Imbalance Mass Research Articles

A hybrid triboelectric-piezoelectric smart squirrel cage with self-sensing and self-powering capabilities

In aero-engines, squirrel cages are commonly used as elastic support parts for bearings, serving to adjust critical speeds and provide vibration damping. Their stable operation is critical for the safety and stability of rotor systems. In this paper, a triboelectric-piezoelectric squirrel cage (TPSC) with self-sensing and self-powering capabilities is proposed. Owing to the ingenious utilization of the supporting structure, a compact design is achieved, enabling energy harvesting from the relative motion of the rotor-stator structure and the vibration of elastic support. Based on a fabricated prototype, a series of experiments are carried out to investigate the effect of the rotating speed, imbalance mass, and contact mode on the output performance of TPSC. Under the rotating frequency of 15 Hz, a maximum power output of 100.0 μW is achieved. The TPSC is capable of sensing rotating speed and detecting rolling bearing faults. A self-powered temperature and humidity sensing system that can transmit data wirelessly every 10 minutes is also realized. The TPSC enables self-powered monitoring of rotor bearing systems with squirrel cages, providing a new option for online condition monitoring of aero-engines.

A method for establishing a bearing residual life prediction model for process enhancement equipment based on rotor imbalance response analysis

A rotating packed bed is a typical chemical process enhancement equipment that can strengthen micromixing and mass transfer. During the operation of the rotating packed bed, the nonreactants and products irregularly adhere to the wire mesh packing in the rotor, thus resulting in an imbalance in the vibration of the rotor, which may cause serious damage to the bearing and material leakage. This study proposes a model prediction for estimating the bearing residual life of a rotating packed bed based on rotor imbalance response analysis. This method is used to determine the influence of the mass on the imbalance in the vibration of the rotor on bearing damage. The major influence on rotor vibration was found to be exerted by the imbalanced mass and its distribution radius, as revealed by the results of orthogonal experiments. Through implementing finite element analysis, the imbalance response curve for the rotating packed bed rotor was obtained, and a correlation among rotor imbalance mass, distribution radius of imbalance mass, and bearing residue life was established via data fitting. The predicted value of the bearing life can be used as the reference basis for an early safety warning of a rotating packed bed to effectively avoid accidents.

Implementation of the dynamic balancing approach of a rotating composite hollow shaft

Balancing is essential in rotating machinery, which is widely employed in many technical sectors, particularly in high-speed rotor-bearing systems. The mass balancing method of the hollow shaft manufactured of composite materials is investigated in this study over the whole speed range of the rotor. The main goal of the balancing technique is to generate a smooth-running machine by removing the commonality imbalance mass through the use of compensating mass unbalance. As a result, MATLAB code is created to produce a functioning mathematical model of the rotor-bearing system. The unbalanced rotor-bearing system finite element model is proposed to set the balancing mass of the composite hollow shaft at a selected speed rotor that allows minimizing the vibration response amplitude of the rotor as much as possible with minimal impact on the rest of the imbalance response within the speed range of the interest. As a consequence, this study validates the process for distributing imbalance in modelling balancing to balance the flexible hollow shaft with an unbalanced mass throughout the complete speed range of the shaft. The balance of the hollow shaft at the critical speed was observed in this approach, and the vibration amplitude was determined by adding extra mass at a specific angle

Correlation Analysis and Its Application on an Asymmetry Rotor Structure with Overhang

Overhung rotors are widely used in the industrial field. However, compared with normal structure rotors, the prediction and control of overhung rotors cannot achieve good performance. The work aims to investigate the dynamical behaviours of an overhung rotor by means of correlation analysis, and find its possible application. In this work, based on a real type of rotor, the dynamic model of the rotor with overhang is established by means of the finite element method. Simulation of the dynamic model with different input positions and support stiffnesses is conducted. Based on the methodology of correlation analysis, by introducing a correlation parameter of a proportion of amplitude of measured signal and imbalance mass, the position which has most effect on the vibration is found. Meanwhile, an experiment on the same type of overhung rotor is carried out to validate the results. The numerical results and corresponding experimental results prove that the overhung node has the most effect on the vibration amplitudes of the measured points. Choosing the overhung node to add trial weight, the overhung rotor can be easily balanced. The theory provides an alternative approach to modal analysis which needs more knowledge of the system.

Nonlinear dynamics of drill string in horizontal well under axial load and supercritical regime of flowing fluid

In this article, the nonlinear vibration of the spinning pipe conveying fluid in a borehole drilling is investigated under the axial compression load, nonlinear fluid forces, internal and external resonances. The spinning pipe is modeled as a simply supported rotor with imbalance mass and eccentricity. When the flowing fluid is in supercritical regime the pipe oscillates around an equilibrium position in the working frequency range of external excitation. Two to one internal resonance condition between forward and backward natural frequencies of the pipe is found at specific values of flow velocity and rotating speed. The multiple scales method is occupied to solve the governing ordinary differential equations and solvability condition is applied to get the modulation equations. The Runge–Kutta integration and the arc-length continuation method are used for directly solving ordinary differential equations. Bifurcation diagrams are plotted and time responses, phase portraits and Fast Fourier transformation of amplitudes are achieved. The Wolf algorithm is used to determine the Lyapunov Exponents. Periodic, multi-periodic, quasi-periodic, double jump and chaotic behaviors can be seen in simulation results.

Optimization of Factors Affecting Vibration Characteristics of Unbalance Response for Machine Motorized Spindle Using Response Surface Method

In this study, the response surface (RS) method and forced rotordynamic analyses together with Finite-Element-Analysis (FEA) have been established to optimize the factors affecting the vibration characteristics. The spindle specification, bearings locations, cutting force, and motor-rotor unbalance mass are proposed to represent the design factors and then they are utilized to develop Machine Motorized Spindle (MMS). The FEA-based Design of Experiment (DOE) is adopted to simulate the output responses with the input factors, wherein these DOE design points are used to carry out the RS models to visualize more obvious factors affecting the dynamic characteristics of MMS. The sensitivities of these factors and their contributions to the vibration of imbalance response have been evaluated by using the RS models. The simulation results show that the motor-rotor shaft inner diameter, the distance of the back bearing location, and the rotating unbalance-mass are highly sensitive to the vibration characteristics compared to the other factors. It is found that more than two-fifths of total vibration response amplitude has been conducted by induced rotating imbalance mass. The results also showed that the proposed factors optimization method is practicable and effective in improving the vibration response characteristics.

Measurements of the Rotordynamic Response of a Rotor Supported on Porous Type Gas Bearing

A test rig is built in this study to measure the rotordynamic response of a rotor supported on porous-type gas bearings. A rotor with a double impulse turbine at one end is driven by compressed air and supported on two porous type journal gas bearings and a pair of bump-type thrust gas bearings. The rotor is accelerated to ∼25 krpm and coasted down in the test. The rotor dynamic response is measured for different bearing supply pressures (i.e., 0.40 MPa, 0.45 MPa, and 0.50 MPa) and imbalance masses (i.e., 85 mg, 150 mg, and 215 mg). Synchronous and subsynchronous amplitudes are extracted from the rotor responses. The critical speed increases as the bearing supply pressure increases, but the damping ratio decreases. The onset speed of subsynchronous motion increases, and the subsynchronous amplitude decreases as the bearing supply pressure increases. The deceleration time is more than 5 min for a bearing supply pressure of 0.5 MPa, which reveals the very low drag friction of the porous gas bearings. The synchronous amplitude increases as the imbalance increases for all the tested bearing supply pressures. The critical speeds for different imbalances are almost the same, except for the out-of-phase imbalance condition under a bearing supply pressure of 0.50 MPa, in which the critical speed increases as the imbalance increases. The normalized synchronous amplitude shows the rotor-bearing system behaves almost in a linear fashion for all in-phase imbalance conditions. Nonlinear behavior is shown around the critical speed for the 215 mg out-of-phase imbalance condition under a bearing supply pressure of 0.50 MPa. The onset speed of the subsynchronous motion decreases as the imbalance increases under the in-phase imbalance condition. The predominant mode of vibration changes from cylindrical to conical and then back to cylindrical as the rotor speed decreases during the coast down test for the in-phase imbalance conditions. However, the rotor vibration mode is predominantly conical during the whole coast down test for the out-of-phase imbalance conditions.

An offset hub active vibration control system for mitigating helicopter vibrations during power loss: Simulation and experimental demonstration

In recent years, hub active vibration control (HAVC) technologies have been developed to attenuate blade pass frequency vibration on helicopters. While these systems provide superior vibration control with reduced weight compared to passive options, in the event of electrical power loss they can exacerbate the vibration problem in a manner that is problematic for helicopter and tiltrotor aircraft. This paper presents an offset hub active vibration control system (OHAVCS) designed to attenuate vibration during a power loss by offsetting the centers of rotation of two imbalance masses. The equations of motion for this system are developed using Lagrangian methods; analysis, simulation and experimental validation of these equations indicate that offsetting the imbalance masses effectively mitigates 1/Rev vibrations during a rotor hub power loss while continuing to cancel N/Rev vibrations during normal operation. These offsets create stabilizing centripetal torques that rotate each imbalance mass to a unique equilibrium angle. Experimental data also indicate that these offsets do not hinder control of the imbalance masses during normal (active) operation, though they do increase system power requirements.

Research on Mass Imbalance Fault of Wind Turbine Based on Virtual Prototype

Wind turbine virtual prototype was set up with SIMPACK software. The influence of different mass in different blades was researched by changing size and position of imbalance mass. Results showed that the period of imbalanced moment inducted by different size of imbalance mass imposing blades at different position was the same as the wind turbine rotor, but the amplitude and phase was different. Electricity generation during starting was associated with not only the size of mass but also the position. After starting, wind turbine would keep the stable state in simulation, power and revolution speed and pitch angle curves would wave periodically, the periods were all the same as the wind turbine rotor, the size of imbalance masses were bigger, the fluctuation amplitude of curves were greater.

A Virtual Crankshaft Dynamic Balance Measuring System Based on VB

A crankshaft dynamic balance system designed based on VB is proposed in this thesis. The imbalance can be measured by using computing software and signal processing technology. The development principle, method, hardware and software system are all introduced. The modular design is used in software system. The touch-screen device is used to realize the data display, storage and analysis. And the imbalance mass and position can be displayed on the virtual instrument interface. Real-time monitoring and accurate information can be completed by the system. The experiment result shows this system is easy in operating, high in capability/price ratio and high in balancing precision. It can meet the producing demands and has good market prospects.

The Identification of Amplitude and Phase in Imbalance Mass of Grinding Wheel

Vibration signal produced by imbalance of grinding wheel is a periodic signal that has a same frequency with rotational speed. To identify the signal accurately is premise of balance for grinding wheel. This paper introduces the composition and basic concept of vibration signal in grinding wheel and further studies how to identify process and calculate about this vibration signal. It will provide theory evidence for grinding wheel’s dynamic balance.

Nonlinear vibration analysis of an axially moving drillstring system with time dependent axial load and axial velocity in inclined well

Abstract In this paper a nonlinear model was developed for a drillstring system in deviated well with axially moving motion and axial loading, using the perturbation techniques. The drillstring was considered as a simply supported axially moving rotor. Governing equations of motion were obtained based on Hamilton's principle and method of multiple scales was employed to solve the nonlinear motion equations in order to obtain the steady state response and stability region of the system. Then the effects of rotating speed, axial compression load, imbalance mass and nonlinear fluid force on the drillstring responses were investigated in detail and nonlinear natural frequencies and their corresponding mode shapes were presented. Analytical and numerical results reveal the rich and interesting nonlinear phenomena such as primary and parametric resonance that is being investigated for the first time in this study on the nonlinear vibration of the drillstring system. Finally in effort to validate the theoretical approach employed in this study, the numerical solutions obtained here were compared with a set of existing experimental data.

Experimental Investigation of Pedestal Looseness in a Rotor-Bearing System

An experimental setup of rotor-bearing system is installed and vibration characteristics of the system with pedestal looseness are investigated. The pretightening bolt between the bearing house and pedestal is adjusted to simulate the pedestal looseness fault. The vibration waveforms, spectra and orbits are used to analyze the nonlinear response of the system with pedestal looseness. Different parameters, including speed, looseness gap, imbalance mass and disk position are changed to observe the nonlinear vibration characteristics. The experiments show that the system motion generally contains the 1/2X fractional harmonic component and multiple harmonic components such as 2X, 3X, etc. Under some special conditions, the pedestal looseness occurs intermittently, that is, occurs in some periods and doesn’t in other periods.

Effect of Side Feed Pressurization on the Dynamic Performance of Gas Foil Bearings: A Model Anchored to Test Data

AbstractComprehensive modeling of gas foil bearings (GFBs) anchored to reliable test data will enable the widespread usage of these bearings into novel high speed turbomachinery applications. GFBs often need a forced cooling gas flow, axially fed through one end of the bearing, for adequate thermal management. This paper presents rotordynamic response measurements on a rigid rotor supported on GFBs during rotor speed run-up and coastdown tests with the GFBs supplied with increasing feed gas pressures to 2.8bars. Rotor speed run-up tests to 35krpm show that the bearing end side feed gas pressurization delays the onset speed of rotor subsynchronous whirl motions. The test data validate closely the predictions of the threshold speed of instability and the whirl frequency ratio derived from a GFB model that implements the axial evolution of gas circumferential flow velocity as a function of the imposed side feed pressure. Rotor speed coastdown tests from 25krpm with a low feed pressure of 0.35bar evidence a nearly linear synchronous rotor response for small and moderately large imbalance mass distributions. A structural finite element rotordynamics model integrates linearized synchronous speed GFB force coefficients and predicts synchronous responses, amplitude, and phase angles, agreeing with the test data. The analysis and measurements demonstrate the profound effect of the end side feed gas pressurization on the rotordynamic performance of GFBs.

The balancing of rotating machinery as non-linear system passing across a resonant region

This paper presents a dynamical balancing method for the rotational part of machine as a nonlinear system with the decrease of rotation speed passing across a resonant region. After analyzing the nonlinear system and measurable vibration signals, a suitable procedure of dynamical balance for determining the magnitude and location of imbalance mass is proposed. A program on PC is made to illustrate the obtained procedure. The results of numeric examples show that it can be used well for dynamical balancing analysis.

A Single-Plane Rotating Imbalance Experiment

A simple experiment to demonstrate single-plane rotating imbalance is described. Inexpensive and commonly available items were used in the experiment to emphasize the concepts presented in an uncluttered manner and to underline the importance of simplicity. Students were also required to assemble the experiment by themselves to maximize experiental learning. The experiment was able to provide accurate predictions of the angular position and magnitude that an imbalance mass imposed.

A MODIFIED APPROACH BASED ON INFLUENCE COEFFICIENT METHOD FOR BALANCING CRANK-SHAFTS

The conventional balancing machines utilize two-plane separation for the determination of equivalent imbalances. However, the imbalance masses of a crank-shaft cannot be corrected at arbitrary locations of the balancing planes. This study has presented a modified method for balancing crank-shafts by using the soft-pedestal machines. The modified influence coefficient method for asymmetrical rotor-bearing systems has been applied to balance crank-shafts. Also, the decomposition method for irremovable masses has been replaced by an iteration method based on an influence coefficient approach. Furthermore, the validity and accuracy of the modified approach are verified in balancing practical crank-shafts.

The balancing of rotating machinery as nonlinear system

In this paper a method for dynamical balancing of rotating machines as a nonlinear system is proposed. After analyzing and identifying the nonlinear system, procedure of dynamical balance including measurement and processing of vibration signals, for calculating magnitude and location of imbalance mass is presented. An example of simulation and calculation is investigated for illustration of the method.

Experimental Verification of Subcritical Whirl Bifurcation of a Rotor Supported on a Fluid Film Bearing

The paper presents the results of the experiments that were conducted on a short fluid film bearing with a simple single disk rotor. The behavior of the journal was analyzed as a function of the rotor system parameters such as the load, speed, and imbalance mass. It was verified that the journal bearing can lose stability through either a subcritical or a supercritical bifurcation. In the supercritical bifurcation, the expected gradual increase in the amplitude of the limit cycle was observed, while in the subcritical bifurcation there was a sudden jump to a large limit cycle. In the case of a subcritical bifurcation, it was also observed that the journal bearing became unstable below the rotor threshold speed of instability, following a small perturbation applied to the rotor. Demarcations were made for the stable regions of operation (regions where the rotor is stable below the threshold speed of instability) for the journal bearing based on the obtained experimental results. Experiments were also performed to analyze the effects of imbalance of the rotor on the threshold speed of instability. It was observed that the flexible unbalanced rotor had a lower threshold speed of instability. The limitations of the linear theory of fluid film bearings in predicting these phenomena are discussed.

Improving Traditional Balancing Methods for High-Speed Rotors

This paper introduces frequency response functions, analyzes the relationships between the frequency response functions and influence coefficients theoretically, and derives corresponding mathematical equations for high-speed rotor balancing. The relationships between the imbalance masses on the rotor and frequency response functions are also analyzed based upon the modal balancing method, and the equations related to the static and dynamic imbalance masses and the frequency response function are obtained. Experiments on a high-speed rotor balancing rig were performed to verify the theory, and the experimental data agree satisfactorily with the analytical solutions. The improvement on the traditional balancing method proposed in this paper will substantially reduce the number of rotor startups required during the balancing process of rotating machinery.