Experiment and Simulation Analysis of the Vibration Response of the Rotor-bearing System

doi:10.21203/rs.3.rs-1951821/v1

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Experiment and Simulation Analysis of the Vibration Response of the Rotor-bearing System

https://doi.org/10.21203/rs.3.rs-1951821/v1

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The unbalanced mass of the rotor-bearing system may cause abnormal vibration of the rotor-bearing system, which may affect the safe operation of the system in severe cases. In this paper, the rotor-bearing system fault simulation test bench and MADYN 2000 were used to test and simulate the single-disk shafting rotor mass unbalance fault. The research analyzes the influence of speed, unbalanced mass, support stiffness, and phase of unbalanced mass on the vibration response of the rotor-bearing system. The results show that when the speed is higher than the first-order critical speed, after the rotor starts, the amplitude gradually increases with the speed, reaches the peak at the first-order critical speed, and then gradually decreases to a stable value. Due to the anisotropy of the bearing support, the rotor has different amplitudes in each direction, but the change trend is the same, the support stiffness is small, and the stable value is reached faster. When the rotation speed and the unbalanced mass phase are the same, the rotor amplitude and the rotor unbalanced mass have a linear relationship. When the speed and unbalanced mass are the same, the rotor amplitude fluctuates with the change of the loading phase, and the fluctuation period is π. The research results have certain reference significance for the fault diagnosis and dynamic characteristics analysis of the unbalanced response of the rotor-bearing system.

rotor-bearing system

mass imbalance

fault simulation test bench

support stiffness

phase

Rotating machinery is an important equipment in the national economy and industry, and has an important position in power energy, military production, etc [1, 2]. The rotor-bearing system is the main rotating component of various types of rotating machinery. In practice, more than half of rotor-bearing system failures are related to rotor unbalance. The occurrence of such faults will be accompanied by abnormal vibration of different degrees, which may lead to mechanical damage or serious safety accidents [3, 4]. Therefore, the analysis of the unbalanced fault of the rotor-bearing system and the research on the related diagnosis methods are one of the hot issues of scholars today [5–7].

Domestic and foreign scholars have done a lot of research on the unbalance problem of the rotor-bearing system. However, the research methods are not the same. The research on unbalanced load mainly focuses on numerical simulation. Chen et al. [8] established a finite element model based on the rotor-disc system and analyzed the influence of rotational speed, unbalance, disc offset and support stiffness on the system's unbalanced vibration response. Zhang et al. [9] established a dimensionless nonlinear differential equation and solved it considering the unbalanced rotor system with bearing clearance. The effects of rotational speed, damping coefficient and friction coefficient on the topological structure and stability of solutions of differential equations are studied. Yang et al. [10] established the bearing control equation according to the virtual displacement principle and used LS-DYNA to establish the finite element model of the rotor-bearing system. Aiming at the problems of rotor unbalance and bearing failure, the vibration response of bearing and the principle of sudden change of rotor axis trajectory are analyzed and verified by experiments. Xia et al. [11] based on an actual generator rotor, established the motion equation of the rotor shaft bending and unbalance coupling fault, and analyzed the amplitude-frequency and phase-frequency characteristics of the three angles between the unbalance force and the bending plane. Yang et al. [12–14] established an equivalent dynamic model of the rotating shaft, and analyzed the influence of the degree of misalignment, shaft diameter and shaft length on the vibration characteristics of the system under the action of coupling misalignment, rotor unbalance and their coupling faults. Desavale [15] used the dimensional analysis method to analyze the vibration characteristics of the rotor-bearing system radial clearance-rotor unbalance coupling fault. The numerical study can reflect the general characteristics of the unbalanced response of the rotor, but it is different from the actual working conditions, and the results lack detailed and effective experimental evidence.

In terms of unbalanced load test research, Ye et al. [16] conducted tests on a water-lubricated bearing test bench. The influence of unbalanced load phase difference between single disk and double disk on the unbalanced response of rotating subsystem is analyzed by time domain, frequency domain and axis orbit. Wang et al. [17] simulated unbalance faults based on rotor unbalance fault simulation test bench. The special software of rotor unbalance response measurement and analysis system based on intercepted pulse analysis is developed and the unbalance response signal is analyzed effectively. Hou et al. [18] conducted finite element modeling and experimental research on the unbalanced vibration of a turbofan engine with a large bypass ratio through the rotor casing rubbing mechanism with adjustable stiffness and frequency. Zhang et al. [19] used a combination of finite element method and experimental research to analyze the unbalanced response characteristics of the rotor system. The experimental research mostly relies on the model test bench, but its cost is relatively large, and the experimental results may be caused by the coupling of multiple factors due to the limitations of operating conditions and environmental influences. Therefore, the analysis of the unbalanced response characteristics of the shafting rotor is still a subject that needs to be further studied in the future.

In this paper, the mass unbalance response characteristics of shafting rotor system under critical speed are analyzed by time history, spectrum, axis orbit and Poincaré section with the help of shafting fault rotor-bearing system simulation test bench, and the factors of shaft speed and rotor unbalance mass are considered. Meanwhile, the rotor dynamics software MADYN 2000 is used to further study the single-disk shafting rotor. Considering the factors such as bearing with different support stiffness, unbalanced mass, unbalanced mass of different phases, and over-critical speed, the motion response characteristics of the shafting rotor are studied.

1.1 Shafting fault simulation test bench and monitoring device

The test is completed on the HZXT-05 shafting fault rotor-bearing system simulation test bench as shown in Fig. 1, which can realize unbalance test, misalignment test and disk-shaft loosening test, etc. The test bench consists of a variable frequency motor, a diaphragm coupling, a rotating shaft, a rotor two symmetrical sliding bearings, a hysteresis brake, a data acquisition system and a control system. The diameter of the rotating shaft is 20mm, the length of the shaft is 550mm, and the diameter of the rotor is 140mm. The rotating shaft and the rotator are rigidly connected, and the sliding bearing adopts brass bearing bush. Figure 2 shows the control system interface of the shafting fault simulation test bench. The speed of the test bench can be adjusted through the interface, and the speed can be controlled within the range of 300-3000rpm. As shown in Fig. 3, monitoring point 1 is a photoelectric sensor used to monitor the speed of the motor, and its model is SZCB-05. Acceleration sensors are arranged at monitoring points 2 and 7 to monitor the angular acceleration of the shafting, and their models are HD-YD-221. Eddy current sensors are arranged at monitoring points 3, 4, 5 and 6 to monitor the axial and rotary displacements, which model is WT0150-A07-B00-C06-D50. Data acquisition device uses HD92000 acquisition system, and the sampling frequency is 1024Hz.

1.2 Simulation test of rotor mass unbalance fault

Install and adjust the test stand for normal operation. The experimental speed is controlled below the first-order critical speed, and the rotor is considered rigid. Figure 4 shows the rotor of mass unbalance fault test bench. The experiment simulates the rotor mass unbalance fault by adding unbalanced screws on the distribution circular holes of the rotor. Figure 5 shows the key phase position of the shafting rotor fault simulation test bench. When the circumferential hole position of the rotor in the horizontal direction is 0 degree of the key phase position, the reflector in the blue circle of the diaphragm coupling can make the photoelectric sensor feedback. The test stand can change unbalanced mass and unbalanced mass loading phase.

2.1 Influence of rotational speed on vibration response of rotor

Figure 6, 7 and 8 are the vibration response characteristic curves of the rotor at three rotational speeds under the normal working conditions of the shafting rotor test bench. Under normal conditions, the axis orbit is approximately circular, and the center of the axis orbit approximately coincides with the centerline of the shaft. By comparing Fig. 6(a), Fig. 7(a) and Fig. 8(a), it is found that the axis orbit is relatively rounded at high speed. With the increase of rotational speed, the axis orbit becomes smoother. The scattered points in Poincaré section form a closed curve, and the motion of the rotor is in a quasi-periodic state. The sliding bearing used in the experiment exhibits anisotropic properties, which also causes the shafting rotor to have different vibration amplitudes in the horizontal direction (Y direction) and vertical direction (Z direction) during the rotation process.

As shown in Fig. 9(a), under normal working conditions, the rotation frequency of the rotor is mainly the rotation frequency of the rotor itself, that is, the frequency doubling of the spectrum graph. However, due to the influence of the experimental environment, the spectrum graph is accompanied by weak frequency doubling components. It can be seen from Fig. 9(b) that below the critical speed, the vibration response of shafting rotor generally increases with the increase of speed. The sliding bearing has anisotropic characteristics, and the axial amplitude of shafting rotor is different at different speeds under normal working conditions, but the amplitude varies with the speed in the same way.

In the rotor mass unbalance fault test, the vibration response characteristics of the unbalanced working condition rotor at different speeds are shown in Fig. 10. When the rotational speed is less than the critical rotational speed, the vibration amplitude in both horizontal and vertical direction increases with the speed increase, which reflects the anisotropy of rotor vibration. During the movement of the rotor, the rotor itself is still dominated by the frequency of the rotor itself. After loading the unbalanced mass, the multi-frequency amplitude present in the original system has also increased.

2.2 The Effect of Unbalanced Mass on Rotor Vibration Response

Figure 11 shows the axis orbit of the rotor at the same rotational speed of 1500rpm, the bonded phase, and different unbalanced masses m_e. It can be clearly seen that the mass of the rotor is eccentric, the axis orbit is eccentric, and the trajectory of the movement is closer to the elliptical shape. As the imbalance mass increases, the phenomenon of motor eccentricity becomes more and more obvious.

Combined with Figs. 9, 10 and 11, the vibration amplitudes in both horizontal and vertical directions of the rotor increase when the unbalance mass is loaded at the key phase position of 8.1g, compared with the normal working condition. The vibration frequency of the rotor is mainly its own frequency, but the multi-frequency component is more obvious, and the amplitude of multi-frequency is also increased. The axis orbit of the rotor is still approximately circular with eccentricity. When the unbalance mass of loading is 11.8g, 15.2g and 24.1g, the vibration characteristics are similar to those of loading 8.1g. When the rotation speed is the same, with the increase of unbalance of the same bond phase position, the amplitude of the rotor increases in all directions, and the eccentricity becomes more obvious. The curves of the three colors in Fig. 12 represent the variation trend of amplitude with unbalanced mass m_e at 1100rpm, 1300rpm and 1500rpm, respectively. The vibration response amplitudes of shafting rotors are different under the same rotation speed and different bond phase positions. The vibration amplitude of shafting rotor increases with the increase of unbalanced mass, and there is an approximate linear relationship between the vibration amplitude of rotor and unbalanced mass.

The single disk rotor system was analyzed by dynamics specialist software MADYN 2000, a program package capable of dynamic analysis of rotor-gear -bearing system. Timoshenko beam theory and finite element with 4th order Hermit polynomials were used to simulate the elastic and inertial characteristics of the rotor, taking into account gyroscopic effects [20]. It can help design analysts predict and verify various conditions in the real state, and complete rotor system dynamics analysis quickly and cheaply.

3.1 Model establishment

The single disk rotor model is shown in Fig. 13. Beam elements are used to simulate the main shaft, which has a diameter of 20mm and a full length of 550mm.

The whole axis is equally divided into 22 units and 23 nodes, and the centralized mass simulation rotor is added at 12 central point nodes of the shaft. The system considers the stiffness and damping of the bearing without considering the sealing, and simplifies the bearing as a radial spring damper. Bearing stiffness and damping in horizontal and vertical directions are defined by four coefficients k₂₂、k₃₃、d₂₂ and d₃₃, which are added at node 4 and node 20 respectively. The shaft is made of 1045 steel with an elastic modulus of 205GPa, Poisson’s ratio of 0.29 and mass density of 7850kg/m3, respectively.

3.2 Analysis of results

The vibration frequencies and whirl conditions of the model under different spring support stiffnesses are shown in Table 1. The vibration frequencies of the first-order, second-order and third-order modes of the model are different under different stiffnesses. When the damping parameters remain unchanged and the support stiffness parameters change, the vibration frequencies of the first and second order modes are less affected, but the vibration frequencies of the third order modes are more affected.

Table 1

Vibration response table under different stiffness parameter models.
Model	Mode	frequencies (Hz)	whirl	stiffness (N/m)	damping (N s/m)
1	Mode 1	91.06	-0.01	k₂₂ = 5e7 k₃₃ = 1e7	d₂₂ = 100 d₃₃ = 100
	Mode 2	93.23	0.01
	Mode 3	315.16	-0.73
2	Mode 1	91.03	-1.00	k₂₂ = 1e7 k₃₃ = 1e7	d₂₂ = 100 d₃₃ = 100
	Mode 2	91.09	+ 1.00
	Mode 3	311.11	-1.00
3	Mode 1	88.51	-0.01	k₂₂ = 5e6 k₃₃ = 1e7	d₂₂ = 100 d₃₃ = 100
	Mode 2	91.06	0.01
	Mode 3	304.51	-0.61
4	Mode 1	72.88	+ 0.00	k₂₂ = 1e6 k₃₃ = 1e7	d₂₂ = 100 d₃₃ = 100
	Mode 2	91.06	-0.00
	Mode 3	216.43	-0.06

Take model 1 as an example to expand and analyze, Fig. 14 shows the modal analysis of the rotor model. Figure 14(a) is the first three order modes, Fig. 14(b) is the third-order modal vibration trajectory of the rotor model. Figure 15 is the Campbell diagram of the critical speed of the model, from which the critical speed of the rotor of the model is obtained, which serves as a reference for subsequent calculation and setting, and avoids working near the critical speed in practical engineering.

The displacement response curves of each node under normal working conditions are shown in Fig. 16. With the increase of rotational speed, the rotor amplitude will gradually increase until the critical rotational speed is reached and the rotor amplitude reaches the maximum value. As the rotational speed continues to increase, the vibration amplitude of rotor will gradually decrease until reaching a stable value after the critical rotational speed.

Figure 17 shows the vibration response characteristics of the rotor speed n = 9000rpm. When the horizontal and vertical support stiffness of the rotor are different, the time required to reach the stable value in the horizontal and vertical directions is different after the critical speed. At the end with small support stiffness, the rotor will reach a stable value faster after the critical speed. After the rotor reaches the stability after passing the critical speed, the vibration frequency of the rotor itself is still mainly rotating frequency.

The unbalance response of rotor model was simulated by adding unbalance mass at node 12. According to the harmonic response analysis and calculation, the basic characteristics of the vibration response under the unbalanced condition are consistent with the normal condition, and the vibration response amplitude is larger.

Figure 18 shows the relation curve between unbalanced mass and rotor amplitude when the speed n = 1500rpm and unbalanced mass are all loaded at the key phase position. The vibration amplitudes in both horizontal and vertical directions of the rotor model increase with the increase of unbalance, and there is a linear relationship between vibration amplitude and unbalance mass.

Figure 19 shows the vibration response curves of different loading phases when the rotor model speed is 1500rpm and the unbalanced loading mass is 24.1g. At the same speed and unbalanced mass, the phase has a certain influence on the vibration amplitude of the rotor model. The change of phase makes the vibration amplitude of the rotor fluctuate in all directions, and the response of the vibration in each direction has a π phase period.

The mass unbalance fault response characteristics of single-disk shafting rotor system were studied by combining experiment and numerical simulation. The shafting rotor test bench and MADYN 2000 have complementary advantages. When the rotational speed is lower than the critical speed, the results of the comparative test study and the numerical simulation analysis are basically consistent, which shows the reliability of the simulation analysis. The vibration response of the over-critical rotor speed is also analyzed, and the influence of the loading phase of the unbalanced mass load on the vibration response of the rotor is considered. After analysis, the following conclusions are drawn:

(1) When the speed is lower than the first-order critical speed, the vibration amplitude of the rotor increases with the increase of the speed. Due to the anisotropy of bearing support, the anisotropic amplitude is different, but the variation trend is consistent with the speed. At the same time, the bearing support stiffness also affects the vibration mode of the rotor.

(2) When the speed is higher than the first-order critical speed, the vibration amplitude of the rotor increases first and then decreases with the increase of the speed after the system starts. The amplitude reaches the maximum value at the critical speed, and then decreases to a stable value. The bearing support stiffness also has an impact on the time required for the speed to decline to the stable value after reaching the peak value, and smaller support stiffness can reach the stable value faster.

(3) When the speed and unbalance mass loading phase are the same, the vibration amplitude of the rotor increases linearly with the unbalance mass. The amplitude of rotor vibration will be affected by the phase of unbalanced mass loading when the rotor speed and unbalanced mass are the same. When the phase of unbalanced mass loading changes, the amplitude of rotor vibration fluctuates, and its fluctuation period is π.

Acknowledgements

Not applicable.

Availability of data and materials

All the data included in this study are available upon request by contact with the corresponding author.

Competing interests

The authors declare no potential conflicts of interest.

Funding

Supported by National Natural Science Foundation of China (Grant Nos. 52179089).

Authors' contributions

BQ: Conceptualization, Methodology, Writing—review & editing. YR: Formal analysis, Writing—original draft, Investigation. QD: Writing—review & editing. WS: Conceptualization, Methodology, Supervision. CM: Resources, Supervision. All authors read and approved the final manuscript.

Authors' information

Bing Qian, Graduated from North China University of Water Resources and Electric Power, Senior Engineer, Deputy General Manager of the Chn Energy Dadu River Repair & Installation Co., LTD. Engaged in the installation and maintenance management of hydro-turbine generator unit.

Yinkang Ran, Graduated from North China University of Water Resources and Electric Power, Engineer, Deputy Director of Shaping Maintenance Project Department of the Chn Energy Dadu River Repair & Installation Co., LTD. Engaged in the maintenance, installation and management of primary electrical equipment for hydro-generators.

Qiang Ding, Graduated from Xi'an University of Technology, director production technology department and engineer of the Chn Energy Dadu River Repair & Installation Co., LTD. Engaged in the installation and maintenance management of hydro-generator units. Weipeng Sun, Ph.D., Lecturer, Institute of Water Resources and Hydro-electric Engineering, Xi’an University of Technology. E-mail: [email protected].

Chenyuan Ma, Ph.D. candidate, Institute of Water Resources and Hydro-electric Engineering, Xi’an University of Technology.

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Experiment and Simulation Analysis of the Vibration Response of the Rotor-bearing System

Status:

Version 1

Abstract

Figures

Introduction

Shafting Fault Test Bench

1.1 Shafting fault simulation test bench and monitoring device

1.2 Simulation test of rotor mass unbalance fault

Analysis Of Experimental Results

2.1 Influence of rotational speed on vibration response of rotor

2.2 The Effect of Unbalanced Mass on Rotor Vibration Response

Simulation Analysis

3.1 Model establishment

3.2 Analysis of results

Conclusion

Declarations

References

Status:

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