Analysis of single-pitch variable pitch rotor profile for screw vacuum pump

A single-head variable-pitch screw rotor new line suitable for oil-free screw vacuum pumps. The end face profile consists of tooth root circle, cycloid, addendum circle and involute line in sequence; the main features of this profile line. Yes: When the profile of the end profile is spirally unfolded along the axial direction, the spiral lead of the rotor gradually increases from the discharge end to the suction end, while the radius of the involute is gradually smaller, making the rotor teeth smaller. The width of the top surface of the profiled surface can be kept constant, so the suction volume at the suction side can be increased, and the backflow leakage at the discharge end can be reduced, thereby increasing the pumping speed and the ultimate vacuum degree of the pump. In the article, the polar equations of the face profile, the axial expansion equation and the calculation equation of the circle radius of the involute are given.

The oil-free screw pump has the characteristics of wide pumping speed range, simple and compact structure, no friction in the pumping chamber components, long life, low energy consumption, no oil pollution, etc. It has been widely used in many industrial fields such as semiconductor, medicine, food, chemical engineering and so on. . The screw rotor is the most critical part of the screw vacuum pump, directly determines the pump's working performance and service life, and its processing and manufacturing costs account for nearly half of the total cost of the entire screw pump. The profile design of the screw rotor is the most critical technology in the entire screw pump design.

The screw rotor in an oil-free screw vacuum pump has two types of structure with equal pitch and variable pitch. The single-head variable-pitch screw rotor, because of its internal pre-compressed exhaust method, has outstanding energy-saving and noise-reduction advantages compared to that of the equal-pitch screw rotor, and is therefore increasingly being designed by oil-free screw vacuum pumps. The user's favor. Many technicians have designed various types of single-head variable-pitch screw rotor lines or conducted in-depth research. However, the existing variable pitch screw rotors generally have the feature that the tip width is large at the suction end and small at the discharge end, and thus affects the performance of the pump.

To solve this problem, this paper develops a single-head variable-pitch screw rotor profile with approximate equal tooth width, which can be used as a reference for related designers.

statement of problem

Although the structure of the single-head variable-pitch screw rotor wire has a variety of structures, its common structural feature is that the lead (pitch) of the screw rotor gradually decreases from the suction end to the discharge end. In the process, the tooth tip width (and corresponding tooth root width) in the rotor tooth profile also gradually becomes narrower in proportion. This structural feature will directly lead to poor pumping performance of the screw pump. Because the gap between the top surface of the rotor tooth and the internal surface of the pump body is the most important leakage path for backflow between gas stages during the exhaust of the rotor, the top width of the rotor tooth profile is equivalent to the depth of the leakage channel, and the top width is wide. The wider, the deeper the leak path, the stronger the resistance to leakage between stages, the smaller the gas return flow between two adjacent stages. The width of the tooth tip of the existing single-pitch variable-pitch screw rotor line gradually narrows from the suction end to the discharge end, and the resistance to leakage between stages is getting weaker and weaker. In the working process of the screw vacuum pump, the closer it is to the exhaust end, the greater the pressure difference between the gas pressure and the stage. This type of structure where the pressure difference becomes large and the width of the tooth head becomes smaller and smaller, will directly lead to an increase in the gas return flow near the exhaust end, which is an obvious irrational situation. Conversely, near the suction end of the pump, the gas pressure and the pressure difference between the stages are relatively small, and here the tooth width of the tooth profile becomes large, which is obviously unnecessary. At the same time, too wide tooth top width will lead to the pump inlet volume (characterized by the volume utilization factor) is too small, which reduces the actual pumping rate.

All in all, the structural characteristics of the conventional variable-pitch screw rotor will directly lead to the following unreasonable conditions: At the suction end of the rotor, the tooth width of the tooth profile will increase unnecessarily, thus reducing the volumetric utilization factor of the pump; At the gas end, there is a large difference in gas pressure between the stages, and the width of the tooth profile is smaller and smaller, resulting in an increase in gas return flow. This will directly lead to a reduction in the ultimate vacuum of the screw vacuum pump and a consequence of the drop in the pumping rate.

The composition of the end profile

In view of the above problems, this paper describes a single-head variable-pitch screw rotor profile capable of keeping the tooth tip width approximately constant (of course, correspondingly, the tooth root width is also kept constant). A variable-pitch screw rotor when the lead of the screw gradually increases from the discharge end to the suction end (P1

This rotor profile introduced in this paper, the composition of the end surface profile is more common, consists of four segments of the sequence of phase connection, followed by the root circle 1, cycloid 2, addendum circle 3 and involute 4. The end surface profile is spirally expanded in the axial direction to form a single-head variable-pitch screw rotor. The tooth profile of the screw rotor corresponding to the four-segment curve is tooth root surface 5, concave tooth surface 6, tooth top surface 7 and helical tooth surface 8. Cycloid 2 can be used in various forms with self-engagement. With the transition curve of the characteristic, the generated transition tooth surface also changes.

Although this type of end profile seems to be the most widely used and widely used type of line in actual production, it can achieve the same effect of maintaining the top width of the screw rotor. The method of realization is that as the variable pitch of the end surface profile expands, the radius of the base circle of the involute 4 in the profile also changes, so that the three-phase curve of the tooth root circle, the involute curve and the addendum circle respectively Occupied angles ∠aoc=θC, ∠coe, ∠eog=θE also change, and it can be ensured that the teeth of the rotor tooth surface will be changed when the spiral lead (pitch) of the rotor is proportional to the spiral expansion angle. The top width remains approximately unchanged.

Design example

Finally, give a design example. An oil-free variable-pitch tooth top wide screw rotor, the structural parameters are as follows: the radius of the tooth root circle is r=36mm, the radius of the addendum circle is R=96mm; the diameter of the pitch circle e=R+r=132mm; the exhaust end face The initial lead of the rotor P1=48mm; the lead end of the rotor at the suction end plane lead P2=192mm; the total length of the rotor work area L=540mm; the variable pitch coefficient λ=1/(6π) is calculated and the number of turns of the spiral is 4.5 circles . The width of the lower top of the right-handed screw rotor is designed to be B(τ) = 20mm. From the above formulae, the involute base circle radius a(τ) is calculated from the spiral unwinding angle τ and the axial coordinate z. relationship. The spiral pitch of the rotor gradually increases from the suction end to the exhaust end, and is proportional to the unfolding angle of the spiral; however, the width of the tooth top always remains unchanged at B=20 mm, while the axial length L occupied by the helical tooth surface increases continuously.

The left rotator paired with the right circumrotator must have the same involute radius of base circle a(τ) on each section as the right rotator, and therefore its axial tooth tip width cannot be kept constant. At the same time, the value of the upper tooth tip width B'(τ) at the side of the left rotator toward the exhaust end at the corresponding helical unwinding angle τ is given. It can be found that this value gradually increases from the suction end to the exhaust end. This is contrary to the changing trend of ordinary variable-pitch screw rotors, which is conducive to improving the pumping performance of the screw pump; and the overall variation is not large, which approximately maintains the characteristics of equal tooth tip width. In addition, the upper tooth top width B′′(τ) of the conventional variable pitch left-handed screw rotor and the lower tooth top width B(τ) of the right-hand screw rotor (under the condition that the involute base circle radius is equal to 24 mm) can be seen This value is great on the suction side and the exhaust side is small.

in conclusion

This paper presents a new single-head variable-pitch variable pitch screw rotor rotor line for oil-free screw vacuum pumps, and gives all the line equations of the end face and the axial variable pitch. The main characteristic of this type of profile is that as the variable pitch of the end surface profile expands, the spiral lead of the rotor gradually becomes larger, and the axial length of the helical tooth surface also gradually increases, but the width of the top surface of the tooth is always constant. Compared with the previous single-head variable-pitch screw rotors, the tip width of the line rotor at the suction end is relatively small, and the volumetric utilization factor of the end profile is large, thereby forming a larger interstage suction volume. The theoretical pumping speed is larger under the same structural parameters; conversely, the tooth tip width at the exhaust end of the profile rotor is relatively large, and it has a stronger inter-stage leakage blocking capability, enabling gas-level leak backflow. Lowering, which helps to improve the ultimate vacuum vacuum pump and the actual effective pumping speed. In addition, the capacity utilization factor of the discharge end becomes smaller, so that the pump suction and exhaust compression ratio becomes larger.

In this paper, only the design equations of the rotor theoretical profile are given. The actual design should consider the necessary meshing clearance. In addition, this kind of rotor dynamic balance design and processing manufacturing process design, has yet to be further studied.

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