The dissipation coefficient and its application to flexible rotor-bearing system design
TL;DR: In this paper, the authors provide information on the design of journal bearings for use in high speed rotating machinery to minimize the energy dissipation due to the out-of-balance of the flexible rotor.
Abstract: This investigation is an attempt to provide information on the design of journal bearings for use in high speed rotating machinery to minimize the energy dissipation due to the out-of-balance of the flexible rotor. The results are presented in the form of design charts for full journal bearings, where the dissipation coefficient has to be selected to be as small as possible at the operating speed and at the critical speed.
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TL;DR: In this paper, the authors used the continuous wavelet transform (CWT) to extract sub-harmonics from the time domain signals of a rotor system coasting down through its critical speed.
Abstract: A Jeffcott rotor with a transverse crack has been considered in the present study. Equations of motion for transient response have been developed and dynamic analysis has been carried out to consider the effects of fluid film bearings. The coast-down phenomenon was analysed by considering the dissipation through the journal film and by evaluating the deceleration for each speed. Characteristic sub-critical response peaks have been found when the cracked rotor decelerates through its critical speed. The continuous wavelet transform (CWT) has been used as a tool to extract the above sub-harmonics from the time domain signals. The use of CWT has been suggested for crack detection and monitoring in a rotor system coasting down through its critical speed.
22 citations
TL;DR: In this article, a cracked Jeffcott rotor supported on fluid film bearings was analyzed and the authors derived the equations of motion with four degrees of freedom, taking into consideration the flexibility, damping and cross coupling of the fluid film bearing.
Abstract: The equations of motion, with four degrees of freedom, taking into consideration the flexibility, damping and cross coupling of the fluid film bearings are derived for a cracked Jeffcott rotor supported on fluid film bearings. Dimensionless equations are developed for dynamic radial load, dynamic pressure developed in the fluid film bearings and coefficient of dissipation considering the journal vibrations in two harmonics; bearing fluid film stiffness and damping coefficients. These are applied to a cracked Jeffcott rotor supported on different types of bearings, i.e., cylindrical journal bearings, offset cylindrical bearings, tilting pad journal bearings and three-lobe bearings. Based on the allowable dynamic pressure developed in the fluid bearings, the severity of cracked shaft and allowable crack depths are estimated in this study. Measurement of dynamic pressure and dissipation for monitoring the crack growth is suggested. However, 2x vibration is the best indicator of cracks in the shafts. Presente...
7 citations
TL;DR: In this paper, the necessary conditions for backward motion of a Jeffcott rotor supported by identical hydrodynamic journal bearings are investigated, and it is shown that backward motion occurs if and only if the load parameter is greater than a limiting value corresponding to the flexibility parameter.
Abstract: The necessary conditions for backward whirling motion of a Jeffcott rotor supported in identical hydrodynamic journal bearings are investigated in this paper. Backward whirling motion of the rotor centre is shown to occur if and only if the load parameter is greater than a limiting value corresponding to the flexibility parameter. In spite of the backward whirling motion of the rotor centre, the journal centre is shown to orbit only in the forward sense.
5 citations
01 Jul 2000
TL;DR: In this article, the effects of fluid film bearings on cracks in a cracked Jeffcott rotor have been analyzed, in addition to the Q factors and dissipation coefficients of the rotor.
Abstract: Dynamic analysis of a cracked Jeffcott rotor has been carried out, considering the effects of fluid film bearings. Q factors and dissipation coefficients have been evaluated in addition to the harmonic responses of the rotor. The coast down phenomenon was analysed for the effects of crack depth. Sensitivity studies were carried out, considering dissipation, response and the Q factor. Measurement of Q factors of second harmonics, Qx1 and Qy2, has been suggested for crack detection, while measurement of Q factors of first harmonics is recommended for crack monitoring as these proved to be more sensitive to cracks compared with other methods.
5 citations
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TL;DR: In this article, the stiffness and damping coefficients for ideal operating conditions were determined and their reliability ascertained by vibration measurements on high-speed rotors for four practically important journal bearing designs and the significant effects on the static load capacity of the bearing and the stability behavior of the rotor-bearing systems are illustrated and discussed.
Abstract: For four practically important journal bearing designs the stiffness and damping coefficients for ideal operating conditions were determined and their reliability ascertained by vibration measurements on high-speed rotors. The effects of static bearing misalignment, variable lubricant viscosity, inertial forces in the lubricant film and turbulent gap flow were investigated in detail. The significant effects on the static load capacity of the bearing and the stability behaviour of the rotor-bearing systems are illustrated and discussed.
56 citations
TL;DR: In this paper, a parametric study of the unbalance response is carried out to show the influence of bearing parameters on the response and to demonstrate the merits of applying optimization techniques in bearing design.
Abstract: Optimization techniques are employed to design hydrodynamic bearings for minimum unbalance response of rotors in synchronous whirl. The analysis for the unbalance response considers the effects of direct and cross coupled coefficients of stiffness and damping in the bearings. A parametric study of the unbalance response is carried out to show the influence of bearing parameters on the response and to demonstrate the merits of applying optimization techniques in bearing design. The bearing parameters optimized are the diameter, clearance, and the oil viscosity. In addition to setting upper and lower limits on the foregoing design variables, the Sommerfeld number is also constrained to be within a certain range for the operational speeds of the rotor. The quantity minimized is the maximum unbalance response of the rotor in the operational speed range. Plain cylindrical, grooved, elliptical, and four shoe tilting pad type bearings are considered in the optimal design of the rotor bearing system. The results indicate that an optimal design of hydrodynamic bearings can reduce the unbalance response of rotors.
22 citations
TL;DR: In this article, a correction in the Reynolds boundary conditions is proposed and a new solution for the pressure distribution is obtained, which shows a sudden change in the pressure gradient at the position of maximum film thickness, which is possible only if the lubricant is added precisely at this position.
Abstract: The well-known solutions for the pressure distribution in the lubricating film of a hydrodynamic journal bearing, satisfying the Reynolds boundary conditions, show a sudden change in the pressure gradient at the position of maximum film thickness, which is possible only if the lubricant is added precisely at this position. Since the pressure develops smoothly because of hydrodynamic action, a correction in the Reynolds boundary conditions is proposed and a new solution for the pressure distribution is obtained. The steady state characteristics of a hydrodynamic journal bearing using the new boundary conditions are compared with the well-known characteristics using the Reynolds boundary conditions.
6 citations
TL;DR: In this paper, the stiffness and damping characteristics of a finite hydrodynamic journal bearing using the new boundary conditions are compared with the wellknown characteristics incorporating the Reynolds boundary conditions.
Abstract: The well-known solutions for the pressure distribution in the lubricating film of a hydrodynamic journal bearing, satisfying the Reynolds boundary conditions, show a sudden change in the pressure gradient at the position of maximum film thickness, which is possible only if the lubricant is supplied precisely at this location. Since the pressure develops smoothly because of hydrodynamic action, a correction in the boundary conditions is applied and a modified solution for the pressure distribution is obtained. The stiffness and damping characteristics of a finite hydrodynamic journal bearing using the new boundary conditions are compared with the wellknown characteristics incorporating the Reynolds boundary conditions. There is a significant change in the dynamic characteristics particularly at low values of the eccentricity ratio which can influence the characteristics of rotor-bearing systems.
3 citations
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