scholarly journals A Novel Comprehensive Method for Modeling and Analysis of Mesh Stiffness of Helical Gear

2020 ◽  
Vol 10 (19) ◽  
pp. 6695
Author(s):  
Shaoshuai Hou ◽  
Jing Wei ◽  
Aiqiang Zhang ◽  
Chunpeng Zhang ◽  
Junhui Yan ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Axial Component ◽  
The Novel ◽  
Mesh Stiffness ◽  
Mean Values ◽  
Modeling And Analysis ◽  
Helical Gears ◽  
Aerospace Applications ◽  
Comprehensive Method ◽  
Helical Angle

The mesh stiffness of gear pairs used in aerospace applications, such as geared turbofan, has a vital influence on vibration and noise. To compensate for the deficiencies of the conventional method that does not consider slice coupling and structure coupling simultaneously, a comprehensive mathematical model for computing the mesh stiffness of helical gears is established. In this novel model, the effect of structure coupling and slice coupling between neighboring sliced gears are considered. The effect of the axial component of meshing force is also taken into account simultaneously. The results obtained by the comprehensive model are consistent with the finite element method and it proves that the novel mathematical model is sound. The influences of the helical angle and addendum modification coefficient on mesh stiffness are studied. The results show that the mesh stiffness of helical gears would be decreased in multiteeth regions caused by structure coupling. With or without consideration of the axial component, the relative mean values of mesh stiffness become larger with an increasing helical angle. The fluctuation value of mesh stiffness decreases when a positive addendum modification coefficient is adopted. The addendum modification also changes the phase of mesh stiffness. This study is helpful for a vibration analysis of gear transmission systems.

scholarly journals A Mathematical Model of Contact Tracing during the 2014–2016 West African Ebola Outbreak

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 608
Author(s):  
Danielle Burton ◽  
Suzanne Lenhart ◽  
Christina J. Edholm ◽  
Benjamin Levy ◽  
Michael L. Washington ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Disease Management ◽  
Ebola Virus ◽  
Virus Disease ◽  
Infected Individual ◽  
Vital Role ◽  
West African ◽  
Contact Tracing ◽  
The Novel ◽  
Using Data

The 2014–2016 West African outbreak of Ebola Virus Disease (EVD) was the largest and most deadly to date. Contact tracing, following up those who may have been infected through contact with an infected individual to prevent secondary spread, plays a vital role in controlling such outbreaks. Our aim in this work was to mechanistically represent the contact tracing process to illustrate potential areas of improvement in managing contact tracing efforts. We also explored the role contact tracing played in eventually ending the outbreak. We present a system of ordinary differential equations to model contact tracing in Sierra Leonne during the outbreak. Using data on cumulative cases and deaths, we estimate most of the parameters in our model. We include the novel features of counting the total number of people being traced and tying this directly to the number of tracers doing this work. Our work highlights the importance of incorporating changing behavior into one’s model as needed when indicated by the data and reported trends. Our results show that a larger contact tracing program would have reduced the death toll of the outbreak. Counting the total number of people being traced and including changes in behavior in our model led to better understanding of disease management.

An Improved Mathematical Model of Galton Board With Velocity-Dependent Restitution

2017 ◽  
Vol 12 (6) ◽  
Author(s):  
Auni Aslah Mat Daud
Keyword(s):  
Mathematical Model ◽  
Random Walk ◽  
Symbolic Dynamics ◽  
Coefficient Of Restitution ◽  
Dynamics Analysis ◽  
The Novel ◽  
Francis Galton ◽  
The Way

A Galton board is an instrument invented in 1873 by Francis Galton (1822–1911). It is a box with a glass front and many horizontal nails or pins embedded in the back and a funnel. Galton and many modern statisticians claimed that a lead ball descending to the bottom of the Galton board would display random walk. In this study, a new mathematical model of Galton board is developed, to further improve three very recently proposed models. The novel contribution of this paper is the introduction of the velocity-dependent coefficient of restitution. The developed model is then analyzed using symbolic dynamics. The results of the symbolic dynamics analysis prove that the developed Galton board model does not behave the way Galton envisaged.

Gear transmission error outside the normal path of contact due to corner and top contact

1999 ◽  
Vol 213 (4) ◽  
pp. 389-400 ◽  
Author(s):  
R. G. Munro ◽  
L Morrish ◽  
D Palmer
Keyword(s):  
Dynamic Test ◽  
Theoretical Models ◽  
Transmission Error ◽  
Helical Gear ◽  
Gear Transmission ◽  
The Novel ◽  
Transmission Systems ◽  
Helical Gears ◽  
Tooth Stiffness ◽  
Top Contact

This paper is devoted to a phenomenon known as corner contact, or contact outside the normal path of contact, which can occur in spur and helical gear transmission systems under certain conditions. In this case, a change in position of the driven gear with respect to its theoretical position takes place, thus inducing a transmission error referred to here as the transmission error outside the normal path of contact (TEo.p.c). The paper deals with spur gears only, but the results are directly applicable to helical gears. It systematizes previous knowledge on this subject, suggests some further developments of the theory and introduces the novel phenomenon of top contact. The theoretical results are compared with experimental measurements using a single flank tester and a back-to-back dynamic test rig for spur and helical gears, and they are in good agreement. Convenient approximate equations for calculation of TEo.p.c suggested here are important for analysis of experimental data collected in the form of Harris maps. This will make possible the calculation of tooth stiffness values needed for use in theoretical models for spur and helical gear transmission systems.

Force tracking control of grinding end effector based on backstepping + PID

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shijie Dai ◽  
Shining Li ◽  
Wenbin Ji ◽  
Zhenlin Sun ◽  
Yufeng Zhao
Keyword(s):  
Mathematical Model ◽  
Linear System ◽  
Control Strategy ◽  
Grinding Force ◽  
Constant Force ◽  
End Effector ◽  
Content Type ◽  
Modeling And Analysis ◽  
The Mathematical Model ◽  
Automobile Wheel

Purpose This study aims to realize the constant force grinding of automobile wheel hub. Design/methodology/approach A force control strategy of backstepping + proportion integration differentiation (PID) is proposed. The grinding end effector is installed on the flange of the robot. The robot controls the position and posture of the grinding end actuator and the grinding end actuator controls the grinding force output. First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. Finally, the feasibility of the proposed method is verified by simulation and experiment. Findings The simulation and experimental results show that the backstepping + PID strategy can track the expected force quickly, and improve the dynamic response performance of the system and the quality of grinding and polishing of automobile wheel hub. Research limitations/implications The mathematical model is based on the pneumatic system and ideal gas, and ignores the influence of friction in the working process of the cylinder, so the mathematical model proposed in this study has certain limitations. A new control strategy is proposed, which is not only used to control the grinding force of automobile wheels, but also promotes the development of industrial control. Social implications The automatic constant force grinding of automobile wheel hub is realized, and the manpower is liberated. Originality/value First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. The nonlinear model of the system is controlled by backstepping method, and in the process, the linear system composed of errors is obtained, and then the linear system is controlled by PID to realize the combination of backstepping and PID control.

scholarly journals Web Application for Statistical Tracking and Predicting the Evolution of Active Cases with the Novel Coronavirus (SARS-CoV-2)

2021 ◽  
pp. 70-74
Author(s):  
Iulia Clitan ◽  
◽  
Adela Puscasiu ◽  
Vlad Muresan ◽  
Mihaela Ligia Unguresan ◽  
...  
Keyword(s):  
Neural Network ◽  
Mathematical Model ◽  
Web Application ◽  
Point Of View ◽  
The Novel ◽  
End User ◽  
First Case ◽  
Novel Coronavirus ◽  
Second Wave ◽  
Over Time

Since February 2020, when the first case of infection with SARS COV-2 virus appeared in Romania, the evolution of COVID-19 pandemic continues to have an ascending allure, reaching in September 2020 a second wave of infections as expected. In order to understand the evolution and spread of this disease over time and space, more and more research is focused on obtaining mathematical models that are able to predict the evolution of active cases based on different scenarios and taking into account the numerous inputs that influence the spread of this infection. This paper presents a web responsive application that allows the end user to analyze the evolution of the pandemic in Romania, graphically, and that incorporates, unlike other COVID-19 statistical applications, a prediction of active cases evolution. The prediction is based on a neural network mathematical model, described from the architectural point of view.

scholarly journals Modeling and analysis of fractional order Zika model

2021 ◽  
Vol 7 (3) ◽  
pp. 3912-3938
Author(s):  
Muhammad Farman ◽  
◽  
Ali Akgül ◽  
Sameh Askar ◽  
Thongchai Botmart ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Fixed Point ◽  
Control Strategy ◽  
Zika Virus ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fractional Operator ◽  
Modeling And Analysis ◽  
Virus Model ◽  
Positivity And Boundedness

<abstract> <p>We propose mathematical model for the transmission of the Zika virus for humans spread by mosquitoes. We construct a scheme for the Zika virus model with Atangna-Baleanue Caputo sense and fractal fractional operator by using generalized Mittag-Leffler kernel. The positivity and boundedness of the model are also calculated. The existence of uniquene solution is derived and stability analysis has been made for the model by using the fixed point theory. Numerical simulations are made by using the Atangana-Toufik scheme and fractal fractional operator with a different dimension of fractional values which support the theoretical outcome of the proposed system. Developed scheme including simulation will provide better understanding in future analysis and for control strategy regarding Zika virus.</p> </abstract>

Crystal Structure of (NH4)2[Mo3S(S2)6] Containing the Novel Isolated Cluster [MO3S13]2-

1979 ◽  
Vol 34 (3) ◽  
pp. 434-436 ◽  
Author(s):  
A. Müller ◽  
S. Pohl ◽  
M. Dartmann ◽  
J. P. Cohen ◽  
J. M. Bennett ◽  
...  
Keyword(s):  
Molecular Structure ◽  
Crystal Structure ◽  
Aqueous Solutions ◽  
Single Crystal ◽  
Ammonium Salt ◽  
Crystal And Molecular Structure ◽  
Monoclinic Space Group ◽  
The Novel ◽  
Mean Values ◽  
X Ray

Abstract The novel tri-nuclear metal-sulfur cluster [Mo3S(S2)6]2- can be obtained as its ammonium salt by the reaction of a Moiv containing aqueous solutions with polysulfide. Its crystal and molecular structure has been determined by a single crystal X-ray study. The crystals are monoclinic (space group Cm, with a = 11.577(6) Å, b = 16.448(7) Å, c = 5.716(2) Å, β = 117.30(3)°, V = 967.2 Å3 , Z = 2, dexptl. = 2.54(2) g/cm3 , dcal = 2.54 g/cm3). The structure consists of isolated [Mo3S(S2)6]2- units, with three Mo atoms at the vertices of a triangle. There are bridging as well as terminal S22--ligands lying above and below the Mo3-plane (bond distances: Mo-Mo = 2.722 Å, Mo-S(terminal) = 2.435, Mo-S(bridging) = 2.452, Mo3-S = 2.353(4) Å and S-S = 2.04 Å (mean values)).

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