Experimental Evaluation of the Exact Point-Speed and Least-Squares Procedures for Flexible Rotor Balancing by the Influence Coefficient Method

1974 ◽  
Vol 96 (2) ◽  
pp. 633-643 ◽  
Author(s):  
J. M. Tessarzik ◽  
R. H. Badgley
Keyword(s):  
Least Squares ◽  
Influence Coefficient ◽  
Critical Speeds ◽  
Flexible Rotors ◽  
Operating Region ◽  
Influence Coefficient Method ◽  
Identical Test ◽  
Slow Passage ◽  
Rotor Balancing ◽  
Exact Point

An experimental test program was conducted to extend the verified operating region of the Influence Coefficient Method’s Exact Point-Speed procedure for balancing of flexible rotating machinery. Also, the Least-Squares procedure (of which the Exact Point-Speed procedure is a particular case) was applied to several test cases which were identical to those investigated by the Exact Point-Speed procedure. A comparison of the effectiveness of both balancing procedures under identical test conditions was thus obtained. The practical aspects of balancing real, flexible rotors were investigated through inclusion of rotor out-of-roundness data at the measurement probe locations. The computer program was demonstrated to be fully capable of handling out-of-roundness data in the investigation. Testing was performed predominantly with a machine having a 41-in. (104 cm) long, 126-lb (57 kg) rotor. This rotor was operated over a speed range encompassing three rotor-bearing system critical speeds. Both balancing procedures were evaluated for several different conditions of initial rotor unbalance. Safe (and slow) passage through all the critical speeds was obtained after two or three balancing runs in most cases. The Least-Squares procedure was found to be generally equivalent in capability to the Exact Point-Speed procedure for the configurations studied.

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.

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.

The Optimization of Balancing Least Squares Influence Coefficient Method Based on Particle Swarm Optimization

2011 ◽  
Vol 105-107 ◽  
pp. 56-61 ◽  
Author(s):  
Xing Xing Wang ◽  
Guo An Yang ◽  
Ya Jun Fan
Keyword(s):  
Particle Swarm Optimization ◽  
Least Squares ◽  
Particle Swarm ◽  
Influence Coefficient ◽  
Residual Vibration ◽  
Swarm Optimization ◽  
Measuring Point ◽  
Influence Coefficient Method ◽  
Rotor Balancing ◽  
Coefficient Method

On the basis of the rotor dynamic balancing theory, the rotor balancing least squares influence coefficient method has been discussed in detail in this paper. In order to solve the problem that the residual vibration in some of the measuring point and the balancing weight are comparatively large in the balance process with least squares influence coefficient method, particle swarm optimization algorithm with cross-factor, which is an improved swarm intelligence algorithm, is introduced into rotor balancing least squares influence coefficient method. Theoretical analysis and numerical examples show that the algorithm has a good convergence, with reducing the balancing weight and residual vibration effectively compared with basic least squares influence coefficient method. The result can achieve better balance effect in the rotor balancing process.

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.

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.

On the Overhung Rigid Rotor Balancing

2000 ◽  
Author(s):  
José A. Méndez-Adriani
Keyword(s):  
Efficient Technique ◽  
Influence Coefficient ◽  
Rigid Rotor ◽  
Cross Effect ◽  
Calibration Process ◽  
The Third ◽  
Influence Coefficient Method ◽  
The Cross ◽  
Rotor Balancing ◽  
Coefficient Method

Abstract This article develops a more efficient technique for the balancing of the overhung rigid rotor, which is a variation of the exact influence coefficient method, that gives directly the correction weights for both balancing planes. During the calibration process, one trial weight is used for the second run and, to reduce the cross effect, only one trial weight to form a couple is used for the third run, improving the field balancing method for maintenance works.

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.

Further Experiments on Balancing of a High-Speed Flexible Rotor

1974 ◽  
Vol 96 (2) ◽  
pp. 431-440 ◽  
Author(s):  
J. Tonnesen
Keyword(s):  
Computer Program ◽  
Least Squares ◽  
High Speed ◽  
Influence Coefficient ◽  
Flexible Rotor ◽  
Minimum Level ◽  
Absolute Level ◽  
Quality Class ◽  
Influence Coefficient Method ◽  
Coefficient Method

The accuracy of the influence coefficient method is experimentally investigated. The influence of the number of measurement transducers, their location, and type is demonstrated on a flexible rotor where simultaneous balancing is performed in up to five planes and passing through three critical speeds. The correction weights are calculated by means of a computer program, based on a least-squares minimizing procedure. The method itself is shown to be accurate and uses only a minimum of balancing runs to reduce the vibrations to a true minimum level. The overall accuracy in determining the unbalance weights is found to be 4.5 percent. The method’s effectiveness is demonstrated on a rotor with four balancing planes and with unbalance distributed at random in six and seven planes. The absolute level of residual vibrations is found to be in the ISO 0.4 quality class [5].

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