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Computational Fluid Dynamics Chenhui Jia , Zhiwu Cui , Shijun Guo

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Computational Fluid Dynamics Chenhui Jia , Zhiwu Cui , Shijun Guo Research on dynamic characteristics of gas film of spherical hybrid gas bearings based on computational fluid dynamics Chenhui Jia1, Zhiwu Cui1*, Shijun Guo2, Wensuo Ma3 1 School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang, China; 2 Cranfield University, School of Aerospace, Transport and Manufacturing, England; 3 Collaborative Innovation Center of Machinery Equipment Advanced Manufacturing of Henan Province, China Corresponding author's email: [email protected] Abstract: The Realizable k-ε turbulence model for the spherical spiral groove hybrid gas bearings film was established based on computational fluid dynamics (CFD). The 6-degrees of freedom (DOF) passive grid was used to numerically calculate the gas film pressure distribution, the bearing capacity and the dynamic characteristic coefficients. The gas flow field dynamic and static pressure coupling mechanism was studied. The effect of rotation speed, gas film thickness eccentricity ratio and gas supply pressure on the dynamic and static pressure bearing capacity and the dynamic characteristic coefficients during operation were analyzed as a method of research into the mechanical mechanism of gas bearing stability. The CFD simulation calculation analysis can simulate the complex gas flow in the transient flow field of the gas film, and find the reasonable operation parameters to optimize dynamic and static pressure coupling effects, which can improve the gas film bearing capacity, dynamic characteristics and the operating stability of gas bearings. Keywords: Gas bearing; 6-degrees of freedom passive grid; Gas film pressure distribution; Dynamic and static pressure coupling effects; Steady Bearing Performance; Dynamic characteristic coefficients NOMENCLATURE br table width bg groove width b groove width ratio bij damping coefficients div()ρ u divergence of velocity vector hg groove area clearance h0 average gas film clearance h groove depth ratio kij stiffness coefficients S the generalized source terms of the conservation of momentum equation t flow time uvw、、 the velocity component of the velocity vector in the x, y, z directions ∆∆FFx、 y variation of bearing gas film force ∆∆xy、 displacement change in x and y directions ∆∆vxy、 v velocity change in x and y directions Greek symbols α wrap angle β helix angle ε dimensionless eccentricity ratio θ gas supply hole angle φ1 diameter of the bearing φ2 diameter of the gas supply hole µ dynamic viscosity ρ air density ω rotation speed 1. Introduction Spherical spiral groove hybrid gas bearings have orifices on the surface of the bearing and spiral grooves on the rotor. On the one hand, the static pressure effect is formed by introducing the external high pressure gas into the bearing clearance through the restrictor. On the other hand, the gas flows through the wedge-shaped gap to form the dynamic pressure effect. They are coupled to form the bearing performance of the bearings. At the same time the bearing has high rotation accuracy, compact structure, and it can provide three degrees of freedom of low friction high-speed movement (Ma et al. 2010; Zhang et al 2011; Lu et al. 2014). Static and dynamic pressure lubrication can meet the needs of low speed, and can maintain stable working ability at high speed. The dynamic pressure effect is greatly influenced by rotation speed, the higher the speed, the large eccentricity ratio and the more obvious the dynamic pressure effect. In order to obtain large bearing capacity, the gas bearing needs to increase the structure of spiral groove, increase eccentricity ratio and reduce the average gas film thickness to enhance the dynamic pressure effect. However, when the rotation speed is high, the gas film force of the gas film whirl is increased, which results in the typical whirl instability (Wang et al. 2016; Rashidi et al. 2010). The change in the stability of the gas film is determined by the mechanical properties of the gas film during high-speed operation of gas bearings. The dynamic characteristic coefficients of the gas film reflect the variation law of the gas film force when the journal deviates from the static equilibrium position and the displacement movement in the vicinity, which has very complex non- linear and stochastic characteristics. The random variation of the gas film dynamic characteristics will cause the change of the gas film motion state. It is expressed as a random change of the stability of the gas film, and directly affects the motion state of the bearing rotor (San Andrés 2006; Yu et al. 2015; Jia et al. 2016). Therefore, the calculation and analysis of dynamic characteristics of bearing gas film is the key to study the stability of gas bearing (Li 2017). Hitherto, the majority of scholars have studied gas bearing stability by using basic experimental and theoretical investigations (Jia et al. 2017; Qi et al. 2007; Zhang et al. 2014). The theoretical calculation is basically based on the Reynolds lubrication equation. By using the Perturbation method, Difference method, Finite element method and other numerical methods, the linear equations are solved, and the dynamic characteristic coefficients are calculated to analyze the stability of the bearing. Because the Reynolds Equation can not accurately reflect the nonlinear coupling relation between the circumferential inertial effect of high speed airflow, the circumferential dynamic pressure effect of the journal and the static pressure diffusion effect, and the effect on the three-dimensional flow field characteristics. Therefore, the calculation of the stiffness and damping of the gas film deviates from the true value and the error is large. The real motion state of the bearing cannot be accurately analyzed (Zhang and Liu 2011; Liu and Wang 2011). However, testing the dynamic characteristic coefficients of the bearing ask for the rigorous experimental conditions. In the test process, various external factors inevitably interfere with the test, which makes the test result have certain error. In this study, the Realizable k-ε turbulence model of the spherical spiral groove hybrid gas bearings gas film was established based on FLUENT. The pressure distribution on the grid point of the gas film was numerically calculated by using 6DOF passive grid, thereby simulating the complex gas flow in the transient flow field of the gas film. The effect of gas film thickness, eccentricity ratio and gas supply pressure on the dynamic and static pressure bearing capacity and the dynamic characteristic coefficients during operation were analyzed. The dynamic and static pressure coupling effects of gas flow field was studied and the mechanical mechanism of gas bearing stability was studied, which can increase the bearing capacity of gas film, optimize the dynamic characteristics, reduce the gas film whirl, and provide a theoretical basis for improving the operating stability of gas bearing. 2. Finite element model of gas bearing 2.1 Three - dimensional model of bearing gas film For researching the spherical spiral groove hybrid gas bearings, the bearing consists of two portions, namely the rotor and stator. A certain number of air holes exist on the stator, while the rotor contains spiral grooves in the groove and platform areas, as illustrated in Fig. 1. Following the introduction of external high-pressure gas by the restrictor to the bearing clearance, a hydrostatic gas film is formed, resulting in hydrostatic bearing capacity. Moreover, a wedging effect between the rotor and stator is produced when the bearing rotates at a high speed; a dynamic pressure gas film is formed, resulting in dynamic bearing capacity. The transient flow field characteristics of the gas film reflect the steady bearing performance, dynamic characteristic coefficients, and stability of the bearing during operation. Fig. 1 Spherical spiral groove hybrid gas bearings profile diagram In Fig 1, β is the helix angle, φ1 is the diameter of the bearing, φ2 is the diameter of the gas supply hole, ω is the rotation speed, br is the table width, bg is the groove width, hg is the groove area clearance, h0 is the average gas film clearance, groove depth ratio h=( hh00 + g )/ h, groove width ratio bb=g/( b rg + b ), θ for the gas supply hole angle, ααα123、、 for the wrap angle, θθ12、 is the axial supply hole angle, θ3 is the tangential angle with reversely tangential gas supply holes. Model structure parameters: φ1 = 15mm , φ2 = 0.2mm , β = 70 , h0 = 10µ m , ααα123=26 , = 32 , = 85 , dimensionless eccentricity ratio ε = 0.3 , groove width ratio b = 0.4 , groove depth ratio h = 3.6 . Using the space spherical coordinate system and the helix, the three-dimensional gas film model was established using Pro/E according to the structural parameters of the bearing. Change the default precision in Pro / E to 1µm to meet the high accuracy requirements of the model. The three- dimensional model of the gas film is shown in Fig 2. Fig. 2 Spherical spiral groove hybrid gas bearings gas film three-dimensional model 2.2 Governing equation In this paper, the lubrication flow field in the gas bearing can be described by the mass conservation equation and the momentum conservation equation. (1) Mass conservation equation ∂ρ +=div(ρ u )0 (1) ∂t Where ρ is the air density; t is the flow time; div()ρ u is the divergence of the velocity vector u . (2) The momentum conservation equation ∂∂()ρρu +div()ρµ uu = div ( gradu ) −+ S ∂∂txu ∂∂()ρρv +div()ρµ vu = div ( gradv ) −+ S ∂∂tyv (2) ∂∂()ρρw +div()ρµ wu = div ( gradw ) −+ S ∂∂tzw Where µ is the dynamic viscosity; SSSuvw、、 is the generalized source terms of the conservation of momentum equation; uvw、、 is the velocity vector on the x, y, z direction of the velocity components. 2.3 Finite element mesh model The gas bearing is meshed by FLUENT pretreatment software ICEM CFD. Due to the large difference in size of the spherical spiral groove hybrid gas bearings in the three directions of the space, the gas film thickness is generally within a few tens of microns.
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