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Abstract
In this article, numerical analyses of hydrodynamic lubrication and dynamics of the crank, rolling piston, and vane were carried out to study the tribological performance of a rotary compressor. Dimensionless Reynolds equations of journal and thrust bearings in dynamic load condition were derived and solved numerically. To deal with the lubrication of the rolling piston, the effect of the nonuniformity of tangential velocity over the bearing surface on the Reynolds equation was taken into account. In addition, combined with the analyses of dynamics and kinematics of the crank, piston, and vane, the angular velocities of the crank and piston as well as the motion mode between the piston and vane were studied. Analysis results illustrate characteristic oil film pressure distributions of the crank and piston bearings, which are different from that of common journal bearings. Under the influences of dynamic load and eccentricity of the cam, the wedge effect as well as the stretch and squeeze effect contribute greatly to hydrodynamic pressure. The relative motion mode between the piston and vane tip is not always pure sliding but accompanies rolling in some cases, which depends on the magnitude of the friction coefficient between the piston and vane tip. The analysis results are helpful for the improvement of rotary compressor design.
NOMENCLATURE
| c | = | Bearing clearance |
| e | = | Eccentricity of the piston and cam, OcOr in Fig. 2 |
| f | = | Rated frequency of the motor |
| Fb | = | Pressure force of the oil film of the lower bearing |
| Fc | = | Centrifugal force of the eccentric cam |
| Fn | = | Normal force of the vane top |
| Fn′, Fr′ | = | Reaction force of Fn, Fr |
| FP | = | Force acting on the piston in the compression chamber |
| FPc, FPs′, FP′ | = | Pressure force on the vane ends |
| FPs | = | Force acting on the piston in the suction chamber |
| Fr | = | Friction force in general, either sliding friction force or static friction force |
| Frp | = | Pressure force of the oil film acting on the cam |
| Frs | = | Sliding friction force when it is sliding between the piston and vane |
| Frt | = | Static friction force when it is rolling between the piston and vane |
| Fs | = | Friction force of the oil film at the inner surface of the piston |
| Fs1 | = | Friction force of oil film at the surface of the cam |
| Fsp | = | Force of the spring |
| Fth | = | Thrust force of the thrust bearing |
| Fu | = | Pressure force of the oil film of the upper bearing |
| Fx, Fy | = | Pressure force of the oil film acting on the piston |
| G | = | Crank gravity |
| H | = | Dimensionless thickness of the oil film |
| h | = | Thickness of the oil film |
| hl | = | Distance between the center of the lower and upper bearings |
| Jx, Jy, Jz | = | Moment of inertia in the X, Y, and Z directions |
| L | = | Width of bearing, general name of Lb, Lc, and Lu |
| Lb | = | Width of the lower bearing |
| Lc | = | Width of the piston |
| Lu | = | Width of the upper bearing |
| Lz | = | Zb + L/2 |
| Mb | = | Friction moment on two side walls of the piston |
| m | = | Mass of the crank |
| mp | = | Mass of the rolling piston |
| mv | = | Mass of the vane |
| O | = | Origin of the coordinate system of XY |
| Oc | = | Circle center of the cam |
| Or | = | Circle center of the piston |
| = | First- and second-order derivatives of OOr | |
| P | = | Dimensionless pressure p |
| Pc | = | Pressure in the compression chamber |
| Ps | = | Pressure in the suction chamber |
| p | = | Pressure of the oil film |
| p0 | = | |
| R | = | Radius of the bearing |
| r | = | Polar radius of the node of the thrust bearing |
| rb | = | Radius of the lower bearing |
| rc | = | Inner radius of the piston |
| ri | = | Inner radius of the thrust bearing |
| ro | = | External radius of the thrust bearing |
| rp | = | External radius of the piston |
| ru | = | Radius of the upper bearing |
| rv | = | Radius of the vane top |
| Tb, Tu, Trp, Tc, TM | = | Moment of Fb, Fu, Frp, Fc, Fth |
| Tm | = | Motor torque |
| u0 | = | Tangential velocity on the inner surface of the piston |
| uh | = | Tangential velocity on the surface of the cam |
| v | = | Tangential relative velocity between the piston and vane top |
| v0 | = | Normal velocity on the inner surface of the piston |
| vh | = | Normal velocity on the surface of the cam |
| vr | = | Tangential velocity of the piston surface |
| Wcam | = | Work of moment of Frp and Fs1 on the Z axis |
| WFr | = | Work of friction of the upper and lower bearings |
| WMt | = | Work of friction of the thrust bearing |
| WMz | = | Work of moment of Fu and Fb on the Z axis |
| WTm | = | Work of motor torque Tm |
| xc, yc | = | Displacement of the centroid of the crank |
| = | Second-order derivative of xc, yc | |
| xor, yor | = | Displacement of the piston center |
| = | First- and second-order derivatives of xor, yor | |
| xv | = | Displacement of the vane |
| = | First- and second-order derivatives of xv | |
| Zb | = | Coordinate in the axial direction of the bearing, Zb∈[−1/2L,1/2L] |
| α | = | Rotation angle OcOX of the cam in Fig. 2 |
| = | First- and second-order derivatives of α | |
| αt, βt | = | Tilt angle of the crank |
| = | Second-order derivative of αt, βt | |
| β | = | Attitude angle of the piston and cam, angle between X and X′ in Fig. 2 |
| γ | = | Angle OrAO in Fig. 2 |
| δ | = | Thickness of the oil film of the side walls of the piston |
| ϵ | = | Eccentricity ratio of the lower or upper bearings |
| ϵc | = | Eccentricity ratio of the piston and cam, ϵc = e/c |
| η | = | Viscosity of the lubrication oil |
| θ | = | Expanding angle of the bearing |
| κ | = | Angle OrOOv in Fig. 1b |
| = | First- and second-order derivatives of κ | |
| λ | = | Angle between ωc·OOc and u0 in Fig. 2, λ = α − β + θ |
| μ | = | Friction coefficient between the piston and vane top |
| ρ | = | Material density of the piston |
| τ | = | Angle between v0 and the X axis in Fig. 2b |
| ϕ | = | Angle OrOvO in Fig. 1b |
| = | First- and second-order derivatives of ϕ | |
| ψ | = | Attitude angle of the lower or upper bearing |
| ωc | = | Angular velocity of the crank |
| ωr | = | Angular velocity of the piston |
| = | First-order derivative of ωr |
Subscripts
| b | = | Lower bearing |
| d | = | Dimensionless |
| u | = | Upper bearing |