Center of rotation

The patented system (15) has stationary disks mounted inside a pressure vessel (horizontal vessel, vertical disks) which is mounted on rollers and can rotate slowly about its axis. A screw conveyor is mounted in the stationary center of rotation it conveys the cake, which is blown off the leaves when they pass above the screw, to one end of the vessel where it falls into a vertical chute. The cake discharge system involves two linear sHde valves that sHde the cake through compartments which gradually depressurize it and move it out of the vessel without any significant loss of pressure. The system rehes entirely on the cake falling freely from one compartment to another as the valves move across. This may be an unrealistic assumption, particularly with sticky cakes when combined with lots of sliding contact surfaces which are prone to abrasion and jamming, the practicality of the system is questionable. 

If the particle is at a given radius from the center of rotation, the plasma now has to apply an inward drag force, E, on the cell to maintain the position of the particle ... 

An uneven distribution of mass about the geometric axis of the system. This distribution causes the center of mass to be different from the center of rotation. 

A deflection of the shaft due to the weight of the rotor, causing further distance between the center of mass and the center of rotation. Additional discrepancies can occur if the shaft has a bend or a bow in it. 

Before the subject of balancing can be properly discussed, unbalance should be described. An unbalance exists when the mass center is displaced from the rotating center. Figure 9-1 a shows a massless disk with a finite mass, m, located at radius, r, from the center of rotation. If the disk rotates at an angular velocity of to, the force, F, exerted by the finite mass, m, is... 

Umdrehung,/. rotation revolution turn, Umdrehungs-achse, /. axis of rotation (or revolution), -bewegung, /. rotatory motion, -geschwindigkeit, /. speed of rotation (or revolution), -punkt, m. center of rotation (or revolution), -richtung, /. direction of rotation (or revolution), -zahl,/. number of revolutions, r.p.m. -zUhler, m. revolution counter. 

Even when parts are precision balanced to extremely close tolerances, vibration due to mechanical imbalance can be much greater than necessary due to assembly errors. Potential errors include relative placement of each part s center of rotation, location of the shaft relative to the bore, and cocked rotors. 

Assembly errors are not simply the additive effects of tolerances, but also include the relative placement of each part s center of rotation. For example, a perfectly balanced blower rotor can be assembled to a perfectly balanced shaft and yet the resultant imbalance can be high. This can happen if the rotor is balanced on a balancing shaft that fits the rotor bore within 0.5 mil (0.5 thousandths of an inch) and then is mounted on a standard cold-rolled steel shaft allowing a clearance of over 2 mils. 

The first pseudo force, Fi, is called the Coriolis force, and its magnitude is directly proportional to the angular velocity of the rotating frame of reference and the linear velocity of the particle in this frame. By definition, this force is perpendicular to the plane where vectors Vi and o are located, Fig. 2.3a, and depends on the mutual position of these vectors. The second fictitious force, F2, is called the centrifugal force. Its magnitude is directly proportional to the square of the angular velocity and the distance from the particle to the center of rotation. It is directed outward from the center and this explains the name of the force. It is obvious that with an increase of the angular velocity the relative contribution of this force... 

Near the surface of the earth, the gravitational acceleration g is essentially constant. For contrast, let us turn our attention next to a centrifugal field, where the acceleration is very sensitive to the distance from the center of rotation. 

The rate of sedimentation is defined by the sedimentation constant 5, which is directly proportional to the polymer mass m, solution density p, and specific volume of the polymer V, and inversely proportional to the square of the angular velocity of rotation o), the distance from the center of rotation to the point of observation in the cell r, and the fractional coefficient /, which is inversely related to the diffusion coefficient D extrapolated to infinite dilution. These relationships are shown in the following equations in which (1 — Vp) is called the buoyancy factor since it determines the direction of macromolecular transport in the cell. 

An alternative approach for determining the molecular weight of a polymer in theta solvents includes the determination of the polymer s concentration at the meniscus (c ,) and at the bottom ic, ) (or alternatively at two other positions Xi and X2) in the cell. These two outstanding positions have a distance of x ix ) and Xh(x2), respectively, from the center of rotation. Then, one obtains the weight-average molecular weight of a polydisperse polymer sample via the equation ... 

Here M is molecular weight, R is the gas constant, T is the absolute temperature in degrees Kelvin, V is the partial specific volume of the solute, p is the density of solution, w is the angular velocity, r is the distance from the center of rotation, and c is the concentration measured at r. Under... 

The force acting on a particle within a centrifugal field is defined by Newton s fundamental force equation FM = mu. Acceleration acting upon the particle, directed loward the center of rotation is a = nr2. Therefore, the centrifugal force ading on the particle is F — mru 2. or expressed as multiples of gravity. 

Torque can be defined as the effectiveness of a force to produce rotation. It is the product of the force and the perpendicular distance from its line of action to the instantaneous center of rotation. 

Figure 4 Spiral trajectory as a particle moves toward the center of rotation.

For case (a), the flow field consists of a single convective cell which circulates around an elliptic point (center) located at X= Y= 0 [28], For case (b) the flow field consists of two counter-rotating cells with centers at X = 0 and Y = 0.58. The cells are separated by the surface Y= 0. For case (c), the flow field is similar to (b) in the sense that the flow field consists of two counter-rotating cells separated by the surface at X= 0. The centers of rotation are at X= 1 and Y = 0. For case (d), the flow field consists of four counter-rotating cells separated by two surfaces at X = 0 and Y = 0. 

M 70a] [P 62] Computational flow simulation of the secondary flow, depicted by velocity vectors, was performed for Dean numbers of 10 and 100 [47]. The helical flow is weak for the smaller Dean number. The center of rotation is located close to the midpoint of the patch. For a Dean number of 100, a notable increase in the relative strength of the helical flow is observed the center of the vortex is shifted towards the outer channel wall. 

---