Plane Recognition on the Basis of Cloud of Points Determined by Photogrammetry

2015 ◽  
Author(s):  
Andrzej Gessner ◽  
Marcin Sobczak ◽  
Michal Kowal
Keyword(s):  
Mathematical Model ◽  
Rapid Assessment ◽  
Geometrical Parameters ◽  
Sample Object ◽  
Structured Light Scanner ◽  
Object Based ◽  
Cartesian Coordinate ◽  
Cloud Of Points ◽  
The Mathematical Model ◽  
Ongoing Project

The article presents the results of research on developing a mathematical model allowing to identify the planes in a measured object, based on a cloud of points located on its walls. A basic mathematical description of surfaces is presented. An algorithm for determining the general equation of the plane on the basis of three points described in the Cartesian coordinate system has been developed. The algorithm has then been used to determine all possible planes in a given set of measured points, which were then subjected to the process of elimination and normalization. Filtered equations of the planes were grouped in order to finally determine the set of the sought-after equations. The designed algorithms have been implemented in a C++ computer program and their effect has been verified on a sample object with 3 methods of measurement: a contact measurement, a structured-light scanner method and with photogrammetry. The calculated equations have been compared with equations developed by a referenced commercial software. The results of the comparison have proved the correctness of the tested algorithms. The mathematical model will be used for rapid assessment of the geometrical parameters of castings and of the size of the machining allowances, as well as in the automatic settings of the casting in the machining space. The research was supported by the National Centre for Research and Development, Poland within the ongoing project No. LIDER / 07/76 / L-3/11 / NCBR / 2012.

Experimental and Theoretical Investigation of Performance of a Solar Chimney Model Part II: Model Development and Validation

2021 ◽  
Vol 5 (2) ◽  
Author(s):  
Ibrahim A Abuashe ◽  
Bashir H Arebi ◽  
Essaied M Shuia
Keyword(s):  
Mathematical Model ◽  
Power Output ◽  
Model Development ◽  
Geometrical Parameters ◽  
Balance Equations ◽  
Solar Chimney ◽  
And Performance ◽  
Development And Validation ◽  
The Mathematical Model ◽  
Good Agreement

A mathematical model based on the momentum, continuity and energy balance equations was developed to simulate the behavior of the air flow inside the solar chimney system. The model can estimate the power output and performance of solar chimney systems. The developed mathematical model is validated by the experimental data that were collected from small pilot solar chimney; (experiment was presented in part I). Good agreement was obtained between the experimental results and that from the mathematical model. The model can be used to analyze the solar chimney systems and to determine the effect of geometrical parameters such as chimney height and collector diameter on the power output and the efficiency of the system

scholarly journals A study of a quasilinear model of the particles of a suspension that are aggregated and settled in an inhomogeneous field

2020 ◽  
Keyword(s):  
Mathematical Model ◽  
Initial Conditions ◽  
Lower Boundary ◽  
Complex Model ◽  
Discontinuity Surface ◽  
Inhomogeneous Field ◽  
Compact Zone ◽  
Quasilinear Systems ◽  
Cartesian Coordinate ◽  
The Mathematical Model

The mathematical model of the sedimentation process of suspension particles is usually a quasilinear hyperbolic system of partial differential equations, supplemented by initial and boundary conditions. In this work, we study a complex model that takes into account the aggregation of particles and the inhomogeneity of the field of external mass forces. The case of homogeneous initial conditions is considered, when all the parameters of the arising motion depend on only one spatial Cartesian coordinate x and on time t. In contrast to the known formulations for quasilinear systems of equations (for example, as in gas dynamics), the solutions of which contain discontinuities, in the studied formulation the basic system of equations occurs only on one side of the discontinuity line in the plane of variables (t; x). On the opposite side of the discontinuity surface, the equations have a different form in general. We will restrict ourselves to considering the case when there is no motion in a compact zone occupied by settled particles, i.e. all velocities are equal to zero and the volumetric contents of all phases do not change over time. The problem of erythrocyte sedimentation in the field of centrifugal forces in a centrifuge, with its uniform rotation with angular velocity ω = const is considered. We have studied the conditions for the existence of various types of solutions. One of the main problems is the evolution (stability) problem of the emerging discontinuities. The solution of this problem is related to the analysis of the relationships for the characteristic velocities and the velocity of the discontinuity surface. The answer depends on the number of characteristics that come to the jump, and the number of additional conditions set on the interface. The discontinuity at the lower boundary of the area occupied by pure plasma is always stable. But for the surface separating the zones of settled and of moving particles, the condition of evolution may be violated. In this case, it is necessary to adjust the original mathematical model.

ON THE EXPRESS ESTIMATION OF GEOMETRICAL PARAMETERS OF A HYDRAULIC FRACTURING CRACK FIXED ON A PROPPANT USING THE METHODS OF MATHEMATICAL MODELING

2020 ◽  
Vol 6 (3) ◽  
pp. 79-92
Author(s):  
Alexey S. Shlyapkin ◽  
Alexey V. Tatosov
Keyword(s):  
Mathematical Model ◽  
Hydraulic Fracturing ◽  
Rapid Assessment ◽  
Geometric Parameters ◽  
Engineering Practice ◽  
Geometrical Parameters ◽  
Technological Parameters ◽  
Additional Information ◽  
Software Products

Improving technologies and increasing the number of activities related to hydraulic fracturing increase the requirements for the speed and quality of engineering support. For hydraulic fracturing design, there are specialized software products-hydraulic fracturing simulators, which are based on mathematical models of various dimensions. Taking into account the influence of filtration leaks into the reservoir and the behavior of proppant particles in the crack largely determine the shape of the fracture crack. In the model representation, these factors are taken into account, but they need to be clarified in order to increase the quality of the forecast and estimate the productivity of the crack, which determines the relevance of this area of study. In this paper, we propose an analysis that allows us to quickly evaluate the geometric parameters of the crack when changing the technological parameters and properties of the fracture fluid. The presented mathematical model is based on a one-dimensional mathematical model in PKN representation (Perkins — Kern — Nordgren model). All calculations presented in this paper were performed using the certified TSH Frac software package designed for modeling the geometric parameters of hydraulic fracturing cracks. The results of the study can be used in engineering practice for rapid assessment of the geometric parameters of a hydraulic fracturing crack. Subsequent adjustment and adjustment of the model can be carried out when additional information is obtained during small-volume test uploads in the well under study.

Parametric Analysis of a PULSCO Vent Silencer

2014 ◽  
Author(s):  
Usama Tohid ◽  
Chris Genger ◽  
John Kaiser ◽  
Ilaria Accorsi ◽  
Arturo Pacheco-Vega
Keyword(s):  
Mathematical Model ◽  
Parametric Study ◽  
Numerical Results ◽  
Operating Conditions ◽  
Working Fluid ◽  
Geometrical Parameters ◽  
Computational Domain ◽  
Hole Size ◽  
Plane Wave Solution ◽  
The Mathematical Model

We have conducted a parametric study via numerical simulations of a PULSCO vent silencer. The overall objective is to demonstrate the existence of an optimum system performance for a given set of operating conditions i.e., temperature, pressure, mass flow-rate and the working fluid, by modifying the corresponding geometry of the device. The vent silencer under consideration consists of a perforated diffuser, the silencer body and a tube module. The tube module consists of a set of tubes through which the working fluid passes. The flow tubes are perforated and surrounded with acoustic packing that is responsible for the attenuation. The mathematical model of the vent silencer is built upon Helmholtz equation for the plane wave solution, and the Delany-Bazley model for the acoustic packing. The geometrical parameters chosen for the parametric study include: the porosity of the diffuser and the flow tubes, the type of packing material used for the tube module, bulk density for the acoustic packing and the hole diameter of the perforated diffuser and flow tubes. The equations of the mathematical model are discretized over the computational domain and solved with a finite element method. Numerical results in terms of transmission loss, for the system, indicate that diffuser hole size of 1/4” with porosity of 0.1, flow tube hole size of 1/8” with porosity of 0.23, packing density of 16 kg/m3 for TRS-10 and 100 kg/m3 for Advantex provided the optimum results for the chosen set of conditions. The numerical results were found to be in agreement with experimental data.

scholarly journals Conditions Of Fuel Filling Dispenser Trouble – Free Operation

2015 ◽  
Vol 2 ◽  
pp. 107
Author(s):  
Vladimirs Gonca ◽  
Yurijs Shvabs ◽  
Svetlana Polukoshko
Keyword(s):  
Mathematical Model ◽  
Fuel Tank ◽  
Geometrical Parameters ◽  
The Mathematical Model

Regularly on the filling stations (FS) there are failures at priming of transport vehicles, when a driver, driving away after priming, forgets to smuggle out of a pistol from the mouth of filling tank of car. Thus, at wedging of pistol in the tank of car, there are not only breaks in a chart a pistol is a hose but also serious destructions of fuel filling dispenser (FFD). In the present paper the mathematical model of functioning of chart is considered vehicle - fuel filling dispenser. From the analysis of the got model, if a car begins motion with the undrawn pistol out of a fuel tank, the geometrical parameters of chart are determined vehicle - fuel filling dispenser, at which slipping out of pistol or his wedging will be in the mouth of tank which possible consequences are considered for (tearing away of pistol from a hose, tearing away of hose from corps of filling vehicle, break of hose, deformation of fuel filling dispenser). The geometrical parameters of chart are determined fuel filling dispenser, at which "forgetfulness" of driver will not result in damages of fuel filling dispenser f, and there will be slipping out of pistol from the mouth of fuel tank of car.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

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