Natural Frequency and Resonance Study of FGM Turbo-Machinery Blade Using Campbell Diagram

Turbo machinery rotating blades are a vital component of aero-engines for transferring the energy of gas flow to kinetic energy. Rotating turbo-machinery blades are prone to fail under working fields with high temperature, high speed, high pressure and resonance of blades with prime engine. Vibration of the turbo-machinery blades need to be studied carefully for safe and reliable operation of the engine. Thermal barrier coatings (TBC) layers are used to protect the blade metal at higher operating temperature though these can be plagued due to phase instability, thermal instability and adherence problems. TBCs also tend to spall due to thermal expansion mismatch with the super alloy substrate or because of erosion/impact caused by particles in the high-velocity combustion gases. Functionally graded materials (FGMs) are a relatively new class of materials that can solve these problems in high-temperature environments and can be considered as potential material for making gas turbine blades. Unlike composite materials the functionally graded materials (FGMs) are free from delamination and debonding and have the ability to withstand high temperature without TBC coatings. In this present study natural frequency of the FGM turbine blade for various rotational speeds during actual operation is determined using finite element technique. As the aero-engine is complex in nature therefore harmonic resonance can always occur in the aero-engine system and it is difficult to determine the natural frequency at varying speed during actual operation. The chances of failure of the blade also increase because of harmonic resonance. Hence, the resonance property is required to investigate of the FGM blade in details. Various rotational speed and operating temperature is considered to determine the natural frequencies of the blade. The resonance studies for each case are performed using the Campbell diagram. Resonance margin is calculated for each case and safe operating speed is determined. This study could serve as ready reference for safe operation of turbo-machinery engine considering FGM blade for specific range of engine speed.

A comparison of methods used to quantify the work of breathing during exercise

The mechanical work of breathing (Wb) is an insightful tool used to assess respiratory mechanics during exercise. There are several different methods used to calculate the Wb, however - each approach having its own distinct advantages/disadvantages. To date, a comprehensive assessment of the differences in the components of Wb between these methods is lacking. We therefore sought to compare the values of Wb during graded exercise as determined via the 4 most popular methods: (i) pressure-volume integration; (ii) the Hedstrand diagram; (iii) the Otis diagram; and the (iv) modified Campbell diagram. Forty-two participants (30 ± 15 years; 16 women) performed graded cycling to volitional exhaustion. Oesophageal pressure-volume loops were obtained throughout exercise. These data were used to calculate the total Wb and, where possible, its subcomponents of inspiratory and expiratory, resistive and elastic Wb, using each of the 4 methods. Our results demonstrate that the components of Wb were indeed different between methods across the minute ventilations engendered by graded exercise (P < 0.05). Importantly, however, no systematic pattern in these differences could be observed. Our findings indicate that the values of Wb obtained during exercise are uniquely determined by the specific method chosen to compute its value - no two methods yield identical results. Because there is currently no "gold-standard" for measuring the Wb, it is emphasized that future investigators be cognizant of the limitations incurred by their chosen method, such that observations made by others may be interpreted with greater context, and transparency.

Analysis of Critical Speed and Natural Frequency of Shaft with Multi – Crack and Multi Masses using different Materials

A natural frequency was analyzed and critical speed was predicted by using Campbell diagram and analysis was also performed for validation. The results represents that a solid shaft with three cracks with two masses and material like structural steel and titanium alloy the critical speed with increase in a RPM continuously found in structural steel. The natural frequency of shaft is compared by using two types of materials and is predicted that at solid shaft with multi – crack and masses of titanium alloy exhibits lower critical speed.

Whirl Analysis of an Overhung Disk Shaft System Mounted on Non-rigid Bearings

Eigenvalues of a simple rotating flexible disk-shaft system are obtained using different methods. The shaft is supported radially by non-rigid bearings, while the disk is situated at one end of the shaft. Eigenvalues from a finite element and a multi-body dynamic tool are compared against an established analytical formulation. The Campbell diagram based on natural frequencies obtained from the tools differ from the analytical values because of oversimplification in the analytical model. Later, detailed whirl analysis is performed using AVL Excite multi-body tool that includes understanding forward and reverse whirls in absolute and relative coordinate systems and their relationships. Responses to periodic force and base excitations at a constant rotational speed of the shaft are obtained and a modified Campbell diagram based on this is developed. Whirl of the center of the disk is plotted as an orbital or phase plot and its rotational direction noted. Finally, based on the above plots, forward and reverse whirl zones for the two excitation types are established.

Calculating the work of breathing during mechanical ventilation.

Left figure: Passive patient esophageal pressure (Pes) in cmH2O on x-axis versus tidal volume in ml on y-axis. Green dashed line represents the chest wall compliance Right figure: same patient actively breathing on pressure support ventilation. (Pes) in cmH2O on x-axis versus tidal volume in ml on y-axis. Green dashed line represents the chest wall compliance. Red shaded area is the Campbell diagram representing the inspiratory work of breathing

The effect of estimating chest wall compliance on the work of breathing during exercise as determined via the modified Campbell diagram

The modified Campbell diagram provides one of the most comprehensive assessments of the work of breathing (Wb) during exercise, wherein the resistive and elastic work of inspiration and expiration are quantified. Importantly, a necessary step in constructing the modified Campbell diagram is to obtain a value for chest wall compliance (CCW). To date, it remains unknown whether estimating or directly measuring CCW impacts on the Wb as determined by the modified Campbell diagram. Therefore, the purpose of this study was to evaluate whether the components of the Wb differ when the modified Campbell diagram is constructed using an estimated versus measured value of CCW. Forty-two participants (n = 26 men, 16 women) performed graded exercise to volitional exhaustion on a cycle ergometer. CCW was measured directly at rest via quasi-static relaxation. Estimated values of CCW were taken from prior literature. The measured value of CCW was greater than that obtained via estimation (214 ± 52 mL∙cmH2O-1 vs. 189 ± 18 mL∙cmH2O-1, p < 0.05). At modest to high minute ventilations (i.e., 50-200 L∙min-1), the inspiratory elastic Wb was greater, and expiratory resistive Wb was lower, when modified Campbell diagrams were constructed using estimated compared with measured values of CCW (p < 0.05). These differences were however small, and never exceeded ±5%. Thus, although our findings demonstrate that estimating CCW has a measurable impact on the determination of the Wb, its effect appears relatively small within a cohort of healthy adults during graded exercise.

Nonlinear Analysis of Rod Fastened Rotor under Nonuniform Contact Stiffness

Rod fastened rotor is widely used in gas turbine, aero engine, and other occasions. The bending stiffness of the contact interface directly affects the stable operation of the rotor. Dynamic model of the rod fastened rotor-bearing system has been established considering nonuniform stiffness of interface. The motion equation of this system has been deduced from Lagrange’s equations. The linear dynamic characteristics of this rotor has been investigated, such as Campbell diagram, critical speed, and formation, and the nonlinear characteristics of this system, such as chaos and bifurcation, has been investigated too. The result shows that “bistable state” characteristic appeared on the rod fastened rotor system; that is, there are two critical speeds for each order, and they are all positive precession critical speed, and the amplitude response to the lower critical speed is much larger than that its counterparts to the higher critical speed. In terms of nonlinear characteristics, the rod fastened bearing system has experienced periodic 1 motion, multiple periodic motion, quasi-periodic motion, periodic 1 motion, and chaotic motion successively.

An Evaluation of Mode Tracking Methods for Practical Rotor Dynamic Analysis

An important precursor to the dynamic analysis of rotating machinery, in either frequency or time domain, is the extraction of its mode shapes and corresponding frequencies. This is often presented as a Campbell diagram, which plots the frequency of each mode as a function of the rotor speed. A typical Campbell diagram has several backward whirl, linear and forward whirl modes leading to numerous intersections. Therefore augmenting the eigenvalue solution with a mode tracking algorithm to output the Campbell diagram is of essential interest to a practicing engineer. This paper presents an evaluation of several mode tracking approaches for rotor dynamic simulations, starting from their theoretical foundations to practical applications using several test cases. These tracking algorithms are implemented in the structural solver, OptiStruct, part of Altair Engineering’s CAE framework. Finally, the conclusions drawn from this exercise offer engineers studying rotating machinery several key insights.

AN OVERVIEW OF TIME-DOMAIN COMPUTATIONAL METHODS FOR AEROELASTIC INSTABILITIES OF MULTI-STAGE COMPRESSOR

Modern gas turbine design continues to move towards improved performance, reduced weight and reduced cost. As turbomachinery blade aerofoils are thinned to improve performance and reduce weight, aeroelastic issues such as flutter, forced response and stall driven vibrations become more predominant. Moreover, as the use of blisks (blade-integrated-disks) with very low mechanical damping becomes more common in modern compressor designs, accurate prediction of compressor aeroelastic stability in a multi-row environment becomes vital. This paper presents a review of aeroelasticity research carried out at Rolls-Royce Vibration University Technology Centre (VUTC) at Imperial College over the past 20 years. The aim is to summarise the unusual aeroelastic issues observed in multi-stage compressors into one document so that it can be used by other researchers in the field. Blade passing forced response is not addressed here as their existence can be detected by a Campbell diagram. The results presented here are based on numerical methods but where possible data from experiments are used to verify the numerical findings.