Vibration Analysis of Rotary Compressors

By theoretically analyzing dynamic behavior of the crankshaft, the rolling piston and the blade inrolling-piston rotary compressors, constraint forces and sliding speed at each pair of movable machine elements were obtained, and unbalanced inertia forces and compressor vibrations were evaluated. It was concluded that theoretical results have a goodagreement with experimental ones. Moreover, it was revealed that one of major factors which cause compressor vibrations is speed variation of the crankshaft and compressor vibrations are not affected by rolling behavior of the piston. of high volumetric efficiency and small mechanical loss and they are compact and light in weight, compared to corresponding reciprocating compressors [ 1 4 ]. In rotary compressors, moreover, vibrations are comparatively small in amplitude as they have few reciprocating elements, and hence have been considered suitable for lowering the noise in air-conditioning equipment. Due to these properties, most air-conditioning compressors presently used in Japan are of the rolling-piston rotary type. It is likely that the popularity of rolling-piston compressors will continue to increase, and at the same time strong demands for reducing vibration and noise which arise from the compressors will also ~ise. To cope with these demands, unbalanced inertia forces due to themotion of machine elements, and vibrations caused by those forces have to be evaluated before a design which reduces the revealed vibrations most effectively can INTRODUCTION Rolling-piston rotary compressors have the advantages --------------Nomenclature a"' 1/2 of blade thickness b"' contact length of blade & cylinder B "' equivalent length of plain bearing a = clearance of piston & crankpin a8 "' clearance of crankshaft & bearing [C] =damping coefficient matrix Cf, Cfa• Cfs• cpa = friction & pressure constant of oil film e =eccentricity of piston center [E] =transfer matrix [F] =exciting force matrix fl. f2 =functions of e Fa= frictional force on -piston Fan, Fat"' constraint & frictional forces on piston & cylinder Fd =frictional force on blade ends Fen= force on piston & crankpin Fgx,Fgy =constraint forces on crankshaft & bearing Fgn],Fgn2,Fgt1> Fgt2 =constraint & frictJ.onal forces on cylinder& blade Fp"' gas force on piston F'f;8 ,Fpa =gas forces on cylinder wall F qx. F qy = gas forces on blade F8 = spring force on blade Fvn.Fvt =forces on blade & piston Fx,Fy,Fz =exciting forces on cylinder center hbu, hbz =height of balancers from cylinder center I a= inertia moment of crankshaft Ip "'inertia moment of piston Ix,Iy,Iz =inertia moment of camp. k =spring constant [K] "'spring constant matrix Z = depth of cylinder Zp = length of piston bearing Zs = length of crank journal M =mass of whole compressor [M] =mass matrix mbu> mb z =mass of balancers ma = total mass of crankpin, crankarm & balancers mp = piston mass mv =blade mass Mp =frictional moment on piston & crankpin Ma =frictional moment on piston ends Mm =motor torque Mq =moment due to gas forces on blade Ms"' frictional moment on crankshaft & journal Mx,My,Mz "'moment on cylinder center Pa,Ps =pressure in compression & suction chamber Pd =pressure inside closed housing R = cylinder radius r,r0 =outside & inside piston radius rbu,rbz =eccentricity of balancers 27S r 8 =radius of crankshaft rv =radius of blade tip VBn =sliding speed of blade & piston Vpc = sliding speed of piston & crankpin [X] =displacement matrix X, Y, Z"' orthogonal coordinate x,y,z =moving orthogonal coordinate x0 , y0 , z0 =X ,Y, Z coordinate of cylinder center XG, YG• ZG =parallel displacement x0 a.Yoa =coordinate of ma center Xop>YOp =coordinate of piston center xv =variable of blade motion a =angle of OG2 & x axis Yl> Y2, Y3, Y4, Ys =function of e Dpb =piston & blade ends clearance Ope"' minimum clearance of piston & cylinder ol,o2,o3,a4 =constant +1 or -1 ~:: "'eccentricity of me gravity center n =rotating angle of Fen ng"' dynamic viscosity of R22 no= dynamic viscosity of oil 8 =rotating angle of crankshaft BXG, BYG, SzG =rotational displacement J.lg, llV = friction coefficient I; = angle of OvOp & x axis ~ "'rotating angle of piston be developed. In this paper, an analytical method to evaluate the vibrations is established, and the experimental confirmation is shown. Discharge pipe Acr:wrrutator ,/ Spring Btade Movable machine elements in a rolling-piston compressor are the rotating crankshaft, the rolling piston and the reciprocating blade. Each machine element moves in connection with the others. Now, theblade motion is a function of the turning angle of the crankshaft, provided that the blade top moves in contact with the piston. In the case of the piston, however, its rotating motion is independent of the crankshaft motion and is determined by all frictional forces exerted on it. Therefore, both equations of the crankshaft motion and the piston motion have to be simultaneously solved to reve_al the dynamic behavior of the movable machine elements. Motor First, in this study, the equations of motion of the movable machine elements are derived, and then they are applied to a small rolling-piston rotary compressor, and one concrete example in which the rotating behavior of the crankshaft and the piston is obtained by numerical calculation is shown. Secondly, the equations which represent unbalanced inertia forces caused by the movable machine elements are presented, and the characteristics of the unbalanced inertia forces and the compressor vibrations which they cause are revealed by numerical calculation. Furthermore, the obtained compressor vibrations are compared with experimental results, and a major factor inducing compressor vibrations is examined. Thirdly, the effect of the piston motion on the compressor vibrations is examined by comparing the approximate solutions to the problem of the vibrations obtained under an assumption that the rotating speed of the piston is zero with exact solutions obtained by precise analysis of the rotating motion of the piston. ROLLING-PISTON ROTARY COMPRESSOR Fig.l(a) shows the construction of a rolling-piston rotary compressor which is used for air-conditioners of the refrigerating capacity 1755 kcal/h. The motor stator and the cylinder block are fixed inside the closed housing which is suspended with three rubber springs on a base. The refrigerant(R22) is sucked into the cylinder through the accumulator. The compressed refrigerant is discharged inside the closed housing and transfered to a condenser through the discharge pipe on the top of the closed housing. The dimensions of the closed housing are 110 mm diameter and 212 lliill high, and the mass of the whole compressor is 8.7 kg. The motor is a single phase induction motor. The synchronous speed is 3600 rpm and the power is 0. 55 kW. The machine part compressing the refrigerant is soaked in the lubricating oil and the gas leakage from the compression chamber isprevented by oil sealing. Fig.l(b) shows the A-A' crosssection of the machine part. The machine part consists of the cylinder with bore 39 mm, the reciprocating blade with thickness 3.2 =, the piston with outside diameter 32.5 mm and the crankshaft system which is composed of the crankshaft, the crankpin and the motor rotor. The eccentricity of the piston center Op from the rotating crankshaft center 0 is 3.26 mm and the cylinder depth is 28 rnm. The center axis of the blade coincides with the cylinder center 0 and the blade tip with radius 3. 2 rnm is p.ushed on the piston by the spring force and the gas force which are 276 Crcmk Crank Suction pipe