the values of the module and the gap should be chosen as the minimum permissible, taking into account the load capacity and the assembly conditions. The eccentricity can be assigned based on the requirements of the manufacturing technology.

Sensitivity optimization of U-shaped fiber optics based on the Taguchi method

The structure of macrobending fiber optics is an ideal structure for constructing fiber optic sensors. This study presents a new design and implementation of U-shaped fiber optics. The basic geometric parameters of U-shaped fiber optics, such as dimension size or curve radius, are analyzed. The Taguchi method was used to optimize the effects of the control and noise factors with respect to dimension size, loop, wavelength, and core size. The control factors were varied at different levels to achieve a novel sensitivity response optimization of the wavelength and core size. The quality characteristics of the signal-to-noise ratio (larger-the-better characteristics) were used to determine the effect of the control parameters in the data analysis. The data of the sensitivity response was analyzed to predict the performance of the U-shaped fiber optics. Results indicate that, by using the Taguchi method, the best control factor setting involves 2.5 cm × 1.5 cm (dimension size) and 1550 nm (wavelength). The percentage contribution of wavelength is the highest at 67.17%, followed by dimension size (13.31%) and number of loops (11.72%) for the fiber optic core size of 50–9–50 μm. For the 9 μm single-mode fiber optics, the corresponding percentages are 61.48%, 16.64%, and 12.81% for wavelength, dimension size, and number of loops, respectively. The Taguchi methodology is suitable for designing sensor geometry.

СИНТЕЗ ТА АНАЛІТИЧНІ ДОСЛІДЖЕННЯ ГЕОМЕТРИЧНИХ ПАРАМЕТРІВ СТАТИЧНО ВИЗНАЧЕНОГО ПРОСТОРОВОГО ШАРНІРНОГО МЕХАНІЗМУ ГАЛТУВАЛЬНОЇ МАШИНИ

Synthesis of a seven-link statically determined spatial hinge mechanism with an additional movable crank link without redundant (passive) connection of the tumbling machine with a complex spatial movement of the working vessel with subsequent analytical study of its design and geometric parameters. Methodology. The analytical method of research is used on the basis of geometric and structural synthesis of a spatial seven-link hinge mechanism with an additional movable crank link without redundant connection of the tumbling machine with a complex spatial movement of the working vessel. The machine was simulated in the SolidWorks-2016 computer-aided design system. Tumbling types of equipment with containers, which perform a different character of movement, are analyzed. On the basis of structural synthesis, the design of a seven-link statically defined spatial mechanism with an additional movable link, a tumbling machine crank, in which the working capacity performs a complex spatial movement, is proposed. Carried out 3D modeling of the machine in the CAD system SolidWorks 2016. Analytical studies of the main geometric parameters of the developed tumbling machine were carried out. Scientific novelty. A relationship has been established between various geometric parameters of the synthesized seven-link statically determined spatial hinge mechanism, in particular, between the center-to-center length of the intermediate connecting rod (working capacity) and the length of the crank, which makes it possible to calculate the necessary ratios of the lengths of the links of the mechanism to ensure the functioning of the machine without jamming its spatial mechanism. Practical significance. A new design of a machine for processing parts has been developed, based on a seven-link statically determined spatial hinge mechanism with an additional movable crank link. Mathematical dependences are obtained for calculating its basic design and geometric parameters. These dependencies can be used in the corresponding design bureaus of machine-building enterprises at the design stage of tumbling equipment with a complex spatial movement of working containers.

ОЧИЩЕННЯ ЗЕРНА КІНОА – ВАЖЛИВИЙ ЕТАП ПІСЛЯЗБИРАЛЬНОЇ ОБРОБКИ

In the world and in Ukraine, the quinoa market is growing rapidly due to its extremely beneficial properties for the body. Quinoa is one of the few gluten-free crops with a high content of easily soluble proteins, which provides the possibility of making special foods for children, people who play sports, vegetarians and diabetics. Quinoa grain contains a lot of protein: from 16.2% to 20%, the amino acid composition of the protein is very balanced, quinoa grain also contains carbohydrates, fats high in lecithic acid, fiber, minerals and vitamins of group B. The dynamics of sown areas and quinoa production in the world. The work is devoted to the organization of the operation of purification of quinoa grain, which is an important stage of its post-harvest processing. Any processing of grain is associated with its purification from impurities. The presence of impurities negatively affects the efficiency of grain storage and its technological features, which leads to a decrease in yield and quality of processed products. Therefore, cleaning operations occupy a central place in the post-harvest processing of grain. We have determined the geometric dimensions and calculated the basic geometric parameters of quinoa grain, which are the main indicators for the organization and conduct of the cleaning process. To identify the necessary working bodies and determine the optimal size of the holes for the separation of the mixture into fractions, the analysis of the variability of the grain size of the main crop and the size of the released impurity. Based on these data, a correlation table is constructed. Analysis of the correlation table shows that for effective cleaning of quinoa grain it is necessary to use sieves with a diameter of 3… 3.5 mm to remove large impurities and sieves 1.0×20, with a diameter of 1.6 and 1.8 mm. Based on the data of the correlation table, a fractional scheme of quinoa grain purification was developed, with the appropriate shapes and sizes of sieve holes. This scheme of purification of quinoa grain is effective and allows to isolate 93% of impurities.

Influence of Selected Model Parameters on the Electromagnetic Levitation Melting Efficiency

The article presents the results of multivariate calculations for the levitation metal melting system. The research had two main goals. The first goal of the multivariate calculations was to find the relationship between the basic electrical and geometric parameters of the selected calculation model and the maximum electromagnetic buoyancy force and the maximum power dissipated in the charge. The second goal was to find quasi-optimal conditions for levitation. The choice of the model with the highest melting efficiency is very important because electromagnetic levitation is essentially a low-efficiency process. Despite the low efficiency of this method, it is worth dealing with it because is one of the few methods that allow melting and obtaining alloys of refractory reactive metals. The research was limited to the analysis of the electromagnetic field modeled three-dimensionally. From among of 245 variants considered in the article, the most promising one was selected characterized by the highest efficiency. This variant will be a starting point for further work with the use of optimization methods.

ВЫБОР МАРКИ СПЛАВА, ПОКРЫТИЯ И ГЕОМЕТРИЧЕСКИХ ПАРАМЕТРОВ РЕЖУЩЕЙ ПЛАСТИНЫ ДЛЯ ТОРЦЕВОГО ФРЕЗЕРОВАНИЯ ВЫСОКОУГЛЕРОДИСТОЙ ЗАКАЛЁННОЙ СТАЛИ 95Х18-Ш

The application of hardened steel parts for the purpose of wear-resistance increase becomes increasing spread in different branches of mechanical engineering. In view of high hardness of the work surface of parts, finishing is carried out by flat grinding. 
 During the hardened steel grinding there are formed burns, cracks, admixtures of abrasive particles in the work surface which are inadmissible defects in a surface layer of critical parts mounted in the fuel unit of an aviation engine. 
 The analysis of literature and company experience has shown that after thermal treatment instead of finishing is necessary to use surface finishing by a face milling method, but there are no sufficient recommendations for tool choice and cutting modes to date. Jointly with the educational department there are carried out theoretical researches of cutters for the face milling of the “selector housing” mass-produced parts consisting of corrosion-resistant 95H18-Sh steel with the hardness of 59÷61 HRC. In the paper there is considered a chemical composition of 95H18-Sh steel, a method for manufacturing a cast, its physical, mechanical and chemical properties. 
 Taking into account data obtained for the face-milling cutter installation on the frame there was chosen Sandvik Coromant material for the replaceable cutting insert the base of which consists of hard alloy 1010 with PVD coating. 
 Later on there was carried out selection of basic geometrical parameters and characteristics of a cutting plate and also a micro-geometry of a major cutting edge and a tip. Mass-produced replaceable through-away plates with R245-12 T3 M-PM number of 1010 hard alloy and PVD coating were obtained from the catalog of Sandvik Coromant company. At the end of the work a conclusion was drawn that the application of face milling will allow ensuring the requirements to the design documentation of the product, decreasing thermal and power stress of the process, increasing productivity, surface quality and excluding the necessity in abrasion, and the investigation results are applicable to the fulfillment of the complete factor experiment and computation of a simulator with the definition of the impact of variable factors upon a response function.

МОДЕЛЮВАННЯ АНІЗОТРОПІЇ ПИТОМОЇ ЕЛЕКТРОПРОВІДНОСТІ БІОЛОГІЧНОЇ ТКАНИНИ, ЯКА ВИНИКАЄ ЗА ЛОКАЛЬНОГО СТИСКАННЯ ЕЛЕКТРОДАМИ ДЛЯ БІПОЛЯРНОГО ЗВАРЮВАННЯ

Current publications on bipolar welding use the electrical characteristics of uncompressed biological tissue. This reduces the accuracy of calculating the distribution of the density of the flowing currents and the strength of the electric fields in the zone of the fabric to be welded when it is squeezed. The aim of the work is to show a methodology for calculating the change in the specific electrical conductivity of biological tissue under local compression by electrodes and the effect of this factor on the results of modeling electrical processes of biological welding. A geometric interpretation of the change in the electrical conductivity of the pig's heart muscle when squeezed by bipolar welding electrodes in relative units is proposed. The principle of similarity of the geometric parameters of the physical experiment and the graphic model of COMSOL multyphysics is used, as a result of which the dependences of the three main geometric parameters of the model on the magnitude of the relative compression are determined. The method of successive approximations of the values of the total electrical resistance of biological tissue in a physical experiment at frequencies of 0,3, 30, and 300 kHz and the calculated resistances on the model with a change in the basic geometric parameters of specific electrical conductivity was used. A model of bipolar welding of biological tissues is obtained, which takes into account the anisotropy factor of the electrical conductivity of biological tissue under compression. Some results of investigations of the regularities of the current flow in the tissue, taking into account the arising anisotropy, are presented. References 12, figures 5, tables 4.

Validation of an image-analysis-based method of measurement of the overall dimensions of seeds

Due to agricultural producers’ increasing awareness and the introduction of increasingly restrictive crop protection standards, producers have to use new technologies that are safer for consumers and the environment. In order to meet the requirements of these standards, it is necessary to take the physical properties of crops and agricultural raw materials (basic geometric parameters, shape factors, and equivalent spherical diameters) into account when designing machinery for the harvesting, transport, and processing of agricultural produce. When designing machinery, methods used for calculating the strength of the machine construction and the discrete element method (DEM) used in computer simulations of processes involving seeds or particles require the provision of the exact geometrical dimensions of particles and seeds. The aim of the study was to develop a universal method of measurement of the overall dimensions of granular material particles using a widely available application based on image analysis. The study presents the possibility of using a new method of measuring overall dimensions by means of the widely available ImageJ application on a specially designed test facility.

Обґрунтування конструктивної схеми пневморешітного сепаратора зерна

The aim of the article is to improve the design of the original centrifugal grain separator. The separator is designed to separate the components of grain materials by size and aerodynamic properties. The basic design satisfactorily performs the technological process, but has large dimensions vertically. Reducing the size will simplify the design and reduce the cost of the machine. The article proposes to replace the double pneumatic cleaning of grain material with a single one. At the same time the car gets rid of the closed aspiration system. The closed aspiration system has operational advantages, however difficult adjustment reduces indicators of technological efficiency of pneumatic cleaning of grain. The original pneumatic cleaning system allows you to remove light impurities without creating significant air resistance, due to the lack of countercurrent movements. In addition, the use of an inclined pneumatic channel does not require the creation of high-speed airflow. As a result of the proposed improvement simplifies the structure and regulation of the separator, as well as reduces its size and weight. In addition to the modernization of the design of the pneumatic-sieve separator, the article presents the method of design engineering calculation of its basic geometric parameters. Depending on the specific capacity of the upper (ear) sieve and the characteristics of the grain mixture is determined by its length and angle. The remaining geometric parameters are derived from the above. Based on preliminary calculations, the following conclusions can be drawn. The use of the proposed scheme will reduce the height and weight of the centrifugal pneumatic sieve grain separator. Replacing the double air cleaning with a single one will simplify the adjustment of the machine. Experimental establishment of indicators of technological efficiency of the proposed separator will theoretically determine the dimensions and automate the design process of grain cleaning machines created by a similar scheme.

Теоретичні аспекти розділення зерна на решеті інерційно-гравітаційного сепаратора

The aim of the article is to substantiate the design, derivation and approbation by calculations of formulas for determining the parameters of the sieve with slits that expand in the direction of movement of the processed material. It is established that grain cleaning machines, which currently work on agricultural and processing enterprises with flat sieves, have been used for many years, are well studied and improved, their technical and economic indicators have reached maximum values. The problem is that to ensure the proper operation of existing grain cleaning machines with traditional flat sieves, a large amount of energy costs are spent on additional operations that are not directly related to the separation process, but without them the normal operation of the machine is impossible. This is directly the transportation of grain and cleaning the sieves from grains that are stuck in the cracks and degrade the quality of their work. The substantiation of the technological scheme of the inertial-gravity separator sieve with slits expanding in the direction of movement of the processed material is performed and the influence of its main parameters on the efficiency of separation of grain mixtures is established. The regularities of the movement of the grain mixture on the surface of the sieve are determined, when favorable conditions are created for the passage through the slits of particles that can pass through it. The method of calculation of the basic geometrical and kinematic parameters of a sieve is offered. To implement the proposed calculation method developed software that allows you to convert blocks developed in analytical form of the calculation method in a form that meets the requirements of the architecture of mathematical models and implements the numerical methods of Runge-Kutt and Nelder-Mead. Tests have shown that the quality of separation of wheat grain on the proposed sieve increases by 12-14% compared to existing ones. When implementing the sieves of the proposed design, the issue of influencing the quality of separation of the magnitude of the bar deflection in the end part and their limits for different crops remains unresolved.

The calculation basis for a four-component jet mixer for fertilizer and water

This article covers calculation basis for a four-component jet mixer for fertilizer and water. The calculation for a four-component jet mixer for fertilizer consists in determining the basic geometric and hydrau-lic parameters of a four-component jet mixer for fertilizer and water and supplying the mixture to irrigated areas, with fertilizing irrigation, which will allow supplying all types of fertilizers and changing the concentration of mixture in the required proportions. All geometric relative parameters are calculated on the basis of the need to scale the mixer dimensions and are taken as the ratio of the diameters of the mixer elements to the cylindri-cal part of the mixing chamber. The above calculation bases determine the main parameter of the mixer necessary for determining all the elements – the cross-sectional area of the annular nozzle. It was founded that when calculating the geometric characteristic, you should be guided by the desire to accept the value of the geometric characteristic m=2.5 ÷ 8.0, corre-sponding to the maximum value of the efficiency up to 40% and higher.

Angular Measurement of High Precision Reducer for Industrial Robot

High precision reducer is the core component of industrial robot. Its performance test is the key to improve product quality and ensure the accuracy of robot operation. One of the basic geometric parameters in performance test is the angle, which refers to the angular displacement of the input or output of the tested reducer. Based on a vertical instrument, angular measurement systems are designed in this article. In order to ensure the precision of results, the angle encoder is as close as possible to the measured object, which shortens the measurement chain and reduces the number of error sources. A cylindrical and disk structure improves the structural stiffness, ensures regular deformation patterns, and minimizes the angular errors caused by weak stiffness supports in the conventional instrument. Another system consisting of an autocollimator and a regular polyhedron, whose output is taken as angular standard, calibrates absolute circular gratings in the instrument. The model based on back propagation neural network can compensate the errors over the whole circumference, and finally get the angular displacement of input and output of the tested reducer in the drive process accurately. After compensation, the angular measurement errors of the instrument are within ±2 arc seconds.

Automation control system of 3d printing robotic platform with implemented wire + arc welding technology

Purpose. Development of the robotic platform automated control system architecture, development of the software control algorithm.
 Methodology. To implement the algorithm of the control program, computer modeling of thermal regimes in CAE systems is used. The basic parameters of the single layer printing technique were obtained by experimental use of the wire plus arc additive manufacturing (WAAM) technology.
 Findings. Requirements for manufacturability and printing quality of the manufactured parts were defined in the form of geometric dimensions, surface waviness, parameters of the desired microstructure state, residual stresses, maintaining of the optimal manufacturing speed. Based on the requirements of manufacturability analysis, an algorithm for the control program was developed. Robotic platform automated control system architecture with feedback device for the thermal mode control, parameters of the geometrical form of the manufactured part and weld pool were developed. Three -level hierarchical model, which gives an ability to consider in the process of 3D printing each level individually in terms of welding bead, layer and wall, was developed. The input data for the operation of the automated control system of the robotic platform using the technology of electric arc welding are determined. Basic geometrical parameters and the simple welding bead and the methods of overlapping of two or more beads were shown. Critical differences between ideal and real welding overlapping models were considered for necessity of taking into account whilst generating robot control software. Analysis of the possibilities for the CAE simulation of the three-dimensional printing using wire plus arc additive manufacturing technology is performed to determine the influence of the temperature parameters, mechanical loads, toolpath change, and based on the data obtained, it became possible to determine residual stresses and defects in manufactured parts.
 Originality. Robotic platform automated control system architecture with feedback device for the control of thermal mode, parameters of the geometrical form of the manufactured part and weld pool was developed. Three-level hierarchical model for the wire plus arc additive manufacturing (WAAM) technology was created. Software control algorithm which provides an opportunity to improve geometrical and mechanical properties of the manufactured parts was developed.
 Practical value. Development of an automated control system for 3D printing robotic platform with WAAM implemented technology, which will provide an opportunity for increase in the printing accuracy of the manufactured parts and will help to reduce manufacturing time.

Quantum chemical modeling in the system polyvinylpyrrolidone—cation of the dinitrosyl iron complex

The structures of a number of the products for the reaction of the NO donor (cation of the dinitrosyl iron complex [Fe(SC(NH2)2)2(NO)2] • Cl•H2O) with poly-N-vinylpyrrolidone in water were studied using the density functional method and QTAIM analysis. The quantum chemical calculations of the basic geometric and energy parameters of the formed compounds were performed. The expected forms of existence of this system in aqueous solutions were described on the basis of the obtained results. The retention of the NO-donor activity in the formed polymeric structures is related to the preservation of the Fe(NO)2 fragment in them.

PERFORMANCE CHARACTERISTICS OF THE LEVER-VAN SHOCK ABSORBER WITH THE HINGE-LEVER CONTROL MECHANISM

The article presents a fundamentally new example of a passive lever-blade shock absorber with an articulated lever mechanism for controlling its operating characteristic, the use of which is effective as part of the torsion bar suspension of a tracked vehicle. The efficiency of the presented device is significantly increased by scientifically substantiated expansion of its mechanical structure with an additional controlling mechanical structure in the form of a pivot-lever mechanism. The developed structural scheme and the corresponding generalized mathematical model of the proposed device are presented. Based on the developed generalized mathematical model, analytical studies have been carried out, on the basis of which mathematical expressions have been obtained that describe the functional interaction between the constituent elements of the proposed lever-blade damper and their influence on the type of working characteristics that is realized in this case. A comparative analysis of the obtained performance with the performance that can be implemented using existing lever-blade shock absorbers is carried out. It was found that the proposed device is able to realize working characteristics that cannot be realized using known samples of passive lever-blade and lever-piston shock absorbers. The basic geometric parameters of both the main mechanical structure of the proposed device and the additional mechanical control structure, the variation of which allows reproducing the target (needed under certain conditions) working characteristics, are highlighted and substantiated. The directions and prospects of further research are given, which make it possible to increase the efficiency of the lever-paddle shock absorber with the articulated-lever control mechanism.

НОВІ МАТЕМАТИЧНІ МОДЕЛІ ПОВЗДОВЖНІХ ГІДРОДИНАМІЧНИХ СИЛ НА КОРПУСІ СУДНА

Development of modern ship's automatic steering systems, navigation simulators, research of ship maneuvers stipulates the necessity of adequate mathematical models of the ship propulsion complex. The main components of the non-inertial forces of the ship propulsion complex are the hydrodynamic forces on the hull. Therefore, the improvement of mathematical models of these forces refers to important scientific and practical problems. This paper proposes a general approach to the construction of mathematical models of hydrodynamic forces on the hull. The approach is based on a multivariate quasilinear regression analysis, considering the values of the multiple correlation coefficient, the significance of the model, and the significance of each explanatory factor (regressor). In particular, the Fisher's criterion was used to test the significance of the models, and the statistical significance of each regressor was checked with the help of the Student's criterion. In addition, the standard error of each regressor was investigated. We also checked the absence of multicollinearity of the obtained models. The inadequacy of many existing mathematical models of hydrodynamic derivatives of longitudinal hydrodynamic forces on the hull is shown. In particular, it was found that one-factor correlation analysis cannot provide the construction of adequate models with high significance for all hydrodynamic derivatives. It has also been proven that applying only the AIC minimum criterion (Akaike Information Criterion) cannot ensure that all the regression analysis criteria are met. New adequate models of hydrodynamic derivatives have been constructed for longitudinal hydrodynamic forces on the hull with a high level of correlation, high indicators of significance of the models as a whole and of each regressor separately. The models are built for the whole range of variation of the block coefficient: (0.5; 0.9) and separately for the two ranges: (0.5; 0.7) and (0.7; 0.9). As regressors, we used the relations of the basic geometric parameters of the vessel, such as length, breadth on the current waterline, draught and the value of the block coefficient.

Investigation of the influence of the geometric parameters of AFM cantilevers on the resonant frequency of their oscillations

This paper presents the results of theoretical and experimental studies aimed at studying the influence of the basic geometric parameters of micromechanical cantilevers on the resonant frequency of their oscillations. The dependences of the oscillation frequency on the length of the cantilever beam, obtained based on mathematical modeling are theoretically investigated by the finite element method. In experimental studies that used AFM cantilever beams, the beams were shortened stepwise by the method of local ion beam etching by focused ion beam (FIB) Ga+. After each step, the change in the resonant frequency of oscillations was monitored. It was found that the application of the FIB method allows you to accurately change the geometric parameters of the probe beams, which, in turn, allows you to change the resonant frequency of cantilever oscillations with high accuracy. During the analysis of the obtained dependences of the resonant frequency of oscillations on the geometric parameters of the beams, it was found that a decrease in the length of the cantilever from 110 to 80 μm leads to an approximately twofold increase in the resonant frequency of oscillations of the cantilever from 320 to 620 kHz. The obtained graphs of the theoretical and experimental dependencies are compared, which showed a good correlation of the results.