The Mathematical Model of Abrasive Waterjet Milling Process

2007 ◽  
pp. 187-190
Author(s):  
Cornel Ciupan ◽  
A. Pop ◽  
Liviu Morar
Keyword(s):  
Mathematical Model ◽  
Milling Process ◽  
Abrasive Waterjet ◽  
The Mathematical Model

The Mathematical Model of Abrasive Waterjet Milling Process

2007 ◽  
Vol 23 ◽  
pp. 187-190
Author(s):  
Cornel Ciupan ◽  
A. Pop ◽  
Liviu Morar
Keyword(s):  
Mathematical Model ◽  
Milling Process ◽  
Abrasive Waterjet ◽  
Output Data ◽  
Energy Preservation ◽  
Material Characteristics ◽  
The Mathematical Model ◽  
Advance Speed

The paper presents the mathematical model of abrasive waterjet milling process. Based on analysis of existing models the authors realize a new mathematical model, considering some simplifying hypothesis. This model uses output data from model [1] and determines the advance speed, the consumption of the abrasive and the productivity of the process. To establish the productivity of the process and the advance speed we’ll use the “energy preservation” model. This model takes in account the material characteristics. The mathematical model has been solved numerical and the results have been interpreted.

An accurate and efficient control over the present numerical model of depth of sputtering in focused ion beam milling

2009 ◽  
Vol 223 (1) ◽  
pp. 9-18 ◽  
Author(s):  
S N Bhavsar ◽  
S Aravindan ◽  
P Venkateswara Rao
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Substrate Material ◽  
Milling Process ◽  
Intensity Function ◽  
Two Parameters ◽  
The Mathematical Model ◽  
Better Than

In many applications, such as fabrication of microtools, microsurgical instruments, microgears, and so on, material must be removed precisely with a focused ion beam (FIB) milling process to generate a specified geometry on substrate material. A mathematical model is available to calculate depth of sputtering at each point on substrate material in order to generate a specified geometry, but the results of the existing model deviates from experimental data. In the current paper, normalized pixel spacing and ratio of redeposition to beam velocity are the two parameters that have been considered in calculation of depth of sputtering during the FIB milling process. A proposed mathematical model incorporating the effect of redeposition has been simulated for parabolic and rectangular trench profiles, and it has been proven to be better than the existing model through comparison with experimental data of parabolic and rectangular geometry on silicon material. In addition, efforts have been made to reduce the amount of numerical calculation in the simulation process by utilizing a Gaussian mask in the existing model instead of the usual Gaussian intensity function. The Gaussian mask prevents the need for repeated calculation of Gaussian intensity function in the mathematical model of depth of sputtering, and in turn reduces the time of computation.

scholarly journals Mathematical modeling of the additional working body of the excavator

2021 ◽  
Vol 136 (3) ◽  
pp. 74-83
Author(s):  
B.D. Suleev ◽  
◽  
A.B. Kenesbek ◽  
B.B. Togizbayeva ◽  
K.G. Balabekova ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Asphalt Concrete ◽  
Cutting Parameters ◽  
Milling Process ◽  
Concrete Pavement ◽  
Milling Cutter ◽  
New Type ◽  
Asphalt Concrete Pavement ◽  
The Mathematical Model

The article discusses measures to modernize the working body of the excavator by installing additional working equipment. There has been studied the state of world practices in this area to achieve this goal. There is proposed a new type of working equipment for repairing asphalt concrete pavement based on an excavator instead of standard attachments that provide ease of installation and removal. The working body consisting of an additional milling cutter is designed for cutting asphalt concrete pavement and is made in the form of attachments combined with the main one. There has been developed a mathematical model of a multipurpose hydraulic excavator with an additional milling cutter. The article proposes a simulation model of the milling cutter operation in the Solidworks program. The authors modeled a disk. In Solidworks, there was tested a sample disk using Simulation. The authors conducted detailed studies. The article considers forces acting on the working body. The authors carried out computer studies. As a result, there were obtained loads that showed the effectiveness of the new working body equipped with a cutter. There have been developed mathematical models to calculate the volume of soil cut by the working body, and the milling process is described by the Sant – Venan model. On this basis, there was obtained a rheological model, according to which there was proposed shear deformation. The authors developed a mathematical model of the excavator working body, according to which there was determined the equivalence force. The mathematical model takes into account the spatial nature of deformation and the interaction of transmission elements. The article investigates that the use of such discs makes it possible to clarify the influence of various cutting parameters on the stress state of the cutting disc, to obtain a stress distribution over the width of the cutting disc. The correspondence of the results of the developed and tested mathematical models in the Solidworks computer program allowed us to confirm the performance of the software system, the effectiveness of its application.

Study on the Mathematical Model of the Milling Force and Residual Stress

2013 ◽  
Vol 568 ◽  
pp. 103-107
Author(s):  
W.W. Song ◽  
H.F. Wang ◽  
J.L. Wang ◽  
X.L. Duan
Keyword(s):  
Mathematical Model ◽  
Residual Stress ◽  
Plastic Deformation ◽  
Deformation Theory ◽  
Milling Process ◽  
Milling Force ◽  
Elastic Plastic ◽  
Machining Deformation ◽  
Nc Milling ◽  
The Mathematical Model

Metal milling processing principle and the elastic-plastic deformation theory were combined in this paper. The mathematical model of milling force and residual stress in the NC milling process was deduced by the theory. By the obtained mathematical model, could further analyze the effect of milling force on the residual stress and then obtain the law of milling force to milling deformation. This proved the strong a theoretic guarantee for controlling the machining deformation.

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. 

The mathematical modelling of corrosion in hot dip galvanized steel reinforced concrete

2011 ◽  
Vol 2 (1) ◽  
pp. 1-12
Author(s):  
A. Hegyi ◽  
H. Vermeşan ◽  
V. Rus
Keyword(s):  
Mathematical Model ◽  
Reinforced Concrete ◽  
Numerical Model ◽  
Equation System ◽  
Galvanized Steel ◽  
Steel Reinforced Concrete ◽  
Numeric Model ◽  
Physical And Mathematical Models ◽  
Physical Phenomena ◽  
The Mathematical Model

Abstract In this paper we wish to present the numerical model elaborated in order to simulate some physical phenomena that influence the general deterioration of steel, whether hot dip galvanized or not, in reinforced concrete. We describe the physical and mathematical models, establishing the corresponding equation system, the initial and boundary conditions. We have also presented the numeric model associated to the mathematical model and the numeric methods of discretization and solution of the differential equations system that describes the mathematical model.

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