The Influence of Fluctuations in the Crankshaft Speed on the Tip Seal Acceleration of the Wankel Rotary Compressor

The acceleration of the tip seal in the rotor of a Wankel rotary compressor is a function of the radii of the fixed and moving pitch circles, the number of lobes, the trochoid ratio, and the speed and acceleration of.the crankshaft. The equations for the tip seal acceleration are well-known and have been used, in conjunction with the compression forces, to determine the spring forces that are necessary to maintain contact between the tip seal and the housing. The equations that are available in the literature, however, are only valid for a constant crankshaft speed; i.e., they do not account for fluctuations in the crankshaft speed. The major purpose of this paper is to derive equations that will provide insight into the tip seal acceleration when fluctuations in the crankshaft speed are included in the analysis. For purpose of illustration, the effects on the tip seal acceleration due to a cyclic fluctuation in the crankshaft speed is compared to the effects using a nominal value. The results presented in the paper can be used by the designer to detect and, thereby, avoid possible leaks in the sealing or unnecessary wear of the seals. NOMENCLATURE The following notation is used consistently throughout this paper: X 1 0 1 Y 1 =fixed Cartesian reference frame (attached to the fixed pitch circle) X2 0 2 Y 2 =moving Cartesian reference frame (attached to the rolling pitch circle) 0 1 = center of the fixed pitch circle , 0 2 = center of the rolling (or generating) pitch circle r1 = radius of the fixed pitch circle = r2 ( T1 ) IT , r2 = radius of the rolling pitch circle T = number of generating lobes fixed to the rolling pitch circle T1 = number of generated lobes on the fixed pitch circle C = center of the generating pin (or arc) , r = radius of the generating pin rc = radius of the epitrochoidal path of point C = 0 2 C e = length of the crank, or trochoid eccentricity = 0 2 0 1 = r2 r1 = r2IT P = pole of the rolling pitch circle (coincident with the instant center) cp = input position (position of the crank relative to the X1-axis) cp = crankshaft speed , $ = crankshaft acceleration a = input variable for harmonic function = cp I T trochoid ratio = rc I r2 and llH = harmonic ratio