Control the Working Process of the Rotor System with Tilting Pad Bearing

Abstract

Various processes take place in rotor systems with tilting pad bearings. It is important not only to control but also to manage these processes. Due to the instability of the oil film layer in a bearing with inclined pads, oil whirl/whip can occur. Such whirl/whip destabilize the operation of the rotor system. Additional elastic elements between the tilt pads suppress oil whirl/whip and thus reduce rotor vibration excitation. By identifying the working zones of such bearings where oil whirl and whip occur, the problems of rotor rotation instability can be solved. In order to determine the effectiveness of the elastic elements between the tilting pads, research was conducted. A special stand with diagnostic equipment was used for the tests. The clearance between the rotor and the bearing was 50 μm. During the research, the rotor rotation speed was varied from 0 to 5000 rpm. After conducting the research, stable and unstable rotor working zones were determined (Zone I: 0 to 1938 rpm; Zone II: 1938–3923 rpm; Zone III: 3923–5000 rpm). Based on the obtained research results, it is possible to control the working process of the rotor system.

1. Introduction

Journal bearings are used in various tools, machines, turbochargers, generators, steam turbines, grinding machines, pumps, turbines, fans, cars, ships, and many other mechanisms. However, significantly less research has been devoted to diagnostics and analyses of systems with sliding bearings than to systems with rolling bearings [1,2,3]. This is due to many reasons. One of the reasons is that it is difficult to use vibro-diagnostic methods because the journal bearings have low vibro-activity [4]. Rotor systems with journal bearings are characterized by unstable operation [5]. Their working vibro-characteristics are very different from the working vibro-characteristics of rolling bearings. If these instabilities occur in the rotor working to a critical resonant rotation speed, the machine’s failure is inevitable. This breakdown is sudden, unexpected, and disastrous [6].

In [7], the random parameters that had the greatest effect over the system’s stochastic response were determined. This analysis enabled identifying the rotor’s rotational frequencies of instability. Nonlinear characteristics are received on their own in the deterministic models. It is necessary to research vibro-diagnostic signals that are difficult to detect in the general background of disturbances [8,9].

In [10], a mechanical model of the circumferentially distributed rods and the nonlinear contact stiffness matrix that characterizes the contact effect between the disks was submitted. The contact stiffness matrix is composed of seven stiffness coefficients that characterize the lateral stiffness, shear stiffness, bending stiffness, and torsional stiffness of the contact interface.

In [11], a new research system for the early detection of oil whirl/whip was presented. Two sensors were used to measure vibrations. A sensor was also installed in the bearing housing to measure the oil whip/whirl.

The essential difference is observed between the rotor vibrations caused by unstable journal bearings, for example, oil whip/whirl, and other excited rotor vibrations, for example, rotor imbalance, temperatures, lubricant film stiffness, etc. [12,13,14,15,16].

The research regarding the stable and unstable causes of rotor rotation is presented in the article in [17].

That article also presents the results of the study of the influence of oil and friction on the stability of rotor rotation.

To avoid fluid-induced instability and high increases in temperature and load capacity inefficiency, in [18], a new concept of a hydrodynamic bearing was proposed in which the bearing’s own motion was considered, thus making it possible to change the average velocity of the lubricating oil film inside the bearing. Further, ref. [19] described the effect of a magnetic field applied to a Ferro fluid-lubricated hydrodynamic bearing. A rotor with a single bearing at one end was built to be the test rig. The experimental results showed that three to eight permanent magnets can all increase the instability threshold of the oil bearing. Especially, the magnetic field formed by eight magnets demonstrated an optimal effect. Depending on the number of magnets, oil whirl/whip occurs when the rotor rotation speed is between 3024 and 4480 rpm and from 3184 to 5268 rpm.

In [20], a tilting pad journal bearing was presented whose pads were controlled by electromagnetic actuators. By mounting the electromagnetic actuators in the bearing casing behind the pads, one can exert electromagnetic forces on the pads and make them change their angular position about the bearing. Hence, one can modify the dynamic characteristics of the rotor bearing system for desired and more appropriate values for a given operational condition. The results of the research demonstrated the effectiveness of the system in reducing the lateral vibrations of the rotor during operation, and a good correlation between the numerical and experimental results was observed. In [21], the oil film was shown, which usually becomes unstable, giving rise to a limit-cycle oscillation. The results demonstrate that instability in the oil film does not lead to a simple circular limit-cycle orbit. The whirl/whip-induced limit-cycle oscillations generated by the oil film are more complex and entail coupled circumferential and radial motion. Thus, whirl/whip instability in the oil film may be interpreted as symmetry breaking.

Excited vibrations of tilting pad bearing oil occurred with spontaneous transversal rotor vibrations. These involve self-excited vibrations, when the energy of oil, steam, or gas is transmitted to the rotor. These vibrations arise due to oil whip/whirl [22]. Further, ref. [23] presented the course of the design process and results of numerical and experimental research regarding a prototype microturbine that uses an innovative rotor bearing system. Due to adverse operating conditions, new tilting pad journal bearings were designed in which the sliding surfaces of the tilting pads were composed of polymeric material, and a low-viscosity medium in liquid form was used as the lubricating medium. The results of tests confirmed that the developed bearings performed very well, ensuring the stable operation of the high-speed rotor of the microturbine over a wide speed range.

The purpose of the research in [24] was the theoretical analysis of the journal bearing of a centrifugal pump and the variations in the eccentricity and the rotation of the bearing to detect the instability resulting from oil whirl/whip. Assuming steady and laminar flow, Reynolds theory modified by the Elrod–Adams cavitation model was utilized. In addition, the finite element method (FEM) was used for the theoretical solution. The research results indicated that the pressure on the bearing shell increased considering the effect of the oil whip phenomenon. Control systems have a significant influence on the working processes of rotor bearing systems, including their hydrodynamic and tribological performance. The aim of [25] was to investigate the feasibility of the joint control of rotor vibration and minimizing friction losses in active hybrid bearing (AHB) rotor systems. The theoretical and experimental results indicated that the rotor vibrations were reduced at the energy-efficient operating modes under complex loads.

By knowing the oil parameters of the dynamic system of “rotor–oil–bearing” and the frequency of rotation of the rotor, the operating stability modes of this system can be determined. When the stable operation modes of the rotor system are exceeded, spontaneous transverse oscillations of the sub-synchronous frequency of the rotor begin, causing oil turbulence in the bearing gaps between the rotor and tilting pads [26,27,28]. Instability is typical for oil whirls because they increase the dynamic forces and whirl [29,30,31]. Oil whirl is characterized by instability because of the increased dynamic forces [32,33,34]. The rotor becomes unstable when the oil cannot maintain the rotor any longer or the whirl frequency coincides with the vibration frequency of the rotor. The latter phenomenon results in excited transversal vibrations of the rotor constant frequency. When the rotor rotates at a certain speed, the amplitude of the transverse vibrations of the rotor reaches an unacceptably high value, which damages the bearings and seals [35]. Stability can be achieved by changing the journal bearing structure using elastic elements [36,37,38,39]. Further, ref. [40] presented a novel method for controlling the spindle trajectory by matching the errors between the front and rear bearings. The proposed approach was implemented on a spindle equipped with rolling bearings as the rear support and a hydrostatic bearing as the front support. The proposed technique actively adjusts the amplitude and phase of the spindle trajectory at the hydrostatic bearing to match that of the rolling bearing using piezoelectric ceramic (PZT) membrane restrictors.

In order to increase the rigidity of the tilting pad bearings and rotor rotational stability in a wider speed range, near the journal bearings, bearings of different designs were implemented: elliptical, tilting pads, etc. [41]. The tilting pad bearing has insufficient damping and rotor rotational stability on uneven load distributions between the pads [42,43]. Using elastic elements in the tilting pad bearing [44,45] can change the distribution of the loads between pads, ensuring uniform hydrodynamic film thickness and thus improving the rotation of the rotor rotational stability in the wider rotation speed range. A radial clearance adjustable bearing was proposed in [46]. The structure and working principles of the adjustable bearing were introduced. This adjustable bearing can change the dynamic characteristics of the bearing by adjusting the radial clearance. In that paper, a simple rotor bearing finite element model was used to study the vibration response of the rotor system. When the rotational speed did not reach the critical speed, reducing the radial clearance could effectively reduce the vibration of the rotor, and the vibration suppression effect could reach 67%.

There are many methodologies and data formats, and any of them can be commonly used for the rotating system condition assessment [47]. For a single data format, the result may not always be accurate and reliable. Using multiple data formats simultaneously enables significantly more reliable results to be obtained [30,48].

After conducting a review of the literature, it can be seen that the problem of the work stability of journal bearings is relevant. Various methods have been used to solve the problems of bearing stability: one way is to create new bearing designs or improve the existing ones. The existing solutions and their results are unsatisfactory. In this paper, an adaptive bearing with elastic elements connecting the tilting pads is researched. The research aims to determine the working characteristics of such bearings at various rotor rotation frequencies. The obtained results will be compared with adaptive bearings without elastic elements connecting the tilting pads. The comparison will show the effectiveness of the elastic elements connecting the tilting pads. During the research, three data formats were used to present the results: spectrogram cascades, spectral density graphs, and orbit graphs.

The results obtained during the research can be applied to predict optimal operating modes and failures of rotor systems with tilting pad bearings.

The purpose is to research the oil whip and whirl influence on tilting pad bearings regarding the stability of rotor rotation and determine the stable work zones of the rotor system, as well as to determine the advantages and disadvantages of the application of elastic elements connecting tilting pads of adaptive bearings.

2. Objective of Research

The research objective involves a rotor system with a tilting pad bearing. The tilting pads are linked by elastic elements. The elastic elements in the tilting pads are inserted into special cavities created in them without any additional fastening. The elastic elements act as a tribological damper and elastic adaptive regulator.

The geometrical parameters of the tilting pad bearing are presented in

Table 1. The tilting pad bearing parameters.

Parameter	Size, Unit
Rotor diameter, D	90, mm
Rotor length, L	800, mm
Rotor roundness deviation	1.0–0.2 μm
Rotor linearity deviation	2–3, μm
Rotor hardness, HV	850–1050
Rotor surface roughness, Ra	0.04–0.08, μm
Tilting pad width, L	70, mm
Tilting pad half width, L/2	35, mm
Tilting pad thickness, B	40, mm
Tilting pad angle, β	60°
Tilting pad fastening angle, α	24°30′
Tilting pad roughness, Ra	0.32, μm
The length of the elastic element, L	70, mm
The hardness of the elastic element, HRC	42–48
Density of the elastic element, ρ	7680 kg/m3 (20 °C), 7660 kg/m3 (100 °C)
Modulus of elastic element, E	2.12 × 10−5 MPa (20 °C), 2.06 × 10−5 MPa (100 °C)

.

The rotor is composed of steel 41CrAlMo7, and the tilting pads are composed of bronze BrT10P1 since bronze has good anti-friction properties compared to steel. The elastic elements between the tilting pads are composed of steel 60MnSiCr4.

The principal construction research of the tilting pad bearing is presented in Figure 1.

The clearance between the rotor neck and tilting pads as well as the rigidity and damping capacity are controlled by varying the hydrostatic pressure. When vibration is induced, the rigidity and damping capacity of the bearing elements are changed separately for each pad, and, using elastic elements, the bearing adapts to changing conditions and damps the vibrations. These properties of control systems enable damping of vibration and ensure the rotor’s rotation at a high degree of accuracy. The rigidity and dissipative characteristics of such tilting pad bearings may be selected depending on the required conditions.

Lubrication is forced. Oil viscosity—6–8 mm²/s; density ρ—870 kg/m³ (40 °C); solidification temperature—18 °C; pressure of supplied oil—10–50 kPa.

3. Mathematics of Tilting Pad Bearing Adaptivity

The tilting pad element adaptation and oscillation are ensured by bearing elements of the tilting pads (Figure 2).

The $h_0$ is determined by the following equation:

$$h_0=\sqrt{h_1{h}_2}$$

(1)

where $h_1$— the thickness of the oil film in the inflow zone; $h_2$—the thickness of the oil film in the outflow zone.

The oil film between the rotor and tilting pad bearing is wedge-shaped; its thickness is determined by the following equation:

$$h=\left(r_i+h_1\right)exp\left(-tg{\theta }_n{\phi }_i\right)-r_i$$

(2)

The reliability and stability of such a bearing depend largely on the interaction of the elements in the bearing. The interaction of elements is limited by hydrodynamic, tribological, and thermoelastic processes and relationships. This affects the stiffness of the bearing. The initial stiffness of the system is created by damping the elastic elements between the tilting pads. In this case, the angle of inclination of the tilting pads is determined according to the static balance equation:

$${\theta }_H^{\left(j\right)}={\displaystyle \frac{P^{\left(j\right)}{B}^2\left(i-1\right)L}{2C_{\theta }\left(i+1\right)}}$$

(3)

where$B=l_1+l_2$, $i={\displaystyle \frac{l_1}{l_2}}={\displaystyle \frac{{\phi }_1}{{\phi }_2}},$ L—tilting pad width, j—tilting pad number, and $C_{\theta }$—stiffness of the elastic element.

The stiffness of the elastic elements is determined by the values of the thickness of the hydrodynamic lubricating film at the inflow and outflow points of the oil under the tilting pad. Stiffness is calculated according to the following equation:

$$2C_{\theta }={\displaystyle \frac{P^{\left(j\right)}{B}^2\left(i-1\right)L}{\left[\left(i+1\right)k_{gn}\left(\frac{-1}{{\phi }_c}ln\left|\frac{1+h_2}{1+h_1}\right|\right)\right]}}$$

(4)

where ${\phi }_c={\phi }_1+{\phi }_2$; $k_{gn}={\displaystyle \frac{{\theta }_H}{{\theta }_n}}$.

The selection of stiffness $C_{\theta }$according to the static criterion $\left(k_{gn}=0\right)$ must be conducted carefully because an unreasonable increase in stiffness reduces the adaptivity of the segments belonging with the dynamic mode, and the elastic element is deformed only from the forced moment and temperature change.

The stiffness of the elastic elements is directly proportional to the hydrodynamic pressure and inversely proportional to the angle of rotation of the tilting pad. The angle of inclination of the wedge-shaped oil layer is determined by the following equation:

$$-tg{\theta }_n={\displaystyle \frac{dh}{\left(r_i^2+h_0\right)d{\phi }_i}}$$

(5)

When $\left({\theta }_n=0\right)$the oil film has the same thickness.

4. Research Equipment and Methodology

The research system consists of the rotor system for tilting pad bearings: bearing lubrication and refrigeration system; transducers of measurements; boosters; computer; and program packets.

The principal research system structures are presented in Figure 3.

Principal scheme of experimental stand is presented in Figure 4.

The experimental stand photograph is presented in Figure 5a. The measuring between transducers must be 90-degree angle. To measure the accuracy of the rotor’s rotation, used Hottinger Baldwin Messtechnik (HBM) two non-contact induction displacement transducers model Tr 102 and (HBM) booster model KWS 503D (Hottinger Brüel & Kjaer GmbH, Darmstadt, Germany). A coupling with two half-couplings connected by two fingers was used. Dimensions: diameter D—80 mm; length L—100 mm. An elastic material was placed on the fingers so that the contact between the two halves is elastic. Before the measurements, the coupling was adjusted so that it would not affect the measurement results. The principal measurement scheme is presented in Figure 5b.

Regulation and calibration of the equipment were performed prior to the research. The research was carried out according to the scheme presented in Figure 3.

The research results were analyzed using computer programs (Origin, Master Data, Excel, Excel, Statistics, etc.). The primary measurement results (rotor vibration displacements) were analyzed mathematically (e.g., Fourier function transformation (FFT), etc.). Domain formats obtained after the analysis are needed to evaluate the quality of the rotor system work (spectrogram cascades, orbits, vibration spectrum, etc.).

The primary clearance between the rotor neck and bearing tilting pads is 50 μm. Change in oil temperature during the experiment 20 °C–75 °C. During the experiment, the rotor speed was changed every 500 rpm from 0 to 5000 rpm.

5. Results of Analysis and Discussion

Three data formats were applied in the research: spectrogram cascade, spectral density, and orbit. The spectrogram-cascade graph of the researching rotor system is provided below (Figure 6).

From the spectrogram-cascade graph (Figure 6), it can be seen that the rotor rotates steadily from 0 to 1938 rpm (I zone). When exceeding 1938 rpm, spontaneous vibrations of the rotor appear, and that effect continues until the rotation speed reaches 3923 rpm (II zone). No spontaneous vibrations are observed when the rotor rotation is in the range 3923–5000 rpm (III zone).

From the research results of bearings [29,30,31,49,50], it can be seen that adaptive bearings without tilting pads connecting the elements have two oil whirl zones and a whip zone. The first oil whirl stage starts when the rotor rotates at 2500–3500 rpm, the second oil whirl stage starts from 4000 rpm and continues to 6500 rpm, and, from 6500 rpm, the oil whip starts. After comparing the spectrogram-cascade graphs of tilting pad bearings with journal bearings, the tilting pad bearings were more stable in a wider range of rotation speed, not only because there was only oil whirl but because there was no oil whip. This confirms that the elastic elements connecting the tilting pads are effective and meaningful. The application of adaptive bearings with elastic elements is useful, although the design and adjustment of these bearings are more complicated.

After the primary measurement results, Fourier function transformation (FFT) was conducted, as indicated in the rotor vibration spectrum graph (Figure 7). It can be seen that the critical speed frequency of the researched system is obtained by a rotor rotation speed of 3300 rpm.

The orbits of the rotor rotation axis depending on the rotation of the rotor rotation speed are provided in Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13. Evidently, the information of the orbits is highly correlated with the rotor vibration spectrum and the spectrogram-cascade graph results.

When the rotor rotation speed is 2000 rpm (Figure 8), the orbital form is irregular and chaotic because the range of oil whirl can reach up to 2500 rpm (Figure 9). Although the effect of oil whip is visible, the orbit slightly stabilizes and its form begins to approach a regular circle. When the rotor rotation speed is 3000 rpm (Figure 10), the form of the orbit is unstable and irregular; beyond the resonant frequency, the orbit starts to stabilize again, which can be viewed in the rotor rotation speed orbit at 3500 rpm (Figure 11). At the end of a zone of whirl and with rotor rotation at 4000 rpm (Figure 12), the orbit is further approaching an ideal circle form and the thickness of the outer ring of the orbit decreases.

When there is no oil whirl/whip, the form of the orbit (Figure 13) becomes more regular and elliptical. This means that the rotor rotates more precisely and more evenly. This means that the oil has a minimum of beating, which is confirmed by the graph of the spectrogram cascade (Figure 6). The diameter of the orbit circle is also decreased.

The ideal case would be if the rotor axis would not move as the rotor rotates, but deviation is inevitable. The purpose is that the rotor axis orbit maximally approaches the ideal circle form.

Research shows that such bearings have both advantages and disadvantages.

Advantages: Bearings with tilting pads are adjustable, so, when changing the gap between the rotor and tilting pads, the parameters of the rotor system change: stiffness, resonance frequency, whirl/whip, etc., which means that the application possibilities of the bearings increase.

Disadvantages: Complex installation, tuning, management, etc.

The advantages outweigh the disadvantages, meaning that these bearings are suitable for use in a wide range of industrial applications and require further research and design improvements.

6. Conclusions

It is evident under the spectrogram-cascade graph that the rotor system with a tilting pad bearing rotor rotating speed in the range from 0 to 5000 rpm has three work zones:

-

I zone: 0–1938 rpm—zone of stable work.

-

II zone: 1938–3923 rpm—rotor rotation critical zone because the rotor is exposed to oil whirl.

-

III zone: 3923–5000 rpm—zone of stable work.

The resonant rotor rotation speed is when the rotor rotation speed reaches 3300 rpm. This means that, with such bearings, such a rotor rotation speed must be strictly avoided.

In the researched tilting pad bearing rotor rotation range from 0 to 5000 rpm, there is oil whirl only and there is no oil whip.

Bearings of different designs have different oil whirl/whip ranges depending on the rotor’s rotation speed and other factors.

The research results confirm that adaptive bearings with tilting pads are effective and meaningful. Bearings with tilting pads work stably, but the additional application of elastic elements between the tilting pads increases the stability of the rotor system. The application of adaptive bearings with elastic elements is useful, although the design and adjustment of these bearings are more complicated.

The rotation orbit of the rotor axis is a significantly more informative data format than other data formats. Therefore, it is recommended to apply formats by conducting research.

The presented research methodology can be used to research other bearings of similar designs.

Numerical modeling of these bearings is planned in the future. The comparative analysis data from the numerical simulation and experimental research results will provide more information on the control and management of these bearings. Then, the possible applications of these bearings will become even broader. Also, it is planned to compare tilting pad bearings without connecting and with connecting elastic elements.