U.S. patent application number 17/577212 was filed with the patent office on 2022-05-05 for rotor pair for a compression block of a screw machine.
The applicant listed for this patent is Kaeser Kompressoren SE. Invention is credited to Gerald Weih.
Application Number | 20220136504 17/577212 |
Document ID | / |
Family ID | 1000006090577 |
Filed Date | 2022-05-05 |
United States Patent
Application |
20220136504 |
Kind Code |
A1 |
Weih; Gerald |
May 5, 2022 |
ROTOR PAIR FOR A COMPRESSION BLOCK OF A SCREW MACHINE
Abstract
The invention relates to a rotor pair for a compressor block of
a screw machine, wherein the rotor pair comprises a secondary rotor
that rotates about a first axis and a main rotor that rotates about
a second axis, wherein the number of teeth of the main rotor is 3
and the number of teeth of the secondary rotor is 4. The relative
profile depth of the secondary rotor is at least 0.5, preferably at
least 0.515, and at most 0.65, preferably at most 0.595. rk1 is an
addendum circle radius drawn around the outer circumference of the
secondary rotor and rf1 is a dedendum circle radius starting at the
profile base of the secondary rotor, wherein the ratio of the axis
distance of the first axis from the second axis and the addendum
circle radius rk1 is at least 1.636, and at most 1.8, preferably at
most 1.733.
Inventors: |
Weih; Gerald; (Rodental,
DE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Kaeser Kompressoren SE |
Colburg |
|
DE |
|
|
Family ID: |
1000006090577 |
Appl. No.: |
17/577212 |
Filed: |
January 17, 2022 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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16530002 |
Aug 2, 2019 |
11248606 |
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17577212 |
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15306592 |
Oct 25, 2016 |
10400769 |
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PCT/EP2015/059070 |
Apr 27, 2015 |
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16530002 |
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Current U.S.
Class: |
418/201.1 |
Current CPC
Class: |
F04C 18/084 20130101;
F04C 2240/30 20130101; F04C 2240/20 20130101; F04C 18/16 20130101;
F04C 2240/60 20130101; F04C 18/20 20130101 |
International
Class: |
F04C 18/08 20060101
F04C018/08; F04C 18/16 20060101 F04C018/16; F04C 18/20 20060101
F04C018/20 |
Foreign Application Data
Date |
Code |
Application Number |
Apr 25, 2014 |
DE |
10 2014 105 882.8 |
Claims
1. A rotor pair for a compressor block of a screw machine, wherein
the rotor pair comprises: a secondary rotor that rotates about a
first axis and a main rotor that rotates about a second axis,
wherein a number of teeth of the main rotor is 3 and a number of
teeth of the secondary rotor is 4, wherein a relative profile depth
of the secondary rotor P .times. T rel = r .times. k 1 - r .times.
f 1 r .times. k 1 ##EQU00028## is between 0.50 and 0.65, wherein
rk.sub.1 is an addendum circle radius drawn around the outer
circumference of the secondary rotor and rf.sub.1 is a dedendum
circle radius starting at the profile base of the secondary rotor,
wherein a ratio of an axis distance a of the first axis from the
second axis and the addendum circle radius rk.sub.1 a rk 1
##EQU00029## is between 1.636 and 1.8, wherein optionally the main
rotor is configured with a wrap-around angle .PHI..sub.HR for which
it holds that 240.degree..ltoreq..PHI..sub.HR.ltoreq.360.degree.,
and wherein preferably for a rotor length ratio L.sub.HR/a:
1.4.ltoreq.L.sub.HR/a.ltoreq.3.4, wherein optionally the rotor
length ratio is formed from a ratio of the rotor length L.sub.HR of
the main rotor and an axis distance a, and the rotor length
L.sub.HR of the main rotor is formed by a distance of a
suction-side main-rotor rotor end face to an opposite pressure-side
main-rotor rotor end face.
2-14. (canceled)
15. A rotor pair for a compressor block of a screw machine, wherein
the rotor pair comprises a secondary rotor that rotates about a
first axis and a main rotor that rotates about a second axis,
wherein a number of teeth of the main rotor is 4 and the number of
teeth of the secondary rotor is 5, wherein a relative profile depth
of the secondary rotor P .times. T rel = r .times. k 1 - r .times.
f 1 r .times. k 1 ##EQU00030## is at least 0.5, optionally at least
0.515, and at most 0.58 wherein rk.sub.1 is an addendum circle
radius drawn around an outer circumference of the secondary rotor
and rf.sub.1 is a dedendum circle radius starting at a profile base
of the secondary rotor, wherein a ratio of an axis distance a of a
first axis from a second axis and the addendum circle radius
rk.sub.1 a rk 1 ##EQU00031## is between 1.683 to 1.836, wherein
optionally the main rotor is configured with a wrap-around angle
.PHI..sub.HR for which it holds that
240.degree..ltoreq..PHI..sub.HR.ltoreq.360.degree., and wherein
optionally for a rotor length ratio L.sub.HR/a:
1.4.ltoreq.L.sub.HR/a.ltoreq.3.3, wherein a rotor length ratio is
formed from a ratio of the rotor length L.sub.HR of the main rotor
and the axis distance a and the rotor length L.sub.HR of the main
rotor is formed by a distance of a suction-side main-rotor rotor
end face to an opposite pressure-side main-rotor rotor end
face.
16-28. (canceled)
29. A rotor pair for a compressor block of a screw machine,
comprising a secondary rotor that rotates about a first axis and a
main rotor that rotates about a second axis, wherein a number of
teeth of the main rotor is 5 and a number of teeth of the secondary
rotor is 6, wherein a relative profile depth of the secondary rotor
P .times. T rel = r .times. k 1 - r .times. f 1 r .times. k 1
##EQU00032## is between 0.44 and 0.495 wherein rk.sub.1 is an
addendum circle radius drawn around an outer circumference of the
secondary rotor and rf.sub.1 is a dedendum circle radius starting
at a profile base of the secondary rotor, wherein a ratio of the
axis distance a of the first axis from the second axis and an
addendum circle radius rk.sub.1 a rk 1 ##EQU00033## is between 1.74
and 1.8, wherein optionally the main rotor is configured with a
wrap-around angle .PHI..sub.HR for which
240.degree..ltoreq..PHI..sub.HR.ltoreq.360.degree., and wherein
optionally for a rotor length ratio L.sub.HR/a
1.4.ltoreq.L.sub.HR/a.ltoreq.3.2, wherein a rotor length ratio is
formed from a ratio of a rotor length Lim of the main rotor and the
axis distance a and a rotor length Lim of the main rotor is formed
by a distance of a suction-side main-rotor rotor end face to an
opposite pressure-side main-rotor rotor end face.
30. The rotor pair according to claim 29, wherein in a transverse
sectional view, circular arcs B.sub.25, B.sub.50, B.sub.75 running
within a secondary rotor tooth are defined, the common centre point
of which is given by the first axis, wherein a radius r.sub.25 of
B.sub.25 has a value r.sub.25=rf.sub.1+0.25*(rk.sub.1-rf.sub.1), a
radius r.sub.50 of B.sub.50 has a value
r.sub.50=rf.sub.1+0.5*(rk.sub.1-rf.sub.1), and a radius r.sub.75 of
B.sub.75 has a value r.sub.75=rf.sub.1+0.75*(rk.sub.1-rf.sub.1),
and wherein the circular arcs B.sub.25, B.sub.50, B.sub.75 are each
delimited by a leading tooth flank F.sub.V and a trailing tooth
flank F.sub.N, wherein tooth thickness ratios are defined as ratios
of the arc lengths b.sub.25, b.sub.50, b.sub.75 of the circular
arcs B.sub.25, B.sub.50, B.sub.75 with
.epsilon..sub.1=b.sub.50/b.sub.25 and
.epsilon..sub.2=b.sub.75/b.sub.25 and at least one of
0.76<.epsilon..sub.1.ltoreq.0.86 and/or
0.62.ltoreq..epsilon..sub.2.ltoreq.0.72.
31. The rotor pair according to claim 29, wherein in a transverse
sectional view, foot points F1 and F2 are defined between an
observed tooth of a secondary rotor and the respectively adjacent
tooth of the secondary rotor and an apex point F5 is defined at a
radially outermost point of the observed tooth, wherein a triangle
D.sub.z is defined by foot points F1, F2 and apex point F5 and
wherein in a radially outer region, the observed tooth projects
beyond the triangle D.sub.z with its leading tooth flank F.sub.V
formed between apex point F5 and F2 with an area A1 and with its
trailing tooth flank F.sub.N formed between foot point F1 and apex
point F5 with an area A2 and wherein 4.ltoreq.A2/A1.ltoreq.7.
32. The rotor pair according to claim 29, wherein in a transverse
sectional view, foot points F1 and F2 are defined between an
observed tooth of the secondary rotor and a respectively adjacent
tooth of the secondary rotor and an apex point F5 is defined at a
radially outermost point of the observed tooth, wherein a triangle
D.sub.z is defined by foot points F1, F2 and apex point F5 and
wherein in a radially outer region of the observed tooth, a leading
tooth flank F.sub.V formed between apex point F5 and foot point F2
projects with an area A1 beyond the triangle D.sub.z and in a
radially inner region is set back with respect to the triangle
D.sub.z with an area A3 and wherein 8.ltoreq.A3/A1.ltoreq.14.
33. The rotor pair according to claim 29, wherein in a transverse
sectional view, foot points F1 and F2 are defined between an
observed tooth of the secondary rotor and a respectively adjacent
tooth of the secondary rotor and an apex point F5 is defined at a
radially outermost point of the observed tooth, wherein a triangle
D.sub.z is defined by foot points F1, F2 and apex point F5 and
wherein in a radially outer region of the observed tooth, a leading
tooth flank F.sub.V formed between apex point F5 and foot point F2
projects with an area A1 beyond the triangle D.sub.z, wherein the
tooth itself has a cross-sectional area A0 delimited by a circular
arc B running between foot points F1 and F2 about a centre point
defined by the first axis and wherein
1.9%.ltoreq.A1/A0.ltoreq.3.2%.
34. The rotor pair according to claim 29, wherein in a transverse
sectional view, foot points F1 and F2 are defined between an
observed tooth of the secondary rotor and a respectively adjacent
tooth of a secondary rotor and an apex point F5 is defined at a
radially outermost point of the observed tooth, wherein the
circular arc B running between foot points F1 and F2 defines a
tooth partition angle .gamma. corresponding to 360.degree./number
of teeth of the secondary rotor about a centre point defined by the
first axis, wherein a point F1t is defined on the half circular arc
B between foot points F1 and F2, wherein a radial half-line R drawn
from a centre point of the secondary rotor defined by the first
axis through the apex point F5 intersects a circular arc B at a
point F12, wherein an offset angle (3 is defined by an offset of
points F11 to F12 viewed in a direction of rotation of the
secondary rotor and wherein 13.5%.ltoreq..delta..ltoreq.18% where
.delta. = .beta. .gamma. * 100 .function. [ % ] . ##EQU00034##
35. The rotor pair according to claim 29, wherein the main rotor is
formed with a wrap-around angle .PHI..sub.HR for which
320.degree..ltoreq..PHI..sub.HR.ltoreq.360.degree..
36. The rotor pair according claim 29, wherein a blow hole factor
.mu..sub.B1 is between 0.03% and 0.25%, wherein .mu. Bl = A Bl A
.times. 6 + A .times. 7 * 100 .function. [ % ] ##EQU00035## and
wherein A.sub.B1 designates an absolute pressure-side blow hole
area and A6 and A7 designate tooth gap areas of the secondary rotor
or the main rotor, wherein an area A6 in a transverse sectional
view is an area enclosed between a profile course of the secondary
rotor between two adjacent apex points F5 and an addendum circle
KK.sub.1 and an area A7 in a transverse sectional view is an area
enclosed between a profile course of the main rotor between two
adjacent apex points H5 and an addendum circle KK.sub.2.
37. The rotor pair according to claim 29, wherein for a blow
hole/profile gap length factor .mu..sub.1*.mu..sub.B1
0.1%.ltoreq..mu..sub.1*.mu..sub.B1.ltoreq.1.26% where .mu. l = l sp
PT 1 , ##EQU00036## where l.sub.sp designates a length of a profile
engagement gap of a tooth gap of the secondary rotor and PT.sub.1
designates a profile depth of the secondary rotor where
PT.sub.1=rk.sub.1 rf.sub.1 and .mu. Bl = A Bl A .times. .times. 6 +
A .times. .times. 7 * 100 .function. [ % ] ##EQU00037## where
A.sub.B1 designates an absolute blow hole area and A6 and A7
designate a profile areas of the secondary rotor or the main rotor,
wherein an area A6 in a transverse sectional view designates a area
enclosed between a profile course of the secondary rotor between
two adjacent apex points F5 and an addendum circle KK.sub.1, and an
area A7 in a transverse sectional view designates an area enclosed
between a profile course of the main rotor between two adjacent
apex points H5 and an addendum circle KK.sub.2.
38. The rotor pair according to claim 29, wherein the main rotor
and the secondary rotor are configured and tuned to one another in
such a manner that a dry compression with a pressure ratio .PI. of
up to 5 is achieved, or alternatively a fluid-injected compression
with a pressure ratio .PI. of up to 20 where a pressure ratio is a
ratio of compression end pressure to suction pressure.
39. The rotor pair according to claim 29, wherein dry compression
the main rotor is configured to be operated relative to an addendum
circle KK.sub.2 at a circumferential speed in a range from 20 to
100 m/s and a fluid-injected compression the main rotor is
configured to be operated relative to an addendum circle KK.sub.2
at a circumferential speed in a range from 5 to 50 m/s.
40. The rotor pair according claim 29, wherein for a diameter ratio
defined by a ratio of an addendum circle radii of the main rotor
and the secondary rotor D v = D .times. k 2 D .times. k 1 = r
.times. k 2 r .times. k 1 ##EQU00038## 1 . 1 .times. 9 .ltoreq. D v
.ltoreq. 1.26 ##EQU00038.2## where Dk.sub.1 designates a diameter
of an addendum circle KK.sub.1 of the secondary rotor and Dk.sub.2
designates a diameter of an addendum circle KK.sub.2 of the main
rotor.
42. The rotor pair according to claim 29, wherein a transverse
sectional view arc lengths b(r), running inside a tooth of the
secondary rotor, of a respectively appurtenant concentric circular
arcs having a radius rf.sub.1<r<rk.sub.1 and a common central
point defined by the first axis are each delimited by a leading
tooth flank F.sub.V and a trailing tooth flank F.sub.N and the arc
lengths b(r) decrease monotonically with increasing radius r.
43. The rotor pair according to claim 29, wherein a transverse
sectional configuration of the secondary rotor is executed in such
a manner that a direction of action of torque which results from a
reference pressure on a partial surface of the secondary rotor
delimiting a working chamber is directed contrary to the direction
of rotation of the secondary rotor.
44. The rotor pair according to claim 29, wherein the main rotor
and secondary rotor are configured and tuned to one another for
conveying air or inert gases.
45. The rotor pair according to claim 29, wherein in a transverse
sectional view, the profile of a tooth of the secondary rotor
relative to the radial half-line R drawn from the centre point
defined by the first axis C1 through the apex point F5 is
configured to be asymmetrical.
46. The rotor pair according to claim 29, wherein in a transverse
sectional view a point C is defined on a connecting section between
the first axis and the second axis where a pitch circles WK.sub.1
of the secondary rotor and WK.sub.2 of the main rotor contact, that
K5 defines a point of intersection of a dedendum circle FK.sub.1 of
the secondary rotor with the connecting section where r.sub.1
determines the distance between K5 and C and that K4 designates a
point of the suction-side part of a line of engagement which lies
at a greatest distance from the connecting section between the
first and second axis, where r.sub.2 determines a distance between
K4 and C and where: 0 . 9 .ltoreq. r 1 r 2 .ltoreq. 0 . 8 .times. 7
.times. 5 .times. z 1 z 2 + 0 . 2 .times. 2 ##EQU00039## where
z.sub.1 is a number of teeth of the secondary rotor and z.sub.2 is
a number of teeth of the main rotor.
47. The rotor pair according claim 29, wherein for a rotor length
ratio L.sub.HR/a it holds:
0.85*(z.sub.1/z.sub.2)+0.67.ltoreq.L.sub.HR/a.ltoreq.1.26*(z.sub.1/z.sub.-
2)+1.18 where z.sub.1 is a number of teeth of the secondary rotor
and z.sub.2 is a number of teeth of the main rotor, wherein a rotor
length ratio L.sub.HR/a denotes a ratio of a rotor length L.sub.HR
to the axial distance a and the rotor length L.sub.HR is the
distance of a suction-side main-rotor rotor end face to the
pressure-side main-rotor rotor end face.
48. A compressor block comprising a compressor housing and a rotor
pair according to claim 29, wherein the rotor pair comprises the
main rotor and the secondary rotor, which are each mounted
rotatably in the compressor housing.
Description
RELATED APPLICATIONS
[0001] The present application is a divisional of U.S. patent
application Ser. No. 16/530,002 filed Aug. 2, 2019, which
application is divisional of U.S. patent application Ser. No.
15/306,592, filed Oct. 25, 2016, which application is a 35 U.S.C.
.sctn. 371 national phase application of PCT International
Application No. PCT/EP2015/059070, filed Apr. 27, 2015, which
claims priority from German Patent Application No. 10 2014 105
882.8, filed Apr. 25, 2014; the disclosures of which are hereby
incorporated herein by reference in their entirety. PCT
International Application No. PCT/EP2015/059070 is published in
German as PCT Publication No. WO 2015/162296.
FIELD OF THE INVENTION
[0002] The invention relates to a rotor pair for a compressor block
of a screw machine, where the rotor pair consists of a main rotor
that rotates about a first axis and a secondary rotor that rotates
about a second axis. The invention further relates to a compressor
block having a corresponding rotor pair.
BACKGROUND
[0003] Screw machines, whether this be in the form of screw
compressors or in the form of screw expanders, have been in
practical use for several decades. Configured as screw compressors,
they have superseded reciprocating piston compressors as
compressors in many areas. With the principle of the intermeshing
pair of screws, not only gases can be compressed by applying a
certain amount of work. The application as a vacuum pump also opens
up the use of screw machines to achieve a vacuum. Finally an amount
of work can also be produced by passing through pressurized gases
the other way round so that mechanical energy can also be obtained
from pressurized gases by means of the principle of the screw
machine.
[0004] Screw machines generally have two shafts arranged parallel
to one another on which a main rotor on the one hand and a
secondary rotor on the other hand are located. Main rotor and
secondary rotor intermesh with a corresponding screw-shaped toothed
structure. Between the toothed structures and a compressor housing
which accommodates the main and secondary rotor, a compression
chamber (working chambers) is formed by the tooth gap volumes.
Starting from a suction region as the rotation of main and
secondary rotor progresses, the working chamber is initially closed
and then continuously reduced in volume so that a compression of
the medium occurs. Finally as rotation progresses, the working
chamber is opened towards a pressure window and the medium is
expelled into the pressure window. Screw machines configured as
screw compressors differ by this process of internal compression
from Roots blowers which operate without internal compression.
[0005] Depending on the required pressure ratio (ratio of output
pressure to input pressure), various tooth number ratios are
appropriate for efficient compression.
[0006] Typical pressure ratios can be between 1.1 and 20 depending
on the tooth number ratio, where the pressure ratio is the ratio of
compression end pressure to suction pressure. The compression can
take place in a single- or multistage manner. Attainable final
pressures can, for example, lie in the range of 1.1 bar to 20 bar.
Insofar as at this point or hereinafter in the present application
reference is made to pressure information in "bar", in each case
this pressure information relates to absolute pressures.
[0007] In addition to the already mentioned function as a vacuum
pump or as a screw expander, screw machines can be used in various
areas of technology as compressors. A particularly preferred area
of application is the compression of gases such as, for example,
air or inert gases (helium, nitrogen, . . . ). However, it is also
possible, although this imposes especially structurally different
requirements, to use a screw machine to compress refrigerants, for
example for air-conditioning systems or refrigeration applications.
For the compression of gases specifically with higher pressure
ratios, usually a fluid-injected compression, in particular an
oil-injected compression is used; however it is also possible to
operate a screw machine according to the principle of dry
compression. In the lower-pressure area, screw compressors are
occasionally also designated as screw blowers.
[0008] Over the past few decades, considerable success has been
achieved in regard to the manufacturability, reliability, smooth
running and efficiency of screw machines. Improvements or
optimizations in this context frequently relate to optimizations of
the efficiency depending on number of teeth, wrap-around angle and
length/diameter ratio of the rotors. The incorporation of the
transverse sections in the optimization process has only taken
place recently.
[0009] Experiments have shown that the transverse section of the
rotors, in particular the transverse section of the secondary rotor
has a substantial influence on the energy efficiency. In order to
obey the toothed structure laws, the transverse section of the
secondary rotor must find its correspondence in the transverse
section of the main rotor. The profile of the rotor in a plane
perpendicular to the axis of the rotor is here designated as
transverse section. Various types of transverse section generation
such as, for example, rotor- or rack-based transverse section
generating methods are now known from the prior art. If a specific
process has been decided upon, a first draft transverse section is
generated in a first step. This is conventionally further optimized
in a plurality of successive (revising) steps according to various
criteria.
[0010] Here both the optimization aims per se (energy efficiency,
smooth running, low costs) and also the fact that the improvements
of one parameter in some cases necessarily result in a
deterioration of another parameter, are known. However, there is a
lack of a specific solution as to how a good overall optimization
result (i.e. a compromise between the various individual parameter
optimizations) can be achieved.
[0011] Some optimization approaches which are known in the prior
art with a view to improving the energy efficiency, smooth running
and costs will be explained as an example hereinafter. Furthermore,
problems which can arise here will also be mentioned.
1 Energy Efficiency
[0012] The energy efficiency of compressor blocks can
advantageously be influenced in a known manner by minimizing the
internal leakages in the compressor block and in particular by
reducing the gap between main rotor and secondary rotor.
Specifically here a distinction should be made between the profile
gap and the blow hole: [0013] Via the profile gap the pressure-side
working chambers have direct communication to the suction side and
therefore the greatest possible pressure difference for backflows.
[0014] Consecutive working chambers are interconnected via a
theoretically unnecessary passage which is designated as blow hole.
In some cases this is also designated as head rounding opening.
This blow hole is obtained through the head rounding of the
profiles, in particular the profile of the secondary rotor. [0015]
Pressure-side working chambers are connected to the respectively
adjacent working chamber via pressure-side blow holes, suction-side
working chambers are connected to the respectively adjacent working
chambers via suction-side blow holes. Unless specified otherwise,
the term "blow hole" is to be understood hereinafter as
"pressure-side blow hole".
[0016] Ideally, in order to minimize internal leakages, a short
profile gap length should be combined with a small (pressure-side)
blow hole. However, the two quantities behave fundamentally
contrarily. That is, the smaller the blow hole is modelled, the
larger the profile gap length must be. Conversely, the blow hole
becomes larger, the shorter is the profile gap length. This is
explained, for example, by Helpertz in his dissertation "Method for
the stochastic optimization of screw rotor profiles", Dortmund,
2003, on page 162.
[0017] The requirement for a short profile gap length can be
achieved in a known manner with a flat profile with a relatively
small relative profile depth of the secondary rotor. Whether a
profile is designed to be rather flat (small profile depth) or deep
(large profile depth) can be clearly quantified here by means of
the so-called "relative profile depth of the secondary rotor" which
relates the difference between addendum and dedendum circle radius
to the addendum circle radius of the secondary rotor. The higher is
the value, the more compact is the compressor block and for
example, has more quantity delivered than a comparable compressor
block with the same external dimensions.
[0018] Profiles designed to be very flat accordingly have a poor
utilization of installation volume, i.e. they result in large
compressor blocks with comparatively high material expenditure or
comparatively high manufacturing costs.
[0019] Pressure-side blow holes as described above must not be
designed to be too large in order to minimize the return flow of
already compressed medium in preceding working chambers (i.e., in
lower-pressure working chambers). Such return flows increase the
energy expenditure for the overall conveying capacity achieved and
result in an undesirable increase in the temperature and pressure
level during compression which overall reduces the efficiency. The
area of the blow hole (blow hole area) can be kept small whereby
the head roundings of the profiles in the transverse section are
designed to be small. Specifically, this can be achieved by a
strong curvature in the head region of the leading tooth flank of
the secondary rotor and in the head region of the trailing tooth
flank of the main rotor. However, the stronger is this curvature,
the more rapidly production-technology limiting regions are reached
since this for example results in high wear on profile millers and
profile grinding disks during the manufacture of main rotor and
secondary rotor.
[0020] Suction-side blow holes on the other hand do not have a
negative influence on the energy efficiency since only working
chambers in the suction region are interconnected via these at the
same pressure.
[0021] Another cause of efficiency-reducing internal leakages is
the so-called chamber interstitial volume which can form during
expulsion of the last working chamber (i.e. the working chamber in
which the highest pressure prevails) into the pressure window. The
working chamber then no longer has a connection to the pressure
window from a certain rotational angle position of the rotors. A
so-called chamber interstitial volume remains between the two
rotors and the pressure-side housing end wall.
[0022] This chamber interstitial volume is disadvantageous because
the enclosed compressed medium can no longer be expelled into the
pressure window and is even further compressed during the further
rotation of the rotors, which leads to an unnecessarily high power
consumption (for the over-compression), an unnecessarily high
additional heat input, evolution of noise and a reduction in the
lifetime, in particular of the roller bearings of the rotors. In
addition, a deterioration in the specific power is caused by the
fact that the fraction enclosed in the chamber interstitial volume
is returned to the suction side after the over-compression and
therefore is no longer available to the compressed air user. In the
case of oil-injected compressors, incompressible oil is
additionally in the chamber interstices and is squeezed.
2 Smooth Running
[0023] However, other properties such as, for example, the smooth
running also have a decisive influence on a good profile for main
rotor or secondary rotor.
[0024] In addition to good osculation of the flanks and low
relative speeds between the tooth flanks of main and secondary
rotor, the division of the drive torque between the two rotors also
has a decisive influence on the two rotors. An unfavourable
distribution is known to frequently result in so-called rotor
rattling of the secondary rotor in which the secondary rotor has
undefined flank contact with the main rotor and the secondary rotor
consequently alternately has contact with the leading and the
trailing main rotor flank. If the two rotors are held at a distance
by means of a synchronous transmission, the aforesaid rotor
rattling is necessarily displaced into the synchronous
transmission. Good smooth running not only ensures low sound
emissions from the compressor block but for example also provides
for a less vibration-prone compressor block, a long lifetime of the
roller bearings and low wear in the tooth structure of the
rotors.
3 Costs
[0025] In particular, the manufacturability and the degree of
utilization of the installation volume have an effect on the
material and manufacturing costs of screw compressor blocks.
Compact compressor blocks with a high utilization of installation
volume are achieved by a large tooth gap volume which in turn
depends on the profile depth and the tooth thickness.
[0026] The further the relative profile depth is increased, the
higher utilization of installation volume is achieved but at the
same time, the risk of problems with running properties and
manufacturability is higher: [0027] With increasing profile depth,
in particular the tooth profiles of the secondary rotor will
necessarily become increasingly thinner and consequently
increasingly flexible. This makes the rotors increasingly
temperature-sensitive and when viewed overall, has an unfavourable
effect on the gaps in the compressor block. The gaps have an
appreciable influence on the internal leakages, i.e. return flows
from higher-pressure compression chambers in the direction of the
suction side, and can thus cause a deterioration in the energy
efficiency of the compressor block. [0028] Furthermore, in the case
of flexible teeth the difficulties with rotor manufacture increase.
[0029] Thus for example, there is an increased risk that the
requirements in particular for the shape tolerances, which are
already high in any case, cannot be adhered to. [0030] Furthermore,
flexible teeth require lower feed and intersection speeds both
during profile milling and also during subsequent profile grinding
and thus increase the processing time and consequently the
manufacturing costs. [0031] An increasing profile depth also has
the result that the rotor per se becomes more flexible. The more
flexible the rotors are designed, the more the risk increases that
the rotors start running amongst one another or in the compressor
housing. In order to ensure operating safety even at high
temperatures or at high pressures, the gaps must consequently have
larger dimensions. This in turn has a negative influence on the
energy efficiency of the compressor block.
SUMMARY
[0032] The above explanations are intended to show that an
optimization of the individual characteristics each for itself is
less expedient but for a good overall result a compromise must be
found between the various (and partly contradictory)
requirements.
[0033] The theoretical calculation principles for producing screw
rotor profiles have already been discussed on many occasions in the
literature and also describe general criteria for good transverse
section profiles. For example, rotor profiles can be created and
modified using the computer program developed by Grafinger
(post-doctoral thesis "Computer-assisted development of flank
profiles for special tooth structures of screw compressors",
Vienna, 2010).
[0034] In his thesis "Method for the stochastic optimization of
screw rotor profiles", Dortmund 2003, Helpertz is concerned with
the automated optimization starting from a draft with regard to
differently weighted characteristics.
[0035] Accordingly it is the object of the present invention to
provide a rotor pair for a compressor block of a screw machine
which is characterized by highly smooth running and a particular
energy efficiency with high operating safety and acceptable
production costs.
[0036] This object is solved with a rotor pair. Advantageous
embodiments are specified in the subclaims. Further, the object is
also solved with a compressor block comprising a suitably
configured rotor pair.
[0037] The rotor geometry is substantially characterized by the
shape of the transverse section as well as by the rotor length and
the wrap-around angle, cf. "Method for the stochastic optimization
of screw rotor profiles", Thesis by Markus Helpertz, Dortmund 2003,
pp. 11/12.
[0038] In a transverse sectional view, secondary rotor or main
rotor have a pre-determined, frequently different number of
identically configured teeth per rotor. The outermost circle drawn
through the axis C1 or C2 via the apex points of the teeth is
designated as addendum circle in each case. A dedendum circle is
defined by the points of the outer surface of the rotors nearest to
the axis in transverse section. The ribs are designated as teeth of
the rotor. The grooves (or recesses) are accordingly designated as
tooth gaps. The surface of the tooth at and over the dedendum
circle defines the tooth profile. The contour of the ribs defines
the course of the tooth profile. Foot points F1 and F2 and an apex
point F5 are defined for the tooth profile. The apex point F5 or H5
is defined by the radially outermost point of the tooth profile. If
the tooth profile has a plurality of points with the same maximum
radial distance from the central point defined by the axis C1 or
C2, the tooth profile therefore follows at its radially outermost
end a circular arc on the addendum circle, the apex point F5 lies
precisely at the centre of this circular arc. A tooth gap is
defined between two adjacent apex points F5.
[0039] The points radially nearest to the axis C1 or C2 between an
observed and the respectively adjacent tooth define foot points F1
and F2. Here it also holds for the case that a plurality of points
come equally close to the axis C1 or C2, i.e. the tooth profile at
its lowest point follows the dedendum circle in sections, that the
corresponding foot point F1 or F2 then lies on the half of this
circular arc lying on the dedendum circle.
[0040] Finally, as a result of the intermeshing of main rotor and
secondary rotor, a pitch circle is defined both for the secondary
rotor and also for the main rotor. In screw machines and also in
gear wheels or friction wheels, there are always two circles in the
transverse section of the toothed structure which roll against one
another during the movement. These circles on which in the present
case main rotor and secondary rotor roll against one another are
designated as respective pitch circles. The pitch circle diameter
of main rotor and secondary rotor can be determined with the aid of
axial distance and tooth number ratio.
[0041] On the pitch circles the circumferential speeds of main
rotor and secondary rotor are identical.
[0042] Finally tooth gap areas between the teeth and the respective
addendum circle KK are defined, namely tooth gap area A6 between
the profile course of the secondary rotor NR between two adjacent
apex points F5 and the addendum circle KK.sub.1 or an area A7 as
tooth gap area between the profile course of the main rotor (HR)
between two adjacent apex points H5 and the addendum circle
KK.sub.2.
[0043] The tooth profile of the secondary rotor (but also of the
main rotor) has a leading tooth flank in the direction of rotation
and a trailing tooth flank in the direction of rotation. In the
secondary rotor (NR) the leading tooth flank is hereinafter
designated by F.sub.V and the trailing tooth flank by F.sub.N.
[0044] The trailing tooth flank F.sub.N in its section between
addendum circle and dedendum circle forms a point at which the
curvature of the course of the tooth profile changes. This point is
hereinafter designated as F8 and divides the trailing tooth flank
F.sub.N into a convexly curved fraction between F8 and the addendum
circle and a concavely curved fraction between the dedendum circle
and F8. Small-part profile variations, possibly due to sealing
strips or due to other local profile restructurings are not taken
into account when considering the previously described change of
curvature.
[0045] In addition to the pure transverse section, for the
three-dimensional configuration, the following terms or parameters
are definitive for a rotor, in particular the secondary rotor:
firstly the wrap-around angle .PHI. is defined. This wrap-around
angle is the angle through which the transverse section is turned
from the suction-side to the pressure-side rotor end face, cf. on
this matter also the more detailed explanations in connection with
FIG. 8.
[0046] The main rotor has a rotor length L.sub.HR which is defined
as the distance of a suction-side main-rotor rotor end face to a
pressure-side main-rotor rotor end face. The distance of the first
axis C1 of the secondary rotor to the second axis C2 of the main
rotor running parallel to one another is hereinafter designated as
axial distance a. It is pointed out that in most cases the length
of the main rotor L.sub.HR corresponds to the length of the
secondary rotor L.sub.NR, where in the case of the secondary rotor
the length is also understood as the distance of a suction-side
secondary-rotor rotor end face to a pressure-side secondary-rotor
rotor end face. Finally a rotor length ratio L.sub.HR/a is defined,
i.e. a ratio of the rotor length of the main rotor to the axial
distance. The ratio L.sub.HR/a is in this respect a measure for the
axial dimensioning of the rotor profile.
[0047] The line of engagement or the profile gap is formed by the
cooperation of main rotor and secondary rotor with one another. In
this case, the line of engagement is obtained as follows: the tooth
flanks or main rotor and secondary rotor contact one another in a
backlash-free toothed structure depending on the rotational angle
position of the rotors at certain points. These points are
designated as engagement points. The geometric location of all the
engagement points is the line of engagement and can already be
calculated in two dimensions by means of the transverse section of
the rotors, cf. FIG. 7j.
[0048] In the transverse sectional view, the line of engagement is
divided by the connecting line between the two central points C1
and C2 into two sections and specifically into a (comparatively
short) suction-side and a (comparatively long) pressure-side
section.
[0049] If the wrap-around angle and the rotor length (=distance
between the suction-side end face and the pressure-side end face)
are additionally specified, the line of engagement can also be
expanded three-dimensionally and corresponds to the line of contact
of main rotor and secondary rotor. The axial projection of the
three-dimension line of engagement on the transverse sectional
plane in turn gives the two-dimensional line of engagement
illustrated by means of FIG. 7j. The term "line of engagement" is
used in the literature both for the two-dimensional and the
three-dimensional analysis. Hereinafter, unless specified
otherwise, "line of engagement" is understood however as the
two-dimensional line of engagement, i.e. the projection onto the
transverse section.
[0050] The profile engagement gap is defined as follows: in a real
compressor block of a screw machine, there is a gap between the two
rotors with the installed axial spacing of main rotor and secondary
rotor. The gap between main rotor and secondary rotor is designated
as profile engagement gap and is the geometrical location of all
the points at which the two paired rotors contact one another or
have the smallest distance from one another.
[0051] Through the profile engagement gap the compressing and the
expelling working chambers are in communication with chambers which
still have contact with the suction side. Therefore the total
maximum pressure ratio is present at the profile engagement gap.
Through the profile engagement gap, already compressed working
fluid is transported back to the suction side and thus reduces the
efficiency of the compression. Since the profile engagement gap in
a backlash-free toothed structure would comprise the line of
engagement, the profile engagement gap is also designated as
"quasi-engagement line".
[0052] Blow holes between working chambers are formed by head
roundings of the teeth of the profile. Via blow holes the working
chambers are connected to the preceding and following working
chambers so that (in contrast to the profile engagement gap) only
the pressure difference from one working chamber to the next
working chamber is present at the blow hole.
[0053] Furthermore, as is known, certain rotor pairs are usual in
screw machines, for example a rotor pair in which the main rotor
has three teeth and the secondary rotor has four teeth or a rotor
pair in which the main rotor has four teeth and the secondary rotor
has five teeth or furthermore a rotor pair geometry in which the
main rotor has five teeth and the secondary rotor has six teeth.
For different areas of application or intended uses, rotor pairs or
screw machines having different tooth number ratios are possibly
used. For example, rotor pair arrangements having a tooth number
ratio of 4/5 (main rotor with four teeth, secondary rotor with five
teeth) are used as a suitable pair for oil-injected compression
applications in moderate pressure ranges.
[0054] In this respect, the tooth number or the tooth number ratio
predefines different types of rotor pairs and resulting from this,
different types of screw machines, in particular screw
compressors.
[0055] For a screw machine or a rotor pair with three teeth in the
main rotor and four teeth in the secondary rotor, a geometry having
the following specifications is claimed, which can be deemed to be
particularly energy-efficient:
[0056] A relative profile depth of the secondary rotor is
configured with
P .times. T rel = r .times. k 1 - r .times. f 1 r .times. k 1
##EQU00001##
where PT.sub.rel is at least 0.5, preferably at least 0.515, and at
most 0.65, preferably at most 0.595, wherein rk.sub.1 is an
addendum circle radius drawn around the outer circumference of the
secondary rotor and rf.sub.1 is a dedendum circle radius starting
at the profile base of the secondary rotor. Furthermore, the ratio
of the axis distance a of the first axis C1 from the second axis C2
and the addendum circle radius rk.sub.1
a rk 1 ##EQU00002##
is specified so that
a rk 1 ##EQU00003##
is at least 1.636 and at most 1.8, preferably at most 1.733,
wherein preferably the main rotor is configured with a wrap-around
angle .PHI..sub.HR for which it holds that
240.degree..ltoreq..PHI..sub.HR.ltoreq.360.degree., and wherein
preferably for a rotor length ratio L.sub.HR/a it holds that:
1.4.ltoreq.L.sub.HR/a.ltoreq.3.4,
wherein the rotor length ratio is formed from the ratio of the
rotor length Lim of the main rotor and the axis distance a and the
rotor length L.sub.HR of the main rotor is formed by the distance
of a suction-side main-rotor rotor end face to an opposite
pressure-side main-rotor rotor end face.
[0057] For a screw machine or a rotor pair with four teeth in the
main rotor and five teeth in the secondary rotor, a geometry having
the following specifications is claimed, which can be deemed to be
particularly energy-efficient: a relative profile depth of the
secondary rotor is configured with
P .times. T rel = r .times. k 1 - r .times. f 1 r .times. k 1
##EQU00004##
wherein PT.sub.rel is at least 0.5, preferably at least 0.515, and
at most 0.58, wherein rk.sub.1 is an addendum circle radius drawn
around the outer circumference of the secondary rotor and rf.sub.1
is a dedendum circle radius starting at the profile base of the
secondary rotor. Furthermore the ratio of the axis distance a of
the first axis C1 from the second axis C2 and the addendum circle
radius rk.sub.1
a rk 1 ##EQU00005##
is specified so that
a rk 1 ##EQU00006##
is at least 1.036 and at most 1.836, preferably at most 1.782,
wherein preferably the main rotor is configured with a wrap-around
angle .PHI..sub.HR for which it holds that
240.degree..ltoreq..PHI..sub.HR.ltoreq.360.degree., and wherein
preferably for a rotor length ratio L.sub.HR/a it holds that:
1.4.ltoreq.L.sub.HR/a.ltoreq.3.3,
wherein the rotor length ratio is formed from the ratio of the
rotor length Um of the main rotor and the axis distance a and the
rotor length L.sub.HR of the main rotor is formed by the distance
of a suction-side main-rotor rotor end face to an opposite
pressure-side main-rotor rotor end face.
[0058] For a screw machine or a rotor pair with five teeth in the
main rotor and six teeth in the secondary rotor, a geometry having
the following specifications is claimed, which can be deemed to be
particularly energy-efficient:
[0059] A relative profile depth of the secondary rotor is
configured with
P .times. T rel = r .times. k 1 - r .times. f 1 r .times. k 1
##EQU00007##
wherein PT.sub.rel is at least 0.44 and at most 0.495, preferably
at most 0.48, wherein rk.sub.1 is an addendum circle radius drawn
around the outer circumference of the secondary rotor and rf.sub.1
is a dedendum circle radius starting at the profile base of the
secondary rotor. Furthermore the ratio of the axis distance a of
the first axis C1 from the second axis C2 and the addendum circle
radius rk.sub.1
a rk 1 ##EQU00008##
is specified so that
a rk 1 ##EQU00009##
is at least 1.74, preferably at least 1.75 and at most 1.8,
preferably at most 1.79, wherein preferably the main rotor is
configured with a wrap-around angle .PHI..sub.HR for which it holds
that 240.degree..ltoreq..PHI..sub.HR.ltoreq.360.degree., and
wherein preferably for a rotor length ratio L.sub.HR/a it holds
that:
1.4.ltoreq.L.sub.HR/a.ltoreq.3.2,
wherein the rotor length ratio is formed from the ratio of the
rotor length L.sub.HR of the main rotor and the axis distance a and
the rotor length L.sub.HR of the main rotor is formed by the
distance of a suction-side main-rotor rotor end face to an opposite
pressure-side main-rotor rotor end face.
[0060] If the values for the relative profile depth on the one hand
and the ratio of axis distance to the addendum circle radius of the
secondary rotor on the other hand for the given teeth-number ratios
lie in the specified advantageous ranges in each case, the basic
conditions for a good secondary rotor profile or a good cooperation
of the secondary rotor profile and main rotor profile are created,
in particular a particularly favourable ratio of blow hole area to
profile gap length is made possible. With regard to the definitive
parameters, reference is additionally made to the illustration in
FIG. 7a for all the addressed tooth number ratios. The relative
profile depth of the secondary rotor is a measure for how deeply
the profiles are cut. With increasing profile depth, the
installation volume utilization increases for example but at the
expense of the flexural rigidity of the secondary rotor. For the
relative profile depth of the secondary rotor it holds that:
PT rel = rk 1 - rf 1 rk 1 = PT 1 rk 1 = rk 1 - ( a - rk 2 ) rk 1 =
1 - a - rk 2 rk 1 ##EQU00010##
where PT.sub.1=rk.sub.1-rf.sub.1 and rf.sub.1=a-rk.sub.2.
[0061] In this respect, there is a relationship with the ratio
of
a rk 1 , ##EQU00011##
axis distance a to the secondary rotor addendum circle radius
rk.sub.1.
[0062] The specified values for the rotor length ratio L.sub.HR/a
and the wrap-around angle .PHI..sub.HR constitute advantageous or
expedient values for the respectively given tooth number ratio in
order to specify an advantageous rotor pair in the axial
dimension.
1. Preferred Embodiments for a Rotor Pair with a Tooth Number Ratio
of 3/4
[0063] Preferred embodiments are set out hereinafter for a rotor
pair with a tooth number ratio 3/4, i.e. for a rotor pair in which
the main rotor has three teeth and the secondary rotor has four
teeth:
[0064] A first preferred embodiment provides that in a transverse
sectional view, circular arcs B.sub.25, B.sub.50, B.sub.75 running
within a secondary rotor tooth are defined, the common centre point
of which is given by the axis C1, wherein the radius r.sub.25 of
B.sub.25 has the value r.sub.25=rf.sub.1+0.25*(rk.sub.1-rf.sub.1),
the radius r.sub.50 of B.sub.50 has the value
r.sub.50=rf.sub.1+0.5*(rk.sub.1-rf.sub.1), and the radius r.sub.75
of B.sub.75 has the value
r.sub.75=rf.sub.1+0.75*(rk.sub.1-rf.sub.1), and wherein the
circular arcs B.sub.25, B.sub.50, B.sub.75 are each delimited by
the leading tooth flank F.sub.V and trailing tooth flank F.sub.N,
wherein tooth thickness ratios are defined as ratios of the arc
lengths b.sub.25, b.sub.50, b.sub.75 of the circular arcs B.sub.25,
B.sub.50, B.sub.75 with .epsilon..sub.1=b.sub.50/b.sub.25 and
.epsilon..sub.2=b.sub.75/b.sub.25 and the following dimension is
adhered to: 0.65.ltoreq..epsilon..sub.1<1.0 and/or
0.50.ltoreq..epsilon..sub.2.ltoreq.0.85, preferably
0.80.ltoreq..epsilon..sub.1<1.0 and/or
0.50.ltoreq..epsilon..sub.2.ltoreq.0.79.
[0065] The aim is to combine a small blow hole with short length of
the profile engagement gap. However the two parameters behave in a
contrary manner, i.e. the smaller the blow hole is modelled, the
larger the length of the profile engagement gap necessarily
becomes. Conversely the blow hole becomes larger, the shorter is
the length of the profile engagement gap. In the claimed ranges a
particularly favourable combination of the two parameters is
achieved. At the same time a sufficiently high flexural rigidity of
the secondary rotor is achieved. Furthermore, advantages are
established as far as the chamber expulsion is concerned and for
the secondary rotor torque. With regard to the illustration of the
parameters, reference is additionally made to FIG. 7c.
[0066] A further preferred embodiment provides that in a transverse
sectional view, foot points F1 and F2 are defined between the
observed tooth of the secondary rotor (NR) and the respectively
adjacent tooth of the secondary rotor and an apex point F5 is
defined at the radially outermost point of the tooth, wherein a
triangle D.sub.z is defined by F1, F2 and F5 and wherein in a
radially outer region, the tooth projects beyond the triangle
D.sub.z with its leading tooth flank F.sub.V formed between F5 and
F2 with an area A1 and with its trailing tooth flank F.sub.N formed
between F1 and F5 with an area A2 and wherein
8.ltoreq.A2/A1.ltoreq.60 is maintained.
[0067] The tooth sub-area A1 at the leading tooth flank FV of the
secondary rotor has a substantial influence on the blow hole area.
The tooth sub-area A2 at the trailing tooth flank F.sub.N of the
secondary rotor on the other hand has a substantial influence on
the length of the profile engagement gap, the chamber expulsion and
the secondary rotor torque. For the tooth sub-area ratio A2/A1
there is an advantageous range which enables a good compromise
between length of the profile engagement gap on the one hand and
the blow hole on the other hand. With regard to the illustration of
the parameters, reference is additionally made to FIG. 7d.
[0068] In a further preferred embodiment the rotor pair comprises a
secondary rotor in which in a transverse sectional view, foot
points F1 and F2 are defined between the observed tooth of the
secondary rotor (NR) and the respectively adjacent tooth of the
secondary rotor, and an apex point F5 is defined at the radially
outermost point of the tooth, wherein a triangle D.sub.z is defined
by F1, F2 and F5 and wherein in a radially outer region of the
tooth, the leading tooth flank F.sub.V formed between F5 and F2
projects with an area A1 beyond the triangle D.sub.Z and in a
radially inner region is set back with respect to the triangle
D.sub.z with an area A3 and wherein 7.0.ltoreq.A3/A1.ltoreq.35 is
maintained. With regard to the illustration of the parameters,
reference is additionally made to FIG. 7d.
[0069] Furthermore, with regard to the configuration of the
secondary rotor, it is considered to be advantageous if in a
transverse sectional view, foot points F1 and F2 are defined
between the observed tooth of the secondary rotor (NR) and the
respectively adjacent tooth of the secondary rotor (NR) and an apex
point F5 is defined at the radially outermost point of the tooth,
wherein a triangle D.sub.z is defined by F1, F2 and F5 and wherein
in a radially outer region of the tooth, the leading tooth flank
F.sub.V formed between F5 and F2 projects with an area A1 beyond
the triangle D.sub.Z and wherein the tooth itself has a
cross-sectional area A0 delimited by the circular arc B running
between F1 and F2 about the centre point defined by the axis C1 and
wherein 0.5%.ltoreq.A1/A0.ltoreq.4.5% is maintained. With regard to
the illustration of the parameters, reference is additionally made
to FIGS. 7d and 7e.
[0070] A further preferred embodiment provides that in a transverse
sectional view, foot points F1 and F2 are defined between the
observed tooth of the secondary rotor (NR) and the respectively
adjacent tooth of the secondary rotor and an apex point F5 is
defined is defined at the radially outermost point of the tooth,
wherein the circular arc B running between F1 and F2 defines a
tooth partition angle .alpha. corresponding to 360.degree./number
of teeth of the secondary rotor (NR) about the centre point defined
by the axis C1, wherein a point F11 is defined on the half circular
arc B between F1 and F2, wherein a radial half-line R drawn from
the centre point of the secondary rotor (NR) defined by the axis C1
through the apex point F5 intersects the circular arc B at a point
F12, wherein an offset angle .beta. is defined by the offset of F11
to F12 viewed in the direction of rotation of the secondary rotor
(NR) and wherein 14%.ltoreq..delta..ltoreq.25% is maintained,
where
.delta. = .beta. .gamma. * 100 .times. [ % ] . ##EQU00012##
[0071] Firstly it is again clarified that the offset angle is
preferably always positive, i.e. the offset is always given in the
direction of the direction of rotation and not contrary to this. In
this respect the tooth of the secondary rotor is curved with
respect to the axis of rotation of the secondary rotor. However,
the offset should be kept in a range specified as advantageous in
order to enable a favourable compromise between the blow hole area,
the shape of the engagement line, the length and the shape of the
profile engagement gap, the secondary rotor torque, the flexural
rigidity of the rotors and the chamber expulsion into the pressure
window. With regard to the illustration of the parameters,
reference is additionally made to FIG. 7f.
[0072] It is considered to be advantageous if in a transverse
sectional view, the trailing tooth flank F.sub.N of a tooth of the
secondary rotor (NR) formed between F1 and F5 has a convex length
component of at least 45% to at most 95%.
[0073] The relatively long convex length component of the trailing
tooth flank F.sub.N of a tooth of the secondary rotor specified
with the range allows a good compromise between length of the
profile engagement gap, chamber expulsion, secondary rotor torque
on the one hand and flexural rigidity of the secondary rotor on the
other hand. With regard to the illustration of the parameters,
reference is additionally made to FIG. 7g.
[0074] Preferably the secondary rotor is configured in such a
manner that in a transverse sectional view, the radial half-line
drawn from the axis C1 of the secondary rotor (NR) through F5
divides the tooth profile into an area component A5 assigned to the
leading tooth flank F.sub.V and an area component A4 assigned to
the trailing tooth flank F.sub.N and wherein
5.ltoreq.A4/A5.ltoreq.14
is maintained. It should be noted once again at this point that the
tooth profile is delimited radially inwards towards the C1 axis by
the dedendum circle FK.sub.1. In this case, it can occur that the
radial half-line R divides the tooth profile in such a manner that
two disjoint area components with a total area component A5 which
are assigned to the leading tooth flank F.sub.V are formed, cf.
FIG. 7g. If the apex point F5 were to be offset with respect to the
leading tooth flank in such a manner that the radial half-line F5
not only touches the leading tooth flank F.sub.V but intersects it
at two points, two disjoint area components assigned to the leading
tooth flank with a total area component A5 are again defined. The
area component A4 assigned to the trailing tooth flank F.sub.N is
then delimited on the one hand by the radial half-line R, in
sections, namely between the two points of intersection of the
leading tooth flank F.sub.V with the radial half-line, on the other
hand by the leading tooth flank F.sub.V.
[0075] A further preferred embodiment comprises a rotor pair which
is characterized in that the main rotor HR is formed with a
wrap-around angle .PHI..sub.HR for which it holds that:
290.degree..ltoreq..PHI..sub.HR.ltoreq.360.degree., preferably
320.degree..ltoreq..PHI..sub.HR.ltoreq.360.degree..
[0076] With increasing wrap-around angle, the pressure window area
can be configured to be larger for the same built-in volume ratio.
In addition, the axial extension of the working chamber to be
expelled, the so-called profile pocket depth, is shortened. This
reduces the expulsion throttle losses in particular at higher
rotational speeds and thus enables a better specific performance. A
too-large wrap-around angle in turn has a disadvantageous effect on
the installation volume and results in larger rotors.
[0077] In addition, in an advantageous embodiment a rotor pair is
provided which is configured in such a manner and interacts with
one another so that a blow hole factor .mu..sub.B1 is at least
0.02% and at most 0.4%, preferably at most 0.25%, wherein
.mu. Bl = A Bl A .times. 6 + A .times. 7 * 100 .times. [ % ]
##EQU00013##
arm wherein A.sub.B1 designates an absolute pressure-side blow hole
area and A6 and A7 designate tooth gap areas of the secondary rotor
(NR) or the main rotor (HR), wherein the area A6 in a transverse
sectional view is the area enclosed between the profile course of
the secondary rotor (NR) between two adjacent apex points F5 and
the addendum circle KK.sub.1 and the area A7 in a transverse
sectional view is the area enclosed between the profile course of
the main rotor (HR) between two adjacent apex points H5 and the
addendum circle KK.sub.2.
[0078] Whereas the absolute magnitude of the pressure-side blow
hole alone does not allow any meaningful prediction about the
effect on leakage mass flows, a ratio of the absolute pressure-side
blow hole area AB1 to the sum of the tooth gap area A6 of the
secondary rotor and the tooth gap area A7 of the main rotor is
substantially more predictive. With regard to the further
illustration of the parameters, reference is additionally made here
to FIG. 7b. The lower the numerical value of .mu..sub.B1, the
smaller is the influence of the blow hole on the operating
behaviour. The pressure-side blow hole area can thus be represented
independently of the installation size of the screw machine.
[0079] In a further preferred embodiment, a rotor pair is
configured and matched to one another in such a manner that for a
blow hole/profile gap length factor .mu..sub.1*.mu..sub.B1 it holds
that
0.1%.ltoreq..mu..sub.1*.mu..sub.B1.ltoreq.1.72%
where
.mu. l = l sp PT 1 , ##EQU00014##
where l.sub.sp designates the length of the profile engagement gap
of a tooth gap of the secondary rotor and PT.sub.1 designates the
profile depth of the secondary rotor, where
PT.sub.1=rk.sub.1-rf.sub.1 and
.mu. Bl = A Bl A .times. 6 + A .times. 7 * 100 .times. [ % ]
##EQU00015##
where A.sub.B1 designates the absolute blow hole area and A6 and A7
designate the profile areas of the secondary rotor (NR) or the main
rotor (HR), wherein the area A6 in a transverse sectional view
designates the area enclosed between the profile course of the
secondary rotor (NR) between two adjacent apex points F5 and the
addendum circle KK.sub.1, and the area A7 in a transverse sectional
view designates the area enclosed between the profile course of the
main rotor (HR) between two adjacent apex points H5 and the
addendum circle KK.sub.2.
[0080] .mu..sub.1 designates a profile gap length factor, where a
length of the profile engagement gap of a tooth gap is related to
the profile depth PT.sub.1. Thus, a measure for the length of the
profile engagement gap can be specified independently of the
installation size of the screw machine, The lower the numerical
value of the characteristic .mu..sub.1, the shorter is the profile
gap of a tooth pitch for the same profile depth and therefore the
smaller is the leakage volume flow back to the suction side. The
factor .mu..sub.1*.mu..sub.B1 gives the aim of combining a small
pressure-side blow hole with a short profile gap. As already
mentioned however, the two characteristics behave in a contrary
manner.
[0081] It is furthermore considered to be advantageous if main
rotor (HR) and secondary rotor (NR) are configured and tuned to one
another in such a manner that a dry compression with a pressure
ratio .PI. of up to 3, in particular with a pressure ratio .PI.
greater than 1 and up to 3 can be achieved, where the pressure
ratio is the ratio of compression end pressure to suction
pressure.
[0082] A further preferred embodiment provides a rotor pair in such
a manner that the main rotor (HR) is configured to be operated
relative to an addendum circle KK.sub.2 at a circumferential speed
in a range from 20 to 100 m/s.
[0083] A further embodiment provides a rotor pair which is
characterized in that for a diameter ratio defined by the ratio of
the addendum circle radii of main rotor (HR) and secondary rotor
(NR)
D v = Dk 2 Dk 1 = rk 2 rk 1 .times. .times. 1 . 1 .times. 4 .times.
5 .ltoreq. D v .ltoreq. 1.30 ##EQU00016##
is maintained, where Dk.sub.1 designates the diameter of the
addendum circle KK.sub.1 of the secondary rotor (NR) and Dk.sub.2
designates the diameter of the addendum circle KK.sub.2 of the main
rotor (HR). 2. Preferred Embodiments for a Rotor Pair with
Tooth-Number Ratio of 4/5
[0084] Preferred embodiments are presented hereinafter for a rotor
pair having a tooth number ratio of 4/5, i.e. for a rotor pair in
which the main rotor has four teeth and the secondary rotor has
five teeth:
[0085] A further preferred embodiment provides that in a transverse
sectional view, circular arcs B.sub.25, B.sub.50, B.sub.75 running
within a secondary rotor tooth are defined, the common centre point
of which is given by the axis C1, wherein the radius r.sub.25 of
B.sub.25 has the value r.sub.25=rf.sub.1+0.25*(rk.sub.1-rf.sub.1),
the radius r.sub.50 of B.sub.50 has the value
r.sub.50=rf.sub.1+0.5*(rk.sub.1-rf.sub.1), and the radius r.sub.75
of B.sub.75 has the value
r.sub.75=rf.sub.1+0.75*(rk.sub.1-rf.sub.1), and wherein the
circular arcs B.sub.25, B.sub.50, B.sub.75 are each delimited by
the leading tooth flank F.sub.V and trailing tooth flank F.sub.N,
wherein tooth thickness ratios are defined as ratios of the arc
lengths b.sub.25, b.sub.50, b.sub.75 of the circular arcs B.sub.25,
B.sub.50, B.sub.75 with .epsilon..sub.1=b.sub.50/b.sub.25 and
.epsilon..sub.2=b.sub.75/b.sub.25 and the following dimension is
adhered to: 0.75.ltoreq..epsilon..sub.1.ltoreq.0.85 and/or
0.65.ltoreq..epsilon..sub.2.ltoreq.0.74.
[0086] The aim is to combine a small blow hole with short length of
the profile engagement gap. However, the two parameters behave in a
contrary manner, i.e. the smaller the blow hole is modelled, the
larger the length of the profile engagement gap must necessarily
be. Conversely, the blow hole becomes larger, the shorter the
length of the profile engagement gap. In the claimed ranges a
particularly favourable combination of the two parameters is
achieved. At the same time, a sufficiently high flexural rigidity
of the secondary rotor is ensured. Furthermore, advantages are
obtained as regards the chamber expulsion and the secondary rotor
torque. With regard to the illustration of the parameters,
reference is additionally made to FIG. 7c.
[0087] A further preferred embodiment provides that in a transverse
sectional view, foot points F1 and F2 are defined on the dedendum
circle between the observed tooth of the secondary rotor (NR) and
the respectively adjacent tooth of the secondary rotor and an apex
point F5 is defined at the radially outermost point of the tooth,
wherein a triangle D.sub.z is defined by F1, F2 and F5 and wherein
in a radially outer region, the tooth projects beyond the triangle
D.sub.z with its leading tooth flank F.sub.V formed between F5 and
F2 with an area A1 and with its trailing tooth flank F.sub.N formed
between F1 and F5 with an area A2 and wherein
6.ltoreq.A2/A1.ltoreq.15 is maintained.
[0088] The tooth sub-area A1 at the leading tooth flank F.sub.V of
the secondary rotor has a substantial influence on the blow hole
area. The tooth sub-area A2 at the trailing tooth flank F.sub.N of
the secondary rotor on the other hand has a substantial influence
on the length of the profile engagement gap, the chamber expulsion
and the secondary rotor torque. For the tooth sub-area ratio A2/A1
there is an advantageous range which enables a good compromise
between length of the profile engagement gap on the one hand and
the blow hole on the other hand. With regard to the illustration of
the parameters, reference is additionally made to FIG. 7d.
[0089] In a further embodiment, the rotor pair comprises a
secondary rotor in which in a transverse sectional view, foot
points F1 and F2 are defined between the observed tooth of the
secondary rotor (NR) and the respectively adjacent tooth of the
secondary rotor (NR), and an apex point F5 is defined at the
radially outermost point of the tooth, wherein a triangle D.sub.z
is defined by F1, F2 and F5 and wherein in a radially outer region
of the tooth, the leading tooth flank F.sub.V formed between F5 and
F2 projects with an area A1 beyond the triangle D.sub.z and in a
radially inner region is set back with respect to the triangle
D.sub.z with an area A3 and wherein 9.0.ltoreq.A3/A1.ltoreq.18 is
maintained. With regard to the illustration of the parameters,
reference is additionally made to FIG. 7d.
[0090] Furthermore with regard to the configuration of the
secondary rotor, it is considered to be advantageous if in a
transverse sectional view, foot points F1 and F2 are defined
between the observed tooth of the secondary rotor (NR) and the
respectively adjacent tooth of the secondary rotor (NR) and an apex
point F5 is defined at the radially outermost point of the tooth,
wherein a triangle D.sub.z is defined by F1, F2 and F5 and wherein
in a radially outer region of the tooth, the leading tooth flank
F.sub.V formed between F5 and F2 projects with an area A1 beyond
the triangle D.sub.z, wherein the tooth itself has a
cross-sectional area A0 delimited by the circular arc B running
between F1 and F2 about the centre point defined by the axis C1 and
wherein 1.5%.ltoreq.A1/A0.ltoreq.3.5% is maintained.
[0091] With regard to the specification of the parameters,
reference is made to FIGS. 7d and 7e.
[0092] A further preferred embodiment provides that in a transverse
sectional view, foot points F1 and F2 are defined between the
observed tooth of the secondary rotor (NR) and the respectively
adjacent tooth of the secondary rotor (NR) and an apex point F5 is
defined at the radially outermost point of the tooth, wherein the
circular arc B running between F1 and F2 defines a tooth partition
angle .alpha. corresponding to 360.degree./number of teeth of the
secondary rotor (NR) about the centre point defined by the axis C1,
wherein a point F11 is defined on the half circular arc B between
F1 and F2, wherein a radial half-line R drawn from the centre point
of the secondary rotor (NR) defined by the axis C1 through the apex
point F5 intersects the circular arc B at a point F12, wherein an
offset angle .beta. is defined by the offset of F11 to F12 viewed
in the direction of rotation of the secondary rotor (NR) and
wherein
14%.ltoreq..delta..ltoreq.18%
is maintained where
.delta. = .beta. .gamma. * 100 .times. [ % ] . ##EQU00017##
[0093] Firstly it is again clarified that the offset angle is
preferably always positive, i.e. the offset is always given in the
direction of the direction of rotation and not contrary to this. In
this respect the tooth of the secondary rotor is curved with
respect to the axis of rotation of the secondary rotor. However,
the offset should be kept in a range specified as advantageous in
order to enable a favourable compromise between the blow hole area,
the shape of the engagement line, the length and the shape of the
profile engagement gap, the secondary rotor torque, the flexural
rigidity of the rotors and the chamber expulsion into the pressure
window. With regard to the illustration of the parameters,
reference is additionally made to FIG. 7f.
[0094] It is furthermore considered to be advantageous if in a
transverse sectional view, the trailing tooth flank F.sub.N of a
tooth of the secondary rotor (NR) formed between F1 and F5 has a
convex length component of at least 55% to at most 95%.
[0095] The relatively long convex length component of the trailing
tooth flank F.sub.N of a tooth of the secondary rotor specified
with the range allows a good compromise between length of the
profile engagement gap, chamber expulsion, secondary rotor torque
on the one hand and flexural rigidity of the secondary rotor on the
other hand. With regard to the illustration of the parameters,
reference is additionally made to FIG. 7g.
[0096] Preferably the secondary rotor is configured such that in a
transverse sectional view, the radial half-line drawn from the axis
C1 of the secondary rotor (NR) through F5 divides the tooth profile
into an area component A5 assigned to the leading tooth flank
F.sub.V and an area component A4 assigned to the trailing tooth
flank F.sub.N and wherein
4.ltoreq.A4/A5.ltoreq.9
is maintained. It should be noted once again at this point that the
tooth profile is delimited radially inwards towards the C1 axis by
the dedendum circle FK.sub.1. In this case, it can occur that the
radial half-line R divides the tooth profile in such a manner that
two disjoint area components with a total area component A5 which
are assigned to the leading tooth flank F.sub.V are formed, cf.
FIG. 7g. If the apex point F5 were to be offset with respect to the
leading tooth flank in such a manner that the radial half-line F5
not only touches the leading tooth flank F.sub.V but intersects it
at two points, two disjoint area components assigned to the leading
tooth flank with a total area component A5 are again defined. The
area component A4 assigned to the trailing tooth flank F.sub.N is
then delimited on the one hand by the radial half-line R, in
sections, namely between the two points of intersection of the
leading tooth flank F.sub.V with the radial half-line, on the other
hand by the leading tooth flank F.sub.V.
[0097] A further preferred embodiment comprises a rotor pair which
is characterized in that the main rotor HR is formed with a
wrap-around angle .PHI..sub.HR for which it holds that:
320.degree..ltoreq..PHI..sub.HR.ltoreq.360.degree., preferably
330.degree..ltoreq..PHI..sub.HR.ltoreq.360.degree..
[0098] With increasing wrap-around angle, the pressure window area
can be configured to be larger for the same built-in volume ratio.
In addition, the axial extension of the working chamber to be
expelled, the so-called profile pocket depth, is shortened. This
reduces the expulsion throttle losses in particular at higher
rotational speeds and thus enables a better specific performance. A
too-large wrap-around angle in turn has a disadvantageous effect on
the installation volume and results in larger rotors.
[0099] In addition, in an advantageous embodiment a rotor pair is
provided which is configured in such a manner and interacts with
one another so that a blow hole factor .mu..sub.B1 is at least
0.02% and at most 0.4%, preferably at most 0.25%, wherein
.mu. Bl = A Bl A .times. 6 + A .times. 7 * 100 .times. [ % ]
##EQU00018##
and wherein A.sub.B1 designates an absolute pressure-side blow hole
area and A6 and A7 designate tooth gap areas of the secondary rotor
(NR) or the main rotor (HR), wherein the area A6 in a transverse
sectional view is the area enclosed between the profile course of
the secondary rotor (NR) between two adjacent apex points F5 and
the addendum circle KK.sub.1 and the area A7 in a transverse
sectional view is the area enclosed between the profile course of
the main rotor (HR) between two adjacent apex points H5 and the
addendum circle KK.sub.2.
[0100] Whereas the absolute magnitude of the pressure-side blow
hole alone does not allow any meaningful prediction about the
effect on leakage mass flows, a ratio of the absolute pressure-side
blow hole area A.sub.B1 to the sum of the tooth gap area A6 of the
secondary rotor and the tooth gap area A7 of the main rotor is
substantially more predictive. With regard to the further
illustration of the parameters, reference is additionally made here
to FIG. 7b. The lower the numerical value of .mu..sub.B1, the
smaller is the influence of the blow hole on the operating
behaviour. The pressure-side blow hole area can thus be represented
independently of the installation size of the screw machine.
[0101] In a further preferred embodiment, a rotor pair is
configured and matched to one another in such a manner that
for a blow hole/profile gap length factor .mu..sub.1*.mu..sub.B1 it
holds that
0.1%.ltoreq..mu..sub.1*.mu..sub.B1.ltoreq.1.72%
where
.mu. l = l sp PT 1 , ##EQU00019##
where L.sub.sp designates the length of the profile engagement gap
of a tooth gap of the secondary rotor and PT.sub.1 designates the
profile depth of the secondary rotor where
PT.sub.1=rk.sub.1-rf.sub.1 and
.mu. Bl = A Bl A .times. 6 + A .times. 7 * 100 .times. [ % ]
##EQU00020##
where A.sub.B1 designates the absolute blow hole area and A6 and A7
designate the profile areas of the secondary rotor (NR) or the main
rotor (HR), wherein the area A6 in a transverse sectional view
designates the area enclosed between the profile course of the
secondary rotor (NR) between two adjacent apex points F5 and the
addendum circle KK.sub.1, and the area A7 in a transverse sectional
view designates the area enclosed between the profile course of the
main rotor (HR) between two adjacent apex points H5 and the
addendum circle KK.sub.2. .mu..sub.1 designates a profile gap
length factor, where a length of the profile engagement gap of a
tooth gap is related to the profile depth PT.sub.1. Thus, a measure
for the length of the profile engagement gap can be specified
independently of the installation size of the screw machine, The
lower the numerical value of the characteristic .mu..sub.1, the
shorter is the profile gap for the same profile depth and therefore
the smaller is the leakage volume flow back to the suction side.
The factor .mu..sub.1*.mu..sub.B1 gives the aim of combining a
small pressure-side blow hole with a short profile gap. As already
mentioned however, the two characteristics behave in a contrary
manner.
[0102] It is furthermore considered to be advantageous if main
rotor (HR) and secondary rotor (NR) are configured and tuned to one
another in such a manner that a dry compression with a pressure
ratio .PI. of up to 5, in particular with a pressure ratio .PI.
greater than 1 and up to 5 can be achieved, or alternatively a
fluid-injected compression with a pressure ratio .PI. of up to 16,
in particular with a pressure ratio .PI. of greater than 1 and up
to 16, where the pressure ratio is the ratio of compression end
pressure to suction pressure.
[0103] A further preferred embodiment provides a rotor pair in such
a manner that in the case of a dry compression the main rotor (HR)
is configured to be operated relative to an addendum circle
KK.sub.2 at a circumferential speed in a range from 20 to 100 m/s
and in the case of a fluid-injected compression the main rotor (HR)
is configured to be operated relative to an addendum circle
KK.sub.2 at a circumferential speed in a range from 5 to 50
m/s.
[0104] A further embodiment comprises a rotor pair which is
characterized in that for a diameter ratio defined by the ratio of
the addendum circle radii of main rotor (HR) and secondary rotor
(NR)
D v = Dk 2 Dk 1 = rk 2 rk 1 ##EQU00021##
it holds that where Dk.sub.1 designates the diameter of the
addendum circle KK.sub.1 of the secondary rotor (NR) and Dk.sub.2
designates the diameter of the addendum circle KK.sub.2 of the main
rotor (HR). 3. Preferred Embodiments for a Rotor Pair with a Tooth
Number Ratio of 5/6
[0105] Preferred embodiments are set out hereinafter for a rotor
pair with a tooth number ratio 5/6, i.e. for a rotor pair in which
the main rotor has five teeth and the secondary rotor has six
teeth:
[0106] A first preferred embodiment provides that in a transverse
sectional view, circular arcs B.sub.25, B.sub.50, B.sub.75 running
within a secondary rotor tooth are defined, the common centre point
of which is given by the axis C1, wherein the radius r.sub.25 of
B.sub.25 has the value r.sub.25=rf.sub.1+0.25*(rk.sub.1-rf.sub.1),
the radius r.sub.50 of B.sub.50 has the value
r.sub.50=rf.sub.1+0.5*(rk.sub.1-rf.sub.1), and the radius r.sub.75
of B.sub.75 has the value
r.sub.75=rf.sub.1+0.75*(rk.sub.1-rf.sub.1), and wherein the
circular arcs B.sub.25, B.sub.50, B.sub.75 are each delimited by
the leading tooth flank F.sub.V and trailing tooth flank F.sub.N,
wherein tooth thickness ratios are defined as ratios of the arc
lengths b.sub.25, b.sub.50, b.sub.75 of the circular arcs B.sub.25,
B.sub.50, B.sub.75 with .epsilon..sub.1=b.sub.50/b.sub.25 and
.epsilon..sub.2=b.sub.75/b.sub.25 and the following dimension is
adhered to: 0.76.ltoreq..epsilon..sub.1<0.86 and/or
0.62.ltoreq..epsilon..sub.2.ltoreq.0.72.
[0107] The aim is to combine a small blow hole with short length of
the profile engagement gap. However the two parameters behave in a
contrary manner, i.e. the smaller the blow hole is modelled, the
larger the length of the profile engagement gap necessarily
becomes. Conversely the blow hole becomes larger, the shorter is
the length of the profile engagement gap. In the claimed ranges a
particularly favourable combination of the two parameters is
achieved. At the same time a sufficiently high flexural rigidity of
the secondary rotor is achieved. Furthermore, advantages are
established as far as the chamber expulsion is concerned and for
the secondary rotor torque. With regard to the illustration of the
parameters, reference is additionally made to FIG. 7c.
[0108] A further preferred embodiment provides that in a transverse
sectional view, foot points F1 and F2 are defined on the dedendum
circle between the observed tooth of the secondary rotor (NR) and
the respectively adjacent tooth of the secondary rotor and an apex
point F5 is defined at the radially outermost point of the tooth,
wherein a triangle D.sub.z is defined by F1, F2 and F5 and wherein
in a radially outer region, the tooth projects beyond the triangle
D.sub.z with its leading tooth flank F.sub.V formed between F5 and
F2 with an area A1 and with its trailing tooth flank F.sub.N formed
between F1 and F5 with an area A2 and wherein
4.ltoreq.A2/A1.ltoreq.7 is maintained.
[0109] The tooth sub-area A1 at the leading tooth flank F.sub.V of
the secondary rotor has a substantial influence on the blow hole
area. The tooth sub-area A2 at the trailing tooth flank F.sub.N of
the secondary rotor on the other hand has a substantial influence
on the length of the profile engagement gap, the chamber expulsion
and the secondary rotor torque. For the tooth sub-area ratio A2/A1
there is an advantageous range which enables a good compromise
between length of the profile engagement gap on the one hand and
the blow hole on the other hand. With regard to the illustration of
the parameters, reference is additionally made to FIG. 7d.
[0110] In a further preferred embodiment, the rotor pair comprises
a secondary rotor in which in a transverse sectional view, foot
points F1 and F2 are defined between the observed tooth of the
secondary rotor (NR) and the respectively adjacent tooth of the
secondary rotor (NR) and an apex point F5 is defined at the
radially outermost point of the tooth, wherein a triangle D.sub.z
is defined by F1, F2 and F5 and wherein in a radially outer region
of the tooth, the leading tooth flank F.sub.V formed between F5 and
F2 projects with an area A1 beyond the triangle D.sub.z and in a
radially inner region is set back with respect to the triangle
D.sub.z with an area A3 and wherein 8.0.ltoreq.A3/A1.ltoreq.14 is
maintained. With regard to the illustration of the parameters,
reference is additionally made to FIG. 7d.
[0111] Furthermore, with regard to the configuration of the rotor,
it is considered to be advantageous if in a transverse sectional
view, foot points F1 and F2 are defined between the observed tooth
of the secondary rotor (NR) and the respectively adjacent tooth of
the secondary rotor (NR) and an apex point F5 is defined at the
radially outermost point of the tooth, wherein a triangle D.sub.z
is defined by F1, F2 and F5 and wherein in a radially outer region
of the tooth, the leading tooth flank F.sub.V formed between F5 and
F2 projects with an area A1 beyond the triangle D.sub.z, wherein
the tooth itself has a cross-sectional area A0 delimited by the
circular arc B running between F1 and F2 about the centre point
defined by the axis C1 and wherein 1.9%.ltoreq.A1/A0.ltoreq.3.2% is
maintained. With regard to the illustration of the parameters,
reference is additionally made to FIGS. 7d and 7e.
[0112] A further preferred embodiment provides that in a transverse
sectional view, foot points F1 and F2 are defined between the
observed tooth of the secondary rotor (NR) and the respectively
adjacent tooth of the secondary rotor (NR) and an apex point F5 is
defined at the radially outermost point of the tooth, wherein the
circular arc B running between F1 and F2 defines a tooth partition
angle .alpha. corresponding to 360.degree./number of teeth of the
secondary rotor (NR) about the centre point defined by the axis C1,
wherein a point F11 is defined on the half circular arc B between
F1 and F2, wherein a radial half-line R drawn from the centre point
of the secondary rotor (NR) defined by the axis C1 through the apex
point F5 intersects the circular arc B at a point F12, wherein an
offset angle .beta. is defined by the offset of F11 to F12 viewed
in the direction of rotation of the secondary rotor (NR) and
wherein
13.5%.ltoreq..delta..ltoreq.18%
is maintained where
.delta. = .beta. .gamma. * 100 .times. [ % ] . ##EQU00022##
[0113] Firstly it is again clarified that the offset angle is
preferably always positive, i.e. the offset is always given in the
direction of the direction of rotation and not contrary to this. In
this respect the tooth of the secondary rotor is curved with
respect to the axis of rotation of the secondary rotor. However,
the offset should be kept in a range specified as advantageous in
order to enable a favourable compromise between the blow hole area,
the shape of the engagement line, the length and the shape of the
profile engagement gap, the secondary rotor torque, the flexural
rigidity of the rotors and the chamber expulsion into the pressure
window. With regard to the illustration of the parameters,
reference is additionally made to FIG. 7f.
[0114] A further preferred embodiment comprises a rotor pair which
is characterized in that the main rotor HR is formed with a
wrap-around angle .PHI..sub.HR for which it holds that:
320.degree..ltoreq..PHI..sub.HR.ltoreq.360.degree., preferably
330.degree..ltoreq..PHI..sub.HR.ltoreq.360.degree.. With increasing
wrap-around angle, the pressure window area can be configured to be
larger for the same built-in volume ratio. In addition, the axial
extension of the working chamber to be expelled, the so-called
profile pocket depth, is shortened. This reduces the expulsion
throttle losses in particular at higher rotational speeds and thus
enables a better specific performance. A too-large wrap-around
angle in turn has a disadvantageous effect on the installation
volume and results in larger rotors.
[0115] In addition, in an advantageous embodiment a rotor pair is
provided which is configured in such a manner and interacts with
one another so that a blow hole factor .mu..sub.B1 is at least
0.03% and at most 0.25%, preferably at most 0.2%, wherein
.mu. Bl = A Bl A .times. 6 + A .times. 7 * 100 .times. [ % ]
##EQU00023##
and wherein A.sub.B1 designates an absolute pressure-side blow hole
area and A6 and A7 designate tooth gap areas of the secondary rotor
(NR) or the main rotor (HR), wherein the area A6 in a transverse
sectional view is the area enclosed between the profile course of
the secondary rotor (NR) between two adjacent apex points F5 and
the addendum circle KK.sub.1 and the area A7 in a transverse
sectional view is the area enclosed between the profile course of
the main rotor (HR) between two adjacent apex points H5 and the
addendum circle KK.sub.2.
[0116] Whereas the absolute magnitude of the pressure-side blow
hole alone does not allow any meaningful prediction about the
effect on leakage mass flows, a ratio of the absolute pressure-side
blow hole area A.sub.B1 to the sum of the tooth gap area A6 of the
secondary rotor and the tooth gap area A7 of the main rotor is
substantially more predictive. With regard to the further
illustration of the parameters, reference is additionally made here
to FIG. 7b. The lower the numerical value of .mu..sub.B1, the
smaller is the influence of the blow hole on the operating
behaviour. The pressure-side blow hole area can thus be represented
independently of the installation size of the screw machine.
[0117] In a further preferred embodiment, a rotor pair is
configured and matched to one another in such a manner that for a
blow hole/profile gap length factor .mu..sub.1*.mu..sub.B1 it holds
that
0.1%.ltoreq..mu..sub.1*.mu..sub.B1.ltoreq.1.26%
where
.mu. l = l sp PT 1 , ##EQU00024##
where L.sub.sp designates the length of the profile engagement gap
of a tooth gap of the secondary rotor and PT.sub.1 designates the
profile depth of the secondary rotor where
PT.sub.1=rk.sub.1-rf.sub.1 and
.mu. Bl = A Bl A .times. 6 + A .times. 7 * 100 .function. [ % ]
##EQU00025##
where A.sub.B1 designates the absolute blow hole area and A6 and A7
designate the profile areas of the secondary rotor (NR) or the main
rotor (HR), wherein the area A6 in a transverse sectional view
designates the area enclosed between the profile course of the
secondary rotor (NR) between two adjacent apex points F5 and the
addendum circle KK.sub.1, and the area A7 in a transverse sectional
view designates the area enclosed between the profile course of the
main rotor (HR) between two adjacent apex points H5 and the
addendum circle KK.sub.2.
[0118] .mu..sub.1 designates a profile gap length factor, where the
length of the profile engagement gap of a tooth gap is related to
the profile depth PT.sub.1. Thus, a measure for the length of the
profile engagement gap can be specified independently of the
installation size of the screw machine. The lower the numerical
value of the characteristic .mu..sub.1, the shorter is the profile
gap for the same profile depth and therefore the smaller is the
leakage volume flow back to the suction side. The factor
.mu..sub.1*.mu..sub.B1 gives the aim of combining a small
pressure-side blow hole with a short profile gap. As already
mentioned however, the two characteristics behave in a contrary
manner.
[0119] It is furthermore considered to be advantageous if main
rotor (HR) and secondary rotor (NR) are configured and tuned to one
another in such a manner that a dry compression with a pressure
ratio .PI. of up to 5, in particular with a pressure ratio .PI.
greater than 1 and up to 5 can be achieved, or alternatively a
fluid-injected compression with a pressure ratio .PI. of up to 20,
in particular with a pressure ratio .PI. of greater than 1 and up
to 20, where the pressure ratio is the ratio of compression end
pressure to suction pressure.
[0120] A further preferred embodiment provides a rotor pair in such
a manner that in the case of a dry compression the main rotor (HR)
is configured to be operated relative to an addendum circle
KK.sub.2 at a circumferential speed in a range from 20 to 100 m/s
and in the case of a fluid-injected compression the main rotor (HR)
is configured to be operated relative to an addendum circle
KK.sub.2 at a circumferential speed in a range from 5 to 50
m/s.
[0121] A further embodiment provides a rotor pair which is
characterized in that for a diameter ratio defined by the ratio of
the addendum circle radii of main rotor (HR) and secondary rotor
(NR) it holds that
D v = D .times. k 2 D .times. k 1 = r .times. k 2 r .times. k 1
.times. .times. 1 . 1 .times. 9 .ltoreq. D v .ltoreq. 1.26
##EQU00026##
where Dk.sub.1 designates the diameter of the addendum circle
KK.sub.1 of the secondary rotor (NR) and Dk.sub.2 designates the
diameter of the addendum circle KK.sub.2 of the main rotor
(HR).
4. Preferred Embodiment for a Rotor Pair Having a Tooth-Number
Ratio of 3/4, 4/5 or 5/6
[0122] It is generally considered to be preferable that in a
transverse sectional view the teeth of the secondary rotor taper
outwards, i.e. all circular arcs running perpendicular to a radial
half-line starting from a centre point defined by the axis C1,
drawn through the point F5, decrease radially outwards starting
from the trailing tooth flank F.sub.N towards the leading tooth
flank F.sub.V in the sequence from F1 to F2 (or at least remain the
same in sections). In other words, in a transverse sectional view
for all the arc lengths b(r), running inside a tooth of the
secondary rotor, of the respectively appurtenant concentric
circular arcs having the radius rf.sub.1<r<rk.sub.1 and the
common central point defined by the axis C1, which are each
delimited by the leading tooth flank F.sub.V and the trailing tooth
flank F.sub.N, it holds that the arc lengths b(r) decrease
monotonically with increasing radius r.
[0123] The teeth of the secondary rotor in this preferred
embodiment are therefore configured in such a manner that no
constrictions are obtained, i.e. the width of one tooth of the
secondary rotor does not increase at any point but decreases
radially outwards or remains at a maximum. This is considered to be
appropriate in order to achieve on the one hand a small
pressure-side blow hole with a nevertheless short profile
engagement gap length.
[0124] Advantageously the transverse sectional configuration of the
secondary rotor (NR) is executed in such a manner that the
direction of action of the torque which results from a reference
pressure on the partial surface of the secondary rotor delimiting
the working chamber is directed contrary to the direction of
rotation of the secondary rotor.
[0125] Such a transverse sectional configuration has the effect
that the entire torque from the gas forces on the secondary rotor
is directed contrary to the direction of rotation of the secondary
rotor. As a result, a defined flank contact is achieved between the
trailing secondary rotor flank F.sub.N and the leading main rotor
flank. This helps to avoid the problem of so-called rotor rattling
which can occur in unfavourable, in particular non-steady-state
operating situations. Rotor rattling is understood to be an
advancement and lagging of the secondary rotor superimposed on the
uniform rotational movement about its axis of rotation which is
accompanied by a rapidly changing impacting of the trailing
secondary rotor flanks against the leading main rotor flanks and
then of the leading secondary rotor flanks against the trailing
main rotor flanks etc. This problem occurs in particular when the
torque from the gas forces together with other torques (e.g. from
bearing friction) on the secondary rotor is undefined (i.e. is
close to zero, which is effectively avoided by the advantageous
transverse sectional configuration.
[0126] In a specifically possible optional embodiment, main rotor
(HR) and secondary rotor (NR) are configured and tuned to one
another for conveying air or inert gases such as helium or
nitrogen.
[0127] It is preferred that in a transverse sectional view, the
profile of a tooth of the secondary rotor relative to the radial
half-line R drawn from the centre point defined by the axis C1
through the apex point F5 is configured to be asymmetrical. In the
secondary rotor therefore leading tooth flank and trailing tooth
flank of each tooth are configured to be asymmetrical with respect
to one another. This asymmetrical configuration is per se already
known for screw compressors. However, it makes a substantial
contribution to efficient compression.
[0128] A further preferred embodiment provides that in a transverse
sectional view a point C is defined on the connecting section C1C2
between the first axis (C1) and the second axis (C2) where the
pitch circles WK.sub.1 of the secondary rotor (NR) and WK.sub.2 of
the main rotor (HR) contact, that K5 defines the point of
intersection of the dedendum circle FK.sub.1 of the secondary rotor
(NR) with the connecting section C1C2, where r.sub.1 determines the
distance between K5 and C and that K4 designates the point of the
suction-side part of the line of engagement which lies at the
greatest distance from the connecting section C1C2 between C1 and
C2, where r.sub.2 determines the distance between K4 and C and
where it hold that:
0 . 9 .ltoreq. r 1 r 2 .ltoreq. 0 . 8 .times. 7 .times. 5 .times. z
1 z 2 + 0 . 2 .times. 2 ##EQU00027##
where z.sub.1 is the number of teeth of the secondary rotor (NR)
and z.sub.2 is the number of teeth of the main rotor (HR).
[0129] Inter alia, the secondary rotor torque (=torque on the
secondary rotor) and the chamber expulsion into the pressure window
can be influenced by means of the profile of the suction-side part
of the line of engagement between the straight-line section C1C2
and the suction-side intersection edge. Characteristic features of
the aforesaid profile of the suction-side part of the line of
engagement can be described by means of the radii ratio
r.sub.1/r.sub.2 of two concentric circles about the point C
(=contact point of pitch circle WK.sub.1 of the secondary rotor and
pitch circle WK.sub.2 of the main rotor). If the radii ratio
r.sub.1/r.sub.2 lies within the specified range, the working
chamber is expelled substantially completely into the pressure
window.
[0130] In a preferred embodiment, the rotor pair is formed and
configured in such a manner that for a rotor length ratio
L.sub.HR/a it holds that:
0.85*(z.sub.1/z.sub.2)+0.67.ltoreq.L.sub.HR/a.ltoreq.1.26*(z.sub.1/z.sub.-
2)+1.18, preferably
0.89*(z.sub.1/z.sub.2)+0.94.ltoreq.L.sub.HR/a.ltoreq.1.05*(z.sub.1/z.sub.-
2)+1.22, where z.sub.1 is the number of teeth of the secondary
rotor (NR) and z.sub.2 is the number of teeth of the main rotor
(HR), wherein the rotor length ratio L.sub.HR/a gives the ratio of
the rotor length Lim to the axial distance a and rotor length
L.sub.HR is the distance of the suction-side main-rotor rotor end
face to the pressure-side main-rotor rotor end face.
[0131] The lower the value of L.sub.HR/a, the higher will be the
flexural rigidity of the rotors (for the same displacement). In the
claimed range the flexural rigidity of the rotors is sufficiently
high so that the rotors do not bend significantly during operation
and therefore the gap (between rotors or between rotors and
compressor housing) can be designed to be relatively narrow without
the risk thereby arising that the rotors run onto one another or
run on in the compressor housing under unfavourable operating
conditions (high temperatures and/or high pressures). Narrow gaps
offer the advantage of low back flows and therefore contribute to
the energy efficiency. At the same time, despite small gap
dimensions, the operating safety is ensured. Also during rotor
manufacture a high flexural rigidity of the rotors is advantageous
for adhering to the high requirements for the shape tolerances.
[0132] On the other hand however, the ratio L.sub.HR/a is so large
that the axial distance a is not excessively large in relation to
the rotor length L.sub.HR. This is advantageous since in
consequence the rotor diameter and quite specifically the end faces
of the rotors are not excessively large. As a result on the one
hand, the gap lengths can be kept small; this results in a
reduction of the back flow into preceding working chambers and as a
result in turn improvement of the energy efficiency. On the other
hand, as a result of small end face dimensions, the axial forces
resulting from the pressurized pressure-side end faces of the
rotors can advantageously be kept small, these axial forces act
during operation on the rotors and in particular on the rotor
mounting. By minimizing these axial forces, the loading of the
(roller) bearings can be minimized or the bearings can have smaller
dimensions.
[0133] It can advantageously be further provided that in a
transverse sectional view the tooth profile of the secondary rotor
(NR) on its radially outer section in sections follows a circular
arc ARC.sub.1 having the radius rk.sub.1, i.e. a plurality of
points of the leading tooth flank F.sub.V and the trailing tooth
flank F.sub.N lie on the circular arc having the radius rk.sub.1
around the centre point defined by the axis C1, wherein preferably
the circular arc ARC.sub.1 encloses an angle relative to the axis
C1 between 0.5.degree. and 5.degree., further preferably between
0.5.degree. and 2.5.degree., wherein F10 is the point at the
furthest distance from F5 on the leading tooth flank on this
circular arc and wherein the radial half-line R10 drawn between F10
and the centre point of the secondary rotor (NR) defined by the
axis C1 contacts the leading tooth flank F.sub.V at least at one
point or at two points, cf. in particular the illustration in FIG.
7h.
[0134] The previously described embodiment of the tooth profile of
the secondary rotor is primarily relevant for a tooth-number ratio
of 3/4 or 4/5. With such a tooth-number ratio, the blow hole area
can be reduced by satisfying the condition reproduced above. For
the tooth-number ratio 5/6 on the other hand, an aforesaid contact
point or aforesaid points of intersection with the leading tooth
flank F.sub.V, does not seem desirable since the teeth of the
secondary rotor then possibly become too thin and in consequence
too flexible.
[0135] Furthermore a compressor block comprising a compressor
housing and a rotor pair as described previously is claimed
according to the invention, wherein the rotor pair comprises a main
rotor HR and a secondary rotor NR, which are each mounted rotatably
in the compressor housing.
[0136] In a preferred embodiment, the compressor block is
configured in such a manner that the transverse sectional
configured is executed in such a manner that the working chamber
formed between the tooth profiles of main rotor (HR) and secondary
rotor (NR) can be expelled substantially completely into the
pressure window.
[0137] In general it is also considered to be advantageous that
with the selection of the profiles of secondary rotor and main
rotor presented here it is possible to completely dispense with a
pressure-relief groove/noise groove or to make this small.
[0138] As a result of the transverse sectional configuration of the
two rotors, it is advantageously achieved that during expulsion of
the working chambers into the pressure window, no chamber
interstitial volume is formed between the two rotors. Compression
can take place particularly efficiently since no back flow of
already-compressed medium to the suction side takes place and with
this no additional heat input accumulates. Furthermore, the entire
compressed volume can be utilized by downstream compressed air
users. As a result, over-compression is avoided, advantages are
obtained for the energy efficiency, for the smooth running of the
compressor block and for the lifetime of the rotor bearings. In
oil-injected compressors, compression of the oil is prevented and
thus the smooth running of the compressor is improved, the loading
of the rotor mounting is reduced and the stressing of the oil is
reduced.
[0139] In a further preferred embodiment a shaft end of the main
rotor is guided out from the compressor housing and configured for
connection to a drive, wherein preferably both shaft ends of the
secondary rotor are accommodated completely inside the compressor
housing.
BRIEF DESCRIPTION OF THE DRAWINGS
[0140] The invention is explained in further detail hereinafter
with regard to further features and advantages by reference to the
description of exemplary embodiments. In the figures:
[0141] FIG. 1 shows a transverse section of a first embodiment with
a tooth-number ratio of 3/4.
[0142] FIG. 2 shows a transverse section of a second embodiment
with a tooth-number ratio of 3/4.
[0143] FIG. 3 shows a transverse section of a third embodiment with
a tooth-number ratio of 4/5.
[0144] FIG. 4 shows a fourth exemplary embodiment in a transverse
sectional view with a tooth number ratio of 5/6.
[0145] FIG. 5 shows an illustration of the isentropic block
efficiency for the second exemplary embodiment for the 3/4
tooth-number ratio compared with the prior art.
[0146] FIG. 6 shows an illustration of the isentropic block
efficiency for the fourth exemplary embodiment for the 5/6
tooth-number ratio compared with the prior art.
[0147] FIG. 7a-7k shows illustration diagrams for the various
parameters of the geometry of the secondary rotor or the rotor pair
consisting of main rotor and secondary rotor.
[0148] FIG. 8 shows an illustration of the wrap-around angle at the
main rotor.
[0149] FIG. 9 shows a schematic sectional drawing of an embodiment
of a compressor block.
[0150] FIG. 10 shows an embodiment for an intermeshed rotor pair
consisting of a main rotor and a secondary rotor in
three-dimensional view.
[0151] FIG. 11 shows a perspective view of one embodiment of a
secondary rotor to illustrate the spatial line of engagement.
[0152] FIG. 12a, 12b shows an illustration of the areas or subareas
of a working chamber of one embodiment of the secondary rotor which
are relevant for the torque effects.
[0153] FIG. 13 shows the transverse section of the embodiment
according to FIG. 1 to explain the profile course of main and
secondary rotor in this embodiment.
[0154] FIG. 14 shows the transverse section of the embodiment
according to FIG. 2 to explain the profile course of main and
secondary rotor in this embodiment.
[0155] FIG. 15 shows the transverse section of the embodiment
according to FIG. 3 to explain the profile course of main and
secondary rotor in this embodiment.
[0156] FIG. 16 shows the transverse section of the embodiment
according to FIG. 4 to explain the profile course of main and
secondary rotor in this embodiment.
DETAILED DESCRIPTION
[0157] The exemplary embodiments according to FIGS. 1 to 4 will be
explained hereinafter.
[0158] All four exemplary embodiments represent suitable profiles
in the sense of the present invention.
[0159] The corresponding geometrical specifications for the main
rotor HR or the secondary rotor NR are given in Tables 1 to 4
reproduced hereinafter.
TABLE-US-00001 TABLE 1 Exemplary Exemplary Exemplary Exemplary
embodi- embodi- embodi- embodi- ment 1 ment 2 ment 3 ment 4 Teeth 3
3 4 5 number HR z.sub.2 Teeth 4 4 5 6 number NR z.sub.1 PT.sub.rel
[--] 0.588 0.54 0.528 0.455 a/rk.sub.1 [--] 1.66 1.72 1.764
1.78
TABLE-US-00002 TABLE 2 The profiles were created with the following
axial distances a: Exemplary Exemplary Exemplary Exemplary embodi-
embod- embodi- embodi- ment 1 iment 2 ment 3 ment 4 Axial distance
a 127 111 [mm]
TABLE-US-00003 TABLE 3 Thus the following transverse-section
principal dimensions are obtained: Exemplary Exemplary Exemplary
Exemplary embodi- embodi- embodi- embodi- ment ment 2 ment 3 ment 4
Dk.sub.2 [mm] 191 186.1 186 154 Dk.sub.1 [mm] 153 147.7 144 124.7
rw.sub.2 [mm] 54.4 56.4 50.5 rw.sub.1 [mm] 72.6 70.6 60.5
TABLE-US-00004 TABLE 4 Further principal dimensions of the rotors:
Exemplary Exemplary Exemplary Exemplary embodi- embodi- embodi-
embodi- ment 1 ment 2 ment 3 ment 4 Rotor length 307 293 235.5
L.sub.HR [mm]
[0160] In the exemplary embodiments presented, the following
features and characteristics according to the invention are
obtained, which are presented in Table 5:
TABLE-US-00005 TABLE 5 Compilation of the further features and
characteristics: Exemplary Exemplary Exemplary Exemplary embodi-
embodi- embodi- embodi- Feature ment 1 ment 2 ment 3 ment 4 Tooth
thickness 0.85 0.82 0.80 0.79 ratio .epsilon..sub.1 [--] Tooth
thickness 0.74 0.64 0.69 0.65 ratio .epsilon..sub.2 [--] Area ratio
A2/A1 15.7 37.8 10.0 6.2 [--] Area ratio A1/A0 2.3 1.1 2.2 2.3 [%]
Area ratio A3/A1 9.9 19.6 12.6 11.6 [--] Tooth curvature 18.5 21.1
15.7% 15.2 ratio .delta. [%] Convex length 66.9% 71.2% 62.7% --
component [%] Radial tooth The tooth thickness of the secondary
rotor thickness teeth decreases monotonically from the profile
addendum circle radius rf.sub.1 to the dedendum circle radius
rk.sub.1 Radial half-line Radial half-line R.sub.10 has two points
of R.sub.10 intersection with the leading tooth flank FV Area ratio
A4/A5 7.5 10.1 5.5 -- [--] Wrap-around 334.7.degree. 330.3 330.3
angle .PHI..sub.HR .mu..sub.B1 [%] 0.159 0.086 0.106 0.18
.mu..sub.B1 * .mu..sub.1 [%] 0.94 0.53 0.631 1.058 Profile
transverse The working chamber can be expelled sectional
substantially completely into the pressure configuration in window
relation to chamber expulsion Profile transverse The direction of
action of the NR torque sectional resulting from the gas forces is
directed configuration in contrary to the direction of rotation of
relation to the secondary rotor secondary rotor torque Shape of
1.037 1.044 0.984 1.0 engagement line r.sub.1/r.sub.2 Diameter
ratio Dv 1.248 1.26 1.292 1.235 Rotor length ratio 2.42 2.42 2.31
2.12 L.sub.HR/a
[0161] The isentropic block efficiency compared to the prior art is
illustrated for the second exemplary embodiment for the 3/4
tooth-number ratio in FIG. 5. Two curves for the same pressure
ratio are reproduced there. The specifically reproduced pressure
ratio is 2.0 (ratio of output pressure to input pressure). The
isentropic block efficiency could be improved significantly
compared with the values attainable with the prior art.
[0162] FIG. 6 shows the isentropic block efficiency compared to the
prior art for the fourth exemplary embodiment (5/6 tooth-number
ratio). Two curves for the same pressure ratio are also reproduced
here. The specifically reproduced pressure ratio is 9.0 (ratio of
output pressure to input pressure). Here also the isentropic block
efficiency could be improved significantly compared with the values
attainable with the prior art.
[0163] The quantity delivered specified in each case in FIGS. 5 and
6 corresponds to the conveyed volume flow of the compressor block
relative to the suction state.
[0164] FIG. 7a shows in a transverse sectional view one embodiment
for secondary rotor NR and main rotor HR with the centre points
given by the corresponding axes C1 and C2. Furthermore, the
geometrical principal dimensions or principal parameters of the
transverse sectional view are shown: [0165] Addendum circle
KK.sub.1 of the secondary rotor with appurtenant addendum circle
radius rk.sub.1 or addendum circle diameter Dk.sub.1 [0166]
Addendum circle KK.sub.2 of the main rotor with appurtenant
addendum circle radius rk.sub.2 or addendum circle diameter
Dk.sub.2 [0167] Dedendum circle FK.sub.1 of the secondary rotor
with appurtenant dedendum circle radius rf.sub.1 or dedendum circle
diameter Df.sub.1 [0168] Dedendum circle FK.sub.2 of the main rotor
with appurtenant dedendum circle radius rf.sub.2 or dedendum circle
diameter Df.sub.2 [0169] Axial distance a between the first axis C1
and the second axis C2 [0170] Pitch circle WK.sub.1 of the
secondary rotor with appurtenant pitch circle radius rw.sub.1 or
pitch circle diameter D.sub.W1 [0171] Pitch circle WK.sub.2 of the
main rotor with appurtenant pitch circle radius rw.sub.2 or pitch
circle diameter D.sub.W2
[0172] Also shown are the direction of rotation 24 of the secondary
rotor and the necessarily resulting direction of rotation of the
main rotor during operation as a compressor.
[0173] The leading tooth flank F.sub.V and the trailing tooth flank
F.sub.N are characterized on a secondary rotor tooth as
representative for all teeth of the secondary rotor. A tooth gap 23
is characterized as representative of all tooth gaps of the
secondary rotor. The profile course of the leading tooth flank
F.sub.V and of the trailing tooth flank F.sub.N shown by reference
to FIG. 7a corresponds to the exemplary embodiment for a
tooth-number ratio of 5/6 illustrated by reference to FIG. 4.
[0174] FIG. 7b shows in a transverse sectional view the tooth gap
areas A6 and A7 as well as a side view of a blow hole. The profile
courses shown in FIG. 7b to explain the tooth gap areas A6 and A7
correspond to the exemplary embodiment for a tooth number ratio of
3/4 illustrated by reference to FIG. 1.
[0175] Furthermore, FIG. 7b shows the position of the coordinate
system of the blow hole area A.sub.B1 shown in FIG. 7k in relation
to the rotor pair.
[0176] The coordinate system is spanned by the u-axis parallel to
the rotor end faces along the pressure-side intersection edge
11.
[0177] The pressure-side blow hole lies in the described coordinate
system and quite specifically in a plane perpendicular to the rotor
end faces between the pressure-side intersection edge 11 and an
engagement line point K2 of the pressure-side part of the line of
engagement.
[0178] In a transverse sectional view the line of engagement 10 is
divided into two sections by the connecting line between the two
centre points C1 and C2: the suction-side part of the line of
engagement is shown below, the pressure-side part is shown above
the connecting line.
[0179] K2 designates the point of the pressure-side part of the
line of engagement 10 which lies at the furthest distance from the
straight lines through C1 and C2. As a result of the intersection
of the addendum circles of the two rotors, a pressure-side
intersection edge 11 and a suction-side intersection edge 12 are
formed. In FIG. 7b the pressure-side intersection edge 11 is shown
as a point in a transverse sectional view. The same applies to the
depiction of the suction-side intersection edge 12.
[0180] The u-axis is a parallel to the rotor end faces and in a
transverse sectional view corresponds to the vector from the
engagement line point K2 to the pressure-side intersection edge 11.
Further details on the pressure-side blow hole area A.sub.B1 are
obtained from FIG. 7k.
[0181] FIG. 7c shows in a transverse sectional view a tooth of the
secondary rotor with the concentric circular arcs B.sub.25,
B.sub.50, B.sub.75 running inside the rotor tooth around the centre
point C1 with the appurtenant radii R.sub.25, B.sub.50, r.sub.75
and the appurtenant arc lengths b.sub.25, b.sub.50, b.sub.75.
[0182] The circular arcs B.sub.25, B.sub.50, B.sub.75 are in each
case delimited by the leading tooth flank F.sub.V and the trailing
tooth flank F.sub.N. The profile course of the leading tooth flank
F.sub.V and the trailing tooth flank F.sub.N shown by reference to
FIG. 7c corresponds to the exemplary embodiment explained by
reference to FIG. 4 for a tooth-number ratio of 5/6.
[0183] FIG. 7d shows in a transverse sectional view foot points F1
and F2 on the addendum circle between the observed tooth of the
secondary rotor and the respectively adjacent tooth of the
secondary rotor and an apex point F5 at the radially outermost
point of the tooth. Furthermore, the triangle D.sub.z defined by
the points F1, F2 and F5 is shown.
[0184] FIG. 7d shows the following (tooth sub-)areas:
[0185] Tooth sub-area A1 corresponds to the area with which the
observed tooth projects with its leading tooth flank F.sub.V formed
between F5 and F2 beyond the triangle D.sub.z in a radially outer
region.
[0186] Tooth sub-area A2 corresponds to the area with which the
observed tooth projects with its trailing tooth flank F.sub.N
formed between F5 and F1 beyond the triangle D.sub.z in a radially
outer region.
[0187] Area A3 corresponds to the area with which the observed
tooth is set back with its leading tooth flank formed between F5
and F2 with respect to the triangle D.sub.z.
[0188] Also shown is the tooth partition angle .gamma.
corresponding to 360.degree./number of teeth of the secondary
rotor. The profile course of the leading tooth flank F.sub.V and
the trailing tooth flank F.sub.N shown by reference to FIG. 7d
corresponds to the exemplary embodiment explained by reference to
FIG. 4 for a tooth-number ratio of 5/6.
[0189] FIG. 7e shows in a transverse sectional view the
cross-sectional area A0 of a tooth of the secondary rotor which is
delimited by the circular arc B running between F1 and F2 about the
centre point C1. The profile course of the leading tooth flank
F.sub.V and the trailing tooth flank F.sub.N shown by reference to
FIG. 7e corresponds to the exemplary embodiment explained by
reference to FIG. 4 for a tooth-number ratio of 5/6.
[0190] FIG. 7f shows in a transverse sectional view the offset
angle (3. This is defined by the offset from point F1l to point F12
observed in the direction of rotation of the secondary rotor. Flt
is a point on the half circular arc B between F1 and F2 about the
centre point C1 and consequently corresponds to the point of
intersection of the angle bisector of the tooth partition angle
.gamma. with the circular arc B.
[0191] F12 is obtained from the point of intersection of the radial
half-line R drawn from the centre point C1 to the apex point F5
with the circular arc B. The profile course of the leading tooth
flank F.sub.V and the trailing tooth flank F.sub.N shown by
reference to FIG. 7f corresponds to the exemplary embodiment
explained by reference to FIG. 4 for a tooth-number ratio of
5/6.
[0192] FIG. 7g shows in a transverse sectional view the turning
point F8 on the trailing tooth flank F.sub.N of the secondary rotor
at which the curvature of the course of the tooth profile changes
between addendum and dedendum circle.
[0193] The trailing tooth flank F.sub.N of the secondary rotor is
divided by the point F8 into a substantially convexly curved
component between F8 and the apex point F5 and a substantially
concavely curved component between F8 and the foot point F1.
[0194] FIG. 7h shows in a transverse sectional view two points of
intersection of the radial half-line R.sub.10 from C1 to F10 with
the leading tooth flank F.sub.V of the secondary rotor, wherein the
point F10 designates that point of the leading tooth flank F.sub.V
which lies on the addendum circle KK.sub.1 and is at the furthest
distance from F5. The tooth flank therefore radially outwards over
a defined section follows a circular arc ARC1 with radius rk.sub.1
about the centre point of the secondary rotor defined by the axis
C1. The profile courses of the leading tooth flank F.sub.V and the
trailing tooth flank F.sub.N explained by reference to FIG. 7h
correspond to the exemplary embodiment according to FIG. 1 for a
tooth-number ratio of 3/4.
[0195] FIG. 7i shows in a transverse sectional view the tooth
profile divided by the radial half-line drawn from C1 to F5.
[0196] Specifically in the embodiment shown, the tooth profile is
divided into an area component A4 assigned to the trailing tooth
flank F.sub.N and an area component A5 assigned to the leading
tooth flank F.sub.V. The profile courses of the leading tooth flank
F.sub.V and the trailing tooth flank F.sub.N explained by reference
to FIG. 7i correspond to the exemplary embodiment according to FIG.
4 described for a tooth-number ratio of 5/6.
[0197] FIG. 7j shows in a transverse sectional view the line of
engagement 10 between main and secondary rotor as well as the two
concentric circles about the point C having the radii r.sub.1 and
r.sub.2 to describe the characteristic features of the course of
the suction-side part of the line of engagement.
[0198] The line of engagement 10 is divided into two sections by
the connecting section between the first axis C1 and the second
axis C2: the suction-side part of the line of engagement is shown
below, the pressure-side part is shown above the connecting section
C1C2.
[0199] Point C is the point of contact of the pitch circle WK.sub.1
of the secondary rotor with the pitch circle WK.sub.2 of the main
rotor.
[0200] K4 designates the point of the suction-side part of the line
of engagement which lies at the greatest distance from the
connecting section between C1 and C2.
[0201] Radius r.sub.1 is the distance between K5 and C, radius
r.sub.2 designates the distance between K4 and C.
[0202] FIG. 7k:
[0203] FIG. 7k shows a pressure-side blow hole area A.sub.B1 of a
working chamber and specifically in a sectional view perpendicular
to the rotor end faces. The delimitation of the blow hole area
A.sub.B1 is formed here from the line of intersection 27 of the
above-described imaginary flat surface with the leading
secondary-rotor tooth flank F.sub.v, the line of intersection 26 of
the plane with the trailing HR flank and a straight line section
[K1 K3] of the pressure-side intersection edge 11.
[0204] The coordinate system of the pressure-side blow hole lies in
the flat surface described in FIG. 7b and is spanned by [0205] the
u-axis parallel to the rotor end faces (vector from the engagement
line point K2 to the pressure-side intersection edge 11) and [0206]
the pressure-side intersection edge 11.
[0207] In FIG. 8 the wrap-around angle .PHI. already discussed
several times is illustrated once again. Specifically this is the
angle .PHI. through which the transverse section is turned from the
suction-side to the pressure-side rotor end face. This is
illustrated in the present case by the turning of the profile
between a pressure-side end face 13 and a suction-side end face 14
through the angle .PHI..sub.HR at the main rotor HR.
[0208] FIG. 9 shows a schematic sectional view of a compressor
block 19 comprising a housing 15 as well as two rotors toothed with
one another in pairs, mounted therein, namely a main rotor HR and a
secondary rotor NR. Main rotor HR and secondary rotor NR are each
mounted rotatably in a housing 15 by means of suitable bearings 16.
A drive power can be applied to a shaft 17 of the main rotor HR,
for example with a motor (not shown) via a coupling 18.
[0209] The compressor block shown is an oil-injected screw
compressor in which the torque transmission between main rotor HR
and secondary rotor NR is accomplished directly by means of the
rotor flanks. In contrast to this in a dry screw compressor any
contact of the rotor flanks can be avoided by means of a
synchronization transmission (not shown).
[0210] Also not shown are a suction connection for suction of the
medium to be compressed and an outlet for the compressed
medium.
[0211] FIG. 10 shows intermeshed main rotor HR and secondary rotor
NR in a perspective view.
[0212] FIG. 11 shows the spatial line of engagement 10 of precisely
one tooth gap 23. The profile gap length I.sub.sp is the length of
the spatial line of engagement of precisely one tooth gap 23. This
therefore corresponds to the profile gap length of precisely one
tooth pitch.
[0213] The entire torque of the gas forces on the secondary rotor
is composed of the sum of the torque effects of the gas pressures
in all working chambers on the sub-surfaces of the secondary rotor
delimiting the respective working chambers. In FIG. 12a such a
sub-surface (22) of the secondary rotor delimiting a working
chamber is shown hatched as an example.
[0214] FIG. 12b shows the division of the sub-surface (22)
delimiting a working chamber, shown in FIG. 12a into an area (28)
shown dotted and an area (29) shown cross-hatched. Only the
cross-hatched area (29) makes a contribution to the torque.
[0215] The sub-surface (22) is obtained from the specific
transverse sectional configuration and pitch of the secondary
rotor. The pitch of the secondary rotor relates to the pitch of the
screw-shaped toothed structure of the secondary rotor. The
three-dimensional line of engagement (10) delimiting the
sub-surface, also shown in FIG. 12a is also specified by the
transverse sectional configuration of the secondary rotor and the
pitch.
[0216] Sub-surface (22) is also delimited by line of intersection
(27). Details on the line of intersection (27) have already been
presented and described within the framework of FIGS. 7b and 7k.
The same applies to the engagement line point K2.
[0217] The specific length of a working chamber in the direction of
the axis of rotation, which is dependent on the angular position of
the secondary rotor with respect to the main rotor, between the
secondary rotor end face (20) on the one hand and the delimitation
by the three-dimensional line of engagement (10) and line of
intersection (27) on the other hand does not play any significant
role here because--as is described in the relevant literature--the
gas pressures on regions of the rotor surface which in a sectional
plane perpendicular to the axis of the rotor correspond to complete
tooth gaps (shown dotted in FIG. 12b) make no contribution to the
torque. The pitch of the secondary rotor only has an effect on the
magnitude but not on the direction of action of the torque.
[0218] The area (28) shown dotted in FIG. 12b and the area (29)
shown cross-hatched in FIG. 12b together form the sub-surface
(22).
[0219] Only the area (29) shown cross-hatched in FIG. 12b makes a
contribution to the torque.
[0220] Thus, in each working chamber, the direction of action of
the torque which is brought about by the gas pressure in the
working chamber (or an arbitrary reference pressure) on the
sub-surface of the secondary rotor delimiting the working chamber,
is specified by the transverse sectional configuration of the
secondary rotor.
[0221] The above-described advantageous transverse sectional
configuration of the secondary rotor (NR) thus results for each
sub-surface (22) of the secondary rotor delimiting a working
chamber and thus for the entire secondary rotor in a direction of
action (25) of the torque from the gas forces which is directed
contrary to the direction of rotation (24) of the secondary rotor,
whereby rotor rattling is effectively avoided.
[0222] The exemplary embodiments presented confirm that with the
present invention a considerable increase in efficiency could be
achieved for a rotor pair used in screw machines consisting of main
rotor and secondary rotor having a corresponding profile
geometry.
[0223] With the present invention it has been possible to further
improve the efficiency and smooth running of rotor profiles
compared with the prior art independently of a specifically claimed
profile definition.
[0224] Although it will easily be possible for the person skilled
in the art using the specified parameter values to produce suitable
profile courses using conventional methods in the prior art, purely
as an example the profile courses in the previously discussed
exemplary embodiments according to FIGS. 1 to 4 will be explained
in detail hereinafter. As is best known to the person skilled in
the art working in the present field, in order to generate profile
courses, profile courses can also be generated using publicly
accessible computer programs.
[0225] Purely as an example in this connection mention is made of
SV_Win, a project of Vienna Technical University, where this
software is described in great detail in the Grafinger
post-doctoral thesis. An alternative, publicly accessible computer
program is moreover the DISCO software and in particular the
SCORPATH module of the City University London (Centre for Positive
Displacement Compressor Technology). General information on this
can be obtained from: http://www.city.compressors.co.uk/.
Information on installation of the software can be obtained from
http://www.staff.city.ac.uk/.about.ra600?DISCO/DISCO/Installation%20instr-
uctions.pdf. A preview of the DISCO software can be found at
http://www.staff.city.ac.uk/.about.ra600/DISC/DISCO%20Preview.htm.
[0226] Another alternative software is the software ScrewView which
is also mentioned in the thesis "Directed Evolutionary Algorithms"
by Stefan Berlik, Dortmund 2006 (p. 173 f). On the internet page
http://pi.information.uni-siegen.de/Mitarbeiter/berlip/projekte/
the ScrewView software is described in detail in connection with
the project "Method for the design of dry-running rotary compressor
machines."
[0227] In FIGS. 13 to 16 a tooth with trailing rotor flank F.sub.N
and leading rotor flank F.sub.V is specifically produced as
follows: the section S1 to S2 is obtained from a circular arc on
the secondary rotor NR about the centre point C1 produced by the
circular arc section T1 to T2 about the centre point C2 on the main
rotor HR. The section S2 to S3 is obtained from an envelope curve
to a trochoid produced by circular arc section T2 to T3 about the
centre point M4 on the main rotor HR. The section S3 to S4 is
defined by a circular arc about the centre point M1. The section S4
to S5 is predefined by a circular arc about the centre point
M2.
[0228] The section S5 to S6 is specified by a circular arc about
the centre point C1. The adjoining section S6 to S7 is predefined
by a circular arc about the centre point M3. The section S7 to S1
is finally predefined by an envelope curve to a trochoid produced
by the circular arc section T7 to T1 about the centre point M5 on
the main rotor HR. The previously described sections each adjoin
one another seamlessly in the specified sequence. The tangents at
the end of one section and at the beginning of the adjacent section
are each the same. The sections in this respect merge into one
another directly, smoothly and free from bends.
[0229] The profile course of the teeth of the main rotor HR is
explained briefly hereinafter for the exemplary embodiment
according to FIGS. 1 to 4 also with reference to FIGS. 13 to 16.
The section T1-T2 is obtained by a circular arc on the main rotor
HR about the centre point C2 on the main rotor HR. The section
T2-T3 is defined by the circular arc on the main rotor HR about the
centre point M4. The section T3-T4 is obtained from an envelope
curve to a trochoid produced by the section S3-S4 on the secondary
rotor NR. The section T4-T5 is predefined by an envelope curve to a
trochoid produced by the section S4-S5 on the secondary rotor. The
section T5-T6 is defined by a circular arc about the centre point
C2 produced by the circular arc section S5-S6 about the centre
point C1 on the secondary rotor NR. The section T6-T7 is obtained
by an envelope curve to a trochoid produced by the section S6-S7 on
the secondary rotor NR. The section T7-T1 finally is specified by a
circular arc about the centre point M5. Here it also applies that:
the previously described sections each adjoin one another
seamlessly in the specified sequence. The tangents at the end of
one section and at the beginning of the adjacent section are each
the same. The sections in this respect merge into one another
directly, smoothly and free from bends.
[0230] In general it should be noted that the profile courses of
secondary rotor NR and main rotor HR are naturally matched to one
another and in this respect the envelope curves to a trochoid each
correspond to circular arc sections on the counter-rotor.
Furthermore, as already mentioned a tangential transition from one
to the next section is ensured. A general procedure for calculating
the profile course of the counter rotor is described for example in
the Helpertz thesis "Method for stochastic optimization of screw
rotor profiles", Dortmund 2003, p. 60 ff.
* * * * *
References