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![Vibration waveform, rotor orbit, frequency spectrum, Poincaré map at ϕ=0∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi =0^\circ $$\end{document} and ω=785\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega =785$$\end{document} rad/s](publication/337841234/figure/fig21/AS:960130686402560@1605924402413/Vibration-waveform-rotor-orbit-frequency-spectrum-Poincare-map-at.png)
Vibration waveform, rotor orbit, frequency spectrum, Poincaré map at ϕ=0∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi =0^\circ $$\end{document} and ω=785\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega =785$$\end{document} rad/s
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Rod fastening rotor (RFR) is characterized by discontinuity of contact interface and unbalance of multiple disks. There are few researches that focus on unbalance effect including magnitude and phase difference on the nonlinear dynamic characteristics of RFR considering contact feature. A typical RFR model is proposed to investigate the nonlinear d...
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Citations
... The rock body is cut into a discontinuous body by a fissure or weak face, and the rock body is supported by anchors, which constitute a structural system of anchored discontinuous rock body. This system consists of anchor rods, rock mass, and fissures that cut the rock mass [7]. Analyzing the interaction law between anchor rods and rock mass and examining in depth the stabilizing effect of anchor rods on the discontinuous rock body have important theoretical significance and practical value for more effective use of anchor rods [8]. ...
Research on the mechanical properties of transverse constraint force of anchor support under different loads can help to improve work safety. In this paper, based on the higher-order shear deformation theory, the higher-order whole-local theory of anchor rods is established with full consideration of the transverse normal strain. The geometric and physical equations in the intrinsic relationship are given for the wet thermodynamic behavior of anchor rods’ transverse restraining force. The equilibrium equations of the whole-local are constructed by combining them with the principle of virtual displacement. The analytical solution of the anchor core material was calculated by applying Navier’s method. The boundary displacement conditions of the anchor core material were solved. The anchor core material was modeled by combining it with ABAQUS finite element software. The mechanical analysis was carried out from the two perspectives of the buckling problem under thermal load and the parameter change of the transverse restraining force, respectively. It was found that when the thickness of the anchor bar increased from 20 mm to 50 mm, the radial displacement of the upper layer decreased by 52.95%, and there was no significant change in the positive stress at the upper and lower interfaces. The peak value of the upper interface shear stress decreases significantly from 0.55MPa to −1.41MPa when the anchor laying method is changed from a single layer to four layers. The combination of higher-order theory with ABAQUS software can effectively analyze the change of transverse constraint force of the anchor support, which can help improve its safety.
... Li et al. [12,13] examined the effect of the bending stiffness of the bolt on the system response and validated the simulation results by experiments. Furthermore, Wang et al. [14] investigated the dynamic behavior of a rod-fastened rotor system with internal damping and analyzed the response amplitudes and instability thresholds at different speeds. They found that internal damping had a dual effect on the RFCR response, which can decrease vibration amplitude at low speeds and significantly increase it at high speeds. ...
... The bolted structure causes structural discontinuity in the rotor system [1,2], the resulting contact stiffness leads to complex nonlinear motions, bifurcations and instability [3]. As rotating machinery tends to develop toward higher speeds and higher power, these phenomena are bound to become more pronounced. ...
... According to the finite element analysis and experimental results, they found that the lumped model predicts the structural response more accurate than the traditional linear model. Wang et al. [2] considered the bolted structures as nonlinear bending springs, and the nonlinear stiffness was simulated by polynomial terms. Zhuo et al. [8] took into account the thermal effect on rod preloads, the thermal effect was reflected in the rotor model by finite element method, then they analyzed the rotor response under different operating conditions. ...
... The results showed that due to the non-uniform stiffness of the rotor connection interface, a characteristic of "bistable state" appeared in the system. Wang et al. [18] modeled the connecting interface of rod-fastening rotor as a nonlinear spring, and established the dynamic model of the rod-fastening rotor-bearing system by applying the d'Alembert principle, then the effect of rotor unbalance on low-frequency instability and nonlinearity of the rod-fastening rotor-bearing system was studied. Luo et al. [19] considered the time-varying stiffness characteristics of rod-fastening rotor connection interface, and studied the influence of rotor time-varying stiffness on the stability of rotor and the influence of unbalanced phase on dynamic characteristics of the rotor-bearing system. ...
The circumferential rod-fastening rotor is composed of multiple disks fastened together by preload provided by tie rods evenly distributed along the circumference of rotor. After the rotor has been running for a period of time, some tie rods will loosen and fail to provide preload due to thermal load, centrifugal load, etc. Which causes the preload that was originally evenly distributed in the circumferential direction to become uneven. Uneven preload introduces anisotropy of contact interface stiffness between rotor disks and generalized bending moments, which have important effects on nonlinear dynamic characteristics of rotor-bearing-seal system. Further, it is common for multiple tie rods to become loose at the same time in practical engineering, the relative position of loose tie rods in the circumferential direction will also have an important impact on rotor dynamics. The relevant research has not been done yet. In this paper, a contact model of the rough machined surface is firstly established by combining the statistical contact theory and fractal contact theory, and then the contact stiffness model between disks is established based on the contact model. Finally, the dynamic model of the circumferential rod-fastening rotor-bearing-seal system is established and solved. The effect of relative phase of loose tie rods on the nonlinear dynamic characteristics of rod-fastening rotor-bearing-sealing system is studied. It can be concluded that relative phase of the loose tie rod has an important influence on the frequency, bifurcation, and periodic motion of the rotor system. At lower speed, the anisotropy of contact stiffness caused by loose rods has little effect on the rotor trajectory, while the generalized bending moment has a greater influence on dynamics of the system. At higher speed, the anisotropy of contact stiffness has a great influence on the axis rail of the rod-fastening rotor.
... The result shows that the RFR system motions differ from those of the integral rotor system. The same stiffness expression was also applied in the literature [10,[22][23][24][25]. Liu et al. [26] estimated the normal stiffness of the interface using a linear partition method. ...
Tie rod bolt loosening is a common fault in the rod-fastening rotor (RFR) system. The preload of tie rod bolts is prone to detuning under long-time periodical alternating load during system operation. Additional moment is produced by the loose bolt and the system global stiffness is decreased, which aggravates the system motion nonlinearity. The RFR system dynamic characteristics under one tie rod bolt loosening are studied in this work. A new RFR system dynamic model is proposed, considering the piecewise linear characteristics of the interface bending stiffness under tie rod bolt loosening. The single impact of tie rod bolt loosening and the coupling effect with initial bolt preload on the system dynamics are numerical analyzed. The simulation results show that periodic-2 motion is excited by tie rod bolt loosening, and the trend of periodic-2 motion to develop into chaos becomes apparent with the decrease in the preload. Meanwhile, the frequency components complicate with the fractional frequency occurring at the same speed range. Similarly, the frequency components of the fractional frequencies increase under a smaller preload. The results obtained from the simulation are well verified by the experiment. The experimental research is conducted on a RFR system test rig with one tie rod bolt loosening under different preloads. This work provides insights into the dynamic characteristics of RFR systems under tie rod bolt loosening and contributes to the bolt loosening fault identification of RFR systems.
... Li et al. [29] derived a semi-analytical model of a thin-walled cylindrical shell connected by a bolted flange and analyzed the dynamic response characteristics and contact state by considering the bilinear stiffness of the bolted joint. Wu et al. [30] and Wang et al. [31,32] developed a mathematical formula of jointed structures, and an in-depth discussion of the effect of joint stiffness on the vibration performance of the rotor system was conducted. ...
This study mainly investigated the nonlinear vibration performance of a rotor-casing coupling system containing a bolted flange connection. The dynamic equations of the coupling system were developed while considering the radial stiffness of the bolted flange structure, which contained a spigot, squirrel cage with ball bearing, and rotor-casing coupling vibration. To study the influence of the disk casing fixed-point rubbing fault on the coupling system’s nonlinear dynamic performance, an analytical model of the nonlinear impact forces was established, which considered the contact and vibration responses of the rotor and casing. The frictional force was obtained based on the Coulomb friction law. The iterative analysis of motion equations was performed utilizing the Newmark method. Then, the nonlinear dynamic behaviors of the coupled systems were examined using data, including a bifurcation diagram, spectrum plot, greatest Lyapunov exponents, etc. The effects of rubbing fault on the dynamic properties of system were investigated in detail, indicating that there were various motion states, which were described as periodic, multi-periodic, and quasi-periodic motions. Comparing the simulation results, it was found that rubbing fault seriously affected the motion stability of the rotor system. Finally, by gathering and examining the vibration data set from a test platform for rotor-casings with bolted joints, the correctness of the numerical simulation findings was confirmed. Additionally, the results of the experimental investigation agreed with that of the simulation. The dynamic distinguishing characteristics that were noticed can be used as an indicator for determining whether the fixed-point rubbing fault between the rotor and casing has become worse.
... The gyroscopic effect and bending stiffness at the contact surface was considered in the above works to improve simulation accuracy. Wang et al. [14,15] developed a mathematical model to obtain the effect of the unbalance of multiple discs and the effect of damping on rotor dynamics, where the contact effects at the mating interface were simulated by a spring with cubic stiffness. The influence of the preload, structure parameters, contact surface and uneven preload on the nonlinear dynamic characteristics of the bolted joint rotor system was numerically studied by Wu et al. [16]. ...
In aero-engines, the rotor systems are frequently designed with multistage discs, in which the discs are fastened together through bolted joints. During operation, rotating machines are susceptible to rotor–stator rubbing faults. Those bolted joints are subjected to friction and impact forces during a rubbing event, leading to a dramatic change in mechanical properties at the contacting interfaces, influencing the rotor dynamics, which have attracted the attention of scholars. In the present work, a mathematical model, which considers the unbalance force, rotor dimensional properties, nonlinear oil-film force and rub-impact effect, is developed to study the bifurcation and stability characteristics of the bolted joint rotor system containing multi-discs subjected to the rub-impact effect. The time-domain waveforms of the system are obtained numerically by using the Runge–Kutta method, and a bifurcation diagram, time domain waveforms, spectrum plots, shaft orbits and Poincaré maps are adopted to reveal the rotor dynamics under the effect of the rub-impact. Additionally, the influences of rubbing position at the multi-discs on rotor dynamic properties are also examined through bifurcation diagrams. The numerical simulation results show that the segments of the rotating speeds for rubbing are wider and more numerous, and the middle disc is subjected to the rub-impact. When the rub-impact position is far away from disc 1, the rubbing force has little effect on the response of disc 1. The corresponding results can help to understand the bifurcation characteristics of a bolted joint rotor system containing multi-discs subjected to the rub-impact effect.
... The phenomenon is not uncommon, since centrifugal forces driven by the mass imbalances overcome the nonlinear bearing reaction forces. Wang et al. [27] report similar findings. ...
Automotive turbochargers (TCs) use an engine oil lubricated bearing system to produce acceptable performance (as per the engine volumetric efficiency) and proven reliability. However, the bearings also cause TC rotordynamic responses that are rich in subsynchronous whirl motions through reaching stable limit cycles. The paper describes the lubrication model for a finite length semi-floating ring bearing (SFRB) system and its coupling to the rotor and ring structure models for prediction of both linear and nonlinear system responses and their characterization in terms of motion amplitudes and whirl frequency content. The SFRB model includes a thermal energy transport network for the inner and outer films in both radial bearings and the thrust bearings located on the end sides of the ring. The large temperature difference between the hot shaft and a cold housing induces a three-dimensional thermal gradient in the fluid films and the floating ring, further exacerbated by the heat generated from drag power losses in the inner films adjacent to the rotor. The temperature gradients affect the lubricant viscosity and the bearing system operating clearances. The integration of the rotor and bearing system (RBS) equations of motion accounts for the SFRB nonlinear forces and starts from static equilibrium position, if existing. The model predictions of nonlinear behavior are accurate when benchmarked to a set of measurements procured in a gas stand test rig. The analysis also investigates the influence of the bearing inner clearance and rotor mass imbalance distribution on the onset, persistence and severity of SSV.
... The dynamic response characteristics of the rotor system with piecewise linear stiffness were captured through the numerical integration method, and an experimental study was conducted through a bolted joint rotor test rig. Wang et al. [36] proposed an eightdegree-of-freedom bolted joint rotor-bearing system by the D'Alembert principle, where the nonlinear contact characteristic at the mating interface was considered in the modeling process. The numerical simulation results indicated rich nonlinear phenomena of the rotor system under different unbalance magnitudes and unbalanced phase differences. ...
... where F cx1 , F cx2 , F cy1 , and F cy2 are nonlinear lateral contact forces at the mating interface, where [36,66] ...
Rotor–stator rub is a common and high-risk fault in large rotating machines. As for the aero-engine rotor system, bolted joints are widely adopted to fasten the multiple rotating parts into an integrated one. During a rubbing event, normal and tangential forces are generated by the contact and friction at the rotor–stator contacting interface. The mechanical properties of the bolted joint change dramatically under the generated forces, which will affect the dynamics of the rotor system. However, little research has been done on the dynamic properties of the bolted joint rotor system subject to rub-impact, and the coupling effect of rubbing and bolted joint on rotor dynamics is still not understood. Thus, the dynamic model of bolted joint rotor system with fixed-point rub-impact is established based upon the proposed bolted joint element and lumped mass modeling method in this work. Then, the vibration responses of the rotor system are captured by using the Newmark-β method. Bifurcation diagrams, three-dimensional spectral plots, Poincaré maps, time-domain waveforms as well as bending stiffness plots are used to demonstrate the effect of rotor–stator rub impact on the vibration characteristics of the rotor system. After that, the influences of the radial stiffness of the stator on the mechanical properties of the bolted joint and rotor dynamics are also examined. Finally, the experimental study is carried out through a bolted joint rotor test rig with a rubbing device. The studies in the present work helped in understanding the dynamic characteristics of the bolted joint rotor system and the mechanical properties of bolted joint undergoing rub-impact force. Moreover, those study results provide insight into the diagnosis of rubbing fault.
... Rod fastening rotor system is mainly composed of pull rods, discs, and blades. Several discs are integrated by the pressure and the friction force provided by the pull rods [2] . Since the global stiffness of the rotor system is closely related to the contact stiffness of the joint interface, it is significant for scholars to master its contact mechanism in advance. ...
The aim of this paper is to gain insight into the nonlinear vibration feature of a dynamic model of a gas turbine. First, a rod fastening rotor-bearing coupling model with fixed-point rubbing is proposed, where the fractal theory and the finite element method are utilized. For contact analysis, a novel contact force model is introduced in this paper. Meanwhile, the Coulomb model is adopted to expound the friction characteristics. Second, the governing equations of motion of the rotor system are numerically solved, and the nonlinear dynamic characteristics are analyzed in terms of the bifurcation diagram, Poincaré map, and time history. Third, the potential effects provided by contact degree of joint interface, distribution position, and amount of contact layer are discussed in detail. Finally, the contrast analysis between the integral rotor and the rod fastening rotor is conducted under the condition of fixed-point rubbing.
