A Semi-Analytic Model for Free Vibration Analysis of Longitudinally Loaded Cantilever Shaft-Disk Systems

2000 ◽  
Author(s):  
Hong-Cheng Sheu ◽  
Lien-Wen Chen
Keyword(s):  
Critical Loads ◽  
Free Vibration Analysis ◽  
Influence Coefficient ◽  
Analytic Model ◽  
Disk System ◽  
Critical Speeds ◽  
Longitudinal Load ◽  
Influence Coefficients ◽  
Cantilever Shaft ◽  
Taylor’S Series

Abstract A semi-analytic model is proposed to study the critical speeds and critical loads of the cantilever shaft-disk systems subjected to longitudinal loads. In the present work, both the exact and approximate stiffness influence coefficients of the longitudinally loaded cantilever shafts are derived. In order to obtain deeper insight into the dynamic behavior of such a shaft-disk system, the present shaft mathematical model has taken account of shear deformation effect. Because the exact stiffness influence coefficients of the shaft are transcendental and difficult to get their characteristics on longitudinal load intuitively, each stiffness influence coefficient is expanded in a Taylor’s series about the longitudinal load. Based on the present approximate stiffness influence coefficients, the critical speeds and critical loads of the cantilever shaft-disk systems can be easily and quickly obtained. Numerical simulations show that the present results are seen to be quite in agreement with the exact solutions.

Additional Investigations Into the Natural Frequencies and Critical Speeds of a Rotating, Flexible Shaft-Disk System

2007 ◽  
Author(s):  
Lyn M. Greenhill ◽  
Valerie J. Lease
Keyword(s):  
Natural Frequencies ◽  
Slenderness Ratio ◽  
Rotor Dynamics ◽  
Axial Position ◽  
Disk System ◽  
Apparent Contradiction ◽  
Critical Speeds ◽  
Shaft Flexibility ◽  
Gyroscopic Effects ◽  
Lumped Masses

Traditional rotor dynamics analysis programs make the assumption that disk components are rigid and can be treated as lumped masses. Several researchers have studied this assumption with specific analytical treatments designed to simulate disk flexibility. The general conclusions reached by these studies indicated disk flexibility has little effect on critical speeds but significantly influences natural frequencies. This apparent contradiction has been reexamined by using axisymmetric harmonic finite elements to directly represent both disk and shaft flexibility along with gyroscopic effects. Results from this improved analysis show that depending on the thickness-to-diameter (slenderness) ratio of the disk and the axial position of the disk on the shaft, there are significant differences in all natural frequencies, for both forward and backward modes, including synchronous crossings at critical speeds.

Comparison of the Influence Coefficient Method and Travelling Wave Mode Approach for the Calculation of Aerodynamic Damping of Centrifugal Compressors and Axial Turbines

2017 ◽  
Author(s):  
K. Vogel ◽  
A. D. Naidu ◽  
M. Fischer
Keyword(s):  
Centrifugal Compressor ◽  
Travelling Wave ◽  
Wave Mode ◽  
Forced Response ◽  
Computational Time ◽  
Influence Coefficient ◽  
Average Deviation ◽  
Aerodynamic Damping ◽  
Influence Coefficients ◽  
Periodic Boundaries

The prediction of aerodynamic damping is a key step towards high fidelity forced response calculations. Without the knowledge of absolute damping values, the resulting stresses from forced response calculations are often afflicted with large uncertainties. In addition, with the knowledge of the aerodynamic damping the aeroelastic contribution to mistuning can be considered. The first section of this paper compares two methods of one-way-coupled aerodynamic damping computations on an axial turbine. Those methods are: the aerodynamic influence coefficient, and the travelling wave mode method. Excellent agreement between the two methods is found with significant differences in required computational time. The average deviation between all methods for the transonic turbine is 4%. Additionally, the use of transient blade row methods with phase lagged periodic boundaries are investigated and the influence of periodic boundaries on the aerodynamic influence coefficients are assessed. A total of 23 out of 33 passages are needed to remove all influence from the periodic boundaries for the present configuration. The second part of the paper presents the aerodynamic damping calculations for a centrifugal compressor. Simulations are predominantly performed using the aerodynamic influence coefficient approach. The influence of the periodic boundaries and the recirculation channel is investigated. All simulations are performed on a modern turbocharger turbine and centrifugal compressor using ANSYS CFX V17.0 with an inhouse pre- and post-processing procedure at ABB Turbocharging. The comparison to experimental results concludes the paper.

scholarly journals An Optimum Balance Weight Search Algorithm

1993 ◽  
Author(s):  
James C. Austrow
Keyword(s):  
Search Algorithm ◽  
Least Square ◽  
Test Case ◽  
Influence Coefficient ◽  
Residual Vibration ◽  
Single Plane ◽  
Vibration Data ◽  
Influence Coefficients ◽  
Balance Weight ◽  
Optimum Balance

A mathematical description for an optimum balance weight search algorithm for single plane multipoint balance is presented. The algorithm uses influence coefficients, either measured or known beforehand, and measured complex vibration data to determine an optimum balance correction weight. The solution minimizes the maximum residual vibration. The algorithm allows user defined balance weights to be analyzed and evaluated. A test case is presented showing actual results and comparison with a least square solution algorithm. An efficient multiplane influence coefficient calculation scheme is also presented.

Influence Coefficients Obtained by Hammer Beat Permit Significant Time Savings When Balancing Simple Flexible Rotors

1999 ◽  
Author(s):  
D. Wiese ◽  
M. Breitwieser
Keyword(s):  
Influence Coefficient ◽  
Significant Time ◽  
Flexible Rotors ◽  
Influence Coefficients ◽  
Flexible Roll ◽  
Influence Coefficient Method ◽  
Time Savings ◽  
Positive Results ◽  
Coefficient Method

Abstract The following paper presents a method for balancing simple flexible rotors with the help of influence coefficients obtained by hammer beat. The method permits time savings of approx. 50% compared to the conventional influence coefficient method. Initial positive results obtained on a flexible roll are also presented.

Analysis of Complex Kinematic Chains With Influence Coefficients

1959 ◽  
Vol 26 (2) ◽  
pp. 184-188
Author(s):  
J. Modrey
Keyword(s):  
Simultaneous Equations ◽  
Influence Coefficient ◽  
Complex Mechanism ◽  
Direct Process ◽  
Kinematic Chains ◽  
Influence Coefficients

Abstract Highly complex kinematic chains such as Fig. 1(c) can be analyzed by the use of simple vector equations involving influence coefficients. The influence-coefficient equations are related to superposition of simple kinematic chains. The technique for determining the necessary influence coefficients is one of sequentially setting all variables but one to zero and relaxing appropriate constraints to maintain mobility. This “zero-relax” process creates a series of mechanisms each simple enough to be solved by a direct process rather than by simultaneous equations. The analysis of the velocities and accelerations for these simpler mechanisms yields the influence coefficients of the related but more highly complex mechanism.

Influence Coefficients for Hemispherical Shells With Small Openings at the Vertex

1955 ◽  
Vol 22 (1) ◽  
pp. 20-24
Author(s):  
G. D. Galletly
Keyword(s):  
Constant Thickness ◽  
Influence Coefficient ◽  
Circular Opening ◽  
Central Angle ◽  
Calculation Time ◽  
Numerical Example ◽  
Hemispherical Shell ◽  
Influence Coefficients ◽  
Hemispherical Shells

Abstract Three methods of obtaining the influence coefficients for a thin, constant-thickness, hemispherical shell with a circular opening at the vertex were investigated and utilized in a numerical example. Bearing in mind both accuracy and calculation time, it was concluded that when the total central angle subtended by the opening is less than approximately 30 deg, good results for the influence coefficient calculation will be obtained by using Method II in the text of the paper.

scholarly journals Usage of the influence coefficient during calculation of a nominal error of gas counters

2019 ◽  
Vol 298 ◽  
pp. 00009
Author(s):  
M.S. Ostapenko ◽  
M.A. Popova ◽  
A.M. Tveryakov
Keyword(s):  
Relative Error ◽  
Gas Flow ◽  
Oil And Gas ◽  
Great Influence ◽  
Operating Conditions ◽  
Effect Of Temperature ◽  
Influence Coefficient ◽  
Technical Documentation ◽  
Flow Meters ◽  
Influence Coefficients

In this paper, we evaluate the method of finding the relative error of gas flow meters taking into account the influence coefficients. A literature analysis was carried out, which showed that flow meters are used at oil and gas enterprises, which show its metrological characteristic, showing specific values of gas flow in operating conditions. Various types of gas flow meters are considered, with a description of the quality indicators of the devices. An additional error was investigated depending on changes in operating conditions. The calculations of the relative error of the meter taking into account the limiting values of the additional errors indicated in the technical documentation, as well as calculations taking into account the coefficients of influence under operating conditions. Based on the obtained values of the influence coefficients, graphs were constructed on which the effect of temperature and pressure on the error was determined. The article provides tabular values of the influence coefficients for petroleum gas, a conclusion is drawn on the applicability of this method.Oil and gas industry have a great influence on development of national economy in our country. Oil and gas have a leading position in energy industry and they are more effective and energy-intense in comparison with other natural substances.

Closed-Form Stress Intensity Factor Solutions for Surface Cracks With Large Aspect Ratios in Plates

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Kisaburo Azuma ◽  
Yinsheng Li ◽  
Steven Xu
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form ◽  
Influence Coefficient ◽  
Maximum Point ◽  
Surface Cracks ◽  
Fourth Degree ◽  
Aspect Ratios ◽  
Influence Coefficients

Abstract Alloy 82/182/600, which is used in light-water reactors, is known to be susceptible to stress-corrosion cracking. The depth of some of these cracks may exceed the value of half-length on the surface. Although the stress intensity factor (SIF) for cracks plays an important role in predicting crack propagation and failure, Section XI of the ASME Boiler and Pressure Vessel Code does not provide SIF solutions for such deep cracks. In this study, closed-form SIF solutions for deep surface cracks in plates are discussed using an influence coefficient approach. The stress distribution at the crack location is represented by a fourth-degree-polynomial equation. Tables for influence coefficients obtained by finite element analysis in the previous studies are used for curve fitting. The closed-form solutions for the influence coefficients were developed at the surface point, the deepest point, and the maximum point of a crack with an aspect ratio a/c ranging from 1.0 to 8.0, where a is the crack depth and c is one-half of the crack length. The maximum point of a crack refers to the location on the crack front where the SIF reaches a maximum value.

Recovery Control for Rotors Established in Stable Periodic Contact Modes

2007 ◽  
Author(s):  
Michael Schlotter ◽  
Patrick Keogh
Keyword(s):  
Contact Point ◽  
Contact Dynamics ◽  
Test Facility ◽  
Flexible Rotor ◽  
Disk System ◽  
Flexible Rotors ◽  
Influence Coefficients ◽  
Highly Nonlinear ◽  
Periodic Contact ◽  
Stable Periodic

Previous research has shown that flexible rotors can become established in potentially damaging stable periodic contact modes after initial impact with housings, seals, or auxiliary bearings. These modes are characterized by periodic motion and a fixed contact point in a rotating frame. A contact recovery strategy is developed, with the aim to destabilize the modes and return the rotor to a contact-free orbit. This is achieved by applying compensation forces through magnetic bearings, which reduces the effective synchronous forcing that is causing the contact to a low level. It is shown that even in presence of highly nonlinear contact dynamics, a linear FEM rotor model can be used to calculate appropriate influence coefficients. The contact recovery principle is demonstrated by simulations of a simple disk system and a simple flexible rotor. It is then applied to an experimental flexible rotor test facility. Error margins are investigated, and possible limitations of the method are discussed.

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