Nonlinear study on a rigid rotor supported by herringbone grooved gas bearings: Theory and validation

TLDR: In this paper, the authors investigated the nonlinear behavior of a rigid rotor supported by herringbone grooved journal gas bearings (HGJBs) and the 2D narrow groove theory (2D-NGT) was adopted to model the HGJBs, and a set of integrated rotor bearing state equations were built by coupling the rotor motion equations and the bearing Reynolds equation.

About: This article is published in Mechanical Systems and Signal Processing.The article was published on 2021-01-01 and is currently open access. It has received 19 citations till now. The article focuses on the topics: Rotor (electric) & Bearing (mechanical).

Figures

Figure 14 Rotor responses with 20 mgmm imbalance at the rotor mass center from 38 krpm to 46 krpm

Figure 15 Rotor responses with 30 mgmm imbalance at the rotor mass center from 38 krpm to 44 krpm

Figure 6 Waterfall plots of the radial displacement measured by four capacitive probes: (a) front X; (b) font Y; (c) rear X; and (d) rear Y

Figure 11 Mode shape predicted for six different speeds after the onset speed of sub-synchronous vibrations using the non-linear model. (a) 38 krpm; (b) 40 krpm; (c) 42 krpm; (d) 44 krpm; (e) 46 krpm; and (f) 48 krpm.

Figure 1 shows the coordinate system for the HGJB model. Since the NGT was adopted, the pressure does not fluctuate as the rotor rotates. Thus, a coordinate system fixed to the bushing was used. The FDM method was adopted to discretize the modified Reynolds equation in the spatial domain. Figure 2 shows the grid and the boundary conditions of the implemented model. The model assumes a perfectlyaligned shaft and ambient pressure at both bearing axial ends. Therefore, the bearing gas pressure distribution is assumed to be symmetrical about the bearing mid-plane. Thus, only half of the bearing is modeled, which significantly reduced the computational cost. Four boundary conditions are applied to constrain the differential equation, which were marked in Fig. 2 and summarized as follows:

Figure 1 shows the coordinate system for the HGJB model. Since the NGT was adopted, the pressure does not fluctuate as the rotor rotates. Thus, a coordinate system fixed to the bushing was used. The FDM method was adopted to discretize the modified Reynolds equation in the spatial domain. Figure 2 shows the grid and the boundary conditions of the implemented model. The model assumes a perfectlyaligned shaft and ambient pressure at both bearing axial ends. Therefore, the bearing gas pressure distribution is assumed to be symmetrical about the bearing mid-plane. Thus, only half of the bearing is modeled, which significantly reduced the computational cost. Four boundary conditions are applied to constrain the differential equation, which were marked in Fig. 2 and summarized as follows:

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Nonlinear study on a rigid rotor supported by herringbone grooved gas bearings: theory and validation" ?

The nonlinear behavior of a rigid rotor supported by herringbone grooved journal gas bearings ( HGJBs ) was investigated in this study. 

Q2. How many mgmm were added to the rotor mass center?

In order to assess the effect of imbalance, imbalances of 20 mgmm, 30 mgmm, and 40 mgmm were added at the rotor mass center position. 

Q3. Why is the sub-synchronous vibration suggested to be self-excited?

Since neither imbalance nor external loads were considered in the simulation above, the reason for the sub-synchronous vibration is suggested to be self-excitation. 

Q4. What is the nonlinear model of the rotor?

The non-linear model allows to analyze the rising limit cycles due to the reduction of the overall effective damping until bearing failure as a function of static and imbalance loads. 

Q5. What is the onset speed of sub-synchronous vibrations?

The onset speed of sub-synchronous vibration increases slowly at low static loads, while it increases more rapidly at higher static loads. 

Q6. How much does the speed of bearing failure decrease in comparison to the 20 mgmm case?

In comparison to the 20 mgmm case, the speed of bearing failure decreases from 47 krpm to 45 krpm, since the synchronous amplitude increases while the sub-synchronous amplitude did not change much. 

Q7. What is the advantage of the coupled Reynolds equation and rotor motion equations?

The advantage is that the coupled Reynolds equation and rotor motion equations can be transformed into a set of state equations, which allows to solve the state variables simultaneously. 

Q8. What is the speed of bearing failure?

The speed of bearing failure decreases from 49 krpm to 47 krpm when the imbalance is considered, since the total rotor response corresponds to the superposition of the self-excited motion and the imbalance-excited motion. 

Q9. What is the effect of the centrifugal force on the performance of a rot?

the performance of HGJBs is very sensitive to the bearing clearance, the rotor expansion caused by the centrifugal force needs to be taken into consideration. 

Q10. What is the onset speed of sub-synchronous vibrations of the horizontal rotor?

The onset speed of sub-synchronous vibrations of the horizontal rotor increases to 40 krpm, which is higher than both the vertically and 45° inclined rotor, suggesting, therefore, that static load delays the appearance of sub-synchronous vibrations. 

Q11. Why are other parameters not included in the predictions?

It should be noted that the deviation of other parameters, such as the rotor and bushing cylindricity (in 1 µm), the rotor imbalance, and the rotor misalignment are not considered in the predictions. 

Q12. What are the advantages of a gas lubricated journal bearing?

Besides the advantages listed above, this type of bearing can operate with radial clearance of several micrometers, which is beneficial for small-scale turbomachinery, since it allows to run them with small tip clearance as suggested by Diehl et al. [10]. 

Q13. What is the rotordynamic stability of the HGJB?

The simulation results suggest stable rotor operation even for a vertically inclined rotor, which demonstrates the inherent stability characteristic of the HGJB compared to plain bearing. 

Q14. How much speed of bearing failure does the synchronous amplitude increase?

Compared to the 20 mgmm and 30 mgmm cases, the synchronous amplitudes increase to ~0.23, while the speed of bearing failure decreases to 43 krpm. 

Q15. What is the speed range between the onset speed of sub-synchronous vibrations and the bearing?

the speed range between the onset speed of sub-synchronous vibrations and the bearing failure speed becomes narrower as the imbalance increases, which make experimental investigations more risky.