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.

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.

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.

Optimization of LM2500 Gas Generator and Power Turbine Trim Balance Techniques

1991 ◽  
Author(s):  
Bruce D. Thompson
Keyword(s):  
Success Rate ◽  
Maximum Amplitude ◽  
Turbine Rotor ◽  
Theoretical Background ◽  
Influence Coefficient ◽  
Gas Generator ◽  
Imbalance Problem ◽  
Influence Coefficients ◽  
Power Turbine ◽  
Good Set

A procedure has been developed by the U.S. Navy to trim balance, in-place, the gas generator and power turbine rotor of the LM2500 Marine Gas Turbine Engine. This paper presents the theoretical background and the techniques necessary to optimize the procedure to balance the gas generator rotor. Additionally, a method was developed to trim balance LM2500 power turbines. To expand the implementation of both gas generator and power turbine trim balancing, a capability had to be developed to minimize the effort required (trial weight runs etc.). The objective was to able to perform consistently what are called “First Shot” trim balances. “First Shot” trim balances require only one weight placement to bring the engine vibration levels to within the specified goals (less than .002 of an inch maximum amplitude) and that being the final trim weight. It was realized that the Least Squares Influence Coefficient method, even with a good set of averaged influence coefficients, can lead to a number of trial weight experiments before the final trim weights can be placed. The method used to maximize the possibility of obtaining a “First Shot” trim balance was to use modal information to tailor the influence coefficient sets to correct the most predominant and correctable imbalance problem. Since the influence coefficients were tailored, it became necessary to be able to identify, in the initial vibration survey, the type of response a particular LM2500 has. Using modal information obtained from a LM2500 rotor dynamics model and from the early trim balance efforts it was possible to identify the modal response of a given LM2500 and optimize the trim balance of that engine. With these improved techniques a 70% success rate for “First Shot” trim balance has been achieved and the success rate of the trim balance procedure, as a whole, has been near 100%.

scholarly journals A method to select correcting faces of a double-face dynamic balancing rotor

2016 ◽  
Vol 8 (12) ◽  
pp. 168781401668289
Author(s):  
Shihai Zhang ◽  
Zimiao Zhang
Keyword(s):  
Influence Coefficient ◽  
Axial Distribution ◽  
Dynamic Balancing ◽  
The Real ◽  
Influence Coefficients ◽  
Total Phase ◽  
Influence Coefficient Method ◽  
Phase Variations ◽  
Distribution Laws ◽  
Design And Practice

Considering the sensitivity and installing position limitation, the real positions for two correcting faces must be selected first in the process of double-face dynamic balancing design and practice for rigid rotor system. According to the principle of influence coefficient method, series of testing weight experiments are conducted in this article. Based on the experimental results, the axial distribution laws of the amplitudes and phases of influence coefficients are found and summarized as follows: the amplitude variations of influence coefficients are very small and the phase variations of influence coefficients are obvious when the correcting positions are changed along shaft, so the phases of influence coefficients have the key effect on the correcting vector in correcting faces. Based on this fact, the total phase difference maximum method of influence coefficients is proposed to select the real axial positions for correcting faces. The principle of the method is analyzed in theory, and the application effect is tested by double-face dynamic balancing experiments.

The Low Reduced Frequency Limit of Vibrating Airfoils: Part II — Numerical Experiments

2015 ◽  
Author(s):  
Almudena Vega ◽  
Roque Corral
Keyword(s):  
Stokes Equations ◽  
Unsteady Aerodynamics ◽  
Mean Value ◽  
Navier Stokes ◽  
Influence Coefficient ◽  
Navier Stokes Equations ◽  
Unsteady Pressure ◽  
Reduced Frequency ◽  
Influence Coefficients ◽  
Frequency Regime

This paper studies the unsteady aerodynamics of vibrating airfoils in the low reduced frequency regime with special emphasis in its impact on the scaling of the work per cycle curves using an asymptotic approach (Part I) and numerical simulations. A perturbation analysis of the linearized Navier-Stokes equations at low reduced frequency is presented and some conclusions are drawn (Part I of the corresponding paper). The first important result is that the loading of the airfoil plays an essential role in the trends of the phase and modulus of the unsteady pressure field caused by the vibration of the airfoil. For lightly loaded airfoils the unsteady pressure and the influence coefficients scale linearly with the reduced frequency whereas the phase departs from π/2 and changes linearly with the reduced frequency. As a consequence the work-per-cycle is proportional to the reduced frequency for any inter-blade phase angle and it is independent of its sign. For highly loaded airfoils the unsteady pressure modulus is fairly constant exhibiting only a small correction with the reduced frequency, while the phase departs from zero varies linearly with it. In this case only the mean value of the work-per-cycle scales linearly with the reduced frequency. This behavior is independent of the geometry of the airfoil and in first approximation of the mode-shape. For symmetric cascades the work-per-cycle scales linearly with the reduced frequency irrespectively of whether the airfoil is loaded or not. Simulations using a frequency domain linearized Navier-Stokes solver have been carried out on a low-pressure turbine airfoil section, the NACA0012 and NACA65 profiles and a flat plate operating at different flow conditions to show the generality and correctness of the analytical conclusions. Both the traveling-wave and influence coefficient formulations of the problem are used in combination to increase the understanding and explore the nature of the unsteady pressure perturbations.

scholarly journals Analysis of Experimental Time-Dependent Blade Surface Pressures From an Oscillating Turbine Cascade With the Influence-Coefficient Technique

1990 ◽  
Author(s):  
T. H. Fransson
Keyword(s):  
Experimental Data ◽  
Leading Edge ◽  
Travelling Wave ◽  
Time Dependent ◽  
Influence Coefficient ◽  
Blade Surface ◽  
Suction Surface ◽  
Local Flow ◽  
Unsteady Aerodynamic ◽  
Influence Coefficients

A two-dimensional section of the last stage of a steam turbine has been investigated experimentally in an annular non-rotating cascade facility as regards to its steady-state and time-dependent aerodynamic characteristics at design and off-design conditions. The unsteady experimental data obtained with the blades vibrating in the “travelling wave” mode indicate that one of the main reasons for the flutter susceptibility of the cascade lies in the high expansion and following shock wave close to the blade suction surface leading edge and the corresponding high unsteady loading. The decomposition of the experimental data into unsteady aerodynamic influence coefficients validates this conclusion and gives also that another reason for the flutter susceptibility can be found in the fact that the cascade is overlapped for a part of the blade surface where the local flow velocities are close to sonic. The unsteady aerodynamic influence coefficients show that the instability arises because of the time dependent aerodynamic coupling effects between, essentially, the reference blade and its immediate suction surface and, to a lesser extent, pressure surface neighbors.

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