Physical modeling of a skip pneumatic winder

Volumetric Efficiency ◽

Similarity Criteria ◽

Experimental Sample ◽

Point Analysis ◽

Analytical Phase ◽

The Mathematical Model ◽

Parameters Calculation

Introduction. The analytical phase of research on mine skip pneumatic winders has been passed, so the theoretical provisions have to be tested by the methods of physical modeling which is aimed at confirming the mathematical model adequacy and assessing the effectiveness of different types of sealing devices. Research methods. Physical modeling phases have been formulated, including modeling by geometric and aerodynamic similarity criteria, constructing aerodynamic characteristics of the installation, carrying out experiments with non-contacting and combined seals, and calculating the values of the installation volumetric efficiency based on the experimental data obtained. Research results. The lifting time of the skip model with different masses of material and seal types has been determined. The installation working points in the “flow rate–pressure” coordinate system have been identified, and the values of the volumetric efficiency have been calculated for each working point. Analysis of the results. A satisfactory convergence of calculated and experimental parameters of the physical model has been established. The model's volumetric efficiency has reached a technically acceptable level. The expected value of the experimental model’s volumetric efficiency has been calculated according to the similarity constants. Conclusions. The model's study revealed the convergence of the experimentally obtained volumetric efficiency of the model with its calculated values and proved the applicability of the mathematical model to experimental sample parameters calculation. The volumetric efficiency of the installation with both non-contacting and combined seals is quite high allowing to recommend the studied sealing devices for mine pneumatic winders.

FEATURES OF APPLICATION OF SMALL RECONNAISSANCE ROBOT

Collection of scientific works of Odesa Military Academy ◽

10.37129/2313-7509.2019.11.29-38 ◽

2019 ◽

pp. 29-38 ◽

Cited By ~ 1

Author(s):

R. Zinko ◽

P. Kazan ◽

D. Khaustov ◽

O. Bilyk

Keyword(s):

Mathematical Model ◽

Armed Forces ◽

Climatic Conditions ◽

Design Stage ◽

Experimental Sample ◽

Single Trial ◽

Test Cycle ◽

Military Equipment ◽

The Mathematical Model ◽

Human Losses

A small intelligence robot (SSR) is a special military intelligence means. It is used to obtain information about the enemy - the collection of intelligence, the search for targets and target indication, observation of the situation, etc. The use of a small intelligence robot is assumed in various natural and climatic conditions: in temperate terrain, on soils with low bearing capacity, at low temperatures, in the desert, on sandy and marshy soils, on rocky soils, in elevated temperature and dustiness of air, and also in conditions highlands In the article an overview of modern developments of remotely controlled robotic military complexes, principles of their construction and perspective directions of development in the armed forces are reviewed. The issues of robotization of existing weapons and military equipment are considered. Every sample of a SSR used in combat action must possess all combat characteristics at once in an optimal ratio between them, ensuring its maximum effectiveness. Ignoring any of the properties or enhancing one property at the expense of others will not enable the full realization of the small surveillance robot. It is reasonable to select the relevant properties at the design stage, using the possibilities of mathematical modeling. The set of tactical and technical characteristics of the SSR allowed forming this. Its characteristics determine the scope and possibilities of application. The mathematical model of the SSR motion is written in the Matlab Simulink environment. Recorded mathematical model of SSR motion, formed single test cycle and input data allowed to conduct computer simulation of motion in possible conditions of operation of small surveillance robot.The single trial cycle presented contains a set of individual sites and reproduces the testing test cycle of a real polygon. On the basis of the developed tactical and technical characteristics of the SSR, the experimental sample was made. An example of the use of SSR for the intelligence of the settlement and at keeping the node of barriers has been provided. The efficiency of performing intelligence units’ tasks and reducing the risk of human losses are shown.

Analysis of the non-stationary mathematical model of a simple hydraulic network with a centrifugal pump

Vestnik IGEU ◽

10.17588/2072-2672.2020.4.064-070 ◽

2020 ◽

pp. 64-70

Author(s):

V.A. Naumov

Keyword(s):

Mathematical Model ◽

Analytical Solution ◽

Centrifugal Pump ◽

Similarity Criteria ◽

Dimensionless Form ◽

Maximum Volume ◽

Stationary Flows ◽

Variable Level ◽

Hydraulic Network ◽

Simple hydraulic networks with a centrifugal pump are not only part of complex networks, but are also widely used in Autonomous water supply and Sewerage systems. The mathematical model of simple networks taking into account the variable level of liquid in reservoirs includes the well-known Bernoulli equation for non-stationary flows. Published works on this problem do not take into account the non-stationary nature of the flow due to the variable liquid level. The conditions for using the quasi-stationary model are not discussed. Similarity criteria for the issue were not found. The purpose of the study is to analyze the non-stationary mathematical model of the object, including the definition of criteria for similarity of the problem and their impact on the solution. The well-known equations of fluid quantity balance and Bernoulli for non-stationary flows with smoothly changing characteristics were used as a mathematical model of a simple hydraulic network. The pressure characteristic of a centrifugal pump is approximated by a well-established dependence in the form of a square three-member. The system of differential equations was reduced to a dimensionless form. Analytical and numerical methods were used to solve the problem. The analysis of the mathematical model of pumping liquid by a centrifugal pump in a hydraulic network with a variable level was carried out. The dimensionless form of the system of equations allowed us to determine three similarity criteria for the problem, including the analog of the Struhal number Str. The analytical solution to the Cauchy problem is found in the quasi-stationary formulation (Str = 0). The solution of the problem in the full statement is obtained by the numerical method. The results of the study of the influence of similarity criteria on the solution are presented. The dimensionless flow rate of the liquid decreases with increasing Str values. In this case, the maximum volume of liquid and the time to reach it increases. Increasing the values of the other two criteria leads to an increase in both the flow rate and the maximum volume of the liquid. The analytical solution in the quasi-rational formulation can be used only for Str < 0,1. The results obtained can be used in the design of Autonomous Water supply and Sewerage systems. Further research for the non-self-similar area of hydraulic resistance and for variable fluid viscosity is promising.

Modelling of Helicopter Main Rotor Aerodynamic Loads in Manoeuvres

Journal of KONES ◽

10.2478/kones-2019-0118 ◽

2019 ◽

Vol 26 (4) ◽

pp. 273-284

Author(s):

Grzegorz Kowaleczko ◽

Andrzej Leśniczak

Keyword(s):

Mathematical Model ◽

Complex Model ◽

Rotor Blades ◽

Main Rotor ◽

Aerodynamic Forces ◽

Aerodynamic Loads ◽

Helicopter Flight ◽

Helicopter Main Rotor ◽

AbstractThe article discusses the method of modelling of the helicopter main rotor aerodynamic loads during steady state flight and manoeuvres. The ability to determine these loads was created by taking into account the motion of each blade relative to the hinges and was a result of the applied method of aerodynamic loads calculating. The first part of the work discusses the basic relationships that were used to build the mathematical model of helicopter flight. The focus was also on the method of calculating of the aerodynamic forces generated by the rotor blades. The results of simulations dedicated to the “jump to hover” manoeuvre were discussed, showing the possibilities of analysing aerodynamic loads occurring in unsteady flights. The main rotor is considered separately in an “autonomous” way and treated as a source of averaged forces and moments transferred to the hub. The motion of individual blades is neglected, and their aerodynamic characteristics are radically simplified. The motion of individual blades is neglected, and their aerodynamic characteristics are radically simplified. This can lead to significant errors when attempting to model dynamic helicopter manoeuvres. The more complex model of helicopter dynamics is discussed.

Research on the Volumetric Efficiency of 2D Piston Pumps with a Balanced Force

Energies ◽

10.3390/en13184796 ◽

2020 ◽

Vol 13 (18) ◽

pp. 4796

Author(s):

Yu Huang ◽

Jian Ruan ◽

Yong Chen ◽

Chuan Ding ◽

Sheng Li

Keyword(s):

Mathematical Model ◽

Rotational Speed ◽

Sliding Friction ◽

Friction Pair ◽

Weight Ratio ◽

Volumetric Efficiency ◽

Load Pressure ◽

Axial Piston Pumps ◽

Working Principle ◽

Axial piston pumps with high rotational speeds are required in many fields to increase the power-to-weight ratio. However, three main sliding friction pairs in the pump restrict the increase in rotational speed. To solve this problem, we propose a 2D piston pump with a balanced force that contains a sliding friction pair. Firstly, the mechanical structure and working principle of the pump are described. Then, the pump volumetric efficiency is studied by mathematical modeling, and volumetric losses containing backflow and leakage are analyzed and discussed from the perspectives of load pressure and rotational speed. A test bench that verifies the mathematical model is built to measure the volumetric efficiency of the tested pump. We have found that the increase in rotational speed can help to increase the pump volumetric efficiency, and the mathematical model is consistent with the tested data for 1000 rpm but demonstrates a remarkable difference from the tested data for 3000 rpm. Thus, the temperature field of the pump and the viscosity-temperature characteristics of the oil must be taken into account to increase volumetric efficiency further.

Mathematical model of centrifugal compressor vaneless diffuser based on CFD calculations

E3S Web of Conferences ◽

10.1051/e3sconf/202017801014 ◽

2020 ◽

Vol 178 ◽

pp. 01014

Author(s):

Olga Solovyeva ◽

Aleksandr Drozdov

Keyword(s):

Mathematical Model ◽

Centrifugal Compressor ◽

Similarity Criteria ◽

Relative Width ◽

Inlet Flow ◽

Flow Angle ◽

Gas Dynamic ◽

Modelling Method ◽

Vaneless Diffusers ◽

The approximate engineering techniques based on mathematical modelling are used in centrifugal compressor design. One of such methods is the well-proven Universal Modelling Method, developed in the scientific and research laboratory “Gas dynamics of turbo machines”, SPbPU. In the modern version of the compressor model, vaneless diffusers mathematical model was applied based on a generalization of the CFD calculations. The mathematical model can be used for vaneless diffusers with a relative width in the range of 1.4 – 10.0%, with a radial length up to 2.0, in the range of inlet flow angles 10 to 90 degrees, the inlet velocity coefficient in the range of 0.39 – 0.82, Reynolds number varying from 87 500 to 1 030 000. The model was also used for calculating low-flow-rate model stages with narrow diffusers with diffusers’ relative width in the range of 0.5 – 2.0%. The mathematical model showed lesser accuracy. To widen the model applicability, new series of CFD-calculations were executed. A series of vaneless diffusers was designed with relative width in the range of 0.6 – 1.2%, The gas-dynamic characteristics of loss coefficients and outlet flow angle versus inlet flow angle of diffuser were calculated. Regression analysis was used to process the calculated data. System of algebraic equations linking geometric, gas-dynamic parameters and similarity criteria was developed. The obtained equations are included in a new mathematical model of the Universal Modelling Method.

Investigation of Electromagnetic Influence on the Liquid Heart of Aluminium Ingots at Continuous Casting in a Direct Chill Mold

Journal of Siberian Federal University Engineering & Technologies ◽

10.17516/1999-494x-0195 ◽

2019 ◽

pp. 952-961

Author(s):

Mikhail V. Pervukhin ◽

Mikhail Y. Kuchinskii ◽

Sergei P. Timofeev

Keyword(s):

Mathematical Model ◽

Continuous Casting ◽

Physical Modeling ◽

Direct Chill ◽

Power Line ◽

Frequency Range ◽

Electromagnetic Process ◽

Chill Mold ◽

Mathematical And Physical Modeling ◽

The mathematical model of system "inductor-ingot" for investigation electromagnetic process at the continuous casting of aluminum ingots in a direct chill mold is considered in this article. Calculation at various parameters of a power line is made, electromechanical characteristics of stirrer are found. The frequency range at which electromagnetic influence of an inductor on a liquid heart of an ingot is most effective is established. The results of mathematical and physical modeling which have shown reliability of mathematical model are compared

Step-by-step analytical synthesis of the mathematical model of automotive unmanned aircraft

«System analysis and applied information science» ◽

10.21122/2309-4923-2021-1-21-28 ◽

2021 ◽

pp. 21-28

Author(s):

A. A. Lobaty ◽

A. Y. Bumai ◽

S. S. Prohorovith

Keyword(s):

Mathematical Model ◽

Center Of Mass ◽

Unmanned Aircraft ◽

Control Synthesis ◽

Aerial Vehicle ◽

Stage Synthesis ◽

The Stability ◽

The Mathematical Model ◽

Analytical Synthesis

The problem of the stage-by-stage synthesis of the mathematical model of the autopilot of an unmanned aerial vehicle (UAV) is considered. At the first stage, an analytical synthesis of the control acceleration applied to the center of mass of the UAV is performed to form a specified trajectory of its flight. On the basis of the results received at the first stage, at the subsequent stages, the problem of synthesizing a mathematical model of the UAV autopilot is solved with the specified requirements for ensuring the stability and dynamic accuracy of UAV control. Under actual assumptions about the corresponding nature of changes in the trajectory parameters and variables that characterize the motion of the UAV in space, the use of a linear mathematical model of the evolution of the state vector of the UAV and its control system is substantiated. When synthesizing a mathematical model of the UAV autopilot, the method of modal control of the system was used for a specified mathematical model of the object. For a specified model of motion and aerodynamic characteristics of the UAV, the law of deviation of the control steering surface is analytically received, which depends on the parameters of the translational and rotational movement of the UAV. Computer simulation of the analytically received results of control synthesis for the specified characteristics of UAVs and specific using conditions was carried out, which clearly showed the efficiency and prospects of using this approach for the synthesis of control systems for UAVs of various purposes and design.

Mathematical Modeling of the Flow behind Propeller

Studies in Engineering and Technology ◽

10.11114/set.v2i1.956 ◽

2015 ◽

Vol 2 (1) ◽

pp. 77

Author(s):

Oleg Solovyov ◽

Vitaliy Kobrin ◽

Sergey Yeryomenko

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Model Problem ◽

Calculation Time ◽

Momentum Theory ◽

The Mathematical Model ◽

Theory Solution

Study of aircraft aerodynamic characteristics with operation of its powerplant engines is a vital task. In this article we represent mathematical modeling of the aircraft flow with operation of its propeller. The considered mathematical model of the propeller is based on the vortex and momentum theory. Solution of the model problem of the flow behind the propeller allows obtaining of the fields of perturbed velocities in the vicinity of the aircraft and its aerodynamic characteristics. The proposed approach is aimed at simplification of the mathematical model and reduction of calculation time.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

Avtoshliakhovyk Ukrayiny ◽

10.33868/0365-8392-2020-1-261-19-26 ◽

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 ◽

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

Avtoshliakhovyk Ukrayiny ◽

10.33868/0365-8392-2019-4-260-10-16 ◽

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 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.