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Abstract

A radial thrust hydrodynamic sliding bearing (RTHSB) with special shaped cavity had been designed. Taking the instantaneous temperature rise characteristics of RTHSB as an analysis object, considering the influence of inlet lubricating oil velocity and transmission shaft speed, a dynamic simulation method of variable viscosity temperature field is proposed, and the mathematical model of instantaneous temperature rise of time-varying oil film is constructed. The correlation equation between instantaneous temperature rise and oil film variable viscosity is analyzed, the lubricating performance of a special-shaped cavity with variable thickness of the oil film considering real-time full operating conditions is revealed, and the alternating transient laws of oil film thickness with variable viscosity and its instantaneous temperature rise for no-load, heavy-load, and different rotating speeds are studied. It is obtained that the higher temperature area of profiled shaped cavity on reverse flow side extends to oil seal side with increase of rotating speed. The dynamic simulation of variable viscosity of RTHSB with different film thickness is simulated by using FLUENT software and the trend of transient film temperature field distribution of in special-shaped cavity is evaluated. The rationality of the mechanism analysis and numerical simulation results in this paper has been verified.

Keywords

Radial thrust hydrodynamic sliding bearing special-shaped cavity time-varying oil film instantaneous temperature rise characteristics variable viscosity temperature field dynamic simulation

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Highlights (for review)

A radial thrust hydrodynamic sliding bearing (RTHSB) with special shaped cavity was designed.

A dynamic simulation method of variable viscosity temperature field was proposed.

Mathematical model of instantaneous temperature rise of time-varying oil film was constructed.

Correlation equation between instantaneous temperature rise and variable viscosity of oil film was analyzed.

Lubrication performance of special-shaped cavity with variable oil film thickness under full working conditions was studied.

Novelty Statement

The novelty and significance of this manuscript are:

The work was studied mainly a radial thrust hydrodynamic sliding bearing (RTHSB) with special shaped cavity had been designed. A dynamic simulation method of variable viscosity temperature field had been proposed. The alternating law of variable viscosity oil film thickness and instantaneous temperature rise under empty load, heavy load, and different rotating speed are revealed. It is obtained that the high temperature region of the profiled cavity on the counter current side extends to the oil seal side with the increase of rotating speed, and the oil seal edge temperature increases with the increase of inlet velocity (the thickness of oil film is 0.05∼0.08 mm). The dynamic simulation of variable viscosity of RTHSB with different oil film thickness is simulated by using FLUENT software and the trend of transient temperature field distribution of oil film in special-shaped cavity is evaluated. The correctness of theoretical analysis and simulation results is verified by experiments.

Introduction

Optimal lubrication performance of a radial thrust hydrodynamic sliding bearing (RTHSB) is the core content of improving the high-precision manufacturing accuracy and process efficiency of modern machinery’s large load and high-precision manufacturing. The fluid instantaneous velocity in special shaped cavity changes in real time and the contact surface friction makes the oil film thick-ness or thin or thick dynamic time-varying, which affects the machining accuracy of the RTHSB and the steady viscosity and temperature characteristics for lubricating oil. The analysis of RTHSB focuses on steady state, and there is little research on time-varying transient oil film with variable viscosity. In the design of structural parameters of hydrodynamic sliding bearing, research on lubrication state, and structural parameter design of RTHSB, a simple analytical method considering effects of loaded oil pressure, oil film gap, viscosity, and input shaft speed on its displacement, was presented by Almqvist et al.¹ The hypothetical analysis model considers that the lubricating fluid in entire oil film interface area is incompressible. Based on this, the structural optimization design and performance improvement of reciprocating air compressor depends in each part on comprehensive lubrication features between the key crankshaft and its journal support bearing presented by Cho.² An improved hydrodynamic lubrication performance with a new star-shaped parallel slider bearings surface texture was reported by Uddin and Liu.³ Gropper et al.⁴ provided a more detailed overview of various modeling and finite element analysis for oil flow state and hydrodynamic influencing factors. Wakuda et al.⁵ had determined that the porosity of the tribologically controlled surface could help reduce the friction effect at the sliding contact interface. The thrust loading pads were assumed to be deformed near the interface contact points and additional errors with different manufacturing types and amplitudes, were comprehensively considered by Zoupasa et al.⁶ Wodtke et al.⁷ calculated the equilibrium position of the thrust loading pad by Newton–Raphson iterative method numerical program. Thrust bearing main performance quantitative indexes (such as maximum film pressure/oil temperature and minimum film thickness/anti-friction torque) were analyzed by Lin et al.⁸ Zhai et al.⁹ proposed the thermoelastic hydrodynamic (TEHD) lubrication analysis of thrust bearings by combining the classic Reynolds equations and the finite element analysis (FEA) method. A large rectangular oil cushion hydrostatic thrust bearing structure was designed by Li et al.,¹⁰ and predicted its practical application lubrication performance. Based on a very detailed numerical model of aluminum foil sandwich, Lehn et al.¹¹ studied the air foil thrust bearings (AFTBs) performances under the conditions of alignment, deformation, and misalignment. Transient contact thermal behavior of dynamic journals and bearings during initial start-up operation was investigated by Cui et al.¹² Zouzoulas and Papadopoulos¹³ performed thermal fluid dynamic lubrication calculations and studies on load-bearing types thrust bearings that exhibited different forms of surface treatments. Henry et al.¹⁴ used an experimental analysis method to verify the thermoelastic behavior of multiple thrust bearings with a determined geometry. Through the sequential quadratic programming (SQP) method, the optimal modification of hydrodynamic film with maximum load-carrying capacity (LCC) in designed thrust bearing was given, and the cubic optimal solution of special case of the two-dimensional stepped contour region, where r had a fixed film depth (quadrilateral modification) and a constant film thickness (radial direction), were analyzed by Fesanghary and Khonsari.¹⁵ Gao et al.¹⁶ considered obvious differences in water/oil physical properties and analyzed the distribution rule and influence trend of eccentricity on water film pressure through computational fluid dynamics (CFD). Kim et al.¹⁷ established a multi-objective function to optimize constraint equations of radial/axial load capacity and interface friction, contact stiffness, and damping coefficient to solve thrust hydraulic bearings with optimal load-bearing performance. Fesanghary and Khonsari¹⁸ analyzed the optimum periodic contact interface grooves by mathematical optimization method, which launched the highest load-carrying capacity (LCC) in parallel planar bearings.

In this research project, dynamic simulation analysis method for solving time-varying law of oil film instantaneous temperature field time-varying rule for a variable viscosity RTHSB with special shaped cavity is utilized to disclosure the lubrication behaviour characteristics of special-shaped cavity with a variable oil film thickness under full working conditions in detail. What’s more, the distribution trend of transient temperature field of oil film in profiled cavity is evaluated.

Mathematical model of oil cushion for RTHSB

To the authors’ knowledge, so far, there has not been extensive research on establishing a special design as a standard for variable–viscosity RTHSB with a special shaped cavity. RTHSB configurations investigated in the present study comprise 12 oil film cushion supporting pads. The geometric configuration of special shaped cavity RTHSB, see Figure 1. With respect to RTHSBs, the answer is clear. The better temperature-pressure characteristics of radial thrust hydrodynamic sliding bearing clearly extends the working range to higher speeds and load capacity. The instantaneous variation of temperature–pressure boundary conditions has a relatively significant impact on fluid lubrication comprehensive performance of RTHSBs. The unique novelty of presented study is as follows:

A more detailed original design model for the special-shaped cavity of an RTHSB is proposed and launched.

The effect of instantaneous variation of temperature–pressure boundary conditions on fluid lubrication performance of RTHSBs is analyzed.

The relatively precise geometry of the supporting oil cushion completely explains the extension of the previous research on RTHSB. It should be noted that this study does not simulate the dynamic geometry of the oil film in more detail, but a simplified oil film stiffness model is used in this paper.

The time-varying rule of temperature field of RTHSB under different inlet flow rate and rotating speed is studied through a dynamic mesh method and the simulation results are verified by experiments.

Figure 1.

Sketch drawing of working process of an RTHSB with special-shaped cavity.

Geometric configuration of special shaped cavity

This study is organized as follows: firstly, the mathematical theoretical model, which is applicable to arbitrary RTHSBs with special-shaped cavity geometries, is briefly recapitulated. An irregular cavity model is chosen as structural model for the supporting oil pad. The smooth supporting oil pad with any shape based on the general tensor expression of the linear elasto-hydrodynamics theory is briefly analyzed. The main assumptions of the linear elasto-hydrodynamics theory are as follows:

Compared with the feature length of the contact surface of the special-shaped cavity and its minimum curvature, the pre-estimated oil film thickness is minimal.¹⁹

Assuming that the overall film thickness on contact interface of the special-shaped cavity has been considered, the lateral shear force relative to sliding along the contact interface is constant.²⁰

External extensions of the thickness of inner oil pad of special-shaped cavity are neglected.²¹

Based on the theory of linear elastic fluid dynamics, a numerical solution equation is proposed, which can be used for a generally smooth supporting oil cushion with a cavity structure of any shape. The governing special-shaped cavity equations are specified for a variable viscosity RTHSB geometry considered in this manuscript.

Metrical and curvature properties of a single supporting oil cushion surface

In the present work, an oil cushion 3D model for numerical simulation analysis is constructed to study the flow direction of hydraulic oil. The metrical and curvature properties of a single supporting oil cushion surface are discussed in detail. Hydraulic oil brand is set to 32#, and set the dynamic viscosity value of the hydraulic oil to 0.0435 Pa s at 30°C, see Figure 2.

Figure 2.

3D solid model of a single-supported oil cushion for an arbitrary profiled cavity.

The preventative section of an arbitrary profiled cavity single-supported oil cushion surface F which is described by a set of convective and curvilinear coordinates $θ^{α}$ is shown in Figure 3(a). The local covariant foundation $a_{i}$ at each point on the oil cushion surface of the special-shaped cavity is used to define by the differential geometry.²²

a_{a} = \frac{\partial r}{\partial θ^{a}} = r_{a}

(1)

a_{3} = \frac{a_{1} \times a_{2}}{| a_{1} \times a_{2} |}

(2)

Figure 3.

A surface metrical characteristics (a) representation of kinematics interconnection of single support oil cushion surface, (b) covariant tensor variables representation, and (c) an arbitrary cavity mathematical model description.

The oil cushion surface indicator attributes of the special-shaped cavity are described by the covariance metric tensor

a_{α β} = a_{α} \cdot a_{β}

(3)

The contra-variant metric tensor and the contra-variant base vectors are defined as:

a_{α ρ} a^{ρ β} = δ_{α}^{β}

(4)

where $δ_{α}^{β}$ denotes the variable increment.

a^{α} = α^{α β} a_{β}

(5)

a^{3} = a_{3}

(6)

The curvature of the oil cushion surface of the special-shaped cavity is revealed, and curvature tensor descriptions are expressed in two forms: covariant and mixed.²³

b_{α β} = a_{3} \cdot a_{α β}

(7)

b_{β}^{α} = a^{α ρ} b_{ρ β}

(8)

Here, in the initial configuration, a line perpendicular to the vector $\vec{F}$ is covered. An arbitrary point B* of the continuous contour cavity continuum and a point B on the surface F of the special-shaped cavity oil pad surface is illustrated in Figure 3(b). In the thermoplastic deformation state, all points on the original normal line of the set vector $\vec{F}$ are always on the same line, and the vector $\vec{d_{3}}$ direction is assumed to be along the cross-sectional plane. Therefore, according to Figure 3(b), the displacement vector v* of an arbitrary point B* is acquired in the following expression:

V^{*} = \bar{r^{*}} - r^{*} = \bar{r} - r + (\bar{d_{3}} - a_{3}) θ^{3} = W θ^{3} + V

(9)

Thus, the displacement field of the oil pad surface with the special-shaped cavity continuum is described by two variables $v_{i}$ and $w_{a}$ , the displacement vector characterized the thermoelastic deformation of the oil pad surface of the profiled cavity. The component quantification $w_{a}$ of the difference vector $W = w_{a} a^{a}$ reflects the rotational deformation and shear effect of the oil pad cross sections. The dynamic relationships between the displacement variables $v_{i}$ , $w_{a}$ and the strain variables $φ_{α β}$ , $k_{α β}$ and $γ_{α}$ are given by Cui et al.²⁴

φ_{α β} = v_{β | α} - v_{3} b_{α β}

(10)

k_{α β} = \frac{1}{2} (w_{α | β} + w_{β | α})

(11)

γ_{α} = w_{α} + v_{3 | α} + v_{λ} b_{α}^{λ}

(12)

Where, a covariant differentiation is denoted by the vertical line in the index.

The moments and forces acting on an oil pad surface element $dF$ of the profiled cavity are described in Figure 3(c).

B = p^{α} a_{α} + p^{3} a_{3}

(13)

An external force vector is represented by

n^{α} = n^{α β} a_{β} + q^{α} a_{3}

(14)

An internal force is expressed by

m^{α} = m^{α β} a_{3} \times a_{β}

(15)

Herein, $n^{α β}$ denotes the stress synthesis tensor, $q^{α}$ is the vector of transverse shear stress, and $m^{α β}$ describes the moment tensor. The correlation between the external/internal forces variables is revealed by the equilibrium equations below.

- p^{β} = n^{α β} |_{α} - q^{α} b_{α}^{β}

(16)

- p^{3} = n^{α β} b_{α β} + q^{α} |_{α}

(17)

m^{α β} |_{α} - q^{β} = O

(18)

Temperature rise equation for RTHSB considering viscosity–temperature relationship

Considering the time-varying characteristics of hydraulic oil at various temperatures, the maximum film temperature is not more than 105°C in this study, the correlation expression of hydraulic oil viscosity and its temperature is given by Sander et al.²⁵

μ = 1.878 \times 10^{- 12} e^{\frac{11848.272}{T - 80.363}}

(19)

Where $μ$ describes the dynamic viscosity ( $Pa s$ ), $T$ denotes the temperature mean of lubricating oil (°C), the fitting equations are compared with these experimental curves, is exposed to Figure 4.

Figure 4.

32# oil viscosity–temperature relationship curves.

A cross section of oil cushion for contact interface region of oil film in special-shaped cavity is a micro-rectangular element and its numerical calculation hydraulic radius ( $R_{s}$ ) is $1.562 mm$ . The maximum flow velocity of lubricating oil in profiled cavity is not more than $u = 3.53 m / s$ .

Figure 4 illustrates that the fitting relationship between the lubricating oil viscosity and its temperature is more consistent with the data collected in the experiment when the temperature is in the range of 30°C to 120°C . Here, dynamic pattern of hydraulic oil is set to laminar flow. The density parameter ( $ρ$ ) is 880 $kg / m^{3}$ , the thermal conductivity is 0.132 $W / (m \cdot K)$ , and the specific heat capacity is 1884 $J / (kg \cdot K)$ .

Lubricating oil dynamic viscosity is set to $0.0665 Pa s$ , and its Reynolds coefficient is as follows.²⁶

R_{e} = \frac{4 u R_{s}}{μ} ρ = \frac{4 \times 3.53 \times 1.562}{0.0665} \times 880

(20)

Therefore, it can be known that the Reynolds coefficient is not greater than 2320, and dynamic flow pattern of lubricating oil in oil film interface is determined as the laminar flow state.

It has been predicted that thermal behavior only causes the increase of oil film interface temperature, and the lubricating oil dynamic viscosity is transient time-varying with the temperature. Then, the shear friction power for RTHSB of the special-shaped cavity is as follows²⁷:

N_{f} = \frac{ξ μ A_{s} ω^{2}}{h} (r_{2}^{2} - r_{1}^{2})

(21)

Where $ξ$ is the ratio coefficient ( $ξ = 0.07532$ ), $ω$ represents the rotation speed of RTHSB thrust integrated tile block ( $ω = 0.215 rad / s$ ), the region of hydraulic oil edge is expressed as $A_{s}$ , $r_{2}$ describes the equivalent radius of the outer circle of the thrust disk ( $r_{2} = 1150 mm$ ), $r_{1}$ expresses the equivalent radius of the inner circle of the thrust disk ( $r_{1} = 420 mm$ ), the formula for calculating the steady-state interface oil film temperature rise of special-shaped cavity oil cushion is characterized as follows²⁸:

T = \frac{N_{f}}{kQc}

(22)

Herein, $c$ indicates the specific heat capacity property of lubricating oil, $k$ expresses the equivalent thermal efficiency, and $Q$ indicates the overall flow of lubricating oil.

Dynamic simulation modeling and related parameter determination

UDF programming and motion regions definition

In this article, UDF is regarded as a professional program for moving specified parts in FLUENT software. It can be seen in this model that the thrust disk in contact interface with oil film moves downward and slides relative to the shaped cavity wall, at which time the oil film interface becomes thinner. The speed at which the thrust disk slides down is expressed in $0.005 m / s$ , and the total exercise time is set to $12 s$ . A compiler VS2012 is used to compile the UDF program to control relative slip trend of boundary layer loaded mesh. Herein, the lubricating oil viscosity characteristics are determined, and its viscosity varies with temperature. In physical properties the viscosity properties are called and defined. And then determine the DEFINE_ PROPERTY (unit viscosity parameter, c and t) macro to control real-time change of lubricating oil viscosity in calculation domain.

Simulation model and parameters

In ICEM&CFD software, a single oil pad geometric structure model proposed in this paper is constructed and the boundary layer mesh is refined, the periodic boundary is determined, the rotation axis and its center are defined, and the relative rotation angle is set to 30°. The boundary conditions are defined and loaded in the FLUENT numerical simulation and its numerical analysis model, as shown in Figure 5.

Figure 5.

Geometric structure model after part generation.

A mesh encryption method is adopted to refine 10 micro blocks for a single oil cushion layer to optimize the mesh quality of the pre-specified local area and further refine it into a hexahedral mesh. The film thickness influence of 0.04 to 0.10 mm on lubricating performance is analyzed. The initial oil film thickness is set to 0.10 mm, and the outlet flow rate (Q L/min) and inlet flow rate (V m/s) are launched considering different initial boundary loading conditions. The numerical calculation results are shown in Table 1.

Table 1.

Preset parameters of initial film thickness (0.10 mm).

Theoretical parameters	Initial boundary load
	5 t	10 t	15 t	20 t	25 t	30 t
Outlet flow rate Q (L/min)	2.64	4.01	5.39	6.73	8.16	9.52
Inlet flow rate V (m/s)	0.12	0.18	0.23	0.32	0.38	0.45

Dynamic simulation analysis of instantaneous oil film temperature field

Influence analysis of inlet flow rate on instantaneous oil film temperature field

The temperature distribution is analyzed by using the variable viscosity fluid simulation and the second order upwind method. The initial temperature is 298.6 K. An input speed of 60 rpm is given. The oil film thickness is 0.08 and 0.04 mm, respectively. The instantaneous temperature distribution and its variation trend are reflected in Figures 6 and 7.

Figure 6.

Instantaneous oil film temperature field of special-shaped cavity oil cushion with inlet flow rate of 0.1853 m/s. (a) Oil film thickness (h = 0.08 mm). (b) Oil film thickness (h = 0.04 mm).

Figure 7.

Instantaneous oil film temperature field of special-shaped cavity oil cushion with inlet flow rate of 0.3156 m/s. (a) Oil film thickness (h = 0.08 mm). (b) Oil film thickness (h = 0.04 mm).

The selected base planes are perpendicular to each other(X = 90 mm, Y = 906 mm, Z = 0 mm). As shown in Figure 8, the time-varying laws of oil film pressure and the transient temperature distribution trend at various points on the intersection line.

Figure 8.

Position distribution of cross section lines.

In Figure 9, the instantaneous oil film temperature distribution trends along radial/circumferential directions are derived. The instantaneous high temperature regions of oil film are mainly distributed around the sealing ring of the special-shaped cavity. When the oil film thickness becomes thinner, the sealing ring temperature is relatively higher, and the instantaneous higher-temperature area expands along the circumferential direction and gradually deviates from its center, the instantaneous temperature of downstream side is lower than that of countercurrent side.

Figure 9.

Instantaneous oil film temperature distribution along radial/circumferential directions under inlet flow rate (0.3156 m/s). (a) Circumferential instantaneous temperature distribution at oil film thickness (h = 0.08 mm). (b) Radial instantaneous temperature distribution at oil film thickness (h = 0.08 mm). (c) Circumferential instantaneous temperature distribution at oil film thickness (h = 0.04 mm). (d) Radial instantaneous temperature distribution at oil film thickness (h = 0.04 mm).

From the above analysis, it can be revealed that the diffusion is not obvious when oil film becomes thicker in low temperature area. As inlet flow rate increases, difference in instantaneous temperature magnitude between countercurrent and downstream sides becomes more and more obvious.

Effect of operating flow rate on instantaneous oil film temperature field in profiled cavity

The inlet flow rate is set to 0.3156 m/s, and film thickness values are set to 80 and 40 µm, respectively, the rotation speeds of 40 and 80 rpm are given respectively, the analysis curves are shown in Figures 10 and 11.

Figure 10.

Instantaneous oil film temperature field with special-shaped cavity at rotating speed (40 rpm). (a) Oil film thickness (h = 0.08 mm). (b) Oil film thickness (h = 0.04 mm).

Figure 11.

Instantaneous oil film temperature field with special-shaped cavity at rotating speed (80 rpm). (a) Oil film thickness (h = 0.08 mm). (b) Oil film thickness (h = 0.04 mm).

Instantaneous oil film temperature distribution along radial/circumferential directions at rotation speed of 40 rpm is shown in Figure 12. Here, the inlet flow rate is regarded as constant, which improves the working speed and oil film maximum temperature on the oil seal edge. The low temperature area of interface oil film in the lubricating oil storage chamber is mainly concentrated at the lower end of contact seal, while the high temperature area of interface oil film in the special-shaped cavity is mainly concentrated in the middle and lower portions of oil seal edge. The instantaneous oil film temperature on the downstream interface is not higher than that of other adjacent areas, and as the film thickness decreases, the instantaneous temperature diffusion tendency becomes more obvious.

Figure 12.

Instantaneous oil film temperature distribution along radial/circumferential directions at rotations speed (40 rpm). (a) Circumferential instantaneous temperature distribution at oil film thickness (h = 0.08 mm). (b) Radial instantaneous temperature distribution at oil film thickness (h = 0.08 mm). (c) Circumferential instantaneous temperature distribution at oil film thickness (h = 0.04 mm). (d) Radial instantaneous temperature distribution at oil film thickness (h = 0.04 mm).

Simulation results and data analysis

The real-time transient temperature at the oil seal edge is extracted, and the distribution trend of instantaneous high temperature area of a single oil film is shown in Figure 13. The working speed is 40, 60, and 80 rpm, respectively. The relationship between instantaneous film temperature/film thickness at variable inlet flow rate is presented in Figure 14.

Figure 13.

Oil film instantaneous high temperature region.

Figure 14.

Relationship curves between oil temperature/film thickness under different inlet flow rates. (a) $ω = 40 rpm$ . (b) $ω = 60 rpm$ . (c) $ω = 80 rpm$ .

In this subsection, further characterization of structural characteristics of special-shaped cavity, as a representative example, the relationship curves between instantaneous oil temperature/film thickness are described in detail. Figure 14 shows the interconnection influence of instantaneous oil temperature/film thickness. Instantaneous oil film temperature difference at inlet flow rate is not obvious, and interface oil film thickness becomes larger. The instantaneous change of inlet flow rate causes the oil pad edge temperature to increase rapidly. When the thickness of oil film is not greater than 0.07 mm, the inlet flow rate increases and the oil cushion edge temperature increases rapidly.

So far, further study shows that the initial liquid film lubrication is transformed into boundary lubrication based on lower film thickness, and the friction resistance increase of contact interface leads to significant and rapid increase of instantaneous oil film temperature in local area. High speed in operating conditions is set to 80 rpm, and film thickness is set in the range of 70 to 100 µm, when the inlet flow rate becomes smaller, the oil temperature at the contact interface of the oil pad edge is higher.

Experimental study and results analysis

Experimental details

The main experimental verification research content of this chapter is to carry out oil film thickness data analysis and oil cavity temperature monitoring. The load values of radial dynamic sliding thrust bearings are set to 0.0, 2.5, and 10.0 t, and the operating speeds are set to 20, 40, 60, 80, 100, and 120 rpm, respectively. In this verification study, a bench running test is carried out on the oil pad contact interface on the cavity by rotating motion. Usually, a load is applied to the contact interface of thrust disk during its rotation, the friction behavior generated along the tangential direction of contact interface is measured by five displacement sensors, and film thickness/oil temperature are refined through indirect conversion by calculating the friction coefficient.

The oil storage cavity material is made of GCr15 bearing steel, the thrust pad oil pad material is 45 steel, and the contact interface is provided with a special shaped recess to satisfy the oil-rich lubricating effect. The workbench material is gray iron 250 whose diameter is 4.5 m and 9.85 t in weight, and the working load had range of 0 to 32 t. 0 to 200 rpm in working speed range, the diameter parameter of oil inlet pad is designed to be 15 mm, the thickness of oil film is set to 3.0 mm, and the thrust disk surface roughness Ra is 0.05 mm to ensure that the interface friction contact is minimized as much as possible. Assuming that the thermal deformation of each part of the experimental device is ignored, only the real-time changes of oil film are considered in Figure 15.

Figure 15.

Experimental schema of a variable viscosity RTHSB with special shaped cavity.

Experimental verification and discussion

According to the above analysis, five preset displacement sensors are arranged in oil cushion central area. The sensors arithmetic mean values with corresponding space installation location at circumferential symmetrical distribution oil film interface in special-shaped cavity are solved. The above specific sensors layout pattern and data acquisition and display are shown in Figure 16.

Figure 16.

Sensor layout pattern and data acquisition and display. (a) Sensors layout pattern. (b) Data acquisition and display.

The rotating speed and oil temperature of the experimental platform under different working conditions are set in advance. During bench experiment operation, the radial displacements of each monitoring point are recorded to capture the required performance parameters related to oil cushion film and its initial thickness at various rotation speeds.

Experimental results and analysis

The oil cushion film thickness and temperature of special-shaped cavity under no-load, 2.5 and 10 t loads are measured under different working conditions.

Under different loads, the variation curves between oil film temperature/rotation speeds of oil cushion with a special-shaped cavity are shown in Figure 17. Analysis from the above figures, it can be seen that oil film thickness decreases as working speed increases. Considering actual conditions that the inlet flow rate is constant, the applied load becomes larger and the thickness of oil film is thinner, which is the most consistent with the previous numerical simulation results in this paper.

Figure 17.

Variation curves of oil film thickness/rotation speeds under different loads. (a) W = 0 t. (b) W = 2.5 t. (c) W = 10 t.

As outlined in Figure 18, oil film interface edge temperatures on the countercurrent and the downstream sides are lower than that of oil pad. The oil pad film temperature with a special-shaped cavity is not lower when the working speed is increased. The working load is 10 t and 0.116 mm in oil film thickness. Table 2 indicates comparison results between the experimental/simulated data of oil pad instantaneous film temperature with a special-shaped cavity under different working speeds.

Figure 18.

Variation curves of instantaneous oil film temperature/rotating speeds under different loads. (a) W = 0 t. (b) W = 2.5 t. (c) W = 10 t.

Table 2.

Simulation/experimental data comparison of instantaneous film temperature (unit: °C) (W < 10 t).

	40 rpm	60 rpm	80 rpm
Simulated data	24.302	24.879	25.336
Experimental data	22.036	22.436	24.561
Error	9.32%	9.82%	3.06%

From Table 2, the comparison results between the experimental/simulated data are dissected. The actual instantaneous oil film temperature rise of the special-shaped cavity oil pad is almost consistent with simulation/calculation results in the case of increased working speeds. The main sources of temperature error are ambient temperature, reading error and transient temperature loss during operation of radial thrust dynamic pressure sliding bearing, and so on.

Conclusions

The surface structure parameters of oil cushion with special-shaped cavity and the influence of oil film parameters controlled by rotating speed and load are studied, and an optimal analysis model considering structural design parameters is proposed. The following novel conclusions are elaborated:

Even if the outer diameter of the best optimized design of the RTHSB becomes larger, the optimal value of oil film thickness of the corresponding oil pad will not decrease, the reason is that the optimal contact specific surface area is closely related to the structure and operation parameters.

The relation expressions of transient oil film temperature rise equations with variable viscosity/constant viscosity in a special-shaped cavity are presented. The automatic updating calculation method of dynamic mesh is constructed, and the variation rules of transient oil temperature under different film thickness distribution are revealed.

Optimum oil film thickness increases while the optimum diameter of a special-shaped cavity decreases as working speed increases and applied load decreases. In the case of an increase in inlet flow rate, the instantaneous oil film temperature rises.

At low speed, high-temperature area in special-shaped cavity is mainly concentrated on countercurrent side edge of oil pad contact interface. At high speed, the high temperature area tends to expand to both sides of contact interface edge, once oil film thickness becomes thinner, instantaneous temperature diffusion trend is obviously prominent.

The experimental verification results show that optimal design model of structural parameters with a special-shaped cavity is reasonable and effective, which provides a reliable theoretical reference for the tribological analysis of oil film interface friction of the radial thrust dynamic sliding bearing oil pad.

Footnotes

Acknowledgements

The authors who participated in the preparation of this article are very grateful for support from the Northeast Forestry University (NEFU) as well as the Heilongjiang Institute of Technology (HLJIT) and the Harbin Institute of Technology (HIT).

Handling Editor: James Baldwin

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research topic is supported by the Special Scientific Research Funds for Forest Non-profit Industry (Grant No. 201504508) and the Youth Science Fund of Heilongjiang Institute of Technology (Grant No. 2015QJ02) and the Fundamental Research Funds for the Central Universities (Grant No. 2572016CB15).

ORCID iD

Xigui Wang

References

Almqvist

Fabricius

Larsson

, et al. A new approach for studying cavitation in lubrication. J Tribol 2014; 136: 011706.

Cho

IS.

The influence of boundary conditions on the lubrication characteristics of a journal bearing for reciprocating compressors. J Mech Sci Technol 2015; 29: 751–758.

Uddin

Liu

YW.

Design and optimization of a new geometric texture shape for the enhancement of hydrodynamic lubrication performance of parallel slider surfaces. Biosurf Biotribol 2016; 2: 59–69.

Gropper

Wang

Harvey

TJ.

Hydrodynamic lubrication of textured surfaces: a review of modeling techniques and key findings. Tribol Int 2016; 94: 509–529.

Wakuda

Yamauchi

Kanzaki

, et al. Effect of surface texturing on friction reduction between ceramic and steel materials under lubricated sliding contact. Wear 2003; 254: 356–363.

Zoupasa

Wodtkeb

Papadopoulosa

, et al. Effect of manufacturing errors of the pad sliding surface on the performance of the hydrodynamic thrust bearing. Tribol Int 2019; 134: 211–220.

Wodtke

Schubert

Fillon

, et al. Large hydrodynamic thrust bearing: comparison of the calculations and measurements. Proc IMechE, Part J: J Engineering Tribology 2014; 228: 974–983.

Lin

Bao

, et al. An investigation into the transient behavior of journal bearing with surface texture based on fluid-structure interaction approach. Tribol Int 2018; 118: 246–255.

Zhai

Luo

Wang

, et al. 3D two-way coupled TEHD analysis on the lubricating characteristics of thrust bearings in pump-turbine units by combining CFD and FEA. Chin J Mech Eng 2016; 29: 112–123.

10.

Cheng

, et al. Theoretical research on mechanical property of rectangular oil pad in hydrostatic thrust bearing based on constant flow. Ind Lubric Tribol 2016; 68: 392–403.

11.

Lehn

Mahner

Schweizer

BH.

Characterization of static air foil thrust bearing performance: an elasto-gasdynamic analysis for aligned, distorted and misaligned operating conditions. Arch Appl Mech 2018; 88: 705–728.

12.

Cui

Wang

, et al. Numerical analysis on the dynamic contact behavior of hydrodynamic journal bearings during start-up. Tribol Int 2018; 121: 260–268.

13.

Zouzoulas

Papadopoulos

CI.

3-D thermohydrodynamic analysis of textured, grooved, pocketed and hydrophobic pivoted-pad thrust bearings. Tribol Int 2017; 110: 426–440.

14.

Henry

Bouyer

Fillon

Experimental analysis of the hydrodynamic effect during start-up of fixed geometry thrust bearings. Tribol Int 2018; 120: 299–308.

15.

Fesanghary

Khonsari

MM.

Topological and shape optimization of thrust bearings for enhanced load-carrying capacity. Tribol Int 2012; 53: 12–21.

16.

Gao

Yin

Jiang

, et al. Numerical analysis of plain journal bearing under hydrodynamic lubrication by water. Tribol Int 2014; 75: 31–38.

17.

Kim

Lee

, et al. Optimal design and experimental verification of fluid dynamic bearings with high load capacity applied to an integrated motor propulsor in unmanned underwater vehicles. Tribol Int 2017; 114: 221–233.

18.

Fesanghary

Khonsari

MM.

On the optimum groove shapes for load-carrying capacity enhancement in parallel flat surface bearings: theory and experiment. Tribol Int 2013; 67: 254–262.

19.

Kim

Iba

DSK

Tatsumi

, et al. Development of a contact-type probe for measurements of ultra-fine-pitch gears and application to pseudo roughness evaluation. J Mech Sci Technol 2017; 31: 5609–5616.

20.

Wang

Chen

, et al. Aerodynamic shape optimized design for wind turbine blade using new air foil series. J Mech Sci Technol 2015; 29: 2871–2882.

21.

Zhang

Jiang

Wang

, et al. Effect of surface roughness on the start-stop behavior of air lubricated thrust micro-bearings. Tribol Int 2015; 119: 436–442.

22.

Belforte

Conte

Manuello Bertetto

, et al. Indirect contact pressure evaluation on pneumatic rod seals. Tribol Int 2018; 118: 240–245.

23.

Wang

Liu

Zou

, et al. Influence of both friction and wear on the vibration of marine water lubricated rubber bearing. Wear 2017; 376–377: 920–930.

24.

Cui

Fillon

, et al. The effects of surface roughness on the transient characteristics of hydrodynamic cylindrical bearings during startup. Tribol Int 2018; 128: 421–428.

25.

Sander

Allmaier

Priebsch

, et al. Simulation of journal bearing friction in severe mixed lubrication-Validation and effect of surface smoothing due to running-in. Tribol Int 2016; 96: 173–183.

26.

Jiao

, et al. Mixed-lubrication analysis of misaligned bearing considering turbulence. Tribol Int 2018; 119: 19–26.

27.

Ettles

López

Borgna

Optimized design of a large reversible thrust bearing. J Tribol 2016; 138: 041701.

28.

Mallya

Shenoy

Pai

Static characteristics of misaligned multiple axial groove water-lubricated bearing in the turbulent regime. Proc IMechE, Part J: J Engineering Tribology 2017; 231: 385–398.

Transient temperature field analysis of variable viscosity RTHSB with a special structural cavity

Abstract

Keywords

Author’s Statement of Originality

Highlights (for review)

Novelty Statement

Introduction

Mathematical model of oil cushion for RTHSB

Geometric configuration of special shaped cavity

Metrical and curvature properties of a single supporting oil cushion surface

Temperature rise equation for RTHSB considering viscosity–temperature relationship

Dynamic simulation modeling and related parameter determination

UDF programming and motion regions definition

Simulation model and parameters

Dynamic simulation analysis of instantaneous oil film temperature field

Influence analysis of inlet flow rate on instantaneous oil film temperature field

Effect of operating flow rate on instantaneous oil film temperature field in profiled cavity

Simulation results and data analysis

Experimental study and results analysis

Experimental details

Experimental verification and discussion

Experimental results and analysis

Conclusions

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

ORCID iD

References