## 1 Introduction
Reference [11] discussed the possibility of hydrodynamic lubrication in the clearance between the screw groove flank and the gate-rotor tooth flank, pointing out that the necessary conditions for hydrodynamic film including wedges, sufficient sliding velocity and liquid flow from big inlet to small outlet are available. [PERSON] suggested that for the water flooded SSCs, the tribology property may get worse because of low viscosity of water and an acceptable working life may not available [12]. [PERSON] calculated the oil film thickness under a certain load by Martin equation and verified the existence of the oil film between the meshing pair by an experiment utilizing the electrical insulation of the oil [13]. [PERSON] and [PERSON] researched the hydrodynamic properties in SSCs, calculating the oil film pressure distribution by finite difference method and comparing the hydrodynamic lubricating characteristics of SSLT and SCT [14; 15]. [PERSON] investigated the oil film force at both sides of the tooth and indicated that the oil film force on leading flank is always smaller than on trailing flank [16]. This numerical result accords with the actual phenomenon that the gate-rotor was always worn seriously on the leading flank [17]. [PERSON] studied the Couette-Poiseuille flow in two-dimensional asymmetric gaps and gave the approximate solution of the pressure distribution, which could serve as a reference for investigating the pressure distribution in meshing pair gaps [18]. [PERSON] optimized the SCT MPP and developed an oil flooded prototype [19]; nevertheless, this study only concentrated on one MPP and no comparison study was conducted. [PERSON] designed a modeling experiment to simulate the motion of the meshing pair with water lubrication and verified that water in the gap can establish hydrodynamic lubrication and tested the water film force [2], but this experiment ignored the Poiseuille effect and the characteristic of synchronous meshing of the three teeth was not taken into consideration. Further, the hydrodynamic lubrication properties of the SSLT and MCT profiles in water flooded SSCs were compared. The numerical results show that the MCT profile generates greater water film pressure and thrust than SSLT profile [20]. However, this work did not propose a comprehensive and intuitive method to evaluate the lubrication properties of the MPPs. In addition, the influences of the working condition and the machine size were not investigated. The wear resistance performance of the MPP under dry friction, boundary or mixed lubrication can be judged by testing the wear loss of gate-rotors or calculating the Hertz contact stress. However,  
Figure 4: Four kinds of meshing pair profiles (MPPs): (**a**) single straight line type (SSLT) (**b**) single column type (SCT) (**c**) multi straight lines type (MSLT) (**d**) multi column type (MCT). how does one evaluate the fluid film lubrication properties of the MPPs? For one gap between the friction pair such as a journal bearing, the lubrication properties can be well described by the liquid film pressure, thrust or thickness. Nevertheless, there are two gaps at leading and trailing sides of the tooth (See Figure 5). The liquid film pressure, thrust or thickness of one gap cannot represent the tooth lubrication properties. Actually, there are always three teeth of the gate-rotor meshing with the screw at the same time (See Figure 2) and six gaps are generated. Therefore, it is more complex for evaluating the MPPs' lubrication properties. It can be inferred that the gate-rotor will rotate slightly in the screw grooves if the liquid in the six gaps applies a resultant torque on the gate-rotor and the gate-rotor will deflect on the axis of the gate-rotor. Taking one of the teeth to study, it deflects about the gate-rotor axis slightly from EFGH to EFG'H' (See Figure 5). Consequently, a geometric parameter named micro deflecting angle \(\delta\) is proposed to describe the micro deflecting motion.