Fault Detection of Planetary Gears Based on Signal Space Constellations

A new method to process the vibration signal acquired by an accelerometer placed in a planetary gearbox housing is proposed, which is useful to detect potential faults. The method is based on the phenomenological model and consists of the projection of the healthy vibration signals onto an orthonormal basis. Low pass components representation and Gram–Schmidt’s method are conveniently used to obtain such a basis. Thus, the measured signals can be represented by a set of scalars that provide information on the gear state. If these scalars are within a predefined range, then the gear can be diagnosed as correct; in the opposite case, it will require further evaluation. The method is validated using measured vibration signals obtained from a laboratory test bench.

Calculating the Efficiency of Complex-Shaped Fins

Calculation of fin efficiency is necessary for the design of heat exchangers. This efficiency can be calculated for individual finned tubes or continuous fins. Continuous fins are mostly used in plate-fin and tube heat exchangers (PFTHEs). In most cases, the basic elements of those PFTHEs are circular, oval or flattened pipes, which contain circular or polygonal fins. Continuous fins, as can be observed in PFTHEs, are divided into virtual fins. Those fins can have a rectangular shape for an inline arrangement of pipes or a hexagonal shape for a staggered arrangement of pipes. This research shows a methodology of using the finite element method for calculating the efficiency of fins of any shape, placed on pipes of any shape. This paper presents examples of determining the efficiency of seeming fins, which are most commonly used in PFTHEs. In the article, we also compare the precision of calculations of the efficiency of complex-shaped fins using exact analytical methods and approximated methods: the equivalent circular fin method (Schmidt’s method) and the sector method. The results of the analytical methods and the approximate methods are compared to the results of numerical simulations. The calculations for continuous fins with complicated shapes of virtual fins, e.g., hexagonal elongated or segmented, are also presented.

Three and Four Centre Oscillators and Their Application in Nuclear Physics

The extension of the nuclear two-centre-oscillator to three and four centres is investigated. Some special symmetry-properties are required. In two cases an analytical solution of the Schrödinger equation is possible. A numerical procedure is developed which enables the diagonalization of the Hamiltonian in a non-orthogonal basis without applying Schmidt's method of orthonormalization. This is important for calculations of arbitrary two-dimensional arrangements of the centres.

The Vulcanization of Thick Sheets of Rubber

Schmidt's method for the determination of temperatures attained by various thicknesses of solid sheets during heating and cooling is adapted for the calculation of the amounts of vulcanization obtained for flat sheets of soft rubber and of the extra time needed to obtain a full vulcanization in the center of the sheets. The uniformity of vulcanization of the central portion of the sheets is investigated.