A combined experimental and computational study of lubrication mechanism of high precision reducer adopting a worm gear drive with complicated space surface contact
Introduction
Analysis of friction and lubrication between two complicated surfaces (e.g. lead screw, bearing, and worm gear drive [[1], [2], [3]]) has been a very challenging and hot topic in tribology research. The most popular approach in friction and lubrication analysis is to combine numerical simulation with experimental validation to obtain a complete understanding of friction and lubrication mechanisms of studied mechanical devices. The method mostly used for the numerical simulation is the finite volume method (FVM) [4]. Based on that method, Laruelle et al. [5] carried out numerical simulations on single bevel gears to find out the effects of speed, lubricant viscosity, and temperature on its lubrication performance. Based on the results, they derived an equation for estimating the churning losses of bevel gear. Liu et al. [6] applied the FVM to develop a CFD model for a dip-lubricated planetary gearbox and ran simulations on that model to acquire oil distribution profiles within that gearbox for future optimizations. Hu et al. [7] studied the impacts of rotation speed, oil fill level of gears, temperature, lubricant viscosity and density, and the helicopter tilt angle on the churning losses of a gearbox with spiral bevel geared transmission via the FVM-based simulation. Renjith et al. [8] employed the FVM to study the lubrication of automotive differential system, with an emphasis on the factors that influence the no-loading losses of such device; and derived an equation for calculating the spin power loss of such system. Jiang and co-workers [9] also followed a similar approach to investigate the influence of an oil guide device on the lubrication performance and internal flow field in spiral level geared transmission. The simulation results were compared with experimental data and a good agreement was achieved. Several studies have shown that the traditional FVM, combined with advanced mesh-handling techniques, could be applied to successfully and effectively model and solve gear systems involving very complex geometries. For example, Concli and Gorla [10,11] developed a specific power loss calculation-tool and a new mesh-handling technique that enable a good prediction accuracy with reasonable computational efforts. Furthermore, the researchers continued to present a new automated mesh-partitioning strategy to extend the applicability of that method to complex gearboxes exceeding the geometrical limitations adopted in the past [[12], [13], [14]]. However, without those specific mesh-handling techniques, it would be very time consuming to use traditional FVM to generate high-quality unstructured meshes in the preprocessing step. Moreover, some complicated surfaces still can hardly be properly meshed. Due to the difficulty of using the FVM and other mesh-based methods in creating accurate meshes from the geometry of a complicated space surface and tracking of fluid flows, a family of meshfree methods, particle methods have been developed and applied for lubrication analysis.
Unlike the FVM and other mesh-based methods, the particle methods do not need explicit surface tracking by a mesh or a scalar quantity but employing a number of particles to describe mechanical processes based on kernel functions. In those methods a continuum is discretized by a discrete number of particles without mesh constraints. Each particle moves accordingly with its own mass, density, velocity, and the external/internal forces applied to it. Compared with the traditional numerical methods, the particle methods can solve more complex geometry and physics problems including large deformation and damage problems. Therefore, those methods are powerful tools for flow field analysis and can be used for simulation of the flow field in speed reducers. Accuracy of the particle methods can be easily controlled by altering the number of particles. Advantages and drawbacks of different modeling approaches in calculating gear power losses and lubricant fluxes were discussed by Concli and Gorla [15].
Common particle methods include the moving particle semi-implicit (MPS) method, the smoothed particle hydrodynamics (SPH) method, and the finite volume point (FVP) method. Ji et al. [16] applied the SPH method to study the oil flow inside a gearbox. A multiphase SPF formulation was used to resolve the complex multiphase flow and obtain the flow field behavior, the quantity and size of bubbles generated due to the rotation of the gears, and the velocity field and profile beneath the oil surface. The numerical results were in comparatively good agreement with the experimental particle image velocimetry results. Imin and Geni [17] also established SPH discrete equations and carried out numerical simulations to capture the stress variation, distribution, and propagation on the tooth profile surface during a gear meshing impact process. The numerical model and the SPH method were validated using experimental data. Keller et al. [18]. used the SPH method to investigate a complex two-phase flow during oil-jet impingement on a rotating spur gear. A significant effect of the inclination angle on the oil spreading and splashing process as well as the resistance torque was determined from their research. Menon et al. [19,20] applied a graphics processing units accelerated SPH method for multiphase gearbox modeling to obtain precise churning losses for a gearbox.
Among the three particle methods (SPH, MPS, and FVP), the SPH method approximates function derivatives based on a kernel derivative, it is more efficient by following an explicit prediction-correction process but its accuracy and stability are lower than the other two methods [[21], [22], [23]]. CFD simulations with the MPS and FVP methods may cost more computational time but would yield results with higher accuracy. Both methods approximate the function derivatives by weight average based on the kernel function. The fundamental difference between these two methods is in the FVP method, the governing equations are discretized following the approach used in the FVM [24,25]. Based on the MPS method, a CFD software, ParticleWorks, has been developed for simulating complex fluid flows such as lubricant behavior in transmission systems [26]. In this study, we use ParticleWorks based on the MPS method to study the lubricant behaviors (splashing, churning losses, and oil pressure distribution) and the influencing factors (rotation speed, viscosity, and immersion depth) in the high precision reducer that employs a roller enveloping worm gear drive to achieve the speed reduction. The authors have previously applied the MPS method to investigate the lubrication mechanism in gearbox of high-speed railway train [27] and understand the influence of various types of rollers on the lubricant behavior in the high precision reducer [28]. The research approach and findings presented in this paper will provide a general methodology for systematic analysis of friction and lubrication between mating gear tooth surfaces with complex shapes.
A combined experimental-computational approach is employed in the present study. The remainder of this paper is organized as follows. Section 2 reviews the MPS method and its theoretical background; section 3 presents the computational study, including the modeling, simulation information, and the simulation results are interpreted in section 4; the experimental analysis is demonstrated in section 5 and we conclude in section 6.
Section snippets
MPS method
The MPS method discretizes fluid into a set of particles and simulate their motion by calculating their velocity and pressure using governing equations and computational algorithms. The churning losses are mainly caused by flow and air resistance. The calculated particle velocity and pressure will be imported into the flow resistance and air resistance models in ParticleWorks to determine churning loss torques for each component in the transmission system. Based on the churning loss torques,
CAD model
A high-fidelity 3D model for the high precision speed reducer was first created. As illustrated in Fig. 1, this reducer features a roller enveloping worm gear drive developed by Deng et al. [29,30].
In order to save the computational time while maintaining the accuracy of simulation, the established detail model was simplified by removing the positioning holes and chamfers outside the casing, but all components inside the casing, especially the roller enveloping worm gear drive, remain intact.
Effects of rotation speed
Influences of the rotation speed on the lubrication performance of the roller enveloping worm gear drive are illustrated through Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig. 10. As shown in Fig. 5, when the rotation speed was 300 and 600 rpm, a portion of lubricant particles adhered to the worm tooth surface. As the speed of the worm increased, more lubricant particles were splashed to inner walls of the casing. It is also found from the simulations that certain amounts of lubricant particles
Discussion
The churning power losses calculated using the MPS method can be subdivided into the churning loss related to surface extension (viscous effects) and the churning loss related to pressure gradient. Fig. 27 plots the percentages of those two power loss contributions at different rotation speeds. From that figure it can be found that the contribution related to surface extension increases while that related to pressure gradient decreases as the rotation speed increases. However, Concli et al. [34
Experimental analysis
An experimental analysis was performed to verify the simulation results and validate the numerical simulation approach. A cylindrical roller speed reducer and a conical roller reducer were manufactured based on relevant design parameters, and a testing platform was constructed for this study (Fig. 28, Fig. 29). In the experiments, transmission efficiency of both reducers was calculated based on the input and output torques measured via sensors. Based on the simulation results, which showed that
Conclusion
In this study, the MPS method was applied to study the lubrication performance of the roller enveloping worm gear drive under various conditions. CFD simulations were performed to systematically reveal for the first time how the rotation speed, immersion depth, worm arrangement, and lubricant viscosity affect the flow field inside the speed reducer. Following conclusions have been drawn from this study:
- (1)
As the rotation speed increases, the pressure fluctuation becomes more evident and results in
CRediT authorship contribution statement
Xingqiao Deng: Supervision. Shisong Wang: Formal analysis. Youssef Hammi: Methodology. Linmao Qian: Methodology. Yucheng Liu: Writing - original draft, Writing - review & editing.
Declaration of competing interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This work was supported by the National Natural Science Foundation of China under grant No. 51875479 and the Sichuan Distinguished Youth Fund under grant No. 19JCQN.
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