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.

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.

Gas-Expanded Lubricant Performance and Effects on Rotor Stability in Turbomachinery

2014 ◽  
Author(s):  
Brian K. Weaver ◽  
Timothy W. Dimond ◽  
Jason A. Kaplan ◽  
Alexandrina Untaroiu ◽  
Andres F. Clarens
Keyword(s):  
Film Thickness ◽  
Power Loss ◽  
High Speed ◽  
Turbine Generator ◽  
Generator System ◽  
Polyol Ester ◽  
Damping Coefficients ◽  
Wide Range ◽  
Bearing Stiffness ◽  
Stiffness And Damping

Gas-expanded lubricants (GELs) are tunable mixtures of synthetic oil and carbon dioxide that enable dynamic control of lubricant viscosity during bearing operation. This control can help reduce bearing power loss and operating temperatures while also providing direct control over bearing stiffness and damping, which can enhance rotordynamic performance. In this work, the bearing and rotordynamic performance of two representative high-speed machines was evaluated when different lubricants, including GELs, were supplied to the machine bearings. The machines chosen for this analysis, an 8-stage centrifugal compressor and a steam turbine-generator system, represent a wide range of speed and loading conditions encountered in modern turbomachinery. The fluids compared for machine performance were standard petroleum-based lubricants, polyol ester synthetic oils, and polyol ester based-GELs. The performance simulations were carried out using a thermoelastohydrodynamic bearing model, which provided bearing stiffness and damping coefficients as inputs to finite element rotordynamic models. Several bearing performance metrics were evaluated including power loss, operating temperature, film thickness, eccentricity, and stiffness and damping coefficients. The rotordynamic analysis included an evaluation of rotor critical speeds, unbalance response, and stability. Bearing performance results for the compressor showed a 40% reduction in power loss at operating speed when comparing the GEL to the petroleum-based lubricant. The GEL-lubricated compressor also exhibited lower operating temperatures with minimal effects on film thickness. GELs were also predicted to produce lower bearing stiffness when compared to standard fluids in the compressor. Rotordynamic results for the compressor showed that the fluid properties had only minor effects on the unbalance response, while GELs were found to increase the stability margin by 43% when compared with standard fluids. The results from the turbine-generator system also demonstrated increases in low-speed bearing efficiency with the use of GELs, though at higher speeds the onset of turbulent flow in the GEL case offset these efficiency gains. Rotordynamic results for this system showed a contrast with the compressor results, with the GELs producing lower stability margins for a majority of the modes predicted due to increased bearing stiffness in the high-speed turbine bearings and negative stiffness in the lightly loaded, low-speed pinion bearings. These results suggest that GELs could be beneficial in providing control over a wide range of machine designs and operating conditions and that some machines are especially well suited for the tunability that these fluids impart.

Gas-Expanded Lubricant Performance and Effects on Rotor Stability in Turbomachinery

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Brian K. Weaver ◽  
Timothy W. Dimond ◽  
Jason A. Kaplan ◽  
Alexandrina Untaroiu ◽  
Andres F. Clarens
Keyword(s):  
Film Thickness ◽  
Power Loss ◽  
High Speed ◽  
Turbine Generator ◽  
Generator System ◽  
Low Speed ◽  
Damping Coefficients ◽  
Wide Range ◽  
Bearing Stiffness ◽  
Stiffness And Damping

Gas-expanded lubricants (GELs) are tunable mixtures of synthetic oil and carbon dioxide that enable dynamic control of lubricant viscosity during bearing operation. This control can help reduce bearing power loss and operating temperatures while also providing direct control over bearing stiffness and damping, which can enhance rotordynamic performance. In this work, the bearing and rotordynamic performance of two representative high-speed machines was evaluated when different lubricants, including GELs, were supplied to the machine bearings. The machines chosen for this analysis, an eight-stage centrifugal compressor and a steam turbine-generator system, represent a wide range of speed and loading conditions encountered in modern turbomachinery. The fluids compared for machine performance were standard petroleum-based lubricants, polyol ester (POE) synthetic oils, and POE-based GELs. The performance simulations were carried out using a thermoelastohydrodynamic bearing model, which provided bearing stiffness and damping coefficients as inputs to finite element rotordynamic models. Several bearing performance metrics were evaluated including power loss, operating temperature, film thickness, eccentricity, and stiffness and damping coefficients. The rotordynamic analysis included an evaluation of rotor critical speeds, unbalance response, and stability. Bearing performance results for the compressor showed a 40% reduction in power loss at operating speed when comparing the GEL to the petroleum-based lubricant. The GEL-lubricated compressor also exhibited lower operating temperatures with minimal effects on film thickness. GELs were also predicted to produce lower bearing stiffness when compared to standard fluids in the compressor. Rotordynamic results for the compressor showed that the fluid properties had only minor effects on the unbalance response, while GELs were found to increase the stability margin by 43% when compared with standard fluids. The results from the turbine-generator system also demonstrated increases in low-speed bearing efficiency with the use of GELs, though at higher speeds the onset of turbulent flow in the GEL case offset these efficiency gains. Rotordynamic results for this system showed a contrast with the compressor results, with the GELs producing lower stability margins for a majority of the modes predicted due to increased bearing stiffness in the high-speed turbine bearings and negative stiffness in the lightly loaded, low-speed pinion bearings. These results suggest that GELs could be beneficial in providing control over a wide range of machine designs and operating conditions and that some machines are especially well suited for the tunability that these fluids impart.

Static and dynamic characteristics and stability analysis of high-speed water-lubricated hydrodynamic journal bearings

2021 ◽  
pp. 135065012110270
Author(s):  
Bo Xu ◽  
Hun Guo ◽  
Xiaofeng Wu ◽  
Yafeng He ◽  
Xiangzhi Wang ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Dynamic Characteristics ◽  
High Speed ◽  
Load Capacity ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Inertia Effect ◽  
Static And Dynamic Characteristics ◽  
Damping Coefficients ◽  
Stiffness And Damping

The purpose of this paper is to analyze the influence of turbulent, inertia, and misaligned effects on the static and dynamic characteristics and stability of high-speed water-lubricated hydrodynamic journal bearings. Based on the Navier–Stokes equation, the mixing-length theory, and the essential assumption that the velocity profile is not strongly affected by inertia force, the fluid lubrication model with turbulent, inertia, and misaligned effects is established, and then the stability analysis of bearings is carried out based on the equation of motion with four degrees of freedom. The model is solved by the finite difference method and the numerical results are compared under different operating conditions. The results show that the turbulent effect greatly increases the load capacity, power consumption, stiffness and damping coefficients, and stability of bearings, and the inertia effect significantly increases the volume flow rate of bearings, and the misaligned effect increases the load capacity, stiffness and damping coefficients, and stability of bearings. In high rotary speed and moderate eccentricity ratios, the influence of the inertia effect on the load capacity, stiffness coefficients, and stability cannot be neglected.

Ball bearing turbocharger vibration management: application on high speed balancer

2020 ◽  
Vol 21 (6) ◽  
pp. 619
Author(s):  
Kostandin Gjika ◽  
Antoine Costeux ◽  
Gerry LaRue ◽  
John Wilson
Keyword(s):  
Dynamic Behavior ◽  
High Speed ◽  
Internal Combustion Engines ◽  
Ball Bearing ◽  
Squeeze Film ◽  
Design And Technology ◽  
Squeeze Film Damper ◽  
Damping Coefficients ◽  
Bearing Loads ◽  
Stiffness And Damping

Today's modern internal combustion engines are increasingly focused on downsizing, high fuel efficiency and low emissions, which requires appropriate design and technology of turbocharger bearing systems. Automotive turbochargers operate faster and with strong engine excitation; vibration management is becoming a challenge and manufacturers are increasingly focusing on the design of low vibration and high-performance balancing technology. This paper discusses the synchronous vibration management of the ball bearing cartridge turbocharger on high-speed balancer and it is a continuation of papers [1–3]. In a first step, the synchronous rotordynamics behavior is identified. A prediction code is developed to calculate the static and dynamic performance of “ball bearing cartridge-squeeze film damper”. The dynamic behavior of balls is modeled by a spring with stiffness calculated from Tedric Harris formulas and the damping is considered null. The squeeze film damper model is derived from the Osborne Reynolds equation for incompressible and synchronous fluid loading; the stiffness and damping coefficients are calculated assuming that the bearing is infinitely short, and the oil film pressure is modeled as a cavitated π film model. The stiffness and damping coefficients are integrated on a rotordynamics code and the bearing loads are calculated by converging with the bearing eccentricity ratio. In a second step, a finite element structural dynamics model is built for the system “turbocharger housing-high speed balancer fixture” and validated by experimental frequency response functions. In the last step, the rotating dynamic bearing loads on the squeeze film damper are coupled with transfer functions and the vibration on the housings is predicted. The vibration response under single and multi-plane unbalances correlates very well with test data from turbocharger unbalance masters. The prediction model allows a thorough understanding of ball bearing turbocharger vibration on a high speed balancer, thus optimizing the dynamic behavior of the “turbocharger-high speed balancer” structural system for better rotordynamics performance identification and selection of the appropriate balancing process at the development stage of the turbocharger.

Performance Analysis of Gas-Expanded Lubricants in a Hybrid Bearing Using Computational Fluid Dynamics

2015 ◽  
Author(s):  
Brian K. Weaver ◽  
Gen Fu ◽  
Andres F. Clarens ◽  
Alexandrina Untaroiu
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Phase Behavior ◽  
Ambient Pressure ◽  
Operating Conditions ◽  
Full Potential ◽  
Dissolved Carbon ◽  
Bearing Stiffness ◽  
Multi Phase ◽  
Stiffness And Damping

Gas-expanded lubricants (GELs), tunable mixtures of synthetic oil and dissolved carbon dioxide, have been previously shown to potentially increase bearing efficiency, rotordynamic control, and long-term reliability in flooded journal bearings by controlling the properties of the lubricant in real time. Previous experimental work has established the properties of these mixtures and multiple numerical studies have predicted that GELs stand to increase the performance of flooded bearings by reducing bearing power losses and operating temperatures while also providing control over bearing stiffness and damping properties. However, to date all previous analytical studies have utilized Reynolds equation-based approaches while assuming a single-phase mixture under high-ambient pressure conditions. The potential implications of multi-phase behavior could be significant to bearing performance, therefore a more detailed study of alternative operating conditions that may include multi-phase behavior is necessary to better understanding the full potential of GELs and their effects on bearing performance. In this work, the performance of GELs in a fixed geometry journal bearing were evaluated to examine the effects of these lubricants on the fluid and bearing dynamics of the system under varying operating conditions. The bearing considered for this study was a hybrid hydrodynamic-hydrostatic bearing to allow for the study of various lubricant supply and operating conditions. A computational fluid dynamics (CFD)-based approach allowed for a detailed evaluation of the lubricant injection pathway, the flow of fluid throughout the bearing geometry, thermal behavior, and the collection of the lubricant as it exits the bearing. This also allowed for the study of the effects of the lubricant behavior on overall bearing performance.

scholarly journals High-Speed Rotor Analytical Dynamics on Flexible Foundation Subjected to Internal and External Excitation

2016 ◽  
Vol 46 (4) ◽  
pp. 3-18
Author(s):  
Venelin S. Jivkov ◽  
Evtim V. Zahariev
Keyword(s):  
Gas Turbines ◽  
High Speed ◽  
Asymptotic Methods ◽  
Numerical Procedure ◽  
Rigid Bodies ◽  
Dynamics Simulation ◽  
Geometrical Approach ◽  
Rotating Machine ◽  
Exciting Frequency ◽  
Stiffness And Damping

Abstract The paper presents a geometrical approach to dynamics simulation of a rigid and flexible system, compiled of high speed rotating machine with eccentricity and considerable inertia and mass. The machine is mounted on a vertical flexible pillar with considerable height. The stiffness and damping of the column, as well as, of the rotor bearings and the shaft are taken into account. Non-stationary vibrations and transitional processes are analyzed. The major frequency and modal mode of the flexible column are used for analytical reduction of its mass, stiffness and damping properties. The rotor and the foundation are modelled as rigid bodies, while the flexibility of the bearings is estimated by experiments and the requirements of the manufacturer. The transition effects as a result of limited power are analyzed by asymptotic methods of averaging. Analytical expressions for the amplitudes and unstable vibrations throughout resonance are derived by quasi-static approach increasing and decreasing of the exciting frequency. Analytical functions give the possibility to analyze the influence of the design parameter of many structure applications as wind power generators, gas turbines, turbo-generators, and etc. A numerical procedure is applied to verify the effectiveness and precision of the simulation process. Nonlinear and transitional effects are analyzed and compared to the analytical results. External excitations, as wave propagation and earthquakes, are discussed. Finite elements in relative and absolute coordinates are applied to model the flexible column and the high speed rotating machine. Generalized Newton - Euler dynamics equations are used to derive the precise dynamics equations. Examples of simulation of the system vibrations and nonstationary behaviour are presented.

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness and Different Pad Preloads

2010 ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul E. Allaire ◽  
John C. Nicholas
Keyword(s):  
Frequency Response ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Theoretical Calculations ◽  
Leading Edge ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
The Subject ◽  
Stiffness And Damping

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to non-synchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are considered using a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced non-synchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

Visualization of Supercritical Carbon Dioxide Flow Through a Converging-Diverging Nozzle

2019 ◽  
Author(s):  
Chang Hyeon Lim ◽  
Gokul Pathikonda ◽  
Sandeep Pidaparti ◽  
Devesh Ranjan
Keyword(s):  
Carbon Dioxide ◽  
Supercritical Carbon Dioxide ◽  
Critical Point ◽  
High Speed ◽  
Operating Conditions ◽  
Higher Plant ◽  
Two Phase ◽  
Pressure Profiles ◽  
Flow Through ◽  
Supercritical Carbon

Abstract Supercritical carbon dioxide (sCO2) power cycles have the potential to offer a higher plant efficiency than the traditional Rankine superheated/supercritical steam cycle or Helium Brayton cycles. The most attractive characteristic of sCO2 is that the fluid density is high near the critical point, allowing compressors to consume less power than conventional gas Brayton cycles and maintain a smaller turbomachinery size. Despite these advantages, there still exist unsolved challenges in design and operation of sCO2 compressors near the critical point. Drastic changes in fluid properties near the critical point and the high compressibility of the fluid pose several challenges. Operating a sCO2 compressor near the critical point has potential to produce two phase flow, which can be detrimental to turbomachinery performance. To mimic the expanding regions of compressor blades, flow through a converging-diverging nozzle is investigated. Pressure profiles along the nozzle are recorded and presented for operating conditions near the critical point. Using high speed shadowgraph images, onset and growth of condensation is captured along the nozzle. Pressure profiles were calculated using a one-dimensional homogeneous equilibrium model and compared with experimental data.

Integrated Dynamic Thermo-Mechanical Modeling of High Speed Spindles, Part 2: Solution Procedure and Validations

2004 ◽  
Vol 126 (1) ◽  
pp. 159-168 ◽  
Author(s):  
Hongqi Li ◽  
Yung C. Shin
Keyword(s):  
High Speed ◽  
Solution Procedure ◽  
Operating Conditions ◽  
Test Results ◽  
Mechanical Modeling ◽  
Spindle Bearing ◽  
Wide Range ◽  
Bearing Stiffness ◽  
Models Validation ◽  
Validation Tests

This paper presents a new solution procedure for an integrated thermo-dynamic spindle model and validation results. Based on the model presented in Part 1 of this paper, a computer program has been developed to generate comprehensive solutions for high speed spindle-bearing systems, such as bearing stiffness, contact load and temperature, spindle dynamic characteristics and response, temperature distributions, and thermal expansions. The model and the solution procedure are modular such that solutions for different spindle set-ups can be easily generated by combining a given spindle model with different toolholder models. Validation test results for thermal and dynamic predictions are presented for four different spindle systems, including the thermal and dynamic validation tests on a specially constructed spindle testbed. The validation results show the model has accurate predictive capabilities for a wide range of operating conditions and various spindle designs.

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