# Structural Design and Optimization of Herringbone Grooved Journal Bearings Considering Turbulent
## 1 Introduction
[PERSON] et al. [18] proposed a bearing with a stepped bottom surface. By optimizing geometric parameters, a larger oil film bearing load capacity and stiffness were obtained. Afterwards, [PERSON] et al. [19] first studied and analyzed herringbone grooved journal bearings on a two-dimensional plane and found that the surface morphology of the herringbone groove can improve the stability of the bearing. [PERSON] et al. [20] found that when the eccentricity is smaller, the stiffness coefficient of the herringbone grooved journal bearing is greater than that of the ordinary smooth journal bearing, and its bearing load capacity is effectively improved, which attributed to the pumping effect and step effect of the herringbone grooved journal bearing. [PERSON] et al. [21] analyzed the static and dynamic performance of herringbone grooved journal bearings under turbulent flow and slip conditions. [PERSON] et al. [22] studied the influence of herringbone groove structure parameters on the performance of thrust bearings and obtained bearing structure parameters that make the bearing perform well. [PERSON] et al. [23; 24] used a new elastic fluid lubrication numerical algorithm to analyze the influence of different chevron bottom shapes on bearing performance. As a result, the triangle on the left side of the surface can significantly improve bearing lubrication performance. Liquid metal is an amorphous and flowable metal. The amorphous liquid form of liquid metal gives it excellent electrical and thermodynamic properties. It is currently widely used in batteries, power equipment, biomedical, 3D printing, and computing fields [25; 26; 27]. In the 1960s, it was found that the application of liquid metal to the nuclear power magnetohydrodynamic bearing can greatly improve the bearing load capacity [28]. [PERSON] et al. [29] of the University of Texas studied the common liquid metal phenomenon at the armature-rail interface. They found that the solid armature track will not corrode when lubricated by the quenched metal deposit of the liquid aluminum. [PERSON] [30; 31; 32; 33] of Northwestern Polytechnical University made a preliminary evaluation of the antifriction performance of gallium-based liquid metal. In their friction experiments, they found that the surface of the material lubricated with gallium liquid metal had no obvious dent, while the surface of the material not lubricated with gallium liquid metal had obvious wear. [PERSON] and others of the State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences [34] used the SRV-IV friction and wear tester to carry out the lubrication performance experiment of liquid metal in a wide temperature range from \(-10\)\({}^{\circ}\)C to 800 \({}^{\circ}\)C. The results show that the liquid metal exhibits excellent tribological properties at \(-10\)\({}^{\circ}\)C and 20 \({}^{\circ}\)C. [PERSON] et al. [35] of Beijing Aerospace Long March Aircraft Research Institute studied the flow of liquid metal in U-shaped pipes under the influence of magnetohydrodynamics. The results of the numerical simulation show that when the flow enters the central area of the U-shaped flow channel, a spiral flow is formed. Its stirring effect may be beneficial to the heat exchange in the pipeline. At present, only a few people are conducting research on the performance of bearings lubricated with liquid metal. Due to the low viscosity of liquid metal, this paper adopts a turbulent flow calculation model and considers the special structure of the herringbone grooves. At present, the groove width of the herringbone grooved journal bearing studied is constant. In order to improve the performance of the traditional constant-width herringbone grooved journal bearings, the convergent herringbone grooved journal bearings were designed.