Squeeze Film Damper Research Articles

Research on Dynamic Characteristic Coefficients of Integral Squeeze Film Damper

Integral squeeze film damper (ISFD) is a new type of structure that appeared on the basis of traditional squeeze film damper (SFD). Since the oil film in ISFD is a segmented structure without annular flow, the nonlinearity of the oil film force has been improved to a great extent. The dynamic characteristic coefficients of ISFD have a close relationship with its damping performance. This work investigates and studies the dynamic characteristic parameters of ISFD by means of numerical analysis and experimental validation techniques in order to examine the dynamic features and unveil the damping mechanism. The ISFD solid and fluid analysis models are created, and the computational fluid dynamics (CFD) and mechanical performance analyses are completed. The force acting on the ISFD’s S-type elastomer under excitation conditions is revealed in the mechanical property analysis, and the flow characteristics of the internal oil film are investigated in the CFD analysis. It is discovered that the ISFD has good linear damping and stiffness characteristics, and numerical analytical values for the ISFD’s damping and stiffness coefficients are obtained. By constructing a bi-directional excitation test rig, the experimental values of the ISFD stiffness coefficient and damping coefficient are determined. These values are in close agreement with the results of the numerical analysis, confirming the accuracy of the ISFD’s numerical analysis conclusions.

A comprehensive methodology to estimate the fatigue life of S-shaped integral squeeze film damper

The Integral Squeeze Film Damper (ISFD) finds widespread application in various rotating machinery, such as gas turbines, turbochargers, and high-speed rotors, to dampen vibrations and improve operational stability. This study presents a comprehensive methodology to predict the fatigue life of an Integral Squeeze Film Damper (ISFD) by combining Low Cycle Fatigue (LCF), High Cycle Fatigue (HCF) test, and Finite Element (FE) simulations. An S-shaped spring specimen is designed and tested under high-cycle fatigue loading to develop the stress amplitude versus the number of the cycles curve. LCF tests are performed to obtain fatigue parameters, and a Chaboche kinematic hardening model is employed for cyclic plasticity FE simulations. FE analysis of the ISFD is conducted to establish its dynamic characteristics, aiding in identifying critical locations based on maximum von Mises stress. The integration of local stress–strain states from FE simulations with experimental fatigue parameters is carried out to predict fatigue life of ISFD. The validity of the methodology is confirmed through experimental and stress analyses, providing valuable insights for optimizing the fatigue performance of ISFD components.

An integrated approach for response prediction in large-scale rotor-bearing system with local nonlinear joints based on FRF-based harmonic balance method

In the development and maintenance of gas turbines, the efficient computation to predict the responses of large-scale and complex rotating structures with local nonlinear joints is crucial. In this paper, a novel integrated strategy as a trade-off between time expense and accuracy for response prediction in large scale rotor-bearing system with local nonlinear joints is developed using the frequency response function based harmonic balance method (FRF-based HBM). To tackle the numerical challenges arising from asymmetrical matrices in rotating systems, a new approach is presented to compute the FRF using a spectral decomposition in second-order state space. Furthermore, the analytical mapping of eigen-solution against rotational speed based on Taylor series expansion is developed to address the computational expenses associated with speed-dependent FRF matrices. Then, a model reduction is adopted to mitigate the additional computational costs arising from the high-order unsymmetric matrices. The superior qualities and practical value in engineering of the new strategy are demonstrated on two numerical cases. The first is a one-dimensional rotor-bearing model subjected to the cubic nonlinear force under investigation, this approach shows an exceptionally high level of accuracy in response prediction, when compared to both the Runge-Kutta method and the harmonic balance method (HBM) without any form of model reduction. Another is a large-scale rotor-bearing model with two squeeze film dampers, the computational speed, being thousands of times faster than the HBM method and several times faster than the HBM considering the CMS model reduction, underscores the efficiency of this approach.

Optimizing high-speed rotating shaft vibration control: Experimental investigation of squeeze film dampers and a comparative analysis using Artificial Neural Networks (ANN) and Response Surface Methodology (RSM)

This research paper presents a comprehensive experimental and statistical approach for the analysis of vibration amplitudes in a high-speed rotating shaft employing a squeeze film damper (SFD). The research combines a comprehensive analysis that connects input parameters and response parameters, with a special emphasis on vibration amplitudes along the X and Z axes. This research utilizes the rigorous procedures of Response Surface Methodology (RSM) together with a Box-Behnken design and harnesses the capabilities of Artificial Neural Network (ANN) optimization techniques. The variables under scrutiny encompass critical factors such as shaft rotational speed, extending up to 8000 rpm, oil pressure, with a range extending up to 100 bar, and various oil mix ratios, spanning from 10 % to 50 %. Various statistical measures are computed to assess the errors and coefficients of determination of the projected models. The artificial neural network (ANN) model has shown somewhat reduced prediction errors and a greater coefficient of determination compared to the Response Surface Methodology (RSM) for both the x and z axes of vibration amplitude. The values of mean absolute error (MAE), root mean squared error (RMSE), and coefficient of determination (R-squared) are found for both x and z axes from RSM (3.50, 3.77), (4.50, 4.72), and (0.81, 0.79), (1.88, 1.70), (2.41, 2.12), and (0.94, 0.95), respectively, using the ANN model. The overall mean absolute percentage error (MAPE) from the ANN model of both the x and z axes (9.73 %, 9.38 %) is found to be lower compared to the RSM model (18.18 %–20.50 %). The conclusive research reveals that the artificial neural network (ANN) prediction model outperforms the regression model based on Response Surface Methodology (RSM), exhibiting superior accuracy in predicting vibration amplitudes. The ANN approach is an excellent option for calculating vibration amplitudes in high-speed rotating shafts. Additionally, it provides significant benefits in terms of effectiveness and time economy. This research provides valuable new insights into the most efficient modeling approaches for vibration management and highlights the benefits of using Artificial Neural Networks (ANN) for predictive assessments in this context. Particle Swarm Optimization is used to minimize the vibration amplitude of the shaft along the x and z axes using experimental data.

Effects of humidity and temperature on quality factor of micro-beam resonators in atmospheric pressure and gas rarefaction

At atmospheric pressure (p=101325 Pa), the effects of humidity and temperature on moist air become important when discussing the quality factor of micro-cantilever and micro-bridge resonators. The squeeze film damping (SFD) problem, the dominant damping source for micro-beam resonators, is modelled using the modified molecular gas lubrication (MMGL) equation with finite element modelling (FEM) in the eigenvalue problem. The MMGL equation is modified with the effective viscosity of moist air (μeff) to account for the effects of humidity and temperature. Other damping sources, such as thermoelastic damping (TED) and the support loss of micro-beam resonators, are also calculated. The quality factor of micro-beam resonators is then discussed over a wide range of temperatures and relative humidity levels at atmospheric pressure and gas rarefaction. The results show that the quality factor of micro-cantilever and micro-bridge resonators increases as both humidity and temperature rise in atmospheric pressure and gas rarefaction. Furthermore, the quality factor of a micro-bridge resonator with changes in humidity and temperature is significantly higher than that of a micro-cantilever resonator in atmospheric pressure and gas rarefaction.

A comprehensive multi-parameter optimization method of squeeze film damper-rotor system using hunter-prey optimization algorithm

The squeeze film damper (SFD) is a damping device that is widely used in turbomachinery. A well-designed SFD structure can effectively mitigate vibration at critical speeds, while a poorly designed SFD may increase vibration. The comprehensive multi-parameter optimization method is used for optimizing the vibration response at critical speed and improving the reliability and overall performance by designing the crucial structural parameters of the SFD. Firstly, the coupling dynamic model is proposed for the rotor and SFD, taking into account the influence of non-linear oil film forces of SFD. The test rig is used to verify the vibration response in a typical SFD-rotor system. To provide the optimal vibration reduction effect within a specific SFD parameter range for a particular rotor, a method for comprehensive multi-parameter optimization is introduced. This method introduces the hunter-prey intelligent optimization (HPO) algorithm and compares its results with the PSO algorithm. The comprehensive optimization method revealed that the key parameters of the SFD, when designed using this approach, can effectively alleviate the vibration response of the entire rotor system, achieving the rotor system amplitude reduction ratio of up to13.89%.

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.

Navigating the Dynamics of Squeeze Film Dampers: Unraveling Stiffness and Damping Using a Dual Lens of Reynolds Equation and Neural Network Models for Sensitivity Analysis and Predictive Insights

The squeeze film damper (SFD) is proven to be highly effective in mitigating rotor vibration as it traverses the critical speed, thus making it extensively utilized in the aeroengine domain. In this paper, we investigate the stiffness and damping of SFD using the Reynolds equation and neural network models. Our specific focus includes examining the structural and operating parameters of SFDs, such as clearance, feed pressure of oil, rotor whirl, and rotational speed. Firstly, the pressure distribution analytical model of the oil film inside the SFD based on the hydrodynamic lubrication theory is established, as described by the Reynolds equation. It obtained oil film forces, pressure, stiffness, and damping values under various sets of structural, lubrication, and operating parameters, including length, clearance, boundary pressure at both sides, rotational speed, and whirling motion, by applying difference computations to the Reynolds equation. Secondly, according to the significant analyses of the obtained oil film stiffness and damping, the following three parameters of the most significance are found: clearance, rotational speed, and rotor whirl. Furthermore, neural network models, including GA-BP and decision tree models, are established based on the obtained results of difference computation. The numerical simulation and calculation of these models are then applied to show their validity with all given parameters and the three significant parameters separately as two sets of model input. Regardless of either set of model inputs, these established neural network models are capable of predicting the nonlinear stiffness and damping of the oil film inside an SFD. These sensitive parameters merely require measurement, followed by the utilization of a neural network to predict stiffness and damping instead of the Reynolds equation. This process serves structural enhancement, facilitates parameter optimization in SFDs, and provides crucial support for refining the design parameters of SFDs.

Vibration response analysis of rotor system coupled with a novel 4-DOF SFD hydrodynamic model considering the influence of rotational displacement

As a damping structure, squeeze film dampers (SFDs) are commonly employed in turbomachinery. Aiming at the problem of hydrodynamic modeling and solution, this paper presents a four-degree-of-freedom (4-DOF) hydrodynamics model of SFD, which not only considers the influence of radial displacement on oil film clearance but also the influence of rotational displacement. The Reynolds equation of the SFD is solved utilizing the finite difference method (FDM). The oil film gap distribution and static properties of the SFD under different rotational displacements and journal eccentricity are analyzed. Then, the hydrodynamic model of the 4-DOF SFD is coupled with the rotor system, and the vibration characteristics of the SFD-rotor system are analyzed. Finally, the experimental verification is carried out. The analysis results reveal that the rotational displacement has little influence on the vibration response of the SFD-rotor system at the non-critical speed. However, near the critical speed, the occurrence of rotational displacement of the SFD is more beneficial to the vibration reduction effect. Moreover, the analysis results of the hydrodynamic characteristics of the SFD show that when the eccentricity is less than 0.4, the rotational displacement has little effect on the oil film gap distribution, load moment, and oil film reaction force. When the eccentricity exceeds 0.4, the rotational displacement has a great influence on the gap distribution, load moment, and oil film reaction force of SFD.

Study on Rotor-Bearing System Vibration of Downhole Turbine Generator under Drill-String Excitation

Downhole turbine generators (DHTG) installed within drill-string are susceptible to internal and external excitation during the drilling process, causing significant dynamic loads on bearings, and thereby reducing the bearing’s service life. In this study, a finite element model of an unbalanced rotor-bearing system (RBS) of DHTG with multi-frequency excitations, based on the Lagrangian motion differential equation, is established. The responses of the RBS under different drill-string excitations in terms of time-domain response, whirl orbit, and spectrum are analyzed. For a constant rotor speed, lateral harmonic translational and lateral oscillation both transform the whirl orbit to quasi-periodic, while axial rotation only changes the response amplitude. Changing the duration of pulse excitation leads to different response forms. Then, the dynamic characteristics of the RBS supported by a squeeze film damper (SFD) are investigated. The results indicate that SFD effectively reduces the displacement response amplitude and bearing force near the critical speed. As the axial rotation angular velocity of the drill-string increases, the first critical speed and displacement response decrease, while the variation of lateral oscillation frequency and amplitude has limited impact on them. The established model provides a means for analyzing the dynamic characteristics of DHTG’s RBS under drill-string excitations during the design stage.

Study of the Effect of Static Eccentricity on Vibration Damping Properties of Squeeze Film Dampers Considering the Two-Phase Flow Case

To analyze the effect of static eccentricity on the air ingestion distribution and vibration damping properties of the SFD, a numerical simulation study of SFDs considering two-phase flow was carried out based on CFD using a transient solution method and dynamic mesh technique. The results show that the angle between the static eccentricity direction and the circumferential direction of the oil supply hole increases and the air ingestion area in the oil film expands. In contrast, the oil film damping decreases, and the larger the static eccentricity distance, the greater its effect on the air ingestion area in the oil film. When the circumferential angle is small, the oil film damping increases with the increase of static eccentricity distance, and when the circumferential angle is large, the oil film damping decreases with the increase of static eccentricity distance and then increases. With the increase of static eccentricity distance, the air ingestion area at both ends of the oil film increases. At the same time, studying the effect of dynamic eccentricity shows that as the dynamic eccentricity increases, the oil film damping first decreases and then increases, and the air ingestion area increases. Comparing the 1 hole, the 2 hole, and the 3 hole oil supplies, the air ingestion area is significantly larger in the 1 hole oil supply than in the 2 hole or the 3 hole oil supplies, and the oil film damping of the 1 hole oil supply is smaller than the oil film damping of the 2 hole or the 3 hole oil supplies. It can be seen from the present study that in the actual installation of the SFD, when the circumferential angle is less than 60°, the static eccentricity can be increased appropriately. When the circumferential angle is greater than 60°, the static eccentricity can be appropriately reduced.

Study on vibration suppression of an aero-engine rotor system with adjustable oil film thickness driven by piezoelectric actuator through critical speed

The squeeze film damper (SFD) is difficult to meet the vibration control requirements of the rotor at both the critical speed and other rotor speeds at the same time due to the fixed structural parameters. The control method of piezoelectric ceramic actuator (PZT) actively changing the SFD oil film gap is proposed to suppress the critical amplitude of the rotor system. The dynamic model of the rotor system with PZT is established. The mechanical controllable characteristics of SFD are revealed, and the vibration damping performance of the controllable SFD (CSFD) is studied at critical speed. Both experiment and theory show that the proposed method can effectively suppress the critical amplitude of the rotor system with different imbalance.

Piezoelectric driven split pad squeeze film damper for the suppression of sudden unbalanced vibrations in rotor system

Blade loss leads to excessive unbalanced vibrations of the rotor system in the gas generator of an aero-turboshaft engine. A squeeze film damper (SFD) cannot meet vibration control requirements owing to its fixed structural parameters. In this study, the outer ring of the SFD oil film is designed as three movable bearing pads. Piezoelectric actuators (PZTs) are used to adjust the oil film force by changing the radial displacement of the bearing pads, and sudden unbalanced vibration control of the rotor system is realised based on a switching control strategy. The oil film force formula of the split-pad squeeze film damper (SSFD) is derived, and a mathematical model of the SSFD-rotor system controlled by PZTs is established using finite element and lumped mass methods. The effects of the bearing pad clearance and stiffness of the PZTs on the rotor vibration characteristics are discussed, and the vibration control effect of the SSFD on the sudden unbalanced response of the rotor system is studied theoretically and experimentally. The results show that rotor vibration can be reduced by reducing the bearing pad clearance and increasing the stiffness of the PZTs. The SSFD can effectively suppress the sudden unbalanced response of the rotor system. The experimental value of the peak transient amplitude of the rotor decrease by 32%, and the rotor orbit in the stable state decreases with increasing PZT voltage.

High-Speed Near-Surface Tracking for Fast Atomic Force Microscope Scan Switching Based on the Squeeze Film Damping Effect

Atomic force microscope (AFM) is a crucial metrology tool in the semiconductor industry. However, the bottleneck of the AFM technique is its low efficiency, primarily owing to the time-consuming scanning point switching. The traditional method takes approximately one minute for a single switching. To shield the probe and sample, the switching should first lift the probe a considerable distance, move it to the next point, and finally engage the probe slowly to the sample surface. We propose a near-surface tracking method for use in fast scanning point switching. The probe-sample distance was sensed by the squeeze air film damping effect, and the probe was kept at a small constant height during the switching via feedback control. The method can decrease the lift and engage distance from approximately 1 mm to 5 μm, which was two order of reduction; thereby shortening the single switching time from 45 s to 6.1 s, which is an 87% reduction. Generally, the fast switching method can improve the measurement efficiency of the existing AFM working in the air, but it can not be used in liquid and vacuum. Furthermore, the proposed squeeze film damping effect based distance sensing method can be applied in various fields, such as vibration sensing and temperature drift measurement.

Identification of Dynamic Force Coefficients for an Additively Manufactured Hermetic Squeeze Film Bearing Support Damper Utilizing a Pass-Through Channel

Abstract The following paper presents breakthrough experimental results for a new hermetic squeeze film damper (HSFD) concept that is integrally designed within an externally pressurized tilting-pad radial gas bearing support. The flexibly damped gas bearing module was designed for a 7.2″ (183 mm) diameter shaft and fabricated using direct metal laser melting (DMLM); also known as additive manufacturing. The bearing and HSFD were sized based on ongoing studies for oil-free supercritical carbon dioxide (sCO2) power turbines in the 8.5 MW–10 MW power range. The development of the new damper concept was motivated by past dynamic testing on HSFD, which generated frequency-dependent stiffness and damping force coefficients. In efforts to eliminate the frequency dependency, a new HSFD architecture was conceived that adds accumulator volumes and a pass-through channel to previously conceived HSFD flow network designs. The other motivation for the work is the need to develop a cost-effective and reliable oil-free bearing technology that is scalable to large power turbomachinery applications. There were several objectives for the following work. The first objective was to successfully design and fabricate a single piece bearing-damper using additive manufacturing, while dimensionally controlling critical design features. The paper discusses the manufacturing steps and shows cut-ups that reveal adequate clearance control capability with internal damper clearances. The second objective was to perform experimental testing with the new HSFD design in efforts to extract stiffness and damping coefficients for excitation frequencies within 20–160 Hz and peak vibration amplitudes between 0.25 mils (6.35 microns) to 1 mil (25.4 microns). The test results for a single HSFD bearing module indicated that the design modifications to the HSFD architecture were successful in eliminating nearly all the frequency dependencies for the stiffness force coefficient. The dynamic tests yielded a stiffness coefficient that varied between 112 klb/in. (19.6 MN/m) and 96 klb/in. (16.8 MN/m). The damping force coefficient however, exhibited relatively more variation with frequency with values residing between 175 lb-s/in. (31 kN-s/m) to 214 lb-s/in. (37 kN-s/m). Finally, the paper advances a three-dimensional fluid-structure interaction (FSI) model using transient finite element analysis (FEA) coupled to a computational fluid dynamics (CFD) model. The FSI analysis performed between 20 Hz and 80 Hz was used to predict the stiffness and damping of the HSFD using a quarter-section model of the damper. The FSI analysis was able to support test results by showing only a 6–7.4% change in the magnitude of force coefficients. Stiffness predictions agree reasonably well with experiments whereas damping is underpredicted.

Research on the Dynamic Characteristics of Cantilever Rotor System With ISFD

Aiming at the common vibration problem of the cantilever rotor system and the nonlinear problem of traditional squeeze film damper (SFD), an integral squeeze film damper (ISFD) for the cantilever rotor system was proposed based on the traditional SFD. In order to investigate the effect of the ISFD on the dynamic characteristics of the cantilever rotor system, the vibration reduction experiment of the rotor system was carried out. The mechanical model and finite element model of the cantilever rotor system were established. The first‐order critical speed, strain energy, stability, and steady‐state response of the cantilever rotor system were numerically analyzed. Experimental research on the vibration reduction of the cantilever rotor system by the ISFD under different unbalance conditions and different rotational speed conditions was carried out on the test rig of the cantilever rotor system. The results showed that the ISFD has remarkable performance, which can reduce the bending deformation and strain energy of the rotating shaft, increase the logarithmic decay rate, and improve the overall stability of the system. Under various working conditions, the ISFD can effectively suppress the unbalanced vibration of the rotor and the shaft center displacement of the rotor, and the amplitude of the rotor system at the working frequency (1X) is greatly reduced.

Squeeze‐film damping model of perforated plate considering border effect

AbstractThe squeeze‐film damping (SQFD) is an important dissipation mechanism of Micro‐Electro‐Mechanical Systems resonators. The current SQFD models of perforated plates treat borders of plate and holes as the constant pressure boundary, without considering border effect. In this paper, the border effect on SQFD is studied by expanding simulation area. At the same time, based on the research of non‐perforated plate border effect, the calculation size of the perforated plate hole cell is modified, and the modified SQFD model of the perforated plate has been built. Compared with simulation results, it shows the border effect has a great influence on SQFD of perforated plate. The precision of the modified model is higher than that of recent models. For a rectangular plate, the maximum error of the modified model is 12%, while for the recent model it is 40%. For a circular plate, the modified model is 38%, while the recent model is 58%.

The Nonlinear Dynamic Characteristics of an Industrial Turbine Engine with Eccentric Squeeze Film Dampers

Squeeze film dampers are often used to suppress vibration in turbine engines and play an important role in rotor systems. In this paper, the nonlinear dynamic characteristics of an industrial turbine engine fitted with squeeze film dampers are investigated with the static eccentricity of the SFDs. A recently developed time domain technique that combines the finite element method and the fixed interface modal synthesis method is applied to predict the nonlinear unbalance response of the industrial turbine engine under different unbalanced and static eccentricity configurations. By comparing the results obtained using SFDs with and without static eccentricity, it can be concluded that increasing the static eccentricity of the SFDs promotes non-periodic motion, while an increase in the unbalance level promotes the jump phenomenon. The efficiency of the rotor system would improve with an appropriate amount of unbalance applied to compressor IV, resulting in a reduction in the vibration level. If static sprung eccentricity occurs, the center of the journal orbit would be offset from the SFD center, rendering it inefficient or even leading to rub impact. Therefore, it is crucial to control the static eccentricity of the SFDs for optimal performance. The time domain technique is verified by the experimental results reported in the literature.

Dynamic analysis of magnetorheological damper incorporating elastic ring in coupled multi-physical fields

The elastic ring assumes a multifunctional role, crucially providing support and reshaping oil-film thickness distribution in applications such as squeeze film dampers, demonstrating its practical efficacy. In this work, a magnetorheological damper (MRD) incorporating an elastic ring is proposed for the first time to improve the performance of damper. The innovative configuration of the elastic ring magnetorheological damper (ERMRD) is fabricated and integrated into a test platform of rotor system. The multi-filed coupling dynamic model of ERMRD is developed involving magnetic field interactions governed by Kirchhoff law, magnetorheological fluid flow dynamics derived from lubrication theory, and the elastic ring deformation based on thin plate theory. The intricate influence mechanisms of elastic ring and excitation current on oil-film characteristic of ERMRD, encompassing oil-film pressure, oil-film force, oil-film stiffness and damping, are investigated in detail. To substantiate the capabilities of ERMRD, it is implemented within the rotor system and a coupled dynamic model is established using Lagrange equation. This is followed by an in-depth analysis of the dynamic response using the Newmark-β method, including a comparative assessment with the conventional MRD. The results reveal that the elastic ring and excitation current influence oil-film pressure distribution in ERMRD from different perspectives, leading the oil-film force to present diverse variation characteristics. Compared to MRD, ERMRD exhibits weaker nonlinearity and superior damping performance.

A hybrid rotordynamic modeling method for a rotor system with flexible foundation and nonlinear support force: Numerical and experimental investigation

The dynamic characteristics of a flexible foundation would greatly affect the dynamic behavior of the rotor system. In this paper, a hybrid dynamic model method in time domain combines the finite element (FE) method and the subspace-based identification method to model a rotor system with the consideration of a flexible foundation and nonlinear support forces. The state-space model of flexible foundation is identified by the subspace state-space system identification algorithm with measured frequency response functions (FRFs). To solve the calculation problem of the hybrid dynamic model in time domain, a general algorithm named the hybrid model fusion solution (HMFS) method is proposed, which combines the linear and nonlinear nodes separation method used in the FE model and the trapezoidal rule used in the state-space model, improving the calculation efficiency of solving transient response with nonlinear forces. Simulations for the hybrid dynamic model under constant speed and speed-up cases were carried out, resulting that the dynamic characteristics of the entire system can be represented when the nonlinear factors of rolling bearings and gravity were also taken into consideration. Additionally, owe to the consideration of tested dynamic behaviors of flexible base, experimental results in the laboratory test rig are well agreed with the numerical ones under two different test configurations. The investigation provides a complete modeling and highly efficient solution framework for the rotor system with a flexible foundation and nonlinear rolling bearings, with the abilities of further consideration of more nonlinear components such as squeeze film dampers and rubbing forces.