Mixed Lubrication Analysis of Vane Tip in Rotary Compressor

This paper shows the mixed lubrication analysis between the vane tip and rolling piston in a rotary refrigerant compressor, coupling the motion equations of vane and rolling piston, the elastohydrodynamic lubrication (EHL) analysis of line contact and the equations of viscosity characteristics of lubricating oil as a function of oil pressure, oil temperature and concentration of refrigerant. The pcY value, that is, the product of solid contact pressure by sliding speed between vane tip and rolling piston, has been calculated. The calculations have been made for various operation conditions and viscosity grades of oil. NOMENCLATURE a: thickness of vane, m Is: length of cylinder slot, m m/s b: halfHertzian length (=R(8w!Jr)), Me: moment of viscosity friction v: relative velocity (=romp+(ro+rv)a), m between rolling piston and shaft, m/s C: constant N · m w: load of vane tip per unit of width Cp: specific heat of vane and piston, Mp: moment of viscosity friction of (=Fvnllp), Nlm 480 J/(kg · K) piston end face, N · m x: coordinate, m £:equivalent Young's module ofvane Mv: rotational moment acting on vane, xe: location where oil film breaks, m and piston, 165 GPa N · m Xend: outlet location, m e: eccentricity (=Rero), m mo: viscosity-temperature property Xm;n: inlet location, m Fe,: viscosity resistance between from the ASTM-Walther equation xv: displacement of vane piston and cylinder, N (=ASTM slope/0.2) (=(rv+ro)cosa+ecosB), m FnJ, Fn2: normal force between vane mv: mass of vane, kg a: attitude angle of rolling piston, rad and cylinder slot, N 0: center point of cylinder ao: viscosity-pressure coefficient, Pa·' Fs: spring force, N Op: center point of eccentric shaft p: viscosity-temperature coefficient, Ft], F12: friction force (=psFn1, JlsFn2), pe: solid contact pressure, Pa 0.025 °C-' N Peom: compression chamber pressure, Fv: viscosity friction force of vane end Pa face, N pd: discharge pressure, Pa Fvn: load of vane tip, N P/ oil film pressure, Pa Fv,: friction force of vane tip, N Psue: suction pressure, Pa F vx, F vy: gas force in direction of x, y R: equivalent curvature radius axes acting on vane, N between vane and rolling piston h: nominal oil film thickness, m (l!R=llro+llrv), m h0 : central oil film thickness, m Rc: radius of cylinder, m h,: average oil film thickness, m r: constant lp: inertial moment of piston, N · m r,: inner radius of piston, m KJO: thermal conductivity of lubricant, ro: outer radius of piston, m 0.125 W/(m· K) rv: radius of vane tip, m KP: thermal conductivity of vane and S: non dimensional average shear piston, 38 W/(m·K) stress kc: constant t: time lp: length of piston, m u: entrainment velocity (=Liu/2+rvci), Fifteenth International Compressor Engineering Conference at Purdue University, West Lafayette, IN, USAJuly 25-28, 2000 LIT: temperature rise of lubricant, aC LITe: temperature rise caused by solid contact, oC Ll'lf: temperature rise at parallel area, oc LIT;n: temperature rise at intake area, oc Llu: sliding velocity at vane tip contact (=romp), m!s 5: elastic deformation, m 7]: viscosity of oil dissolving refrigerant, Pa·s 7]o: viscosity of oil dissolving refrigerant at atmospheric pressure, Pa · s B: rotational angle of shaft, rad p: coefficient of boundary friction