Simulating the dynamic behavior of planetary gearbox based on improved Hanning function

Planetary gearboxes are widely used in industrial machines. They usually work in harsh environments giving rise to damages and high maintenance costs. Condition monitoring is a key action allowing one to detect the presence of such damage ensuring healthy running conditions. The knowledge of the dynamic behavior of such a gearbox can be achieved using modeling tools as a primary step before conditioning the monitoring subject. In addition, modeling a gear set can help in the stage of design in order to optimize physical and geometric parameters of the system. Therefore, in this work, a two-dimensional lumped parameter model is adopted to build all vibration sources. The time-varying mesh stiffness is approximated as a square wave form. A novel mathematical formulation is proposed to model the amplitude modulation phenomenon due to the rotational motion of the planets around the center of the gearbox. Finally, the overall vibration signal is concluded as a summation of all vibration components influenced by the modulation function.     

Mechanochemical synthesis and thermal stability of phases in the Y2O3–Yb2O3 system

Substitutional, continuous solid solution of the general formula Y_2–xYb_xO₃ was obtained from the mixture of Y₂O₃ and Yb₂O₃ oxides, for the first time by the mechanochemical method in a high-energy ball milling. The monophasic samples of nanocrystalline solid solution for x?>?0.00 and x?<?2.00 were examined by the methods: XRD, DTA, SEM, IR and UV–Vis–DR. As follows from the results, the solid solution crystallizes in cubic system and is isostructural with Y₂O₃ and Yb₂O₃. The solution is stable in the air atmosphere up to at least 900°C, and its decomposition temperature decreases with the increase in x, that is, with decreasing number of Yb³⁺ ions replacing Y³⁺ ions in the crystal lattice of Y₂O₃. The energy band gap estimated for the solid solution varies from?~?5.30 eV for x?=?0.50 to?~?4.90 eV for x?=?1.50, which means that it is an insulator.

     

Farbstoffe

Ohne Zusammenfassung     

Moment problem with contractive solutions: the regular case

An operator multivariate moment problem with contractive solutions having regular unitary dilation is characterized in terms of the initial data. This extends a recent result of Sebestyén and Popovici, but the ideas of our proof differ from those used by them. The connection between the operator multivariate moment problem and harmonizable multivariate discrete processes is mentioned.

     

A Monte Carlo algorithm for solving systems of non-linear equations

A Monte Carlo method for solving systems of non-linear equations is presented and discussed. The method does not require the differentiation of left side functions of the system and provides the solution with arbitrary accuracy, although it may be applied only to systems with not too large a number of equations. Illustrative examples are given.     

Elastic backscattering of electrons from surfaces

A Monte Carlo algorithm is proposed for calculating the elastic reflection coefficient, η_E, for elements. The algorithm accounts for the multiple elastic scattering of electrons in solids. The calculated values of η_E compare well with the literature data for elements with atomic number up to 47 and at primary energies above 2 keV. The proposed Monte Carlo method makes it possible to determine the functional relation between η_E and the inelastic mean free path, λ. This relation turned out to be non-linear, arid it deviates from a similar relation based on published earlier single elastic scattering model. The deviation is especially pronounced for elements with medium atomic numbers. The calculated function $\text{η}{}_{\mathrm{<mtext>E</mtext>}}\text{=}\text{f}\text{(λ)}$ offers a convenient method for determining the inelastic mean free path. The values of λ derived in the present work from published experimental values of η_E compare very well with the literature data.     

Experimental determination of the electron elastic backscattering probability and the surface excitation parameter for Si,Ni, Cu and Ag at 0.5 and 1 keV energies

Electron spectra are generally presented in arbitrary units. The experimental elastic peak intensity I_espec(E) is determined by the elastic backscattering probability I_e(E) of electrons backscattered elastically within the solid angle of the spectrometer. The experimental elastic peak I_espec(E) is converted to I_e(E) backscattering probability using our new procedure based on the Goto i_e(E) elastic backscattering current database. The elastic backscattering probability I_c(E) was calculated applying the EPESWIN software of Jablonski. I_e(E) < I_c(E) due to the surface losses of electrons, characterized by the surface excitation parameter P_se (SEP). P_se(E) was determined experimentally using the Goto database and the relationship of Tanuma. Our new procedure is applied to angular‐resolved (AREPES) spectra of Jablonski and Zemek presented in arbitrary units. In their AREPES experiments, the experimental elastic peak intensity I_espec = I_e(E, α_d, ΔΩ) was measured at α_d angle of detection (35–74°) with a small HSA, with ΔΩ solid angle. The experimental value at 42° $I_{e}(E, {\it{42}}\deg{\hbox{}}, {\Delta}\Omega)$ was converted to probability with the Goto database. It was corrected with a SEP parameter P_se, determined by trial and error method for Si, Ni, Cu and Ag for E = 0.5 and 1 keV primary energies. Copyright © 2010 John Wiley & Sons, Ltd.     

Dependence of the AES backscattering correction factor on the experimental configuration

We present an analysis of the dependence of the backscattering correction factor (BCF) in Auger-electron spectroscopy (AES) on the analyzer acceptance angle. Illustrative BCF calculations are presented for Pd M₅N₄₅N₄₅ Auger electrons as a function of primary-electron energy for primary-electron angles of incidence, θ₀, of 0° and 80° and for various values of the analyzer acceptance angle. It was necessary to generalize the BCF definition for the case of an analyzer with an arbitrarily large acceptance angle; this was done with a new function, the integral emission depth distribution function. BCFs calculated from an advanced model of electron transport in the surface region of the Pd sample varied weakly with analyzer half-cone angle for θ₀ = 0° but more strongly for θ₀ = 80° where there were BCF differences varying between 19% at a primary energy of 1 keV and 6% at a primary energy of 5 keV. These BCF differences are due in part to variations of the BCF with emission angle and in part to variations of the density of inner-shell ionizations within the information depth for the detected Auger electrons. The latter variations are responsible for differences larger than 10% between BCFs from the widely used simplified BCF model and those from the more accurate advanced model for primary energies less than about 5 keV for θ₀ = 80°. For normal incidence of the primary beam, differences greater than 10% between BCFs from the simplified and advanced models were found for primary energies between 1 keV and 4 keV. These BCF differences indicate that the simplified model can provide only approximate BCF values. In addition, the simplified model does not provide any BCF dependence on Auger-electron emission angle or analyzer acceptance angle.     

Identification of minority compounds in natural ilmenites by X-ray absorption spectroscopy

Natural ilmenites are used all over the world as raw materials in white pigment (TiO₂) production. Besides the FeTiO₃ in the raw material many other compounds are present. The chemical compounds based on the minority elements influence quality of the final product and are difficult to identify. The knowledge about chemical bonding of the minor elements enables to properly adjust chemical reactions during production processes and to improve quality of the final product. In this paper the X-ray absorption spectroscopy (XAS) identification of the chemical compounds formed by Mg, Mn and Cr in natural ilmenites originating from different places is presented.