Application of mechanized mathematics to rotor dynamics

2002 ◽  
Vol 23 (9) ◽  
pp. 1045-1053
Author(s):  
Hu Chao ◽  
Wang Yan ◽  
Wang Li-guo ◽  
Huang Wen-hu
Author(s):  
Liguo Wang ◽  
Wenhu Huang ◽  
Chao Hu

Abstract The mechanized mathematics-Wu elimination method is a vigorous method in solving nonlinear algebraic equations in China, but it is still not so popular in the West. In this paper the mechanized mathematics-Wu elimination method is introduced in brief and is used to solve the problem of dynamic behavior of a rotor-bearing system with nonlinear supports. The whirl equations of a short bearing-rotor system with two disks considering gyro-moment are studied. The idea of the characteristic set of Wu method is combined with Maple’s symbolic calculation. The whirl parameter of a rotor mounted on two supports are analyzed. The analytical results showing the relations of the bearing parameters and instability speed are presented.


2018 ◽  
Author(s):  
Qi Li ◽  
Adam J. Zaczek ◽  
Timothy M. Korter ◽  
J. Axel Zeitler ◽  
Michael T. Ruggiero

<div>Understanding the nature of the interatomic interactions present within the pores of metal-organic frameworks</div><div>is critical in order to design and utilize advanced materials</div><div>with desirable applications. In ZIF-8 and its cobalt analogue</div><div>ZIF-67, the imidazolate methyl-groups, which point directly</div><div>into the void space, have been shown to freely rotate - even</div><div>down to cryogenic temperatures. Using a combination of ex-</div><div>perimental terahertz time-domain spectroscopy, low-frequency</div><div>Raman spectroscopy, and state-of-the-art ab initio simulations,</div><div>the methyl-rotor dynamics in ZIF-8 and ZIF-67 are fully charac-</div><div>terized within the context of a quantum-mechanical hindered-</div><div>rotor model. The results lend insight into the fundamental</div><div>origins of the experimentally observed methyl-rotor dynamics,</div><div>and provide valuable insight into the nature of the weak inter-</div><div>actions present within this important class of materials.</div>


10.29007/7kx8 ◽  
2018 ◽  
Author(s):  
Joe Hurd

This invited talk will look at logic solvers through the application lens of constructing and processing a theory library of mechanized mathematics. In fact, constructing and processing theories are two distinct applications, and each will be considered in turn. Construction is carried out by formalizing a mathematical theory using an interactive theorem prover, and logic solvers can remove much of the drudgery by automating common reasoning tasks. At the theory library level, logic solvers can provide assistance with theory engineering tasks such as compressing theories, managing dependencies, and constructing new theories from reusable theory components.


Author(s):  
L M Zhai ◽  
L Cao ◽  
J W Cao ◽  
H M Lei ◽  
S H Ahn ◽  
...  

Author(s):  
A. Arroyo ◽  
M. McLorn ◽  
M. Fabian ◽  
M. White ◽  
A. I. Sayma

Rotor-dynamics of Micro Gas Turbines (MGTs) under 30 kW have been a critical issue for the successful development of reliable engines during the last decades. Especially, no consensus has been reached on a reliable MGT arrangement under 10 kW with rotational speeds above 100,000 rpm, making the understanding of the rotor-dynamics of these high speed systems an important research area. This paper presents a linear rotor-dynamic analysis and comparison of three mechanical arrangements of a 6 kW MGT intended for utilising Concentrated Solar Power (CSP) using a parabolic dish concentrator. This application differs from the usual fuel burning MGT in that it is required to operate at a wider operating speed range. The objective is to find an arrangement that allows reliable mechanical operation through better understanding of the rotor dynamics for a number of alternative shaft-bearings arrangements. Finite Element Analysis (FEA) was used to produce Campbell diagrams and to determine the critical speeds and mode shapes. Experimental hammer tests using a new approach based on optical sensing technology were used to validate the rotor-dynamic models. The FEA simulation results for the natural frequencies of a shaft arrangement were within 5% of the measurements, while the deviation for the shaft-bearings arrangement increased up to 16%.


2003 ◽  
Vol 9 (4) ◽  
pp. 255-262 ◽  
Author(s):  
M. Kalkat ◽  
Ş. Yıldırım ◽  
I. Uzmay

Adirect-coupled rotor system was designed to analyze the dynamic behavior of rotating systems in regard to vibration parameters. The vibration parameters are amplitude, velocity, and acceleration in the vertical direction. The system consisted of a machine analyzer, shaft, disk, master-trend software, and power unit. Four different points were detected and measured by the experimental setup. The vibration parameters were found and saved from master-trend software. These parameters were employed as the desired parameters of the network. A neural network is designed for analyzing a system's vibration parameters. The results showed that the network could be used as an analyzer of such systems in experimental applications.


2015 ◽  
Vol 84 ◽  
pp. 54-66 ◽  
Author(s):  
Mikhael Tannous ◽  
Patrice Cartraud ◽  
David Dureisseix ◽  
Mohamed Torkhani
Keyword(s):  

1981 ◽  
Vol 14 (2) ◽  
pp. 107-111 ◽  
Author(s):  
B.S. Prabhu ◽  
B.V.A. Rao
Keyword(s):  

Author(s):  
Jiazhong Zhang ◽  
Bram de Kraker ◽  
Dick H. van Campen

Abstract An elementary system with gears and excited by unbalance mass has been constructed for analyzing the interaction between torsion and bending vibration in rotor dynamics. For this system, only the interaction caused primarily by unbalance mass has been investigated. The stability and bifurcation characteristics of the system have been studied by numerical computation based on Hopf bifurcation and Floquet theory. The results show that the interaction between torsion and bending vibrations can affect the stability and bifurcation of the unbalance response, in particular the onset speed of instability. In addition to the above, the interaction also affects the steady-state response. To investigate the influence of unbalance mass, the periodic solution and its stability have been studied near the first bending critical speed of the decoupled system. All the results show that the coupling of torsion and bending vibrations can have a significant influence on the nonlinear dynamics of the whole system.


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