Limit-Cycle Analysis of Three-Dimensional Flexible Shaft/Rigid Rotor/Autobalancer System With Symmetric Rigid Supports

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
DaeYi Jung ◽  
H. A. DeSmidt
Keyword(s):  
Limit Cycle ◽  
Three Dimensional ◽  
Design Parameters ◽  
Rigid Rotor ◽  
Modal Shape ◽  
Flexible Shaft ◽  
Flexible Mode ◽  
Automatic Balancing ◽  
Rigid Supports ◽  
Limit Cycle Behavior

In recent years, there has been much interest in the use of automatic balancing devices (ABD) in rotating machinery. Autobalancers consist of several freely moving eccentric balancing masses mounted on the rotor, which, at certain operating speeds, act to cancel rotor imbalance. This “automatic balancing” phenomenon occurs as a result of nonlinear dynamic interactions between the balancer and rotor wherein the balancer masses naturally synchronize with the rotor with appropriate phase to cancel the imbalance. However, due to inherent nonlinearity of the autobalancer, the potential for other undesirable nonsynchronous limit-cycle behavior exists. In such situations, the balancer masses do not reach their desired synchronous balanced positions resulting in increased rotor vibration. To explore this nonsynchronous behavior of ABD, the unstable limit-cycle analysis of three-dimensional (3D) flexible shaft/rigid rotor/ABD/rigid supports described by the modal coordinates has been investigated here. Essentially, this paper presents an approximate harmonic analytical solution to describe the limit-cycle behavior of ABD–rotor system interacting with flexible shaft, which has not been fully considered by ABD researchers. The modal shape of flexible shaft is determined by using well-known fixed–fixed boundary condition due to symmetric rigid supports. Here, the whirl speed of the ABD balancer masses is determined via the solution of a nonlinear characteristic equation. Also, based upon the analytical limit-cycle solutions, the limit-cycle stability of three primary design parameters for ABD is assessed via a perturbation and Floquet analysis: the size of ABD balancer mass, the ABD viscous damping, and the relative axial location of ABD to the imbalance rotor along the shaft. The coexistence of the stable balanced synchronous condition and undesirable nonsynchronous limit-cycle is also studied. It is found that for certain combinations of ABD parameters and rotor speeds, the nonsynchronous limit-cycle can be made unstable, thus guaranteeing asymptotic stability of the synchronous balanced condition at the supercritical shaft speeds between each flexible mode. Finally, the analysis is validated through numerical simulation. The findings in this paper yield important insights for researchers wishing to utilize ABD in flexible shaft/rigid rotor systems and limit-cycle mitigation.

Limit-Cycle Analysis of Three Dimensional Rigid Rotor/Shaft/Autobalancer System With Symmetric Bearing Support

2012 ◽  
Author(s):  
DaeYi Jung ◽  
Hans DeSmidt
Keyword(s):  
Limit Cycle ◽  
Three Dimensional ◽  
Rigid Rotor ◽  
Dynamic Interactions ◽  
Single Plane ◽  
Rotor Shaft ◽  
Gyroscopic Effects ◽  
Automatic Balancing ◽  
Transverse Deflection ◽  
Limit Cycle Behavior

In recent years, there has been much interest in the use of automatic balancing devices (ABDs) in rotating machinery. Autobalancers consist of several freely moving eccentric balancing masses mounted on the rotor, which, at certain operating speeds, act to cancel rotor imbalance. This “automatic balancing” phenomena occurs as a result of nonlinear dynamic interactions between the balancer and rotor wherein the balancer masses naturally synchronize with the rotor with appropriate phase to cancel the imbalance. However, due to inherent nonlinearity of the autobalancer, the potential for other undesirable non-synchronous limit-cycle behavior exists. In such situations, the balancer masses do not reach their desired synchronous balanced positions resulting in increased rotor vibration. Although several researchers have explored limit-cycle behavior of single-plane ABD-rotor systems, a limit-cycle analysis of a full three dimensional rigid ABD/shaft/rotor considering transverse deflection, out-plane tilting and gyroscopic effects has not been investigated. This paper considers an approximate harmonic analytical solution to describe the limit-cycle behavior in a three dimensional rigid rotor/ABD system. Essentially, the solutions presented here capture both in-plane transverse deflection and out-plane tilting motion of the system under the limit-cycle condition. Here the whirl speed of the ABD balancer masses is determined via the solution of a non-linear characteristic equation. Also, based upon the limit-cycle solutions, the limit-cycle stability is assessed via a perturbation and Floquet analysis exploring three main parameters; ABD balancer mass, ABD damping, and axial location of ABD along the shaft. The coexistence of the stable balanced synchronous condition and undesired non-synchronous limit-cycle is studied. It is found that for certain combinations of ABD parameters and rotor speeds, the non-synchronous limit-cycle can be made unstable thus guaranteeing global asymptotic stability of the synchronous balanced condition. Finally, the analysis is validated through numerical simulation. The findings in this paper yield important insights for researchers wishing to utilize automatic balancing devices in rotor/shaft systems and limit-cycle mitigation.

scholarly journals Strength and dynamic characteristics analyses of wound composite axial impeller

2012 ◽  
Vol 2 (1) ◽  
Author(s):  
Jifeng Wang ◽  
Jorge Olortegui-Yume ◽  
Norbert Müller
Keyword(s):  
Dynamic Characteristics ◽  
High Performance ◽  
Low Cost ◽  
Three Dimensional ◽  
Design Parameters ◽  
Modal Shape ◽  
Kevlar Fiber ◽  
Start Up ◽  
High Performance Composite ◽  
Wound Composite

AbstractA low cost, light weight, high performance composite material turbomachinery impeller with a uniquely designed blade patterns is analyzed. Such impellers can economically enable refrigeration plants to use water as a refrigerant (R718). A strength and dynamic characteristics analyses procedure is developed to assess the maximum stresses and natural frequencies of these wound composite axial impellers under operating loading conditions. Numerical simulation using FEM for two-dimensional and three-dimensional impellers was investigated. A commercially available software ANSYS is used for the finite element calculations. Analysis is done for different blade geometries and then suggestions are made for optimum design parameters. In order to avoid operating at resonance, which can make impellers suffer a significant reduction in the design life, the designer must calculate the natural frequency and modal shape of the impeller to analyze the dynamic characteristics. The results show that using composite Kevlar fiber/epoxy matrix enables the impeller to run at high tip speed and withstand the stresses, no critical speed will be matched during start-up and shut-down, and that mass imbalances of the impeller shall not pose a critical problem.

Imbalance Vibration Suppression of a Supercritical Shaft via an Automatic Balancing Device

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
H. A. DeSmidt
Keyword(s):  
Fixed Point ◽  
Vibration Suppression ◽  
Hard Disk Drives ◽  
Disk System ◽  
Dynamic Interactions ◽  
Single Plane ◽  
Flexible Shaft ◽  
Flexible Mode ◽  
Equilibrium Configurations ◽  
Automatic Balancing

This research explores the use of automatic balancing (AB) devices or “autobalancers” for imbalance vibration suppression of flexible shafts operating at supercritical speeds. Essentially, an autobalancer is a passive device consisting of several freely moving eccentric masses or balancer balls free to roll within a circular track mounted on a rotor that is to be balanced. At certain speeds, the stable equilibrium positions of the balls are such that they reduce or cancel the rotor imbalance. This “automatic balancing” phenomenon occurs as a result of the nonlinear dynamic interactions between the balancer balls and the rotor transverse vibration. Thus, autobalancer devices can passively compensate for unknown imbalance without the need for a control system and are able to naturally adjust for changing imbalance conditions. Autobalancers are currently utilized for imbalance correction in some single plane rotor applications such as computer hard-disk drives, CD-ROM drives, machine tools and energy storage flywheels. While autobalancers can effectively compensate for imbalance of planar, disk-type, rigid rotors, the use of autobalancing devices for nonplanar and flexible shafts with multiple modes of vibration has not been fully considered. This study explores the dynamics and stability of an imbalanced flexible shaft-disk system equipped with a dual-ball automatic balancing device. The system is analyzed by solving a coupled set of nonlinear equations to determine the fixed-point equilibrium conditions in rotating coordinates, and stability is assessed via eigenvalue analysis of the perturbed system about each equilibrium configuration. It is determined that regions of stable automatic balancing occur at supercritical shaft speeds between each flexible mode. Additionally, the effects of bearing support stiffness, axial mounting offset between the imbalance and autobalancer planes, and ball/track viscous damping are explored. This investigation develops a new, efficient, analysis method for calculating the fixed-point equilibrium configurations of the flexible shaft-AB system. Finally, a new effective force ratio parameter is identified, which governs the equilibrium behavior of flexible shaft/AB systems with noncollocated autobalancer and imbalance planes. This analysis yields valuable insights for balancing of flexible rotor systems operating at supercritical speeds.

Limit-Cycle Analysis of Planar Rotor/Autobalancer System Supported on Hydrodynamic Journal Bearing

2011 ◽  
Author(s):  
DaeYi Jung ◽  
Hans DeSmidt
Keyword(s):  
Steady State ◽  
Limit Cycle ◽  
Journal Bearing ◽  
Cross Coupling ◽  
Numerical Continuation ◽  
Radial Clearance ◽  
Oil Viscosity ◽  
Rotor Systems ◽  
Automatic Balancing ◽  
Limit Cycle Behavior

In recent years, there has been much interest in the use of so-called automatic balancing devices (ABD) in rotating machinery. Essentially, ABDs or “autobalancers” consists of several freely moving eccentric balancing masses mounted on the rotor, which, at certain operating speeds, act to cancel rotor imbalance at steady-state. This “automatic balancing” phenomena occurs as a result of nonlinear dynamic interactions between the balancer and rotor wherein the balancer masses naturally synchronize with the rotor with appropriate phase and cancel the imbalance. However, due to inherent nonlinearity of the autobalancer, the potential for other, undesirable, non-synchronous limit-cycle behavior exists. In such situations, the balancer masses do not reach their desired synchronous balanced steady-state positions resulting in increased rotor vibration. Such automatic behavior has been widely studied and is well understood for rotor systems on idealized bearings with symmetric supports. This paper presents a comprehensive study into automatic balancing behavior of an imbalanced planar rigid rotor/ABD system mounted in two different widely-used types of hydrodynamic bearings; i) the short journal bearing with asymmetric stiffness, damping and cross-coupling terms and ii) a so-called tilting-pad bearing. In this study the non-dimensional characteristic curves of stiffness and damping of these two fluid film bearings are employed and the rotor/bearing/ABD system autobalancing behavior is studied as a function of rotor speed, bearing eccentricity and bearing journal radial clearance. These two essential bearing parameters in turn are directly determined by the rotor static loading, bearing structure, and oil viscosity. Consequently, this research focuses on the connectivity between the bearing parameters and the corresponding synchronous balancing and non-synchronous limit-cycle behavior of the system. Here, solutions for rotor limit-cycle amplitudes and corresponding autobalancer ball speeds are obtained via a harmonic balance and numerical continuation solution approach. Furthermore, an exact solution for the limit-cycle is obtained for the special case of symmetric support stiffness together with a so-called Alford’s force cross-coupling term. In each case, the limit-cycle stability is assessed via a perturbation and Floquet analysis and the coexistence of the stable balanced synchronous limit-cycle and undesired non-synchronous limit-cycle is studied. It is found that for certain combinations of bearing parameters and operating speeds, the non-synchronous limit-cycle can be made unstable thus guaranteeing global asymptotic stability of the synchronous balanced condition. Finally, the analysis is validated through numerical time-domain simulation. The findings in this paper yield important insights for researchers wishing to utilize automatic balancing devices in practical rotor systems.

Imbalance Vibration Suppression of Supercritical Shafts With Automatic Balancing Devices

2007 ◽  
Author(s):  
Hans DeSmidt
Keyword(s):  
Vibration Suppression ◽  
Hard Disk Drives ◽  
Type Systems ◽  
Disk System ◽  
Single Plane ◽  
Cd Rom ◽  
Flexible Shaft ◽  
Flexible Mode ◽  
Rotating Coordinates ◽  
Automatic Balancing

This research explores the use of automatic balancing devices (autobalancers) for imbalance suppression of flexible shafts operating at supercritical speeds. Essentially, autobalancers are passive devices consisting of several balls free to roll within an oil-filled circular track mounted on a rotor or shaft to be balanced. At certain speeds, the stable equilibrium positions of the balls is such that they reduce or cancel the rotor imbalance. This “automatic balancing” phenomena occurs as a result of the non-linear dynamic interaction between the balancer balls and the rotor transverse vibrations. Thus, autobalancer devices can passively compensate for unknown imbalance without the need for a control system and naturally adjust for gradually changing imbalance conditions. Single-plane autobalancers are widely utilized for imbalance correction of computer hard-disk drives and CD-ROM drives as well as for balancing machine tools. While autobalancers can effectively compensate for imbalance of planar disk-type systems and rigid rotors, the use of autobalancing devices on flexible shafts has not been fully considered. This study explores the dynamics and stability of an imbalanced flexible shaft-disk system equipped with a dual ball autobalancer by solving a coupled set of nonlinear equations to determine the fixed-point equilibrium conditions in rotating coordinates. Stability is assessed via eigenvalue analysis of a perturbed system about each equilibrium configuration. It is determined that regions of stable automatic balancing occur at supercritical shaft speeds between each flexible mode. Additionally, the effects of bearing stiffness, autobalancer/imbalance-plane axial offset distance, and relative ball-track viscous damping are each explored. This investigation yields valuable analysis methods and insights for the application of automatic balancing devices to flexible shaft and rotor systems operating at supercritical speeds.

Design and optimization of bump (compression surface) for diverterless supersonic inlet

2021 ◽  
pp. 095441002110029
Author(s):  
Irsalan Arif ◽  
Hassan Iftikhar ◽  
Ali Javed
Keyword(s):  
Fitness Function ◽  
Supersonic Jet ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Least Square ◽  
Pressure Recovery ◽  
Design Parameters ◽  
Inlet System ◽  
Design And Optimization ◽  
Supersonic Inlet

In this article design and optimization scheme of a three-dimensional bump surface for a supersonic aircraft is presented. A baseline bump and inlet duct with forward cowl lip is initially modeled in accordance with an existing bump configuration on a supersonic jet aircraft. Various design parameters for bump surface of diverterless supersonic inlet systems are identified, and design space is established using sensitivity analysis to identify the uncertainty associated with each design parameter by the one-factor-at-a-time approach. Subsequently, the designed configurations are selected by performing a three-level design of experiments using the Box–Behnken method and the numerical simulations. Surrogate modeling is carried out by the least square regression method to identify the fitness function, and optimization is performed using genetic algorithm based on pressure recovery as the objective function. The resultant optimized bump configuration demonstrates significant improvement in pressure recovery and flow characteristics as compared to baseline configuration at both supersonic and subsonic flow conditions and at design and off-design conditions. The proposed design and optimization methodology can be applied for optimizing the bump surface design of any diverterless supersonic inlet system for maximizing the intake performance.

scholarly journals Research on the Computed Tomography Pebble Flow Detecting System for HTR-PM

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Xin Wan ◽  
Ximing Liu ◽  
Jichen Miao ◽  
Peng Cong ◽  
Yuai Zhang ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Three Dimensional ◽  
Helical Ct ◽  
Design Parameters ◽  
Three Dimensional Model ◽  
Safe Operation ◽  
Cross Sectional ◽  
Ct System ◽  
Near Future ◽  
Pebble Flow

Pebble dynamics is important for the safe operation of pebble-bed high temperature gas-cooled reactors and is a complicated problem of great concern. To investigate it more authentically, a computed tomography pebble flow detecting (CT-PFD) system has been constructed, in which a three-dimensional model is simulated according to the ratio of 1 : 5 with the core of HTR-PM. A multislice helical CT is utilized to acquire the reconstructed cross-sectional images of simulated pebbles, among which special tracer pebbles are designed to indicate pebble flow. Tracer pebbles can be recognized from many other background pebbles because of their heavy kernels that can be resolved in CT images. The detecting principle and design parameters of the system were demonstrated by a verification experiment on an existing CT system in this paper. Algorithms to automatically locate the three-dimensional coordinates of tracer pebbles and to rebuild the trajectory of each tracer pebble were presented and verified. The proposed pebble-detecting and tracking technique described in this paper will be implemented in the near future.

scholarly journals Reliability Evaluation of Fan-Out Type 3D Packaging-On-Packaging

Micromachines ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 295
Author(s):  
Pao-Hsiung Wang ◽  
Yu-Wei Huang ◽  
Kuo-Ning Chiang
Keyword(s):  
Finite Element ◽  
Thermal Cycling ◽  
Glass Substrate ◽  
High Speed ◽  
Coefficient Of Thermal Expansion ◽  
Three Dimensional ◽  
Design Parameters ◽  
Time To Failure ◽  
Wafer Level ◽  
Fine Pitch

The development of fan-out packaging technology for fine-pitch and high-pin-count applications is a hot topic in semiconductor research. To reduce the package footprint and improve system performance, many applications have adopted packaging-on-packaging (PoP) architecture. Given its inherent characteristics, glass is a good material for high-speed transmission applications. Therefore, this study proposes a fan-out wafer-level packaging (FO-WLP) with glass substrate-type PoP. The reliability life of the proposed FO-WLP was evaluated under thermal cycling conditions through finite element simulations and empirical calculations. Considering the simulation processing time and consistency with the experimentally obtained mean time to failure (MTTF) of the packaging, both two- and three-dimensional finite element models were developed with appropriate mechanical theories, and were verified to have similar MTTFs. Next, the FO-WLP structure was optimized by simulating various design parameters. The coefficient of thermal expansion of the glass substrate exerted the strongest effect on the reliability life under thermal cycling loading. In addition, the upper and lower pad thicknesses and the buffer layer thickness significantly affected the reliability life of both the FO-WLP and the FO-WLP-type PoP.

Research on the Reliability of Box for Gear Test Bed

2011 ◽  
Vol 121-126 ◽  
pp. 1744-1748
Author(s):  
Xiang Yang Jin ◽  
Tie Feng Zhang ◽  
Li Li Zhao ◽  
He Teng Wang ◽  
Xiang Yi Guan
Keyword(s):  
Power Flow ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Design Parameters ◽  
The Finite Element Method ◽  
Test Bed ◽  
Kinematics Simulation ◽  
Beveloid Gears ◽  
Overall Performance

To determine the efficiency, load-bearing capacity and fatigue life of beveloid gears with intersecting axes, we design a mechanical gear test bed with closed power flow. To test the quality of its structure and predict its overall performance, we establish a three-dimensional solid model for various components based on the design parameters and adopt the technology of virtual prototyping simulation to conduct kinematics simulation on it. Then observe and verify the interactive kinematic situation of each component. Moreover, the finite element method is also utilized to carry out structural mechanics and dynamics analysis on some key components. The results indicate that the test bed can achieve the desired functionality, and the static and dynamic performance of some key components can also satisfy us.

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