Method to determine the reasonable design area of rotor profile of roots pump and its application

Patent metadata

Field	Value
Publication number	US-11168682-B2
Application number	US-202017137512-A
Country	US
Kind code	B2
Filing date	Dec 30, 2020
Priority date	Dec 28, 2018
Publication date	Nov 9, 2021
Grant date	Nov 9, 2021

Abstract

The disclosure discloses a method for determining reasonable design area of roots pump rotor profile of roots pump and its application, and belongs to the field of mechanical design. According to the method of the disclosure, after a relation between the roots pump rotor profile and performance parameters is established, constraint conditions for avoiding a closed volume and undercutting are further determined, so that a reasonable design region of a roots pump rotor blade peak curve is determined. Reference is given when the roots pump rotor profile is designed, i.e., the rotor profile with the blade peak curve being not within the reasonable design region inevitably causes the problem of closed volume or undercutting in application, so that the design of the rotor profile that causes the closed volume or undercutting can be avoided when the roots pump rotor profile is designed. The problem that the design unreasonableness of the rotor profile is not found until the design is completed is solved, so that the design efficiency of the rotor profile is improved.

First claim

What is claimed is:

1. A method comprising:
step 1: establishing a relation of a rotor profile of a roots pump and a performance parameter of the roots pump, wherein the performance parameter is a pumping rate of the roots pump, wherein the relation is expressed as:

s
th

=

2
⁢

V
·

n

6
⁢
0

·

10

-
6

=

2
·

10

-
6

⁢
π
⁢

R
a
2

⁢
L
⁢

n

6
⁢
0

⁢
λ

,
and

(
3
)

λ
=

π
⁢

R
a
2

-

S
r

π
⁢

R
a
2

,

(
4
)

wherein s th is the pumping rate in units of liters per second of the roots pump; V is a volume of a medium discharged by the roots pump when one rotor of the roots pump rotates for a circle, in units of mm 3 ; n is a rotating speed of the rotor, in units of revolutions per minute (rpm); λ is a rotor area utilization coefficient, which is unitless; R a is a rotor tip radius in units of mm; L is a rotor length, in units of mm; S r refers to an area of a single roots pump rotor, in units of mm 2 ;
step 2: determining constraint conditions for avoiding a closed volume;
step 3: determining constraint conditions for avoiding undercutting; and
step 4: determining range of a blade peak curve of the rotor profile based on the relation, the constraint conditions for avoiding the closed volume and the constraint conditions for avoiding undercutting;
wherein in step 2, the determining constraint conditions for avoiding the closed volume comprises:
taking an arbitrary point on the roots pump rotor blade peak curve to make normal line of the blade peak curve at the point, and setting a slope of the normal line to be k, the coordinate of an intersection point of the normal line and the pitch circle arc to be (x 1 ,y 1 ), and

{

x
1

=

x
1

⁡

(
t
)

y
1

=

y
1

⁡

(
t
)

⁢

;

⁢
and

(
10
)

making a normal line B1B′1 on a point B1 on the blade peak curve, and setting the coordinate of the point B1 is (x b , y b ), then the constraint conditions for avoiding the closed volume being:

{

Assignees

• Univ Jiangnan

Inventors

• He Xueming
• Huang Hainan
• Liu Zhenchao
• Yu Jiachuan
• Liu Ping

Classifications

• F04C2/126 Primary

  with radially from the rotor body extending elements, not necessarily co-operating with corresponding recesses in the other rotor, e.g. lobes, Roots type · CPC title

• G06F17/10

  Complex mathematical operations {(function generation by table look-up G06F1/03; evaluation of elementary functions by calculation G06F7/544)} · CPC title

• F04C2/084 Primary

  Toothed wheels · CPC title

• F04C2250/301

  compression chamber profile defined by a mathematical expression or by parameters · CPC title

• F04C18/084

  Toothed wheels · CPC title