Unbalanced Excitation Research Articles

Analysis of the Nonlinear Complex Response of Cracked Blades at Variable Rotational Speeds

The operation of an aero-engine involves various non-stationary processes of acceleration and deceleration, with rotational speed varying in response to changing working conditions to meet different power requirements. To investigate the nonlinear dynamic behaviour of cracked blades under variable rotational speed conditions, this study constructed a rotating blade model with edge-penetrating cracks and proposes a component modal synthesis method that accounts for time-varying rotational speed. The nonlinear response behaviours of cracked blades were examined under three distinct operating conditions: spinless, steady speed, and non-constant speed. The findings indicated a competitive relationship between the effects of rotational speed fluctuations and unbalanced excitation on crack nonlinearity. Variations in rotational speed dominated when rotational speed perturbation was minimal; conversely, aerodynamic forces dominated when the effects of rotational speed were pronounced. An increase in rotational speed perturbation enhanced the super-harmonic nonlinearity induced by cracks, elevated the nonlinear damage index (NDI), and accentuated the crack breathing effect. As the perturbation coefficient increased, the super-harmonic nonlinearity of the crack intensified, resulting in a more complex vibration form and phase diagram.

Dynamic modeling and vibration analysis for motorized spindle with uncertainties

Abstract Uncertainties inevitably exist in motorized spindle and it is difficult to accurately describe its dynamics based on a deterministic model. In this paper, a dynamic model of motorized spindle with uncertainty is proposed. The deterministic dynamic model of the motorized spindle rotor system is built by the finite element method, and the uncertainties are constructed by the polynomial chaotic expansion (PCE) method. The impact of each uncertainty parameter on the critical speed of the system is investigated by adopting the Sobol global sensitivity analysis method. The effects of uncertainties including the bearing stiffness, the material Young’s modulus, the disc mass and the unbalanced excitation on the vibration response of motorized spindle are analyzed. The modal experiments are carried out to verify the effectiveness of the model. The results show that the uncertainties have a great influence on the vibration characteristics of the motorized spindle system, in which the bearing stiffness mainly affects the high-order frequency response of the system, while the Young’s modulus affects all the order frequency response of the system. The influence of hybrid uncertainties on the frequency response of the system is more complex. This study provides a guidance to the design of motorized spindle.

Nonlinear dynamics of a dual-rotor system with active elastic support/dry friction dampers based on complex nonlinear modes

In this study, the nonlinear dynamics of a dual-rotor system with active elastic support/dry friction dampers (ESDFDs) are investigated based on complex nonlinear modes (CNMs). The finite element method (FEM) combined with a full-3D friction model is introduced to construct the governing equation for the system. Additionally, the Craig–Bampton technique is applied to downscale the finite element model of the system. Based on the reduced order model (ROM), the nonlinear modal damping ratio of the target mode is employed to measure the dry friction damping performance of active ESDFD. The effects of the active ESDFD position, normal force, and tangential contact stiffness on the nonlinear modal damping ratio and modal frequency are analysed. Moreover, the softening characteristics of the active ESDFD are revealed, and the critical speed intervals of the active ESDFD/dual-rotor system are determined. Furthermore, by using the harmonic balance–alternating frequency/time domain (HB–AFT) method, the steady-state response of the system under unbalanced excitation is calculated. The accuracy and effectiveness of nonlinear modal analysis are validated based on the relationships between nonlinear modes and steady-state unbalanced responses. Conversely, the vibration mitigation effects of active ESDFD are determined by the unbalanced response amplitude. Additionally, the controllable region and optimal normal force for effective vibration control in the target mode are defined. Depending on the controllable region, a control strategy for turning on/off the optimal normal force is developed. The findings demonstrate that the developed control strategy enables the active ESDFD to significantly reduce the response amplitude of the dual-rotor system across various excitation levels, showing substantial potential for engineering applications.

Effects of Unbalanced Incentives on Threshing Drum Stability during Rice Threshing

As a result of the uneven growth of rice, unbalanced vibration of threshing drum caused by stalk entanglement in combine harvester is more and more severe. In order to reveal the influence of unbalanced excitation on the roller axis locus during rice threshing, the stability of threshing drum was studied. The dynamic signal test and analysis system are used to test the axial trajectory of threshing drum. At the same time, the influence of the unbalanced excitation caused by the axis winding on the axis trajectory is analyzed by the experimental results. Axis locus rules under no-load and threshing conditions are obtained. In order to simulate the axial and radial distribution of unbalanced excitation along the threshing drum, the counterweight was distributed on the threshing drum instead of the entangled stalk. Then, the definite effect of unbalanced excitation on the rotating stability of threshing drum is analyzed. Results show that the amplitude of stem winding along the grain drum is larger in the vertical direction and smaller in the horizontal direction when compared with the unloaded state under 200 g weight. It was found that the amplitude in both horizontal and vertical directions decreased after 400 g and 600 g counterweights were added, respectively, to simulate the radial distribution of stalk winding along the grain barrel. Finally, it can be seen that with the increase in the weight of the counterweight, the characteristics of the trajectory misalignment of the threshing cylinder axis become more and more obvious. This study can provide reference for reducing the unbalanced excitation signal of threshing drum and improving driving comfort.

Nonlinear Dynamic Properties of Rigid–Elastic–Liquid Coupled Ball Bearings Considering External Load Excitation

In this study, a novel dynamic model of a ball bearing based on rigid–elastic–liquid (REL) coupling structure considering external load excitation is established, and the dynamic response of its outer ring under external load excitation is examined. First, the differential equation of the journal motion (i.e. the outer ring) is derived based on Newton’s law, and the oil film force induced by the REL coupling structure is determined by using the central finite difference method, planar bending theory of thin ring, and Simpson’s rule. Further, the fourth and fifth-order variable step length Runge–Kutta method is used to solve the kinematic differential equation. Second, the dynamic characteristics of the outer ring of the bearing under different speeds and elastic support structural parameters are examined. Finally, the feasibility of the theoretical model is verified through experiments. The results show that compared with the traditional squeeze film damper (SFD) system, the ball bearing with REL coupling structure is more stable, and the vibration damping effect is better under higher bearing speed, lower squirrel cage stiffness, and smaller elastic ring flexibility coefficient. The above findings provide useful insights into the dynamic characteristics of REL coupled ball bearings under unbalanced excitation, which can serve as a reference for the optimization design of such ball bearings.

Analysis of Nonlinear Vibration Characteristics and Whirl Behavior of Dual-Rotor Systems with Inter-Shaft Rub Impact

Previous studies on rub-impact faults have mainly focused on the rub-impact between rotors and stators, with less research on inter-rotor rub impact. The impact of inter-rotor rub impact on rotor nonlinear vibration is particularly significant. This study investigates the effects of inter-shaft rub impact on the vibration characteristics and whirl behavior of dual-rotor systems. Initially, a dual-rotor model with inter-shaft bearings is established using the finite element method, and inter-shaft rub-impact forces are derived based on contact mechanics. Next, the system response is solved using the Newmark method. Vibration characteristics are analyzed through Campbell diagrams, 3D waterfall plots, time-frequency domain plots, and steady-state rub-impact force plots. Finally, the influence of inter-shaft rub impact on the whirl behavior of the dual-rotor system is studied based on the theory of full-spectrum analysis. The study concludes that inter-shaft rub-impact faults shift the system’s resonance points backward, increase harmonic and combination frequency components, and significantly affect the system response under dual-rotor co-rotation. Excessive friction can lead to self-excited vibrations and sudden amplitude increases, particularly in the LP rotor frequency. Additionally, inter-shaft rub impact primarily affects the whirl behavior of the LP-compressor disk1, showing multiple cycles of forward and backward whirl alternation during acceleration due to combined unbalanced and rub-impact excitations.

Mechanical and vibration characteristics investigation of the elastic ring squeeze film damper-rotor considering oil film sealing and leakage

Elastic ring squeeze film damper (ERSFD) is extensively used in industrial rotating systems due to its excellent noise control and vibration suppression characteristics. However, the oil film sealing and leakage has a profound effect on the mechanical and vibration characteristics of the ERSFD and the ERSFD-rotor during operation. The sealing and leakage reduce the axial flow of the oil film, leading to changes in the initial boundary conditions of the flow field, which in turn affects the oil film pressure and damping coefficient of ERSFD. Meanwhile, the sealing causes an increase in the oil film force of ERSFD, which in turn affects the response of the rotor system. But there is relatively little research on the impact of sealing and leakage on the dynamic performances of ERSFD-rotor. In this paper, a mathematical model of ERSFD under different sealing conditions (no end seal, complete end seal, piston ring seal, O-ring seal) is established by changing the initial boundary equations of the flow field of ERSFD and the coupled solution of the Reynolds equation of ERSFD with different sealing and leakage boundary equations is realized. Then, the characteristics of oil film pressure and force of ERSFD under different sealing conditions is studied. After that, an ERSFD-rotor model considering oil film sealing and leakage is established based on displacement compatibility conditions and force balance principles. Meanwhile, the impact of sealing and leakage on the amplitude-frequency relation and sudden imbalance of an ERSFD combined support rotor is researched. The research results reveal that good sealing can significantly increase the damping of the system, thereby reducing the vibration amplitude of the ERSFD-rotor system. In addition, good sealing conditions can also shorten the transient process of sudden unbalanced excitation. Finally, the effectiveness of some simulation results was verified through experiments on the ERSFD rotor test bench.

Vibration Response Analysis of a Time-varying Stiffness Wheel with Contrate Gear under Unbalanced Excitation

The vibration and response of multi-contact interface micro-motion time-varying stiffness wheel are analyzed, and the nonlinear vibration response characteristics caused by the unbalance force of multi-contact interface contrate gear face of a gas turbine rotor are studied. Firstly, the local sliding model of dry friction-damped contact is extended to establish a holistic and local unified sliding model. The equivalent stiffness and damping of the damping device are calculated by means of the equivalent linearization method and the first harmonic balance method. Finally, the finite element model of multi-contact contrate gear rotor wheel is established to analyze the influence of different unbalanced masses on vibration response under nonlinear frictional contact. The results show that the response caused by the unbalance mass of multi-contact interface wheel with contrate gear is mainly radial response, and the peak value of resonance response increases with the increase of unbalance force.

Nonlinear Dynamic Analysis on Dual‐Rotor‐Bearing‐Casing System for Marine Gas Turbine

Taking the marine gas turbine as a research background, a dual‐rotor‐bearing‐casing system model was established considering the bearing nonlinearities and unbalanced excitation. Based on Lagrange’s equation of motion and rotor dynamics theory, the effects of key parameters such as radial clearance of intershaft bearing, rotor mass eccentricity, and rotational speed on the nonlinear characteristics of the system are investigated. The results indicate that the typical parameters have a significant effect on the system’s nonlinearities. To alleviate the vibration jump phenomenon, the radial clearance should be reduced to improve the coupling between the high‐ and low‐pressure rotors. Reducing the mass eccentricity can effectively degrade the resonance peaks, but it will highlight the hard resonance characteristics. The work process should pass through the resonant‐speed regions and the low‐speed regions of start‐stop phase as soon as possible. The research findings contribute to understanding the nonlinear dynamic characteristics of dual‐rotor systems, providing a theoretical basis for their stable operation and the optimal design of working speeds.

Bending-torsional coupling vibration characteristics of asynchronous motorized spindle considering electromechanical coupling and multi-excitation effect

For the asynchronous motorized spindle directly driven by the induction motor, the load-dependent slip ratio determines that its transient characteristics are sensitive to load. For the accurate evaluation of transient characteristics, it is necessary to deeply analyze the bending-torsional coupling vibration characteristics of the asynchronous motorized spindle with the non-ideal energy source. In this work, starting from energy conservation and clarifying the multi-physical field coupling mechanism, the bending-torsional coupling dynamic model is developed. Considering the speed fluctuation, the mass eccentricity excitation is deconstructed to explore its contribution to the coupling vibration. From the load-displacement relationship, the unbalanced excitation experienced by the journal from the bearing is modeled, considering the friction. According to the T-type equivalent circuit and mechanical characteristics of the induction motor, the electromagnetic torque considering power conservation is obtained. Furthermore, combined with Maxwell's stress formula, the electromagnetic excitation from electromagnetic torque and magnetic pull is obtained, considering the tangential and normal magnetic stress. Based on the projection and synthesis of forces, the semi-empirical mechanical cutting force model is employed to calculate the milling load. And a numerical algorithm for the fast acquisition of state-dependent delay is proposed. In particular, to reasonably characterize the energy characteristics in the system, the influence of structural vibration as an energy sink on the multi-physical field composed of mechanical, electromagnetic, and thermal fields is explored from the energy conservation. The proposed model was validated experimentally. The effects of electrical and mechanical parameters on the response are numerically discussed.

Vibration response analysis of gas generator rotor system with squeeze film damper based on dynamic similarity

For the aero-engine rotor system with complex vibration responses, a simplified model based dynamic similarity is proposed to study the vibration characteristics of that. On the basis of the principle of dynamic similarity, a simplified model of the combustion-driven rotor is obtained, with the criteria of the same critical speed of each order and similar vibration modes, while keeping the layout of the structure unchanged. By comparing the vibration characteristics of the actual rotor with those of the simplified model through theoretical analysis, there is less than 2.59 % error between the simplified model and the actual rotor. The rationality of the research method, which is developing the simplified model based on dynamic similarity to study the vibration response law of the original rotor, is demonstrated. Then, the unbalance response law of the rotor with a squeeze film damper is explored expanding on the produced model, and the study shows that the unbalanced excitation can significantly reduce the response. Finally, the influence law of the phase of unbalance excitation is experimentally verified on the test rotor. The results show that the simplified model of the actual rotor based on dynamic similarity can well reflect the vibration characteristics of the original rotor, and the proposed analysis method has an important reference role in studying the vibration mechanism of the aero-engine rotor system.

A New Geometrical Design to Overcome the Asymmetric Pressure Problem and the Resulting Response of Rotor-Bearing System to Unbalance Excitation

Improving the bearing design helps in reducing the negative consequences related to errors in installation, manufacturing, deflections under severe loading conditions, progressive wear of machine elements, and many other aspects. One of the methods of such a design improvement effort is changing the bearing profile along the bearing width to compensate for the reduction in the geometrical gap between the shaft and the bearing inner surface due to the aforementioned causes. Since in all rotating machinery, unbalance usually exists at some level, this paper deals with the response of this modified bearing to unbalanced excitation to evaluate the effectiveness of such geometrical design on the dynamic characteristics of the rotor-bearing system. The numerical solution is performed using the finite difference method by assuming Reynolds boundary conditions to determine the cavitation limits, and the 4th-order Range-Kutta method is used to determine the time responses resulting from the unbalance excitation. The time responses to this type of excitation show that the rotor-bearing with the improved geometrical design is more stable, particularly at high speeds. In addition, this modification leads to an improvement in the lubricant layer thickness and the reduction in the levels of the generated pressure between the surfaces despite the presence of large deviations from the perfectly aligned bearing system. Furthermore, the suggested geometrical design overcomes the problem of asymmetricity in the pressure field resulting from the shaft deviation to a large extent. The results of this work (the enhancement in the level of the film thickness and the improvement in the dynamic response of the system as well as the reduction of the maximum pressure value) extend the range of misalignment in which the rotor bearing systems can operate safely which represents a significant step in designing the rotor-bearing system.

Vibration Isolation Characteristics of Impedance-balanced Ship Equipment Foundation under Unbalanced Excitation

A new type of impedance-balanced ship equipment foundation structure based on the principle of impedance balancing using a “discontinuous panel-vibration isolation liquid layer-foundation structure” is proposed to solve the problem of poor low-frequency vibration isolation of the foundation under unbalanced excitation of shipboard equipment. Based on the finite element method, the influence of characteristic parameters of the foundation panel structure on its vibration reduction characteristics under unbalanced excitation is explored. The results show that the vibration isolation level of the impedance-balanced foundation is 10 dB higher than the traditional foundation in the low-frequency band of 10-500 Hz when subjected to combined excitation of concentrated force and moment. Increasing the thickness of the impedance-balanced foundation panel can enhance the isolation effect. Increasing the number of sub-panels can effectively reduce the vibration response of the foundation panel and enhance the isolation performance of the foundation. The connection stiffness between sub-panels has a small effect on the isolation performance of the foundation.

Dynamic modeling of GTF star gear-rotor coupling system considering structural flexibility

This paper establishes a dynamic model of Geared turbofan (GTF) star gear-rotor coupling system, in which the flexibility of shaft, disk, shell, diaphragm coupling, ring gear, and carrier are all taken into consideration. Additionally, an internal meshing model for flexible ring gear is developed, and the matrix reduction techniques is introduced to enhance the computational efficiency. Based on the dynamic model, the modal characteristics of the coupling system are extracted, and the influence of structural flexibility are investigated. Considering gyroscopic effect of the rotor, the Campbell diagram and the critical speeds are obtained. In addition, the vibration amplitudes under unbalanced excitation and time-varying mesh stiffness (TVMS) excitation are calculated and compared. The results of modal characteristics analysis indicate that many of the star gear train models are greatly affected by structural flexibility. Besides, the counter-rotating between the low-pressure rotor and the fan rotor results in frequency veering in the Campbell diagram, which is rarely observed in parallel gear-rotor system. The vibration responses indicate that unbalanced excitation of the rotor has relatively less effect on the gear vibration, while the low frequency excitation at star gear train is capable of exciting resonant vibration of the rotor.

Performance analysis of a stand-alone synchronous reluctance generator under unbalanced conditions

<span lang="EN-US">A stand-alone self-excited wind energy conversion system (WECS) is considered commonly used in remote areas due to its simple control and low cost. This paper introduces the performance analysis of a stand-alone self-excited reluctance generator (SERG) under balanced and unbalanced operations. An asymmetrical component is proposed to obtain the positive and negative sequence components of voltages and currents in addition to the unbalanced voltage factor of SERG. The obtained results have been validated and compared with experimental results obtained from a laboratory prototype of a 5.5 kW synchronous reluctance generator driven by a dc motor as a prime-mover under unbalanced excitation capacitors and unbalanced loads. The comparison verifies the applicability of the proposed model.</span>

Single-sensor-based dynamic response reconstruction of blades under base excitation

Blades in the turbo-machinery are inevitably excited by base excitation in addition to unbalanced excitation of the rotor during operation. Accurate measurements of the dynamic response under base excitation are especially critical, which feasibly provides essential guidance on vibration fatigue analysis and remaining life prediction of blades. However, due to some practical factors such as the restriction of the sensor installation position and the inability to directly obtain the external load information, there are still significant challenges in obtaining dynamic response of blades at critical positions under base excitation. In this paper, a novel method is proposed to reconstruct the dynamic response of blades under base excitation, where the measurement of only one sensor is adopted. The method comprises mostly of two steps. The measured signal is first divided into single-frequency response components using empirical mode decomposition with intermittency criteria (EMDIC), and the response components are then classified into two groups depending on whether the frequency is the blade's natural frequency. Then, by combing the time-domain and frequency-domain response transmissibility matrices under base excitation (RTMBE) derived in this paper, the dynamic response of the blade can be reconstructed, whether the blade is in the resonant or non-resonant state. This paper presents numerical simulation and experimental research on a titanium alloy fan blade. The effects of single-and multi-frequency excitation, measurement noise, and measuring point selection on the results of response reconstruction are all investigated. The results demonstrate the feasibility of the response reconstruction method presented in this work for the dynamic response reconstruction of blades under base excitation.

Adjustable Vibration Exciter Based on Unbalanced Motors.

In European industry, such as metallurgical, mining and processing, construction, food, and chemical, vibration exciters are used, which indicates their wide and, in some cases, unique technological capabilities. The most common are electromagnetic and unbalanced vibration exciters. The advantages of electromagnetic vibration exciters include the ability to control the amplitude of the vibration by changing the electrical power supplied; the disadvantages are high material consumption. However, unbalanced vibration exciters have low energy efficiency, which is associated with difficult start-up conditions and with an overestimated mechanical power of the vibration exciter in relation to the power required by the technology itself, which is due to the need to minimize the effect of the technological load on the operating mode of the vibrating unit. Adjusting the amplitude of the disturbing force of unbalanced vibration exciters, regardless of the vibration frequency, will make it possible to reduce the installed power of the unit by passing the resonant frequency with a minimum disturbing force and compensating for the effect of the process load by means of a closed-loop electric drive. In the course of the study, an analytical description of the interaction of the rotating unbalances located on a common movable platform was obtained. On the basis of these analytical dependencies, a mathematical model was developed that takes into account the dynamic characteristics of a frequency-controlled asynchronous electric drive of a closed-loop control system for the mutual arrangement of rotating unbalances. The simulation results confirmed the possibility of using the specified electric drive to control the oscillation amplitude directly in the process of operation of a four-unbalanced vibration exciter. A physical experiment was carried out to determine the transient processes of changing the angular velocity of an induction motor with an abrupt change in the frequency converter setting. On the basis of this experiment, the previously created mathematical model was refined in terms of describing the dynamic parameters of the electric drive. The proposed structure of the control system, the performance of which has been confirmed by mathematical modeling, makes it possible to implement an adjustable four-unbalanced vibration exciter using single commercially available asynchronous vibrators.

Study on material distribution and equal-thickness formation mechanism of variable trajectory combined equal-thickness screen

ABSTRACT Equal-thickness screens are widely used in coal processing due to their advantages in overcoming the problems of material accumulation, low utilization of the screen surface, and poor screening accuracy. In this paper, the variable amplitude equal-thickness method was introduced into the combined screen, a novel variable trajectory combined equal-thickness screen was proposed and the combined excitation coefficient was introduced. The motion of the variable trajectory combined equal-thickness screen under different combined excitation coefficients was investigated using vibration test analysis system and the particle motion characteristics and the spatial distributions of materials in the screening process were analyzed using a high-speed camera system. The distribution law of the material was studied by screening experiment. The results show that when the combined excitation coefficient D is increased, the first section screen amplitude increases, the material transport speed of the first section increases, the material accumulation situation of the first section is resolved. When the unbalanced excitation coefficient k is increased, the material layer at the feeding end of each screen becomes thinner, the material transport speed of the first section screen is accelerated, the screen body does variable amplitude elliptical motion, the material is equal-thickness. When D = 1.2, k = 1.2, an optimum screening efficiency of 96.12% was obtained, with a total misplaced material content of only 1.82%.

Frekventno regulisani pogon vibracionih sita sa debalansnim pobuđivačima - praktična realizacija i eksperimentalni rezultati

The paper presents a practically realized technical solution for frequency control of the AC power drive of vibrating sieves based on unbalanced vibration exciters. The operation of vibrating screen used in the industry for sieving and separating material fractions of different granulations is determined to a significant extent by the tilting angle of the vibrating sieve, its amplitude, the angle of attack of the excitation force and the frequency of oscillation. The frequency control of the vibrating sieves drive in this particular case made it possible to obtain the amplitude-frequency (AF) characteristic of the vibrating screen and based on it, the optimal operating frequency, which ensures the best separation of individual material fractions was determined. The solution was applied to two process lines in silos for deashing in the system of transport and separation of boiler slag from ash at the Thermal Power Plant "Nikola Tesla" B (TPP-B) in Obrenovac. The paper presents the key experimental results that were obtained during exploitation and testing of two implemented systems of regulated vibrating sieves.

Unbalance Vibration Suppression of Maglev High-Speed Motor Based on the Least-Mean-Square

The harmonic response caused by unbalanced excitation vibration for the high-speed rotating machinery will reduce the control accuracy and stability of the maglev high-speed motor, and limit the increase of its speed. When the active magnetic bearing is used to solve the unbalanced vibration, it will increase additional electromagnetic force and energy consumption, sometimes leading to the saturation of the power amplifier, and will transfer to the bearing foundation, causing the foundation to vibrate. In this paper, we analyzed periodic unbalance excitation force and the principle of rotor unbalanced vibration suppression, and the unbalance vibration model of the maglev rotor is derived. The Least-Mean-Square (LMS) algorithm is introduced into the PID control, an unbalance vibration control strategy based on real-time filtering compensation of rotor displacement signal is proposed, the vibration is eliminated by filtering the synchronous frequency and harmonic signal of the input of the PID control. The experimental results show that the proposed method can improve the maglev rotor’s rotation accuracy, reduce the magnetic bearing’s maximum control current, and decrease the vibration of the supporting foundation.