A study of an elbow mechanism generated by a conical cutter

2007 ◽  
Vol 221 (6) ◽  
pp. 727-738 ◽  
Author(s):  
S-C Yang
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Von Mises Stress ◽  
Tooth Contact Analysis ◽  
Rapid Prototyping And Manufacturing ◽  
Von Mises ◽  
Design And Manufacture ◽  
The Mathematical Model ◽  
Further Development ◽  
Kinematic Errors

This paper presents a method for determining the mathematical model of an elbow mechanism with a convex tooth and a concave tooth. Based on this method, the mathematical model presents the meshing principles of a conical cutter meshed with a tooth that is either convex or concave. Using the developed mathematical models and the tooth contact analysis, kinematic errors are investigated according to the obtained geometric modelling of the designed gear meshing when assembly errors are present. The influence of misalignment on kinematic errors has been investigated. The goal of the current study is to investigate von-Mises stress for three teeth contact pairs. A structural load is assumed to act on a gear of the proposed mechanism. The von-Mises of the proposed gear is determined. The conical cutter used in the design and manufacture of the convex and concave gear is shown. For example, the proposed mechanism with a transmission ratio of 3:2 was determined with the aid of the proposed mathematical model. Using rapid prototyping and manufacturing technology, an elbow mechanism with a convex gear, a concave gear and a frame was designed. The RP primitives provide an actual full-size physical model that can be analysed and used for further development. Results from these mathematical models are applicable to the design of an elbow mechanism.

A mathematical model of a worm mechanism generated by a conical cutter

2009 ◽  
Vol 224 (8) ◽  
pp. 1707-1716 ◽  
Author(s):  
S-C Yang
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Stress Analysis ◽  
Geometric Model ◽  
Gear Ratio ◽  
Worm Gear ◽  
Von Mises Stress ◽  
The Family ◽  
Gear Mechanism ◽  
Von Mises

In this article, an imaginary conical cutter was used to determine the geometric models of the worm—gear mechanism including a worm and a gear. Mathematical models of the worm and the gear were derived using an imaginary conical cutter and gear theory. Based on the geometric relations between the worm and conical cutter surfaces and between the gear and conical cutter surfaces, the worm and the gear were regarded as an envelope to the family of conical cutter surfaces when they rotated for one cycle. Using the developed mathematical model, the stress analysis of the proposed mechanism was examined. The results show that the von Mises stress and volume of the proposed worm and gear were smaller than those of the conventional worm—gear mechanism. Lastly, a numerical example was used to illustrate the geometric model of a gear and a worm with a gear ratio of 30:1.

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 Analysis on Present Mathematical Model for Predicting the Crop Production

2020 ◽  
Vol 9 (12) ◽  
pp. 168-170
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Real World ◽  
Crop Production ◽  
Ghg Emissions ◽  
Data Set ◽  
Factors Affecting ◽  
The Government ◽  
The Mathematical Model ◽  
Government Website

India is a worldwide agriculture business powerhouse. Future of agriculture-based products depends on the crop production. A mathematical model might be characterized as a lot of equations that speak to the conduct of a framework. By using mathematical model in agriculture field, we can predict the production of crop in particular area. There are various factors affecting crops such as Rainfall, GHG Emissions, Temperature, Urbanization, climate, humidity etc. A mathematical model is a simplified representation of a real-world system. It forms the system using mathematical principles in the form of a condition or a set of conditions. Suppose we need to increase the crop production, at that time the mathematical model plays a major role and our work can be easier, more significant by using the mathematical model. Through the mathematical model we predict the crop production in upcoming years. .AI, ML, IOT play a major role to predict the future of agriculture, but without mathematical models it is not possible to predict crop production accurately. To solve the real-world agriculture problem, mathematical models play a major role for accurate results. Correlation Analysis, Multiple Regression analysis and fuzzy logic simulation standards have been utilized for building a grain production benefit depending model from crop production. Prediction of crop is beneficiary to the farmer to analyze the crop management. By using the present agriculture data set which is available on the government website, we can build a mathematical model.

BASIC MATHEMATICAL MODELS AND AN APPROXIMATE METHOD OF FILTRATION THEORY

2021 ◽  
pp. 25-31
Author(s):  
Alla A. Mussina
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Mathematical Models ◽  
Heterogeneous Porous Media ◽  
Effective Management ◽  
Filtration Theory ◽  
New Device ◽  
Scientific Papers ◽  
The Mathematical Model ◽  
Inhomogeneous Liquids

The article defines the basic concepts of filtration theory and provides an overview of the existing mathematical models of inhomogeneous liquids in porous media. The paper considers the Stefan problem. The number of scientific papers devoted to the study of porous structures has recently increased. This is primarily due to the fact that the prob-lems of oil and uranium production have been identified, and the solution of environmental problems is overdue. Therefore, a new device is needed to develop models of liquid filtration. With the advent and development of computer technology, it has become easier to solve problems that require numerical methods for their solution. Understanding the movement of fluids and the mechanism of dissolution of rocks under the action of acids in heterogeneous porous media is of great importance for the extraction and production of oil and the effective management of these processes. The article examines the mathematical model of the theory of isothermal filtration. Possible variants of the solva-bility of the model are shown. The research scheme consists of the output of a mathematical model, the formulation of the problem, one variant of the solution of the problem, the algorithm of the numerical method of solving the problem.

scholarly journals Performance Evaluation of a Gravity-Assisted Heat Pipe-Based Indirect Evaporative Cooler

Energies ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 200 ◽  
Author(s):  
Krzysztof Rajski ◽  
Jan Danielewicz ◽  
Ewa Brychcy
Keyword(s):  
Mathematical Model ◽  
Heat Pipe ◽  
Cooling Capacity ◽  
Operating Conditions ◽  
Coefficient Of Performance ◽  
Mass Transfer Processes ◽  
Air Cooler ◽  
Evaporative Cooler ◽  
The Mathematical Model ◽  
Further Development

In the present work, the effects of different operating parameters on the performance of a gravity-assisted heat pipe-based indirect evaporative cooler (GAHP-based IEC) were investigated. The aim of the theoretical study is to evaluate accurately the cooling performance indicators, such as the coefficient of performance (COP), wet bulb effectiveness, and cooling capacity. To predict the effectiveness of the air cooler under a variety of conditions, the comprehensive calculation method was adopted. A mathematical model was developed to simulate numerically the heat and mass transfer processes. The mathematical model was validated adequately using experimental data from the literature. Based on the conducted numerical simulations, the most favorable ranges of operating conditions for the GAHP-based IEC were established. Moreover, the conducted studies could contribute to the further development of novel evaporative cooling systems employing gravity-assisted heat pipes as efficient equipment for transferring heat.

scholarly journals Diagnostics of supercapacitors

2018 ◽  
Vol 182 ◽  
pp. 01009 ◽  
Author(s):  
Valeriy Martynyuk ◽  
Oleksander Eromenko ◽  
Juliy Boiko ◽  
Tomasz Kałaczyński
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Methodological Approach ◽  
Frequency Dispersion ◽  
Technical Condition ◽  
Transient Processes ◽  
Nonlinear Frequency ◽  
Diagnostic Reliability ◽  
General Reliability ◽  
The Mathematical Model

The paper represents the mathematical model for diagnostics of supercapacitors. The research objectives are the problem of determining a supercapacitor technical condition during its operation. The general reliability of diagnostics is described as the methodological and instrumental reliabilities of diagnostics. The instrumental diagnostic reliability of supercapacitor includes the probabilities of errors of the first and second kind, α and β respectively. The methodological approach to increasing the reliability of supercapacitor diagnostic has been proposed, in terms of multi-parameter supercapacitor diagnostic by applying nonlinear, frequency dependent mathematical models of supercapacitors that take into account nonlinearity, frequency dispersion of parameters and the effect of transient processes in supercapacitors. The more frequencies, operating voltages and currents are applied in the supercapacitor diagnostics, the more methodological reliability of diagnostics will increase in relation to the methodological reliability of supercapacitor diagnostics when only one frequency, voltage and current are applied.

Research on Noise Simulation of Infrared Detector

2012 ◽  
Vol 433-440 ◽  
pp. 4120-4123
Author(s):  
Shu Li Lou ◽  
Yan Li Han ◽  
Jian Cun Ren ◽  
Xiao Hu Yuan ◽  
Xiao Dong Zhou
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Infrared Imaging ◽  
Imaging System ◽  
Infrared Detector ◽  
System Research ◽  
Infrared Imaging System ◽  
Noise Simulation ◽  
And Performance ◽  
The Mathematical Model

Noises of infrared detector have an important influence on sensitivity of infrared imaging system, and it affect the imaging quality and performance of infrared system. Research on noises of infrared detector is a challenging topic in designing, simulating and evaluating of infrared imaging system. All kinds of noises are studied in detail, and mathematical models are built. The method of simulating noises of detector is proposed, and noises are simulated based on the mathematical model.

Modeling and Analyses of the N-Link Bent-Arm PenduBot

2010 ◽  
Vol 171-172 ◽  
pp. 644-647
Author(s):  
Shao Qiang Yuan ◽  
Xin Xin Li
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Nonlinear Model ◽  
Condition Number ◽  
Kinematics And Dynamics ◽  
Controllability Matrix ◽  
Human Arm ◽  
The World ◽  
The Mathematical Model ◽  
Natural Characteristics

Bent-arm PenduBot is more similar to human arm, which attaches more and more robot experts’ attention around the world. As the foundation of the multi-link PenduBot control, the mathematical model should be established first. Based on the method of kinematics and dynamics, the N-link bent-arm PenduBot mathematical models are established in this paper, including the nonlinear model and the linear model. The natural characteristics of different pendulum are analyzed. By using the condition number of the controllability matrix, the control difficulty for higher order systems is compared.

Utilization of Multiple Cues in Paired Comparisons

1969 ◽  
Vol 11 (4) ◽  
pp. 361-378
Author(s):  
James V. Bradley
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Predictive Validity ◽  
Performance Data ◽  
Paired Comparisons ◽  
Thought Process ◽  
Multiple Cues ◽  
The Mathematical Model

Subjects were given one, two, or three cues with which to make an either-or decision. Certain hypotheses were formulated to describe the subject's thought process in utilizing the multiple cues, and mathematical models were constructed to simulate them. The models were then used on data for the single-cue case to predict performance in the multiple-cue case. Predicted performance “data” were then compared with actually observed data for the same multiple-cue case, thus testing the predictive validity of the mathematical model and the tenability of the corresponding hypothesis.

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