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Mathematical Rotordynamic Model Regarding Excitation Due to Elliptical Shaft Journals in Electrical Motors Considering the Gyroscopic Effect  [PDF]
Ulrich Werner
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.48A009
Abstract:

The paper presents a mathematical rotordynamic model regarding excitation due to elliptical shaft journals in sleeve bearings of electrical motors also considering the gyroscopic effect. For this kind of excitation, a mathematical rotordynamic model was developed considering the influence of the oil film stiffness and damping of the sleeve bearings, the stiffness of the end-shields and bearing housings, the stiffness of the rotor, the electromagnetic stiffness in the air gap of the electrical motor and the mass moment of inertia of the rotor and therefore also considering the gyroscopic effect. The solution of the linear differential equation system leads to the mathematical description of the absolute orbits of the shaft centre, the shaft journals and the bearing housings and to the relative orbits between the shaft journals and the bearing housings. Additionally, the bearing housing velocities can also be derived with this mathematical rotordynamic model.

Dependence of Gravity Induced Absorption Changes on the Earth’s Magnetic Field as Measured during Parabolic Flight Campaigns  [PDF]
Werner Schmidt
Journal of Modern Physics (JMP) , 2013, DOI: 10.4236/jmp.2013.411190
Abstract:

Various spectroscopic experiments performed on the AIRBUS ZERO G—located in Bordeaux, France—in the years 2002 to 2012 exhibit minute optical reflection/absorption changes (GIACs) as a result of gravitational changes between 0 and 1.8 g in various biological species such as maize, oats, Arabidopsis and particularly Phycomyces sporangiophores. During a flight day, the AIRBUS ZERO G conducts 31 parabolas, each of which lasts about three minutes including a period of 22 s of weightlessness. So far, we participated in 11 parabolic flight campaigns including more than 1000 parabolas performing various kinds of experiments. During our campaigns, we observed an unexplainable variability of the measuring signals (GIACs). Using GPS-positioning systems and three dimensional magnetic field sensors, these finally were traced back to the changing earth’s magnetic field associated with the various flight directions. This is the first time that the interaction of

Gravireception in Phycomyces: Threshold Determination on the Sounding Rocket TEXUS 50  [PDF]
Werner Schmidt
Journal of Modern Physics (JMP) , 2015, DOI: 10.4236/jmp.2015.610143
Abstract: Under parabolic flight conditions microgravity is not lower than 3 to 5 times 10-2 g. In contrast to parabolic flights, sounding rocket flights are virtually vibrational-free allowing microgravity as low as 10-5 g. Thus, a rotating platform serving as centrifuge allows the precise generation of gravitational forces ranging from 5 to 100 mg (not possible during parabolic flights). On this basis we determined the threshold1 for optical reflection/absorption changes in Phycomyces to be lower than 25 × 10-3 g. This compares well with the threshold determination of gravitropism in Phycomyces on a clinostat centrifuge. Kinetics of gravity-induced absorption changes and gravity as generated by the on-board centrifuge do not coincide but show a distinctive hysteresis with a latency of 4 s (75 mg-ramp, pull-up).
Near-Optimal Placement of Secrets in Graphs  [PDF]
Werner Poguntke
Open Journal of Discrete Mathematics (OJDM) , 2016, DOI: 10.4236/ojdm.2016.64020
Abstract: We consider the reconstruction of shared secrets in communication networks, which are modelled by graphs whose components are subject to possible failure. The reconstruction probability can be approximated using minimal cuts, if the failure probabilities of vertices and edges are close to zero. As the main contribution of this paper, node separators are used to design a heuristic for the near-optimal placement of secrets sets on the vertices of the graph.
Mathematical Multibody Model of a Soft Mounted Induction Motor Regarding Forced Vibrations Due to Dynamic Rotor Eccentricities Considering Electromagnetic Field Damping  [PDF]
Ulrich Werner
Journal of Applied Mathematics and Physics (JAMP) , 2017, DOI: 10.4236/jamp.2017.52032
Abstract: The paper presents a mathematical multibody model of a soft mounted induction motor with sleeve bearings regarding forced vibrations caused by dynamic rotor eccentricities considering electromagnetic field damping. The multibody model contains the mass of the stator, rotor, shaft journals and bearing housings, the electromagnetic forces with respect of electromagnetic field damping, stiffness and internal (rotating) damping of the rotor, different kinds of dynamic rotor eccentricity, stiffness and damping of the bearing housings and end shields, stiffness and damping of the oil film of the sleeve bearings and stiffness and damping of the foundation. With this multibody model, the bearing housing vibrations and the relative shaft vibrations in the sleeve bearings can be derived.
Influence of the Foundation on the Threshold of Stability for Rotating Machines with Roller Bearings—A Theoretical Analysis  [PDF]
Ulrich Werner
Journal of Applied Mathematics and Physics (JAMP) , 2017, DOI: 10.4236/jamp.2017.56114
Abstract: The paper presents a mathematical model for analyzing the threshold of stability for rotating machines, where the rotor is linked to the stator by roller bearings, bearing housings and end-shields and where the stator feet are mounted on a soft foundation. The internal (rotating) damping of the rotor is the only source of instability, which is considered in the paper. After the mathematical coherences of the multibody model are described, a procedure is presented for deriving the threshold of stability. Additionally, a numerical example is shown, where the threshold of stability is calculated for different boundary conditions. It could be demonstrated, that the stiffness of the foundation—even if the foundation stiffness is isotropic—can help stabilizing this kind of vibration system in the same way as orthotropic bearing stiffness or orthotropic bearing housing and end-shield stiffness for a rigid foundation.
Hyper Gravity-Induced Transients in Phycomyces as Measured by Single Beam Spectrophotometer on the Sounding Rocket TEXUS 50  [PDF]
Werner Schmidt
Journal of Modern Physics (JMP) , 2018, DOI: 10.4236/jmp.2018.92019
Abstract: In the first paper of two referring to the TEXUS 50 campaign using micro dual wavelength spectrometers (MDWS) we kinetically determined the threshold1 for GIACs (gravity-induced absorption changes) in Phycomyces to be lower than 25 × 103 g (http://file.scirp.org/pdf/JMP_2015082810060783.pdf). In this second paper, we attended measurement of GIAC-spectra. Unexpectedly, during the upwards movement, i.e. the hypergravity phase up to top acceleration values reaching 11.6 g at 35.4 s after liftoff we observed transient GIAC-spectra ranging from 380 to 750 nm. In addition, during the whole acceleration phase of 68.2 s, another component near 700 nm develops which remains stable during the whole “free fall trajectory parabola” for 381.3 s. The subsequent reentry of the rocket leads to extraordinary deceleration values up 37.8 g, completely destroying Phycomyces sporangiophores excluding their spectral measurement. During the microgravity phase and by centrifuge operation we were unable to detect any GIAC-spectra (in contrast to kinetic MDWS-measurements, first paper).
Analysis of Different Vibration Control Strategies for Soft Mounted Induction Motors with Sleeve Bearings Using Active Motor Foot Mounts  [PDF]
Ulrich Werner
Journal of Applied Mathematics and Physics (JAMP) , 2019, DOI: 10.4236/jamp.2019.73045
Abstract: The paper presents a theoretical analysis of different vibration control strategies of soft mounted induction motors with sleeve bearings, using active motor foot mounts. After the vibration model is presented, different controllers in combination with different feedback strategies are mathematically investigated. The focus is here on the forced vibrations, caused by dynamic rotor eccentricityrotor mass eccentricity, magnetic eccentricity and bent rotor deflection. After the mathematically coherences are described, a numerical example is shown, where the forced vibrations caused by bent rotor deflection are investigated, for different control strategies, where the mass matrix, the stiffness matrix and the damping matrix are influenced by different control parameters. The aim of the paper is to show the mathematically coherences and the possibility to influence the vibration behaviour, by different control strategies to optimize the vibration behaviour of soft mounted induction motors.
An Extension of the Black-Scholes and Margrabe Formulas to a Multiple Risk Economy  [PDF]
Werner Hürlimann
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.24053
Abstract: We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a stochastic differential equation of diffusion type. For the simple class of log-normally distributed instantaneous rates of return, we construct an explicit state-price deflator. Since this includes the Black-Scholes and the Vasicek (Ornstein-Uhlenbeck) return models, the considered deflator is called Black-Scholes- Vasicek deflator. Besides a new elementary proof of the Black-Scholes and Margrabe option pricing formulas a validation of these in a multiple risk economy is achieved.
Did Major Impacts Affect Sedimentologic/Sequence-Analytical Pattern of the Early Palaeozoic Sedimentary Systems of Jordan, Arabian Plate?  [PDF]
Werner Schneider, Elias Salameh
Open Journal of Geology (OJG) , 2012, DOI: 10.4236/ojg.2012.24024
Abstract: Based on profound sequence-analytical data of the early Palaeozoic sedimentary systems of Jordan, Arabian Plate, a correlation attempt is proposed with regard to possible major impact events after Price [10]. His methodological concept tells that abrupt 441 Ma. Referring to the fact that major impacts may trigger, respectively influence, exogenic and endogenic processes on an over-regional, even global, extent, this paper put the “sensitive” geological setting of Jordan at the Arabian Platform’s margin into focus. That mainly concerns the early Palaeozoic coastlines as to sea level change as well as the Jordan Valley Rift as being possibly to susceptible for tectonic re-activation changes of both direction and speed of plate motions would indicate such convulsive processes as occurred on: 550 Ma, 526.5 Ma, 514 Ma, 502 Ma, 456/455.4 Ma, and following triggering of magmatism at the Precambrian/Cambrian boundary. The following phenomena are taken into account: Faulting and magmatism triggered along the Jordan Valley Rift (Wadi Araba) in connection with the Pan-African Orogeny, anoxic sediments, temporary high detrital input onto the adjoining stable platform from Gondwana hinterlands, and significant chemical weathering in the Gondwana source areas by intensive acid (nitric) rain directing mineral content variation in the “Nubian Sandstones” (e.g. feldspar, kaolinite/dickite, tourmaline).
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