Stick-Slip Model for PDC Bits Accounting for Coupled Torsional and Axial Oscillations

Drilling with PDC bits can cause severe torsional and axial oscillations. These oscillations are accompanied by periodic sticking of the bit followed by accelerated rotation. The so-called “stick-slip” increases bit wear and fatigue and causes premature failure of BHA and drillstring components. It is well known that these torsional oscillations are nonlinear and self-induced. The present study investigates the coupling between axial and torsional oscillations. The cutting process is based on the Detournay model, which provides for the effect of the bottomhole pressure and the local pore pressure. The axial stiffness of the drillstring is taken into account with the axial motion equations coupled with the torsional equations, in contrast to previous models where axial equations were considered independently. Axial oscillations are allowed to occur even when the bit is in the stick phase. The new model also includes bit “bouncing” when it loses contact with the bottomhole. The equations are solved by time integration. By results of the analysis of transient processes the spectral density is determined. The objective of the paper is to improve understanding of stick-slip oscillation nature and assess the contribution of parameters that influence their intensity. The study includes the effect of the rotor rpm, intrinsic specific energy of rock, number of PDC blades, wear flat length of blades, etc. Results of the study will help drillers to select and change drilling parameters more efficiently to reduce severe stick-slip oscillations.

Integrated Methodology for Investigation of Wagon Bogie Concepts by Simulation

Implementation of a new bogie concept is an integrated part of the vehicle design which must follow a rigorous testing and validation procedure. Use of multibody simulation helps to reduce the amount of time and effort required in selecting a new concept design by analysing results of simulated dynamic behaviour of the proposed design. However, the multibody simulation software mainly looks at the dynamics of a single vehicle; hence, forces from the train configuration operational dynamics are often absent in such simulations. Effects of longitudinal-lateral and longitudinal-vertical interactions between rail vehicles have been found to affect the stability of long trains [1,2]. The effect of wedge design on the vertical dynamics of a bogie has also been discussed in [3,4]. It is important to apply the lateral and vertical forces from a train simulation into a single multibody model of a wagon to check its behaviour when operating in train configuration. In this paper, a novel methodology for the investigation of new bogie designs has been proposed based on integrating dynamic train simulation and the multibody vehicle modelling concept that will help to efficiently achieve the most suitable design of the bogie. The proposed methodology suggests that simulation of any configuration of bogie needs to be carried out in three stages. As the first stage, the bogie designs along with the wagon configurations need to be presented as a multibody model in multibody simulation software to test the suitability of the concept. The model checking needs to be carried out in accordance with the wagon model acceptance procedure established in [5]. As the second stage, the wagon designs need to be tested in train configurations using a longitudinal train dynamics simulation software such as ‘CRE-LTS’ [2], where a train set consisting of the locomotives and wagons will be simulated to give operational wagon parameters such as lateral and vertical coupler force components. As the third stage, the detailed dynamic analysis of bogies and wagons needs to be performed with a multibody software such as ‘Gensys’ where lateral and vertical coupler force components from the train simulation (second stage) will be applied on the multibody model to replicate the worst case scenario. The proposed methodology enhances the selection procedure of any alternate bogie concept by the application of simulated train and vehicle dynamics. The simulated case studies show that simulation of wagon dynamic behaviour in multibody software combined with data obtained from longitudinal train simulation is not only possible, but it can identify issues with a bogie design that can otherwise be overlooked.

Active Performance Optimization of Cantilever Piezoelectric Energy Harvester

A Piezoelectric Energy Harvester (PEH) of cantilever beam type is developed to optimize the generated power by means of active control of moment of inertia of the beam. Distributed parameter equations of vibration of the beam are developed. Then the electromechanical response of the piezoelectric actuator is discussed. The harvester configuration is then described and it is shown that such a configuration can avoid the drastic power drop in presence of uncertainty around resonance frequency by applying voltage to the piezoelectric actuator. Finally the proposed harvester output power working frequency span is compared to conventional methods to show that the significant performance optimization in proposed method is achieved.

Two-Stroke Marine Diesel Engine Variable Injection Timing System Performance Evaluation and Optimum Setting for Minimum Fuel Consumption at Acceptable NOx Levels

Currently the most promising solution for marine propulsion is the two-stroke low-speed diesel engine. Start of Injection (SOI) is of significant importance for these engines due to its effect on firing pressure and specific fuel consumption. Therefore these engines are usually equipped with Variable Injection Timing (VIT) systems for variation of SOI with load. Proper operation of these systems is essential for both safe engine operation and performance since they are also used to control peak firing pressure. However, it is rather difficult to evaluate the operation of VIT system and determine the required rack settings for a specific SOI angle without using experimental techniques, which are extremely expensive and time consuming. For this reason in the present work it is examined the use of on-board monitoring and diagnosis techniques to overcome this difficulty. The application is conducted on a commercial vessel equipped with a two-stroke engine from which cylinder pressure measurements were acquired. From the processing of measurements acquired at various operating conditions it is determined the relation between VIT rack position and start of injection angle. This is used to evaluate the VIT system condition and determine the required settings to achieve the desired SOI angle. After VIT system tuning, new measurements were acquired from the processing of which results were derived for various operating parameters, i.e. brake power, specific fuel consumption, heat release rate, start of combustion etc. From the comparative evaluation of results before and after VIT adjustment it is revealed an improvement of specific fuel consumption while firing pressure remains within limits. It is thus revealed that the proposed method has the potential to overcome the disadvantages of purely experimental trial and error methods and that its use can result to fuel saving with minimum effort and time. To evaluate the corresponding effect on NOx emissions, as required by Marpol Annex-VI regulation a theoretical investigation is conducted using a multi-zone combustion model. Shop-test and NOx-file data are used to evaluate its ability to predict engine performance and NOx emissions before conducting the investigation. Moreover, the results derived from the on-board cylinder pressure measurements, after VIT system tuning, are used to evaluate the model’s ability to predict the effect of SOI variation on engine performance. Then the simulation model is applied to estimate the impact of SOI advance on NOx emissions. As revealed NOx emissions remain within limits despite the SOI variation (increase).

Linear Control Root-Clustering of Uncertain Systems

In the design of linear control systems, it is desired to assign the closed loop spectrum in sub-regions (as opposed to locations) of the complex plane. The present paper establishes a matrix root-clustering criterion for an important class of regions, and develops a linear feedback control that assigns the closed loop spectrum in the desired region. This is done for both nominal and uncertain systems.

Robot Assisted Modal Analysis on a Stationary Bladed Wheel

This paper shows an automated procedure to experimentally find the eigenmodes of a bladed wheel with highly three-dimensional geometry. The stationary wheel is supported in free-free conditions, neglecting stress-stiffening effects. The single input / multiple output approach was followed. The vibration speed was measured by means of a laser-Doppler vibrometer, and an anthropomorphic robot was used for accurate orientation and positioning of the measuring laser beam, allowing multiple measurements during a limited testing time. The vibration at corresponding points on each blade was measured and the data elaborated in order to find the initial (lower frequency) modes. These modal shapes were then compared to finite element simulations and accurate frequency matching and exact number of nodal diameters obtained. Being the modes cyclically harmonic, the complex formulation could be attractive, being not affected by the angular phase of the mode representation. Nevertheless, stationary modes were experimentally detected, rather than rotating, and then the real representation was necessary. The discrete Fourier transform of the blade displacements easily allowed to find both the angular phase and the correct number of nodal diameters. Successful MAC experimental to analytical comparison was finally obtained with the real representation after introducing the proper angular phase for each mode.

Experimental Investigation of Oil Flowrate in a Hermetic Reciprocating Compressor

The aim of this experimental study is to investigate the mass flow rate of the lubricating oil in a hermetic reciprocating compressor. Essential parameters affecting the performance of the lubrication are the rotational speed of the crankshaft, the viscosity of the oil, the operating temperature and the submersion depth of the crankshaft. An experimental setup was built as to measure the oil mass flow rate with respect to the oil temperature variation during different operating conditions. The influence of the governing parameters such as the rotational speed, temperature (viscosity) and the submersion depth on the mass flow rate from crankshaft outlet are studied in detail. In addition, the oil flow visualization from the upper hole of the crankshaft is performed using a high-speed camera in order to observe the effectiveness of the lubrication of the various parts of the compressor. This study reveals that with increasing rotational speed, the submersion depth of the crankshaft and with decreasing viscosity of the lubricant, the mass flow rate from the crankshaft increases.

Application of Recent Variance Expressions Associated With Binary Markov Processes for Detecting Changes in Bandwidth and Power With Application to Health Monitoring

Health condition monitoring often entails monitoring and detecting changes in the structure of associated random processes. A common trigger for an alarm is when the process amplitude exceeds a specified threshold for a certain period of time. A less common trigger for an alarm is when the process bandwidth changes significantly. This latter type of change occurs, for example, in EEG just prior to the onset of an epileptic seizure [Sherman (2008)]. One can monitor the process directly, or one can convert the process to a 0/1 process where 0 denotes ‘within’ and 1 denotes ‘outside of’ a specified tolerance. Such a process is given many names. One is a binary process, another is a Bernoulli process. If the underlying process is a Gauss-Markov process, then the associated 0/1 process becomes a Markov 0/1 process. The main parameters associated with such a process are the following probabilities: (i), (ii), and (iii). In this work we use the variance expressions for the estimators of these probabilities that were reported in Sherman (2011), in order to detect changes with specified false alarm probabilities. We demonstrate their value in detecting bandwidth change via zero-crossing estimates, and detecting amplitude change via threshold excursion estimates.

Development and Comparison of Laplace Domain Models for Non-Slender Beams and Application to a Half-Car Model With Flexible Body

Math models of flexible dynamic systems have been the subject of research and development for many years. One area of interest is exact Laplace domain solutions to the differential equations that describe the linear elastic deformation of idealized structures. These solutions can be compared to and complement finite order models such as state-space and finite element models. Halevi (2005) presented a Laplace domain solution for a finite length rod in torsion governed by a second order wave equation. Using similar methods Van Auken (2010, 2012) presented a Laplace domain solution for the transverse bending of an undamped uniform slender beam based on the fourth order Euler-Bernoulli equation, where it was assumed that rotary inertia and shear effects were negligible. This paper presents a new exact Laplace domain solution to the Timoshenko model for an undamped uniform non-slender beam that accounts for rotary inertia and shear effects. Example models based on the exact Laplace domain solution are compared to finite element models and to slender beam models in order to illustrate the agreement and differences between the methods and models. The method is then applied to an example model a half-car with a flexible body.