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Aiming at a Top Gas Recovery Turbine Unit (TRT) with double support rotor and the extending disk end, theoretical and experimental analysis about influence of cylindrical bearing and four-lobe bearing on vibration of TRT rotor system are conducted in this paper. The results indicate that vibration of the rotor supported by cylindrical bearing is more stable than that supported by four-lobe bearing at the driving end (DE) and the nondriving end (NDE). The amplitude of rotor is supported by both of these types of bearing increases as the speed increases at the NDE, while the amplitude of the DE remains unchanged. Comparing with the result of theoretical analysis, the practical test results are more consistent with the theoretical response analysis conducted by applying unbalanced mass at the extending disk end. This paper presents an analysis method of the critical characteristics of a double support rotor system with the extending disk end and provides reference value for dealing with vibration fault of double support rotor system with the extending disk end.

The vibration problems of the rotor system within rotating machinery are an important safety issue in engineering. With the development of industry, more complex rotor structure and higher operating parameters (high rotational speed, large flow rate, high operating pressure, etc.) will bring more challenges for the vibration problems of rotor system. Since Jeffcott discovered the phenomenon that rotor will automatically center after exceeding the critical state in 1919 which laid the foundation of the theory of rotating machinery operating in high rotational speed [

In this paper, the dynamic characteristics of a double support rotor with extending disk end in a Top Gas Recovery Turbine Unit (TRT) is analyzed and tested to study the impacts of bearing on vibration characteristics of rotor.

The analysis of TRT rotor system dynamic model is the same as the classic finite element analysis method of multidisc rotor system. Through the analysis of the axial discs, shaft section, and bearing seat, the relationship between node force and node displacement is established, combining the equation of motion of each unit. Finally, the motion differential equation of system with the node displacement as generalized coordinates can be obtained. Thus converting the problem into a rotor vibration problem with finite degree of freedom, the critical speed of the rotor can be obtained by solving a set of linear algebraic equations [

For a rotor system with

TRT is a typical double support rotor system with extended discs whose impeller and hub are located between the two bearings, The free end is fitted with a gear plate for turning the rotor at start-up. The rotor model is shown in Figure

TRT rotor model.

The working speed of the TRT is 3000 r·min^{−1} and its original bearing is four-lobe bearing. The structural parameters and operating parameters of the bearing are shown in Table

The structural and operating parameters of the four-lobe bearing.

Structural parameters | Value | Operating parameters | Value |
---|---|---|---|

Bearing diameter/mm | 180 | Fulcrum coefficient | 0.5 |

Bearing width/mm | 150 | The type of oil | L-TSA46 |

Gap ratio/ |
1.5 | Preload | 0.892 |

Cornerite of pad/° | 71 | Load/N | 20210/21530 |

The results of eigenvalue analysis of four-lobe bearing-rotor system are shown in Figure

Modal analysis of four-lobe bearing-rotor system.

The bode charts of unbalanced response of four-lobe bearing.

Unbalance in the middle

Unbalance in the gear wheel of the extension end

The bode charts of the two bearings of the rotor which can be obtained by applying unbalance of 14.93 kg·mm at the middle of the rotor are shown in Figure ^{−1} and 3300 r·min^{−1}, respectively, the NDEs (nondriving end) are 3420 r·min^{−1} and 3300 r·min^{−1}, respectively, and the avoidance rate is above 11% to meet the design requirements. There is a vibration peak in horizontal direction at 3000 r·min^{−1} which coincides with the working speed.

The bode charts of the two bearings of the rotor which can be obtained by applying unbalance of 14.93 kg·mm at the cantilever end of the rotor are shown in Figure ^{−1} and 4500 r·min^{−1}, respectively.

After systematically analysis of the various structures and parameters of tilting pad bearing, elliptical bearing, and cylindrical journal bearing, it can be found that the response characteristics of the rotor system supported by cylindrical bearing are the best. The structural parameters of the cylindrical bearing are shown in Table ^{−1} and 3300 r·min^{−1}, respectively; the NDE-bearings are 3420 r·min^{−1} and 3300 r·min^{−1}, respectively; the avoidance rate is above 16% to meet the design requirements. From Figure ^{−1} which is the same as the NDE-bearings. For the cylindrical bearing, the process of acceleration is stable and there is no vibration peak existing near the working speed and the magnification factor is smaller, which makes the characteristics of the rotor system supported by cylindrical bearing better.

The structural and operating parameters of the cylindrical bearing.

Parameters | Value |
---|---|

Bearing diameter/mm | 180 |

Gap ratio/ |
1.5 |

Bearing width/mm | 135 |

Modal analysis of the cylindrical bearing-rotor system.

The bode chart of unbalanced response of cylindrical bearing.

Unbalance in the middle

Unbalance in the gear wheel of the extension end

The test of this paper is for a real energy recovery turbine unit, and it was carried out by conducting a trial run in a table driven by a 3200 kW motor. Through the variable speed fluid coupling and gearbox, the power is transmitted to the TRT device to realize the control of speed and force. Each device including TRT, gear case, and motor carries out bearing pad temperature monitoring and shaft’s vibration monitoring. At the same time, the inlet and outlet temperature of lubricating oil are tested and these monitoring data are fed back to the control platform by converting into electrical signals. The specific test system is no longer detailed. The test object of this paper is a TRT unit and the vibration of rotor supported by four-lobe bearing and cylindrical bearing is tested separately. The temperature of the bearing and the temperature of the lubricating oil at the inlet and outlet will not be presented in this paper. The bearing temperature test rig and the installation of vibration and speed probe are shown in Figure

TRT test platform and the installation of vibration and speed probe.

Test platform

Installation of vibration probe

Two types of bearings.

Four-lobe bearing

Cylindrical bearing

The vibration tests of four-lobe bearing and cylindrical bearing are carried out, respectively, under the condition of speed-up, operation, and shutdown. The test results are shown in Figures

The vibrational trend of four-lobe bearing-rotor system.

The vibrational trend of cylindrical bearing-rotor system.

Comparison of the vibration of rotor supported by four-lobe bearing and cylindrical bearing.

NDE

DE

It can be seen from Figure ^{−1}. However the amplitude at the NDE increases as the speed increases and reaches the maximum which is nearly 30 ^{−1}. Besides, there is a vibration peak at the speed of 2240 r·min^{−1}.

As for the cylindrical bearing, it can be seen from Figure ^{−1}. Comparing with the four-lobe bearing, there is no vibration catastrophe of the rotor supported by cylindrical bearing in the process of acceleration and deceleration.

From Figure

The vibration characteristics of the rotor supported by the cylindrical bearing are better than four-lobe bearing. The amplitude at the NDE of rotor supported by both of these types of bearing increases as the speed increases, while the amplitude at the DE remains unchanged. Comparing with the theoretical analysis, it can be found that the actual test results of the double supports rotor system with extending disc are more in agreement with theoretical analysis conducted by applying unbalance at the extending end. Besides, there is a vibration catastrophe of the four-lobe bearing-rotor system at the NDE when the speed reaches 2240 r·min^{−1}. It should be caused by the low frequency eddies (approximately half of the critical speed which is 4500 r·min^{−1}), while the vibration catastrophe of the test results of 2# probe at DE when the speed is 2660 r·min^{−1} is mainly caused by the influences of external environment.

The bearing affects the critical characteristics of the rotor. For a double support bearing-rotor system with an extending end, if the vibration of cantilever end is severe after applying eigenvalue analysis, it is necessary to conduct the unbalance response analysis of the cantilever end and dynamic balance treatment even though the unit is expander and its rotor is stubby.

At the working speed of 3000 r·min^{−1}, the amplitude at NDE is about 20

This paper studies the impacts of cylindrical bearing and four-lobe bearing on the vibration of rotor system combining theoretical analysis and experimental analysis. The result shows that different bearing types have effects on the critical characteristics of rotor system, and the vibration of rotor supported by cylindrical bearing is more stable than four-lobe bearing. The test results are in good agreement with theoretical analysis.

For a double support bearing-rotor system with an extending end, if the vibration of cantilever end is severe after applying eigenvalue analysis, the unbalance response analysis of the cantilever end and dynamic balance treatment are necessary to conduct.

The authors declare that they have no conflicts of interest.

This work is supported by the National Natural Science Foundation of China (no. 11372234) and the Key Project of Natural Science Foundation of Xi’an Jiaotong University (no. zrzd2017025).