Erratum: “On the Influence of Back Pressure and Size on the Performance of Safety Valves” [ASME 2002 Pressure Vessels and Piping Conference, Piping and Component Analysis and Diagnosis, Vancouver, BC, Canada, August 5–9, 2002, Conference Sponsors: Pressure Vessels and Piping Division, ISBN: 0-7918-4658-X, Copyright © 2002 by ASME. Paper No. PVP2002-1514, pp. 35-41; 7 pages; doi:10.1115/PVP2002-1514]

This erratum corrects errors that appeared in the paper “On the Influence of Back Pressure and Size on the Performance of Safety Valves” which was published in Proceedings of the ASME 2002 Pressure Vessels and Piping Conference, Piping and Component Analysis and Diagnosis, pp. 35–41, August 2002, PVP2002-1514, doi: 10.1115/PVP2002-1514.

Analysis of Rotating Blade Forced Vibration Due to Torsional Excitation Using the Method of Harmonic Balance

This paper presents an analysis of the forced vibration of rotating blade due to torsional excitation. The model analyzed is a multi-modal forced second order ordinary differential equation with multiple harmonically varying coefficients. The method of Harmonic Balance (HB) is employed to find approximate solutions for each of the blade modes in the form of truncated Fourier series. The solutions have shown multi resonance response for the first blade vibration mode. The examination of the determinant of the harmonic balance solution coefficient matrix for stability purposes has shown that the region between the two resonance points is an unstable vibration region. Numerical integration of the equations is conducted at different frequency ratio points and the results are discussed. This solution provides a very critical operation and design guidance for rotating blade with torsional vibration excitation.

Elastic Shakedown in Pressure Vessel Components Under Non-Proportional Loading

Bounding techniques for calculating shakedown loads are of great importance in design since this eliminates the need for performing full elasto-plastic cyclic loading analyses. The classical Melan’s lower bound theorem is widely used for calculating shakedown loads of pressure vessel components under proportional loading. Polizzotto extended the Melan’s theorem to the case of non-proportional loading acting on a structure. This paper presents a finite element method, based on Polizzotto’s theorem, to estimate the elastic shakedown load for a structure subjected to a combination of steady and cyclic mechanical loads. This method, called non-linear superposition, is then applied to investigate the shakedown behaviour of a pressure vessel component — a nozzle/cylinder intersection and that of a biaxially loaded square plate with a central hole. Results obtained for both problems are compared with those available in the literature and are verified by means of cyclic elasto-plastic finite element analysis.

Cross Property Correlations for Metals Subjected to Fatigue Damage Accumulation

A new method of evaluation of elastic property deterioration due to accumulated damage is suggested and experimentally verified. It is based on the explicit correlations between two groups of anisotropic properties – conductivity and elasticity, recently established for porous/microcracked materials with anisotropic microstructures. An experimental study of fatigue has been done to verify the theoretical predictions. The electrical resistance and Young’s modulus are measured as functions of the number of loading cycles in the standard fatigue tests. The agreement between the theoretical predictions and the direct experimental data is better than 10% in all cases. The results allow one to use the measurement of electric resistance to estimate the damage accumulated in metal structures and decrease in the elastic modulus.

Utilization of Micro-Electronic-Machine Systems (MEMS) to Possible Future Use in the Enhanced Analysis of Safety in Nuclear Power Plants

The focal point of this paper is to go in-depth in to the potential utilization of MEMS to further enhance safety measures within nuclear power plants. Robots, which are being researched and developed in Sandia National Laboratories, sometimes built as small as the size of a pollen grain, can be utilized to constantly monitor the stress analysis within all aspects of running a Nuclear Power Plant. From cooling towers to detecting miniscule cracks within pipes, MEMS can be utilized to constantly detect and even possibly repair minor faults within the overall structure of a nuclear power plant. MEMS technologies provide the ability to reliably produce micro actuators and sensors to meet these mission requirements. MEMS technologies are also attracting an increasing interest from the commercial sector for various applications. Currently, Sandia National Laboratories has been developing MEMS technologies to support its core missions of weapon surety, stockpile maintenance, and national security interests. Already, the project has been responsible for numerous electromechanical systems in nuclear weapons, which ensure nuclear safety and provide reliable arming, fusing and firing. With these factors in consideration, the main idea of this paper is to present ideas for producing sensors and robots on a micro scale, which could be programmed to communicate and work within each other to have enhanced safety and efficiency within a nuclear power plant.

Reliability, Availability and Maintainability Analysis of Steam Turbines Used in an Oil Refinery

Weibull reliability and maintainability analysis have been used to analyze the time between failures and time to repair data of a group of steam turbines being used in a large oil refinery. Failure history of a set of steam turbines was obtained from the Computerized Maintenance Management System of the plant. Out of 50 steam turbines in operation, 13 are identified as bad actors which have experienced ≥3 failures in five years. The Pareto analysis performed on this set of turbines further narrowed down the 10 most critical (worst performing) turbines. This group of most critical turbines is the primary target for this Weibull reliability and maintainability analysis. The Weibull reliability and maintainability analysis provides an indication of the equipment reliability and maintainability characteristics including their failure rates and repair rates. In addition to the failure and repair data, the associated maintenance cost for this group of turbines was also collected over a period of five years, and the trends in cost increase with respect to time are plotted.

Determination of the Regional Function of the Heart

Unlike many other engineering designs, the heart, a pressure vessel, shows variations within its chambers and surface in terms of mechanical function. This necessitates a whole field technique with high spatial resolution. Computer aided speckle interferometry (CASI), a nondestructive examination technique, is herein developed for this purpose. A speckle pattern was created on the surface of isolated rabbit hearts. Images of the beating hearts werc acquired with a charge-couple device (CCD) camera for one second at a rate of 50 frames per second. CASI was used to determine the 2-D displacement vectors over regions of approximately 4 × 6 mm. Regional area stroke work (the integral of the left ventricular pressure with respect to area), the first invariant of the 2-D strain tensor, and the principle strains were used to determine the regional function. After occluding the blood supply to a region of the heart, significant changes were detected in all the previously mentioned parameters. Commonly used techniques cannot determine 2-D strain and lack the high spatial resolution of CASI. Determination of the 2-D strain can provide useful data on the functionality of the heart.

On the Influence of Back Pressure and Size on the Performance of Safety Valves

The paper presents the results of an extensive experimental research programme performed on safety valves in order to clarify the effects of back pressure and valve size on the flow capacity of a valve. As well known, back pressure strongly influences valve operating characteristics and can also reduce the discharge coefficient. This flow rate reduction can be related to the occurrence of a subsonic flow regime along the flow path and to insufficient disc lift. Last mentioned features can play a different role on different valve sizes because of the non exact geometrical scaling within the same valve size range. This happens because the requirements of typical application design standards, such as the API Standard 526, are such that the valve inlet, valve outlet and face to face dimension are not exactly scaled with respect to the orifice diameter. Moreover, face to face dimension can limit the body bowl volume leading to different device performances the same operational conditions. In order to clarify and evaluate the influence of the above mentioned parameters on the flow capacity of safety valves, many tests were carried on a single valve for different pressure ratios, disc lifts and for different valve outlet areas and body volumes representing different sizes derived from API Standard 526. Test results show significant differences on the flow capacity of safety valves under back pressure regime. This would suggest testing every valve size of the considered valve size range at different expansion ratios to confirm performance. Since this procedure leads to an excessive number of experimental tests, a sensitivity analysis on the influence of the most important geometrical parameters has been carried out. In order to minimize the number of experimental tests required for characterizing the flowing capacity of the whole valve size range, the paper proposes an experimental correlation for the prediction of the above mentioned non similarity effects.

Discussion of the Available Methods for Blade Vibration Measurement

Blade vibration has been recognized as one major and costly cause of failure in turbo-machinery. Its vibration measurement has attracted many investigators where until now there is no single reliable approach can be identified. Blade vibration measurement techniques can be classified into two broad categories, namely; (1) the direct approach that includes using strain gages, optical/laser methods, etc., to monitor directly the blade motion at one or more points on the blade span, (2) the indirect approach by extracting some vibration information form the lateral main rotor vibration and the casing/bearing cap vibration, pressure fluctuations, performance monitoring and thermal changes. Recently, a new indirect method has received attention of investigators which is monitoring the torsional vibration of the main rotor. This technique has been investigated by theoretical and experimental studies. The direct and indirect techniques are described in this survey paper and advantages and draw backs are discussed. From the results of this survey it seems that the indirect approach using the torsional vibration measurement is the most promising among all indirect techniques and further theoretical and experimental investigations are recommended.

Non-Linear Free Vibrations of a Rotating Beam Carrying a Tip Mass With Rotary Inertia

The non-linear, for each of the first three modes, of planar, large amplitude flexural free vibrations of a beam clamped with an angle to a rigid rotating hub and carrying a tip mass with rotary inertia are investigated. The shear deformation and rotary inertia effects are assumed to be negligible, but account is taken of axial inertia, non-linear curvature and the inextensibility condition. The Lagrangian dynamics in conjunction with the assumed mode method, assuming constant hub rotation speed, is utilized in deriving the non-linear unimodal temporal problem. The time transformation method is employed to obtain an approximate solution to the frequency-amplitude relation of the beam-mass free vibration, since the order of the nonlinear terms is not small which includes static and inertial geometric stiffening as well as inertial softening terms. Results in non-dimensional form are presented graphically, for the effect beam root-attachment angle, hub radius and the attached inertia element ratio on the variation of the natural frequency with vibration amplitude.