An Integrated Approach Toward the Dynamic Analysis of High-Speed Spindles: Part II — Dynamics Under Moving End Load

1993 ◽  
Author(s):  
C. H. Chen ◽  
K. W. Wang
Keyword(s):  
High Speed ◽  
Integrated Approach ◽  
Structural Instability ◽  
Operating Conditions ◽  
Rotating Shaft ◽  
High Rotational Speed ◽  
System Equilibrium ◽  
Load Effects ◽  
Specific Interests ◽  
Bearing Dynamics

Abstract This paper presents an integrated study of a rotor/bearing structure, with specific interests toward high speed spindle systems under rotating end loads. Considering the coupling between the rotating shaft and the nonlinear bearings, an iterative method is developed to derive the system equilibrium configuration for given operating conditions. With moving end loads, structural instability caused by high rotational speed is analyzed. The critical speeds and unstable speed regions are discussed. Machining chatter instability lobes are also derived using the spindle model. It is shown that significant errors will occur in predicting spindle characteristics and stability if the speed and load effects on the shaft/bearing dynamics are neglected.

An Integrated Approach Toward the Dynamic Analysis of High-Speed Spindles: Part 2—Dynamics Under Moving End Load

1994 ◽  
Vol 116 (4) ◽  
pp. 514-522 ◽  
Author(s):  
C. H. Chen ◽  
K. W. Wang
Keyword(s):  
High Speed ◽  
Integrated Approach ◽  
Structural Instability ◽  
Operating Conditions ◽  
Rotating Shaft ◽  
High Rotational Speed ◽  
System Equilibrium ◽  
Load Effects ◽  
Specific Interests ◽  
Bearing Dynamics

This paper presents an integrated study of a rotor/bearing structure, with specific interests toward high-speed spindle systems under rotating end loads. Considering the coupling between the rotating shaft and the nonlinear bearings, an iterative method is developed to derive the system equilibrium configuration for given operating conditions. With moving end loads, structural instability caused by high rotational speed is analyzed. The critical speeds and unstable speed regions are discussed. Machining chatter instability lobes are also derived using the spindle model. It is shown that significant errors will occur in predicting spindle characteristics and stability if the speed and load effects on the shaft/bearing dynamics are neglected.

scholarly journals Dynamic Instability of High-Speed Rotating Shaft with Torsional Effect

2018 ◽  
Vol 15 (4) ◽  
pp. 6034-6051
Author(s):  
A. M. A. Wahab ◽  
Z. Yusof ◽  
Z. A. Rasid ◽  
A. Abu ◽  
N. F. M. N. Rudin
Keyword(s):  
Parametric Resonance ◽  
High Speed ◽  
Dynamic Instability ◽  
Parametric Instability ◽  
Degree Of Freedom ◽  
Rotating Shaft ◽  
Torsional Deformation ◽  
High Rotational Speed ◽  
The Difference ◽  
Frequency Ratios

Today’s design of machine rotor requires the rotor to operate at a high rotational speed to improve the efficiency of the machine. However, the existence of disturbances such as periodic axial load may cause parametric resonance to the rotor system in addition to the common force resonance. Previous studies on this parametric resonance of shaft typically included the element of translational and rotary inertia, gyroscopic moments and bending and shear deformation but surprisingly neglected the effect of the axial torque. This paper investigated the parametric instability behaviour of the shaft rotating at high speed while considering the torsional effect of the shaft. Based on the finite element method, a shaft model that includes torsional deformation as one of its degree of freedom was established. The Mathieu-Hill equation was derived, and then the Bolotin’s method was used to solve the equation by establishing the parametric instability chart. Two types of the rotary system were studied: a shaft with different boundary conditions and shaft with different bearing types. The results were initially validated with past findings. Following that the results were compared to the results correspond to the Timoshenko’s beam formulation that omits the torsional degree of freedom. The effect of axial torsional deformation was found to be very significant especially at high speed. The developed model in this study shows that at the shaft speed of 40000 rpm, the effect of torsional deformation has given the difference of more than 100% in the frequency ratios correspond to the 4DOF and 5DOF models for the case of fix-free boundary condition.

Transient Analysis of Gas-Expanded Lubrication and Rotordynamic Performance in a Centrifugal Compressor

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Brian K. Weaver ◽  
Jason A. Kaplan ◽  
Andres F. Clarens ◽  
Alexandrina Untaroiu
Keyword(s):  
Carbon Dioxide ◽  
High Speed ◽  
Operating Conditions ◽  
Damping Coefficients ◽  
Rotating Machine ◽  
Rapid Changes ◽  
Fluid Properties ◽  
Bearing Stiffness ◽  
Stiffness And Damping ◽  
Bearing Dynamics

Gas-expanded lubricants (GELs) have the potential to increase bearing energy efficiency, long-term reliability, and provide for a degree of control over the rotordynamics of high-speed rotating machines. Previous work has shown that these tunable mixtures of synthetic oil and dissolved carbon dioxide could be used to maximize the stability margin of a machine during startup by controlling bearing stiffness and damping. This allows the user to then modify the fluid properties after reaching a steady operating speed to minimize bearing power loss and reduce operating temperatures. However, it is unknown how a typical machine would respond to rapid changes in bearing stiffness and damping due to changes in the fluid properties once the machine has completed startup. In this work, the time-transient behavior of a high-speed compressor was evaluated numerically to examine the effects of rapidly changing bearing dynamics on rotordynamic performance. Two cases were evaluated for an eight-stage centrifugal compressor: an assessment under stable operating conditions as well as a study of the instability threshold. These case studies presented two contrasting sets of transient operating conditions to evaluate, the first being critical to the viability of using GELs in high-speed rotating machinery. The fluid transitions studied for machine performance were between that of a polyol ester (POE) synthetic lubricant and a GEL with a 20% carbon dioxide content. The performance simulations were carried out using a steady-state thermoelastohydrodynamic (TEHD) bearing model, which provided bearing stiffness and damping coefficients as inputs to a time-transient rotordynamic model using Timoshenko beam finite elements. The displacements and velocities of each node were solved for using a fourth-order Runge–Kutta method and provided information on the response of the rotating machine due to rapid changes in bearing stiffness and damping coefficients. These changes were assumed to be rapid due to (1) the short lubricant residence times calculated for the bearings and (2) rapid mixing due to high shear rates in the machine bearings causing sudden changes in the fluid properties. This operating condition was also considered to be a worst-case scenario as an abrupt change in the bearing dynamics would likely solicit a more extreme rotordynamic response than a more gradual change, making this analysis quite important. The results of this study provide critical insight into the nature of operating a rotating machine and controlling its behavior using GELs, which will be vital to the implementation of this technology.

scholarly journals Instability Study of Magnetic Journal Bearing under S-CO2 Condition

2021 ◽  
Vol 11 (8) ◽  
pp. 3491
Author(s):  
Dokyu Kim ◽  
SeungJoon Baik ◽  
Jeong Ik Lee
Keyword(s):  
High Pressure ◽  
High Speed ◽  
Journal Bearing ◽  
Magnetic Bearing ◽  
Operating Conditions ◽  
Magnetic Bearings ◽  
Brayton Cycle ◽  
Functional Requirements ◽  
Rotating Shaft ◽  
Levitation Performance

A supercritical CO2 (S-CO2)-cooled Brayton cycle is under development for distributed power applications for remote regions. In order to successfully develop it, issues of controlling shaft levitation with bearings have to be solved. From several studies, magnetic bearings have been suggested for reliable levitation performance with reduced cost and complexity. However, several studies on magnetic bearing show that instability issues under high-pressure fluid and high-speed operating conditions may exist. The purpose of this research is to provide background for understanding the instability of magnetic bearings under S-CO2 conditions and propose functional requirements of the magnetic bearing. Thus, the rotating shaft with magnetic bearings operating under high pressure fluid was first analyzed. To test the theory, a magnetic bearing test rig was constructed. By comparing experimental data to the analysis results, the analysis results were verified. Therefore, the analysis results can be used for predicting instability in the future and can contribute to the development of better magnetic bearing controllers.

Investigation of Magnetic Journal Bearing Instability Issues in Supercritical CO2 Turbomachinery

2019 ◽  
Author(s):  
Dokyu Kim ◽  
SeungJoon Baik ◽  
Jeong Ik Lee
Keyword(s):  
Supercritical Co2 ◽  
High Speed ◽  
Magnetic Bearing ◽  
Operating Conditions ◽  
Physical Contact ◽  
Analysis Model ◽  
Rotating Shaft ◽  
Power Cycles ◽  
Power Cycle ◽  
Lubrication Performance

Abstract With the increasing emphasis on reducing the CO2 emission while improving power generation efficiency, new power cycles are being developed. One of those promising power cycles is a supercritical CO2 (S-CO2) power cycle. To generate over 10MW electricity with S-CO2 power cycle, a magnetic bearing can be a good option for the hermetic type turbomachinery. However, from several studies on the magnetic bearing, the instability issues under high density fluid and high speed operating conditions were repeatedly mentioned. The instability in the magnetic bearing was observed to be related to the fluid conditions, mostly pressure and density. Because of this issue, the magnetic bearing sometimes cannot maintain enough clearance for the rotor leading to physical contact and consequently damaging the system. Thus, these instability issues should be thoroughly studied and be resolved for the successful and steady operation of the power system. The instability due to fluid force around the rotating shaft can be modeled with the Reynolds lubrication equation. The steady lubrication force analysis model is developed based on this equation. The model results imply that the lubrication performance is quite sensitive to the thermal condition of the CO2 especially density gradient around the shaft. Based on the modeling results, an experimental system is designed to investigate the issue. To study the instability issues experimentally, an impeller of the operating S-CO2 compressor is removed and the discharge line is blocked. Therefore, the main instability factor in this experiment will be the interaction between the rotor and the bearing only. The shaft position can be measured with inductive sensors. The forces exerted from the electromagnet is calculated from the electric current data which is applied by the controller. From these experimental data, the lubrication force is calculated. These results are compared with the analytical lubrication model to verify the model. From this study, it is expected that it will be possible to define the unstable operating conditions and suggest the required magnetic bearing performance for S-CO2 conditions.

Transient Analysis of Gas-Expanded Lubrication and Rotordynamic Performance in a Centrifugal Compressor

2015 ◽  
Author(s):  
Brian K. Weaver ◽  
Jason A. Kaplan ◽  
Andres F. Clarens ◽  
Alexandrina Untaroiu
Keyword(s):  
Carbon Dioxide ◽  
High Speed ◽  
Operating Conditions ◽  
Damping Coefficients ◽  
Rotating Machine ◽  
Rapid Changes ◽  
Fluid Properties ◽  
Bearing Stiffness ◽  
Stiffness And Damping ◽  
Bearing Dynamics

Gas-expanded lubricants (GELs) have the potential to increase bearing energy efficiency, long-term reliability, and provide for a degree of control over the rotordynamics of high-speed rotating machines. Previous work has shown that these tunable mixtures of synthetic oil and dissolved carbon dioxide could be used to maximize the stability margin of a machine during startup by controlling bearing stiffness and damping. This allows the user to then modify the fluid properties after reaching a steady operating speed to minimize bearing power loss and reduce operating temperatures. However, it is unknown how a typical machine would respond to rapid changes in bearing stiffness and damping due to changes in the fluid properties once the machine has completed startup. In this work, the time-transient behavior of a high-speed compressor was evaluated numerically to examine the effects of rapidly changing bearing dynamics on rotordynamic performance. Two cases were evaluated for an 8-stage centrifugal compressor: an assessment under stable operating conditions as well as a study of the instability threshold. These case studies presented two contrasting sets of transient operating conditions to evaluate, the first being critical to the viability of using GELs in high-speed rotating machinery. The fluid transitions studied for machine performance were between that of a polyol ester synthetic lubricant and a GEL with a 20% carbon dioxide content. The performance simulations were carried out using a steady-state thermoelastohydrodynamic (TEHD) bearing model, which provided bearing stiffness and damping coefficients as inputs to a time-transient rotordynamic model using Timoshenko beam finite elements. The displacements and velocities of each node were solved for using a fourth order Runge-Kutta method and provided information on the response of the rotating machine due to rapid changes in bearing stiffness and damping coefficients. These changes were assumed to be rapid due to 1) the short lubricant residence times calculated for the bearings, and 2) rapid mixing due to high shear rates in the machine bearings causing sudden changes in the fluid properties. This operating condition was also considered to be a worst-case scenario as an abrupt change in the bearing dynamics would likely solicit a more extreme rotordynamic response than a more gradual change, making this analysis quite important. The results of this study provide critical insight into the nature of operating a rotating machine and controlling its behavior using gas-expanded lubricants, which will be vital to the implementation of this technology.

Experimental and Analytical Investigation of High Speed Turbocharger Ball Bearings

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Ankur Ashtekar ◽  
Farshid Sadeghi
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Analytical Investigation ◽  
Rotor System ◽  
Operating Conditions ◽  
Experimental Results ◽  
Test Rig ◽  
Angular Contact Ball Bearing ◽  
Turbine Wheel ◽  
Bearing Dynamics

The objectives of this investigation were to design and construct a high speed turbocharger test rig (TTR) to measure dynamics of angular contact ball bearing rotor system, and to develop a coupled dynamic model for the ball bearing rotor system to corroborate the experimental and analytical results. In order to achieve the objectives of the experimental aspect of this study, a test rig was designed and developed to operate at speeds up to 70,000 rpm. The rotating components (i.e., turbine wheels) of the TTR were made to be dynamically similar to the actual turbocharger. Proximity sensors were used to record the turbine wheel displacements while accelerometers were used to monitor the rotor vibrations. The TTR was used to examine the dynamic response of the turbocharger under normal and extreme operating conditions. To achieve the objectives of analytical investigation, a discrete element ball bearing model was coupled through a set of interface points with a component mode synthesis rotor model to simulate the dynamics of the turbocharger test rig. Displacements of the rotor from the analytical model were corroborated with experimental results. The analytical and experimental results are in good agreement. The bearing rotor system model was used to examine the bearing component dynamics. Effects of preloading and imbalance were also found to have significant effects on turbocharger rotor and bearing dynamics.

ANALYSIS AND ASSESSMENT OF METHODS AND MEANS OF DESTRUCTING INFORMATION FROM MAGNETIC MEDIA AS AN ELEMENT OF MODERN INFORMATION SECURITY

2019 ◽  
pp. 99-112 ◽  
Author(s):  
O. Semenenko ◽  
Y. Dobrovolsky ◽  
V. Koverga ◽  
O. Sechenev
Keyword(s):  
Information Security ◽  
Information Exchange ◽  
Integrated Approach ◽  
Operating Conditions ◽  
Security Requirements ◽  
Magnetic Media ◽  
Security Technologies ◽  
Analysis Of Means ◽  
Complex Development ◽  
Modern Information

Evolution of security technologies shows that only the concept of an integrated approach to information security can provide modern information security requirements. A comprehensive approach means the complex development of all the necessary methods and means of information protection. Today, the information exchange and information systems in the Ministry of Defense of Ukraine have certain means and approaches to the destruction of information, but each of them has different estimates of the effectiveness of their use, as well as different cost of their purchase and use. Therefore, the main purpose of the article is to carry out a comprehensive analysis of means of destroying confidential information of methods of its destruction in order to formulate practical recommendations for choosing the most effective and economically feasible for the Ministry of Defense of Ukraine. The perfection of methods and means of destroying information from magnetic media is an important element of modern information security. The results of the analysis carried out in the article are the disclosure of the main features of modern devices for the elimination of magnetic records, as well as the ability to formulate a list of basic requirements for modern devices for the destruction of information from magnetic media. Today, technical means of information security, in particular, the elimination of information on magnetic media, are constantly being improved, absorbing the latest advances in modern security technologies. Their model range, which takes into account the diversity of customer requirements, such as the type of energy supply, the level of mobility, reliability and operating conditions, expands. All this determines the relevance of research topics in this direction in the future.

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