High-Order Sub-Harmonic Synchronisation in a Rotor System with a Gear Coupling

Gear couplings transmit torque from driving to driven shafts whilst accommodating unavoidable misalignments and axial displacements. The friction forces at the sliding teeth transfer energy from the driving engine to the lateral oscillations of the shaft. Instability of the stationary motion, self-excitation, can result. The self-excited oscillations, in character related to the eigen-oscillations of the linear system, interact with the external excita-tion by unbalance forces. For a two degrees of freedom rotor-bearing system we show how to study systemati-cally cases of higher-order synchronisation (frequency locking) which can help to interpret observed motions; numerical calculations and perturbation techniques are combined

Wechselwirkungen zwischen Polygonalisation und Antrieb bei Eisenbahnrädern

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Berechnung von Blechumformprozessen auf der Grundlage der Abbildung von Flächen

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Tilt Angles

Tilt angles, in contrast to Euler angles, tilt the body frame first about the line of nodes which is defined in the equator-plane of a reference frame. Thereafter only the proper rotation of the body frame takes place, through the angleabout an axis perpendicular to its own equator-plane. Thus, the two motions are clearly separated, their order is exchangeable. The tilt is described either in polar form  wheredetermines the direction of the node line and the magnitude of the tilt, or in axial form where  together determine node line and tilt by rotations about two perpendicular axes. When the tilt is visualized by geographical coordinates on a sphere,are regular except for the N- and the S-pole, whereas the  are regular, separately, on the northern and the southern hemisphere. Together the three charts provide an atlas for unlimited rotations about a fixed point. The basic relations for tilts are established for Cartesian and cylinder coordinates. Two examples demonstrate their versatility

High-Frequency Self-Excitation in Paper Calenders

High-frequency self-oscillations can occur in paper calenders due to the compression of the paper in the nip together with the friction between paper and cylindrical rolls. Wear will follow and corrugate the rolls. This article elaborates a model demonstrating this effect and gaining insight into some details of the mechanism. The model parameters are chosen rather roughly so that the numerical values of the results will have little practical relevance. But the model uncovers parameters which, when changed, stabilize or destabilize the system. These tendencies might be compared with observations at machines to check the model

A Simple Mechanism For The Polygonalization Of Railway Wheels By Wear

A mechanism is presented which explains the growing non-circularity of railway wheels by wear as a result of the interaction between the deviation from the circle and the rotational inertia of the wheels. The behaviour of the model is investigated by perturbation techniques, including the method of multiple time scales. Results conform with observations: The faster the train the quicker surge lower harmonics of the non-circularity. The procedure can be applied to study various other wear mechanisms even such where wear is influenced by locally variable material characteristics. 1 Introduction Railway wheels become non-circular by wear, periodic wear patterns develop on their circumferences, railway engineers speak of polygonalization. The effect is especially strong in the recent fast trains ([1], [3]). In [7], to my knowledge the first paper which succeeded to compute such patterns numerically, the authors say in their Abstract: "1. The wheelset axle torsional vibrations combined wit..