Mass Unbalance Research Articles

The physical basis of the vibration of the upper part of the pipe string when drilling wells

The article discusses the fundamental issues related to the assessment of the dynamics of the top drive system as one of the sources of vibration when drilling wells. The operational parameters of the drive load at which a resonance phenomenon is observed are determined. The optimal parameters for reducing the amplitudes of forced oscillations, their resonance phenomena are revealed. Methods of protecting the derrick and equipment for protecting unbalanced masses of the top drive from vibration are considered. The prospect of using the layout of the columns, including alloy pipes, is to protect the bit.

MEMS-Enabled Retrofitting of Automobile Wheel Balancer for Automatic Unbalance Detection

The presence of asymmetries in the mass distribution of automobile tires causes anomalous forces and torques, which lead to vibrations and to ride disturbances. For this reason, detection of unbalanced masses is fundamental in order to perform a careful balancing, improving both safety and comfort. To this aim, traditional wheel balancers are passive devices that allow one to detect unbalances relying on force sensors. The major drawbacks of this technology are the high production costs and the loss of accuracy of the force sensors during the wheel balancer lifetime. In this article, a new sensors layout for the next generation of wheel balancers is proposed together with a structural modification of the machine that allows us to magnify the information provided by the sensors. Notably, these modifications are quite practical, and allows retrofitting traditional machines. The goal is to prove the effectiveness of accelerometers and gyroscopes, which are low-cost devices requiring minimum calibration effort, for unbalance detection purposes. To this aim, an unbalance detection algorithm is developed. Starting from the amplitudes and phases of the signals acquired by the sensors, the severity and the angular position of the unbalance are determined relying on a regression model. Then, the proposed detection strategy is experimentally tested in different unbalance conditions.

Identification of Unbalance in Rotating Machinery Using Vibration Analyse Solution

Vibrations in rotating machinery are normally the consequence of mechanical faults such as mass unbalance, manufacturing, mechanical looseness, assembly, installed machines, coupling misalignment, and many other causes. However, unbalance is the most popular reason of machine vibration. An unbalanced rotor always causes more vibration and generates excessive force in the bearing area and reduces the life of the machine. In this paper, experimental studies were performed on a rotor with two mounted disks to identify the unbalance in rotor using order tracking technique based on one key phasor. After calculation of the coefficients of influence α of each experimental test, the matrix of influence coefficient [C] and the global matrix of coefficients [H] can be obtained. Finally, the two suitable masses are identified in order to reduce the unbalance of the rotor systems.

A Study of New Washing Process Which Combines Deflection and Abrasion Action

This study aimed to determine the optimum washing of laboratory washing model that design to stimulate the active washing process and passive commercial washing machine are compared in order to determine the best washing result. Variables of the study include water speed, washing time and radial nozzle inclination angle. The rotational system of an automatic washing machine has two major technical difficulties. One is the collision of the tub against the frame at the beginning of its early spinning stage. A factor that causes such instability of the rotational object can be attributed to the deflection of the liquid inside the liquid balancer due to the unbalance mass. Proposed a new washing technology and new design of the washing machine can be as a base of its new type. These machines have better outcome data; improve quality of washing process and effective use of washing liquid. New washing machine is simple design, does not have rotary parts at all and uses active process of washing process with squeezing of linens and more productive then known washing machines. Also, this machine can recycle and feed cleaned washing liquid. Additionally, in use of ultrasonic technology of washing process, new machine today will be perfect design.

Nonlinear forced vibration analysis of aircraft wings with rotating unbalanced mass of the propeller system

In this paper, the aeroelastic response of a wing containing a propeller system with rotating unbalanced mass is presented. Nonlinear structural model of the wing carrying a propeller system is extracted and coupled with an incompressible unsteady aerodynamic model. The governing equations and boundary conditions are determined via Hamilton’s variational principle. Galerkin’s approach is used to transfer the resulting partial differential equation into ordinary nonlinear differential equations. Using the method of multiple scales, frequency response function of the system in different primary resonance cases is obtained analytically and the flutter occurrence possibility in each case is investigated. According to the results, jump phenomenon can be observed in each two primary resonance cases. Also, for the case of non-resonant excitation, the stability of the system is independent of the rotating unbalanced mass parameter.

Dynamic stability and bifurcation phenomena of an axially loaded flexible shaft-disk system supported by flexible bearing

The present research studies the vibration and bifurcation analysis of a spinning rotor-disk-bearing system to carefully scrutinize the dynamic stability under extrinsic mass unbalance and pulsating axial load. The shaft is flexible and taken into account the geometrical nonlinearities due to large elastic deformation in bending. The rotor is supported by flexible bearings, which are modeled as an equivalent spring-damper system having linear and nonlinear stiffness elements. Equation of motion of the rotating system, which includes flexible shaft, rigid disk, and flexible bearing, is derived using extended Hamilton principle with the assumption of the Euler's beam theory. We studied initially the modal analysis to determine the modal parameters, i.e. natural frequency and mode shapes prior to the investigation of the dynamics of the system. Further, we developed the bifurcation diagram for steady-state solutions and to study the subsequent dynamic stability and verify with the findings solved numerically. The interactive behavior among the nonlinear shaft-bearing, axial load and an unbalance has been analyzed. Numerical simulation tools, i.e. frequency–response characteristics, time history, phase trajectories, and Poincaré map have been used to highlight the presence of nonlinear phenomena and its important role towards evaluating the system dynamics and subsequent stability. This current research showed that flexible bearings stabilize the system as a result of increasing the restoring force. Analyzing the bifurcation diagrams of pulsating axial load, we found that the system exhibits complex phenomena as multiple but stable periodic orbits leading to period doubling. The present system is highly vulnerable to catastrophic failure due to the S–N and Pitchfork bifurcation. The present research enables the notability of axial load and mechanical unbalance on the overall system behavior and stability in real working conditions.

Characterization and Evaluation of Rotation Accuracy of Hydrostatic Spindle under the Influence of Unbalance

The paper studies the characterization and evaluation technology of rotation accuracy of hydrostatic spindle under the influence of unbalance. The dynamic model of the motion error of the hydrostatic spindle is established based on the dynamic parameters. The variation law of motion error of spindle rotor is analyzed under the unbalanced mass. The paper finds that with the increase of the spindle speed, the amplitude of the spindle error motion will increase, and the inclination angleθerror is more sensitive to the change in the rotational speed. In the total synthesis accuracy, the proportion of synchronization error decreases with the increase of the rotational speed. Finally, the least squares evaluation algorithm is used to evaluate the rotation error of the hydrostatic spindle, and a method for evaluating the rotation accuracy of the hydrostatic spindle with high calculation accuracy and calculation efficiency is proposed.

A Corrected Adaptive Balancing Approach of Motorized Spindle Considering Air Gap Unbalance

Motorized spindles widely used for high-speed precision machine tools are very sensitive to the mass unbalance of rotors; thus, their balancing problem is always a research hotspot. Although many significant studies were done regarding the theory and application of various rotor balancing technologies for motorized spindles, the particularity of motorized spindles is not carefully considered in the existing balancing approaches. When the rotor unbalance of a motorized spindle occurs in operation, it is subject to both the mass unbalance-induced inertia force and air gap unbalance-induced electromagnetic force, which is an important feature that distinguishes the motorized spindle from a mechanical spindle. This paper describes an investigation into the corrected adaptive balancing approach of a motorized spindle by newly introducing a coefficient representing the removing effect of the air gap unbalance of the motor on the balancing capacity into the balancing formula. The determination of the newly defined coefficient refers to the calculation of electromagnetic force caused by the dynamic air gap eccentricity of motor; thus, much attention is paid to the analytical derivation of the unbalanced magnetic pull (UMP). Finally, a motorized spindle with an electromagnetic ring balancer was developed; then, the balancing tests and vibration signal analysis were done to validate the effectiveness of the newly proposed balancing approach in residual vibration reduction. It can be seen from the test results under different cases that the proposed balancing approach is effective.

Aeroelastic flutter control of a bridge using rotating mass dampers and winglets

Flutter control of a bridge deck section using a combination of aerodynamic and mechanical measures, that is controllable winglets and rotating mass dampers, is considered. Deck and winglets are considered as flat plates for their aerodynamics. Self-excited wind forces are represented in the time domain using the Scanlan–Tomko model with Roger’s rational function approximation for flutter derivatives. Winglet rotation relative to the deck is the control input generated by the variable-gain output feedback controller that uses vertical and torsional displacements of the deck as measured outputs. Control using winglets enhances the critical speed to twice the uncontrolled flutter speed. Further attenuation of vertical response is obtained by using rotating mass dampers configured to provide only a resultant vertical force due to counter-rotating unbalanced masses. The rotors are driven at a constant angular speed, and start–stop criteria are applied. This generates additional vertical force on the deck that is mostly out of phase with its vertical velocity. It yields better control than the damper operated in a continuous rotation mode for a fixed number of cycles. A maximum reduction of 15% in root mean square vertical response is obtained when compared with control using winglets only.

Vibration control of FSAE quarter car suspension test rig using magnetorheological damper

Recently MRF damper -which has a significant controllable damping force - used frequently in many active and semi-active suspension systems. However, MRF damper needs controller to estimate the desired force to dissipate the occurred vibration instantaneously. PID controller is one of the effective feedback controllers which shows robustness and simplicity in control MRF dampers, but still the parameters of the PID controller under study to find out the optimum values. This study focused on the vibration control using Magneto-rheological (MR) damper on a FSAE quarter car suspension test rig to study and obtain the optimum running condition. The test rig was designed, modified and then tested using a P-controller integrated with MR damper, unbalance mass used as disturbance and analyzed using LABVIEW software in time and frequency domains. The natural frequency obtained was 2.2 Hz were similar to the actual FSAE car natural frequency. Based on the acceleration against time graph with different proportional gain value the optimal value for proportional gain, Kp was 1. Hence, the experiment work could be used as the initial stage to study and develop a robust controller to suppress vibration on a car.

Natural Frequency of Rotating Single-Walled Carbon Nanotubes with Considering Gyroscopic Effect

This paper investigates the bending vibration of rotating single-walled carbon nanotubes (SWCNTs) based on nonlocal theory. To this end, the rotating SWCNTs system modeled as a beam with a circular cross section and the Euler-Bernoulli beam theory (EBT) is applied with added effects such as rotary inertia, gyroscopic effect and rotor mass unbalance. Using nonlocal theory, two coupled sixth order partial differential equations that govern the vibration of rotating SWCNTs are derived. To obtain the natural frequency and dynamic response of the nanorotor system, the equation of motion for the rotating SWCNTs are solved. It is found that there are two frequencies in the frequency spectrum. The positive rootintroduced as forward whirling mode, while the negative root represents backward whirling mode. The detailed mathematical derivations are presented while the emphasis is placed on investigating the effect of the several parameters such as, tube radius, angular velocity and small scale parameter on the vibration behavior of rotating nanotubes. It is explicitly shown that the vibration of a spinning nanotube is significantly influenced by these effects. To validate the accuracy and efficiency of this work, the results obtained herein are compared with the existing theoretical and experimental results and good agreement is observed. To the knowledge of authors, the vibration of rotating SWCNTs considering gyroscopic effect has not investigated analytically yet and then the results generated herein can be served as a benchmark for future works.

A Comparison of Time-Frequency Methods for Nonlinear Dynamics and Chaos Analysis in an Energy Harvesting Model

In this paper, an energy harvesting model based on a portal frame structure, modeled as a duffing system, with a non-ideal excitation force, DC motor with an unbalanced mass, is presented and the piezoelectric coupling is designed to exhibit nonlinear characteristics. Nonlinearity included provides higher power output over a wide frequency range. This analysis was carried out by numerical simulation of the proposed mathematical formulation. Thus, the bifurcation diagram and the largest Lyapunov exponents are plotted to investigate the dynamic behavior by ranging the voltage applied to the DC motor. In this way, power harvesting is analyzed for two different dynamic responses: periodic and chaotic behavior. Furthermore, this work exhibits an application of frequency-domain techniques, such as short-time Fourier transform, continuous wavelet transform, synchrosqueezed wavelet transform, and Wigner-Ville distribution methods. These methods are often used to analyze non-stationary signals, allowing the verification of dynamic behavior and power harvesting. Therefore, this paper aims to apply the time-frequency methods, mentioned previously, to analyze the mechanical system response in different behaviors.

Dynamic Balance Method for Grading the Chain Drive Double Threshing Drum of a Combine Harvester

Although the individual threshing drum of a combine harvester was balanced on a dynamic balancing machine before it is assembled, there were still unbalances after multiple drums were assembled with the chain drive. In this paper, the double drums with a chain drive of a crawler combined harvester were selected as the research subject. The aim of this study was to develop a dynamic unbalance mode for grading chain drive double drums. Based on the dynamic unbalance characteristics of the main driven drum, the experimental research on the radial balance of the driven drum end face was carried out. It was known that the chain drive had a direct and obvious influence on the unbalanced phase of the drum. The unbalance of the drive load had an obvious effect on unbalanced amplitude of an active drum through the transfer characteristics of the chain drive. For the multi-stage transmission characteristics of a combine harvester, a step-by-step balanced grading chain drive double drum dynamic balancing method was practiced. Results showed that the unbalanced amplitude after balancing threshing drum I chain transmission mode of the combine harvester can be reduced by a maximum of 91%. Simultaneously, the unbalanced amplitude of threshing drum II can reduced by a maximum of 69.2%. The size and position of the wrap angle of the chain drive would directly affect the phase of the two equivalent unbalanced masses.

Effect of Shaft Misalignment on Hypoid Gear Pair Driven Through a Universal Joint

An enhanced hypoid geared rotor system model incorporating a universal joint that connects driveline propeller shaft and pinion shaft is introduced in this study. The effect of shaft misalignment and pinion mass unbalance on hypoid gear dynamic response is evaluated under different assembly conditions. A nonlinear 14-DOF lumped parameter model based on coupled multi-body dynamics is applied by considering large rotational displacement in torsional direction. Results demonstrate three main influences from shaft misalignment and mass unbalance including speed and torque fluctuation as well as external bending moment on pinion shaft. It is also observed that bending moment generated can exert additional load on pinion shaft bearings which is found to be more sensitive to misalignment angle compared to dynamic response along line-of-action. Besides, shaft misalignment and mass unbalance excitation will interact with gear internal excitation from transmission error (TE) which can affect mesh parameters.

Magnetic Bearings for Marine Rotor Systems—Effect of Standard Ship Maneuver

In order to ensure safe motion of ships, the International Maritime Organization has laid down Standards for Ship Maneuverability, and has also specified standard maneuvers for testing of vessels. If an active magnetic bearing (AMB) is used to levitate and support a rotor shaft in a ship, the maneuvering motion of the ship will also be transferred to the AMB. This work analyzes the performance of an AMB used for supporting a marine rotor system under the effect of ship maneuvering. Vibration time response of the rotor shaft and the AMB control current for a standard maneuver, namely, the Zig-Zag-20, is particularly focused upon. A finite element model of the rotor shaft AMB system subject to motion of the base is first presented. The performance of the AMB in compensating for the rotor vibrations with and without the maneuvering of the base is studied. The numerical simulations reveal that the vibration amplitudes caused by the maneuvering of the ship is higher than that caused by mass unbalance in the rotor shaft. Certain design modifications in the AMB is suggested, so as to make it suitable for marine rotor application. Results with two different control laws with optimum control gains are presented.

Effect of AMB winding configurations on static and dynamic performances and power consumptions of the AMB-rotor system

Active magnetic bearings (AMBs) bring extraordinary benefits such as free of contact, elimination of lubrication, active control of rotor position, and a built-in monitoring system. In the design of AMBs, the bearing structure is of significance since it has an important impact on bearing performances. However, the effect of winding configurations of AMBs is still obscure. In this paper, the system-level implications of two radial AMB winding configurations termed the Ortho and the Cross types are investigated, including the bearing characteristics, power consumptions and rotor dynamic behaviors. The simulation results demonstrate that the Cross type contributes to larger load capacity in the direction of gravity. In condition of a heavier gravity load (−200 N), the Cross-type winding configuration saves power consumption with a percentage of 17.2% at steady state (20,000 rpm) and 12.7% considering unbalance mass during the run-up process. However, the rotor vibrations of the Cross type in case of external loads and unbalance mass are larger than the Ortho type. The proposed results of this paper provide some useful information for the AMB winding configuration design.

A Vectorial Approach to Unbalanced Optimal Mass Transport.

Unbalanced optimal mass transport (OMT) seeks to remove the conservation of mass constraint by adding a source term to the standard continuity equation in the Benamou-Brenier formulation of OMT. In this study, we show how the unbalanced case fits into the vector-valued OMT framework simply by adding an auxiliary source layer and taking the flow between the source layer and the original layer(s) as the source term. This allows for unbalanced models both in the scalar and vector-valued density settings. The results are demonstrated on a number of synthetic and real vector-valued data sets.

Generator of periodic inertia force concentrated in one direction

The paper is devoted to the problem of design for generator of periodic mechanical force based on use of inertia forces. Suggested construction transforms rotational motion of a crank of special type into swinging motion of pair of unbalanced masses. This creates inertia force of a constant sign directed along certain axes. Analytic and graphic representations for dependences of periodic force on time are presented in the article revealing the harmonic type of the force. Given construction has wide set of parameters for control and adaptation of the produced force.

Analysis of ways and methods of deformation measuring of rigid mounted axially symmetrical device elements.

In this article some technologies of modern devices manufacturing are reviewed which are intended to achieve the needed device accuracy. The imprecision of sensing element (SE) manufacturing and different factors influencing on it are observed too. Functioning of axially symmetric non-ideal gear under high-frequency load leads to deflection of SE axis from vertical direction which is result of unbalanced mass and moments influence. Many researches were devoted to develop some methods of this disbalance evaluation. Some of them are based on theoretical approaches to disbalance elimination, but it is impossible to make it real even on contemporary technology achievements. In other researches the procedure is sufficiently simplified but it could not reach the needed accuracy of balancing. The solutions are known which allow to evaluate the deflection of SE axis under load throughout the shift of the bar free end but such processing is made not for the final stage of manufacturing. Thus the additional structural element is in the SE design. After removing this additional element the balancing of the SE could be ruined. In this article the other method of deformations evaluation in dynamics is offered when the shift caused by non-ideal SE condition needs appropriate balancing. The rigid mounting of the SE is offered, when the base end of the bar is fixed and the other end becomes free after last technological operation. The procedure of measuring of the shifts caused by unbalancing masses and moments is made through the bar mounting place. The questions of unbalancing mass and moments influence on shifts values in the sensors balance area are studied. According to the given geometry and physical and mechanical properties of sensors the best combinations of geometry and device sizes are offered with mounting area restrictions and shifts measuring kept in mind.

Coupled Dynamic Modeling and Analysis of the Single Gimbal Control Moment Gyroscope Driven by Ultrasonic Motor

A control moment gyroscope (CMG) is a key actuator for spacecraft's attitude and stability control. But there exist micro-vibrations from high-speed flywheel, which will affect the performance of the spacecraft greatly. Due to the unbalanced mass and the supporting structure, the high-speed rotating flywheel could generate disturbance torque, which will be passed to the gimbal to deteriorate the gimbal servo system. At the same time, the rotation of the gimbal will increase the disturbance torque for gyroscopic effect. According · to the bearing theory, the stiffness of the bearing is affected by the load that applied on it, which results the influence on the flywheel vibration and the generated disturbance torque. This means that there is a coupling effect in the CMG. In this article, we focused on this coupling relationship between the flywheel vibration and the gimbal rotation in a single gimbal control moment gyroscope (SGCMG) system. Firstly, a vibration model of the flywheel with variable stiffness supporting is established. And the rotation model of the gimbal is also developed. The flywheel model and the gimbal model are coupled with each other through the variable stiffness supporting and gyroscope effect. Based on the numerical simulations the interactions among the bearing stiffness, the flywheel vibration and the gimbal rotation are analyzed. Finally, experiments are carried out on the prototype. The experimental results have verified the theoretical analysis and the simulations, and which would support the design of high-performance control system.