CA 02393411 2002-06-04
INTERNAL-AXIS SCREW DISPLACEMENT MACHINE
The invention relates to a displacement machine, in particular for use
as a vacuum pump, with screw rotors, with a thread number ratio of (x+1 ):x,
in
mutual, meshing engagement, movably disposed in an axis-parallel way in a
housing, which screw rotors form variable chambers, axially staggered,
shifting
during operation, and which screw rotors are designed in an internal-axis
construction as hollow outer rotor with inner spiral thread and inner rotor
with
outer spiral thread, with varying or constant pitches as well as varying screw
rotor
transverse proftles in each case along the rotor axes.
Z 0 In the following, external-axis and internal-axis screw-type
displacement machines are compared to one another, with reference to some
typical sets of problems. Internal-axis machines having the same output can be
built more compactly than external-axis ones. With both types, the
synchronization of the rotors can be achieved via toothed wheels or
synchronous
belts, for example, whereby dry operation, aimed-far nowadays for many
applications, is easier to achieve with internal-axis machines. Rotor cooling
is
also easier to achieve with internal-axis machines, and pumps of this type are
thermally less critical. Manufacture of the rotors is relatively costly for
both types
of screw-type displacement machines. Metallic materials are primarily used,
which are not infrequently cast, metal-removing machining being practically
20 always necessary, however. With internal-axis machines sometimes at least
one
of the rotors has to be manufactured in multiple pieces so that the rotors can
be
mounted at all. With external-axial, screw-type displacement machines an inner
compression of up to about 1:3 is attainable without any difficulty. Internal-
axis
machines, on the other hand, achieve an inner compression of up to about 1:5
without any difficulty. Equipping external-axis machines with slides is known,
when a limitation of pressure is supposed to be achieved, which can be
advisable
with high inner compression in order to avoid an overheating of the machine.
In
the case of internal-axis machines, exhaust lead channels and corresponding
valves can be installed for this purpose. Adjustment of the gap between rotor
outer diameter and housing is known with external-axis machines, for example
in
order to take into consideration the thermal expansion during operation. Such
an
30 adjustment is extremely expensive. Adequate adjustment in the case of
internal-
axis machines is not known to the applicant. The measuring and adjusting of
the
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CA 02393411 2002-06-04
play between the rotors tends to be more difficult to accomplish with internal-
axis
machines than with external-axis machines. Mounting of the rotors in the
housing
takes place relatively simply with external-axis machines, at least with
rotors
having a cylindrical outer generated surface. With state-of the-art internal-
axis
s machines, the inner rotor must be inserted into the outer rotor with a
rotating
movement. With rotors having variable pitch, however, this is usually not
possible, so it is often necessary to construct one of the rotors in multiple
pieces.
Finally, for the reasons just mentioned, access to the pump chamber for repair
and maintenance purposes is usually easier with external-axis machines than
with
lo internal-axis ones.
Other sets of problems, such as dynamic sealing or rotor balancing are
very similar for both of the said types of machines. All in all, however, for
the
reasons explained above, the internal-axis machines offer a better point of
departure for attaining the goals mentioned further below.
is Disclosed in the French patent document 695539 is a displacement
machine usable as a pump or a motor, in which a hollow outer rotor with inner
spiral thread and a solid inner rotor with at least one outer spiral thread
are in
meshing engagement with each other. The rotors are disposed axis-parallel, and
the outer rotor has a number of threads per unit greater by one compared to
that
20 of the inner rotor.
The Swedish patent document 85331 shows, for example in Figure 14,
a displacement machine with rotors disposed axis-parallel in mutual meshing
engagement, which are designed as hollow outer rotor with inner spiral thread
and inner rotor with outer spiral thread, in an internal-axis construction.
2s Achieved in none of these machines, however, is a variable pitch or an
absence of axial undercutting of the spiral threads of the rotors.
Disclosed also in the German published patent application 2434782 is
a displacement machine, in which a hollow outer rotor with inner spiral thread
and
an inner rotor with outer spiral thread are in meshing engagement with each
other,
so AMENDED PAGE
CA 02393411 2002-06-04
2a
the profiles over the length of the rotor having an alternating pitch. So that
these
rotors can be mounted, the outer rotor is designed in two pieces.
Besides the above-described internal-axis screw-type displacement
machines, internal-axis machines are also known in which the rotor profile has
s spirals with axially progressive profile contour. Examples of such machines
are
described in the patents U.S. 5,603,614 and CH 263 376. Unlike machines of the
screw type, the rotors in these machines turn in the ratio 1:1.
With the state of the art as the point of departure, the objects of the
invention are as follows. The manufacture of the rotors should be greatly
to simplified, mounting and dismounting of the rotors being improved at the
same
time, whereby access to the pump chamber for maintenance and cleaning
20
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CA 02393411 2002-06-04
purposes is also made easier. Furthermore, adjustment of the gap should be
possible in a simple way, and an adjustment of pressure should be achievable
at
high rates of compression with minimal effort. These objects should be
achieved
through the invention without all too negative consequences for the
construction
s size and the inner compression of the displacement machine, or for the
synchronization and cooling of the rotors.
These objects are attained through a displacement machine which has
the characterizing features of claim 1.
More specifically, these objecfs are attained through a displacement
io machine, in particular for use as a vacuum pump, with rotors in mutual,
meshing
engagement, movably disposed in an axis-parallel way in a housing, which
rotors
form variable chambers, axially staggered, shifting during operation, and
which
rotors are designed in an internal-axis construction as hollow outer rotor
with
inner spiral thread and inner rotor with outer spiral thread, with selectively
varying
is pitches as well as varying rotor transverse profiles in each case along the
rotor
axes, wherein that the axial projections of any two transverse profiles of one
and
the same rotor in the same plane have no common points, the rotors are thus
free
of any axial undercutting, and as such can be placed in the working positions
in a
simple way through axial movements, and in engagement can be adjusted axially
2o with respect to one another.
Besides the aforementioned advantage of simple mounting, the
absence of axial undercutting of the rotors brings still further advantages.
The
pitch is also freely definable for one-piece rotors, so that, in interaction
with the
cross-sectional course, a course for the volume can be determined in order to
2s achieve a desired compression. The rotors can be produced in one piece in
very
simple fashion by means of moulds, for example through casting. The moulds for
both the outer rotor and the inner rotor can be separated in such a way that
the
lines of separation do not run over the rotor profiles, which brings about a
minimization of the necessary finishing work. Finally, even during operation,
with
3o a corresponding configuration of the machine, the play between the rotors
can be
adjusted very easily through axial adjustment of the relative rotor positions.
Special embodiments of the displacement machine according to the
invention are described in the dependent claims.
' - CA 02393411 2002-06-04
4
The invention will be described more closely in the following, with
reference to the embodiment examples shown in the drawings. Shown are:
Figure 1 a view, in perspective, partially in section, of the rotor pair;
Figure 2 a longitudinal section of the outer rotor;
s Figure 3 a view in perspective of the inner rotor;
Figure 4 the geometric relationships and mutual arrangement of inner rotor,
outer rotor and support;
Figure 5 a cross-section through the outer rotor;
Figure 6 a cross-section through the inner rotor, in the same plane as the
cross-
io section through the outer rotor according to Figure 5; and
Figure 7 Cross-sectional evolution and possible course of pitch of the outer
rotor.
In the view in perspective of Figure 1, the outer rotor 1 is shown half
cutaway so that the inner rotor 11 is visible. The spiral threads of the outer
rotor 1
is are designated by 2, whereas those of the inner rotor 11 are designated by
12.
Located on the upper, suction-side end of the outer rotor 1 is a cylindrical
projection 4 with which the outer rotor 1 is borne in a support.
Figure 2 shows the outer rotor 1 in an axial longitudinal section in
which the inner spiral threads 2 are more visible than in Figure 1.
2o The view in perspective, according to Figure 3, of the inner rotor 11
substantially corresponds to that of Figure 1.
With reference to an example, Figure 4 shows diagrammatically the
geometric relationships and mutual arrangement of outer rotor 1 and inner
rotor
11. Assumed in the example is a double-threaded outer rotor 1 with oval, inner
2s cross-section, in which a single-threaded inner rotor 11 meshes. The
reference
numeral 3 designates the axis of the outer rotor 1. The reference numeral 13
designates the axis of the inner rotor 11, and the reference numeral 14 the
centre
M CA 02393411 2002-06-04
of the profile section of the inner rotor 11. The inner, oval area of the
outer rotor 1
is designated by 5, and the outer circular area of the inner rotor 11 bears
the
reference numeral 15.
The symbols used in the formulas which follow have the following
s significance:
a - angle of wrap at the outer rotor
1
Fa - cross-sectional area at the location
a
s - eccentricity
R<a> radius R dependent upon a
=
io as differential quotient
-
R; - reference radius R at the location
a = 2~
1 <_ undercut factor
k -
T - constant (see [4])
W - axial position of a cross-section
is L; reference increment (in a = 2n)
-
Lj
- reference pitch (in a = 2n)
2~
dW - dynamic pitch = differential quotient
of W
da
a2 - upper limit of the integral
- pi (3.9495...).
2o For this profile, the chamber cross-sectional area is
Fa =4s(1-cosa~t<a> [1]
The requirement of absence of axial undercutting is expressed
mathematically as dR z 2Eda . The function selected here, namely
R < a >= R~ +2kE(a-2n), fulfils this condition for all k >_ 1. There results
Zs therefrom
R < a > =1 + T(a - 2n) [2]
R~
with R~ = R < 2~ > [3]
> CA 02393411 2002-06-04
6
T - 2ks [4]
R~
The curve corresponding to formula [2] and the conditions [3] and [4] is
designated by 31 in the diagram according to Figure 7.
Valid for a linear course of pitch is
L; _dw _ ~;
s W < a >= 2~ a' da 2~
Generally valid for a non-linear course of pitch is
_dw __ ~j g < a > and therefrom
da 2~
dw=2~g<a>da [5]
wherein g<a> is a pure function >0.
io The chamber volume is generally calculated
«~
VW = f Fadw [6]
az-2n
with insertion of [5] ~
L. «z
Vw =-'' jF«g < a > da (general) [6a]
27L "z-2n
and with insertion of [1 ]
2sL. "~
Is V~,h = ' J(1-cosa)R < a > g < a > da (profile-specific) [6b]
«z-2n
This formula [6b] applies for the chamber volume with stationary rotors
in the starting position for a2=2~,4~ and 6n.
CA 02393411 2002-06-04
7
For any desired rotor positions with az=2~ ... oca the formula is
«,
Vin - 2ELi ['(1- cos(a -a2 ))R < a > g < a > da [6c]
n «~J-zn
With setting g < a >= Ri ~ h < a >, whereby h<a> is again a pure
R<a>
function, one obtains
Vdyn - 2sLiRi «~(1- ~s(a - az )~'t < a > da [6d]
«,-zn
W= ~i Jg<axla= ~i j h<a' da [5a]
2~c 2~ R < a >
Ri
From the formula [6d], the following adequate condition can be derived
for an isochoric machine:
h < a >;$o= constant ~ h < a >;so= g < °~' R < °~'' = constant =
A
1
1o and if dW <a=2n>= ~' g<2~>, R<2~>=Ri, g<2~>=1 ~
da 2~
1~R.
h<a>;so=A= R' =1 ~
i
LiRi 1 a
W;~ _ (' ~a ~
2~ ~R<a>
LiRi 2kE
W < a >;SO= 4k~E I 1 + Rl - 4k~cs a
k.ze 2n.w
a. - Ri - 4k~t~ a R; ~ L; _ 1
2ks
CA 02393411 2002-06-04
g
L;R; R
W~so = 4k~s In R j - 4knE
_2kE.2n_W
R~so = ~R1- 4k~ts~~ a R'
R. R
g < a > ~so = ' ~ h < a >,$o = '
R<a> R<a>
g < a >iso= 1 [7]
1 + 2k R (a - 2n~
l
R L
s V;~o = 4sL;R~ = 4E3 Ej E
Figure 5 shows a cross-section through the outer rotor 1 with the inner
recess (area 5), of oval cross-section, and the axis 3, the ends of the oval
having
the radius R. Figure 6 shows a cross-section through the inner rotor 11 in the
same plane as the cross-section through the outer rotor 1 according to Figure
5.
io The radius R of the circular cross-sectional area (area 15) corresponds to
the
aforementioned radius R at the inner rotor 11.
Figure 7 illustrates, using a diagram, possible courses of pitch for the
rotor spiral threads of the outer rotor as a function of the angle of wrap,
the angle
of wrap a being plotted on the abscissa. The curve 31 corresponds to a change
is in cross-section with an increase in radius as defined under [2] to achieve
the
absence of undercutting. The curve 32 corresponds to the formula [7], and is
proportional to the course of pitch of the outer rotor of an isochorically
operating
machine. The curve 33 is proportional to the course of pitch of the outer
rotor of a
machine in which compression rates of over 1:1 to 1:5 are achieved in
2o combination with cross-sectional changes corresponding to curve 31. Suction
side at a=0.
The curve 34 is proportional to the course of pitch of the outer rotor of a
machine in which compression rates of 1:2 to 1:10 are achieved in combination
with cross-sectional changes corresponding to curve 31. Suction side at a=aa.
