Abstrict This invention relates to a positive displacement flow meter with
helical toothed rotors, in which respective tooth profiles are continuously
contacted with each other in order not to cause any blockage of
fluid between the respective tooth profile curves. The flow meter
has a pair of helical toothed rotors which are rotatable each other
with no pulsation and the tooth-to-tooth surface contact pressure
is maintained zero. Each of the two rotors has the same profile
and the same size. Further, a plurality of curved projections can
be mounted on a tooth profile of each rotor.
Claims What is claimed is:
1. A positive displacement flow meter with helical toothed rotors,
in which respective tooth profile curves are continuously contacted
with each other in order not to cause any blockade of fluid between
the respective tooth profile curves, each of the rotors has the
same profile and the same size, and the twist ratio i=L (tan/M.pi.)B;
wherein i is a positive integral number, M=module, L=axial length
of the helical toothed rotor, B=twist angle, whereby a pair of helical
toothed rotors are rotatable to each other with no pulsation and
a tooth-to-tooth surface contact pressure being maintained at zero,
and wherein the twist ratio is 1 and the number of teeth in each
rotor is 3 whereby the discharge of the flow meter approaches the
maximum theoretical discharge.
2. A positive displacement flow meter as defined in claim 1 wherein
two curved projections are provided at the toothed profile on each
flank of each tooth, respectively inwardly spaced from the addendum
circle and the pitch circle.
3. A positive displacement flow meter as defined in claim 1 wherein
the flank of each tooth comprises between the addendum circle and
the pitch circle a circular arc having its center at the pitch circle
to be followed by a cycloid.
Description BACKGROUND OF THE INVENTION
The present invention relates to a positive displacement flow meter
with helical toothed rotors in which a pair of rotors are rotatable
with no pulsation, thereby a tooth-to-tooth surface contact pressure
being intended to become zero because of non-existence of energy
transmission between the two rotors.
Conventionally, there is known a flow meter with a pair of Roots-type
rotors as a positive displacement rotor. A pair of Roots-type rotors
are engaged with each other by means of pilot gears directly connected
with respective axes of the Roots-type rotors. And it is widely
known the disadvantage that an equal rotation of the Roots-type
rotors brings about a certain pulsation. The present invention aims
to overcome the above disadvantage of the conventional art.
BRIEF SUMMARY OF THE INVENTION
It is an object of this invention to provide a positive displacement
flow meter with helical toothed rotors in which a pair of rotors
are rotatable with no pulsation, thereby a tooth-to-tooth surface
contact pressure being intended to be zero because of non-existence
of energy transmission between the two rotors. Unlike the conventional
positive displacement flow meter, additional pilot gears are not
necessary. Moreover, there are employed a pair of rotors with helical
toothed structure, in which respective tooth profiles curves are
continuously contacted with each other in order not to cause any
block of fluid between the respective tooth profile curves, each
of the two rotors has the same profile and same size, the twist
ratio i of each rotor being given by a positive integral number
i.sub.o like 1 2 3 . . . .
It is another object of this invention to provide a positive displacement
flow meter with helical toothed rotors, in which the twist ratio
is 1(one) or the approximate amount and the number of teeth is 3(three),
thereby a pair of rotors is made providing a maximum of the theoretical
discharge. Thus, there is obtained a positive displacement flow
meter in which a pair of rotors are rotatable with no pulsation,
consequently a tooth-to-tooth surface contact pressure being able
to be maintained zero because of non-existence of energy transmission.
It is a further object of this invention to provide a positive
displacement flow meter with helical toothed rotors in which a plurality
of curved projections (called the "primary tooth profile")
each having slipping ratio zero are formed on tooth profile curve
(called the "secondary tooth profile") of each tooth in
the rotor. The above structure is adaptable for measuring waste
liquid such as sludges.
Other objects, features and advantages of this invention will be
apparent from the following description taken in connection with
the accompanying drawings.
BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
FIG. 1 is a partial, sectioned view of a pair of rotors in a plane
normal to the axes of the rotors in a positive displacement flow
meter according to this invention.
FIG. 2 is a development view of a sealing line of respective tooth
profile curves in a pair of rotors.
FIG. 3 is a chart showing a relationship of Ro/R controlling the
theoretical discharge amount and the twist ratio i for different
numbers of teeth.
FIG. 4 is a section view of a pair of rotors in a plane normal
to the axes of the rotors under the optimum conditions of the number
of teeth: 3(three) and the twist ratio i=1(one).
FIG. 5 is a section view of a pair of rotors in a plane normal
to the axes of the rotors in which each rotor is provided with a
plurality of curved projections.
FIG. 6 is a perspective view of the helical toothed rotors of the
present invention.
DETAILED DESCRIPTION OF THE INVENTION
Preferred embodiments of this invention will now be described in
connection with the accompanying drawings.
FIG. 1 is an embodiment of a positive displacement flow meter according
to this invention, in which there is shown a section view of a pair
of rotors 1 2 in a plane normal to the rotor axes. Each of the
rotors, 1 2 interengageable with each other is provided with an
optional number of teeth, each of which has the same profile and
the same size. The pair of rotors 1 2 are respectively rotatable
about axes 3 4 in a casing of a preferred flow meter body. Numerals
5 and 6 are respectively the pitch circle of and the addendum circle
of the rotor 1 having their centers at 3 while numerals 7 and 8
are respectively the pitch circle of and the addendum circle of
the rotor 2 having their centers at 4. Numerals 9 10 are deddendum
circles of the two rotors 1 2 respectively. The curve A.sub.1
B.sub.1 C.sub.1 of the rotor 1 and the curve A.sub.2 B.sub.2
C.sub.2 of the rotor 2 are tooth profile curves which are formed
on respective addendums. For example, the curve A.sub.1 B.sub.1
and the curve A.sub.2 B.sub.2 are provided with arcuate tooth profiles
having their centers respectively at O.sub.2 and P.sub.1 on the
pitch circles 5 7. Further, the curve B.sub.1 C.sub.1 and the curve
B.sub.2 C.sub.2 are respectively provided with a cycloid tooth profile.
Further, the curve C.sub.1 D.sub.1 and the curve C.sub.2 D.sub.2
are tooth profile curves which are formed on deddendums of the two
rotors 1 2 and are provided with arcuate tooth profiles having
a center on the pitch circles 5 7 of the two rotors 1 2.
The end portions of the curved tooth profiles positioned on the
addendum portion and deddendum portion of each of the two rotors
1 2 are integrally associated with adjacent curved profiles in
relation to radii from the axes 3 4 of the respective rotors 1
2.
When a pair of rotors, each of which has the same profile and the
same size, are rotated in mutual contact with no slipping, the path
of contacting line of both rotors can be indicated by the curves
P'MQ to be followed by PMQ'.
In FIG. 2 there is shown a longitudinal development of the contacting
line i.e. a sealing line of the two rotors 1 2 interengagement.
Hence, the following equation is obtained.
[R: radius of the pitch circle]
wherein i=twist ratio, .beta.=a twist angle of helical tooth of
each of the rotors 1 2 L=axial length of the rotor, Z=tooth number,
M=module
In case of i=1 the rotation torque T.sub.1 T.sub.2 of the two
rotors 1 2 are expressed by the following equation. ##EQU1## wherein
Rr: radius of the deddendum circle
Ro: radius of the addendum circle
Rc: distance from the axis up to the cycloid B.sub.1 C.sub.1
ae: an angle formed between two ends A.sub.1 on the addendum circle,
positioned in a radius direction from the axis center
Accordingly, in each interengaging position the rotation torque
of the two rotors 1 2 is constant.
Likewise, when the twist ratio i is 2 3 . . . , like i=1 T.sub.1
+T.sub.2 =constant and further T.sub.1 -T.sub.2 =0 so that the
rotors 1 2 are rotated with an equal speed and with no pulsation.
Since there exists no transmission of energy between the two rotors,
there is obtained an ideal rotation of a pair of rotors 1 2 which
has no tooth-to-tooth surface contact pressure.
We will now study on a theoretical discharge amount q. The theoretical
discharge amount q is approximately obtained by the following equation.
Accordingly, as Ro/R is larger, so the theoretical discharge amount
q becomes larger and more advantageous.
Now, in relation with the number of teeth, Ro/R will be obtained
as follows:
First of all,
Accordingly,
When Z=2 Ro/R=1.7654
When Z=3 Ro/R=1.5176
When Z=4 Ro/R=1.3902
When Z=2 it is natural that Ro/R is maximum.
The rotor needs a shaft and a bearing therefor, so that it is advantageous
to reduce very much the core diameter of the rotor. Accordingly,
we may say that the level of Ro/R=1.5 will be the optimum rate.
On the other hand, in case of helical toothed rotors, it is required
to consider the danger of its dismounting from a casing. That is,
the twist angle .beta. is limited, since the twist ratio i must
satisfy the following formula.
FIG. 3 is illustrated at the result of the calculation of the above
equation (5).
As obviously shown in FIG. 3 in order that the twist ratio i may
be 1(one) in case of Z=2 it is necessary to make Ro/R very small,
but that is not practical to do so.
When Z=3 i=1 while when Z=4 i=2. However, the difference of
the theoretical discharge amount at the time of (Ro/R)max in the
equation (4) is 40% between Z=3 and Z=4. Accordingly, the optimum
example capable of making maximum the theoretical discharge amount
of a positive displacement flow meter with helical toothed rotors
in which respective tooth profile curves are continuously contacted
with each other as given under the conditions of the number of teeth
in each rotor 1 or 2: 3(three) teeth and the twist ratio i: 1(one)
or its approximate ratio.
The embodiment of FIG. 5 will now be described. On one surface
of the tooth profile curve A.sub.1 B.sub.1 C.sub.1 to be formed
on the addendum of each of the two rotors 1 2 there are formed
convexly curved projections 11 12 as the primary tooth profiles,
while on one surface of the tooth profile curve A.sub.2 B.sub.2
C.sub.2 there are formed concavely curved projections 13 14 as
the primary tooth profiles, each of the projections 13 14 having
the slipping ratio: zero. Due to the curved projections 11 12
13 14 the other curved portions are placed under a non-contact
condition only by the slight projection height .increment.. This
is the feature of the tooth profile curve in one rotor's tooth.
Since the tooth profile curve of the other rotor is identical with
the former, its description is omitted.
With the above structure, when a pair of rotors 1 2 each having
the same profile and the same size are rotated in mutual engagement
of the curved projections 11 12 13 14 with no slipping, a path
of the contacting line of the two rotors 1 2 can be indicated by
the curves P'MQ, to be followed by PMQ'.
As described above, a positive displacement flow meter is provided
with a pair of rotors each having an optimal number of teeth. Since
each tooth has the same profile and the same size, a tooth-to-tooth
continuous surface contact causes no blockade of fluid between the
respective tooth profile curves. In other words, such a space that
any liquid can exist between the respective tooth profile curves
of the two rotors is completely removed. That is, no liquid blockade
takes place therebetween. In addition, by defining the twist ratio
i as a positive integral number or its approximate amount, a pair
of rotors 1 2 are rotatable with no pulsation, thereby the tooth-to-tooth
surface contact pressure becomes zero because of non-existence of
energy transmission between the two rotors.
Further, under the condition of the twist ratio: i=1 or its approximate
amount and the number of teeth in each rotor: 3(three) teeth, there
is obtained a highly accurate positive displacement flow meter providing
the maximum of its theoretical discharge.
Still further, a preferred number of curved projections are mounted
on a tooth profile curve formed on both addendum and deddendum of
each rotor, whereby a pair of rotors are rotated in mutual engagement
of the curved projections.
The positive displacement flow meter with helical toothed rotors
according to this invention is suitable for measuring waste fluid
such as sludges. As necessity arises, it can be used for a hydraulic
motor, pump and other fluid devices. |