scholarly journals Mathematical modelling of vertical and longitudinal-angular vibrations in the composition of the rigidity and damping of the hierarchical parts of the tractor taking into account road impact

2021 ◽  
Vol 264 ◽  
pp. 04066
Author(s):  
Farkhod Matmurodov ◽  
Dilafruz Ermatova
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Machine Design ◽  
Dynamic Parameters ◽  
Systems Of Equations ◽  
Generalized Systems ◽  
Vertical Vibrations ◽  
Linear Oscillation ◽  
The Mathematical Model

The article contains generalized systems of equations describing the vertical and longitudinal-angular vibrations of the main parts of the tractor with the mathematical model of the hierarchical vertical linear oscillation of the tractor, the irregularities of the roads, taking into account the rigidity and damping. It includes systems: equations describing the vertical vibrations of the skeleton over the propellers of a tractor on an uneven road; equations describing the vertical vibrations of the cab of the rear of the tractor, taking into account the walking of the tractor on uneven roads. Equation systems have also been compiled that describe the vertical oscillations of the uppermost hierarchical link - the seat of the tractor operator, taking into account the walking of the tractor on an uneven road. The use of this original mathematical model will make it possible to find random unwanted oscillations of the new designed machine design. It will help to optimize their geometric and dynamic parameters.

Mathematical Modelling the Process of Cup Wheel Precision Grinding of Rotating Concave Paraboloid

2016 ◽  
Vol 693 ◽  
pp. 837-842
Author(s):  
Fu Yi Xia ◽  
Li Ming Xu ◽  
De Jin Hu
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Abrasive Particle ◽  
Influence Factors ◽  
Machining Process ◽  
Quadric Surface ◽  
Precision Grinding ◽  
Cup Wheel ◽  
The Mathematical Model ◽  
Trajectory Equation

A novel principle of cup wheel grinding of rotating concave quadric surface was proposed. The mathematical model of machining process was established to prove the feasibility of precision grinding of rotating concave paraboloid based on the introduced principle. The conditions of non-interference grinding of concave paraboloid were mathematically derived. The processing range and its influence factors were discussed. The trajectory equation of abrasive particle was concluded. Finally, the math expressions of numerical controlled parameters was put forward in the process of grinding of the concave paraboloid.

scholarly journals Development of a subsystem for automatic protection of submersible pumps based on mathematical modeling

2018 ◽  
Vol 226 ◽  
pp. 04028
Author(s):  
Alexander V. Pilipenko ◽  
Andrei A. Tashev ◽  
Nail K. Sharifov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mathematical Modelling ◽  
Protection System ◽  
Piston Pump ◽  
The Mathematical Model

In this paper, the authors produce a mathematical modelling of a piston pump, develop algorithms for the operation of a protection system, taking into account the results of mathematical modelling. The authors test the mathematical model on the operation of real equipment and analyze its accuracy.

Multi-Objective Optimization Design of Screw Conveyor Using Genetic Algorithm

2013 ◽  
Vol 732-733 ◽  
pp. 402-406
Author(s):  
Duan Yi Wang
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Optimization Design ◽  
Optimization Problem ◽  
Machine Design ◽  
Screw Conveyor ◽  
Optimized Design ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
The Mathematical Model

The weight minimum and drive efficiency maxima1 of screw conveyor were considered as double optimizing objects in this paper. The mathematical model of the screw conveyor has been established based on the theory of the machine design, and the genetic algorithm was adopted to solving the multi-objective optimization problem. The results show that the mass of spiral shaft reduces 13.6 percent, and the drive efficiency increases 6.4 percent because of the optimal design based on genetic algorithm. The genetic algorithm application on the screw conveyor optimized design can provided the basis for designing the screw conveyor.

scholarly journals Mathematical modelling of the drying process of sugar beet pulp with macro and microelement additions in order to improve the feed quality

2020 ◽  
Vol 180 ◽  
pp. 03020
Author(s):  
Elena Mihaela Nagy ◽  
Constantin Coţa ◽  
Zoltan Gyorgy ◽  
Teodora Deac
Keyword(s):  
Mathematical Model ◽  
Sugar Beet ◽  
Phosphoric Acid ◽  
Mathematical Modelling ◽  
Animal Feed ◽  
Hydrated Lime ◽  
Experimental Measurements ◽  
Drying Process ◽  
Beet Pulp ◽  
The Mathematical Model

In this paper a kinetic study is performed on the drying process of beet pulp with additions of macro-elements (Ca2+, Mg 2+, PO42+) from hydrated lime, hydrated dolomite lime, phosphoric acid and microelements (Co2+, Zn 2+, Fe2+, Mn2+), with the purpose of obtaining premixes with substantially improved value for animal feed. The experimental measurements made served to elaborate the mathematical model by means of which the speed with which the drying process is carried out is described, thus being able to calculate the stationing time of the material in the dryer. The equations for calculating the stationary time of the material in the dryer can be used for designing dryers (sizing them).

Method of evaluating transport tasks in the army with the use of mathematical modelling

2021 ◽  
Vol 63 (1) ◽  
pp. 24-29
Author(s):  
Eliza Łagowska
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Empirical Evaluation ◽  
Armed Forces ◽  
Motor Vehicles ◽  
Logistics System ◽  
Material Resources ◽  
Technical Material ◽  
Development Tendency ◽  
The Mathematical Model

The article analyzes military transport operating within the Armed Forces logistics system. The proprietary method of its evaluation was presented. The technical subsystem has been characterized with the specification of the requirements it is faced with. General criteria for the assessment of the technical subsystem were identified, distinguishing the equipment, personnel, technical material resources, training and experience of soldiers, as well as their combat readiness and flexibility. The essential part of the discussion is devoted to empirical evaluation. It was made through the analysis of completed transport tasks. The research conducted with respect to the mileages of motor vehicles allows to ascertain whether the system is sufficient to meet the current needs. The mathematical model proposed allows to estimate the development tendency, based on which it is possible to formulate improvement proposals.

scholarly journals Mathematical Modelling of Acetaminophen Release in HPC/PAAm Hydrogel: Synthesis and Application

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Abigail M. Díaz-Guerrero ◽  
Claudia A. Castillo-Miranda ◽  
Carlos F. Castro-Guerrero ◽  
Hernán Peraza-Vázquez ◽  
Ana B. Morales-Cepeda ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Phosphate Buffer Solution ◽  
Absolute Error ◽  
Programming Algorithm ◽  
Test Results ◽  
Buffer Solution ◽  
Drug Molecules ◽  
Hydrogel Synthesis ◽  
The Mathematical Model

Hydrogels are commonly used as Drug Delivery Systems (DDS) as patches due to its ability to store drug molecules within their structures. The release can be activated under certain stimuli, such as temperature and pH. In this paper, the mathematical modelling of acetaminophen release in hydroxypropyl cellulose with polyacrylamide (HPC/PAAm) is reported. The HPC/PAAm gel was synthesized in proportions of 25/75 wt% and was characterized by FTIR, DSC, optical microscopy, SEM, and TGA, with and without acetaminophen. The release tests were performed for hypothermic, normal, and febrile human body conditions, at 35, 37, and 39°C, respectively, on two release media: water and phosphate buffer solution. In order to describe the release of acetaminophen in HPC/PAAm gel, a genetic programming algorithm was used to accomplish Multigene Symbolic Regression (MSR). Characterization results showed that the drug was crystallized on the surface of the HPC/PAAm gel. Release test results showed that several simultaneous processes occurred in the acetaminophen diffusion phenomenon. A unique mathematical model was obtained by MSR. This model was able to describe the release of acetaminophen in HPC/PAAm gel with high values of R2 and adjusted R2 and to simulate the drug release at times beyond the end of the experiment. High values of R2 and low values of Coefficient of Variation (CV), Root-Mean-Square Error (RMSE), and Mean Absolute Error (MAE) were obtained from the comparison between the simulated and the experimental data. This allows to conclude that the mathematical model is reliable to represent and simulate the acetaminophen release in HPC/PAAm gel at 35, 37, and 39°C.

scholarly journals Mathematical Modelling of Electric Discharge Machining of Al (6351)-SiC-B4C Hybrid Composite

2020 ◽  
Vol 8 (4S4) ◽  
pp. 163-166
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Surface Roughness ◽  
Mathematical Modelling ◽  
Electric Discharge ◽  
Electrode Wear ◽  
Electric Discharge Machining ◽  
Pulse On Time ◽  
The Mathematical Model ◽  
Time Pulse

The Electric Discharge Machining (EDM) has emerged as one of the major machining method for the machining of hard-to- machine materials and composites. This paper aims at creating a mathematical model for the machining of the Al(6351)-SiC-B4C composites based on the experimental data and compare the same to identify the level of errors between the mathematical model and the experimental results. This paper was aimed as an attempt to develop a mathematical model for the output parameters viz. Electrode Wear ratio and Surface roughness based on the input parameters viz. current, pulse-on-time, pulse duty-factor and gap voltage.

scholarly journals Positioning uncertainty of the Tricept type parallel kinematic structure

ACTA IMEKO ◽  
2015 ◽  
Vol 4 (4) ◽  
pp. 9
Author(s):  
Eva Kureková ◽  
Milada Omachelová ◽  
Martin Halaj ◽  
Ilja Martišovitš
Keyword(s):  
Mathematical Model ◽  
Machine Design ◽  
Kinematic Structure ◽  
Positioning Accuracy ◽  
Parallel Structures ◽  
Final Design ◽  
Geometrical Imperfections ◽  
Parallel Kinematic ◽  
The Mathematical Model

The paper discusses theoretical aspects that arised during determination of theoretical positioning accuracy of parallel kinematic structures (PKS) with special regard to the Tricept type PKS. Apart from the conventional serial structures that employ translate or rotational movement (or their combination) of individual driving axes, parallel structures comprise a set of telescopic driving rods that are joined together via solid platform. Due to this fact, the mathematical model describing relationship between the driving actions of telescopic rods and resulting coordinates of the desired effector's endpoint is rather complex. To determine the theoretically achievable positioning accuracy of the endpoint, authors investigated theoretical influence of geometrical imperfections of the machine design and employed the law of uncertainties propagation. Their aim was to investigate theoretically achievable positioning accuracy of the machine prior to the final design solutions thus helping the designer to optimize the machine's design.

scholarly journals Measurement and improvement of efficiency of Library by mathematical modelling and finding reliability

2021 ◽  
Vol 7 (2) ◽  
pp. 1-5
Author(s):  
Yakshi Bahl ◽  
Tarun Kumar Garg
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Mathematical Modelling ◽  
Exponential Distribution ◽  
Death Process ◽  
Library System ◽  
The Mathematical Model ◽  
Server System ◽  
Birth Death

Here in this paper we have developed  the mathematical model of the library server using  Markov birth – death process assuming that library system server system is based on exponential distribution. The model so developed by victimisation Chapman Kolmogorov differential equation and is solved by using Mathematica. The solution so obtained is analysed for various rates of failures and repair. The finding so obtained are discussed with the concerned authorities of the library to boost the efficiency of the library.

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