# Numerical and Experimental Investigation of the Sealing Effect of a Specific Labyrinth Seal Structure

Authors: Shiping Yang; Bosi Tan; Xiaofen Deng
Journal: Mathematical Problems in Engineering
 (2019)

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## Abstract

A numerical simulation and experimental study were performed to investigate the sealing effect of the labyrinth seal used in a wheel-side reducer. A three-dimensional computational fluid dynamics model was established based on the labyrinth structure. The effects of the temperature and viscosity of lubricant, rotor speed, pressure ratio, clearance, and cavity size of the sealing structure on the sealing were analyzed, and the leakage amount under the corresponding values of different factors was also analyzed. The results indicated that increase in the lubricating oil temperature, viscosity, pressure ratio, and seal clearance lead to decrease in the sealing effect and increases in the leakage. And the effect of rotational speed on the seal is low. To verify numerical simulation, the results of numerical analysis, a test bench was set up to simulate the work of the reducer, and the sealing effect of the sealing structure was examined. The simulation result was compared with the actual results. Both the numerical simulation and experiment indicate that the labyrinth seal achieves the desired sealing effect.


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## Body

## 1. Introduction

It is difficult to ensure the long-term operation of a contact seal owing to its contact friction and limited service life. However, a labyrinth seal is a type of noncontact seal with clearance or throttle seal. Direct contact between the rotating shaft and sealing tooth is absent, and the gap is small. Thus, there is no contact, wear, and need for lubrication. A gap exists between the rotating shaft and sealing teeth. This permits thermal expansion and the increase of operating speed of the machine. The labyrinth seal is a classical dynamic seal that is used in rail transit gear boxes, industrial gear boxes, and compressors [1, 2]. A labyrinth seal implies that a certain number of throttling gears exist between moving parts and stationary parts leading to the formation of several twists and turns between the tooth and wall of the chamber. Hence, throttling effect and energy effect occur when the mediators go through the seal teeth and the seal chamber, thereby reducing the amount of leakage [3]. It is characterized by a high-pressure ratio, simple structure, and high reliability [4]. Thus, it is crucial to perform an in-depth investigation of the mechanism of labyrinth seal to design a reasonable labyrinth seal structure.Given a host of in-depth studies in the labyrinth seal field, significant experience and improvement were gained globally in recent years. Kervistin [5] designed an apparatus for an engine that adjusts the labyrinth seal clearance and used the principles of thermal expansion and contraction. Yucel et al. [6] combined numerical and experimental investigations to analyze the main factors that affect the performance of the labyrinth seal including temperature and pressure differences, number of cavities, and tooth shape. Willey et al. [7] used the top of a turbine blade to replace the labyrinth seal tooth to seal the rotor, thereby breaking conventional the limitations of the labyrinth seal application and expanding its scope of applications.Nowadays, numerical simulation has been proven as a promising technique since it can provide much information which cannot be measured via experimental tools [8, 9]. In the labyrinth seal research method, computational fluid dynamics (CFD) is increasingly used to analyze the flow inside labyrinth seals [10, 11]. Hodkinson [12] initially adopted a fluid mechanics method as opposed to the thermodynamics method to analyze the direct action of the fluid and used a special treatment of the outlet based on the nozzle model. Subsequently, Kearton and Keh [7] used the nozzle method to simulate the flow at the seal outlet, although they used a reduced nozzle and considered blocking flow. While calculating the discharge coefficient, they also considered the factors corresponding to seal clearance and pressure ratio. Wu Te [13] considered the labyrinth seal at the small-gear motor end of the high-speed EMU drive gearbox as the research object and established a numerical simulation model of the labyrinth seal. He considered the effect of cavity depth on sealing performance, determined optimum cavity depth, and investigated the effect of pressure difference and rotational speed on leakage.The study discusses the labyrinth seal structure that is designed for a wheel reducer. Taking the effect of the sealing structure into account, an analytical and computational model is established, and the flow characteristics of fluid in the labyrinth are analyzed via the CFD analysis method. The effects of temperature, inlet and outlet pressure, liquid viscosity, rotational speed of the rotor, and geometric size of the labyrinth on labyrinth sealing effect are investigated via the variable control method.To verify the actual effect of the sealing structure, the sealing structure entity is manufactured, and a test bench is set up to perform the test. The sealing effect of the labyrinth seal structure is tested at different oil heights, speeds, and clearances.


## 2. Structure of Labyrinth Seal

The labyrinth seal is applied to the wheel-side reducer, as shown in Figure1 which details the position and structure of a labyrinth seal.Figure 1
A labyrinth seal of hub reduction gear.


## 3. Calculation Method of Simulation

### 3.1. Fluid Model Structure

The cross-section size of the flow field is shown in Figure2(a), and the parameters are shown in Table 1. The sealing structure of the wheel-side reducer should conform to the actual situation. Thus, the rotational speed of the rotating part is designated in the range of 29.7–45.9 r/min.Table 1
Parameters of the labyrinth seal structure.
Parameters H 1/mm H 2/mm C/mm B/mm E/mm R/mm Value 13 11 0.3 1.5 8 170Figure 2
Schematic diagram of a labyrinth seal. (a) Two-dimensional section of labyrinth structure. (b) Three-dimensional flow model of labyrinth.
(a) (b)Under actual working conditions, the internal flow field of labyrinth seal comprising radial, axial, and circumferential turbulent flow is extremely complex. The authenticity of the results is affected if two-dimensional flow field analysis is used. Therefore, the 3D CFD method is used to model the labyrinth seal [14], as shown in Figure 2(b). The complete labyrinth model is large and the internal flow is symmetrical. Hence, 1/24 model of the flow field is selected to simulate the model to decrease calculation time and improve calculation efficiency.


### 3.2. Mesh Generation

The computational region needs to be meshed to examine the flow field inside the labyrinth seal. To achieve computational accuracy and decrease computational time, the model is structured in several blocks and meshes are refined in special regions. The results of the meshing are shown in Figure3.Figure 3
Mesh division of labyrinth fluid computation.


### 3.3. Condition Setting and Calculation

The internal flow of the labyrinth is described by the governing equation of energy-conserving fluid. In the study, we reference common boundary condition types that are widely used for seal models [15–17] and adopt the following assumptions to simplify initialization parameters.(1) The working medium in the flow field corresponds to liquid. In addition to analyzing the effect factors of viscosity, all other calculation models use water as the working medium.(2) The boundary condition of the wall is set as the adiabatic boundary.(3) The flow inside the labyrinth corresponds to turbulent flow.(4) The radial and axial displacements of the rotor are ignored in the numerical simulation because of the high symmetry of the structure.The outlet pressure corresponds to 1 atm. Inlet pressure is 1.4 times the outlet pressure and is equal to 141855 Pa. Adiabatic wall and the fluid medium correspond to water, we use k-ε two-equation turbulence model, and the continuity equation is discretized by a second-order upwind scheme and solved via a coupled implicit solver.The residual values of continuity equation, directional velocity, turbulent kinetic energyk, and dissipation rate are less than 10−3, and the difference between inlet and outlet flow rate is less than 0.1%. In the calculation process, the residual error in every direction infinitely approaches the convergence standard as shown in Figure 4.Figure 4
Residual curve.We set the inlet pressureP0 as 141855 Pa, outlet pressure Pn as 101325 Pa, and inlet temperature as 313 K with an adiabatic wall and liquid medium as Lubricating oil. The calculation obtains the pressure field of the labyrinth, as shown in Figure 5.Figure 5
Pressure field cloud map of the three-dimensional flow field in the labyrinth.The rationality of the calculation results and the principle of the labyrinth seal are verified by the velocity cloud chart and velocity vector diagram of the labyrinth flow field. The results are shown in Figures6 and 7.Figure 6
Velocity cloud map of the labyrinth flow field.Figure 7
Velocity vector diagram of the labyrinth flow field.


## 3.1. Fluid Model Structure

The cross-section size of the flow field is shown in Figure2(a), and the parameters are shown in Table 1. The sealing structure of the wheel-side reducer should conform to the actual situation. Thus, the rotational speed of the rotating part is designated in the range of 29.7–45.9 r/min.Table 1
Parameters of the labyrinth seal structure.
Parameters H 1/mm H 2/mm C/mm B/mm E/mm R/mm Value 13 11 0.3 1.5 8 170Figure 2
Schematic diagram of a labyrinth seal. (a) Two-dimensional section of labyrinth structure. (b) Three-dimensional flow model of labyrinth.
(a) (b)Under actual working conditions, the internal flow field of labyrinth seal comprising radial, axial, and circumferential turbulent flow is extremely complex. The authenticity of the results is affected if two-dimensional flow field analysis is used. Therefore, the 3D CFD method is used to model the labyrinth seal [14], as shown in Figure 2(b). The complete labyrinth model is large and the internal flow is symmetrical. Hence, 1/24 model of the flow field is selected to simulate the model to decrease calculation time and improve calculation efficiency.


## 3.2. Mesh Generation

The computational region needs to be meshed to examine the flow field inside the labyrinth seal. To achieve computational accuracy and decrease computational time, the model is structured in several blocks and meshes are refined in special regions. The results of the meshing are shown in Figure3.Figure 3
Mesh division of labyrinth fluid computation.


## 3.3. Condition Setting and Calculation

The internal flow of the labyrinth is described by the governing equation of energy-conserving fluid. In the study, we reference common boundary condition types that are widely used for seal models [15–17] and adopt the following assumptions to simplify initialization parameters.(1) The working medium in the flow field corresponds to liquid. In addition to analyzing the effect factors of viscosity, all other calculation models use water as the working medium.(2) The boundary condition of the wall is set as the adiabatic boundary.(3) The flow inside the labyrinth corresponds to turbulent flow.(4) The radial and axial displacements of the rotor are ignored in the numerical simulation because of the high symmetry of the structure.The outlet pressure corresponds to 1 atm. Inlet pressure is 1.4 times the outlet pressure and is equal to 141855 Pa. Adiabatic wall and the fluid medium correspond to water, we use k-ε two-equation turbulence model, and the continuity equation is discretized by a second-order upwind scheme and solved via a coupled implicit solver.The residual values of continuity equation, directional velocity, turbulent kinetic energyk, and dissipation rate are less than 10−3, and the difference between inlet and outlet flow rate is less than 0.1%. In the calculation process, the residual error in every direction infinitely approaches the convergence standard as shown in Figure 4.Figure 4
Residual curve.We set the inlet pressureP0 as 141855 Pa, outlet pressure Pn as 101325 Pa, and inlet temperature as 313 K with an adiabatic wall and liquid medium as Lubricating oil. The calculation obtains the pressure field of the labyrinth, as shown in Figure 5.Figure 5
Pressure field cloud map of the three-dimensional flow field in the labyrinth.The rationality of the calculation results and the principle of the labyrinth seal are verified by the velocity cloud chart and velocity vector diagram of the labyrinth flow field. The results are shown in Figures6 and 7.Figure 6
Velocity cloud map of the labyrinth flow field.Figure 7
Velocity vector diagram of the labyrinth flow field.


## 4. Simulation Results and Analysis

The study mainly explores the optimal size of the labyrinth seal with decrease in the leakage and also analyzes the effects of viscosity and temperature, pressure ratio, and rotational speed on the leakage.


### 4.1. Effects of Viscosity and Temperature on Leakage Rate

The calculation model is the same as that in a labyrinth seal of hub reduction gear. The fluid medium is varied. Five brands of lubricating oil are used for the analysis. The temperature range is set as 10–60°C. The used parameters are shown in Table2.Table 2
Leakage values (kg/s) of different lubricant brands with varying viscosity and temperature.
Lubricating oil brands Temperature (°C) 10 20 30 40 50 60 VG22 0.00404 0.00728 0.01250 0.01825 0.02435 0.03036 VG32 0.00227 0.00363 0.00681 0.01259 0.01847 0.02587 VG46 0.00193 0.00297 0.00466 0.00978 0.01308 0.01861 VG68 0.00150 0.00208 0.00340 0.00525 0.00966 0.01344 VG100 0.00128 0.00176 0.00240 0.00371 0.00587 0.00945In the analysis, the variation curves of viscosity and temperature on leakage rate are obtained, as shown in Figure8.Figure 8
Variation in the leakage rate relates to the temperature for different viscosity values.As shown in Figure8, the viscosity of lubricating oil decreases with increases in the working temperature (from 10°C to 60°C ) decreases in the lubricating oil grade (from VG100 to VG22) leakage increases. Therefore, the operation of the transmission device should select grease with higher viscosity and avoid higher working temperature.


### 4.2. Effects of Pressure Ratio and Speed on Leakage Rate

The calculation model is the same as that in a labyrinth seal of hub reduction gear. The pressure ratio and speed vary. The outlet pressure is 101325 Pa, the pressure ratio ranges from 1.2 to 2.0, and the rotational speeds correspond to 200 r/min, 300 r/min, 400 r/min, and 500 r/min. The data are shown in Table3.Table 3
Leakage value (kg/s) under different speeds and pressure ratios.
Working conditions Speed (r/min) 200 300 400 500 Pressure ratio (P0/Pn) 1.2 0.004226 0.004256 0.004241 0.004227 1.3 0.004596 0.004560 0.004566 0.004515 1.4 0.004889 0.004863 0.004862 0.004787 1.5 0.005204 0.005166 0.005162 0.005109 1.6 0.005465 0.005464 0.005453 0.005424 1.7 0.005739 0.005740 0.005748 0.005634 1.8 0.005958 0.005964 0.005958 0.005939 1.9 0.006194 0.006188 0.006245 0.006183 2.0 0.006417 0.006463 0.006461 0.006462The values of leakage under different speeds and pressure ratios are obtained via numerical analysis, as shown in Figure9.Figure 9
Variation in the leakage rate relative to the pressure ratio for different speeds.Pressure ratio and rotational speed are two important factors that affect leakage. The results indicate that increases in the pressure ratio at both ends of straight-through labyrinth seal lead to increases in the leakage [18, 19]. When the rotational speed is lower than a certain value in a low speed range, it is generally believed that the effect of rotational speed on the leakage of labyrinth seal is extremely low. When the rotational speed exceeds the value, increases in the rotational speed will decrease the leakage of the labyrinth seal to a certain extent, although the effect is extremely low and does not exceed 4% of the overall sealing, as verified by the numerical simulation.


### 4.3. Effect of Labyrinth Clearance Magnitude to the Leakage Rate

The calculation model is the same as that in a labyrinth seal of hub reduction gear, except for the fact that the axial clearanceC ranges from 0.15 mm to 0.95 mm. The leakage rate under different pressure ratios is calculated, and the change in leakage rate with the sealing gap is observed. As shown in Figure 10, the leakage increases with increasing the advance of clearance when the pressure ratio is fixed. This is because increases in the clearance decrease the throttling effect when fluid passes the clearance, vortex weakens after fluid enters the cavity, and energy dissipation decreases. Additionally, the leakage exhibits the same trend under different pressure ratios and the slope of the curve increases with increases in the pressure ratio. The reason for the phenomenon is that the fluid velocity flowing into the cavity increases and the vortex expands. Hence, the leakage value increases with the advance of the pressure ratio. This shows that labyrinth clearance magnitude significantly affects leakage. A lower clearance should be selected if permitted by processing costs and easy installation conditions [12].Figure 10
Change of leakage with clearance under different pressure ratios.


### 4.4. Effect of Cavity Depth to the Leakage Rate

Except for the fact that the cavity depthH1 ranges from 4.3 mm to 19.3 mm andH2 ranges from 4.3 mm to 16.8 mm, the calculation model is the same as that in a labyrinth seal of hub reduction gear. Figure 11 shows the four types of pressure distribution at different cavity depths. Evidently, the pressure changes with increases in the cavity depth. The vortex is not evident in Figure 11(a), and it is evident in Figures 11(b) and 11(c). However, in Figure 11(d), the vortex only happens in a small part. This reveals that cavity depth promotes the formation of vortices within a certain range, and the cavity fluid vortex weakens when cavity depth increases constantly and results in decreases in energy dissipation.Figure 11
Pressure cloud chart with different cavity depth values.
(a)
H 1 = 4.3 mm, H2 = 4.3 mm (b)
H 1 = 10.3 mm, H2 = 9.8 mm (c)
H 1 = 16.3 mm, H2 = 13.8 mm (d)
H 1 = 19.3 mm, H2 = 16.8 mmFigure12 shows the leakage curve with different cavity depths. It reveals that leakage decreases rapidly when the cavity depth increases from 4.3 mm to 6.0 mm, and the leakage decreases slowly when the depth continues to increase. Specifically, the H1 value increases from 10 mm to 14 mm, the H2 value increases from 8 mm to 12 mm, and the leakage stabilized at approximately 0.068kg/s, while the leakage increases as the cavity depth continues to increase. It is concluded that increases in the cavity depth effectively decrease the leakage within a certain range. In the actual working conditions, there is an optimum size range of cavity depth that effectively decreases leakage to satisfy sealing requirements and the production process requirement.Figure 12
Plot of leakage with different cavity depths.


### 4.5. Effects of Cavity Width on the Leakage Rate

The calculation model is the same as Figure2, and only the cavity widthE ranges from 2 mm to 18 mm. Figure 13 shows the velocity contour and velocity vector under different cavity widths. As shown in Figure 13(a), the cavity width is extremely narrow, there are four effective vortexes that drive fluid flowing in the cavity, and kinetic energy is converted to thermal energy. As shown in Figure 13(b), there are two vortexes in cavity that form the contraction in the cavity outlet, and the fluid generates intense friction in the cavity during the process. There is no evident vortex in the cavity in Figure 13(c), and the sealing effect weakens.Figure 13
Velocity contour and velocity vector under different cavity widths.
(a)
E= 2 mm (b)
E= 10 mm (c)
E= 18 mmFigure14 shows the curve of leakage with different cavity widths. It reveals that leakage increases slowly when the cavity width increases from 2 mm to 10 mm. The slope of the curve increases rapidly when the cavity width continues increasing. The increase in cavity width almost does not affect the leakage within a certain range. However, leakage increases when the cavity width continues expanding to a certain value.Figure 14
Graph of leakage with respect to the cavity width.There is a certain width value below which the decrease in the width weakens the leakage. However, the smaller size makes the process and installation more difficult. Therefore, rational design of the cavity width dimension should be based on the effect of cavity width on leakage in actual working conditions such that it satisfies sealing requirements and the production process requirements.


### 4.6. Effects of the Ratio of Depth to Width on the Leakage Rate

This section numerically analyzes the effect of the ratio of depth to width on the leakage rate, as shown in Figure15. The leakage exhibits the same changing trend and increases in the ratio effectively induce the decrease of leakage within a certain range. Leakage increases if the ratio exceeds a certain value and continues expanding, as shown in Figures 15(a), 15(b), and 15(c). The ratio of depth to width exhibits different effects on leakage under different cavity widths. A lower leakage is observed in the range of 1.1 to 3.0 when the width corresponds to 4 mm, and the range of optimum ratio decreases with increases in the width. There is an optimum ratio of depth to width of about 1.1 in actual working conditions. The effect of the ratio on leakage increases with the advance of width.Figure 15
Plot of leakage with respect to the ratio of depth to width.
(a)
E = 4 (b)
E= 8 (c)
E= 12


## 4.1. Effects of Viscosity and Temperature on Leakage Rate

The calculation model is the same as that in a labyrinth seal of hub reduction gear. The fluid medium is varied. Five brands of lubricating oil are used for the analysis. The temperature range is set as 10–60°C. The used parameters are shown in Table2.Table 2
Leakage values (kg/s) of different lubricant brands with varying viscosity and temperature.
Lubricating oil brands Temperature (°C) 10 20 30 40 50 60 VG22 0.00404 0.00728 0.01250 0.01825 0.02435 0.03036 VG32 0.00227 0.00363 0.00681 0.01259 0.01847 0.02587 VG46 0.00193 0.00297 0.00466 0.00978 0.01308 0.01861 VG68 0.00150 0.00208 0.00340 0.00525 0.00966 0.01344 VG100 0.00128 0.00176 0.00240 0.00371 0.00587 0.00945In the analysis, the variation curves of viscosity and temperature on leakage rate are obtained, as shown in Figure8.Figure 8
Variation in the leakage rate relates to the temperature for different viscosity values.As shown in Figure8, the viscosity of lubricating oil decreases with increases in the working temperature (from 10°C to 60°C ) decreases in the lubricating oil grade (from VG100 to VG22) leakage increases. Therefore, the operation of the transmission device should select grease with higher viscosity and avoid higher working temperature.


## 4.2. Effects of Pressure Ratio and Speed on Leakage Rate

The calculation model is the same as that in a labyrinth seal of hub reduction gear. The pressure ratio and speed vary. The outlet pressure is 101325 Pa, the pressure ratio ranges from 1.2 to 2.0, and the rotational speeds correspond to 200 r/min, 300 r/min, 400 r/min, and 500 r/min. The data are shown in Table3.Table 3
Leakage value (kg/s) under different speeds and pressure ratios.
Working conditions Speed (r/min) 200 300 400 500 Pressure ratio (P0/Pn) 1.2 0.004226 0.004256 0.004241 0.004227 1.3 0.004596 0.004560 0.004566 0.004515 1.4 0.004889 0.004863 0.004862 0.004787 1.5 0.005204 0.005166 0.005162 0.005109 1.6 0.005465 0.005464 0.005453 0.005424 1.7 0.005739 0.005740 0.005748 0.005634 1.8 0.005958 0.005964 0.005958 0.005939 1.9 0.006194 0.006188 0.006245 0.006183 2.0 0.006417 0.006463 0.006461 0.006462The values of leakage under different speeds and pressure ratios are obtained via numerical analysis, as shown in Figure9.Figure 9
Variation in the leakage rate relative to the pressure ratio for different speeds.Pressure ratio and rotational speed are two important factors that affect leakage. The results indicate that increases in the pressure ratio at both ends of straight-through labyrinth seal lead to increases in the leakage [18, 19]. When the rotational speed is lower than a certain value in a low speed range, it is generally believed that the effect of rotational speed on the leakage of labyrinth seal is extremely low. When the rotational speed exceeds the value, increases in the rotational speed will decrease the leakage of the labyrinth seal to a certain extent, although the effect is extremely low and does not exceed 4% of the overall sealing, as verified by the numerical simulation.


## 4.3. Effect of Labyrinth Clearance Magnitude to the Leakage Rate

The calculation model is the same as that in a labyrinth seal of hub reduction gear, except for the fact that the axial clearanceC ranges from 0.15 mm to 0.95 mm. The leakage rate under different pressure ratios is calculated, and the change in leakage rate with the sealing gap is observed. As shown in Figure 10, the leakage increases with increasing the advance of clearance when the pressure ratio is fixed. This is because increases in the clearance decrease the throttling effect when fluid passes the clearance, vortex weakens after fluid enters the cavity, and energy dissipation decreases. Additionally, the leakage exhibits the same trend under different pressure ratios and the slope of the curve increases with increases in the pressure ratio. The reason for the phenomenon is that the fluid velocity flowing into the cavity increases and the vortex expands. Hence, the leakage value increases with the advance of the pressure ratio. This shows that labyrinth clearance magnitude significantly affects leakage. A lower clearance should be selected if permitted by processing costs and easy installation conditions [12].Figure 10
Change of leakage with clearance under different pressure ratios.


## 4.4. Effect of Cavity Depth to the Leakage Rate

Except for the fact that the cavity depthH1 ranges from 4.3 mm to 19.3 mm andH2 ranges from 4.3 mm to 16.8 mm, the calculation model is the same as that in a labyrinth seal of hub reduction gear. Figure 11 shows the four types of pressure distribution at different cavity depths. Evidently, the pressure changes with increases in the cavity depth. The vortex is not evident in Figure 11(a), and it is evident in Figures 11(b) and 11(c). However, in Figure 11(d), the vortex only happens in a small part. This reveals that cavity depth promotes the formation of vortices within a certain range, and the cavity fluid vortex weakens when cavity depth increases constantly and results in decreases in energy dissipation.Figure 11
Pressure cloud chart with different cavity depth values.
(a)
H 1 = 4.3 mm, H2 = 4.3 mm (b)
H 1 = 10.3 mm, H2 = 9.8 mm (c)
H 1 = 16.3 mm, H2 = 13.8 mm (d)
H 1 = 19.3 mm, H2 = 16.8 mmFigure12 shows the leakage curve with different cavity depths. It reveals that leakage decreases rapidly when the cavity depth increases from 4.3 mm to 6.0 mm, and the leakage decreases slowly when the depth continues to increase. Specifically, the H1 value increases from 10 mm to 14 mm, the H2 value increases from 8 mm to 12 mm, and the leakage stabilized at approximately 0.068kg/s, while the leakage increases as the cavity depth continues to increase. It is concluded that increases in the cavity depth effectively decrease the leakage within a certain range. In the actual working conditions, there is an optimum size range of cavity depth that effectively decreases leakage to satisfy sealing requirements and the production process requirement.Figure 12
Plot of leakage with different cavity depths.


## 4.5. Effects of Cavity Width on the Leakage Rate

The calculation model is the same as Figure2, and only the cavity widthE ranges from 2 mm to 18 mm. Figure 13 shows the velocity contour and velocity vector under different cavity widths. As shown in Figure 13(a), the cavity width is extremely narrow, there are four effective vortexes that drive fluid flowing in the cavity, and kinetic energy is converted to thermal energy. As shown in Figure 13(b), there are two vortexes in cavity that form the contraction in the cavity outlet, and the fluid generates intense friction in the cavity during the process. There is no evident vortex in the cavity in Figure 13(c), and the sealing effect weakens.Figure 13
Velocity contour and velocity vector under different cavity widths.
(a)
E= 2 mm (b)
E= 10 mm (c)
E= 18 mmFigure14 shows the curve of leakage with different cavity widths. It reveals that leakage increases slowly when the cavity width increases from 2 mm to 10 mm. The slope of the curve increases rapidly when the cavity width continues increasing. The increase in cavity width almost does not affect the leakage within a certain range. However, leakage increases when the cavity width continues expanding to a certain value.Figure 14
Graph of leakage with respect to the cavity width.There is a certain width value below which the decrease in the width weakens the leakage. However, the smaller size makes the process and installation more difficult. Therefore, rational design of the cavity width dimension should be based on the effect of cavity width on leakage in actual working conditions such that it satisfies sealing requirements and the production process requirements.


## 4.6. Effects of the Ratio of Depth to Width on the Leakage Rate

This section numerically analyzes the effect of the ratio of depth to width on the leakage rate, as shown in Figure15. The leakage exhibits the same changing trend and increases in the ratio effectively induce the decrease of leakage within a certain range. Leakage increases if the ratio exceeds a certain value and continues expanding, as shown in Figures 15(a), 15(b), and 15(c). The ratio of depth to width exhibits different effects on leakage under different cavity widths. A lower leakage is observed in the range of 1.1 to 3.0 when the width corresponds to 4 mm, and the range of optimum ratio decreases with increases in the width. There is an optimum ratio of depth to width of about 1.1 in actual working conditions. The effect of the ratio on leakage increases with the advance of width.Figure 15
Plot of leakage with respect to the ratio of depth to width.
(a)
E = 4 (b)
E= 8 (c)
E= 12


## 5. Experimental Verification

The above sections analyzed the theoretical calculation method of leakage of the labyrinth seal and used a numerical simulation analysis method to examine the mechanism of the labyrinth seal and provide an important basis for designing the labyrinth seal of the gearbox. The internal flow field is extremely complex with the exception of the simulation, and thus experimental verification is required.


### 5.1. Structure Design of the Labyrinth Seal

The experiment is based on factors of leakage that are designed based on the numerical calculation. The numerical results indicate that decreases in the clearance lead to improvement in the sealing performance. However, an excessively low clearance leads to collision, structural abrasion, and even sealing failure if the machining accuracy is not extremely high. Thus, we attempt to select a smaller clearance under the condition of meeting processing costs and installation requirements. This is based on the following empirical expression:(1)C=0.2+0.3~0.6d1000Rotor diameterd corresponds to 340 mm, and calculated clearanceC corresponds to 0.3 mm. Based on the numerical calculation results, cavity depth H1 value corresponds to 13 mm, H2 value corresponds to 11 mm, and cavity widthE value corresponds to 10 mm.


### 5.2. Test Device

Based on the design shape of labyrinth seal, a few parts in Figure13 are processed, and the test rig is assembled. Figure 16 shows the structure diagram of the test-bed.Figure 16
Structure diagram of labyrinth seal test-bed. 1: lip-type packing; 2: bolt; 3: screw-a; 4: input shaft end cover; 5: screw-b; 6: O-type ring-a; 7: shell; 8: screw-c; 9: sealing element-a; 10: oil plug; 11: bond; 12: screw-d; 13: shaft; 14: circlips for shaft; 15: thrower; 16: taper roller bearing; 17: O-type ring-b; 18: sealing element-b.The physical structure of the test-bed is shown in Figure17. A layer of white paint is coated on the surface of the seal prior to the test to clearly observe the leakage. This can be observed in the test pictures shown in Figure 18.Figure 17
Sealing test bench.Figure 18
Spray developer.


### 5.3. Effects of Lubrication Oil Levels on Leakage Rate

The volume of lubricant required for different liquid level fillings is calculated; the relevant volume of lubricant is then injected, and liquid height is selected as shown in Figure19. We control the rotation speed increasing from 0 to 300 rpm. The test is completed, and the data is recorded, as shown in Figure 20 and Table 4.Table 4
Test record with different liquid levels.
Liquid level/mm Leakage Liquid level/mm Leakage 5 No oil leaking 40 No oil leaking 10 No oil leaking 45 Leaking in stationary state No leaking in running state 15 No oil leaking 50 Leaking in stationary state No leaking in running state 20 No oil leaking 55 Leaking in stationary state No leaking in running state 25 No oil leaking 60 Leaking in stationary state No leaking in running state 30 No oil leaking 65 Leaking in stationary state No leaking in running state 35 No oil leakingFigure 19
Schematic diagram of the liquid level.Figure 20
Condition of the seal with different liquid levels.
(a)
Liquid level is 30 mm (b)
Liquid level is 60 mmThe results indicate that when the liquid level reaches 45 mm, the sealing surface begins to leak while the labyrinth seal is in the stationary state. The leakage increases when the liquid level continues increasing. Additionally, oil leakage is absent in the running state. This is because in the stationary state, increases in the liquid level increase cavity pressure. Furthermore, increases in the pressure increase the leakage. In the running state, a throttling effect is observed on the seal tooth interstice, and the pressure decreases when the fluid passes through the labyrinth seal, and thus the leakage decreases.


### 5.4. Effects of Rotation Speed on Leakage Rate

In order to investigate the effect of rotation speed on leakage rate, the experiment was done with the motor speed increasing from 30 rpm to 300 rpm. The liquid level is 35 mm and the other conditions are constant. Data are observed and recorded every thirty minutes. The results are shown in Table5. No leak was found. The seal does not change with increases in the motor speed. The consistence of experiment and numerical simulation conclusions verified the accuracy of the numerical simulation method.Table 5
Test record with different motor speeds.
Time(min) Speed(r/min) Leakage 30 40 No oil leaking 60 80 No oil leaking 90 120 No oil leaking 120 160 No oil leaking 150 200 No oil leaking 180 240 No oil leaking 210 280 No oil leaking 240 300 No oil leaking


### 5.5. Effects of Labyrinth Clearance

In order to examine the influence of clearance on leakage, the motor speed is maintained at 40 rpm and the clearance is adjusted from 0 mm to 0.8 mm by the spacer in the connection of the sealing element-a with the shaft. The result is shown in Figure21 and Table 6. It reveals that the leakage rate increases with increases in the clearance. The experiment results are consistent with the numerical simulation. This proves that the structure is reasonable and the numerical simulation is accurate.Table 6
Test record with different clearance values.
Clearance/mm 0.3 0.4 0.5 0.6 0.7 0.8 Leakage No oil leaking No oil leaking A little oil marks A little oil marks Obvious oil marks Oil dropFigure 21
Effects of sealing with different clearance values.
(a)
0.3 mm (b)
0.5 mm (c)
0.8 mm


## 5.1. Structure Design of the Labyrinth Seal

The experiment is based on factors of leakage that are designed based on the numerical calculation. The numerical results indicate that decreases in the clearance lead to improvement in the sealing performance. However, an excessively low clearance leads to collision, structural abrasion, and even sealing failure if the machining accuracy is not extremely high. Thus, we attempt to select a smaller clearance under the condition of meeting processing costs and installation requirements. This is based on the following empirical expression:(1)C=0.2+0.3~0.6d1000Rotor diameterd corresponds to 340 mm, and calculated clearanceC corresponds to 0.3 mm. Based on the numerical calculation results, cavity depth H1 value corresponds to 13 mm, H2 value corresponds to 11 mm, and cavity widthE value corresponds to 10 mm.


## 5.2. Test Device

Based on the design shape of labyrinth seal, a few parts in Figure13 are processed, and the test rig is assembled. Figure 16 shows the structure diagram of the test-bed.Figure 16
Structure diagram of labyrinth seal test-bed. 1: lip-type packing; 2: bolt; 3: screw-a; 4: input shaft end cover; 5: screw-b; 6: O-type ring-a; 7: shell; 8: screw-c; 9: sealing element-a; 10: oil plug; 11: bond; 12: screw-d; 13: shaft; 14: circlips for shaft; 15: thrower; 16: taper roller bearing; 17: O-type ring-b; 18: sealing element-b.The physical structure of the test-bed is shown in Figure17. A layer of white paint is coated on the surface of the seal prior to the test to clearly observe the leakage. This can be observed in the test pictures shown in Figure 18.Figure 17
Sealing test bench.Figure 18
Spray developer.


## 5.3. Effects of Lubrication Oil Levels on Leakage Rate

The volume of lubricant required for different liquid level fillings is calculated; the relevant volume of lubricant is then injected, and liquid height is selected as shown in Figure19. We control the rotation speed increasing from 0 to 300 rpm. The test is completed, and the data is recorded, as shown in Figure 20 and Table 4.Table 4
Test record with different liquid levels.
Liquid level/mm Leakage Liquid level/mm Leakage 5 No oil leaking 40 No oil leaking 10 No oil leaking 45 Leaking in stationary state No leaking in running state 15 No oil leaking 50 Leaking in stationary state No leaking in running state 20 No oil leaking 55 Leaking in stationary state No leaking in running state 25 No oil leaking 60 Leaking in stationary state No leaking in running state 30 No oil leaking 65 Leaking in stationary state No leaking in running state 35 No oil leakingFigure 19
Schematic diagram of the liquid level.Figure 20
Condition of the seal with different liquid levels.
(a)
Liquid level is 30 mm (b)
Liquid level is 60 mmThe results indicate that when the liquid level reaches 45 mm, the sealing surface begins to leak while the labyrinth seal is in the stationary state. The leakage increases when the liquid level continues increasing. Additionally, oil leakage is absent in the running state. This is because in the stationary state, increases in the liquid level increase cavity pressure. Furthermore, increases in the pressure increase the leakage. In the running state, a throttling effect is observed on the seal tooth interstice, and the pressure decreases when the fluid passes through the labyrinth seal, and thus the leakage decreases.


## 5.4. Effects of Rotation Speed on Leakage Rate

In order to investigate the effect of rotation speed on leakage rate, the experiment was done with the motor speed increasing from 30 rpm to 300 rpm. The liquid level is 35 mm and the other conditions are constant. Data are observed and recorded every thirty minutes. The results are shown in Table5. No leak was found. The seal does not change with increases in the motor speed. The consistence of experiment and numerical simulation conclusions verified the accuracy of the numerical simulation method.Table 5
Test record with different motor speeds.
Time(min) Speed(r/min) Leakage 30 40 No oil leaking 60 80 No oil leaking 90 120 No oil leaking 120 160 No oil leaking 150 200 No oil leaking 180 240 No oil leaking 210 280 No oil leaking 240 300 No oil leaking


## 5.5. Effects of Labyrinth Clearance

In order to examine the influence of clearance on leakage, the motor speed is maintained at 40 rpm and the clearance is adjusted from 0 mm to 0.8 mm by the spacer in the connection of the sealing element-a with the shaft. The result is shown in Figure21 and Table 6. It reveals that the leakage rate increases with increases in the clearance. The experiment results are consistent with the numerical simulation. This proves that the structure is reasonable and the numerical simulation is accurate.Table 6
Test record with different clearance values.
Clearance/mm 0.3 0.4 0.5 0.6 0.7 0.8 Leakage No oil leaking No oil leaking A little oil marks A little oil marks Obvious oil marks Oil dropFigure 21
Effects of sealing with different clearance values.
(a)
0.3 mm (b)
0.5 mm (c)
0.8 mm


## 6. Conclusions

The following conclusions are obtained:(1) The simulation results confirmed that the reduction in the viscosity of the lubricant oil (such as elevating temperature and reducing lubricant oil grade) led to the increase in leakage, the pressure ratio significantly affected leakage, and they were positively related. When the speed was lower than a certain value in a low speed range, the effect of rotation speed was extremely weak.(2) Cavity depth can effectively decrease the leakage rate in certain range, width effect is not obvious. The numerical simulation showed that there was an optimum ratio of depth to width of about 1.1.(3) The experiment results indicated that in a stationary state, the leakage exacerbated when the liquid level continued increasing after it reached a certain value and, under that value, there is no leakage. In the running state, there was no leakage when the liquid level or motor speed increased.



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*Source: 9851314-2019-06-24.xml*