Paul Goldman

Bio: Paul Goldman is an academic researcher from Dynamics Research Corporation. The author has contributed to research in topics: Rotor (electric) & Bearing (mechanical). The author has an hindex of 8, co-authored 13 publications receiving 319 citations.

Chaotic responses of unbalanced rotor/bearing/stator systems with looseness or rubs

Abstract: The first part of this paper presents results of numerical simulation of the dynamic behavior of a one-lateral-mode unbalanced and radially side-loaded rotor with either a loose pedestal (looseness in a stationary joint), or with occasional rotor-to-stator rubbing. The nonlinearities of these systems (variable stiffness, impacting, and friction) are associated with the rotor intermittent contacts with the stationary element. The results, based on a newly developed local impact model [P. Goldman and A. Muszynska, Analytical and experimental simulation of loose pedestal dynamic effects on a rotating machine vibrational response, Rotating Machinery Dynamics, DE-Vol. 35, ASME, Miami, Florida, pp. 11–17 (1991); P. Goldman and A. Muszynska, Analytical model of the impact between rotating and nonrotating elements and its application in rotor-to-stator rubbing, BRDRC Report 1, (1992); P. Goldman and A. Muszynska, Chaotic behavior of rotor-to-stator systems with rubs, ASME Turbo EXPO Conference, 93-GT-34, Cincinnati, Ohio, Transactions of the ASME (to appear); P. Goldman and A. Muszynska, Dynamic effects in mechanical structures with gap and impacting: Order and chaos, Trans. of ASME, J. Vibration and Acoustics (1994)] exhibit regular periodic vibrations of synchronous (1×) and subsynchronous ( 1 2 ×, 1 3 × , …) orders, as well as chaotic vibration patterns of the rotor, all accompanied by higher harmonics. The second part of the paper presents experimental vibration characteristics of rotors with looseness or rubs, obtained from rotor rigs. The results display similar patterns as those obtained analytically.

Rotor-to-stator, rub-related, thermal/mechanical effects in rotating machinery

Abstract: The thermal effects of rotor-to-stator rub, and their influence on the rotor vibrational response, are discussed in this paper. Based on machinery observations, it is assumed in the analysis that velocities of transient thermal effects are considerably lower than that of rotor vibrations, and thermal effects affect only rotor steady-state vibrational responses. These responses would change due to thermally induced bow of the rotor, which can be considered slowly varying in time for the purposes of rotor vibration calculation. Thus uncoupled from the thermal problem, the rotor vibration is analyzed. The major consideration is given to the rotor, which experiences intermittent contact with the stator due to predetermined thermal bow of the rotor, unbalance force, and radial constant load force. In the case of an inelastic impact, this causes an on/off step-change in the stiffness of the system. A specially developed transformation is applied to the system model which contains discontinuities, and an averaging technique is then used to analyze stability of the different resonance regimes of rotor motion that were obtained. These regimes are further used to calculate the heat generated during rotor-to-stator contact stages, as a function of thermal conditions and rotor thermal bow modal parameters. The calculated heat input is used as a boundary condition for the rotor heat transfer problem. The latter is treated as quasi-static, which allows the application of an asymptotic method to the problem. The solution at its first approximation is used to adjust the rotor thermal bow value. As a result of this calculation, an ordinary differential equation with complex variables is obtained for the thermal bow, and it is investigated from the stability standpoint.

Full Annular Rub in Mechanical Seals, Part I: Experimental Results

Abstract: This paper presents the results of recent experimental studies on rotor/seal full annular rub, including forward and reverse precession. It was found that reverse precessional full annular rub (dry whip) could occur repeatedly in small clearance cases without any outside disturbance. The rotor rubbed against the seal with almost constant amplitude and frequency, which was higher than the natural frequency of the original rotor system and lower than of that of the coupled rotor/seal system. Once generated, the reverse precessional rub could be sustained over the whole speed range as long as slippage was maintained. Radius-to-clearance ratio varied from 10 to 40. The experimental studies include forward rub jump phenomena, reverse rub triggering mechanism, and effects of mass unbalance, surface lubrication, shaft speed, and seal stiffness. The results of both forward and reverse precession are discussed in detail, with emphasis on the reverse and the transition from the forward to the reverse.

Full Annular RUB in Mechanical Seals, Part II: Analytical Study

Abstract: This paper outlines the analytical study of the rotor lateral response under conditions of contact between the rotor and mechanical seal. The seal is modeled as an added stiffness and dry friction force, applied to the rotor during contact. The rotor is assumed sliding in the mechanical seal circular clearance due to unbalance force. The resulting equations allow for rotor synchronous circular response with stable and unstable branches of the amplitude-frequency characteristics. It is typical for jump phenomena. Nonlinear equations of motion are investigated for the stability of this particular solution. Root locus plots are utilized. Instability zones are determined to lead to the self-excited limit cycle reverse precession known as ＂dry whip＂. Destabilizing factors are rotor-seal dry friction coefficient and seal stiffness. A stability study is also performed for the self-excited limit cycle reverse precession. The conditions for the rotor-mechanical seal parameters are derived to avoid ＂dry whip＂ under any amount of unbalance.

Thermal Bending of the Rotor Due to Rotor-to-Stator Rub

Abstract: The rotor thermal bending due to the rotor-to-stator rubbing can lead to one of three types of observed rotor lateral motion: (1) spiral with increasing amplitude, (2) oscillating between rub]no-rub conditions, and (3) asymptotical approach to the rotor limit cycle. Based on the machinery observations, it is assumed in the analytical part of the paper that the speed scale of transient thermal effects is considerably lower than that of rotor vibrations, and that the thermal effect reflects only on the rotor steady-state vibrational response. This response would change due to thermally induced bow of the rotor, which can be considered to slowly vary in timefor the purpose of rotor vibration calculations. Thus uncoupled from the thermal problem, the rotor vibration is analyzed. The major consideration is given to the rotor which experiences intermittent contact with the stator, due to predetermined thermal bow, unbalance force, and radial constant load force. In the case of inelastic impact, it causes an on/off, step-change in the stiffness of the system. Using a specially developed variable transformation for the system with discontinuities, and averaging technique the resonance regimes of motion are obtained. These regimes are used to calculate the heat generated during contact stage, as a function of thermal bow modal parameters, which is used as a boundary condition for the rotor heat transfer problem. The latter is treated as quasi-static, which reduces the problem to an ordinary differential equation for the thermal bow vector. It is investigated from the stability standpoint.

Cracked shaft detection and diagnostics: A literature review

Abstract: Cracks in shafts have long been identified as factors limiting the safe and reliable operation of turbomachines. They can sometimes result in catastrophic failure of equipment (rotor bursts) and, more often, in costly process upsets, repairs and premature scrapping and replacement of equipment. Cracked shafts still pose a significant and real threat to equipment in spite of the great advances made in the areas of metallurgy, manufacturing and design. In the past two decades, much research and many resources have gone into developing various on-line and off-line diagnostic techniques to effectively detect cracks before they cause serious damage. Because of the enormous amount of ongoing research in this area (more than 500 technical papers have been published in English alone in the past 30 years), there is a real need to periodically condense and summarize the information. This paper reviews literature on cracked shaft detection and diagnostics published after 1990.

Chaotic responses of unbalanced rotor/bearing/stator systems with looseness or rubs

Abstract: The first part of this paper presents results of numerical simulation of the dynamic behavior of a one-lateral-mode unbalanced and radially side-loaded rotor with either a loose pedestal (looseness in a stationary joint), or with occasional rotor-to-stator rubbing. The nonlinearities of these systems (variable stiffness, impacting, and friction) are associated with the rotor intermittent contacts with the stationary element. The results, based on a newly developed local impact model [P. Goldman and A. Muszynska, Analytical and experimental simulation of loose pedestal dynamic effects on a rotating machine vibrational response, Rotating Machinery Dynamics, DE-Vol. 35, ASME, Miami, Florida, pp. 11–17 (1991); P. Goldman and A. Muszynska, Analytical model of the impact between rotating and nonrotating elements and its application in rotor-to-stator rubbing, BRDRC Report 1, (1992); P. Goldman and A. Muszynska, Chaotic behavior of rotor-to-stator systems with rubs, ASME Turbo EXPO Conference, 93-GT-34, Cincinnati, Ohio, Transactions of the ASME (to appear); P. Goldman and A. Muszynska, Dynamic effects in mechanical structures with gap and impacting: Order and chaos, Trans. of ASME, J. Vibration and Acoustics (1994)] exhibit regular periodic vibrations of synchronous (1×) and subsynchronous ( 1 2 ×, 1 3 × , …) orders, as well as chaotic vibration patterns of the rotor, all accompanied by higher harmonics. The second part of the paper presents experimental vibration characteristics of rotors with looseness or rubs, obtained from rotor rigs. The results display similar patterns as those obtained analytically.