Application of the Principle of Reciprocity to Flexible Rotor Balancing

1982 ◽  
Vol 104 (2) ◽  
pp. 329-333 ◽  
Author(s):  
M. S. Darlow ◽  
A. J. Smalley
Keyword(s):  
Numerical Study ◽  
Influence Coefficient ◽  
Theoretical Discussion ◽  
Vibration Level ◽  
Flexible Rotor ◽  
Stabilization Time ◽  
Vibration Sensors ◽  
Start Up ◽  
Desirable Feature ◽  
Rotor Balancing

The least desirable feature of most flexible rotor balancing procedures is the considerable number of trial mass runs required. This is of particular importance in the balancing of machines which require a substantial stabilization time during start-up. Using an adaptation of the principle of reciprocity, it is possible to significantly reduce the required number of trial mass runs for certain rotors when using either influence coefficient balancing or the Unified Balancing Approach. When applied to flexible rotor balancing, the principle of reciprocity states that, given two rotor axial locations, A and B (at which both balancing planes and vibration sensors are located), the influence coefficient relating the vibration level at A to the unbalance at B is identical to that relating the vibration level at B to the unbalance at A. This is true even in the presence of damping. This paper begins with a theoretical discussion of the principle of reciprocity and its application to flexible rotor balancing. The particular means by which reciprocity can be applied to improve the influence coefficient and Unified Balancing Approach procedures are then described in detail. A numerical study was conducted to verify this application of reciprocity, as well as to investigate any possible limitations. The results of this study are reported along with those of a similar experimental study using two substantially different test rotors.

Demonstration of a Unified Approach to the Balancing of Flexible Rotors

1981 ◽  
Vol 103 (1) ◽  
pp. 101-107 ◽  
Author(s):  
M. S. Darlow ◽  
A. J. Smalley ◽  
A. G. Parkinson
Keyword(s):  
Power Transmission ◽  
Substantial Reduction ◽  
Influence Coefficient ◽  
Flexible Rotor ◽  
Unified Approach ◽  
Test Rig ◽  
Multiple Mode ◽  
Flexible Rotors ◽  
Transmission Shaft ◽  
Rotor Balancing

A flexible rotor balancing procedure, which incorporates the advantages and eliminates the disadvantages of the modal and influence coefficient procedures, has been developed and implemented. This new procedure, referred to as the Unified Balancing Approach, has been demonstrated on a supercritical power transmission shaft test rig. The test rig was successfully balanced through four flexural critical speeds with a substantial reduction in effort as compared with the effort required in modal and influence coefficient balancing procedures. A brief discussion of the Unified Balancing Approach and its relationship to the modal and influence coefficient methods is presented. A series of tests which were performed to evaluate the effectiveness of various balancing techniques are described. The results of the Unified Balancing Approach tests are presented and discussed. These results confirm the superiority of this balancing procedure for the supercritical shaft test rig in particular and for multiple-mode balancing in general.

Experimental Evaluation of Multiplane-Multispeed Rotor Balancing Through Multiple Critical Speeds

1976 ◽  
Vol 98 (3) ◽  
pp. 988-998 ◽  
Author(s):  
J. M. Tessarzik ◽  
R. H. Badgley ◽  
D. P. Fleming
Keyword(s):  
Experimental Tests ◽  
Influence Coefficient ◽  
Critical Speeds ◽  
Vibration Data ◽  
Vibration Sensors ◽  
Flexible Rotors ◽  
Speed Range ◽  
Full Speed ◽  
Influence Coefficient Method ◽  
Rotor Balancing

Experimental tests have been conducted to further demonstrate the ability of the Influence Coefficient Method to achieve precise balance of flexible rotors of virtually any design for operation through virtually any speed range. Four distinct practical aspects of flexible-rotor balancing were investigated in the present work: (1) Balancing for operation through multiple bending critical speeds; (2) balancing of rotors mounted in both rigid and flexible bearing supports, the latter having significantly different stiffnesses in the horizontal and vertical directions so as to cause severe ellipticity in the vibration orbits; (3) balancing of rotors with various amounts of measured vibration response information (e.g., numbers of vibration data sets, and numbers and types of vibration sensors), and with different number of correction planes; (4) balancing of rotors with different (though arbitrary) initial unbalance configurations. Tests were made on a laboratory quality machine having a 122-cm (48-in.) long rotor weighing 50 kg (110 lb) and covering a speed range up to 18,000 rpm. The balancing method was found in every instance to be effective, practical, and economical, permitting safe rotor operation over the full speed range covering four rotor bending critical speeds.

Flexible rotor balancing without trial runs using experimentally tuned FE based rotor model

2021 ◽  
Vol 21 (1) ◽  
pp. 20-26
Author(s):  
Yahya Muhammed Ameen ◽  
Jaafar Khalaf Ali
Keyword(s):  
Mode Shapes ◽  
Influence Coefficient ◽  
Flexible Rotor ◽  
Rotating Disks ◽  
Finite Elements Analysis ◽  
Response Data ◽  
Flexible Rotors ◽  
Low Efficiency ◽  
Rotor Balancing ◽  
Rotor Model

A method based on experimentally calibrated rotor model is proposed in this work for unbalance identification of flexible rotors without trial runs. Influence coefficient balancing method especially when applied to flexible rotors is disadvantaged by its low efficiency and lengthy procedure, whilst the proposed method has the advantage of being efficient, applicable to multi-operating spin speeds and do not need trial runs. An accurate model for the rotor and its supports based on rotordynamics and finite elements analysis combined with experimental modal analysis, is produced to identify the unbalance distribution on the rotor. To create digital model of the rotor, frequency response functions (FRFs) are determined from excitation and response data, and then modal parameters (natural frequencies and mode shapes) are extracted and compared with experimental analogies. Unbalance response is measured traditionally on rotor supports, in this work the response measured from rotating disks instead. The obtained results show that the proposed approach provides an effective alternative in rotor balancing. Increasing the number of balancing disks on balancing quality is investigated as well.

scholarly journals In Situ Balancing of Flexible Rotors Using Influence Coefficient Balancing and the Unified Balancing Approach

1983 ◽  
Author(s):  
Mark S. Darlow
Keyword(s):  
Subsequent Development ◽  
Commercial Application ◽  
Influence Coefficient ◽  
Production Operation ◽  
Steam Turbines ◽  
Flexible Rotor ◽  
Large Computer ◽  
Flexible Rotors ◽  
Rotor Balancing

A number of sophisticated procedures for balancing flexible rotors have been developed during the past two decades. For a variety of reasons, none of these methods has gained general acceptance by practicing balancing engineers. Several of these balancing techniques require a great deal of operator insight and expertise. This has tended to discourage many potential users where this expertise was not already available in-house, particularly where balancing is required as a production operation. In other cases (for example large steam turbines), the machinery owner has had to rely on the manufacturer to provide this balancing expertise when it is needed often resulting in excessive downtime and maintenance costs. Other balancing methods have been developed which are more systematic so as to reduce the level of expertise required of the user. Unfortunately, these methods have invariably required the collection of large quantities of data and very complex computations. Thus, originally, this data was taken by hand and transcribed for input to a large computer. The results of the balancing calculations were returned some time later for use by the balancing engineer. Such an operation was clearly not conducive to effective commercial application. With the development of minicomputers, the situation was alleviated to a certain extent through the use of more accessible, and even on-line computers to perform these calculations. However even with these minicomputers, in-place flexible rotor balancing facilities were expensive and inconvenient to assemble, and in situ balancing of flexible rotors was impractical if not impossible. The subsequent development of the microcomputer has made in situ balancing of flexible rotors a possibility. This paper describes a completely portable, microcomputer-based flexible rotor balancing system that uses influence coefficient balancing and the Unified Balancing Approach two of the systematic methods which have been shown to be very effective for balancing flexible rotors. The results of a series of verification tests are also presented.

A Generalized Minmax Influence Coefficient Method for Flexible Rotor Balancing

2005 ◽  
Author(s):  
Costin Untaroiu ◽  
Paul Allaire
Keyword(s):  
High Speed ◽  
Optimization Problem ◽  
Current Method ◽  
Linear Matrix ◽  
Influence Coefficient ◽  
Flexible Rotor ◽  
Influence Coefficient Method ◽  
Rotor Balancing ◽  
Practical Constraints ◽  
Coefficient Method

Rotor balancing is a requirement for the smooth operation of high-speed rotating machinery. In field balancing, minimization of the residual vibrations at important locations/speeds under practical constraints is usually a challenging task. In this paper, the generalized minmax coefficient influence method is formulated as an optimization problem with flexible objective functions and constraints. The optimization problem is cast in a Linear Matrix Inequality (LMI) form and a balancing code is developed to solve it. Two balancing examples are run to verify the efficiency and flexibility of the proposed method. Over the existing methods, current method is more flexible for the various requirements encountered in field balancing and can be solved accurate with current mathematical software.

Flexible Rotor Balancing Taking Bearing Non-Linearity Into Account

2001 ◽  
Author(s):  
Peter Y. P. Chen ◽  
Ningsheng Feng ◽  
Eric J. Hahn
Keyword(s):  
Measurement Error ◽  
Field Measurement ◽  
Numerical Experiments ◽  
Measurement Accuracy ◽  
Identification Accuracy ◽  
Influence Coefficient ◽  
Flexible Rotor ◽  
True Solution ◽  
Linear Approach ◽  
Rotor Balancing

Abstract This paper outlines a balancing method for non-linear rotor bearing systems with hydrodynamic bearings which utilises the unbalance response measured at a discrete number of measurement planes at a select number of speeds, as during a single rundown. Numerical experiments confirm that provided the system has been modelled correctly, the unbalance distribution is identified more accurately than by using the influence coefficient approach which assumes system linearity and increasingly so as the response orbits at the bearing increase. The identification accuracy is sensitive to measurement error, and if measurements are limited to field measurement accuracy of two digits, it is necessary to apply constraints, determined with the help of the linear approach, or otherwise reduce the number of unknown unbalances relative to the number of measurements, to extract the true solution.

Flexible Rotor Balancing by the Exact Point-Speed Influence Coefficient Method

1972 ◽  
Vol 94 (1) ◽  
pp. 148-158 ◽  
Author(s):  
J. M. Tessarzik ◽  
R. H. Badgley ◽  
W. J. Anderson
Keyword(s):  
Influence Coefficient ◽  
Flexible Rotor ◽  
Critical Speeds ◽  
Angle Measurements ◽  
Flexible Rotors ◽  
Speed Range ◽  
Influence Coefficient Method ◽  
Rotor Balancing ◽  
Exact Point ◽  
Coefficient Method

A test program was conducted to confirm experimentally the validity of the exact point-speed influence coefficient method for balancing rotating machinery, and to assess the practical aspects of applying the method to flexible rotors. Testing was performed with a machine having a 41-in. long, 126-lb rotor. The rotor was operated over a speed range encompassing three rotor-bearing system critical speeds: two “rigid-body” criticals and one flexural critical. Rotor damping at the flexural critical was very low due to the journal bearings being located at the nodal points of the shaft. The balancing method was evaluated for three different conditions of initial rotor unbalance. The method was found to be effective and practical. Safe passage through all the critical speeds was obtained after a reasonable number of balancing runs. Success of the balancing method was, in large part, due to the accuracy of the instrumentation system used to obtain phase-angle measurements during the balancing procedure.

Modal Balancing of Quasi-Rigid Jet Engine Rotors With Exchangeable Rotor Modules

1995 ◽  
Author(s):  
Hatto Schneider
Keyword(s):  
Flexible Rotor ◽  
Index Procedure ◽  
Jet Engine ◽  
Vibration Problems ◽  
Rotor Balancing ◽  
Rigid Rotors ◽  
Engine Rotors

Abstract Flexible rotor assemblies often consist of two or more rotor modules which are index-balanced against each other with the purpose of eliminating the need for re-balancing if a module should have to be exchanged. However, the index procedure may cause vibration problems because it ignores certain flexible rotor balancing requirements. This paper describes a modal balancing approach based on jet engine rotors which are typically balanced as ISO Class 2 (quasi-rigid) rotors. Appreciation is expressed to Prof. R. Gasch of TU Berlin for his valuable suggestions.

An Investigation in Optimal Locations by Genetic Algorithm for Balancing Flexible Rotor-Bearing Systems

2005 ◽  
Author(s):  
Tsu-Wei Lin ◽  
Yuan Kang ◽  
Chun-Chieh Wang ◽  
Chuan-Wei Chang ◽  
Chih-Pin Chiang
Keyword(s):  
Genetic Algorithm ◽  
Finite Element Method ◽  
Steady State ◽  
Hermitian Matrix ◽  
Influence Coefficient ◽  
Steady State Response ◽  
Flexible Rotor ◽  
The Finite Element Method ◽  
State Response ◽  
Rotor Bearing

This study utilizes genetic algorithm to minimize the condition number of Hermitian matrix of influence coefficient (HMIC) to reduce the computation errors in balancing procedure. Then, the optimal locations of balancing planes and sensors would be obtained as fulfilling optimization. The finite element method is used to determine the steady-state response of flexible rotor-bearing systems. The optimization improves the balancing accuracy, which can be validated by the experiments of balancing a rotor kit.

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