Procedure for design calculation of cantilevered shafts in equipment with mixing devices

Abstract

The design calculation procedure set forth in this article is based on a solution of the problem described in [1 ]; this procedure is suitable for the design of cantilevered shafts of constant or variable section, with any number of mixing devices. In calculating a constant-section shaft, the following are given (see also Fig. 1): N is the maximum power used by the shaft, in W; w is the working angular velocity of the shaft, in rad/sec; n is a standardizing factor accounting for the viscosity and density of the medium being mixed; p is the density of the shaft material, in kg/mS; E is the modulus of elasticity of the shaft material, in N/m2; e is the eccentricity of the center of equivalent mass of the shaft with the mixing devices, in m; l is the length of the supported part of the shaft, in m; L is the length of the overhung part of the shaft, in m; x is the distance to the stuffing box from the start of the overhung part of the shaft, in m; M i are the masses of the mixing devices, in kg (here i = 1, 2, 3 ..... s, where s is the number of mixing devices on the shaft); ~i are the distances to the centers of gravity of the masses M i from the start of the overhung part of the shaft, in m; I i are the moments of inertia of the masses Mi, in kg-m2; era is the allowable stress for the shaft material, in N/m2; 5 is the allowable runout (wobble) of the shaft, in m; Wa is the allowable deflection of the shaft at the location of the stuffing box, in m; ,~a is the allowable angle of twist of the shaft per meter of length, in rad/min; ,~a is the allowable angle of rotation of the shaft sections at the locations of the bearings, in rad. According to RTM [Guideline Technical Material] 145-66 [2], at the sites of the stuffing-box seals, the allowable shaft deflection should be within the limits 0.5-10-4- < wa -< 10 -4 m, the allowable angles of rotation of the shaft sections with radial bearings being ,~a = 0.01 rad, and for spherical bearings Sa = 0.05 rad. According to the data given in [3], the allowable twist angle per meter of shaft length Ca = 4.36. 10 -3 rad /m.