High-Frequency Torsional Oscillation Research Articles

Laboratory Experiments Qualify Bit Influence on High-Frequency Torsional Oscillations

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 212566, “Qualifying Bit Influence on High-Frequency Torsional Oscillations Based on Full-Scale Laboratory Experiments,” by Armin Kueck, Eliah Everhard, and Xu Huang, Baker Hughes, et al. The paper has not been peer reviewed. _ High-frequency torsional oscillations (HFTOs) generate dynamic loads that can damage drilling tools, resulting in cracks, twistoffs, or broken electronics. Recently, a full-scale drilling test rig was proven to generate verified HFTO behavior under laboratory conditions. This rig allows for a comprehensive study of the influences of bit characteristics on HFTO. The complete paper presents methods to qualify bit features to suppress HFTO. Laboratory Rig Setup Test-Rig Design. The full-scale laboratory test rig drills rocks in a pressurized rock chamber. Rate of penetration (ROP), weight on bit (WOB), rotational speed, pressure, bit type, and rock type can be varied. The simulator consists of an open-loop mud-circulation system with capacity for 200 bbl of fluid, two 1,000-hp triplex pumps capable of up to 500 gal/min, a hoisting mechanism for raising and loading the drillstring up to 10,000 lbf, a 1,000-hp rotary drive capable of up to 10,000 ft-lbf, and a pressure vessel rated to 10,000 psi. High-frequency measurement instrumentation, including in-bit vibration sensors, records the tangential accelerations and dynamic torque at various positions in the BHA. The mounted device can be seen in the top left photo in Fig. 1. Measurement. To initially characterize the frequency response of the system, an impact test was performed on the system in a suspended nonoperating state with roving accelerometers (sensors) positioned as indicated by the blue lines in Fig. 1. Also indicated are the free-end and fixed-end boundary conditions at the bit (left) and drive (right), respectively, as well as the point of reference impact. The data from each pair of sensors are then processed to separate the torsional motions from lateral. Because HFTO is a self-excited vibration, it must be validated that this type of vibration is actually excited in the laboratory setup. To demonstrate that the excitation mechanism is representative for the field, one of the test results was used as a reference. A laboratory investigation showed that the measured vibration matches characteristics of self-excited vibrations. Investigations in the laboratory will, therefore, lead to valid solutions in the field.

Modeling and Investigation of the Velocity-Dependent Cutting Process with PDC Cutters Using the Discrete Element Method

Polycrystalline diamond compact (PDC) bits with multiple fixed cutters drill through deep formations and are used in oil and gas, geothermal, and mining industry. The bit-rock interaction excites drill string vibrations, which need to be mitigated to improve drilling performance. A velocity-weakening characteristic of the bit torque can cause severe self-excited high-frequency torsional oscillations (HFTO) of the bottom hole assembly (BHA). The dependency on velocity can be attributed to rate-sensitive rock cutting forces at each cutter. The purpose of this paper is to model the rate effect of cutting forces and determine influencing factors in the single-PDC cutting process. In this paper, a modified bonded-particle model (discrete element method, DEM) for rock in deep drilling environments is applied to the pressurized cutting process. Potential modification strategies considering rate indicators at different scales are compared and discussed to reproduce rate dependency in the particle contact model. Two specific models, incorporating cutting-speed-dependent bond strength or grain elastoplasticity, are implemented and verified. The relationship between rate-sensitive cutting forces and the causal rock failure mechanisms is then clarified by interpreting the results from a continuum perspective. Moreover, the influences of axial force and cutter wear state on the rate dependency are investigated. In cutting simulations at a constant depth of cut and various cutting speeds, both models result in rate-dependent cutting forces in good qualitative agreement with rock experiments: Significant hardening is reflected in the axial force component. The modification of contact models combined with a macroscopic rate indicator (i.e. cutting speed) has proven to be a feasible and effective way to reproduce the rate effects in the cutting simulations. In subsequent simulations with constant axial force, the steady-state tangential force decreases as the cutting speed increases, matching the reduction of torque on the bit with increasing RPM. Rate dependency intensifies at higher axial forces or with dull cutters, which agrees with laboratory full-scale bit tests in the literature. This study proposes a practical approach to integrating observed rate effects of downhole rock cutting processes into numerical rock models. The results enhance our understanding of the rock cutting process and have positive implications for the improvement of the cutter design against undesirable rate effects.

Case Study: Automated Stringer Detection Boosts Drilling Efficiency With Less Downtime

_ Horizontal drilling has evolved over decades to become a trusted well construction technique in mature oil-producing regions. However, many challenges remain in geologically complex drilling environments. One challenging drilling scenario arises when the drill bit encounters hard stringers interbedded within softer formations like sandstone. The sudden change in rock mechanics in moving from the formation to the stringer often results in deflection of the drill bit and a deviation in the well path known as a dogleg. The rapid directional changes caused by doglegs lower drilling efficiency by moving the drilling assembly off its planned path, and sometimes, out of the desired reservoir zone. The static loads generated in a dogleg can damage the bottomhole assembly (BHA) and lead to premature bit wear, shortened run life, higher maintenance costs, and more trips downhole. The curved path also increases the risk of stuck casing or completions strings, which can prevent the well from being completed to planned target depth (TD). An operator of a mature field in the North Sea faced such challenges while drilling multilateral wells through reservoir sections containing hard calcite stringers interspersed in sand formations with low unconfined compressive strength. The operator aimed to keep its lifting costs low by increasing the gross rate of penetration (ROP) through these sections. But the doglegs created at each stringer often required pulling back to perform a costly, time-consuming reaming operation to smooth out the well path and allow drilling to continue to TD. On average, the operator amassed 2.7 hours of invisible lost time (ILT) on reaming for every 3,300 ft (1000 m) drilled and achieved significantly lower gross ROP—both of which increased the operator’s per-well lifting costs above plan. Working with the operator, Baker Hughes developed an automated stringer detection service that would identify stringers earlier than previously possible to minimize local doglegs, reduce reaming time, and efficiently deliver wells to plan. Developing an Early-Warning Stringer Detection Service With operator input, the service provider developed an automated service that provided reliable, consistent, and early stringer detection to guide fast corrective action. The service includes an automated stringer-detection module embedded in an advanced measurement-while-drilling (MWD) sensor sub. The sub contains several dynamic sensors that collect a range of vibration and load measurements. The detection module uses a physics-based algorithm that combines two MWD measurements—tangential acceleration and dynamic torque at the bit—to calculate a value for high-frequency torsional oscillation (HFTO) in the BHA. HFTOs are torsional vibrations with frequencies between 50 Hz and 450 Hz that only occur during bit-rock interactions in hard formations. The distinct change in HFTO response during the transition from soft formations to hard formations makes it a leading indicator for detecting stringers in real time during drilling.

Technology Focus: Bits and Bottomhole Assemblies (December 2021)

Well construction must always be executed safely at reduced operational costs, while ensuring appropriate wellbore quality and placement, per asset team requirements. Consequently, analysis of drilling efficiency, a critical performance indicator, has moved from maximizing rate of penetration (ROP) to improving cycle time. This recognition establishes the need for holistic solutions that address drilling challenges and promote efficient improvement strategies. This endeavor achieves well construction objectives, with associated reductions in cycle time and operations costs. Holistic solutions must start with project analysis and comparisons to offsets to identify application differences and similarities. These evaluations establish project risks, which ultimately have positive or negative effects on well construction. Consequently, implications from these risks (limiters and potential dysfunctions) must be addressed in the planning phase, or preparations must be made for their remediation during project execution. It is not enough to know what worked or failed. Rather, it is essential to understand why and how specific trends, events, results, or relationships come about. Effective and permanent remediations for all drilling dysfunctions must focus on identification and analysis of their initiating risks. Additionally, holistic solutions require detailed analysis of drilling systems, which include bits and reamers, bottomhole assemblies (BHAs), drive systems, hydraulics considerations, and drilling-parameter ranges and roadmaps. In addition to establishing component relevance, this effort must ensure their functional compatibility and effectiveness at addressing project risks. Drilling-parameter roadmaps must focus on well construction objectives and cycle time reduction, not ROP maximization. In this regard, cycle time is defined as the cumulative time associated with the following operations: pick up the BHA, drill out, drill ahead, trip out of hole, and run casing. Bits and BHAs have a major role in this discussion. The industry’s fast-developing capabilities with modeling and deeper under-standing of downhole tools and systems, coupled with applications based on big data analytics, are leading these efforts. The door has been kicked open. Let’s walk through. Recommended additional reading at OnePetro: www.onepetro.org. SPE 205965 - Oil and Gas Drilling Optimization Technologies Applied Successfully to Unconventional Geothermal Well Drilling by Junichi Sugiura, Sanvean Technologies, et al. SPE 205993 - Using Downhole Sampled High-Frequency Torsional Oscillation Measurements for Identifying Stringers and Minimizing Operational Invisible Lost Time by Andreas Hohl, Baker Hughes, et al. SPE 206064 - Mud Motor PDM Dynamics: An Analytical Model by Robello Samuel, Halliburton, et al.

A Review of the Research and Development of High‐Frequency Measurement Technologies Used for Nonlinear Dynamics of Drillstring

High‐frequency measurements can provide much more new insights for drillstring dynamics compared to traditional instruments, leading to a new realm of understanding of drillstring behaviors in great detail than before. In this paper, data acquisition tools with high‐frequency sample rates and the data processing are introduced. Based on high‐frequency data, progress of drilling dynamics is summarized, including new understandings of low‐frequency drillstring dynamics, high‐frequency torsional oscillations (HFTOs), and high‐frequency axial oscillations (HFAOs) and new findings for the coupling of vibrations and motions, as well as models and simulation methods to deeply comprehend high‐frequency dynamics of drillstring. High‐frequency measurements have been used for enabling drillers to improve drill performance, especially for field decision making, BHA selection, and bit design, usually through the ways of minimizing vibrations to obtain high‐efficient drilling conditions, the high‐frequency response near bit can also be used for lithology identification during drilling. Though there still exists a gap between research perspective and drilling practice, the industry of high‐frequency measurements has gotten off a good start, which has huge potential to avoid nonproductive time thereupon reducing drilling cost in the future.

Technology Focus: Bits and Bottomhole Assemblies (December 2020)

Achieving and sustaining performance drilling’s intended benefits - improved drilling efficiency with minimal down-hole tool failures and the associated reductions in project cycle time and operational costs - requires new protocols in drilling-system analysis. Drilling-system components [bits, reamers, bottomhole assemblies (BHAs), drive systems, drilling parameters, and hydraulics] must be analyzed independently for their relevance on the basis of application types and project challenges. Additionally, the drilling system must undergo holistic evaluations to establish functional compatibility and drilling-parameter responses and effects, considering project objectives and key performance indicators. This comprehensive physics-based approach ensures durability and rate-of-penetration (ROP) improvements without compromising stability and downhole tool reliability. The success of this process is strongly dependent on vibration control. Considering the different vibration modes - axial, torsional, lateral, stick/slip, and whirl - and their many dissimilar initiating and amplification factors, their sources always must be identified. Researchers have challenged the usual classification of erratic torque and revolution-rate behavior as stick/slip. BHA design and drilling-parameter ranges, considering blade spacing, can produce unfavorable tubular deformations, contact points, and side loads. This condition creates torque and revolution-rate fluctuations that have been linked to lateral vibrations. Awareness of these vibration modes, particularly their sources and intensifying conditions, ensures development of effective remediation solutions. Improved borehole quality, with regard to tortuosity and rugosity, must always be considered as a critical requirement in performance drilling. This condition reduces borehole drag, enhances drilling-parameter transfer, and improves ROP and overall run lengths. Most importantly, it reduces vibrations, leading to improvements in downhole tool life and directional drilling performance. In addition to formation drillability effects, drilling-systems components and operational practices have strong effects on borehole quality. Consequently, this must be part of the drilling-system analysis. The industry’s advancements at developing physics-based solutions for drilling challenges have matured. Continuing to ask questions that help us understand how and why we fail or succeed puts more wind beneath our wings to accelerate learning and reduce cycle times. Recommended additional reading at OnePetro: www.onepetro.org. SPE 200740 Digital Twins for Well Planning and Bit-Dull-Grade Prediction by Mehrdad Gharib Shirangi, Baker Hughes, et al. SPE 201616 Validating Bottomhole-Assembly Analysis Models With Real-Time Measurements for Improved Drilling Performance by Mark Smith, Premier Directional Drilling, et al. IADC/SPE 199658 Simulation and Measurement of High-Frequency Torsional Oscillation (HFTO)/High-Frequency Axial Oscillation and Downhole HFTO Mitigation: Knowledge Gains Continue by Using Embedded High-Frequency Drilling Dynamics Sensors by Junichi Sugiura, Sanvean Technologies, et al.

Simulation and Measurement of High-Frequency Torsional Oscillation (HFTO)/High-Frequency Axial Oscillation (HFAO) and Downhole HFTO Mitigation: Knowledge Gains Continue Using Embedded High-Frequency Drilling Dynamics Sensors

Summary High-torque, low-speed drilling mud motors are typically used to drive rotary-steerable systems (RSS) to improve the rate of penetration (ROP) of the RSS bottomhole assemblies (BHA). Downhole drilling dysfunctions are common when powered RSS BHAs are pushed to the limit for maximum drilling performance. High-frequency (HF) continuous recording compact drilling dynamics sensors were embedded into the bit, bit box of the RSS, slow-rotating housing (SRH) of the RSS, bit box of the mud motor, and top subassembly (sub) of the mud motor to better understand drilling conditions in different shale plays throughout North America. Embedded sensors placed on the outer diameter of the BHA vs. centerline-mounted sensors give a different measurement response and a different vision of the actual dynamics being experienced in the BHA. The HF sensors were deployed in the in-house developed push-the-bit RSS and mud motors, allowing us to model the motor-assist RSS BHAs with analytical models and finite-element analysis models to predict the HF torsional oscillation (TO) and axial oscillation (AO) frequencies. The derivation of the high-frequency axial oscillation (HFAO) and TO analytical equations is detailed in the paper. In one of the example motor-assist RSS BHA analyses, the simulation results reveal that the fundamental high-frequency torsional oscillation (HFTO) frequency is 11.1 Hz whereas the fundamental HFAO frequency is 32.9 Hz, which is approximately three times higher than the fundamental-mode HFTO frequency. A good correlation was observed between the simulation result and the field data gathered from the HF accelerometer and gyro sensors embedded in the RSS and mud motors. Two new types of HF axial drilling dynamics with a polycrystalline diamond compact (PDC) bit—(1) the third-order-mode HFAO and (2) the harmonics of the HFTO coupled to the longitudinal axis—were discovered and reported in detail. One example in this paper shows that the dominant HFTO frequency shifts occurred in the middle of drilling a stand with no connection involved and no surface parameter changes. The examination of the time-domain signal reveals that (1) the “baseline” HFTO-induced tangential accelerations are due to the mud motor output revolutions per minute (RPM) (2) the variation of the HFTO-induced peak tangential accelerations comes from the drillstring stick/slip, which is transmitted to the drill bit through the mud motor, and (3) the 76 and 114 Hz HFTO-induced accelerations are both approximately in a sinusoidal waveform, except in the 3-second transition period, where the mixture of both frequencies is observed. The 114 Hz-HFTO-induced tangential acceleration measured at the bit box is coupled with the 0.16 Hz drillstring stick/slip oscillation. The analytical equation is provided to describe the HFTO coupled with stick/slip as an analogy to communication theory. In addition, the extensive modeling and field measurement of the HFTO and HFAO lead to the mitigation measure of the harmful HF drilling dynamics in motor-assist RSS BHAs. The proposed HFTO mitigation mechanism is modeled, simulated, and demonstrated in the paper. The latest-generation embedded HF drilling dynamics sensors are placed on the outside diameter of the BHA, as well as along the centerline of the BHA. The different responses of the sensors due to their placement are reported and analyzed. The quality of 1000 Hz continuous-sampled gyro data are discussed, comparing against low-frequency-sampled gyro data. Additionally, this paper shows the downhole HFTO-damping mechanism and lesser known drilling dynamics, such as HFAO with a PDC bit in detail. CORRECTION NOTICE: This paper has been updated from its original version to correct the provenance statement. In addition, the equation numbering on pages 567 and 568 has been corrected from Eqs. 9, 10, and 11 to Eqs. 5, 6, and 7.

Isolator Tool for High-Frequency Torsional Oscillation Proves Effective

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 193313, “Simulation and Testing of an Isolator Tool for High-Frequency Torsional Oscillation,” by Dennis Heinisch, SPE, Baker Hughes, a GE Company; Vincent Kulke, Braunschweig Technical University; Volker Peters, Andreas Hohl, Cord Schepelmann, and Hanno Reckmann, Baker Hughes, a GE Company; and Georg-Peter Ostermeyer, SPE, Braunschweig Technical University, prepared for the 2018 Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 12–15 November. The paper has not been peer reviewed. During downhole drilling, severe vibration loads can occur that affect the reliability and durability of tools in bottomhole assemblies (BHAs). Such high-frequency torsional oscillation (HFTO) can cause•premature damage to tools or their subcomponents. This paper presents dynamic simulations, prototype testing, and field-test results of a BHA component that isolates the upper part of the BHA from HFTO. The isolator tool reduced torsional vibrations and improved tool reliability, lifetime, and service delivery, especially while drilling in formations that are liable to excite HFTO. Introduction HFTO is a self-excited torsional vibration of the drillstring caused by the interaction of the drill bit and the rock. The latest downhole measurement devices can measure and record torsional accelerations at frequencies greater than 100 Hz and enable observation of HFTO in the field. Consequently, this phenomenon has been well-described and analyzed. In contrast to stick/slip, which occurs at the first torsional eigenfrequency of the drillstring, HFTO occurs at a higher natural torsional frequency, typically between 50 and 500 Hz. In most cases, the mode exhibiting the highest excitability is the stick/slip mode. However, the mode with the second-highest excitability has a frequency that is typically between 50–500 Hz with modal amplitudes concentrated at the BHA. Whereas the frequency of the stick/slip mode varies with the length of the overall drillstring, the BHA-concentrated HFTO modes remain constant in frequency and amplitude, independent of drillstring length. An HFTO mode and the stick/slip mode can occur simultaneously. Isolation of HFTO Previous laboratory tests have shown that the critical HFTO mode shapes of a BHA predicted by finite-element simulation can be reproduced accurately by torsional harmonic excitation using an electrodynamic shaker. The concept of isolation is based on restricting potential damaging HFTO vibrations to a part of the BHA that is by design strong enough to survive HFTO. On the basis of modeling research and experimental analysis of HFTO, a tool for isolating HFTO has been developed. This new isolator tool is part of the BHA and isolates HFTO from the lower to the upper part of the BHA. By the design of the isolator tool, the torsional dynamics of the BHA are modified so that critical HFTO mode shapes only have significant amplitudes in the section below the isolator tool, where the BHA is designed to cope with HFTO. Above the tool, the amplitudes are comparatively low. This effect significantly improves the performance and reliability of measurement-while-drilling (MWD) and logging-while-drilling (LWD) tools and reduces damages and consequent failures caused by HFTO. In addition, the effect opens design freedom for BHA components no longer subjected to these•vibrations.

A Drill Bit and a Drilling Motor With Embedded High-Frequency (1600 Hz) Drilling Dynamics Sensors Provide New Insights Into Challenging Downhole Drilling Conditions

Summary Drilling motors are typically used in every well drilled globally with conventional steerable bottomhole assemblies (BHAs) and powered rotary–steerable BHAs. Downhole drilling dysfunctions are common when mud motors are pushed to the limit for maximum drilling performance. High–frequency (1600 Hz) continuous–recording compact drilling dynamics sensors were embedded into the bit, bit box, and top subassembly (sub) of the motor to better understand the dynamic role played by drilling conditions in different shales throughout North America. In the drilling industry, most downhole measurements for drilling dynamics use relatively low–frequency sensors (up to 100 Hz). Typically, the measurements are burst and not continuous. These low–frequency burst acceleration devices cannot reliably measure high–frequency torsional oscillations (HFTOs), which are known to be problematic while drilling in certain shale basins. Newly developed high–frequency (1600 Hz) compact drilling dynamics sensors can now be embedded into the drill bit, mud–motor bit box, and top sub to record three–axis accelerations continuously at high–speed sampling rates. The embedded sensors do not add any extra length to the steerable motor and, therefore, capture the true dynamic response of the system. Embedding the high–frequency sensors at both ends of the mud motor provides two unique data sets of dynamic measurements. With conventional steerable motors and motor–assist rotary–steerable systems (RSSs), HFTO dominant frequencies between 100 and 400 Hz were commonly observed. In some cases, HFTO dominant frequencies between 400 and 700 Hz and their harmonics were captured, which have not been previously reported. In most cases, the HFTO-induced acceleration amplitudes are between 20 and 200g (where g is the gravitational acceleration = 9.806 m/s2) peak (or between 40 and 400g peak to peak). On some occasions, ±200g self–perpetuating HFTO-induced accelerations were recorded in memory where their calculated angular acceleration is more than 25 000 rad/s2. The transitions between low–frequency stick/slip and HFTOs were captured in high–speed recording. Negative string–rotation speeds were commonly observed at the top sub of the motor while in the rotary mode. It was noted that the bit would slow down to stop but never turn backward, resulting in the backward rotation of the motor top sub. During very–high–amplitude multiple–axis shocks at the bit, there was a significant increase in temperature because of the loss of energy from bit dysfunctions. The newly reported drilling dynamics phenomena, such as multiple dominant HFTO frequency shifts, microsticks, and microslips, will be detailed in this paper. Monitoring and understanding high–frequency drilling dynamics dysfunctions allow us to make systematic changes to bits, BHAs, and drilling parameters to reduce the dysfunction magnitude, improve the overall drilling efficiency, and minimize component wear.

Field Validation of a New Bottomhole-Assembly Model for Unconventional Shale Plays

Summary A new drillstring model has been developed that determines the static and dynamic behavior of bottomhole assemblies (BHAs) in 3D wellbores. An attempt at validating this model with field data is presented, and it shows a close agreement between observed and calculated downhole BHA behavior. Validation tests were conducted using high-frequency downhole data measured within a motor-assisted rotary-steerable BHA. The gathered data were used to verify the calculated mechanical loads, predicted lateral natural frequencies of the BHA, estimated directional performance of the downhole assembly, and the torsional resonance resulting from high-frequency torsional oscillations (HFTOs). Results from the field tests show a strong correlation between measured and calculated bending-moment values, as well as lateral natural frequencies of the BHA, with an average of 3% error across all data sets. The primary source of error is thought to be borehole spiraling, which is quantified through analysis of the downhole bending-moment data. In addition, the model is shown to provide close estimates of the actual directional performance of both steerable mud motors and rotary-steerable BHAs. However, the directional-calculation vs. -measurement comparison does reveal a need to incorporate a rate-of-penetration (ROP) dependency within the directional-prediction algorithms.

Technology Update: A Holistic Approach To Controlling Torsional Dynamics in the Drillstring

Technology Update Understanding drilling dynamics, the downhole shock and vibration that occur while drilling, is a crucial step to improving drilling efficiency and reducing nonproductive time (NPT). Industry statistics suggest that 20% to 30% of all downhole failures are related to adverse drilling dynamics (SPE 127413 and SPE 98150), and that drilling tool providers spend roughly USD 750 million per year on repair and maintenance. This amount pales compared with the untold costs borne by exploration and production companies as the result of drilling and completion inefficiencies, NPT, and tools lost in the hole. Preventing adverse dynamics requires a strong understanding of the fundamentals, particularly in addressing torsional dynamics: time-based variations in downhole rotational speed and torque. A common misconception is that torsional dynamics is limited to stick/slip. However, stick/slip is only one of three distinct modes of torsional dynamics, each with its own unique indicators, potential for damage, effect on drilling efficiency and—importantly—most effective means of mitigation. Differing Dynamics In addition to full stick/slip (FSS), the modes include low-frequency torsional oscillation (LFTO) and high-frequency torsional oscillation (HFTO) (Fig. 1). LFTO and FSS both typically occur at less than 2 Hz; HFTO occurs at between 50 and 250 Hz. LFTO, probably the most common of all three modes, is the excitation of a fundamental torsional natural frequency of the drillstring. The excitation causes the drillstring to act as a long torsional spring, which results in sinusoidal oscillations in bit speed and torque. The oscillation frequency is a function of the drillstring length and stiffness, and is typically less than 0.5 Hz for all drillstrings (SPE 21945). LFTO is characterized by a maximum revolutions per minute (RPM) of up to twice the average drillstring RPM and a bit that may stop, but only instantaneously.

An induction motor model for high-frequency torsional vibration analysis

High-frequency torsional oscillations of a 50 horsepower (hp) induction motor are investigated up to approximately 30 kHz. It is experimentally determined that torsional oscillations, due to the switching harmonics of the motor drive, contribute significantly to the torsional oscillation of the output shaft. Two torsional vibration models are developed. One model assumes the rotor to be rigid, while the other has a compliant rotor. The compliant model allows for greater transmission of high-frequency oscillations, and a better prediction of the measured output shaft vibration.

Internal dynamics of proteins. Short time and long time motions of aromatic sidechains in PTI

Theoretical approaches to the internal dynamics of proteins are outlined and illustrated by application to the aromatic sidechain motions of tyrosines in the bovine pancreatic trypsin inhibitor. High frequency torsional oscillations are obtained from a molecular dynamics simulation, while the longer time ring rotations are analyzed by use of adiabatic energy minimization and special transition-state trajectory techniques.

High-frequency torsional oscillations—I: Penny-shaped crack in an inhomogeneous medium

The problem of an inhomogeneous medium, whose shear modulus and density vary exponentially with radius, containing a penny-shaped crack undergoing high-frequency torsional oscillations is reduced asymptotically to Wiener-Hopf integral equation and solved by Carleman's method. Uniformly valid asymptotic results are obtained. Explicit expressions are derived for the normal displacement gradient outside the crack region, the stress-intensity factor and the energy of the crack.

High-frequency torsional oscillations—II: The Reissner-Sagocci problem at high frequencies

The Reissner-Sagocci Problem at high-frequencies for an elastic medium with exponentially varying shear modulus and density in the radial direction is asymptotically reduced to a Wiener-Hopf integral equation whose solution is obtained by Carleman's method. Uniform asymptotic results are obtained. Explicit results are given for the displacement outside the rigid disc, the moment of the applied forces necessary to oscillate the disc, and the amplitude of oscillation of the disc.