About the Profile Accuracy of the Involute Gear Hob

Abstract Gear hobs are the most widely and frequently used gear cutting tools. During the time passed between the moment of invention (Schiele, 1876) and the present, gear hobs reached a considerable evolution regarding the geometry, the profile of the edge, the relieving technologies finalizing in the latest constructive and design solutions. This paper deals with the calculus of the edge profile in the case the basic worm of the hob has involute helicoid surfaces. In order to obtain a constant grinding allowance on the relief faces of the gear hob teeth it is necessary to compute the edge of the roughing relieving cutter. The equations are deduced considering that the provenience involute worm is a one teethed helical gear with shifted profile. The presented mathematical model proves that linearizing the relieving cutter profile is not an adequate solution if aspiring to higher precision.

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Mathematical model for design and analysis of power skiving tool for involute gear cutting

Mechanism and Machine Theory ◽

10.1016/j.mechmachtheory.2016.03.021 ◽

2016 ◽

Vol 101 ◽

pp. 195-208 ◽

Cited By ~ 12

Author(s):

Chung-Yu Tsai

Keyword(s):

Mathematical Model ◽

Gear Cutting ◽

Power Skiving ◽

Involute Gear

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Modelling the impact of delaying vaccination against SARS-CoV-2 assuming unlimited vaccine supply

Theoretical Biology and Medical Modelling ◽

10.1186/s12976-021-00143-0 ◽

2021 ◽

Vol 18 (1) ◽

Author(s):

Marcos Amaku ◽

Dimas Tadeu Covas ◽

Francisco Antonio Bezerra Coutinho ◽

Raymundo Soares Azevedo ◽

Eduardo Massad

Keyword(s):

Mathematical Model ◽

Vaccination Campaign ◽

Vaccination Rate ◽

Sao Paulo ◽

The State ◽

São Paulo ◽

Health Authorities ◽

The World ◽

The Moment ◽

The Impact

Abstract Background At the moment we have more than 177 million cases and 3.8 million deaths (as of June 2021) around the world and vaccination represents the only hope to control the pandemic. Imperfections in planning vaccine acquisition and difficulties in implementing distribution among the population, however, have hampered the control of the virus so far. Methods We propose a new mathematical model to estimate the impact of vaccination delay against the 2019 coronavirus disease (COVID-19) on the number of cases and deaths due to the disease in Brazil. We apply the model to Brazil as a whole and to the State of Sao Paulo, the most affected by COVID-19 in Brazil. We simulated the model for the populations of the State of Sao Paulo and Brazil as a whole, varying the scenarios related to vaccine efficacy and compliance from the populations. Results The model projects that, in the absence of vaccination, almost 170 thousand deaths and more than 350 thousand deaths will occur by the end of 2021 for Sao Paulo and Brazil, respectively. If in contrast, Sao Paulo and Brazil had enough vaccine supply and so started a vaccination campaign in January with the maximum vaccination rate, compliance and efficacy, they could have averted more than 112 thousand deaths and 127 thousand deaths, respectively. In addition, for each month of delay the number of deaths increases monotonically in a logarithmic fashion, for both the State of Sao Paulo and Brazil as a whole. Conclusions Our model shows that the current delay in the vaccination schedules that is observed in many countries has serious consequences in terms of mortality by the disease and should serve as an alert to health authorities to speed the process up such that the highest number of people to be immunized is reached in the shortest period of time.

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Development of an Intelligent CAD System for Involute Cylindrical Gear Cutting Tools

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.532.249 ◽

2014 ◽

Vol 532 ◽

pp. 249-252

Author(s):

Ying Hua Liao ◽

Gao Jun Liu ◽

Xiang Guo Sun

Keyword(s):

Expert Knowledge ◽

Cutting Tools ◽

3D Models ◽

Tool Design ◽

Cylindrical Gear ◽

Intelligent Cad ◽

Forward Reasoning ◽

Cad System ◽

Gear Cutting ◽

2D And 3D

An intelligent CAD system for Involute cylindrical gear cutting tools is developed by VC++ and SQL server, and it includes four modules, such as user interface, instance query, intelligent gear tool design and database. The intelligent gear tool design is the key to the intelligent CAD system, and it is based on the forward reasoning production system, and as the Intelligent reasoning technology is used for gear tool design, a lots of expert knowledge could be made full use of. The design results by the developed intelligent CAD system are more reasonable than those by a traditional CAD system, and the efficiency and quality of the gear tool design also could be improved. The developed intelligent CAD system supports both 2D and 3D models, which can lay foundation for CAD/CAE/CAM integration of gear cutting tools.

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Modern trends in the development of forklifts

10.36652/1684-1298-2021-5-36-40 ◽

2021 ◽

pp. 36-40

Author(s):

D.A. Semenov

Keyword(s):

Parametric Model ◽

Transport Equipment ◽

Automated Control ◽

Modern Design ◽

Current Trends ◽

History Of ◽

Design Solutions ◽

The Moment ◽

And Storage ◽

Storage Facilities

This article helps to understand what a forklift is, what it was and what it is at the moment. In the text below, a brief history of the appearance of the loader is well traced, the constructive component and its features are described. The main aspects of the development of a loader in the system of lifting and transporting machines and storage facilities are highlighted. The current trends in the development of forklifts are summarized, an analysis of the market of European and domestic consumers is provided and a conclusion about popular manufacturers is formulated. The information about modern design solutions for machines of this type was also not spared, the principles of operation were described, and also its own design-parametric model of a forklift was proposed, which is able to make work in warehouses more economical and profitable. In the conclusion, the main theses about the modernized machine are formulated, which can subsequently give an impetus to the development of automated control on domestically produced loaders. Keywords: forklift, modernization, improvement, lifting and transport equipment

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DIFFERENTIAL EQUATIONS FOR TRAIN STARTING WITH ELASTIC CONNECTIONS

Fundamental and Applied Problems of Engineering and Technology ◽

10.33979/2073-7408-2021-346-2-18-26 ◽

2021 ◽

Vol 2 ◽

pp. 18-26

Author(s):

I.P. POPOV

Keyword(s):

Mathematical Model ◽

Differential Equations ◽

Friction Force ◽

Static Friction ◽

Longitudinal Vibrations ◽

Maximum Tension ◽

Inert Mass ◽

The Moment ◽

Elastic Couplings ◽

Selection Of

The starting mode for the train is the most difficult. An effective method of pulling is the selection of coupling clearances. In this case, the cars are set in motion sequentially and the inert mass, as well as the static friction force immediately at the moment of starting, are minimal. This method has two significant drawbacks - a small fixed value of the gaps in the couplings and the shock nature of the impulse transfer. These disadvantages can be avoided by using elastically deformable couplings. The aim of this work is to construct a mathematical model of "easy" starting of a train with elastic couplings. The softening of the train start-off mode is essentially due to the replacement of the simultaneous start-off of the sections with alternate ones. To exclude longitudinal vibrations of the composition, after reaching the maximum tension of the coupling, the possibility of its harmonic compression should be mechanically blocked.

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