Optimum screw

A screw pump is disclosed in which a screw portion of the pump is constructed having an eccentric portion e, wherein the pitch S of the screw is equal to 4e. The screw channel depth h, is equal to 2e (twice the eccentricity). The resulting screw has an optimum geometric shape allowing maximum pumping capability to be achieved.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to devices for pumping materials and, more 
particularly, to pumps containing a double-threaded stator accommodating a 
single-threaded screw-rotor. The device of the present invention can be 
used for pumping various materials in different branches of industry, 
including petroleum products, oils, latexes, alkalies, clay solutions and 
various liquid food products. 
2. Description of the Related Art 
Known in the art are pumps constructed in accordance with USSR Inv. Cert. 
No. 1,079,894, 1984, MK F 04 c 5/00, in which an outer threaded surface of 
a screw-rotor and an internal surface of a stator (conveying tube) are 
conically shaped. For the purpose of increasing the stability of the pump 
in the course of operation, the diameter of the threaded surface varies 
inversely with variations of the external surface diameter. 
A disadvantage of this construction is that the coupling of the conical 
screw-rotor with the stator does not result in maximum specific volume 
(and, consequently, the capacity) of the area between the rotor threads 
and the stator. 
Also known in the art is a pump constructed in accordance with U.S. Pat. 
No. 4,406,602, having a parabolic screw. However, a disadvantage of this 
construction is that the parabolic curve results in a screw geometry that 
does not maximize the capacity of the pump. 
Another known pump is the single-threaded rotary pump II8-OHA manufactured 
in the USSR. The vertical longitudinal profile of the screw of the II8-OHA 
represents the reiterative concave and convex catenary lines of arbitrary 
curvature. When the screw rotates, the material in the closed spaces 
between the internal and external surfaces of the screw and stator is 
conveyed by pressure from one closed space to the next over the entire 
pump length until it reaches the outlet pipe. The screw pump capacity 
depends on the size of the closed space between the screw and stator 
surfaces, and the maximum size of the closed space depends on the area 
defined by the cross-sectional vertical longitudinal profile of the screw. 
A disadvantage of a pump constructed in this manner is that, for the given 
geometry of the screw, the capacity is not maximized since its vertical 
profile is formed by a catenary line, i.e., by a curve which fails to 
maximize the use of the area in the screw cross-section. 
SUMMARY OF THE INVENTION 
The object of the present invention is to provide a screw that obtains the 
maximum pump capacity while retaining the same general geometric 
parameters of existing screws. 
According to the present invention, the screw portion of the pump is 
constructed having an eccentric portion e, wherein the pitch S of the 
screw is equal to 4e. The screw channel depth h, is equal to 2e (twice the 
eccentricity).

DESCRIPTION OF THE PREFERRED EMBODIMENT 
The present invention is described below with reference to FIGS. 1-3. A 
helical screw rotor 10 is situatable in a conveying tube 20. Conveying 
tube 20 is a cylinder in which the screw rotor 10 will snugly fit, but be 
able to rotate about its longitudinal axis. The basic parameters for 
manufacturing the screw are the outer diameter D, defined as the diameter 
of a circle described by the cross section of a cylinder into which the 
helical screw rotor will snugly fit (essentially, this is the diameter of 
the vertical cross section of conveying tube 20); the cross-section 
diameter (d), selected based on the strength of the material used; the 
eccentricity (e), defined as the distance between the center of the 
circles defined by outer diameter D and cross-section diameter d; the 
channel depth h, defined as the distance between the mid-point of a line 
tangent to the outermost points of two successive spiral convolutions of 
the screw and the point at which a line perpendicularly bisecting said 
tangent line at said midpoint intersects with said screw; and the pitch S 
of the screw, defined as the distance between the outmost points of two 
successive spiral convolutions of the screw. 
The optimum geometry for this screw having the above parameters can be 
achieved by satisfying the following equations: 
EQU Channel depth h=outer diameter D-cross-section diameter d; (1) 
EQU Pitch S=2h; and (2) 
EQU Eccentricity e=1/2D-1/2d. (3) 
It can be derived from the above equations that the channel depth h can be 
determined by the equation h=2e, and the outer diameter D of the screw is 
determined by the equation D=d+2e. 
Such construction forms a conveying cavity 30 between the screw rotor 10 
and the wall of the conveying tube 20. The shape of the cross-section of 
the conveying cavity is semicircular, thereby maximizing the conveying 
capacity of the screw. The semicircle is described by the radius R 
extending from a center C lying on a line tangent to the outermost points 
40 and 45 of two successive spiral convolutions of the screw. The radius R 
is equal to twice the length of the eccentric portion e of the screw and 
is therefore also equal to the screw channel depth h. 
By constructing the screw in the above-described manner, the geometric 
shape of the screw, which is the main working element of the pump, is 
optimized. This results in the maximum pump capacity while retaining the 
general geometric parameters of existing screws. 
To construct the optimum screw shape, the cross-section of a single turn 
over the length of one pitch S was considered. 
To determine the dimensions of the optimum screw shape, it is necessary to 
solve the equation for a line y=f(x) of the length e=S+2h which, when 
going through points 40 and 45 of FIG. 3, defines the maximum conveying 
cavity area F.sub.max. 
The volume Q of disperse medium forced out per revolution of the screw will 
be the maximum when, 
EQU Q=F.sub.max .multidot.L (4) 
where L is the developed length of the helical line at one revolution of 
the screw calculated according to the following equation: 
##EQU1## 
The area limited by the curve y=f(x) is calculated as the functional: 
##EQU2## 
The conditions of constancy of the curve length 1=S+2h is calculated as the 
functional: 
##EQU3## 
Solving the functionals 6 and 7 of the family of curves y=f(x) going 
through points 40 and 45, the extremum (at fixed pitch S and depth h) 
results from the single curve which is essentially the equation of the 
circle: 
##EQU4## 
where .lambda. is the circle radius. The coordinates of the circle center 
are solved by the equations: 
##EQU5## 
As is obvious from FIG. 3, the circle coordinate C lies on the vertical 
line between point 40 and point 45. 
The shape of the cavity 30 formed is a semicircle, resulting in the maximum 
cavity area. 
Referring to FIG. 3, maximum cavity area F.sub.max. is solved as follows: 
EQU F.sub.max =F.sub.sec -2F.sub.tr (10) 
where F.sub.sec is the area of sector ANBM, and 2F.sub.tr is double the 
area of triangle AON; 
##EQU6## 
where .alpha. is central angle ANB; and 
##EQU7## 
Thus, the actual output volume of the screw pump for one revolution will be 
equal to: 
##EQU8## 
Analysis of equation 13 shows that the size of conveying cavity is 
maximized when y.sub.cen is tending to zero, i.e., when circle center 
(point C) lies at the center of the line tangent to points 40 and 45 of 
the screw-rotor. 
The optimum disposition of the zero radius center describing the screw 
cavity profile is in the middle of the line tangent to the screw external 
surface. If the curvature center is higher than point C in the vertical 
line, then the screw profile depth will be decreased and, consequently, 
the capacity will be decreased. 
If the center of curvature is lying in the vertical line below point C, 
then when the screw and stator are coupled, a void area is formed and the 
material being pumped will be rotated without being displaced along the 
longitudinal axis. In addition, the displacement of center C downwards 
will bring about a decrease of the screw cross-section, i.e., a reduction 
of its strength. 
Taking into account that the screw channel depth (h) is equal to double the 
eccentricity (e), to obtain the optimum construction of the screw the 
pitch S should be equal to: 
EQU S=4e, (14) 
and the curvature radius is equal to the double eccentricity. 
The optimum outer diameter D of the screw should be equal to: 
EQU D=d+2e, (15) 
where d is the screw cross-section diameter. 
Testing has been performed comparing a standard screw pump with one 
constructed according to the present invention. As the test results show 
(See Table 1 below), the capacity of the screw constructed according to 
the present invention is 1.7 times greater than the prior art screw 
tested. 
TABLE 1 
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Screw pumps parameters 
Prior Art Present Invention 
______________________________________ 
Step, mm 48 48 
External diameter, mm 
60 60 
Center curvature 30 0 
coordinate, mm 
Screw rotational 175 175 
frequency, rpm 
Amplitude, mm 5 12 
Screw section diameter, mm 
50 30 
Screw capacity, m.sup.3 /min 
8.1 .times. 10.sup.-3 
14.2 .times. 10.sup.-3 
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The many features and advantages of the invention are apparent from the 
detailed specification and thus it is intended by the appended claims to 
cover all such features and advantages of the invention which fall within 
the true spirit and scope thereof. Further, since numerous modifications 
and changes will readily occur to those skilled in the art, it is not 
desired to limit the invention to the exact construction and operation 
illustrated and described, and accordingly all suitable modifications and 
equivalents may be resorted to, falling within the scope of the invention.