U.S. patent application number 12/027513 was filed with the patent office on 2008-08-14 for roots-type fluid machine.
This patent application is currently assigned to KABUSHIKI KAISHA TOYOTA JIDOSHOKKI. Invention is credited to Toshiro Fujii, Takayuki Hirano, Daisuke Masaki, Yoshiyuki Nakane, Kazuho Yamada.
Application Number | 20080193315 12/027513 |
Document ID | / |
Family ID | 39685985 |
Filed Date | 2008-08-14 |
United States Patent
Application |
20080193315 |
Kind Code |
A1 |
Masaki; Daisuke ; et
al. |
August 14, 2008 |
ROOTS-TYPE FLUID MACHINE
Abstract
A roots-type fluid machine including a set of rotors and a rotor
housing is disclosed. The rotor housing accommodates the rotors and
has a suction space. The set of rotors mesh with each other and
rotate in the rotor housing so that fluid is drawn into the suction
space and discharged from the rotor housing. Each of the set of
rotors includes a tooth having a twisted portion and a different
shape variation portion. The twisted portion has a twist angle that
changes linearly or non-linearly about a rotation axis of the
corresponding rotor with respect to the variation of the position
in the direction of the axis. The different shape variation portion
has a twisted angle that changes by a smaller degree than the
variation of the twist angle of the twisted portion.
Inventors: |
Masaki; Daisuke;
(Kariya-shi, JP) ; Hirano; Takayuki; (Kariya-shi,
JP) ; Nakane; Yoshiyuki; (Kariya-shi, JP) ;
Yamada; Kazuho; (Kariya-shi, JP) ; Fujii;
Toshiro; (Kariya-shi, JP) |
Correspondence
Address: |
KNOBLE, YOSHIDA & DUNLEAVY
EIGHT PENN CENTER, SUITE 1350, 1628 JOHN F KENNEDY BLVD
PHILADELPHIA
PA
19103
US
|
Assignee: |
KABUSHIKI KAISHA TOYOTA
JIDOSHOKKI
KARIYA-SHI
JP
|
Family ID: |
39685985 |
Appl. No.: |
12/027513 |
Filed: |
February 7, 2008 |
Current U.S.
Class: |
418/201.3 ;
418/150; 418/196 |
Current CPC
Class: |
F01C 1/084 20130101;
F01C 1/126 20130101 |
Class at
Publication: |
418/201.3 ;
418/150; 418/196 |
International
Class: |
F04C 18/14 20060101
F04C018/14; F04C 18/18 20060101 F04C018/18; F04C 29/12 20060101
F04C029/12 |
Foreign Application Data
Date |
Code |
Application Number |
Feb 8, 2007 |
JP |
2007-029183 |
Feb 14, 2007 |
JP |
2007-033473 |
Feb 5, 2008 |
JP |
2008-025310 |
Feb 5, 2008 |
JP |
2008-025311 |
Claims
1. A roots-type fluid machine comprising a set of rotors and a
rotor housing, which accommodates the rotors and has a suction
space, the set of rotors meshing with each other and rotate in the
rotor housing so that fluid is drawn into the suction space and
discharged from the rotor housing, wherein each of the set of
rotors includes a tooth having a twisted portion and a different
shape variation portion, the twisted portion having a twist angle
that changes linearly or non-linearly about a rotation axis of the
corresponding rotor with respect to a variation of the position in
the direction of the axis, and the different shape variation
portion having a twisted angle that changes by a smaller degree
than the variation of the twist angle of the twisted portion.
2. The fluid machine according to claim 1, wherein the twisted
potion is helical and the different shape variation portion has a
straight line form parallel to the rotation axis.
3. The fluid machine according to claim 1, wherein the twisted
potion is helical and the different shape variation portion has a
form the twist angle of which changes with respect to the variation
of the position in the axial direction of the rotation axis in a
manner represented by a nonlinear function.
4. The fluid machine according to claim 1, wherein the different
shape variation portion is provided at a position including the
center of the rotor in the direction of the rotation axis.
5. The fluid machine according to claim 4, wherein the twisted
portion is provided on each side of the different shape variation
portion in the direction of the rotation axis, and the lengths of
the twisted portions are equal.
6. The fluid machine according to claim 1, wherein the different
shape variation portion is provided at a position including midway
between the center of the rotor in the direction of the rotation
axis and each of the ends of the associated rotor.
7. The fluid machine according to claim 1, wherein each rotor is
configured by laminating a plurality of flat plates having the same
shape and the same size in the direction of the rotation axis, and
the length of the different shape variation portion in the
direction of the rotation axis is greater than the thickness of
each flat plate.
8. The fluid machine according to claim 1, wherein, in each rotor,
the length of the different shape variation portion in the
direction of the rotation axis is shorter than the length of the
twisted portion in the direction of the rotation axis.
Description
BACKGROUND OF THE INVENTION
[0001] The present invention relates to a roots-type fluid machine
in which a set of rotors mesh with each other and rotate in a rotor
housing so that fluid is drawn into a suction space in the rotor
housing and discharged from the rotor housing.
[0002] A roots-type fluid machine with rotors having helical teeth
is disclosed in, for example, Japanese Laid-Open Patent Publication
No. 2-227588. The teeth of the rotors are monotonically twisted
into helical form around the rotation axes of the rotors. In the
roots-type fluid machine that uses helical rotors, the rotors are
helically twisted from one end to the other end. When the following
equation (1), in which the twist angle of the rotors is expressed
by .PHI., is satisfied, the volumetric change (the suction amount
of fluid to a suction space per unit time) does not fluctuate in
the suction space, which is located between the pair of meshed
rotors and communicates with an inlet formed in the rotor
housing.
.PHI.=(360.degree./2n).times.X (1)
[0003] in which n is the number of the teeth of the rotors (number
of lobes), and X is a positive integer. In a structure where the
volumetric change in the suction space does not fluctuate, the
suction pulsation basically does not occur.
[0004] However, in the roots-type fluid machine, which is operated
without providing oil between the rotor housing and the rotors and
between the rotors for lubrication, since a clearance is provided
for avoiding sliding contact between the rotor housing and the
rotors and between the rotors, fluid leaks between the rotor
housing and the rotors and between the rotors. Thus, although the
volumetric change of the suction space does not fluctuate, the
suction pulsation does not become zero, and the suction pulsation
of fundamental order caused by fluid leakage remains. For example,
if the rotors each have a three-lobe transverse cross section as
disclosed in Japanese Laid-Open Patent Publication No. 2-227588,
the suction pulsation of the fundamental order of sixth order
remains.
[0005] FIGS. 17A and 17B show a roots-type fluid machine with
three-lobe rotors 37, 38. The roots-type fluid machine includes an
inlet J1 and a suction space S, which communicates with the inlet
J1. The roots-type fluid machine further includes a discharge space
P and an outlet J2, which communicates with the discharge space P.
FIG. 17A shows a state where the distal end portion of a tooth 371
of the rotor 37 is fitted in a tooth bottom portion 382 of the
rotor 38. FIG. 17B shows a state where the rotors 37, 38 are
rotated by 30.degree. from the state in FIG. 17A, and where the
side portion of the tooth 371 of the rotor 37 has come close to the
side portion of the tooth 381 of the rotor 38.
[0006] The size of a minimum clearance CL1 at a closest portion K1
shown in FIG. 17A is equal to the size of a minimum clearance CL2
at a closest portion K2 shown in FIG. 17B. The clearance increases
as the distance from the minimum clearance CL1 increases along
circumferential direction of the distal end portion of the tooth
371 of the rotor 37. The clearance increases as the distance from
the minimum clearance CL2 increases along the circumferential
direction of the side portion of the tooth 371 of the rotor 37.
[0007] However, the change in the size of the clearance of the
closest portion K1 shown in FIG. 17A (the change along the
circumferential direction of the distal end portion of the tooth
371 of the rotor 37) is smaller than the change in the size of the
clearance at the closest portion K2 shown in FIG. 17B (the change
along the circumferential direction of the side portion of the
tooth 371 of the rotor 37). Thus, the fluid leakage between the
rotors 37, 38 in the state shown in FIG. 17A (fluid leakage to the
suction space S from the discharge space P via the space between
the rotors 37, 38) is small, and the fluid leakage between the
rotors 37, 38 in the state shown in FIG. 17B is great.
[0008] The state similar to that shown in FIG. 17A occurs six times
while the rotors 37, 38 rotate once, and the state similar to that
shown in FIG. 17B occurs six times while the rotors 37, 38 rotate
once. Thus, in the roots-type fluid machine, which uses three-lobe
helical rotors 37, 38, the suction pulsation of the fundamental
order of sixth order is generated due to fluid leakage.
[0009] If the transverse cross-sectional view of the rotors is
two-lobe in shape, the suction pulsation of the fundamental order
of fourth order caused by fluid leakage remains.
SUMMARY OF THE INVENTION
[0010] Accordingly, it is an objective of the present invention to
reduce suction pulsation caused by fluid leakage in a roots-type
fluid machine that uses rotors including twisted portions. The
twist angle of each twisted portion about the rotation axis of the
associated rotor changes linearly or nonlinearly with respect to
changes in the position in the axial direction of the rotation axis
of the rotor.
[0011] To achieve the above objective, and in accordance with one
aspect of the present invention, a roots-type fluid machine
including a set of rotors and a rotor housing is provided. The
rotor housing accommodates the rotors and has a suction space. The
set of rotors mesh with each other and rotate in the rotor housing
so that fluid is drawn into the suction space and discharged from
the rotor housing. Each of the set of rotors includes a tooth
having a twisted portion and a different shape variation portion.
The twisted portion has a twist angle that changes linearly or
non-linearly about a rotation axis of the corresponding rotor with
respect to the variation of the position in the direction of the
axis. The different shape variation portion has a twisted angle
that changes by a smaller degree than the variation of the twist
angle of the twisted portion.
[0012] Other aspects and advantages of the invention will become
apparent from the following description, taken in conjunction with
the accompanying drawings, illustrating by way of example the
principles of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] The invention, together with objects and advantages thereof,
may best be understood by reference to the following description of
the presently preferred embodiments together with the accompanying
drawings in which:
[0014] FIG. 1A is a plane cross-sectional view illustrating a fluid
machine according to a first embodiment of the present
invention;
[0015] FIG. 1B is a side view illustrating one of the rotors;
[0016] FIG. 1C is a side view illustrating one of the rotors;
[0017] FIG. 2A is a cross-sectional view taken along line 2A-2A in
FIG. 1A;
[0018] FIG. 2B is a cross-sectional view taken along line 2B-2B in
FIG. 2A;
[0019] FIG. 3A is a graph showing a variation in a twist angle;
[0020] FIG. 3B is a graph showing suction pulsation;
[0021] FIG. 3C is a graph showing antiphase pulsation;
[0022] FIG. 4A is a side view illustrating a rotor according to a
second embodiment;
[0023] FIG. 4B is a side view illustrating a rotor according to the
second embodiment;
[0024] FIG. 5 is a graph showing a variation in a twist angle;
[0025] FIG. 6A is a side cross-sectional view illustrating a rotor
according to a third embodiment;
[0026] FIG. 6B is a side cross-sectional view illustrating a rotor
according to the third embodiment;
[0027] FIG. 7 is a cross-sectional view illustrating the rotors
according to the third embodiment;
[0028] FIG. 8A is a side view illustrating a rotor according to a
fourth embodiment;
[0029] FIG. 8B is a side view illustrating a rotor according to the
fourth embodiment;
[0030] FIG. 9 is a graph showing a variation in a twist angle;
[0031] FIG. 10A is a side view illustrating a rotor according to a
fifth embodiment;
[0032] FIG. 10B is a side view illustrating a rotor according to
the fifth embodiment;
[0033] FIG. 11A is a graph showing a variation in twist angle;
[0034] FIG. 11B is a graph showing suction pulsation;
[0035] FIG. 11C is a graph showing antiphase pulsation;
[0036] FIG. 12A is a cross-sectional view illustrating rotors
according to a sixth embodiment;
[0037] FIG. 12B is a side view illustrating one of the rotors;
[0038] FIG. 12C is a side view illustrating one of the rotors;
[0039] FIG. 13A is a graph showing a variation in a twist
angle;
[0040] FIG. 13B is a graph showing the suction pulsation;
[0041] FIG. 13C is a graph showing antiphase pulsation;
[0042] FIG. 14 is a graph showing a modified embodiment;
[0043] FIG. 15 is a graph showing a modified embodiment;
[0044] FIG. 16 is a graph showing a modified embodiment;
[0045] FIG. 17A is a schematic diagram for explaining suction
pulsation caused by fluid leakage; and
[0046] FIG. 17B is a schematic diagram for explaining suction
pulsation caused by fluid leakage.
DESCRIPTION OF THE PREFERRED EMBODIMENT
[0047] A first embodiment of the present invention will now be
described with reference to FIGS. 1A to 3C.
[0048] As shown in FIG. 1A, a partition wall 12 is coupled to the
rear end of a front housing member 11, and an electric motor M is
coupled to the partition wall 12 with a gear housing member 13. The
front housing member 11, the partition wall 12, the gear housing
member 13, and a housing member M1 of the electric motor M
configure a housing assembly of a roots-type fluid machine 10.
[0049] The front housing member 11 and the partition wall 12
configure a rotor housing 23, which forms a pump chamber 231. A
shaft hole 121 extends through the partition wall 12, and a shaft
hole 141 is formed in an end wall 14 of the front housing member
11. The end wall 14 of the front housing member 11 and the
partition wall 12 rotatably support a rotary shaft 15 of the
electric motor M with radial bearings 16, 17 fitted in the shaft
holes 121, 141. Similarly, a shaft hole 122 extends through the
partition wall 12, and a shaft hole 142 is formed in the end wall
14 of the front housing member 11. A rotary shaft 18 is inserted in
the shaft holes 122, 142. The end wall 14 of the front housing
member 11 and the partition wall 12 rotatably support the rotary
shaft 18 with radial bearings 19, 20 fitted in the shaft holes 122,
142. The rotary shafts 15, 18 are arranged in parallel to each
other. Lip seal type shaft seals 29, 30 are provided.
[0050] As shown in FIG. 2B, a rotor 21 is secured to the rotary
shaft 15, and a rotor 22 is secured to the rotary shaft 18. The
rotors 21, 22 are accommodated in the pump chamber 231 in a state
where the rotors 21, 22 mesh with each other with a slight gap kept
in between.
[0051] The rotor 21 has three teeth 24, which protrude in the
radial direction of the rotary shaft 15. The rotor 22 has three
teeth 25, which protrude in the radial direction of the rotary
shaft 15. The three teeth 24 of the rotor 21 are arranged at equal
angular intervals of 120.degree. about a rotation axis 151 of the
rotary shaft 15, and the rotor 21 has rotational symmetry of
120.degree. about the rotation axis 151. Similarly, the three teeth
25 of the rotor 22 are arranged at equal angular intervals of
120.degree. about a rotation axis 181 of the rotary shaft 18, and
the rotor 22 has rotational symmetry of 120.degree. about the
rotation axis 181.
[0052] As shown in FIG. 1B, each tooth 24 includes a first twisted
portion 241, which is helically twisted clockwise about the
rotation axis of the rotor 21 (that is, the rotation axis 151 of
the rotary shaft 15), and a second twisted portion 242, which is
helically twisted clockwise about the rotation axis 151.
Furthermore, each tooth 24 includes a non-twisted portion 240,
which is located between the first twisted portion 241 and the
second twisted portion 242. The twist angle of the first twisted
portion 241 and the second twisted portion 242 changes linearly
along the axial direction of the rotation axis 151. The non-twisted
portion 240 is a straight line, which is parallel to the rotation
axis 151. That is, the non-twisted portion 240 does not twist along
the axial direction of the rotation axis 151.
[0053] As shown in FIGS. 1C and 2A, each tooth 25 includes a first
twisted portion 251, which is helically twisted counterclockwise
about the rotation axis of the rotor 22 (that is, the rotation axis
181 of the rotary shaft 18), and a second twisted portion 252,
which is helically twisted counterclockwise about the rotation axis
181. Furthermore, each tooth 25 includes a non-twisted portion 250,
which is located between the first twisted portion 251 and the
second twisted portion 252. The twist angle of the first twisted
portion 251 and the second twisted portion 252 changes linearly
along the axial direction of the rotation axis 181. The non-twisted
portion 250 is a straight line, which is parallel to the rotation
axis 181. That is, the non-twisted portion 250 does not twist along
the axial direction of the rotation axis 181.
[0054] The length of the first twisted portion 241 in the direction
of the rotation axis 151 is equal to the length of the first
twisted portion 251 in the direction of the rotation axis 181. The
length of the second twisted portion 242 in the direction of the
rotation axis 151 is equal to the length of the second twisted
portion 252 in the direction of the rotation axis 181. The length
of the non-twisted portion 240 in the direction of the rotation
axis 151 and the length of the non-twisted portion 250 in the
direction of the rotation axis 181 are the same length L (shown in
FIGS. 1B, 1C, and 3A). The length L of the non-twisted portions
240, 250 is shorter than the length of the first twisted portions
241, 251 and the length of the second twisted portions 242, 252.
The first twisted portion 241 of the rotor 21 meshes with the first
twisted portion 251 of the rotor 22, and the second twisted portion
242 of the rotor 21 meshes with the second twisted portion 252 of
the rotor 22. The non-twisted portion 240 of the rotor 21 meshes
with the non-twisted portion 250 of the rotor 22.
[0055] As shown in FIG. 1A, the rotary shaft 18 extends through the
partition wall 12 and protrudes inside the gear housing member 13.
Gears 26, 27 are fastened to parts of the rotary shafts 15, 18
located in the gear housing member 13 in a state where the gears
26, 27 mesh with each other. When the electric motor M is driven,
the rotary shaft 15 is rotated in the direction of arrow R1, and
the rotor 21 is rotated integrally with the rotary shaft 15 in the
direction of arrow R1. The rotary shaft 18 receives driving power
from the electric motor M via the gears 26, 27. The rotary shaft 18
is rotated in the opposite direction from the rotary shaft 15 as
shown by arrow R2, and the rotor 22 is rotated integrally with the
rotary shaft 18 in the direction of arrow R2.
[0056] As shown in FIG. 2B, an inlet 281 and an outlet 282 are
formed in a circumferential wall 28 of the front housing member 11
to be connected to the pump chamber 231. The rotors 21, 22 define a
suction space S, which communicates with the inlet 281, in the pump
chamber 231. When the electric motor M is operated, the rotary
shaft 15 is rotated in the direction of arrow R1, and the rotary
shaft 18 is rotated in the direction of arrow R2, and the rotors
21, 22 are rotated integrally with the rotary shafts 15, 18. As the
rotors 21, 22 are rotated, fluid (air in the first embodiment) is
drawn into the suction space S from the inlet 281. The air that is
drawn into the suction space S is transferred to the outlet 282,
and the air that is transferred to the outlet 282 is discharged
from the outlet 282.
[0057] In the first embodiment, the air that is discharged from the
outlet 282 is supplied to a fuel cell (not shown). A restrictor is
located in a passage (not shown) downstream of the fuel cell, and
the air discharged from the outlet 282 is supplied to the fuel cell
as compressed air.
[0058] A variation line E1 in the graph of FIG. 3A shows the
relationship between the position H in the axial direction of the
rotation axis 151 and the twist angle .PHI. regarding parts of the
rotor 21 where the lengths of the radial lines, which extend from
the rotation axis 151 of the rotor 21 to the circumferential
surfaces of the teeth 24, are equal (for example, the vertexes of
the teeth 24 of the rotor 21). The position of an end surface 211
of the rotor 21 is represented by the position H=0, the position of
an end surface 212 of the rotor 21 is represented by the position
H=He. The twist angle corresponding to the position of the end
surface 211 is represented by the twist angle .PHI.=0.degree., and
the twist angle corresponding to the position of the end surface
212 is represented by the twist angle .PHI.=.PHI.e. A straight
segment E11 of the variation line E1 represents a variation in the
twist angle of the first twisted portion 241, and a straight
segment E12 of the variation line E1 represents a variation in the
twist angle of the second twisted portion 242. A straight segment
E10 of the variation line E1 represents a variation in the twist
angle of the non-twisted portion 240.
[0059] The first twisted portion 241 and the second twisted portion
242 are twisted portions where the twist angle .PHI. about the
rotation axis 151 monotonically (in this case, linearly) changes
with respect to the change in the position H in the axial direction
of the rotation axis 151. The twist angle variation of the first
twisted portion 241 is equal to the twist angle variation of the
second twisted portion 242. The non-twisted portion 240 is a
different shape variation portion having a twist angle, which
varies by a smaller degree compared to the twist angle variations
of the first twisted portion 241 and the second twisted portion
242.
[0060] A variation line E2 in the graph of FIG. 3A represents the
relationship between the twist angle .PHI. and the position H in
the axial direction of the rotation axis 181 regarding parts of the
rotor 22 where the lengths of the radial lines, which extend from
the rotation axis 181 of the rotor 22 to the circumferential
surfaces of the teeth 25, are equal (for example, the vertexes of
the teeth 25 of the rotor 22). The position of an end surface 221
of the rotor 22 is represented by the position H=0, the position of
an end surface 222 of the rotor 22 is represented by the position
H=He. The twist angle corresponding to the position of the end
surface 221 is represented by the twist angle .PHI.=0.degree., and
the twist angle corresponding to the position of the end surface
222 is represented by the twist angle .PHI.=-.PHI.e. A straight
segment E21 of the variation line E2 represents a variation in the
twist angle of the first twisted portion 251, and a straight
segment E22 of the variation line E2 represents a variation in the
twist angle of the second twisted portion 252. A straight segment
E20 of the variation line E2 represents a variation in the twist
angle of the non-twisted portion 250.
[0061] The first twisted portion 251 and the second twisted portion
252 are twisted portions where the twist angle .PHI. about the
rotation axis 181 monotonically (in this case, linearly) changes
with respect to the change in the position H in the axial direction
of the rotation axis 181. The twist angle variation of the first
twisted portion 251 is equal to the twist angle variation of the
second twisted portion 252. The non-twisted portion 250 is a
different shape variation portion having a variation in a twist
angle that is smaller than the twist angle variations of the first
twisted portion 251 and the second twisted portion 252.
[0062] In the first embodiment, .PHI.e=60.degree., and
-.PHI.e=-60.degree.. Also, the straight segment E10 is at a
position of .PHI.=30.degree., and the straight segment E20 is at a
position of .PHI.=-30.degree.. That is, the length of the first
twisted portion 241 of the rotor 21 in the direction of the
rotation axis 151 is equal to that of the second twisted portion
242. Furthermore, the non-twisted portion 240 is located between
the position corresponding to the twist angle .PHI.=30.degree. of
first twisted portion 241 and the position corresponding to the
twist angle .PHI.=30.degree. of the second twisted portion 242. The
non-twisted portion 240 is located at a position overlapping the
center of the rotor 21 in the direction of the rotation axis 151.
Similarly, the length of the first twisted portion 251 of the rotor
22 in the direction of the rotation axis 181 is equal to that of
the second twisted portion 252. Furthermore, the non-twisted
portion 250 is located between the position corresponding to the
twist angle .PHI.=-30.degree. of the first twisted portion 251 and
the position corresponding to the twist angle .PHI.=-30.degree. of
the second twisted portion 252. The non-twisted portion 250 is
located at a position overlapping the center of the rotor 22 in the
direction of the rotation axis 181.
[0063] A waveform G1 in FIG. 3C represents the pulsation generated
by fluctuation of the volumetric change in the suction space S. The
volumetric change in the suction space S refers to the amount of
change in the volume of the suction space S per unit time (suction
amount of fluid to the suction space S per unit time). The
rotational angle .theta.=0.degree. represents the rotation position
of the rotors 21, 22 in the state shown in FIG. 2B. In the case of
conventional helical rotors, which do not have the non-twisted
portions 240, 250 and are formed by only the first twisted portions
241, 251 and the second twisted portions 242, 252, the volumetric
change in the suction space is constant. However, in the case of
the rotors 21, 22, the volumetric change in the suction space S
fluctuates due to the existence of the non-twisted portions 240,
250. Valleys of the pulsation shown by the waveform G1 are in the
vicinity of the rotational angle .theta.=30.degree..times.(2n-1)
since the non-twisted portion 240 is located between the position
corresponding to the twist angle .PHI.=30.degree. of the first
twisted portion 241 and the position corresponding to the twist
angle .PHI.=30.degree. of the second twisted portion 242, and the
non-twisted portion 250 is located between the position
corresponding to the twist angle .PHI.=-30.degree. of the first
twisted portion 251 and the position corresponding to the twist
angle .PHI.=-30.degree. of the second twisted portion 252. Here, n
is an integer greater than or equal to one. Hereinafter, the
pulsation shown by the waveform G1 is referred to as an antiphase
pulsation G1.
[0064] A waveform Fo6 shown in FIG. 3B shows one example of the
suction pulsation caused by fluid leakage in a case where rotors
without the non-twisted portions 240, 250 are used. Hereinafter,
the suction pulsation shown by the waveform Fo6 is referred to as a
suction pulsation Fo6 caused by fluid leakage. In the case of the
roots pump that uses the rotors with three teeth, the fundamental
order of the suction pulsation caused by fluid leakage is sixth
order. The peaks of the suction pulsation Fo6 caused by fluid
leakage are in the vicinity of the rotational angle
.theta.=30.degree..times.(2n-1), and the valleys of the suction
pulsation Fo6 caused by fluid leakage are in the vicinity of the
rotational angle .theta.=30.degree..times.2n. Here, n is an integer
greater than or equal to one.
[0065] A waveform F1 in FIG. 3B shows one example of suction
pulsation when the rotors 21, 22 including the non-twisted portions
240, 250 are used. The suction pulsation shown by the waveform F1
is obtained by overlapping the suction pulsation Fo6 caused by
fluid leakage on the antiphase pulsation G1. Hereinafter, the
suction pulsation shown by the waveform F1 is referred to as a
suction pulsation F1. Since the valleys of the antiphase pulsation
G1 generated due to the existence of the non-twisted portions 240,
250 are in the vicinity of the rotational angle
.theta.=30.degree..times.(2n-1), the upper limit of the peaks of
the suction pulsation F1 is suppressed. Here, n is an integer
greater than or equal to one.
[0066] The first embodiment has the following advantages.
[0067] (1) The combination of the non-twisted portions 240, 250 and
the twisted portions 241, 242, 251, 252 cause the volumetric change
in the suction space S to periodically fluctuate. The valleys of
the antiphase pulsation G1 generated by the fluctuation of the
volumetric change in the suction space S match the peaks of the
suction pulsation Fo6 caused by fluid leakage. Thus, the degree of
the suction pulsation F1 (the difference A1 between the maximum
amplitude and the minimum amplitude of the suction pulsation F1
shown in FIG. 3B) is reduced compared to the degree of the suction
pulsation Fo6 caused by fluid leakage (the difference Ao between
the maximum amplitude and the minimum amplitude of the suction
pulsation Fo6 caused by fluid leakage shown in FIG. 3B). That is,
the suction pulsation caused by fluid leakage is reduced by
selecting an optimum phase of the fluctuation of the volumetric
change in the suction space S by combining the non-twisted portions
240, 250 and the twisted portions 241, 242, 251, 252.
[0068] (2) Increasing the length L of the non-twisted portions 240,
250 in the axial direction of the rotation axes 151, 181 (shown in
FIGS. 1B, 1C, and 3A) increases the fluctuation of the volumetric
change in the suction space S, and reducing the length L of the
non-twisted portions 240, 250 in the axial direction of the
rotation axes 151, 181 reduces the fluctuation of the volumetric
change in the suction space S. Setting the length L of the
non-twisted portions 240, 250 in the axial direction of the
rotation axes 151, 181 in an appropriate manner further reduces the
suction pulsation caused by fluid leakage.
[0069] (3) Changing the arrangement position of the non-twisted
portions 240, 250 in the axial direction of the rotation axes 151,
181 changes the position of the valleys of the antiphase pulsation
G1 relative to the rotational angle .theta.. Setting the position
of the non-twisted portions 240, 250 in the axial direction of the
rotation axes 151, 181 in an appropriate manner further reduces the
suction pulsation caused by fluid leakage.
[0070] As described above, by changing the setting position of the
different shape variation portions (non-twisted portion 240) in the
axial direction of the rotation axes 151, 181 of the rotors and
changing the range of the different shape variation portions in the
axial direction of the rotation axes 151, 181, the phase of the
pulsation generated by the fluctuation of the volumetric change in
the suction space S is changed. By matching the valleys of the
phase of the pulsation generated by the fluctuation of the
volumetric change with the peaks of the suction pulsation caused by
the fluid leakage, the suction pulsation caused by the fluid
leakage is reduced. That is, the suction pulsation caused by fluid
leakage is reduced by setting the phase of the suction pulsation
caused by the fluctuation of the volumetric change such that the
waveform of the suction pulsation generated by the fluctuation of
the volumetric change caused by providing the different shape
variation portions and the waveform of the suction pulsation caused
by fluid leakage cancel each other to be reduced. That is, if an
optimum phase of the pulsation, which is caused by the fluctuation
of the volumetric change in the suction space S, is selected by
combining the different shape variation portions and the twisted
portions, the suction pulsation caused by fluid leakage is
reduced.
[0071] (4) The periodical fluctuation of the volumetric change in
the suction space S is preferably great in a range where the
rotational angle .theta. is narrow. The non-twisted portions 240,
250, which are the different shape variation portions having a
straight line form, are optimal in increasing the periodical
fluctuation of the volumetric change in the suction space S in a
range where the rotational angle .theta. is narrow.
[0072] (5) The configuration in which the non-twisted portions 240,
250 are located at the positions overlapping the center of the
rotors 21, 22 in the axial direction of the rotation axes 151, 181
is convenient in matching the valleys of the antiphase pulsation G1
generated by the fluctuation of the volumetric change in the
suction space S with the peaks of the suction pulsation Fo6 caused
by fluid leakage.
[0073] A second embodiment will now be described with reference to
FIGS. 4A to 5. Like or the same reference numerals are given to
those components that are like or the same as the corresponding
components of the first embodiment.
[0074] As shown in FIG. 4A, teeth 24A of a rotor 21A have a loosely
twisted portion 244 between the first twisted portion 241 and the
second twisted portion 242. As shown in FIG. 4B, teeth 25A of a
rotor 22A have a loosely twisted portion 254 between the first
twisted portion 251 and the second twisted portion 252. A straight
segment E10a in the graph of FIG. 5 represents the twist angle
variation of the loosely twisted portion 244, and a straight
segment E20a represents the twist angle variation of the loosely
twisted portion 254. The loosely twisted portion 244 has the twist
angle .PHI. about the rotation axis 151 which monotonically (in
this case, linearly) changes with respect to the change in the
position H in the axial direction of the rotation axis 151. The
loosely twisted portion 254 has the twist angle .PHI. about the
rotation axis 181 which changes monotonically (in this case,
linearly) with respect to the change in the position H in the axial
direction of the rotation axis 181. The loosely twisted portions
244, 254 are different shape variation portions having a variation
in a twist angle smaller than the twist angle variations of the
first twisted portions 241, 251 and the second twisted portions
242, 252.
[0075] When the length of the non-twisted portions 240, 250 in the
axial direction of the rotation axes 151, 181 according to the
first embodiment is equal to the length of the loosely twisted
portions 244, 254 in the axial direction of the rotation axes 151,
181, the degree of the fluctuation of the volumetric change in the
suction space S is smaller in the second embodiment than in the
first embodiment. However, in the second embodiment also, the
antiphase pulsation similar to the antiphase pulsation G1 of the
first embodiment is obtained, and the suction pulsation caused by
fluid leakage is reduced.
[0076] A third embodiment will now be described with reference to
FIGS. 6A to 7. Like or the same reference numerals are given to
those components that are like or the same as the corresponding
components of the first embodiment.
[0077] As shown in FIG. 6A, a rotor 21B is configured by laminating
flat plates 31 in the axial direction of the rotation axis 151, and
a non-twisted portion 240B of the rotor 21B is configured by
laminating the flat plates 31 (four in the third embodiment).
Similarly, as shown in FIG. 6B, a rotor 22B is configured by
laminating flat plates 32 in the axial direction of the rotation
axis 181, and a non-twisted portion 250B of the rotor 22B is
configured by laminating the flat plates 32 (four in the third
embodiment). The flat plates 31, 32 have the same shape and the
same size, and the length of the non-twisted portions 240B, 250B in
the axial direction of the rotation axes 151, 181 is greater than
the thickness of the flat plates 31, 32.
[0078] The third embodiment also has the same advantages as the
first embodiment. Furthermore, in the third embodiment, first
twisted portions 241B, 251B and second twisted portions 242B, 252B
are easily formed by laminating the flat plates 31, 32 in a twisted
state, and the non-twisted portions 240B, 250B are also easily
formed by laminating the flat plates 31, 32.
[0079] A fourth embodiment will now be described with reference to
FIGS. 8 to 9. Like or the same reference numerals are given to
those components that are like or the same as the corresponding
components of the first embodiment.
[0080] As shown in FIG. 8A, teeth 24C of a rotor 21C each have a
nonlinear twisted portion 245 between a first twisted portion 241
and a second twisted portion 242. The twist angle .PHI. of the
nonlinear twisted portion 245 changes with respect to the variation
of the position in the axial direction of the rotation axis 151 in
a manner represented by a nonlinear function (for example,
quadratic function). As shown in FIG. 8B, teeth 25C of a rotor 22C
each have a nonlinear twisted portion 255 between a first twisted
portion 251 and a second twisted portion 252. The twist angle .PHI.
of the nonlinear twisted portion 255 changes with respect to the
variation of the position in the axial direction of the rotation
axis 181 in a manner represented by a nonlinear function (for
example, quadratic function). A curved segment E10c in the graph of
FIG. 9 represents the twist angle variation of the nonlinear
twisted portion 245, and a curved segment E20c represents the twist
angle variation of the nonlinear twisted portion 255. The nonlinear
twisted portions 245, 255 have different shape variation portions
245r, 255r, respectively. The different shape variation portions
245r, 255r have a smaller twist angle variation than the twist
angle variations of the first twisted portions 241, 251 and the
second twisted portions 242, 252.
[0081] The fourth embodiment provides an antiphase pulsation
represented by a waveform, in which the peaks and the valleys of
the antiphase pulsation G1 in FIG. 3C in a bent form is turned into
a curved line. With such an antiphase pulsation also, the suction
pulsation caused by fluid leakage is reduced. That is, the
different shape variation portions (255) the twist angle .PHI. of
which changes in a manner represented by a nonlinear function
reduce the suction pulsation caused by fluid leakage.
[0082] A fifth embodiment will now be described with reference to
FIGS. 10A to 11C. Like or the same reference numerals are given to
those components that are like or the same as the corresponding
components of the first embodiment.
[0083] As shown in FIG. 10A, teeth 24D of a rotor 21D each include
a helically twisted first twisted portion 241D, a helically twisted
second twisted portion 242D, and a helically twisted third twisted
portion 243. Furthermore, each tooth 24D includes a non-twisted
portion 246, which is located between the first twisted portion
241D and the second twisted portion 242D, and a non-twisted portion
247, which is located between the second twisted portion 242D and
the third twisted portion 243.
[0084] As shown in FIG. 10B, teeth 25D of a rotor 22D each include
a helically twisted first twisted portion 251D, a helically twisted
second twisted portion 252D, and a helically twisted third twisted
portion 253. Furthermore, each tooth 25D includes a non-twisted
portion 256, which is located between the first twisted portion
251D and the second twisted portion 252D, and a non-twisted portion
257, which is located between the second twisted portion 252D and
the third twisted portion 253.
[0085] A straight segment E31 of a variation line E3 in the graph
of FIG. 11A represents the twist angle variation of the first
twisted portion 241D, a straight segment E32 of the variation line
E3 represents the twist angle variation of the second twisted
portion 242D, and a straight segment E33 of the variation line E3
represents the twist angle variation of the third twisted portion
243. A straight segment E34 of the variation line E3 represents the
twist angle variation of the non-twisted portion 246, and a
straight segment E35 of the variation line E3 represents the twist
angle variation of the non-twisted portion 247.
[0086] A straight segment E41 of a variation line E4 in the graph
of FIG. 11A represents the twist angle variation of the first
twisted portion 251D, a straight segment E42 of the variation line
E4 represents the twist angle variation of the second twisted
portion 252D, a straight segment E43 of the variation line E4
represents the twist angle variation of the third twisted portion
253. A straight segment E44 of the variation line E4 represents the
twist angle variation of the non-twisted portion 256, and a
straight segment E45 of the variation line E4 represents the twist
angle variation of the non-twisted portion 257.
[0087] The non-twisted portion 246 is located between the position
corresponding to the twist angle .PHI.=15.degree. of the first
twisted portion 241D and the position corresponding to the twist
angle .PHI.=15.degree. of the second twisted portion 242D, and the
non-twisted portion 247 is located between the position
corresponding to the twist angle .PHI.=45.degree. of the second
twisted portion 242D and the position corresponding to the twist
angle .PHI.=45.degree. of the third twisted portion 243. That is,
the non-twisted portion 246 is located at a position midway between
the center of the rotor 21D in the axial direction of the rotation
axis 151 and one end of the rotor 21D (the end surface 211), and
the non-twisted portion 247 is located at a position midway between
the center of the rotor 21D in the axial direction of the rotation
axis 151 and the other end of the rotor 21D (the end surface
212).
[0088] The non-twisted portion 256 is located between the position
corresponding to the twist angle .PHI.=-15.degree. of the first
twisted portion 251D and the position corresponding to the twist
angle .PHI.=-15.degree. of the second twisted portion 252D, and the
non-twisted portion 257 is located between the position
corresponding to the twist angle .PHI.=-45.degree. of the second
twisted portion 252D and the position corresponding to the twist
angle .PHI.=-45.degree. of the third twisted portion 253. That is,
the non-twisted portion 256 is located at a position midway between
the center of the rotor 22D in the axial direction of the rotation
axis 181 and one end of the rotor 22D (the end surface 221), and
the non-twisted portion 257 is located at a position midway between
the center of the rotor 22D in the axial direction of the rotation
axis 181 and the other end of the rotor 22D (the end surface
222).
[0089] A waveform G2 in FIG. 11C represents the pulsation generated
by the fluctuation of the volumetric change in the suction space S.
In the case with the rotors 21D, 22D, the volumetric change in the
suction space S fluctuates due to the existence of the non-twisted
portions 246, 247, 256, 257. The valleys of the pulsation shown by
the waveform G2 are in the vicinity of the rotational angle
.theta.=15.degree..times.(2n-1). Here, n is an integer greater than
or equal to one. Hereinafter, the pulsation represented by the
waveform G2 is referred to as an antiphase pulsation G2.
[0090] A waveform Fo12 in FIG. 11B shows one example of the order
component that is double the fundamental order of the suction
pulsation caused by fluid leakage when rotors without the
non-twisted portions 246, 247, 256, 257 are used. In the case of
the roots pump that uses the rotors with three teeth, the double of
the fundamental order of the suction pulsation caused by fluid
leakage is 12th order. Hereinafter, the suction pulsation of the
12th order component shown by the waveform Fo12 is referred to as a
12th order component pulsation Fo12 caused by fluid leakage. The
peaks of the 12th order component pulsation Fo12 caused by fluid
leakage are in the vicinity of the rotational angle
.theta.=15.degree..times.(2n-1), and the valleys of the 12th order
component pulsation Fo12 caused by fluid leakage are in the
vicinity of the rotational angle .theta.=15.degree..times.2n. Here,
n is an integer greater than or equal to one.
[0091] The waveform F2 in FIG. 11B shows one example of the suction
pulsation when the rotor 21D having the non-twisted portions 246,
247 and the rotor 22D having the non-twisted portions 256, 257 are
used. The suction pulsation shown by the waveform F2 is obtained by
overlapping the 12th order component pulsation Fo12 caused by fluid
leakage on the antiphase pulsation G2. Hereinafter, the suction
pulsation shown by the waveform F2 is referred to as a suction
pulsation F2. Since the valleys of the antiphase pulsation G2
generated due to the existence of the non-twisted portions 246,
247, 256, 257 are in the vicinity of the rotational angle
.theta.=15.degree..times.(2n-1), the upper limit of the peaks of
the suction pulsation F2 is suppressed. Here, n is an integer
greater than or equal to one.
[0092] The fifth embodiment is advantageous in reducing the suction
pulsation component of the order that is double the fundamental
order.
[0093] A sixth embodiment will now be described with reference to
FIGS. 12A to 13C. Like or the same reference numerals are given to
those components that are like or the same as the corresponding
components of the first embodiment.
[0094] As shown in FIG. 12A, a rotor 33 includes two teeth 35,
which protrude in the radial direction of the rotary shaft 15, and
a rotor 34 includes two teeth 36, which protrude in the radial
direction of the rotary shaft 18. The two teeth 35 of the rotor 33
are located at equal angular intervals of 180.degree. about the
rotation axis 151 of the rotary shaft 15, and the rotor 33 has a
rotational symmetry of 180.degree. about the rotation axis 151.
Similarly, the two teeth 36 of the rotor 34 are located at equal
angular intervals of 180.degree. about the rotation axis 181 of the
rotary shaft 18, and the rotor 34 has a rotational symmetry of
180.degree. about the rotation axis 181.
[0095] As shown in FIG. 12B, each tooth 35 includes a first twisted
portion 351, which is helically twisted clockwise about the
rotation axis of the rotor 33 (that is, the rotation axis 151 of
the rotary shaft 15), a second twisted portion 352, which is
helically twisted clockwise about the rotation axis 151, and a
non-twisted portion 350, which is located between the first twisted
portion 351 and the second twisted portion 352. The twist angle of
the first twisted portion 351 and the second twisted portion 352
change linearly along the axial direction of the rotation axis 151.
The non-twisted portion 350 has a straight line form parallel to
the rotation axis 151 (that is, a form that does not twist along
the axial direction of the rotation axis 151).
[0096] As shown in FIG. 12C, each tooth 36 includes a first twisted
portion 361, which is helically twisted counterclockwise about the
rotation axis of the rotor 34 (that is, the rotation axis 181 of
the rotary shaft 18), a second twisted portion 362, which is
helically twisted counterclockwise about the rotation axis 181, and
a non-twisted portion 360, which is located between the first
twisted portion 361 and the second twisted portion 362. The twist
angle of the first twisted portion 361 and the second twisted
portion 362 change linearly along the axial direction of the
rotation axis 181. The non-twisted portion 360 has a straight line
form parallel to the rotation axis 181 (that is, a form that does
not twist along the axial direction of the rotation axis 181).
[0097] The first twisted portion 351 of the rotor 33 meshes with
the first twisted portion 361 of the rotor 34, and the second
twisted portion 352 of the rotor 33 meshes with the second twisted
portion 362 of the rotor 34. The non-twisted portion 350 of the
rotor 33 meshes with the non-twisted portion 360 of the rotor
34.
[0098] A variation line E7 in the graph of FIG. 13A represents the
relationship between the twist angle .PHI. and the position H in
the axial direction of the rotation axis 151 regarding parts of the
rotor 33 where the lengths of the radial lines, which extend from
the rotation axis 151 of the rotor 33 to the circumferential
surfaces of the teeth 35, are equal (for example, the vertexes of
the teeth 35 of the rotor 33). The position of an end surface 331
of the rotor 33 is represented by the position H=0, the position of
an end surface 332 of the rotor 33 is represented by the position
H=He. The twist angle corresponding to the position of the end
surface 331 is represented by the twist angle .PHI.=0.degree., and
the twist angle corresponding to the position of the end surface
332 is represented by the twist angle .PHI.=.PHI.e. A straight
segment E71 of the variation line E7 represents the twist angle
variation of the first twisted portion 351, and a straight segment
E72 of the variation line E7 represents the twist angle variation
of the second twisted portion 352. A straight segment E70 of the
variation line E7 represents the twist angle variation of the
non-twisted portion 350.
[0099] A variation line E8 in the graph of FIG. 13A represents the
relationship between the twist angle .PHI. and the position H in
the axial direction of the rotation axis 181 regarding parts of the
rotor 34 where the lengths of the radial lines, which extend from
the rotation axis 181 of the rotor 34 to the circumferential
surfaces of the teeth 36, are equal (for example, vertexes of the
teeth 36 of the rotor 34). The position of an end surface 341 of
the rotor 34 is represented by the position H=0, the position of an
end surface 342 of the rotor 34 is represented by the position
H=He. The twist angle corresponding to the position of the end
surface 341 is represented by the twist angle .PHI.=0.degree., and
the twist angle corresponding to the position of the end surface
342 is represented by the twist angle .PHI.=-.PHI.e. A straight
segment E81 of the variation line E8 represents the twist angle
variation of the first twisted portion 361, and a straight segment
E82 of the variation line E8 represents the twist angle variation
of the second twisted portion 362. A straight segment E80 of the
variation line E8 represents the twist angle variation of the
non-twisted portion 360.
[0100] In the sixth embodiment, .PHI.e=90.degree., and
-.PHI.e=-90.degree.. Also, the straight segment E70 is at the
position of .PHI.=45.degree., and the straight segment E80 is at
the position of .PHI.=-45.degree.. That is, the length of the first
twisted portion 351 of the rotor 33 in the direction of the
rotation axis 151 is equal to that of the second twisted portion
352. Furthermore, the non-twisted portion 350 is located between
the position corresponding to the twist angle .PHI.=45.degree. of
the first twisted portion 351 and the position corresponding to the
twist angle .PHI.=45.degree. of the second twisted portion 352, and
the non-twisted portion 350 is located at a position overlapping
the center of the rotor 33 in the direction of the rotation axis
151. Similarly, the length of the first twisted portion 361 of the
rotor 34 in the direction of the rotation axis 181 is equal to that
of the second twisted portion 362. Furthermore, the non-twisted
portion 360 is located between the position corresponding to the
twist angle .PHI.=-45.degree. of the first twisted portion 361 and
the position corresponding to the twist angle .PHI.=-45.degree. of
the second twisted portion 362, and the non-twisted portion 360 is
located at a position overlapping the center of the rotor 34 in the
direction of the rotation axis 181.
[0101] A waveform G3 in FIG. 13C represents the pulsation generated
by the fluctuation of the volumetric change in the suction space S.
In the case where the rotors 33, 34 are used, the volumetric change
in the suction space S fluctuates due to the existence of the
non-twisted portions 350, 360. The valleys of the pulsation shown
by the waveform G3 are in the vicinity of the rotational angle
.theta.=45.degree..times.(2n-1). Here, n is an integer greater than
or equal to one. Hereinafter, the pulsation shown by the waveform
G3 is referred to as an antiphase pulsation G3.
[0102] A waveform Fo4 in FIG. 13B shows one example of the suction
pulsation caused by fluid leakage in a case where rotors without
the non-twisted portions 350, 360 are used. In the case of the
roots pump which uses the rotors with two teeth, the fundamental
order of the suction pulsation caused by fluid leakage is fourth
order. Hereinafter, the suction pulsation shown by the waveform Fo4
is referred to as a suction pulsation Fo4 caused by fluid leakage.
The valleys of the suction pulsation Fo4 caused by fluid leakage
are in the vicinity of the rotational angle
.theta.=45.degree..times.(2n-1), and the peaks of the suction
pulsation Fo4 caused by fluid leakage are in the vicinity of the
rotational angle .theta.=45.degree..times.2n. Here, n is an integer
greater than or equal to one.
[0103] A waveform F3 in FIG. 13B shows one example of the suction
pulsation when the rotors 33, 34 including the non-twisted portions
350, 360 are used. The suction pulsation shown by the waveform F3
is obtained by overlapping the suction pulsation Fo4 caused by
fluid leakage on the antiphase pulsation G3. Hereinafter, the
suction pulsation shown by the waveform F3 is referred to as a
suction pulsation F3. Since the valleys of the antiphase pulsation
G3 generated due to the existence of the non-twisted portions 350,
360 are in the vicinity of the rotational angle
.theta.=415.degree..times.(2n-1), the upper limit of the peaks of
the suction pulsation F3 is suppressed. Here, n is an integer
greater than or equal to one.
[0104] The present invention may also be embodied in the following
forms.
[0105] A pair of rotors (rotors having three teeth) represented by
variation lines E13, E14 shown in FIG. 14 may be used. Straight
segments E130, E140 of the variation lines E13, E14 correspond to
the straight segments E10, E20 of FIG. 3A, and curved segments
E131, E132, E141, E142 represent the twist angle variation of the
twisted portions the twist angle of which monotonically (in this
case, nonlinearly) changes. Changing monotonically means that the
twist angle varies in a manner represented by a monotonically
increasing function or a monotonically decreasing function.
[0106] A pair of rotors (rotors having three teeth) represented by
variation lines E15, E16 shown in FIG. 15 may be used. Straight
segments E150, E160 of the variation lines E15, E16 correspond to
the straight segments E10, E20 of FIG. 3A, and curved segments
E151, E152, E161, E162 represent the twist angle variation of the
twisted portions the twist angle of which monotonically (in this
case, nonlinearly) changes.
[0107] A pair of rotors (rotor having three teeth) represented by
variation lines E17, E18 shown in FIG. 16 may be used. Curved
segments E170, E180 of the variation lines E17, E18 correspond to
the curved segments E10c, E20c of FIG. 9, and straight segments
E171, E172, E181, E182 represent the twist angle variation of the
twisted portions the twist angle of which monotonically (in this
case, linearly) change.
[0108] According to the first to fifth embodiments, and embodiments
illustrated in FIGS. 14, 15, and 16, the rotors including three
teeth are used, and the twist angle .PHI. is set to 60.degree.. In
such a case where the rotors including three teeth are used, the
twist angle .PHI. may be greater than 60.degree., and may be an
integral multiple of 60.degree..
[0109] In the case where the rotors including three teeth are used,
it is optimal that the twist angle .PHI. satisfies the equation (1)
when 3 is substituted for n. However, the present invention may be
applied even when the twist angle .PHI. does not satisfy the
equation (1).
[0110] In the sixth embodiment, the rotors including two teeth are
used, and the twist angle .PHI. is set to 90.degree.. In such a
case where the rotors including two teeth are used, the twist angle
.PHI. may be greater than 90.degree., and may be an integral
multiple of 90.degree..
[0111] In the case when the rotors including two teeth are used, it
is optimal that the twist angle .PHI. satisfies the equation (1)
when 2 is substituted for n. However, the present invention may be
applied even when the twist angle .PHI. does not satisfy the
equation (1).
[0112] The present invention may be applied to rotors including
four or more teeth.
[0113] The rotors 33, 34 according to the sixth embodiment may be
configured by laminating flat plates.
[0114] The present invention may be applied to a serial or parallel
roots-type fluid machine, in which a set of rotors (the set of
rotors 21, 22 according to the first embodiment) accommodated in
the pump chamber 231, which communicates with the inlet 281, and at
least one pump chamber different from the pump chamber 231 are
arranged next to one another in the axial direction of the rotation
axis.
[0115] The present invention may be applied to a roots-type fluid
machine in which a set of three or more rotors are accommodated in
the rotor housing.
* * * * *