Fig 7 - uploaded by Sergio Guillermo Torres-Cedillo
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Sensor positions over the casing (dimensions mm): (a) first sensor locations test and (b) second sensor locations test.
Source publication
The high pressure (HP) rotor in an aero-engine assembly cannot be accessed under operational conditions because of the restricted space for instrumentation and high temperatures. This motivates the development of a non-invasive inverse problem approach for unbalance identification and balancing, requiring prior knowledge of the structure. Most such...
Contexts in source publication
Context 1
... the studies of this research there will be 6 sensor locations, distributed along the casing (see Fig. 7). The inverse method relies directly on such readings to identify the equivalent unbalance in three chosen planes of the HP rotor (Fig. ...
Context 2
... methodology comprises three steps. The first step is to take casing vibration data for the unbalanced system ( Fig. 3 (b) and Table 1) from various locations (Fig. 7) and chosen operating speeds. In this paper the unbalance data were obtained as per Section 4 at seven speeds (8500, 9500, 10,500, 11,500, 12,500, 13,500 and 14,500 rev/min) which cover the typical operating speed range of the HP rotor of an aero-engine [9][10][11]. The data at these speeds was used to build Eqs. ...
Context 3
... Sections 3.2 and 3.3. The previous study [12] has reported that the best balancing planes to be at disk 1, disk 5 and disk 10 (see Figs. 1(a,b) and 5). The present study therefore uses these same planes. When constructing the inverse operator, it is noted that the inverse operator for balancing system A1 employs just one sensor reference (P 1 , Fig. 7) to express the SFD forces in terms of the unbalance and the synchronous components of the velocity measurements (see Eq. (28)). On the other hand, the inverse operator for system A2 used two reference locations (P 1 andP 6 , Fig. 7), since the HP rotor was supported by two SFD ...
Context 4
... operator, it is noted that the inverse operator for balancing system A1 employs just one sensor reference (P 1 , Fig. 7) to express the SFD forces in terms of the unbalance and the synchronous components of the velocity measurements (see Eq. (28)). On the other hand, the inverse operator for system A2 used two reference locations (P 1 andP 6 , Fig. 7), since the HP rotor was supported by two SFD ...
Context 5
... first validation study assesses the degree of sensitivity of the proposed balancing method to the use of different sensor locations along the casing. Fig. 7a and b illustrates two alternatives for the sensor installation at six locations -these are respectively referred to as installations I, II respectively. Fig. 8 shows PVRs for the balancing of system A1 ( Fig. 1(a)) where VPVR is the PVR for the y vibration and HPVR is the PVR for the x vibration. Fig. 8(a), (b) respectively present the ...
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Citations
... The commercial model was created to characterize the bearing model and to study the effects of wear on the dynamic response. Cedillo and Bonello [10] proposed a methodology for balancing the rotor system with nonlinear squeeze film dampers. They assumed that the bearing and the rotor have a linear connection in addition to the nonlinear connections. ...
To minimize carbon footprints and improve volumetric efficiency and power output, modern internal combustion engine technology employs turbochargers in automobile and marine engines as well as in several diesel generator sets. During its operation, a minor imbalance or flaw in turbocharger rotors could lead to the system catastrophic failures. The two floating ring bearings that support a turbocharger allow it to operate at high speeds. The exhaust gases impacting the turbine and the inlet air impacting the compressor cause axial forces in the turbine, resulting in axial displacements. To balance these two components of axial forces, a thrust bearing is used in the turbocharger. The present work focuses on the comparative study of the turbocharger with and without the thrust bearing. The thrust bearing's pressure distribution is first calculated, and the nonlinear bearing forces acting on the turbocharger rotor are obtained. The exhaust gas forces are considered radial direction excitations, while blade passing excitations are taken as axial forces. The critical speeds of the rotor are first estimated using the Campbel diagram. An experimental study on an automobile turbocharger rotor is performed to validate the frequencies obtained from the present finite element model. Further, the system stability with and without thrust bearings at different operating speeds is illustrated. The influence of the thrust bearing location and preload is investigated on the system response. It is found that the thrust bearing has a significant effect on the system stability at higher speeds. The system stability condition at different operating conditions is identified by the trained neural network models.
... Rotor dynamics is a central issue of concern in the research areas of nonlinear dynamics. The rotor-bearing system is the core structure of the engine, whose assembly parameters are numerous and multiple nonlinear factors are coupled [1][2][3]. It is a high-dimensional complex time-varying dynamic system that contains a large number of components [4]. ...
... The configuration space variable of -dimensional complex system is , whose discrete time series obtained by experiment or numerical simulation can be denoted as . Project this signal to the space spanned by a complete normal orthogonal basis , as is shown [22]: (1) This set of normal orthogonal basis should satisfy the minimum constraint condition under the square norm, and satisfies the following equation [21]: (2) where , , represents the average operator the inner product in the Hilbert space, and the norm respectively. The orthogonal basis required above could be calculated by the Lagrange multiplier. ...
In this paper, a double-disc rotor system with two support rolling bearings is reduced by the proper orthogonal decomposition (POD) method. The finite element method (FEM) is used to establish the rotor system model (96DOFs). The basic theory of the POD method and the concrete expression in the rotor system is introduced. The rotor system is reduced to 12, 5, and 2 DOFs by the POD method, respectively. The time history curves, and frequency spectrums of the reduced and original systems are compared for verifying the accuracy of the POD method. The 2-DOFs reduced system is solved by the Harmonic balance and alternating frequency/time domain (HB-AFT), whose results are in good agreement with those by the Runge-Kutta method.
... T.S. Morais proposed a pseudorandom optimization method combined with FEM to identify unbalance in the rotor, which nonlinearities derived by a magnetic actuator [10]. An intrusive inverse problem method was presented in [11], which needs prior knowledge of the structure and system. Also, the Receptance Harmonic Balance Method (RHBM) was introduced to generate the backward operator using the vibration signals at the engine casing, provided there is at least one linear connection between the rotor and casing. ...
... Expressing Eqs. (11) in complex form as follows: ...
The basis of rotor dynamic balancing procedures relies on the linearization hypothesis of the system. However, some mechanical elements constituting a rotor system behave in various types of nonlinearities. Therefore, the balancing method must be extended to the nonlinear rotor systems. Nonlinear normal modes (NNMs) can provide valuable insight into nonlinear dynamics. So, this paper innovatively integrates NNMs into the modal balancing. There are three main procedures. First, express the unbalance response and the nonlinear mode shape as complex amplitude vectors using complex Fourier series. Second, calculate the correction coefficients of each order of harmonics, considering the harmonic resonance and internal resonance. Third, superimpose the corrections of each harmonic to form the total unbalance corrections. Several cases with different nonlinearities and eccentricities are discussed. The responses after balancing with NNMs are presented and compared with the linear modal method to demonstrate the accuracy and effectiveness of the proposed method. Simulation results show that balancing with NNMs is significantly better than the linear modal method.
... Ding et al. proposed a multi-level rotation optimization assembly technology and a revolving part assembly deviation propagation model to achieve vibration suppression [14]. Sergio et al. used the receptance harmonic balance method (RHBM) to generate the reverse operator by measuring the vibration of equipment casing and used the least square method to generate the equivalent unbalanced distribution to reduce the unbalanced amount of asymmetric rotors [15]. Chen et al. developed an assembly error propagation model of multistage asymmetric rotors that take into account the alignment process and distribution of the screw holes of adjacent asymmetric rotors [16]. ...
The unbalanced exciting force of high-speed rotary asymmetric rotor equipment is the main factor causing rotor vibration. In order to effectively suppress the vibration of the asymmetric rotor equipment, the paper establishes a multistage asymmetric rotor coaxial measurement stacking method that minimizes the exciting force. By analyzing the propagation process of the centroid of the multistage asymmetric rotor assembly and analyzing the relationship between the geometric center and the centroid of a single asymmetric rotor, a multistage asymmetric unbalanced rotor propagation model based on geometric center stacking is established. The genetic algorithm is used to optimize the unbalance of the multistage asymmetric rotors. Combined with the vibration principle under the exciting force, the vibration amplitude of the left bearing at different rotation speeds under the minimization of the exciting force and the random assembly phase is analyzed. Finally, the experimental asymmetric rotors are dynamically measured, combined with the asymmetric rotors’ geometric error measurement experiment. The experimental results confirm that the vibration amplitude of the assembly phase with the minimum exciting force is smaller than the vibration amplitude under the random assembly phase at three-speed modes, and the optimization rate reached 73.2% at 9000 rpm, which proves the effectiveness of the assembly method in minimizing the exciting force.
... Hence, considering rotor nonlinear aspects in balancing procedures is desirable, since this fact can improve the balancing efficacy. Unfortunately, few researchers have developed balancing procedures that take into account nonlinear vibration conditions and have practical application, as seen in [16][17][18][19] . Turpin and Sharan [20] , proposed a series of linearization to the rotor -nonlinear bearing system in order to apply the balancing procedure. ...
Rotating machines are key components in several industrial sectors, mainly, in energy generation. In this way, a rotating component supported on hydrodynamic bearings creates typical problems, being high vibrations amplitudes due to unbalance, one of the most common. To avoid failures and ensure a safe operation, the rotor should be balanced, and influence coefficient methods are usually used. Since balancing by the traditional influence coefficients method requires trial masses, the machine can sometimes experience a long setup time, causing financial losses. Also, this method assumes a linear rotor response that can hamper the balancing procedure for nonlinear situations, which happens when the rotor experiences high vibrational motion. Thus, this work proposes a balancing identification that considers nonlinear bearings and avoids trial masses. For this, a mixed-integer gradient-based optimization is presented. The theoretical model of a rotor supported by hydrodynamic bearings is obtained using the Finite Element method and solving the Reynolds equation. In order to save computational time, the bearing forces are approximated by a fifth order Taylor series expansion. The presented results show that nonlinear bearing consideration can improve the machine diagnosis.
... Thus, the four scalar quantities () XA Ω (20) Then, the difference between the simulated , pq X and the measured () m X vibrations is calculated, normalizing the result: ...
Rotor balancing is probably the most discussed topic in the entire literature about rotor dynamics. It would therefore seem that, from the point of view of theory, this is a problem of little interest, however, balancing is very relevant in the industrial practice and sometimes there are very particular cases that cannot be addressed and solved by traditional methods. Moreover, many papers deal with only simulated results or with small-scale tests-rigs, which can hardly reproduce the behavior of real rotors. The case described in this paper is just one of these and presents what could be defined as “predicting the effect of balancing” at rotational speeds that are higher than those possible on balancing machines. Rotordynamics modeling, identification techniques developed by the authors and the available vibration measurements allow the simulation of the behavior, i.e. the vibrations, of the considered turbine rotor on the balancing machine, even at rotational speeds higher than those are possible to be reached, but that correspond to the trip speed in the plant.
... Moreover, he used an iterated re-weighted least squares algorithm to account for measurement noise and modeling error and concluded promising estimations of excitations using Huber's M-estimators. Cedillo and Bonello [18] have taken a non-invasive inverse problem approach to identify unbalance in inaccessible high-pressure rotors. The method uses vibrations at the engine casing and employs least squares to determine the equivalent unbalance distribution in prescribed planes of the rotor. ...
Mass unbalance is one of the most prominent faults that occurs in rotating machines. The identification of unbalance in the case of large flexible rotors is crucial because in industrial applications such as paper machines and roll grinders, high vibrations can adversely affect the quality of the end product. The objective of this research is to determine the unbalance location, magnitude and phase for a large flexible rotor with few measured coordinates. To this end, an established force-based method comprising of modal expansion and equivalent load minimization is applied. Due to the anisotropic behavior of the test rotor, the force method required at least six measured coordinates to predict the unbalance with an error of 4 to 36%. To overcome this limitation, an alternate method, eliminating the use of modal expansion, is proposed. Here, displacements generated by varying the location of a reference unbalance along the rotor axis, are compared to measured displacements to detect the unbalance location. Furthermore, instead of force-based fault models, the minimization of displacements at measured locations determines the unbalance parameters. The test case in this study is the guiding roll of a paper machine and its different unbalance states. The algorithm is tested initially with a simulation-based model and then validated with an experimental set up. The results show that the displacement method can locate the unbalance close to the actual location and it can predict the unbalance magnitude and phase with only two measured coordinates. Lastly, using measured data from 15 measurement points across the tube section of the test rotor, a comparison shows how the selection of the two measured locations affects the estimation accuracy.
... This is beyond the scope of this paper, although the nonlinear inverse unbalance reconstruction method of Refs. [21][22][23] could be used. A simple attempt is made to apply an unbalance on a disk to calculate the unbalanced response of the nonlinear rotorbearing system using the identified nonlinear parameters. ...
A strongly nonlinear rotor-bearing system often has multiple solutions under harmonic excitations and jump phenomena. It's challenging to measure all of these multiple responses and establish an accurate dynamic model from experimental data to predict these phenomena. This paper used a fixed frequency test method to measure all of these multiple responses under harmonic excitations and developed a novel strategy to characterize and identify nonlinearities in a strongly nonlinear rotor-bearing system based on reconstructing constant response tests from fixed frequency test data. The fixed frequency tests are achieved by monotonically increasing the voltage applied to the exciter at a fixed frequency, and using the force drop-out phenomenon through the resonance to control the force applied to the structure. This test method could measure multivalued response curves of a strongly nonlinear rotor-bearing system in a non-rotating state. The constant response tests could be reconstructed from these multivalued response curves. The relationship of equivalent stiffness versus displacement can be established and hence the nonlinear stiffness is characterized and identified from constant response tests. A rotor-bearing system with a strongly nonlinear support is used to demonstrate the method, and the nonlinear support stiffness parameters are identified and validated in a non-rotating state. The identified nonlinear rotor-bearing model also could predict the jump phenomena in the acceleration or deceleration process. The results demonstrate the feasibility and effectiveness of the approach, and also show the potential for practical applications in engineering.
... In the vibration test of gas turbine engines, it is generally impossible to measure the response of the rotors or bearings directly. Therefore, the engine fault diagnosis, 1,2 whole machine balancing, 3,4 vibration standard formulation 5 and other related work are based on the response analysis of measuring points on the casing. Moreover, bearings and SFD of gas turbine engine are the key connecting part between the rotors and thin-walled flexible casing system, which influence the response of measuring points greatly. ...
... Relevant studies show that the rotor system with non-linear rolling bearings or SFD exhibits complex dynamic characteristics, and the non-linear supporting forces are affected by many factors, such as preload condition, surface waviness, Hertz contact and bearing clearance. 4,[25][26] Influenced by these factors, the vibration response on the measuring points of gas turbine casing is not uniform for different condition or different engines on the same assembly line. But it is difficult to derive the theoretical result of this engineering nonlinear problem. ...
Bearings in a gas turbine engine are the key connecting components transmitting force and motion between rotors and thin-walled flexible casing. The bearing stiffness and damping of squeeze film damper (SFD) nearby bearings are easily affected by many factors, such as assembly process, load condition and temperature variation, resulting in uncertainties. The uncertainties may influence the response of the measuring point on the casing. Hence, it is difficult to carry out the fault diagnosis, whole machine balancing and other related works. In this paper, a double integral quantitative evaluation method is proposed to simultaneously analyze the influence of two uncertain dynamic coefficients on the response amplitude and phase of casing measuring points. Meanwhile, the coupling influence of stiffness and damping accompanied by dramatic changes with rotational speeds are essentially discussed. As an example, a typical engine bearing-casing system with complex dynamic characteristics is analyzed. The impact of uncertain dynamic coefficients on the unbalance response is quantitatively evaluated.
... Therefore, most of these methods deal with linear problems. In addition, some scholars have extended it to nonlinear cases [21,22]. ...
