Screw rotor for screw pump device having negative torque on the female rotor

A screw rotor for a screw pump device includes a male rotor and a female rotor meashing with the male rotor and adapted to be driven by the male rotor, wherein a tooth profile of the female and male rotors is unsymmetrical such that the sum of absorbing torques of the female rotor is negative. Accordingly, a negative torque is always positively applied to the female rotor, thereby preventing the generation of abnormal noise and abnormal vibration due to collision of the tooth surfaces of both the rotors. As a result, a volumetric efficiency and an adiabatic efficiency can be improved.

BACKGROUND OF THE INVENTION 
The present invention relates to a screw rotor for a screw pump device such 
as a screw compressor and a screw vacuum pump. 
FIGS. 5 to 11 show a known screw compressor including a casing 13 having a 
suction opening 11 at one end and a discharge opening 12 at the other end, 
and a pair of female and male screw rotors 14 and 15 (which will be 
hereinafter referred simply to as rotors) rotatably mounted in the casing 
13 and meshing with each other. The male rotor 15 is driven, and the 
female rotor 14 meshing with the male rotor 15 is rotated by the male 
rotor 15 in a direction as depicted by an arrow. Gas sucked from the 
suction opening 11 is enclosed among tooth spaces A of the female and male 
rotors 14 and 15 and the casing 13. While being compressed during rotation 
of the rotors 14 and 15, the gas is discharged from a discharge port 16 
(see FIGS. 6 to 11) to the discharge opening 12. 
FIGS. 6 to 11 show a time dependent change in the tooth spaces A of both 
the rotors 14 and 15 as viewed from an end surface on the side of the 
discharge opening 12. FIG. 6 shows a reference condition where a 
rotational angle .alpha. of the male rotor 15 is 0.degree., and FIGS. 7 to 
11 show the conditions where the rotational angles .alpha. are 12.degree., 
24.degree., 36.degree., 43.2.degree. and 60.degree., respectively. 
In the conditions shown in FIGS. 6 to 10, the tooth space A has a portion 
opening into the discharge port 16, and is gradually reduced in volume to 
discharge the compressed gas contained therein to the discharge port 16. 
On the other hand, in the condition shown in FIG. 11, the tooth space A is 
completely isolated from the discharge port 16 to define an enclosed 
space. Under such an enclosed condition, the volume of the enclosed space 
is reduced toward zero, causing a very high gas pressure in the enclosed 
space. As a result, both the rotors chatter during rotation to cause the 
generation of abnormal noise and abnormal vibration. 
Such a problem is caused by the fact that the rotor tooth has an 
unsymmetrical tooth profile. While there have been proposed various 
unsymmetrical tooth profiles in Japanese Patent Publication Nos. 60-35557 
and 60-42359 and Japanese Patent Laid-open Publication No. 60-153486, the 
above-mentioned problem occurs in any of the proposed unsymmetrical tooth 
profiles. 
The cause of this problem will now be described in more detail. In the 
conditions shown in FIGS. 6 to 10, the rotor teeth meshing with each other 
receive a force from the compressed gas in such a direction counter to the 
rotational direction of the female rotor 14. Accordingly, a torque of the 
male rotor 15 is transmitted to the female rotor 14 in such a manner that 
a trailing tooth surface of the female rotor 14 is urged by a leading 
tooth surface of the male rotor 15. In contrast, in the condition shown in 
FIG. 11, since the gas pressure in the enclosed tooth space A is 
abnormally high, the rotor tooth of the female rotor 14 receives a torque 
(negative torque) which functions to rotate the female rotor 14 in its 
rotational direction contrary to the case of FIGS. 6 to 10. Accordingly, 
the female rotor 14 is rotated in such a manner that a leading tooth 
surface of the female rotor 14 contacts a trailing tooth surface of the 
male rotor 15. Upon transition from the condition of FIG. 10 to the 
condition of FIG. 11, the tooth surfaces of both the rotors strike against 
each other to cause the generation of abnormal noise. 
Particularly in case of an oil-cooling type device, a liquid oil is 
enclosed in the tooth space A under the condition shown in FIG. 11. 
Therefore, the above problem is remarkable, and there is a possibility 
that the rotors will be broken occasionally. 
In order to prevent this defect, there has been proposed a device for 
eliminating the abnormal high pressure in the enclosed space, wherein a 
recess is formed on the end surface of the casing 13 on the discharge 
opening side facing the rotor accommodating chamber, so as to be 
communicated with the space on the suction opening side, so that the gas 
and/or oil contained in the enclosed space may be relieved through the 
recess to the space on the suction opening side (see Japanese Patent 
Publication No. 62-358). 
Further, there has been proposed a tooth profile intended to prevent the 
generation of the negative torque (see Japanese Patent Laid-open 
Publication No. 58-113595). 
However, in the device disclosed in Japanese Patent Publication No. 62-358, 
since the high-pressure gas in the enclosed space is relieved to the space 
on the suction opening side so as to prevent the generation of the 
negative torque, volumetric efficiency and adiabatic efficiency are 
deteriorated. 
In the device disclosed in Japanese Patent Laid-open Publication No. 
58-113595, there is a possibility of the negative torque being generated 
because of any factors such as a shape of the discharge port and a 
rotating speed of the rotors. Thus, there remain indefinite factors as to 
the generation of the negative torque in this prior art device. 
In any case, these prior art devices are so designed as to aim to reduce or 
eliminate the negative torque. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide a screw rotor for a 
screw pump device which may prevent the generation of abnormal noise and 
abnormal vibration to thereby improve the volumetric efficiency and the 
adiabatic efficiency by positively applying the negative torque to the 
female rotor at all times. 
According to the present invention, there is provided a screw rotor for a 
screw pump device comprising a male rotor and a female rotor meshing with 
said male rotor and adapted to be driven by said male rotor, wherein a 
tooth profile of said female and male rotors is unsymmetrical such that 
the sum of absorbing torques of said female rotor is negative. 
With this construction, the negative torque is always applied to the female 
rotor, and the female rotor is rotated to follow the male rotor under the 
condition where the leading tooth surface of the female rotor is always in 
contact with the trailing tooth surface of the male rotor. Accordingly, 
the collision between both the tooth surfaces can be prevented. 
Other objects and features of the invention will be more fully understood 
from the following detailed description and appended claims when taken 
with the accompanying drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
There will now be described a preferred embodiment of the present invention 
with reference to the drawings. 
Referring to FIG. 1, a pair of female and male rotors 1 and 2 mesh with 
each other, and the condition shown in FIG. 1 corresponds to the condition 
shown in FIG. 6 where the rotational angle .alpha. is 0.degree. and the 
tooth space A is defined below the meshing teeth. As will be described 
hereinafter, a negative torque is always applied to the female rotor 1, 
and the female rotor 1 is rotated to follow male rotor 2 under the 
condition where a leading tooth surface 1f of a rotor tooth 1a of the 
female rotor 1 is in contact with a trailing tooth surface 2r of a rotor 
tooth 2a of the male rotor 2. 
In FIG. 1, OF and OM denote centers of the female rotor 1 and the male 
rotor 2, respectively; PF and PD denote pitch circles of the female rotor 
1 and the male rotor 2, respectively; AD denotes an addendum circle of the 
male rotor 2; DM denotes a diameter of the addendum circle AD of the male 
rotor 2; l1 denotes an addendum of the female rotor 1; and DE1 denotes an 
opening angle of a sectionally arcuate portion having a radius R and a 
center O as formed by the contact of a leading tooth surface 2f of the 
rotor tooth 2a of the male rotor 2 with a trailing tooth surface 1r of the 
rotor tooth 1a of the female rotor 1 under the condition of the rotational 
angle .alpha.=0.degree.. 
The relationship between the rotational angle .alpha. and a torque of the 
female rotor 1 to be absorbed from the male rotor 2 during rotation of 
both the rotors will now be discussed in case of adapting the rotors in 
this preferred embodiment to the device shown in FIG. 5. 
Basically, a time dependent change of the condition of the rotors at the 
end surface on the discharge opening side corresponds to that shown in 
FIGS. 6 to 11 in accordance with the respective rotational angle .alpha., 
and the torque to be applied to the female rotor 1 is generated by the 
tooth space A to be defined in the stage between that where it opens into 
the discharge port 16 and that where it communicates with the suction 
opening 11. The other tooth spaces do not contribute to the generation of 
the torque since the pressure in each tooth space is balanced. 
The relationship between the rotational angle .alpha. and the torque to be 
absorbed by the female rotor 1 is shown in FIG. 2. The torque curve shown 
in FIG. 2 is repeated per a given angle .alpha..sub.0 during rotation of 
the female rotor 1. In this preferred embodiment, the given angle 
.alpha..sub.0 is 72.degree. (=360.degree./5) since the number of teeth of 
the male rotor 2 is five. In another case where the number of teeth is 
four, for example, the given angle .alpha..sub.0 would be 90.degree.. 
Further, a positive absorbing torque of the female rotor 1 means that the 
female rotor 1 receives from the compressed gas a force which functions to 
rotate the female rotor 1 in a direction counter to the rotational 
direction thereof. 
While the time dependent change of the condition of the rotor as shown in 
FIGS. 6 to 11 occurs at the end surface of the rotor on the discharge 
opening side, the conditions shown in FIGS. 6 to 11 also govern each 
condition of cross sections perpendicular to a rotor shaft at given axial 
positions in the axial direction of the rotor shaft at an appropriate 
moment. For example, when the rotors are in the condition shown in FIG. 11 
as viewed from the end surface on the discharge opening side, the 
conditions of the cross sections at the given axial positions toward the 
suction opening are varied from FIG. 11 to FIG. 6. That is, the change in 
the conditions of the cross sections is reverse to the time dependent 
change. Even thus considering the relationship between the rotor axial 
position and the rotor rotational angle, it can be said that the condition 
of each cross section is repeated with a given phase difference from FIG. 
6 to FIG. 11 and that the torque curve shown in FIG. 2 defines an 
absorbing torque of the female rotor 1 with respect to an axial position 
of the cross sections of the female rotor 1. 
Accordingly, the sum of the torques to be absorbed by the overall length of 
the female rotor 1 at an appropriate moment can be represented by an 
integral of the torque curve shown in FIG. 2. That is, the sum of the 
absorbing torques can be represented by an area (A.sub.1 +A.sub.2 -A.sub.3 
+A.sub.4). According to the present invention, this area is set to be 
negative at all times, so that the negative torque may be always applied 
to the female rotor 1. 
The sum of the absorbing torques is dependent upon a tooth profile of the 
rotor. FIG. 3 shows the relationship between the sum of the absorbing 
torques and an addendum % Ap represented by (l1/DM).times.100 with the 
opening angle De1 being used as a parameter. According to the present 
invention, the sum of the absorbing torques belongs to a negative region 
as hatched. As apparent from FIG. 3, there is a case where the addendum % 
becomes negative. 
Accordingly, a boundary of the addendum % to be included in the present 
invention should be determined for each value of De1. FIG. 4 shows the 
relationship between the boundary of the addendum % and the value of DE1. 
As apparent from FIG. 4, a hatched region is included in the present 
invention wherein the sum of the absorbing torques becomes negative, and 
the relationship can be expressed as follows: 
EQU DE1.gtoreq.7.7 Ap+33 
Although the present invention is particularly suitable for an oil-cooling 
type screw pump device, it is not limited to this type but may be applied 
to an oil-free type.