A Study of the Modal Truncation Error in the Component Mode Analysis of a Dual-Rotor System

1982 ◽  
Vol 104 (3) ◽  
pp. 525-532 ◽  
Author(s):  
D. F. Li ◽  
E. J. Gunter
Keyword(s):  
Critical Speed ◽  
Truncation Error ◽  
Synthesis Method ◽  
Equation Of Motion ◽  
Mode Analysis ◽  
Turbine Engine ◽  
Generalized Coordinates ◽  
Acceptable Accuracy ◽  
Speed Stability ◽  
Modal Truncation

In the component mode synthesis method, the equation of motion in the generalized coordinates is built upon the undamped eigenvalue data of the component structures. Error is inevitable when truncated modes are used. In this paper, two model truncation schemes were evaluated with regard to the critical speed, stability, and unbalance response of a two-spool gas turbine engine. The numbers of modes required to yield acceptable accuracy in these cases were determined. Guidelines for modal truncation were derived from these results.

Investigation of the Transient Response of a Dual-Rotor System With Intershaft Squeeze Film Damper

1985 ◽  
Author(s):  
Qihan Li ◽  
James F. Hamilton
Keyword(s):  
High Pressure ◽  
Gas Turbine ◽  
Transient Response ◽  
Synthesis Method ◽  
Gas Turbine Engine ◽  
Rotor System ◽  
Squeeze Film ◽  
High Pressure Turbine ◽  
Turbine Engine ◽  
Squeeze Film Damper

A method is presented for calculating the dynamics of a dual-rotor gas turbine engine equipped with a flexible intershaft squeeze-film damper. The method is based on the functional expansion component synthesis method. The transient response of the rotor due to a suddenly applied unbalance in the high-pressure turbine under different steady-speed operations is calculated. The damping effects of the intershaft damper and stability of the rotor system are investigated.

Dynamic Substructuring Based on a Double Modal Analysis

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
S. Besset ◽  
L. Jézéquel
Keyword(s):  
Finite Element Method ◽  
Forthcoming Paper ◽  
Synthesis Methods ◽  
Generalized Coordinates ◽  
Multimodal Analysis ◽  
Modal Synthesis ◽  
Dynamic Substructuring ◽  
Primal And Dual ◽  
Modal Truncation ◽  
Continuous Formulation

Modal synthesis methods have long been studied because the use of generalized coordinates makes it possible to reduce calculation costs. Our approach uses modes to describe each part of the assembly of several substructures. This method, called “Double Modal Synthesis,” is presented through primal and dual formulations. As modal truncation usually introduces a lack of precision, we will use an ω2 development if necessary. These formulations will first be explained using a continuous formulation. A finite element method will then be proposed. Another aim of the paper is to introduce formulations needed to understand the multimodal analysis methods that will be presented in a forthcoming paper.

Component Mode Synthesis of Large Rotor Systems

1982 ◽  
Vol 104 (3) ◽  
pp. 552-560 ◽  
Author(s):  
D. F. Li ◽  
E. J. Gunter
Keyword(s):  
Space Shuttle ◽  
Synthesis Method ◽  
Component Mode Synthesis ◽  
Squeeze Film ◽  
Response Analysis ◽  
Turbine Engine ◽  
Modal Expansion ◽  
Rotor Systems ◽  
Mode Method ◽  
Modal Equation

A scheme is presented for calculating the vibrations of large multi-component flexible rotor systems based on the component mode synthesis method. It is shown that, by a modal expansion of the elastic interconnecting elements, the system modal equation can be conveniently constructed from the undamped eigen representations of the component subsystems. The capability of the component mode method is demonstrated in two examples: a transient simulation of a two-spool gas turbine engine equipped with a squeeze-film damper; and an unbalance response analysis of the Space Shuttle Main Engine oxygen turbopump in which the dynamics of the rotor and the housing are both considered.

Circular Saw Vibration Control by Induction of Thermal Membrane Stresses

1981 ◽  
Vol 103 (1) ◽  
pp. 81-89 ◽  
Author(s):  
C. D. Mote ◽  
G. S. Schajer ◽  
S. Holo̸yen
Keyword(s):  
Vibration Control ◽  
Induction Heating ◽  
Transverse Vibration ◽  
Critical Speed ◽  
Dimensional Accuracy ◽  
Optimal Temperature ◽  
Blade Vibration ◽  
Circular Saw ◽  
Speed Stability ◽  
Circular Saws

Circular saw transverse vibration and product dimensional accuracy were measured during a series of production experiments in which sawblade vibration was controlled by the deliberate introduction of thermal membrane stresses. Induction heating near the saw collar was used to control the temperature difference between two concentric annular zones on the sawblade surface. Optimal temperature conditions were predicted using the critical speed stability theory for symmetrical circular saws and these predictions were verified through production experiments. Feedback control of sawblade temperature was successfully demonstrated in production as a means of reducing blade vibration and improving dimensional accuracy.

scholarly journals Error Caused by Damping Formulating in Multiple Support Excitation Problems

2020 ◽  
Vol 10 (22) ◽  
pp. 8180
Author(s):  
Han Qin ◽  
Luyu Li
Keyword(s):  
Numerical Simulation ◽  
Spectral Analysis ◽  
Truncation Error ◽  
Equation Of Motion ◽  
Rayleigh Damping ◽  
Modal Damping ◽  
Multiple Support ◽  
Support Excitation ◽  
Large Mass Method ◽  
Bridge Models

The effect of multiple support excitation is an important issue in studying large-span structures. Researchers have shown that the damping related terms in the equation of motion can induce errors in the analysis. Wrongly modelling the damping matrix can induce false damping forces between the structure and the reference coordinates. In multiple support excitation problems, this error is increased when absolute coordinates are used. In this paper, this part of the error is defined as virtual damping error. The error caused by using Rayleigh damping instead of Modal damping is called damping truncation error. This study focuses on the virtual damping error and the damping truncation error that exist in the modeling methods widely used in multiple support excitation problems, namely, large mass method (LMM), relative motion method (RMM), and absolute displacement method (ADM). A new Rayleigh damping formula is proposed for LMM to prevent virtual damping error. A form of equation of motion derived from the converged LMM was proposed in the authors’ previous work. This equation of motion is proved in this paper to be equivalent to RMM when modal damping and the new Rayleigh damping formula are used. RMM is proved free from the virtual damping error. The influence of multiple support excitation effect on the damping formulating errors is studied by spectral analysis. One simplified spring-mass model and two bridge models are used for numerical simulation. The results from the numerical simulation testify to the conclusions from the spectral analysis.

Small Gas Turbine Engine Operating With High-Temperature Foil Bearings

2006 ◽  
Author(s):  
Hooshang Heshmat ◽  
Michael J. Tomaszewski ◽  
James F. Walton
Keyword(s):  
High Temperature ◽  
Gas Turbine ◽  
Critical Speed ◽  
Ball Bearing ◽  
Gas Turbine Engine ◽  
System Stability ◽  
Exhaust Gas ◽  
Turbine Engine ◽  
Foil Bearing ◽  
Bearing Life

A 134 Newton thrust class, 120,000 rpm turbojet was redesigned to incorporate a high-temperature compliant foil bearing aft of the turbine rotor and a compliantly mounted ball bearing forward of the centrifugal compressor–cold section. Two rotor-bearing system configurations were evaluated, one for operation above the bending critical speed and one for rigid rotor operation. Required characteristics for the foil bearing and ball bearing equipped with compliant foil damper mount were determined through a series of design tradeoff studies evaluating critical speeds and system stability. Following the design studies, the necessary hardware was fabricated, the engine assembled and operation to full speed achieved. Engine speed, rotor vibrations, compressor discharge pressure, exhaust gas temperature, thrust and fuel consumption were all recorded for both a baseline fluid lubricated ball bearing supported engine and the new turbojet engine using the hybrid foil bearing support system. Issues related to high-speed operation above the bending critical speed are identified and recommendations offered. Engine test data show that approximately 10% less fuel is consumed by the hybrid foil bearing mount system than the baseline conventional design. It is also shown that the foil bearing life was longer than the ball bearing life even though the foil bearing operated in the exhaust gas stream at temperatures exceeding 800°C. The results of this program demonstrate the feasibility of developing a completely oil-free foil bearing gas turbine engine.

Component Modal Synthesis Methods Based on Hybrid Models, Part I: Theory of Hybrid Models and Modal Truncation Methods

1994 ◽  
Vol 61 (1) ◽  
pp. 100-108 ◽  
Author(s):  
L. Jezequel ◽  
H. D. Seito
Keyword(s):  
Synthesis Method ◽  
Integral Operators ◽  
Hybrid Models ◽  
Force Distribution ◽  
Synthesis Methods ◽  
Displacement Distribution ◽  
New Methods ◽  
Modal Synthesis ◽  
Intermediate Problem ◽  
Modal Truncation

The assembly of structures along continuous boundaries poses great difficulties for expressing generalized boundary coordinates in modal synthesis, especially in the context of experiments. In order to solve such problems, a hybrid modal synthesis method is proposed in this study. This approach is based on the intermediate problem theory of Weinstein and brings out the duality between the formulation in displacement and the formulation in force. Generalized boundary coordinates are defined by introducing static deformations resulting from force distribution or displacement distribution along the boundaries depending on which formulation is to be used. By introducing integral operators associated with intermediate problems, two new methods of modal truncation can be proposed.

Sign in / Sign up

Export Citation Format

Share Document