Effect of Residual Shaft Bow on Unbalance Response and Balancing of a Single Mass Flexible Rotor—Part I: Unbalance Response

1976 ◽  
Vol 98 (2) ◽  
pp. 171-181 ◽  
Author(s):  
J. C. Nicholas ◽  
E. J. Gunter ◽  
P. E. Allaire
Keyword(s):  
Phase Angle ◽  
Response Speed ◽  
Rotor Speed ◽  
Flexible Rotor ◽  
Simple Method ◽  
Unbalance Response ◽  
Single Mass ◽  
Reverse Situation ◽  
Rigid Supports ◽  
Timing Mark

The effect of residual shaft bow on the unbalance response of a single mass rotor on rigid supports has been examined with a theoretical analysis. The analysis determined the amplitude, phase angle, and peak rotor response speed for various combinations of residual bow and unbalance. For most combinations the phase angle corresponding to the peak rotor response speed was significantly different from the 90 degrees observed in the conventional unbowed rotor. If the residual bow and unbalance were exactly out of phase, the rotor amplitude was zero for a rotor speed equal to the square root of the ratio of residual bow amplitude to unbalance eccentricity. The results of the study suggested a simple method for determining the relative amplitudes of residual bow and unbalance eccentricity based upon the motion of a timing mark on an oscilliscope screen. If the residual bow was less than the unbalance eccentricity, the timing mark moved first in the direction of rotor rotation as the speed is increased and then moved in the opposite direction at a speed less than the critical speed. In the reverse situation, the timing mark moved opposite to the direction of rotation as the speed is increased. At some speed above the critical, it reversed direction. Part II of this paper presents theoretical and experimental results for balancing of a single mass rotor with a residual bow.

Iterative Determination of Squeeze Film Damper Eccentricity for Flexible Rotor Systems

1982 ◽  
Vol 104 (2) ◽  
pp. 334-338 ◽  
Author(s):  
L. M. Greenhill ◽  
H. D. Nelson
Keyword(s):  
System Analysis ◽  
Squeeze Film ◽  
Flexible Rotor ◽  
Rotor Systems ◽  
Root Finding ◽  
Unbalance Response ◽  
Rotor Bearing ◽  
Single Mass ◽  
Stiffness And Damping ◽  
Film Stiffness

A method is presented to determine the eccentricity of multiple squeeze film dampers used in multishaft rotor bearing unbalance response analyses. The procedure is iterative and is based upon the secant root finding algorithm. Unbalance response is calculated using the iteratively determined eccentricity in closed form expressions of squeeze film stiffness and damping coefficients, for either long or short bearing theory. Circular centered synchronous operation is assumed. The method is demonstrated by determining the response of a single mass centrally preloaded rotor, a multimass flexible rotor supported by two squeeze films, and a multishaft flexible rotor system employing three squeeze film supports. The results obtained in the flexible rotor analysis are compared to test data, with the correlation found to be good. Due to rapid convergence and multiple squeeze film capability, the procedure is particularly suited to large multishaft flexible rotor-bearing system analysis.

Unbalance Response of an Elastic Rotor in Damped Flexible Bearings at Supercritical Speeds

1971 ◽  
Vol 93 (2) ◽  
pp. 265-275 ◽  
Author(s):  
Neville F. Rieger
Keyword(s):  
Critical Speed ◽  
Mode Shapes ◽  
Rotor Speed ◽  
Flexible Rotor ◽  
Relative Stiffness ◽  
Unbalance Response ◽  
Fluid Film Bearings ◽  
Transmitted Force ◽  
Rotor Mass ◽  
Bearing System

The unbalance response of a uniform flexible rotor in fluid-film bearings has been analyzed for speeds up to 20 times the lowest rigid-bearing critical speed. Rotor mass and elasticity are distributed uniformly along the length of the rotor. A single radial speed-dependent force is used to represent the rotor unbalance. The rotor is assumed to operate in stable plain cylindrical bearings which are represented by direct and cross-coupled spring and damping forces. The influence of rotor speed, bearing operating eccentricity, relative stiffness of rotor and bearings, and unbalance location along rotor on the performance of the rotor-bearing system has been determined. Results are presented as charts of rotor maximum whirl amplitude and of bearing maximum whirl transmitted force for wide ranges of the foregoing parameters. Mode shapes at critical speeds are also included.

Identification of Bearing Force Coefficients From Measurements of Imbalance Response of a Flexible Rotor

2004 ◽  
Author(s):  
Luis San Andre´s ◽  
Oscar C. De Santiago
Keyword(s):  
High Performance ◽  
Fluid Film ◽  
Flexible Rotor ◽  
Simple Method ◽  
Force Coefficients ◽  
Fluid Film Bearings ◽  
Support Force ◽  
Bearing Force ◽  
Rotor Structure ◽  
Motion Amplitude

Field identification of fluid film bearing parameters is critical for adequate interpretation of rotating machinery performance and necessary to validate or calibrate predictions from restrictive computational fluid film bearing models. This paper presents a simple method for estimating bearing support force coefficients in flexible rotor-bearing systems. The method requires two independent tests with known mass imbalance distributions and the measurement of the rotor motion (amplitude and phase) at locations close to the supports. The procedure relies on the modeling of the rotor structure and finds the bearing transmitted forces as a function of observable quantities (rotor vibrations at bearing locations). Imbalance response measurements conducted with a two-disk flexible rotor supported on two-lobe fluid film bearings allow validation of the identification method estimations. Predicted (linearized) bearing force coefficients agree reasonably well with the parameters derived from the test data. The method advanced neither adds mathematical complexity nor requires additional instrumentation beyond that already available in most high performance turbomachinery.

Method of Judging the Energy Measurement Device Error Wiring Based on Checking Tables

2010 ◽  
Vol 139-141 ◽  
pp. 2247-2251
Author(s):  
Xing Zhong Zhang
Keyword(s):  
Phase Angle ◽  
Energy Measurement ◽  
Test Results ◽  
Measurement Device ◽  
Electric Parameter ◽  
Simple Method ◽  
Line Voltage ◽  
Three Phase ◽  
Working Efficiency

Focused on the complexity and Time-consuming of judging the error wiring of the energy measurement device, It extracts a series of electric parameter tables including phase angle table, such as the voltage sequence table, the line voltage location table, phase angle transform table, and phase angle table. And proposes a simple method of judging the error wiring of Three-phase three-wire error wiring of two components energy measurement device. The method based only on the four tables, inspectors only need to look-up the tables in accordance with the measured dates and get the error wiring instead of drawing vector plots. Because these tables root from vector plots. It greatly simplifies inspectors to judge wiring mistake, improves the working efficiency and makes the test results more accurate.

Performance of Quiet Helicopter

2020 ◽  
Vol 2020 (1) ◽  
pp. 1-17
Author(s):  
Jarosław Stanisławski
Keyword(s):  
Equations Of Motion ◽  
Rotor Blades ◽  
Main Rotor ◽  
Rotor Speed ◽  
Flexible Rotor ◽  
Slowing Down ◽  
Helicopter Flight ◽  
Operational Envelope ◽  
The Galerkin Method ◽  
Lower Limits

AbstractNoise generated by helicopters is one of the main problems associated with the operation of rotorcrafts. Requirements for reduction of helicopter noise were reflected in the regulations introducing lower limits of acceptable rotorcraft noise. A significant source of noise generated by helicopters are the main rotor and tail rotor blades. Radical noise reduction can be obtained by slowing down the blade tips speed of main and tail rotors. Reducing the rotational speed of the blades may decrease rotor thrust and diminish helicopter performance. The problem can be solved by attaching more blades to main rotor. The paper presents results of calculation regarding improvement of the helicopter performance which can be achieved for reduced rotor speed but with increased number of rotor blades. The calculations were performed for data of hypothetical light helicopter. Results of simulation include rotor loads and blade deformations in chosen flight conditions. Equations of motion of flexible rotor blades were solved using the Galerkin method which takes into account selected eigen modes of the blades. The simulation analyzes can help to determine the performance and loads of a quiet helicopter with reduced rotor speed within the operational envelope of helicopter flight states.

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