Mechanisms and Mitigation of 3D Coupled Vibrations in Drilling with PDC Bits

In this paper we present a new type of vibration related to PDC bits in drilling and its mitigation: a vibration coupled in axial, lateral and torsional directions at a high common frequency (3D coupled vibration). The coupled frequency is as high as 400Hz. 3D coupled vibration is a new dysfunction in drilling operation. This type of vibration occurred more often than stick-slip vibration. Evidences reveal that the coupled frequency is an excitation frequency coming from the bottom hole pattern formed in bit/rock interaction. This excitation frequency and its higher order harmonics may excite axial resonance and/or torsional resonance of a BHA. The nature of 3D coupled vibration is more harmful than low frequency stick-slip vibration and high frequency torsional oscillation (HFTO). The correlation between the occurrence of 3D coupled vibration and bit design characteristics is studied. Being different from prior publications, we found the excitation frequency is dependent on bit design and the occurrence of 3D coupled vibration is correlated with bit design characteristics. New design guidlines have been proposed to reduce or to mitigate 3D coupled vibration.

Nested Bloch waves in elastic structures with configurational forces

Small axial and flexural oscillations are analysed for a periodic and infinite structure, constrained by sliding sleeves and composed of elastic beams. A nested Bloch–Floquet technique is introduced to treat the nonlinear coupling between longitudinal and transverse displacements induced by the configurational forces generated at the sliding sleeve ends. The action of configurational forces is shown to play an important role from two perspectives. First, the band gap structure for purely longitudinal vibration is broken so that axial propagation may occur at frequencies that are forbidden in the absence of a transverse oscillation and, second, a flexural oscillation may induce axial resonance, a situation in which the longitudinal vibrations tend to become unbounded. The presented results disclose the possibility of exploiting configurational forces in the design of mechanical devices towards longitudinal actuation from flexural vibrations of small amplitude at given frequency. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.

Axial Vibration Characteristics of a Metal Diaphragm Coupling

In this article, a metal diaphragm coupling is introduced. It is assembled by interference fit with the shafts. Based on two axial vibration styles, self-exited vibration and external exited vibration, of the coupling, physical model of the coupling is established. Stiffness and damping of the coupling are also solved and analyzed. Then, natural vibration of the coupling is researched and natural frequencies are acquired by analyzed and simulated method. Finally, axial vibration response of the coupling was presented based on a calculation example. Techniques are presented which permit the coupling designer to predictably modify the coupling and thereby make in-place retrofits should an axial resonance condition occur in the field.

Notizen: The Fluorine-19 NMR Spectrum of Methylthiotetrafluorophosphorane

The low-temperature 19F NMR spectrum of the stereochemically non-rigid compound, CH3SPF4, shows three fluorine environments, one for the equatorial and two for the nonequivalent axial fluorine atoms. Each of the twelve lines of the upfield 19F- (axial) resonance shows further fine structure, due to coupling between 19F and the protons of the CH3S group. The center peaks of the two multiplet components reveal apparent quintet structure which, based on a computer simulation of the 19F spectrum of CH3SPF4, is rationalized in terms of accidental overlap of two quartets.

The Axial Vibration of Diesel Engine Crankshafts

The paper describes an investigation carried out to determine the magnitude of axial vibration of engine crankshafts, with the object of establishing that axial resonance may occur within the normal running range of an engine. The author gives the results of tests on various makes of engine using a portable vibrograph to record the axial movement of the crankshaft. In some cases the torsional osculation was measured simultaneously by means of a universal vibrograph. The vibrograph records show that at certain speeds some engines are subject to a very marked increase in axial vibration of a magnitude consistent with a condition of axial resonance. The author describes a test in which the natural frequency of axial vibration of a crankshaft is determined experimentally by using an a.c. electromagnet as a means of applying an alternating force. Expressions are derived for calculating the axial deflexion of a crankshaft due to the piston load, and also for calculating the axial deflexion under an axial load. It is suggested that the relation between these two deflexions determines the magnitude of the axial force set up by the piston loading. From a series of load-deflexion tests, carried out on a number of crankshafts, the author determines the value of empirical factors to be used in estimating the axial stiffness.