Unbalance Vibration Research Articles

Automation of low-frequency unbalanced vibration modules

The problem of the automation of low-frequency unbalanced vibration modules is studied. The aspects of this problem which are covered in this paper are the calculation of the power of the drive for rotation of unbalanced masses of a centrifugal vibrator module, an analysis of the rigidity of the pneumatic matching device, and optimization of operating conditions of the electric drive for rotation of unbalanced masses. Control algorithms are formulated which optimize the operation of an electric drive rotating unbalanced masses. These algorithms can be implemented with standard computational technology or a digital computer.

Rotational Ratio Response Analysis of Flexible Rotor Vibrating System

In this study, a new method is developed for analysing rotor vibration due to harmonic excitation, in particular, to excitation with frequency multiple of rotational speed, with aim at a computer aided designing for unbalance vibration. vibration due to balls or blades passing. and so on. This new technique, developed by expaning the concept of quasi-modal transformation. is more applicable than the usual modal one. The quasi-modal transformation is characterized by mode synthesis of the following two mode shapes. One is a mode shape obtained by undamped critical speed analysis of rotor shafting restricted at its bearing points. The other is a deflection mode shape caused by forced displacement on the bearing points. Only this new method is effective especially to the analysis of harmonic vibration response of rotor with multi-level shafting. The effectiveness is demonstrated by a 3-disc rotor, and an X-ray tube unitincluding a casing.

Method of Determining Locations of Unbalances in Rotating Machines

This paper presents a method of determining the locations of unbalances on a rotor when the unbalances occur abruptly during rotor running. The method makes use of journal vibrations, because, generally, there is a relation between the locations of unbalances and the unbalance vibration modes of a rotor. At critical speeds, where this relation is particularly significant, the phase angle of an unbalance vibration shifts 90 deg, and unbalance distributions excite vibration modes. Which mode or modes is excited depends on the location of an unbalance on a rotor. In this paper, a rotor is assumed to be divided lengthwise into three sections on which unbalances are assumed to be distributed. A simple algorithm, which is derived from the characteristics of the foregoing vibrations and assumptions, allows four unbalance distributions to be determined on a rotor, at the center, on the either side (right or left side), on the right and left sides (out of phase), and on the right and left sides (in phase) of a rotor.

Q-Factor Analysis of Unbalance Vibration in Rotor-Bearing Systems

Q-factor is usually a pratical means for predicting maximum amplitude at critical speeds. However, it is not accurate in the case of systems with strong gyroscopic effect, large damping coefficients and asymmetric properties in bearing dynamics. In this study these problems are solved through a new definition of the Q-factor. The unbalance vibration is formulated at each damped critical speed, based upon orthogonality of the undamped critical speed mode, and rearranged by the equation derived from the corresponding damped eigenvalues. The result proves that Q-factor and damped critical speed Ωc are not functions of only modal damping ratio ζ, but also vary with gyroscopic factor γ which is the ratio of modal gyro per modal mass, as follows. [numerical formula1] [numerical formula2] [numerical formula3] The new definition is characterized by value γ reflecting the gyroscopic effect in the system. The value γ=0 is an old and incorrect definition as it does not consider gyroscopic effect. To demonstrate the validity of the method, numerical examples are shown for a 3-disk rotor supported with symmetric and tilting pad type bearings.

Balancing of a Flexible Rotor : 7th Report, In Case of a Rotor Supported by Members Having any Mechanical Impedances

Unbalanced vibration and way of balancing of a flexible rotor supported at its both ends by members having any mechanical impedances are studied theoretically by aids of 'forced mode' method, and the results are further verified by experiments. Following facts are revealed and confirmed. (1) Vibration of the system can be expressed theoretically in a serial form, consisting of two parts of different natures. The one is the term influenced by dynamic character of the supports and the other coincides with that of 'simply supported' (i.e. supported by pinned-pinned ends) rotor. (2) If the rotor is balanced in 'simply supported' modes combined with dynamic balancing, the state of balance is maintained on any other supports having different mechanical impedances. (3) The rotor can be satisfactorily balanced only by measuring the vibration of the shaft and bearings at a speed, without knowing mechanical properties of the supports.

Balancing of a Flexible Rotor : 5th Report, Vibration and Balancing of a Flexible Rotor on Flexible Bearing with Viscous Damping

Unbalanced vibration of a flexible rotor supported on two bearings is analysed in this paper for the case of flexible support with viscous damping. The analytical solution is obtained by using the concept of "forced mode", which makes the vibration phenomena for the system in consideration more understandable than before. Based on this solution, the condition as well as a possible procedure to balance such a rotor is theoretically demonstrated, conclusions of which are: (i) It is possible to obtain the universal state (in a practical sense) of balance of a flexible rotor which is satisfactory irrespective of its bearing properties, the magnitude of elasticity and viscous damping, through dynamic balancing and modal balancing of the rotor for the simply supported end condition, and (ii) this can be successfully be achieved by measuring shaft vibration of the rotor on flexible bearing with viscous damping.

Analysis of Lateral Vibration Characteristics of Rotating Shafts with Flexible and Axi-asymmetric Bearings

A method is presented to calculate the unbalance vibration behaviours using transfer matrix method in which such factors related to the vibration are covered as the interaction characteristics of load displacement between horizontal and vertical directions at oil film bearings, the dynamic stiffness of bearing support structures, etc. In case of the rotor systems with multi-spans, the numerical accuracy is occasionally deteriorated when number of sections, number of bearings and rotating speed exceed a certain boundary as far as the conventional method is applied. The authors developed a method to suppress the propagation of the error by modifying the procedure of matrix operations and solving the simultaneous linear equations at the last step of the computation works.

二軸ファン・ジェット・エンジンの不つりあい振動

In the previous report (ref. 2), it was cleared that the unbalance vibration of single spool turbo-jet engines and vibration damping effect of the squeeze film damper bearing can be estimated accurately enough for design purpose, by the theoretical calculation.Following these results, calculations of unbalance vibration of typical 2 models of 2 spool fan-jet engine were made, considering different rotational speeds of rotors.The results of the calculation show that-(1) Medium to large size 2 spool fan-jet engines have many resonance frequencies in their speed ranges, and at some speeds and at some positions, amplitude of vibration will exceed critical value, in the case of no damper bearing.(2) In the most cases, amplitude of vibration at the critical speeds can be suppressed to safe value, by using one or two damper bearing (s) at the adequate position (s).

単軸ジェット・エンジンの不つりあい振動とダンパ軸受によるその防止

Experiments and theoretical analysis were made on the unbalance vibration of the single spool turbo-jet engine JR 200 and of its simplified model which simulated vibration characteristics of the engine.The results of theoretical analysis by the method of transfer matrix agree well with the experimental results in the case of simplified model.In the case of JR 200 engine which has rather small length/diameter ratio, agreement of theoretical values with experimental values are not so good as in the case of the model. However, this, theoretical analysis is considered to be useful for estimating and improving vibration characteristics of a new engine, in the early stage of development.By the experiments on the model with and without squeeze film damper bearing, it is proved that the damper of this type is very effective to reduce vibration severity at the critical speeds.

Unbalance Vibration of a Rotor-Bearing System Supported by Floating-Ring Journal Bearings

This paper presents an analytical solution for floating-ring journal bearing and a theretical analysis of unbalance vibration of a rotor-bearing system. Theoretical solutions for fluid film force, friction coefficient and stifness and damping coefficients are derived. The effect of a floating-ring journal bearing on unbalance vibrations of a symmetrical rotor-bearing system and some design recommendations for optimum bearing dimensions are discussed.

浮動ブシュ軸受でささえられた回転軸系の不つりあい振動

浮動ブシュ軸受でささえられた回転軸系の不つりあい振動

Analysis of Unbalance Vibration of Rotating Shaft System with Many Bearings and Disks

A method is presented for calculating the unbalance vibration of a rotating shaft system consisting of variable cross sections, disks, journal bearings and unbalances. Property of oil film bearing is assumed to be that of the springs and dampers including those which give resistance to the change of inclination angles and velocities of inclination angles. These latter springs or dampers will be called springs or dampers. These coefficients of cylindrical journal bearings are derived from the short bearing approximation. It is concluded that the property of rotational springs and dampers of oil film in the bearing cannot be neglected, and that the calculated results obtained by means of this method agree very well with most of the experimental results for the case of rotating shaft systems with two or three cylindrical journal bearings, that of an overhung shaft system, and that of a shaft system with distortion.

多軸受多円板回転軸系の不つりあい振動の解析(<小特集>回転機械の振動)

多軸受多円板回転軸系の不つりあい振動の解析(<小特集>回転機械の振動)

Calculations and Experiments on the Unbalance Response of a Flexible Rotor

The results of a combined analytical and experimental investigation of the unbalance vibrations of a rotor are presented. The analysis applies to a general rotor-bearing system in which the dynamic bearing forces are represented by four spring coefficients and four damping coefficients. The rotor can be represented as either a lumped or a distributed parameter system, and gyroscopic moments are included. In general, the unbalance whirl motion of the rotor will be elliptical. The analysis has been programmed for a digital computer to obtain results for comparison with the experimental data. The test rotor is a uniform, flexible shaft with heavy wheels mounted at the ends and in the middle. The rotor is supported in two silicone fluid-lubricated, tilting-pad bearings. The rotor amplitude caused by an induced unbalance has been measured over a speed range of 3000 to 24,000 rpm for three different rotor configurations, obtained by removing one or both end wheels. This speed range extends to or through the third critical speed for each of the rotor configurations. The results are compared with the theoretical values and, in general, the agreement is found to be good.

On the Vibration of a Rotating Shaft Supported by Journal Bearings : 1st Report, Unbalance Vibration

The unbalance vibration of a rotating shaft supported by cylindrical journal bearings is reported in this paper. Elastic and damping properties of oil-film bearings of finite length are obtained using a digital computer from Reynolds equation for two dimensional flow with squeezefilm effect. These properties play a very important role in limiting the vibration amplitude to a small value and in reduction of the critical speeds. Elastic and damping properties of oil-film have nonlinear characteristics, and if their non-linearity is neglected in the calculation, the unbalance vibration may result in by far larger amplitude at resonance than the actual case, unless the static displacement of the journal center from the bearing center it large in comparison with the amplitude of the journal center. If the nonlinear characteristics are taken into consideration, the vibrational behavior will be estimated in good approximation to experimental results.

Some dynamic properties of oil-film journal bearings with reference to the unbalance vibration of rotors : A. C. Hagg and G. O. Sankey. Journal ofapplied mechanics, v. 23, June 1956, p. 302–306

Some dynamic properties of oil-film journal bearings with reference to the unbalance vibration of rotors : A. C. Hagg and G. O. Sankey. Journal ofapplied mechanics, v. 23, June 1956, p. 302–306

Closure to “Discussions of ‘Some Dynamic Properties of Oil-Film Journal Bearings With Reference to the Unbalance Vibration of Rotors’” (1957, ASME J. Appl. Mech., 24, pp. 158–159)

Closure to “Discussions of ‘Some Dynamic Properties of Oil-Film Journal Bearings With Reference to the Unbalance Vibration of Rotors’” (1957, ASME J. Appl. Mech., 24, pp. 158–159)

Some Dynamic Properties of Oil-Film Journal Bearings With Reference to the Unbalance Vibration of Rotors

Abstract Some dynamic properties of oil films have been determined experimentally and their significance in the problem of unbalance vibration and critical speeds of rotor systems is illustrated by an example. It is shown that oil films have an important role in the imbalance-vibration behavior of rotor systems, particularly the vibration magnification at resonance.