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Diagnostics procedure for identification of rubs in rotor bearings
Abstract
it is well known that old design high-power generating machines were on duty for more than 35-40 years and will successfully continue operation after proper renovations and overhauls, this paper considers vibrational characteristics of the old continuously operated 110 mw turbounit with steam turbines and electric generator rotating system running at nominal speed of 3000 rpm. vibration and technological parameters were systematically monitored in the course of 5 years after installation of condition monitoring and diagnostics system, which is based on measurements of rotor relative vibration displacement, it is demonstrated that application of optimized vibration monitoring and diagnostic system and several vibration data formats is effective in evaluation of overhaul quality through vibration severity of rotor system and identification of causes of these vibrations, the research focus in the reported research work is placed on inspection of mechanical effect of horizontal rotor-to-stator rubbing in upper part of journal bearing. the validity of the results is verified during overhauls and renovations, and can reduce the possibility of bearing failures.
... In this paper, the Kuhn-Tucker law of Coulomb friction is used to detect the contact between rotor and stator, and the contact condition is solved by the augmented Lagrangian method of friction [30]. ese ensure that the disc and the elastic rod meet the contact conditions and do not penetrate each other. ...
... For this result, the authors research the effect of indefinite constants on the weighted contribution rate. First, the obtained NOFRFs values are taken into equation (16) to calculate Rn, the range of indefinite constant ρ is [− 30,5], and a curve of Rn respect to ρ is then made under three different rub-impact clearances (normal, clearance A � 90 μm, and clearance B � 30 μm). ...
Rub-impact between the rotating and static parts is a more common fault. The occurrence of faults is often accompanied by the generation of nonlinear phenomena. However, it is difficult to find out because the nonlinear characteristics are not obvious at the beginning of the fault. As a new frequency domain-based method, nonlinear output frequency response functions (NOFRFs) use the vibration response to extract the nonlinear characteristics of the system. This method has a better recognition rate for fault detection. Also, it has been applied in structural damages detection, but the high-order NOFRFs have the characteristics that the signals are weak and the features are difficult to extract. On this basis, the concept of the weighted contribution rate of the NOFRFs is proposed in this paper. The variable weighted coefficients with orders are used to amplify the influence of high-order NOFRFs on the nonlinearity of the system so as to extract its fault characteristics. The new index RI is proposed based on Clenshaw–Curtis quadrature formula to eliminate the effect of artificially selected weighted coefficients on sensitivity. Especially in the early stage of the fault, the new index varies greatly with the deepening of the fault. Both simulation and experimental results verify the validity and practicability of the new index. The new index has certain guiding significance in the detection of mechanical system faults.
... Numerical modelling of rotary systems dynamics is useful not just for design, but also for prediction of their parameters (e.g. changes of dynamics caused by long term exploitation) during exploitation [1,2,5,7,8]. ...
... There are known several methods of analytical or numerical modelling of rotary systems dynamics and other physical phenomena [1,2,[6][7][8][9][10][11][12][13][14][15][16]. Applications of complex 3D models are rather computationally expensive. ...
Precise modelling of dynamics of complex technological systems is complicated problem requiring signif-icant human and computational resources. Therefore, aiming to create model of rational size and complexity, some adjustments of models should be done applying experimentally obtained parameters of rotary systems and their elements. This paper presents results of modelling of vibrations of rigid rotor caused by the degradation of hydrodynamic bearings. Model is composed applying equations of nonlinear hydrodynamic forces and measured parameters of a real rotary machine.
... The 13.34×10 9 Number of bearing balls N b 9 Bearing radial clearance r 0 /μm 0-45 rolling element has no contact with the inner ring of the bearing, and there is no support reaction force at this time. Otherwise, the bearing support reaction force along x and y directions will be generated [40]: ...
Affected by manufacture, assembly, and operating conditions, the rotor is prone to rub-impact fault, resulting in instability of a system. The nonlinearity of a system response includes instability and fault characteristics. Based on this, this paper proposes a novel health assessment approach for bearing-rotor system that combines data-driven and NOFRFs (nonlinear output frequency response functions), revealing the intrinsic relationship between NOFRFs-based feature and rub-impact fault. Before utilizing the approach, the vibration and stability of the bearing-rotor with rub-impact are simulated and analyzed. Based on Hertz contact theory, the nonlinear bearing forces are obtained. Then the dynamic model of the rolling bearing-rotor system considering unbalance and rub-impact is established. The influence of rub-impact on the nonlinear vibration and stability of the bearing-rotor system is analyzed by combining the orbit, the Poincaré map, and the bifurcation diagram. A rolling bearing-rotor test rig is built, and the rub-impact experiment was completed. The data-driven model of the system is identified by the filtered vibration displacement. The NOFRF-based feature of the data-driven model is extracted. With the increase of rub-impact severity, the dispersion of feature gradually increases, and the stability of the system decreases. The standard deviation of the feature is solved as a new health indicator. The result shows it is more effective for the evaluation of rub-impact than the conventional indicators.
... The schematic diagram of fixed-point rub-impact is shown in Fig. 5(b). In order to ensure that the disk and the elastic rod meet the contact condition and do not penetrate each other, the contact detection between the rotor-stator is carried out by Kuhn-Tucker condition of Coulomb friction, and the contact constraint condition is calculated by the augmented Lagrangian method [32]. ...
The rub-impact fault of the rotor system is the research object in this paper, and the system is modeled by the finite element method. In the process of the study, the high-order harmonic components appear in the output response of the rotor system, which imply that the rotor system is nonlinear. Nonlinear output frequency response functions (NOFRFs) solve nonlinear problems in the frequency domain and explain these nonlinear phenomena. Based on NOFRFs, a method named weighted contribution rate of NOFRFs (WNOFRFs) is used to improve the weak high-order harmonic components proposed by the authors. In this paper, the multi-parameter optimized genetic algorithm is used to calculate the obstacle parameters of the stochastic resonance (SR) which is used to enhance weak signal components. In view of the fact that both WNOFRFs and SR can improve the weak signal components, a new method of weighted contribution rate of NOFRFs incorporating stochastic resonance (WNS) algorithm is proposed in this paper. Based on the algorithm, the variations of index WS show a trend of approximately linear growth, which indicates that index WS has certain advantages for the fault diagnosis of the rotor rub-impact.
... In this paper, the Kuhn-Tucker condition based on Coulomb friction is used to detect contact. And the friction-based augmented Lagrange method is used to deal with the contact constraint conditions [14,15] to ensure that the contact depth of the contact boundary is within the specified allowance range when the disk is in contact with the casing. Therefore, rubbing-force F rub can be decomposed into a normal bounding force F r and tangential rubbing force F t , the expression is shown as ...
The phenomenon of oil film oscillation and frequency locked may occur in a healthy rotor system which is supported by sliding bearing. The dynamic behavior of the rotor system with misalignment and rubbing coupling fault supported by sliding bearing is also very complex. To solve the problem of fault diagnosis in this case, a dynamical model of rotor system is proposed in this paper. The short bearing oil film force, the equivalent misalignment moment, and Hertz contact theory are applied to establish the model. For rubbing faults, the Augmented Lagrange method is used to deal with the contact constraints to ensure that the boundary penetration depth is within the specified tolerance range. Furthermore, the dynamic behavior of the faulty rotor system under different rubbing stiffness conditions is analyzed in this paper. Meanwhile, the fault signal is divided into equal-band by the wavelet basis functions to find out the fault frequency band of the rotor system. Finally, the accuracy of the simulation study is verified by measurements obtained from the faulty rotor test platform. The following findings are made in this paper. The rubbing fault is dominant in the coupling fault. With the increasing of the speed, the frequency components of the system are dominated by high frequency. The double frequency is the main fault feature frequency band. It can be seen that the rotor system moves gradually from a quasi-periodic state into chaos due to the Lyapunov exponent. At the same time, due to the effects of misalignment moment and friction force, the phenomenon of oil film instability is partially suppressed. The lagging of the first and second-order oil film oscillations occurs.
... Characteristic of Rotor System. In the role of oil film force, the system will show oil film instability phenomenon [21][22][23][24][25]. To clearly observe the dynamics characteristic of rotor system under the oil film force, then specially draw the threedimensional spectrum on the right neck (node 25) of the rotor system without fault, shown in Figure 5. ...
For the diagnosis of looseness-rubbing coupling fault of rotor-sliding bearing system caused by bolt looseness fault, the mechanical model and finite element model of dual-disc rotor system with looseness-rubbing coupling fault are established based on the nonlinear finite element method, nonlinear oil film force, looseness stiffness model, and Hertz contact theory. With the augmented Lagrange method, contact constraint conditions are dealt with to ensure that the rotary disk and casing contact with each other meeting boundary penetrating depth within the prescribed tolerance range. And then the dynamics characteristics of the health rotor system supported by sliding bearing are studied. Combined with experimental study and simulation analysis, it is found that the looseness-rubbing coupling fault is often characterized by rubbing fault, the lower part of the time-domain fluctuated shape is denser, while the upper part is relatively loose, and multiple nested half ellipse is shown in orbit diagram. Because of the loosing stiffness and rubbing force, the phenomenon of unstable oil film is depressed. The appearance of the first- and second-order oil film oscillation phenomenon is delayed. It could be used as a theoretical basis for diagnosing looseness-rubbing coupling fault of rotor-sliding bearing system.
A model for a rotor system simulated with finite element method and a test bench are established in this paper. The fixed-point rub-impact fault on rotor system is studied (There are six clearances to be discussed). It is found that the nonlinear compositions are contained in the output responses by analyzing these vibration signals of the rotor system with fixed-point rub-impact, which implies that a nonlinear term appears in the system. In order to extract these compositions, a nonlinear method, named weighted contribution rate of nonlinear output frequency response functions (WNOFRFs), is adopted for analyzing the mechanism of these nonlinear problems in frequency domain. Furthermore, the Clenshaw-Curtis numerical integration method and the minimum mutual entropy principle (MMEP) are used to extract the fault diagnosis index J for identifying the fixed-point rub-impact fault of the system. At last, according to the simulation and experiment research, WNOFRFs can improve these higher-order nonlinear characteristics. And these findings prove that the index J has certain advantages compared with other indexes in the diagnosis of the rotor rub-impact fault.
The rub-impact between a rotor and a stator is a common fault of the rotor system. Various methods are available to detect the rub impact using vibration signals. However, the noise in vibration signals causes inconvenience when extracting characteristic signals. Nonlinear output frequency response functions (NOFRFs) comprise an effective method for using input and output signals to detect damage of a structure or system. A new evaluation method named the NOFRFs weighted contribution rate has been proposed in this paper. This method is an extension of traditional NOFRFs-based indexes and attempt to obtain a new index with higher recognition of faults. As a new index extracted by this method, the second-order optimal weighted contribution rate of the NOFRFs optimally amplify the extracted fault features. The characteristic signal after amplification is significantly enhanced. The new index is applied to the evaluation of a rub-impact fault. The simulation and experimental results demonstrate the sensitivity of the new index to rub-impact faults. Especially in the initial stage of the occurrence of rub-impact, the new index shows better superiority. The findings demonstrated that the second order optimal weighted contribution rate has a high application value in the fault diagnosis of rub-impact.
For the diagnosis of misalignment-rubbing coupling fault of rotor-sliding bearing system caused by misalignment fault, based on nonlinear finite element method, the mechanical model and finite element model of dual-disc rotor system with misalignment-rubbing coupling fault are established by short bearing oil film force, equivalent misalignment torque and Hertz contact theory. And with the augmented Lagrange method contact constraint conditions is dealt to ensure that the rotary table and casing contact each other meet boundary penetrating depth within the prescribed tolerance range. Combined with experimental study and simulation analysis, relevant dynamic characteristic of misalignment-rubbing coupling fault rotor-sliding bearing system is studied, with the different speed conditions. It is shown that rubbing fault is the leading role in the coupling fault, misalignment fault will inspire high power spectrum in a subordinate position. With the increasing of rotational speed, the main composition of the system frequency is the high power frequency. And it is gradually from the quasi periodic motion to chaos motion state. As the result of misalignment moment and rubbing force, the phenomenon of oil film instability is partial inhibition. The first and the second order of oil film oscillation phenomena are lagging behind. The results of the study provided the basis for the diagnosis of misalignment-rubbing coupling fault of rotor-sliding bearing.
The paper presents the study of dynamics of rotor machines. The investigation is performed on the basis of linear theory of vibrations with application of the proposed analytical model to a specific case of washing - machines. Basic requirements have been defined for the design of the machines that enable reduction of their vibro-activity.
For the misalign-rubbing coupling fault rotor-bearing system caused by misaligned bearing, the mechanical model and finite element model of dual-disk misalign-rubbing coupling fault rotor-bearing system were established in this paper. The research on dynamics characteristics about the effect of rubbing stiffness, misaligned angle, friction coefficient, rubbing interval and rotational speed on the system was done with the equivalent misaligned moment, nonlinear finite element method and contact theory. Through the relevant research and analysis, it was found that misalign-rubbing coupling fault mainly embodied in the rubbing fault. It was also found that frequency-doubled appeared very early and its peak increased rapidly. This feature can be as a basis which can diagnose misalign-rubbing coupling fault.
Blade rubbing is one of the most destructive mechanical faults that frequently manifest in rotating machinery. Its occurrence is mainly caused by two distinctively different mechanisms and root causes, namely creep (elongated blades) and rotor eccentricity (diminished blade tip clearance). A successful classification of the types of blade rubbing is important as it could lead to identification of the root cause of the problem. This study explores a vibration method to classify blade rubbing based on the analysis of casing deflection profile. Different types of blade rubbing were simulated in an experimental rotor rig and vibration responses of the rotor casing under the influence of blade rubbing were measured and studied. Experimental results indicate that vibration characteristics of rotor casing change in accordance to different mechanisms of blade rubbing, resulting in fairly distinctive casing deflection profile. A quantitative method to classify blade rubbing was formulated based on the analysis of obtained results. A comparison made against the vibration spectrum analysis suggests that the analysis of casing deflection profile provides a more effective means to classify blade rubbing and therefore could be applied for detailed blade rubbing diagnosis in rotating machinery.
Models can be applied for simulating dynamical behavior of rotating machinery or specific faulty conditions. Efficient model updating techniques could be very useful for increasing model accuracy. Model updating of rotor systems is significantly different with respect to the well-known model updating techniques and related modal analyses performed in the field of vibrating structures. This paper investigates both the difficulties and the conditions of rotor vibrations measurement tests as well as the approximations introduced in the rotor model. Some experimental cases of turbo-generator machines indicate the difficulties and problems in the identification of eigen-frequencies and damping modal parameter. In the second part of the paper uncertainties and non-linearity of the model are investigated. An example of updating of some shaft and bearing parameters by means of an evolutionary algorithm, for fitting the natural frequencies of a shaft line, is presented and discussed. Model updating techniques of bearing coefficients are also discussed and a procedure is proposed to avoid misleading results of widely-used model updating approaches.