Title of Invention

A PLURAL SCREW POSITIVE DISPLACEMENT MACHINE

Abstract Plural Screw positive Displacement Machines Helical intermeshing main and gate rotors (1,2) are mounted for rotation about their axes in respective interscting bores in a housing. The profiles of the rotors as seen in cross-section are generated by the same rack formation (Figure 3). The high pressure flanks of the lobes of the main rotor (l) and of the grooves of the gate rotor (2) are both generated by a preferably cycloidal portion ( GHA) of the rack R. Figures 2 and 3.
Full Text

The present invention relates to plural screw positive displacement machines comprising a housing having at least two intersecting bores the axes of which are coplanar in pairs, and usually parallel,' and male and female rotors mounted for rotation about their axes which coincide one with each of the housing bore axes, the rotors each having helical lands which mesh with helical grooves between the lands of at least one other rotor, .the or each male rotor having as seen in cross section a set of lobes corresponding to the lands and projecting outwardly from its pitch circle, the or each female rotor having as seen in cross section a set of depressions extending inwardly of its pitch circle and corresponding to the grooves of the female rotor(s), the number of lands and grooves of the male rotor(s) being different to the number of lands and grooves of the female rotor(s).
Examples of such machines, which may be used as compressors or expanders are disclosed in GB 1,197,432, GB 1,503,488 and GB 2,092,676.
A plural screw positive displacement machine according to the invention is characterised in that, as seen in cross section, the profiles of at least those parts of the lobes projecting outwardly of the pitch circle of the male rotor (s) and the profiles of at least the depressions extending inwardly of the pitch circle of the female rotor(s) are generated by the same rack formation, the latter being curved in one direction about the axis of the male rotor(s) and in the opposite direction about the axis of the female rotor(s), the portion of the rack which

generates the higher pressure flanks of the rotors being generated by rotor conjugate action between the rotors.
Advantageously, a portion o£ the rack, preferably that * portion which forms the higher pressure flanks of the rotor lobes, has the shape of a cycloid. Alternatively, this portion may be shaped as a generalized parabola, for example of the form: ax+by^l.
Normally, the bottoms of the grooves of the male rotor(s) lie inwardly of the pitch circle as Medendum" portion and the tips of the lands of the female rotor(s) extend outwardly of its pitch circle as ^addendum" portions. Preferably, these dedendum and addendum portions are also generated by the rack formation.
The invention will now be described by way of example with reference to the drawings, in which:
Figure l is a diagrammatic cross section of a twin screw
machine;
Figure 2 shows one unit of a rack for generating the
profiles of the rotors sbowxi in Figure 1/
Figure 3 shows the relationship of the rack formation of
Figure 2 to the rotors shown in Figure l, and
Figure 4 shows the outlines of the rotors shown in Figure
3 superimposed on a prior art rotor pair by way of
comparison.
The main or male rotor l and gate or female rotor 2 shown in Figure l roll on their pitch circles, Plf P2 about their centres 0* and 02 through respective angles i|f and T-zx/ZaiMr/i

The pitch circles P have radii proportional to the number of lands and grooves on the respective rotors.
If an arc is defined on either main or gate rotor as an arbitrary function of an angular parameter $ and denoted by subscript d;

the corresponding arc on the other rotor is a function of
both 0 and ty ;- '

ty is the rotation angle of the main rotor for which the primary and secondary arcs have a contact point- This angle meets the conjugate condition described by Sakun in: "Vintovie kompressori", Mashgiz Leningrad 1960


which is the differential equation of an envelope of all M" curves. Its expanded form is;

This can be expressed as a quadratic equation of sin ty. Although it can be solved analytically, its numerical solution is recommended due to its mixed roots. Once determined, \|r is inserted in (3) and (4) to obtain conjugate curves on the opposite rotor. This procedure requires the definition of only one given arc. The other arc is always found by a general procedure.
These equations are valid even if their coordinate system is defined independently of the rotors. Thus, it is possible to specify all ud" curves without reference to the rotors. Such an arrangement enables some curves to be expressed in a more simple mathematical form and/ in addition, can simplify the curve generating procedure.
A special coordinate system of this type is a rack (rotor of infinite radius) coordinate system, indicated at R in Fig. 2. An arc on the rack is then defined as an arbitrary function of a parameter 4>:


Secondary arcs on the rotors are derived from this as a function of both, and iir.

ilr represents a rotation angle of the rotor where a given arc is projected, defining a contact point. This angle satisfies the condition (5) which is:

The explicit solution i|r is then inserted into (9) and (10) to find conjugate arcs on rotors. Fig. 3 shows the rack and rotors generated by the rack.
Wherever curves are given, their convenient form may be:

which is a *general circle" curve. For p = q = 2 and a a Jb « 1/r it is a circle, unequal a and b will give ellipses, a and b of opposite sign, hyperbolae, p = 1 and g - 2 will give parabolae.
In addition to the convenience of defining all given curves with one coordinate system, rack generation offers

two advantages compared with rotor coordinate systems: a) a rack profile represents the shortest contact path in comparison with other rotors. This means that points from the rack will be projected onto the rotors without any overlaps or other imperfections, b) a straight line on the rack will be projected onto the rotors as involutes.
In order to minimize the blow hole area on the high pressure side of a rotor profile, the profile is usually produced by a conjugate action of both rotors, which undercuts the high pressure side of them- The practice is widely used; thus in GB-A-1197432, singular points on main and gate rotors were used, in GB-A-2Q92676 and 2112460 circles, in GB-A-21G6186 ellipses were used and in EP-0166531 parabolae were used. An appropriate undercut has not hitherto been achievable directly from a rack. In arriving at the invention, it has been found that there exists only one analytical curve on a a rack which can exactly replace the conjugate action of rotors. In accordance with a preferred aspect of the present invention, this is a cycloid, which is undercut as an epicycloid on the main rotor and as a hypocycloid on the gate rotor. This is in contrast to the undercut produced by singular points which produces epicycloids on both rotors. The deficiency of this is usually minimized by a considerable reduction in the outer diameter of the gate rotor within its pitch circle. This reduces the blow-hole area, but also reduces the throughput.
A conjugate action is a process when a point {or points on a curve) on one rotor during a rotation cuts its (their) path(s) on another rotor. An undercut occurs if there exists two or more common contact points at the same time,

which produces ^pockets" in the profile. It usually happens if small curve portions (or a point) generate long curve portions, when a considerable sliding occurs.
This invention overcomes this deficiency by generating the high pressure part of a rack by a rotor conjugate action which undercuts an appropriate curve on the rack. This rack is later used for the profiling of both the main and gate rotors by the usual rack generation procedure.
The following is a detailed description of a simple rotor lobe shape of a rack generated profile family designed for the efficient compression of air, common refrigerants and a number of process gases, obtained by the combined procedure. This profile contains almost all the elements of modern screw rotor profiles given in the open literature, but its features offer a sound basis for additional refinement and optimisation.
The coordinates of all primary arcs on the rack are summarised here relative to the rack coordinate system.
The lobe of this profile is divided into several arcs. The divisions between the profile arcs are denoted by capital letters and each arc ia defined separately, as shown in Fig. 2.
Segment A-B is a general arc of the type
ax§ + by% = ion the rack with p = 0.43 and q « 1.
Segment B-C is a straight line on the rack, p « q - 1.

Segment C-D is a circular arc on the rack, jp = q =* 2, a * b.
Segment D-E is a straight: line on the rack.
Segment B-F is a circular arc on the rack, p « g * 2, a *
Segment F-G is a straight line.
Segment G-H is an undercut of the arc G2-H3 which is a general arc of the type ax| + byl fc= 1, p = 1, the main rotor.
Segment H-A on the rack is an undercut of the arc Ax-tix which is a general arc of the type a*§ + by% - 1, p ~ 1, At each junction A,..,-K, the adjacent segments have a common tangent.
The rack coordinates are obtained through the procedure inverse to equations (7)-(11),
As a result, the rack curve E-H-A is obtained and shown in Fig, 3.
Figure 4 shows the profiles of main and gate rotors 11,12 generated by this rack procedure superimposed on the well-known profiles 21,22 of corresponding rotors generated in accordance with GB-A-2 092 676, in 5/7 configuration.

With the same distance between centres and the same rotor diameters, the rack-generated profiles give an increase in displacement of 2.7% while the lobes of the female rotor are thicker and thus stronger.
Tn a modification of the rack shown in Fig. 3, the segments GH and HA are formed by a contiuous segment GHA of a cycloid of the form: y=R0cos-e-Rp, y=R0sinX"RpT# where R-, is the outer radius of the main rotor (and thus of its bore) and RP is the pitch circle radius of the main rotor.
The segments AB, BC, CD, DS, EF and FG are all generated by equation (l2)above. For AB, a^b,p«0.43, q=l. For the other segments, a~b*l/r,and p=q=2. The values of p and q may vary by ±10%- For the segments BC, DE and FG r is greater than the pitch circle radius of the main rotor, and is preferably infinite so that each such segment is a straight line* The segments CD and EF are cicular arcs when p=q=2, of curvature a*b.





Claims
1. A plural screw positive displacement machine
comprising a housing having at least two intersecting
bores the axes of which are coplanar in pairs, and male
and female rotors mounted for rotation about their axes
which coincide one with each of the housing bore axes, the
rotors each having helical lands which mesh with helical
grooves between the lands of at least one other rotor, the
or each male rotor having as seen in cross section a sat
of lobes corresponding to the lands and projecting
outwardly from its pitch circle, the or each female rotor
having as seen in cross section a set of depressions
extending inwardly of its pitch circle and corresponding
to the grooves of the female rotor(s), the number of lands
and grooves of the male rotor(s) being different to the
number of lands and grooves of the female rotor(s),
characterised in that, as seen in cross section, the
profiles of at least those parts of the lobes projecting
outwardly of the pitch circle of the male rotor(s) and the
profiles of at least the depressions extending inwardly of
the pitch circle of the female rotor(s) are generated by
the same rack formation, the latter being curved in one
direction about the axis of the male rotor(s) and in the
opposite direction about the axis of the female
rotor(s),the portion of the rack which generates the higher pressure flanks of the rotors being generated by rotor conjugate action between the rotors.
2. A machine according to claim 1, wherein the bottoms
of the grooves of the male rotor(s) which lie inwardly of
the pitch circle as Medendum" portion and the tips of the
lands of the female rotor(s) which extend outwardly of its

pitch circle as ^addendum" portions are also generated by the rack formation,
3. A machine according to claim 1 or 2, wherein the portion of the rack which generates those pares of the lobes extending outwardly of the pitch circle of the male rotor is formed toy a straight line CB merging at B into a curve BA of the type axp+by*=if where p«G.43, which curv£ BA in turn merges at A into a curve AH of the type ax+by^i, where q=0.25 and which curve AH merges at H into a curve HG of the type ax+by*5*! where q*0.75, and the curve HG merges at G into a straight line GF.
4. A machine according to claims 2 and 3, wherein the portion of the rack which generates those parts of the grooves of the male rotor which lie inwardly of the pitch circle is formed by a curve DEF consisting of a straight line DE tangential at D to the curve CD and a circular arc EF to which the line D£ is tangential at E and which merges with the curve CD at D.
5. A machine according to claim 1 or 2, wherein a portion (GHA) of the rack which generates at lease a part of a rotor lobe flank is a cycloid.
6. A machine according to claim 5, wherein the said rotor lobe flank i$ the higher pressure flank.
7. A machine according to claim 5 or 6, wherein at least a portion of the other flank of the lobe is generated by a rack portion of the form axp +bya*l, where p=G.4'3±lO%,
qssl + 10%, a=b.

8. A machine according to claim 1, wherein root portions of the main rotor and tip portions of the gate rotor are generated by rack portions of tha form axp +by^-l where paq*2±10%f a»b=the curvature.
9 . A machine according to claim 8, wherein the rack segments comprise, in sequence, the cycloid GHA, the lobe flank portion AB of claim 6, a substantially straight line portion BC, a substantially circular arc CD, a substantially straight line portion DE and a further substantially cicular arc FG.
10. A plural screw positive displacement machine substantially as herein described with reference to the accompanying drawings.


Documents:

1030-mas-1997- abstract.pdf

1030-mas-1997- claims duplicate.pdf

1030-mas-1997- claims original.pdf

1030-mas-1997- correspondence others.pdf

1030-mas-1997- correspondence po.pdf

1030-mas-1997- description complete duplicate.pdf

1030-mas-1997- description complete original.pdf

1030-mas-1997- drawings.pdf

1030-mas-1997- form 1.pdf

1030-mas-1997- form 26.pdf

1030-mas-1997- form 3.pdf

1030-mas-1997- form 4.pdf

abs-1030-mas-1997.jpg


Patent Number 207563
Indian Patent Application Number 1030/MAS/1997
PG Journal Number 26/2007
Publication Date 29-Jun-2007
Grant Date 14-Jun-2007
Date of Filing 15-May-1997
Name of Patentee M/S. CITY UNIVERSITY
Applicant Address NORTHAMPTON SQUARE, LONNDON, EC1V OHB
Inventors:
# Inventor's Name Inventor's Address
1 NIKOLA-RUDI STOSIC 29B KING EDWARD ROAD, BARNET, HERTS, EN5 5AW.
PCT International Classification Number F04C18/08
PCT International Application Number N/A
PCT International Filing date
PCT Conventions:
# PCT Application Number Date of Convention Priority Country
1 9610289.2 1996-05-16 U.K.