Determining Power Losses in Helical Gear Mesh: Case Study

2003 ◽  
Author(s):  
Petra Heingartner ◽  
David Mba
Keyword(s):  
Mathematical Model ◽  
Capital Expenditure ◽  
Rolling Friction ◽  
Power Losses ◽  
Energy Usage ◽  
Helical Gears ◽  
Gear Mesh ◽  
The Individual ◽  
The Mathematical Model

Currently legislation is in place to encourage a reduction in energy usage. As such there is an increased demand for machinery with higher efficiencies, not only to reduce the operational costs of the machinery, but also to cut capital expenditure. The power losses associated with the gear mesh can be divided into speed and load dependant losses. This paper reviews some of the mathematical models proposed for the individual components associated with these losses, such as windage, churning, sliding and rolling friction loses. A mathematical model is proposed which predicts the power losses on helical gears highlighting the major contributor to losses in the gear mesh. Furthermore, the mathematical model is validated with a case study.

Modelling and Simulation of NO2 Dispersion Phenomenon in Atmosphere by Analytical-Experimental Methods

2008 ◽  
Vol 59 (10) ◽  
Author(s):  
Delia Perju ◽  
Harieta Pirlea ◽  
Gabriela-Alina Brusturean ◽  
Dana Silaghi-Perju ◽  
Sorin Marinescu
Keyword(s):  
Mathematical Model ◽  
Nitrogen Dioxide ◽  
Modeling And Simulation ◽  
Human Health ◽  
Experimental Methods ◽  
Negative Effects ◽  
Real Situation ◽  
Experimental Values ◽  
The Mathematical Model

The European laws and recently the Romanian ones impose more and more strict norms to the large nitrogen dioxide polluters. They are obligated to continuously improve the installations and products so that they limit and reduce the nitrogen dioxide pollution, because it has negative effects on the human health and environment. In this paper are presented these researches made within a case study for the Timi�oara municipality, regarding the modeling and simulation of the nitrogen dioxide dispersion phenomenon coming from various sources in atmosphere with the help of analytical-experimental methods. The mathematical model resulting from these researches is accurately enough to describe the real situation. This was confirmed by comparing the results obtained based on the model with real experimental values.

scholarly journals Developing an Analytical Model and Computing Tool for Optimizing Lapping Operations of Flat Objects Made of Alloyed Steels

Materials ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1343 ◽  
Author(s):  
Tudor Deaconescu ◽  
Andrea Deaconescu
Keyword(s):  
Mathematical Model ◽  
Surface Roughness ◽  
Material Properties ◽  
Depth Of Cut ◽  
Operation Optimization ◽  
Abrasive Grains ◽  
Finishing Process ◽  
Real World Applications ◽  
The Mathematical Model

Lapping is a finishing process where loose abrasive grains contained in a slurry are pressed against a workpiece to reduce its surface roughness. To perform a lapping operation, the user needs to set the values of the respective lapping conditions (e.g., pressure, depth of cut, the rotational speed of the pressing lap plate, and alike) based on some material properties of the workpiece, abrasive grains, and slurry, as well as on the desired surface roughness. Therefore, a mathematical model is needed that establishes the relationships among the abovementioned parameters. The mathematical model can be used to develop a lapping operation optimization system, as well. To this date, such a model and system are not available mainly because the relationships among lapping conditions, material properties of abrasive grains and slurry, and surface roughness are difficult to establish. This study solves this problem. It presents a mathematical model establishing the required relationships. It also presents a system developed based on the mathematical model. In addition, the efficacy of the system is also shown using a case study. This study thus helps systematize lapping operations in regard to real-world applications.

scholarly journals Applied Mathematical Approach for Decision-Making in Building Plan Design

2018 ◽  
Vol 3 (9) ◽  
pp. 39
Author(s):  
Grit Ngowtanasuwan
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Publishing House ◽  
Unit Cost ◽  
Construction Cost ◽  
Model Unit ◽  
International Publishing ◽  
Plan Design ◽  
The Mathematical Model

This article presents a method for solving decision in building plan design by using a mathematical model (nonlinear programming). First objective is to formulate mathematical models for analysis in dividing rooms and dimensions in a building plan. Secondly, to calculate the dimensions and room sizes which have minimum construction cost. A case study of a condominium building plan was analyzed in this research. The results found application of the mathematical model was applicable. The mathematical models were formulated, the minimum construction cost was ฿723,000 (US$24,100) and usable area in the condominium was 67.5 m2 and followed the assigned design constraints.Keywords: Building plan design; Mathematical model; Unit cost;eISSN 2398-4295 © 2018. The Authors. Published for AMER ABRA cE-Bs by e-International Publishing House, Ltd., UK. This is an open-access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer–review under responsibility of AMER (Association of Malaysian Environment-Behaviour Researchers), ABRA (Association of Behavioural Researchers on Asians) and cE-Bs (Centre for Environment-Behaviour Studies), Faculty of Architecture, Planning & Surveying, Universiti Teknologi MARA, Malaysia. DOI:

scholarly journals A General Modeling Approach for Shock Absorbers: 2 DoF MR Damper Case Study

2021 ◽  
Vol 7 ◽  
Author(s):  
Jorge de-J. Lozoya-Santos ◽  
Juan C. Tudon-Martinez ◽  
Ruben Morales-Menendez ◽  
Olivier Sename ◽  
Andrea Spaggiari ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Linear Models ◽  
Mr Damper ◽  
Shock Absorbers ◽  
Magneto Rheological ◽  
The Mathematical Model ◽  
Force Displacement ◽  
Standard Tests

A methodology is proposed for designing a mathematical model for shock absorbers; the proposal is guided by characteristic diagrams of the shock absorbers. These characteristic diagrams (Force-Displacement, Velocity-Acceleration) are easily constructed from experimental data generated by standard tests. By analyzing the diagrams at different frequencies of interest, they can be classified into one of seven patterns, to guide the design of a model. Finally, the identification of the mathematical model can be obtained using conventional algorithms. This methodology has generated highly non-linear models for 2 degrees of freedom magneto-rheological dampers with high precision (2–10% errors).

scholarly journals An Estimation of Dates Production Function in Karbala Governorate For The Agricultural Season 2020 (Al-jadual Al-gharby District A case Study)

2021 ◽  
Vol 923 (1) ◽  
pp. 012070
Author(s):  
Sadeq H. Hussein ◽  
Hayder Hamed Blaw
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Production Function ◽  
Returns To Scale ◽  
Ordinary Least Squares ◽  
Total Production ◽  
Logarithmic Function ◽  
The Mathematical Model

Abstract This study aimed to detect the most important factor that affects dates production. About 108 questionary forms collecttted palm orchard farmers in Karbala to estimate the dates production function in Karbala governorate for the agricultural season 2021 (the district of Al-jadual Al-Gharby). The study distributed those formmmsss for about 10% of the total palm orchards in Al-jadual Al-Gharby district of the holy governorate of Karbala. The study used the method of ordinary Least squares (OLS) to estimate the mathematical model of the function. The results showed that the double Logarithmic function in terms of its estimation of the estimated Coefficients by one unit leads to a corresponding change in the produced quality of dates and the same direction by 0.188 0.808) % respectively, and that the capital variable is more in fluently in production than the work variable. As for the total production elasticity (the sum of the partial elasticities of the resources used), which represents returns to scale, it amounted to about (0.996), which indicates a decrease in the return to scale.

scholarly journals Incomplete Cross-Bonding in the MV Line. Experience from the Operation of MV Single Cable Lines

Energies ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 5292
Author(s):  
Krzysztof Dobrzynski ◽  
Zbigniew Lubosny ◽  
Jacek Klucznik ◽  
Janusz Grala ◽  
Dominik Falkowski
Keyword(s):  
Mathematical Model ◽  
Power Systems ◽  
Power Losses ◽  
Cable Line ◽  
Medium Voltage ◽  
Economic Justification ◽  
Line Section ◽  
Short Circuits ◽  
Cable Lines ◽  
The Mathematical Model

Cable lines are one of the basic components of power systems. Medium and high voltage cables mainly comprise a metallic sheath, which is concentric to the main core conductor. There are several operating schemes of such cable lines, which differ in the place of earthing of sheaths and the possible use of the sheaths and/or conductors crossing. The sheaths cross-bonding is typically done in two places of one cable line section, and it allows to reduce power losses. Nevertheless, the use of incomplete sheaths crossing—only in one place on cable route may have economic justification. The paper presents an incomplete sheaths cross-bonding analysis of an existing medium voltage cable line. The results obtained by the mathematical model are validated by measurements taken on 30 October 2019 on an existing cable line. Measurements recorded on a real object for various systems of crossing sheaths are presented. The influence of incorrect sheaths crossing on the measured quantities was shown. In addition, the risk of excess voltage on the sheaths during short-circuits has been verified using a mathematical model.

scholarly journals Estimating the Optimum Tilt Angles for South-Facing Surfaces in Palestine

Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 623 ◽  
Author(s):  
Ramez Abdallah ◽  
Adel Juaidi ◽  
Salameh Abdel-Fattah ◽  
Francisco Manzano-Agugliaro
Keyword(s):  
Mathematical Model ◽  
Solar Radiation ◽  
Tilt Angle ◽  
Peak Power ◽  
Horizontal Surface ◽  
Geographical Information ◽  
Solar Panels ◽  
Energy Gains ◽  
The Mathematical Model

The optimum tilt angle of solar panels or collectors is crucial when determining parameters that affect the performance of those panels. A mathematical model is used for determining the optimum tilt angle and for calculating the solar radiation on a south-facing surface on a daily, monthly, seasonal, semi-annual, and annual basis. Photovoltaic Geographical Information System (PVGIS) and Photovoltaic Software (PVWatts) is developed by the NREL (US National Renewable Energy Laboratory) are also used to calculate the optimum monthly, seasonal, semi-annual, and annual tilt angles and to compare these results with the results obtained from the mathematical model. The results are very similar. PVGIS and PVWatts are used to estimate the solar radiation on south-facing surfaces with different tilt angles. A case study of a mono-crystalline module with 5 kWP of peak power is used to find out the amount of increased energy (gains) obtained by adjusting the Photovoltaic (PV) tilt angles based on yearly, semi-annual, seasonal, and monthly tilt angles. The results show that monthly adjustments of the solar panels in the main Palestinian cities can generate about 17% more solar energy than the case of solar panels fixed on a horizontal surface. Seasonal and semi-annual adjustments can generate about 15% more energy (i.e., it is worth changing the solar panels 12 times a year (monthly) or at least 2 times a year (semi-annually). The yearly optimum tilt angle for most Palestinian cities is about 29°, which yields an increase of about 10% energy gain compared to a solar panel fixed on a horizontal surface.

An Integer Programming Approach to Optimize the Plantation in Order to Reduce Global Warming

2012 ◽  
Vol 548 ◽  
pp. 767-771 ◽  
Author(s):  
C. Vanlisuta ◽  
Suksan Prombanpong
Keyword(s):  
Mathematical Model ◽  
Linear Programming ◽  
Objective Function ◽  
Programming Model ◽  
Programming Approach ◽  
Profit Function ◽  
Carbon Credit ◽  
Integer Linear Programming Model ◽  
The Mathematical Model

The objective of this paper is to determine the number and species of trees to be planted in order to maximize a profit through an integer linear programming model. The mathematical model is developed in terms of the profit function. This objective function is therefore, a difference between carbon credit revenue and costs of plantation. The economical plants are only considered in the model. Consequently, fourteen different tree species are to be investigated. The objective function is subjected to several constraints i.e. planting area, carbon sequestration and so on. The planting envelope of each tree is assigned 4 by 4 meters. In this paper, the Eastern part of Thailand is considered the case study. It is found that three kinds of plants, Copper pod, Cananga, and Bullet wood are suitable for planting. A number of trees to be planted in 1600 square meter are twenty, thirty, and fifty plants respectively. The profit earned is of 12,112 $ per year in the next fifth year.

scholarly journals NUMERICAL SIMULATION OF THE DYNAMICS OF A FLEXIBLE ROTOR WITH TWO BALL AUTO-BALANCERS

2020 ◽  
pp. 31-44
Author(s):  
Nikolay Zaytsev ◽  
◽  
Denis Zaytsev ◽  
Andrey Makarov ◽  
Dmitriy Mineev ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Cross Sections ◽  
Experimental Studies ◽  
Element Model ◽  
Rolling Friction ◽  
Published Data ◽  
Flexible Rotor ◽  
Flexible Rotors ◽  
The Mathematical Model

Ball auto-balancing devices can to compensate changes of unbalance "on the move" only for rotors operating at supercritical speeds. For automatic balancing of such rotors, classified as flexible rotors, several auto-balancers located in different cross sections of the shaft are necessary. This makes it necessary to account bending fluctuations on studies of dynamics of the rotor with auto-balancers, that is especially important in the design of the real rotors. In view of the complexity of experimental studies of such rotors in the article the method of direct numerical simulation of the dynamics of the flexible rotor system – supports – auto-balances is considered. The methodological basis of this method is the use of a discrete multi-mass rotor model, which is equivalent in dynamic characteristics to a real rotor, and also the equations of dynamics of the system discrete rotor – supports – auto-balancers, obtained in the direct form of recording. For definition of discrete masses and a matrix of coefficients of influence of stiffness of rotor cross-sections it is supposed to use calculations for finite-element model of a real rotor by existing software complexes of the engineering analysis. The mathematical model of the system dynamics obtained by the Lagrange method takes into account the non-stationarity of the rotor rotation speed, the influence of gravity and the rolling friction of the balls in the auto-balancer cages. Verification of the mathematical model was performed by reproducing the published data using a computational model for a two-support single-disk three-mass rotor with a two-ball auto-balancer. For a four-mass rotor with two two-ball auto-balancers, the results of numerical simulation of dynamics for the modes of acceleration, steady-state rotation and deceleration are presented. It is shown that for the system under consideration, only partial auto-balancing takes place in the steady rotation mode, including after a stepwise increase of the imbalance.

CASE STUDY REGARDING THE PREDICTION OF THE LAMINATING FORCE

2020 ◽  
Vol 34 (2) ◽  
pp. 43-51
Author(s):  
Angela Elena Pop ◽  
Keyword(s):  
Mathematical Model ◽  
Rolling Mill ◽  
Probabilistic Modelling ◽  
Degree Of Deformation ◽  
Whole Process ◽  
Deformation Length ◽  
Length Width ◽  
The Mathematical Model ◽  
Modelling Approach

Based on the mathematical model existent in the literature, the object of this study is a way to improve and simplify the way that the laminating force is determined. The whole process is realized using a provided rolling mill. The mathematical model that determines the laminating force has a theoretical base and it can approximately predict how the laminating force will vary. The relative degree of deformation tells us that de sample suffered an uneven deformation length, width and height wise. After the first lamination, the material loses plasticity and the reduction has to be as follows: higher at first, after which it drops, as the reduction degrees indicate. We created a probabilistic modelling approach that learns as new data is introduced.

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