Complex modal analysis of a vertical rotor through finite element method

Natural frequencies were analyzed (axial, torsional and flexural) and frequency response of a vertical rotor with a hard disk at the edge through the classical and complex modal analysis. The mathematical modeling was based on the theory of Euler-Bernoulli beam. The equation that rules the movement was obtained through the Lagrangian formulation. The model considered the effects of bending, torsion and axial deformation of the shaft, besides the gravitational and gyroscopic effects. The finite element method was used to discretize the structure into hollow cylindrical elements with 12 degrees of freedom. Mass, stiffness and gyroscopic matrices were explained consistently. This type of tool, based on the use of complex coordinates to describe the dynamic behavior of rotating shaft, allows the decomposition of the system in two submodes, backward and forward. Thus, it is possible to clearly visualize that the orbit and direction of the precessional motion around the line of the rotating shaft is not deformed. A finite element program was developed using Matlab ®, and numerical simulations were performed to validate this model.

Effects of Drive Speed Modulation on Dynamics of Slender Rotating Structures

Slender rotating structures are used in many mechanical systems. These structures can suffer from undesired vibrations that can affect the components and safety of a system. Furthermore, since some these structures can operate in a harsh environment, installation and operation of sensors that are needed for closed-loop and collocated control schemes may not be feasible. Hence, the need for an open-loop non-collocated scheme for control of the dynamics of these structures. In this work, the effects of drive speed modulation on the dynamics of slender rotating structures are studied. Slender rotating structures are a type of mechanical rotating structures, whose length to diameter ratio is large. For these structures, the torsion mode natural frequencies can be low. In particular, for isotropic structures, the first few torsion mode frequencies can be of the same order as the first few bending mode frequencies. These situations can be conducive for energy transfer amongst bending and torsion modes. Scenarios with torsional vibrations experienced by rotating structures with continuous rotor-stator contact occur in many rotating mechanical systems. Drill strings used in the oil and gas industry are an example of rotating structures whose torsional vibrations can be deleterious to the components of the drilling system. As a novel approach to mitigate undesired vibrations, the effects of adding a sinusoidal excitation to the rotation speed of a drill string are studied. A portion of the drill string located within a borewell is considered and this rotating structure has been modeled as an extended Jeffcott rotor and a sinusoidal excitation has been added to the drive speed of the rotor. After constructing a three-degree-of-freedom model to capture lateral and torsional motions, the equations of motions are reduced to a single differential equation governing torsional vibrations during continuous stator contact. An approximate solution has been obtained by making use of the Method of Direct Partition of Motions with the governing torsional equation of motion. The results showed that for a rotor undergoing forward or backward whirling, the addition of sinusoidal excitation to the drive speed can cause an increase in the equivalent torsional stiffness, smooth the discontinuous friction force at contact, and reduce the regions of negative slope in the friction coefficient variation with respect to speed. Experiments with a scaled drill string apparatus have also been conducted and the experimental results show good agreement with the numerical results obtained from the developed models. These findings suggest that the extended Jeffcott rotordynamics model can be useful for studies of rotor dynamics in situations with continuous rotor-stator contact. Furthermore, the results obtained suggest that the drive speed modulation scheme can have value for attenuating drill-string vibrations.

Análise do comportamento dinâmico de um rotor vertical através do método dos elementos finitos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Pliensbachian magnetostratigraphy: new data from Paris Basin (France)

Sampling of an industrial drill string from the northeastern Paris Basin (Montcornet, France) provides early Jurassic magnetostratigraphic data coupled with biochronological control. About 375 paleomagnetic samples were obtained from a 145 m thick series of Pliensbachian rocks. A composite demagnetization thermal up to 300 C and an alternating field up to 80 mT were used to separate the magnetic components. A low unblocking temperature component (<250degreesC) with an inclination of about 64 is interpreted as a present-day field overprint. The characteristic remanent component with both normal and reversed antipodal directions was isolated between 5 and 50 mT. Twenty-nine polarity intervals were recognized. Correlation of these new results from the Paris Basin with data from the Breggia Gorge section (Ticino, southern Alps, Switzerland), which is generally considered as the reference section for Pliensbachian magnetostratigraphy, reveals almost identical patterns of magnetic polarity reversals. However, the correlation implies significant paleontological age discrepancies. Revised age assignments of biostratigraphic data of Breggia as well as an objective evaluation of the uncertainties on zonal boundaries in both Breggia and Moncornet resolve the initial discrepancies between magnetostratigraphic correlations and biostratigraphic ages. Hence, the sequence of magnetic reversals is significantly strengthened and the age calibration is notably improved for the Pliensbachian, a stage for which sections combining adequate magnetic signal and biostratigraphic constraints are still very few. (C) 2002 Elsevier Science B.V. All rights reserved.

Desenvolvimento de misturas ternárias para remoção de reboco de fluido de perfuração sintético

The construction of wells is one of the most important activities of the oil industry. The drilling process is the set of activities and operations to design, program and perform the opening thereof. During this process, the cuttings are removed by the drilling fluid, or mud, and carted to the surface. This fluid is injected into the drill string and returns to the surface through the annular space between the well walls and the drill string. After the descent of the column casing, the annular space between the casing string and the walls of the borehole is filled with cement so as to secure the spine and prevent any migration of fluids between the various permeable zones traversed by the well behind of the coating. To ensure the good quality of the cementation scrubbers are used mattresses which are pumped ahead of the cement slurry so as to avoid contamination of the drilling fluid paste, or vice versa, and assist in the removal of plaster, formed by drilling fluid of the borehole walls, thus enabling a better cement bond to the well. Within this context, this work aims to evaluate the efficiency of mattresses scrubbers, the basis of ionic and nonionic surfactants, on the removal of nonaqueous drilling fluid, based on n-paraffin in oil wells, and the compatibility between the Mattress relations washer / drilling fluid bed scrubber / cement paste mattress washer / cement slurry / drilling fluid and the drilling fluid / cement slurry using laboratory tests rheology, thickening time and compressive strength. Also technique was performed X-ray diffraction (XRD) for a more detailed analysis of these mixtures with hydrated cement paste. In compatibility tests the conditions of temperature and pressure used in the same laboratory procedure simulating the conditions of oil wells, the well is considered the depth of 800 m. The results showed that the compositions of the mattress washer nonionic, KMS obtained a 100% efficient in removing the non-aqueous drilling fluid, and the best formulation showed good results with respect to compliance testing

Complex modal analysis of a slender vertical rotor by finite elements method

In this paper, natural frequencies were analyzed (axial, torsional and flexural) and frequency response of a vertical rotor with a hard disk at the edge through the classical modal and complex analysis. The equation that rules the movement was obtained through the Lagrangian formulation. The model considered the effects of bending, torsion and axial deformation of the shaft, besides the gravitational and gyroscopic effects. The finite element method was used to discretize the structure into hollow cylindrical elements with 12 degrees of freedom. Mass, stiffness and gyroscopic matrices were explained consistently. The classical modal analysis, usually applied to stationary structures, does not consider an important characteristic of rotating machinery which are the methods of forward and backward whirl. Initially, through the traditional modal analysis, axial and torsional natural frequencies were obtained in a static shaft, since they do not suffer the influence of gyroscopic effects. Later research was performed by complex modal analysis. This type of tool, based on the use of complex coordinates to describe the dynamic behavior of rotating shaft, allows the decomposition of the system in two submodes, backward and forward. Thus, it is possible to clearly visualize that the orbit and direction of the precessional motion around the line of the rotating shaft is not deformed. A finite element program was developed using MATLAB (TM) and numerical simulations were performed to validate this model. Natural frequencies and directional frequency forced response (dFRF) were obtained using the complex modal analysis for a simple vertical rotor and also for a typical drill string used in the construction of oil wells.

(Table S1) Cation compositions of titanomaghemite in DSDP Hole 89-462A basalts

Cretaceous lava flows overlie Jurassic to Early Cretaceous oceanic crust in the Nauru Basin of the western equatorial Pacific, but their exact age and origin is controversial. In one model, they are generically related to volcanism forming the Ontong Java Plateau. However, paleomagnetic data from basalts recovered by ocean drilling in the Nauru Basin have been interpreted as recording numerous geomagnetic reversals, suggesting the Nauru Basin basalts are older than the Early Aptian flows on the Ontong Java Plateau, and the correlative volcanism seen in the western equatorial and southwestern Pacific Ocean basin. Here, we examine the magnetic fidelity of the Nauru Basin basalts through rock magnetic and paleomagnetic approaches. We find the magnetic carriers in the lavas are unlike most basaltic units recovered by oceanic drilling in that they are magnetically soft. This quality makes the rocks especially prone to the acquisition of secondary magnetic components induced during drilling. We demonstrate that the reversed polarity intervals are illusory, and instead record subtle changes in magnetic hardness that result in partial and complete overprinting by the magnetic field associated with the drill string (e.g., the core barrel, drill pipe and bit). The recognition of these magnetic overprints, the identification of only normal polarity in the Nauru Basin basalts, and a critical consideration of the available radiometric and biostratigraphic age data lead us to conclude that coeval formation of the Nauru Basin basalts and Ontong Java Plateau in Aptian times remains a viable hypothesis.

Magnetic properties of basalts and sediments of ODP Leg 135 sites

Paleomagnetic and rock-magnetic investigations of basalts from Hole 834B in the Lau backarc basin and of sediments from Holes 841A and 841B at the Tonga Ridge are reported. Three groups of blocking temperatures in the basalts suggest the presence of at least three magnetic phases: pure magnetite, a Ti-poor titanomagnetite, and a Ti-rich phase. The drill-string-induced remanence in the basalts is typically between three and six times the original normal remanent magnetization intensity, but it is mostly removed by alternating-field (AF) cleaning in 5 mT. Volume susceptibility values range from 0.04 * 10**-3 to 4 * 10**-3 cgs. The modified Q-ratio J5/sus ranges from 0.5 to 10. The drill-string-induced remanence behaves different in the two sediment cores from Holes 841A and 841B, which may be the result of differences in the sediment or caused by the different drilling equipment used. The AF-cleaned inclinations of the sediment in Holes 841A and 841B suggest a slight flattening with increasing depth (up to 6° under a load of 400 m of sediment) to be present. This flattening is likely to be caused by the differential rotation of detrital particles under compaction during diagenesis.

(Table 1) Magnetozone boundaries at DSDP Site 68-503

The paleomagnetic measurement procedure at Site 503 was similar to that described for Site 502 (See preceding chapter). Each core section was measured with the longcore spinner magnetometer at 10-cm intervals. In addition, one or more discrete samples were taken from each core section for measurement of the total magnetic vector and its stability against progressive AF demagnetization. There were noteworthy differences in conditions at Site 503, however, that affected the quality and interpretation of the magnetic data and require comment. The most serious problem we encountered was the presence of rust scale from the drill string. Although the dark flecks typically were concentrated near the top of every recovered sediment core, they also smeared down a meter or more between the core liner and sediment, even when the sediment showed no indication of drilling disturbance. Individual rust scales proved to be highly magnetic - presumably because they incorporate small pieces of unoxidized metal. The anomalously high remanent intensities, several orders of magnitude above the uncontaminated sediment values, and scattered remanent directions observed in long-core magnetic measurements on many cores from Site 503 could be attributed to the presence of rust scale.

(Table 1) Summary of basalt unit thickness, vesicularity, number of flow units, and average porosity at ODP Site 135-839

An inflatable drill-string packer was used at Site 839 to measure the bulk in-situ permeability within basalts cored in Hole 839B. The packer was inflated at two depths, 398.2 and 326.9 mbsf; all on-board information indicated that the packer mechanically closed off the borehole, although apparently the packer hydraulically sealed the borehole only at 398.2 mbsf. Two pulse tests were run at each depth, two constant-rate injection tests were run at the first set, and four were run at the second. Of these, only the constant-rate injection tests at the first set yielded a permeability, calculated as ranging from 1 to 5 * 10**-12 m**2. Pulse tests and constant-rate injection tests for the second set did not yield valid data. The measured permeability is an upper limit; if the packer leaked during the experiments, the basalt would be less permeable. In comparison, permeabilities measured at other Deep Sea Drilling Project and Ocean Drilling Program sites in pillow basalts and flows similar to those measured in Hole 839B are mainly about 10**-13 to 10**-14 m**2. Thus, if our results are valid, the basalts at Site 839 are more permeable than ocean-floor basalts investigated elsewhere. Based on other supporting evidence, we consider these results to be a valid measure of the permeability of the basalts. Temperature data and the geochemical and geotechnical properties of the drilled sediments all indicate that the site is strongly affected by fluid flow. The heat flow is very much less than expected in young oceanic basalts, probably a result of rapid fluid circulation through the crust. The geochemistry of pore fluids is similar to that of seawater, indicating seawater flow through the sediments, and sediments are uniformly underconsolidated for their burial depth, again indicating probable fluid flow. The basalts are highly vesicular. However, the vesicularity can only account for part of the average porosity measured on the neutron porosity well log; the remainder of the measured porosity is likely present as voids and fractures within and between thin-bedded basalts. Core samples, together with porosity, density, and resistivity well-log data show locations where the basalt section is thin bedded and probably has from 15% to 35% void and fracture porosity. Thus, the measured permeability seems reasonable with respect to the high measured porosity. Much of the fluid flow at Site 839 could be directed through highly porous and permeable zones within and between the basalt flows and in the sediment layer just above the basalt. Thus, the permeability measurements give an indication of where and how fluid flow may occur within the oceanic crust of the Lau Basin.

Polarity chron boundaries and interval sedimentation rates of ODP Leg 162 sites

Magnetic polarity stratigraphies for Sites 980-984 are based on shipboard measurements from the pass-through magnetometer after alternating field (AF) demagnetization at a peak field of 25 mT and shore-based stepwise AF demagnetization of discrete samples. The characteristic magnetization component was determined after AF demagnetization removed the steep downward drill-string-related magnetic overprint. Peak AF fields in the 20-30 mT range were required to resolve the component, carried by magnetite, that was used to produce unambiguous Pliocene-Pleistocene magnetic stratigraphies at all five sites. At Sites 980 and 983, magnetic stratigraphies were resolved to the base of the recovered advanced hydraulic piston corer (APC) section, which lies in the Matuyama Chron (1r.2r) and Olduvai Subchron (2n), respectively. At Sites 981 and 982, magnetization intensities decrease sharply in the normal polarity zone corresponding to the Gauss Chron (2An), and magnetic stratigraphies below this level could not be resolved. At Site 984, the resolution of magnetic stratigraphy was curtailed at ~250 meters below seafloor (Olduvai Subchron) by core deformation at the base of the APC section and in the underlying extended core barrel section. As the magnetic stratigraphies at all four sites are unequivocal, polarity chron interpretations can be made without aid from the biostratigraphy. Mean sedimentation rates within polarity chrons have been calculated and Pliocene-Pleistocene biomagnetostratigraphic correlations tested.

Downhole logging of the AND-2A borehole, Victoria Land Basin, McMurdo Sound, Antarctica

Under the framework of the ANDRILL Southern McMurdo Sound (SMS) Project successful downhole experiments were conducted in the 1138.54 metre (m)-deep AND-2A borehole. Wireline logs successfully recorded were: magnetic susceptibility, spectral gamma ray, sonic velocity, borehole televiewer, neutron porosity, density, calliper, geochemistry, temperature and dipmeter. A resistivity tool and its backup both failed to operate, thus resistivity data were not collected. Due to hole conditions, logs were collected in several passes from the total depth at ~1138 metres below sea floor (mbsf) to ~230 mbsf, except for some intervals that were either inaccessible due to bridging or were shielded by the drill string. Furthermore, a Vertical Seismic Profile (VSP) was created from ~1000 mbsf up to the sea floor. The first hydraulic fracturing stress measurements in Antarctica were conducted in the interval 1000-1138 mbsf. This extensive data set will allow the SMS Science Team to reach some of the ambitious objectives of the SMS Project. Valuable contributions can be expected for the following topics: cyclicity and climate change, heat flux and fluid flow, seismic stratigraphy in the Victoria Land Basin, and structure and state of the modern crustal stress field.

A Real-Time Synthesis Oriented Tanpura Model

Physics-based synthesis of tanpura drones requires accurate simulation of stiff, lossy string vibrations while incorporating sustained contact with the bridge and a cotton thread. Several challenges arise from this when seeking efficient and stable algorithms for real-time sound synthesis. The approach proposed here to address these combines modal expansion of the string dynamics with strategic simplifications regarding the string-bridge and string-thread contact, resulting in an efficient and provably stable time-stepping scheme with exact modal parameters. Attention is given also to the physical characterisation of the system, including string damping behaviour, body radiation characteristics, and determination of appropriate contact parameters. Simulation results are presented exemplifying the key features of the model.

Mechanism of Muscle Vibrations During Stimulated and Voluntary Isometric Contractions of Mammalian Skeletal Muscle

When a muscle contracts it produces vibrations. The origin of these vibrations is not known in detail. The purpose of this study was to determine the mechanism associated with muscle vibrations. Mechanisms which have been proposed in the literature were described as theories (cross-bridge cycling, vibrating string and unfused motor unit theories). Specific predictions were derived from each theory, and tested in three conceptually different studies. In the first study, the influence of recruitment strategies of motor units (MUs) on the vibromyographic (VMG) signal was studied in the in-situ cat soleus using electrical stimulation of the soleus nerve. VMG signals increased with increasing recruitment and decreased with increasing firing rates of MUs. Similar results were obtained for the human rectus femoris (RF) muscle using percutaneous electrical stimulation of the femoral nerve. The influence of MU activation on muscle vibrations was studied in RF by analyzing VMG signals at different percentages (0-100%) of the maximal voluntary contraction (MVC). In our second study, we tested the effects of changing the material properties of the in-situ cat soleus (through muscle length changes) on the VMG signal. The magnitude of the VMG signal was higher for intermediate muscle lengths compared to the longest and the shortest muscle lengths. The decreased magnitude of the VMG signal at the longest and at the shortest muscle lengths was associated with increased passive stiffness and with decreased force transients during unfused contractions, respectively. In the third study, the effect of fatigue on muscle vibrations was studied in human RF and vastus lateralis (VL) musc1es during isometric voluntary contractions at a leveI of 70% MVC. A decrease in the VMG signal magnitude was observed in RF (presumably due to derecruitment of MUs) and an increase in VL (probably related to the enhancement of physiological tremor, which may have occurred predorninantly in a mediolateral direction) with fatigue. The unfused MU theory, which is based on the idea that force transients produced by MUs during unfused tetanic contraction is the mechanism for muscle vibrations, was supported by the results obtained in the above three studies.