scholarly journals Mathematical model of the impact assessment of roughness and waviness deviations of races surfaces of rolling bearings on the level of generated vibration

Mechanik ◽  
2019 ◽  
Vol 92 (1) ◽  
pp. 35-37
Author(s):  
Paweł Zmarzły
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Impact Assessment ◽  
Ball Bearings ◽  
Vibration Level ◽  
Rolling Bearings ◽  
Shape Deviations ◽  
Specific Frequency ◽  
The Impact ◽  
Dominant Influence

The article presents mathematical models allowing to describe the level of vibration generated by ball bearings 6304-2z type depending on the value of roughness and waviness deviations of inner and outer bearings races. This models will allow to estimate what type of shape deviations have dominant influence on the vibration level generated in specific frequency ranges.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

scholarly journals Multi-Dimensional Mathematical Wear Models of Vibration Generated by Rolling Ball Bearings Made of AISI 52100 Bearing Steel

Materials ◽  
2020 ◽  
Vol 13 (23) ◽  
pp. 5440
Author(s):  
Paweł Zmarzły
Keyword(s):  
Mathematical Models ◽  
Total Curvature ◽  
Bearing Steel ◽  
Radial Clearance ◽  
Ball Bearings ◽  
Wear Process ◽  
Rolling Ball ◽  
Aisi 52100 ◽  
Aisi 52100 Steel ◽  
The Impact

The paper features the development of multi-dimensional mathematical models used for evaluating the impact of selected factors on the vibration generated by 6304ZZ type rolling ball bearings from three manufacturers in the aspect of the wear process. The bearings were manufactured of AISI 52100 bearing steel. The analyzed factors included the inner and outer raceways’ roundness and waviness deviations, radial clearance and the total curvature ratio. The models were developed for vibration recorded in three frequency ranges: 50–300 Hz, 300–1800 Hz and 1800–10,000 Hz. The paper includes a specification of the principles of operation of innovative measuring systems intended for testing bearing vibration, raceway geometries and radial clearance. Furthermore, it features a specification of particular stages of the multi-dimensional mathematical models’ development and verification. Testing with the purpose of statistical evaluation of the analyzed factors is also presented. The test results and mathematical models indicate that the inner raceway’s waviness deviation had a dominant impact on the vibration examined in all frequencies. The roundness and waviness deviation of bearing raceways made of AISI 52100 steel propagates the bearing wear process.

scholarly journals Universal mathematical model of network planning transport and process streams of timber

2017 ◽  
Vol 6 (2) ◽  
pp. 100-105
Author(s):  
Сушков ◽  
Sergey Sushkov ◽  
Пильник ◽  
Yuliya Pilnik
Keyword(s):  
Mathematical Model ◽  
Economic Development ◽  
Mathematical Models ◽  
Production Process ◽  
Network Planning ◽  
Forestry Sector ◽  
Main Components ◽  
The Impact

Consideration of transport as one of the main components of the production process and the analysis of the linkages of forestry sector with other sectors of production are based on the study of the proportions between the volumes and the structure of harvested timber and the products of all other industries. The analysis in this part of the proposed conduct on the basis of mathematical models, in particular, for the analysis of quantitative relationships of the production process, assess the impact of various factors on the dynamics of economic development, to analyze the prospects of their development.

scholarly journals The Mathematical Model for Research of the UAV Longitudinal Moving

2021 ◽  
Vol 13 (5) ◽  
pp. 29-39
Author(s):  
Sergii Zhdanov ◽  
◽  
Natalia Kadet ◽  
Valerii Silkov ◽  
Mariia Zirka ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Frequency Response ◽  
Unmanned Aerial Vehicles ◽  
Control Systems ◽  
Aerial Vehicles ◽  
General Mathematical Model ◽  
Logarithmic Frequency ◽  
The Impact ◽  
The Mathematical Model

The paper presents one of the perspective directions of the development to modern aviation, which is connected with designing and producing unmanned aerial vehicles (UAV) of various functionalities for applying in both military and civilian spheres. The syntheses of UAV control systems, regardless of their type and purpose presumes creation of adequate mathematical models, first of all adequate aerodynamic mathematical models. In the paper results that forms and justify the aerodynamic mathematical model and as well as the results of building a general mathematical model of the longitudinal movement of the perspective UAV are presented. Also factors that forms the mathematical model on given aerodynamic, geometric, mass and inertial data for a hypothetical perspective altitude long-range UAV are submitted. Assessment of the impact of these data on the dynamic, temporal, and logarithmic frequency response UAV also has been given in this paper.

scholarly journals A unified activities-based approach to the modelling of viral epidemics and COVID-19 as an illustrative example

2020 ◽  
Author(s):  
Yulii D. Shikhmurzaev ◽  
Vladislav D. Shikhmurzaev
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Social Interactions ◽  
Clinical Picture ◽  
Simple Mathematical Model ◽  
New Approach ◽  
Social Distancing ◽  
The Uk ◽  
The Impact

AbstractA new approach to formulating mathematical models of increasing complexity to describe the dynamics of viral epidemics is proposed. The approach utilizes a map of social interactions characterizing the population and its activities and, unifying the compartmental and the stochastic viewpoints, offers a framework for incorporating both the patterns of behaviour studied by sociological surveys and the clinical picture of a particular infection, both for the virus itself and the complications it causes. The approach is illustrated by taking a simple mathematical model developed in its framework and applying it to the ongoing pandemic of SARS-CoV-2 (COVID-19), with the UK as a representative country, to assess the impact of the measures of social distancing imposed to control its course.

Stress Analysis of Underground Arch Structure

2011 ◽  
Vol 243-249 ◽  
pp. 938-941
Author(s):  
Bin He ◽  
Jun Long Lu
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Structural Analysis ◽  
Finite Element Model ◽  
Mathematical Models ◽  
Stress Analysis ◽  
Element Model ◽  
Arch Structure ◽  
The Impact ◽  
Actual Stress

To research the safety of an underground defense project and the impact to other buildings, applying basic mechanics principles, established two types of mathematical model for arch about the project, and analyzed stress in different directions of ground arch structure. The data shows that the results were very different in different mathematical models, and mathematical models should be considered as close to actual stress situation in structural analysis. In the structural analysis involved soil, spatial finite element model is more accurate and reasonable than truss finite element model.

scholarly journals Review on the Thermal Performance on the Basis of Different Types of Material used in Ball Bearings

2021 ◽  
pp. 61-66
Author(s):  
Vinay Kumar Shukla
Keyword(s):  
Thermal Performance ◽  
Ball Bearings ◽  
Operating Environment ◽  
Rolling Bearings ◽  
Movable Object ◽  
Different Types ◽  
Operations And Maintenance ◽  
Frictional Forces ◽  
Materials Used ◽  
The Impact

Bearing is a movable object, so frictional forces must be overcome in terms of moving the Bearing. To decrease the friction force on the movable methodology, different kinds of bearings have been used. The bearing gets its characterized by the fact that it is used to support a rotating axle or shaft. Because rolling bearings utilize balls or rollers, they are referred to as "rolling components." one can measure bearing expected lifespan depending on the material exhaustion if one can understand the operations and maintenance of loads and speeds. These computations should be based on the assumption that now the bearing is appropriately installed, lubricated, and moreover treated. It is unable to account for the impact of detrimental operating environment. Damaged bearing has a significant economic and industrial implications. Numerous substance are used in the bearing sector to several bearing elements. To achieve maximum bearing performance and durability, the products are deposited to obtain intended characteristics. The components listed in this are the most frequently used. The different materials used in ball bearings are discussed in this paper.

scholarly journals The mathematical model for forecasting the accumulation of heavy metals in pig production

2020 ◽  
pp. 120-127
Author(s):  
О. Chala ◽  
О. Chaly ◽  
S. Nagorny
Keyword(s):  
Heavy Metals ◽  
Mathematical Model ◽  
Body Weight ◽  
Mathematical Models ◽  
Cadmium Concentration ◽  
The Body ◽  
Incorporation Rate ◽  
Regression Equations ◽  
Cadmium And Lead ◽  
The Impact

The results of research represent the impact of extensive doses of heavy metals such as lead and cadmium in store pigs bodies. Heavy metals were fed jointly and individually in the doses exceeding the maximum allowable concentrations in the fodder by 10 and 20 times. Therefore, the process of intoxication of the biological object (a swine) by heavy metals is modeled in a way similar to that, which might occur as the result of environmental pollution. The study was performed in order to determine the targets and the extent of the impact of heavy metals exerted upon the body weight, weight of inner parts of the animal body, and the incorporation rate of heavy metals in the swine breeding products. Statistical processing of the obtained data allowed developing mathematical models and determining the correlational relationships between the aspects under investigation. It is determined that heavy metals exert an essential negative impact upon the rate of animal growth and the power of influence increases with the dose. It is also confirmed by a high value of correlational relationship between these parameters (the correlation coefficient (r) is 0.854). Thus, the body weight of swine during the latter of I-II stagesdecreased by 5.5 to 14.8% as it was compared to the control under the influence of hemotoxic substances. The extent of the impact was also dependent upon the toxin itself. Thus, the largest negative effect was observed both under the impact of cadmium only and of cadmium and lead taken together. The highest accumulation of heavy metals was observed in the liver and kidneys, whereas the lowest – in the muscles. The built regression equations showed that increasing of the dose of the relevant element in the fodder exerted the main impact on concentration of cadmium and lead in the body and meat. The content of cadmium in the fodder exerted an impact upon concentration of lead in the meat – with the increase of cadmium concentration the content of lead in the meat decreased. The results of the studies provide an overview of the targets and the extent of the impact exerted by heavy metals upon biological objects. The mathematical models may be used for prediction of the impact and the incorporation rate value of the hemotoxic substances in the swine breeding products. Key words: lead, cadmium, swine breeding products, ecocide environmental impact, migration of xenobiotic, mathematical model.

The Impact of Light Polarisation on Light Field of Scenes with Multiple Reflections

2020 ◽  
pp. 108-115 ◽  
Author(s):  
Vladimir P. Budak ◽  
Anton V. Grimaylo
Keyword(s):  
Mathematical Model ◽  
Light Field ◽  
Global Illumination ◽  
Multiple Reflections ◽  
Software Environment ◽  
The Monte Carlo Method ◽  
Mueller Matrices ◽  
Volume Integration ◽  
The Impact

The article describes the role of polarisation in calculation of multiple reflections. A mathematical model of multiple reflections based on the Stokes vector for beam description and Mueller matrices for description of surface properties is presented. On the basis of this model, the global illumination equation is generalised for the polarisation case and is resolved into volume integration. This allows us to obtain an expression for the Monte Carlo method local estimates and to use them for evaluation of light distribution in the scene with consideration of polarisation. The obtained mathematical model was implemented in the software environment using the example of a scene with its surfaces having both diffuse and regular components of reflection. The results presented in the article show that the calculation difference may reach 30 % when polarisation is taken into consideration as compared to standard modelling.

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