Experimental Study on Non-contact Labyrinth Seal under Negative Pressure Intervention

The non-contact labyrinth seal structure of a high-speed gearbox was taken as the research object, a non-contact labyrinth seal structure under negative pressure intervention was designed, and its rationality was verified by simulation analysis. An airfoil-shaped acquisition device for collecting negative pressure was designed, and its rationality was analyzed by simulation. According to the design, a test platform for non-contact labyrinth seal under negative pressure intervention was built to measure the pressure data of each sealing chamber of the non-contact labyrinth seal under different working conditions. The results showed that it was effective to balance the internal and external pressure of the non-contact labyrinth seal by using the negative pressure collected by the airfoil-shaped device in the complex flow field of the high-speed gearbox. It also showed that the non-contact labyrinth seal structure under negative pressure intervention designed in this paper is an effective way to solve the leakage problem of the non-contact labyrinth seal used in high-speed gearbox.


Introduction
With the accelerating pace of industrialization, people have conducted in-depth research on high-speed gear box which is the core component of the transmission system.Due to the high circular speed of the shaft, high-speed gearbox generally adopts the structure of non-contact labyrinth seal, which has the advantages of long life, high reliability, simple manufacturing, low maintenance cost, etc., and is widely used in high-speed and high-pressure rotating machinery [1].The air flow in the gearbox is complex, and the pressure in the seal of the high-speed gearbox is usually unbalanced, which leads to leakage at the seal and seriously affects the safe use of the gearbox [2][3].
In view of the related topics of non-contact labyrinth seal, researchers at home and abroad have been carrying out extensive research unremittingly, and have obtained a lot of results.With the development of computer technology and fluid mechanics, people use theoretical analysis, numerical analysis and experimental research to study the non-contact labyrinth sealing technology.Wang Nengmao et al. [4], predicted the stability of a straight-through labyrinth seals by solving aerodynamic work and damping.The results showed that the change of structural parameters would affect the stability of the labyrinth seal to a certain extent.Włodzimierz Wróblewski et al. [5], studied the labyrinth seal of honeycomb structures.A straight-through labyrinth seal with two fins was optimized by them.Finally, the flow coefficient of the optimized structure was reduced by 18%.E. Saber et al. [6], studied the influence of different labyrinth parameters on leakage rate and obtained the performance of labyrinth seals with different geometric configurations.Qin Haiqi et al. [7], designed and manufactured a new rectangular trapezoidal sealing tooth for non-rotating labyrinth seal of throttle valve, and the experimental and numerical studies on its flow characteristics was conducted.Jia Xinyun et al. [8], proposed a T-shaped labyrinth seal to reduce the excitation force caused by the flow in the sealed area, thus the vibration of the aeroengine rotor was reduced.Phibel [9] compared the effects of the computational fluid dynamics (CFD) program and the three-control model and the two-control model on the numerical results of the aeroelastic stability of the labyrinth seal.Mare [10] used the energy method to calculate the aeroelastic stability of labyrinth seal, and studied the difference of the aeroelastic stability with different number of teeth.The flow field inside the non-contact labyrinth seal was analyzed by using theoretical analysis, simulation analysis and experimental study [11], the characteristics of the non-contact labyrinth seal were discussed, and the various factors affecting the characteristics of the non-contact labyrinth seal were studied.Among them, the most representative content was in-depth research on sealing principle and sealing leakage of non-contact labyrinth from various perspectives, which was of great significance for guiding the design of non-contact labyrinth sealing structure in the future.
In this paper, an idea of balancing internal and external pressure difference is proposed to solve the problem of sealing leakage caused by internal pressure imbalance, and a non-contact labyrinth sealing structure is proposed to solve the problem of sealing leakage caused by pressure imbalance.It is proposed to solve the leakage problem by using the negative pressure which is the pressure below the atmospheric pressure generated by the complex flow field inside the gearbox to balance the internal and external pressure of the sealing structure.

Design and Analysis of Non-contact Labyrinth Seal under Intervention of Negative Pressure
When the gear of high speed gearbox rotates at high speed, the flow field in the gearbox becomes more complicated, the internal pressure of the gearbox is greater than the standard atmospheric pressure, resulting in the leakage of the non-contact labyrinth seal.In order to solve the problem of oil leakage in the gear box, some methods are proposed.
According to the principle of air flow, the method of introducing the source of negative pressure could balance the pressure of non-contact labyrinth seal theoretically.If a certain air hole was set in a sealing chamber of the non-contact labyrinth sealing structure, and the air hole would be connected with a low-pressure source lower than the standard atmospheric pressure, the stable pressure distribution in the sealing chamber would be formed, and the pressure in the outer sealing chamber would be lower than the standard atmospheric pressure outside the gear box, the leakage problem could be completely solved.The pressure below atmospheric pressure is called negative pressure.The schematic diagram is shown in figure 1.In the selection of negative pressure source, this paper has two ideas: the first is to add a pump to the suction hole, so that the sealing chamber of the outermost side can be pumped into negative pressure state.The second is to use the negative pressure area formed inside the high-speed gearbox to pump the non-contact labyrinth seal structure, and forming the inner circulation of the high-speed gearbox itself, without adding other auxiliary equipment.Compared with the first way, the second way is more energy conservation and environmental protection.
According to the basic principles of fluid mechanics, when a fluid flows through a solid surface, it exerts pressure on the surface.According to the relationship between pressure, density and velocity in Formula 1 of Bernoulli equation, it can be seen that the faster the flow rate is, the lower the pressure is, and the slower the flow rate is, the higher the pressure is.At the same time, referring to the design principle of the aircraft wing, the flow velocity on the upper and lower surfaces of the wing is different, so the upper and lower surfaces of the aircraft wing form an upward pressure difference.
In Formula, p and ρ and v are the pressure, density and velocity of the fluid respectively, and h is vertical height, and g is the acceleration of gravity, and c is constant.
Based on the design principle of aircraft wing, a structure of collecting negative pressure in highspeed gearbox was designed.When the high-speed air flow in the gearbox passes over the surface of the airfoil structure for pressure collection, a negative pressure area was formed on the surface of the structure, as shown in figure 2 below.The upper surface of the airfoil was connected with the outermost sealing chamber of the non-contact labyrinth seal through the air pipe.
In order to verify the effectiveness of negative pressure acquisition device, the airfoil structure for acquisition was simulated and analyzed.Figure 3 showed the pressure cloud diagram of the airfoil acquisition structure when the airflow velocity was 70m/s.It could be seen from figure 3 that the pressure on the upper surface of the airfoil acquisition structure was relatively stable with small variation.The area with maximum curvature of the lower surface of the airfoil device formed a negative pressure area.A non-contact labyrinth seal structure with negative pressure intervention is designed in this study.A negative pressure source is introduced into the outermost sealing chamber area of the non-contact labyrinth seal to pump the structure of non-contact labyrinth seal.The geometric structure diagram of the non-contact labyrinth seal under negative pressure intervention is shown in figure 4. Based on the non-contact labyrinth seal, four negative pressure suction holes are set up.The suction holes are designed in the outermost sealing chamber of the non-contact labyrinth seal, and the circumference of the four negative pressure suction holes is distributed outside the sealing chamber.The suction holes and the negative pressure sources are connected by the pipes.Based on the parameters of non-contact labyrinth seal structure of a certain type of high-speed gearbox, a non-contact labyrinth seal structure with intervention of negative pressure is designed.The specific structural parameters are shown in table 1. Simulation software is used to calculate the non-contact labyrinth seal under negative pressure intervention.Compared with the non-contact labyrinth seal under non-negative pressure intervention, the non-contact labyrinth seal with negative pressure intervention has four more suction holes.A threedimensional model was established, and its three-dimensional mesh diagram is shown in figure 5.A "negative pressure" is applied to the four suction holes.The negative pressure is formed on the lower surface of the airfoil acquisition device.A pressure of 111457Pa is applied inside the seal of the non-contact labyrinth seal, and 101325Pa is applied outside the gearbox of the non-contact labyrinth seal.The pressure at the four suction holes is set to 95000Pa, so that the difference of internal and external pressure is 10132Pa.The sealing medium is ideal gas.Ideal gas is completely turbulent in a sealed structure.According to the principles of fluid mechanics, the movement of the sealing medium in the non-contact labyrinth seal under intervention of negative pressure conforms to the three basic laws of fluid mechanics, and the flow of the sealing medium in the sealed chamber is calculated by the standard k -ε turbulence model.The sealing body and sealing teeth of the non-contact labyrinth seal are set as fixed non-sliding wall, the rotor is set as rotating and sliding wall, and the speed is set as 5000r/min.
Figure 6 is the cloud diagram for pressure of non-contact labyrinth seal under intervention of negative pressure.It can be seen from the figure that the pressure in the sealing chamber from the inside of the seal to the suction hole is decreasing step by step, and the pressure in the chamber is also decreasing from the outside of the gearbox to the sealing chamber where the suction hole is.As can be seen from figure 6, the sealing medium will flow from the high-pressure end to the low-pressure position.In the process of flow, the sealing medium flows in the direction of pressure reduction.The effect of pressure's difference makes the sealing medium flow into the sealing structure from the inside of the seal, and from the outside of the seal, and finally flows into the four suction holes.It also shows that this structure can solve the leakage problem of non-contact labyrinth seal caused by the pressure's difference between the inside and outside of labyrinth seal.

Experimental Study on Non-contact Labyrinth Seal under Negative Pressure Intervention
The test platform for non-contact labyrinth seal of high-speed gearbox was built to complete the performance test of non-contact labyrinth seal under intervention of negative pressure.The pressure in each chamber under negative pressure and non-negative pressure with different rotational speeds were analyzed, verifying the effectiveness of the non-contact labyrinth seal under negative pressure.

Setup of Test Rig
The test device is consisted of non-contact labyrinth seal for high-speed gearbox, power drive system, oil station and test system.The parameters of the test high-speed gearbox GS710-500/1.840are seen in table 2. The motor is connected to the test gearbox through the other gearbox, and the oil station supplies oil to the gearbox and provides lubrication.The pressure sensor measures the pressure in each seal chamber by piping to the non-contact labyrinth seal chamber of the test gearbox.When the gearbox works stably at different speeds, the pressure data measured by the sensor is collected by the acquisition card and displayed on the computer.The non-contact labyrinth seal under negative pressure is mounted on gearbox's high speed shaft.The sealing chamber from the inside of the seal to the outside of the gearbox is named as the first chamber, the second chamber, the third chamber and the fourth chamber, as shown in figure 7. The pipe connection of high-speed gearbox for experiment is shown in figure 8.After the alignment of connection and the installation of sensor, the test platform is set up, as shown in figure 9.

Experimental Results and Data Analysis
This test mainly measures the pressure value of each sealing chamber in the non-contact labyrinth seal for high-speed gearbox, and studies the effectiveness and rationality of the non-contact labyrinth seal under negative pressure.The non-contact labyrinth seal of the test object was installed at the end of high-speed shaft in the gearbox.The speed of the high-speed gear was measured in six steps, and the speed of the high-speed gear was 370r/min, 1480r/min, 2590r/min, 3700r/min, 4440r/min and 5180r/min respectively.The corresponding gear linear speed was 10m/s, 40m/s, 70m/s, 100m/s, 120m/s and 140m/s respectively.The pressure data in each sealed chamber at different speeds without intervention of negative pressure were measured through tests, as shown in table 3. The pressure data of each sealing chamber at different speeds under negative pressure were shown in table 4.  The two groups of test data in table 3 and table 4 were compared and analyzed, and the comparison of pressure data curved at different speeds were drawn, as shown in figure 10.It could be seen from figure 10 (a) and (b) that there was little difference in the pressure of each labyrinth seal chamber under negative pressure compared with non-negative pressure, which indicated that when the circular line velocity of the gear was small, the effect of the collection device for negative pressure was not obvious.It could also be seen from figure 10 (c) to (f) that with the increase of gear speed, the circular speed of gear pitch increased, the pressure of each sealing chamber of non-contact labyrinth seal under negative pressure was significantly lower than the data in control group which showed that when the circular speed of gear pitch reached 120m/s and 140m/s, the acquisition device for negative pressure had obvious effect and the effect for pumping was remarkable.The change curves for pressure of each sealing chamber at different speeds under negative pressure were drew according to table 4 and were showed in figure 11.It could be seen from the graph, with the increase of rotational speed, which meant the circle linear velocity of gear pitch in high-speed gearbox increased, the pressure inside the seal would also increase.The reason was due to the changes of rotational speed inside the high-speed gearbox, the complex flow field was cased to form, which led to local high-pressure area inside the sealed, the pressure also increased with the increase of rotational speed.Due to the complex flow field and the existence of local high-pressure area, the difference for pressure between the inside and outside of the non-contact labyrinth seal was formed, which eventually led to the leakage.The pressure of the first sealing chamber increased slightly with the increase of rotational speed, and the pressure of the second sealing chamber and the third sealing chamber decreased slightly with the increase of rotational speed, and the pressure of the fourth sealing chamber decreased significantly.The reason was that with the increase of gear speed and the circular speed of gear section, the high-speed air flow formed a larger negative pressure area on the surface of the airfoil device in the body of gearbox, and the pressure in the fourth sealing chamber connected with it also decreased.It could also be seen from figure 11 that the pressure from the inside of the seal to the fourth sealing chamber gradually decreased at the same speed.At the same time, by comparing the pressure values of the four sealing chambers, the pressure's change rate of the fourth sealing chamber with the increase of speed was the largest, followed by the third sealing chamber, and the second sealing chamber was the smallest.The pressure of the first sealing chamber increased slowly with the increase of rotational speed.This was because the fourth sealing chamber was the outermost sealing chamber and was connected with the suction pipe for negative pressure, so the pressure's change rate was relatively large.Due to the sealing effect of non-contact labyrinth seal, the pressure values of each sealing chamber decreased step by step from the outside to the inside.The first sealing chamber was close to the inside of the seal, so it was greatly affected by the high pressure inside the seal.Under the action of the high pressure inside the seal and the negative pressure of the fourth sealing chamber, the pressure of the first sealing chamber was slightly greater than the standard atmospheric pressure, and the change rate was the smallest.
The measurement data and analysis results of the test were compared with the analysis of simulation.

Figure 1 .
Figure 1.Schematic diagram of solution for negative pressure.

Figure 2 .
Figure 2. Schematic diagram of airfoil structure for pressure acquisition.

Figure 3 .
Figure 3. Pressure cloud diagram of airfoil structure for acquisition.

Figure 4 .
Figure 4. Geometric structure diagram of non-contact labyrinth seal under intervention of negative pressure.

Figure 5 .
Figure 5. Three-dimensional meshing diagram of non-contact labyrinth seal under intervention of negative pressure.

Figure 6 .
Figure 6.Cloud diagram for pressure of noncontact labyrinth seal under intervention of negative pressure.

Figure 10 .
Figure 10.Comparison for pressure of sealing chamber under negative pressure and non-negative pressure at different speeds.

Figure 11 .
Figure 11.Pressure variation diagram of each sealing chamber at different speeds under negative pressure.

Table 1 .
Parameters related to sealing structures.

Table 2 .
Table of related parameters of high speed gear box for test.

Table 3 .
Pressure of different sealing chambers at different speeds without negative pressure.

Table 4 .
Pressure of different sealing chambers at different speeds under negative pressure.