CN104696223B - screw vacuum pump self-balancing screw rotor - Google Patents

Abstract

The invention provides a kind of screw vacuum pump self-balancing screw rotor, belong to mechanical engineering technical field.The pitch curve it solving existing screw rod needs symmetric design, it is impossible to meet different operating condition design requirement.This screw vacuum pump self-balancing screw rotor has the eccentric asymmetric contrate tooth profile of position of centre of gravity and the change pitch relevant with looping angle；In the range of inspiratory limb, pitch curve is unsymmetric structure with pitch curve in the range of interlude, between the pitch curve by total looping angle, determined, the compression ratio determined, the pitch curve determined and the screw vacuum pump compression ratio determined and the inspiratory limb screw rod helical pitch parameter determined and the interlude screw rod helical pitch parameter determined, Equation for Calculating realizes static equilibrium and at least up to more than 80% dynamic equilibrium of 100%, and improves dynamic equilibrium by changing the geometry at screw rotor end.The screw rotor designed by above-mentioned strategy is suitable for different actual condition demands.

Description

Screw vacuum pump self-balancing screw rotor

Technical field

The invention belongs to mechanical engineering technical field, relate to a kind of fluid varactor machine, particularly a kind of screw vacuum Pump self-balancing screw rotor.

Background technology

Screw vacuum pump is developed by screw air compressor, is used for extracting gas, produces vacuum pump environment, owing to it is one The preferable pumping equipment of kind, simple in construction, easy to maintenance, the most environmentally friendly, pollution will not be produced, Through becoming the industry first-selection pumping equipments such as microelectronics, quasiconductor, pharmacy, Precision Machining.Screw vacuum pump is in oil-free, does Under the state of formula run, screw molded lines needs special handling, could obtain preferable service behaviour, consider further that manufacturing cost because of Element, based on the screw vacuum pump of single head on market, significantly can save process time and reduce cost.Along with dry type screw rod The development trend of vacuum pump high speed, it is necessary to screw rotor is carried out dynamic balance optimization calculating in the design phase, to carry The raising of high screw pump integral working and service life.

D.THOMAS proposes a kind of internal compression screw arbor vacuum pump (DE102010019402), and screw rod uses continuous gradation Crossing form, end face uses symmetrical molded line, and this screw rod is applied to compression in the SrewLine series screw oil-free of Germany Leybold Vacuum pump, is a kind of dry pump exclusively for commercial Application design, solves in commercial Application, such as the operating mode such as dust, tar not Vacuum problem time good, its screw rod uses at inspiratory limb loss of weight, and built-in compression ratio is designed to more than 3.5, and screw rod is just easy to reach More satisfactory dynamic balancing, but sacrifice half number of compression stages.

M.H.NORTH devises a kind of conjugation conical screw (WO2007068973), and its pitch keeps constant, by the axial end Footpath taper change causes internal compression change in volume, and this conjugation conical screw is that Britain Edwards pushes away for severe vacuum environment The commercial Application gone out, uses the mode of balancing head to reach the dynamic balancing of screw rod, but adds the difficulty of screw rod axial seal.

B.ULRICH devises the varying pitch twin-screw rotor (WO0208609A2) that a kind of balance quality is good, face type Line keeps constant, and pitch is ascending, then to little, finally keeps constant, and this screw rod is applied to Busch company of Germany COBRA series screw pump, manufacturing process is preferable, self can reach the balance of more than 85%, then assists two end face losss of weight can Reach complete equipilibrium, but screw design form is fixed, lack change, it is impossible to meet different operating condition design requirement.

In order to meet different operating condition design requirement, it is proposed that dry screw vacuum pump varying pitch screw before applicant (CN102937094A), it is proposed that two end faces go quality, the dynamic balancing mode of assist tooth end face centering, this balance mode breaks It is broken tooth top surface structure, it is impossible to adapt to severe process environments.

Summary of the invention

The present invention proposes a kind of screw vacuum pump self-balancing screw rotor, and how the technical problem to be solved in the present invention is Propose another kind and be suitable for the screw vacuum pump self-balancing screw rotor that different operating condition design requires and dynamic balance performance is excellent.

Solving the technical problem that of the present invention can be realized by following technical proposal:

This screw vacuum pump self-balancing screw rotor has the eccentric asymmetric contrate tooth profile of position of centre of gravity and and looping angle Relevant change pitch；When the winding number of turns is 2 circle, pitch starts toward the end face direction of interlude and in suction from the end face of inspiratory limb Gas section increases, and reduces at interlude；When winding number of turns ＞ 2 is enclosed, pitch starts the end face side toward exhaust section from the end face of inspiratory limb To and inspiratory limb increase, interlude reduce, exhaust section maintain an equal level；When being wound around a circle, pitch arrives maximum, is being wound around During two circles, pitch arrives minima；In the range of inspiratory limb, pitch curve is unsymmetrical knot with pitch curve in the range of interlude Structure, the screw vacuum pump compression ratio c by total looping angle, determined, inspiratory limb screw rod helical pitch parameter m determined₁, the centre that determines Section screw rod helical pitch parameter m₂, the pitch curve that determines and the screw vacuum pump compression ratio c determined and the inspiratory limb screw rod determined Helical pitch parameter m₁With interlude screw rod helical pitch parameter m determined₂Between equation, calculate the static equilibrium and at least realizing 100% Reach more than 80% dynamic equilibrium, and improve dynamic equilibrium by changing the geometry at screw rotor end.

In above-mentioned screw vacuum pump self-balancing screw rotor, the parametric equation of pitch curve in the range of described inspiratory limb For

$\begin{array}{c}{P}_1^{\′}\left(\mathrm{\α}\right)=c\frac{p}{2\mathrm{\π}}+3C_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^2+3D_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^2\mathrm{\α}+D_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3\\ +3E_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^2{\mathrm{\α}}^2+2E_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3\mathrm{\α}\end{array},0\≤\mathrm{\α}\≤2\mathrm{\π};$

In formula

C is screw vacuum pump compression ratio, and p is exhaust section screw rod helical pitch, m₁For inspiratory limb screw rod helical pitch parameter；Inspiratory limb spiral shell Bar helical pitch parameterP in formula₁For inspiratory limb screw rod helical pitch；

In the range of described interlude, the parametric equation of pitch curve is

$\begin{array}{c}{P}_2^{\′}\left(\mathrm{\α}\right)=c\frac{p}{2\mathrm{\π}}+3C_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^2+3D_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^2(\mathrm{\α}-2\mathrm{\π})\mathrm{\α}+3D_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3\\ +3E_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^2{(\mathrm{\α}-4\mathrm{\π})}^2+2E_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3(\mathrm{\α}-4\mathrm{\π})\end{array},2\mathrm{\π}\≤\mathrm{\α}\≤4\mathrm{\π};$

In formulaC is screw vacuum pump compression Ratio, p is exhaust section screw rod helical pitch, m₂For interlude screw rod helical pitch parameter, interlude screw rod helical pitch parameterP in formula₂For Interlude screw rod helical pitch.

In above-mentioned screw vacuum pump self-balancing screw rotor, screw vacuum pump compression ratio c and inspiratory limb screw rod helical pitch Parameter m₁With interlude screw rod helical pitch parameter m₂Between the equation that determines be

m₁+m₂=c+1；M in formula₁≠m₂, 1 ＜ m₁＜ c, 1 ＜ m₂＜ c.

In above-mentioned screw vacuum pump self-balancing screw rotor, the parametric equation of pitch curve in the range of described inspiratory limb P₁' the equation P of pitch parameter in the range of (α) and interlude₂' (α) meet following formula relation:

P₂' (α)=p (c+1)-P₁' (α-2 π), in formula, p is exhaust section screw rod helical pitch, and c is screw vacuum pump compression ratio, and α is The winding angle of spiral curve.

In above-mentioned screw vacuum pump self-balancing screw rotor, the length L=p (m of screw rotor₁+m₂+ n), in formula, p is Exhaust section screw rod helical pitch, m₁For inspiratory limb screw rod helical pitch parameter, m₂For interlude screw rod helical pitch parameter, n is exhaust section progression, 0≤ n≤6。

In above-mentioned screw vacuum pump self-balancing screw rotor, the axial parametric equation of circular helix of screw rotor:

The axial parametric equation of circular helix of inspiratory limb is

$P_1\left(t\right)=m_{1}p+c\frac{p}{2\mathrm{\π}}(\mathrm{\α}-2\mathrm{\π})+C_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3+D_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3\mathrm{\α}+E_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3{\mathrm{\α}}^2;$

0≤α≤2 π in formula,

C is screw vacuum pump compression ratio, and p is exhaust section screw rod helical pitch, m₁For inspiratory limb screw rod helical pitch parameter, α is spiral The winding angle of curve；

The axial parametric equation of circular helix of interlude is

$\begin{array}{c}{P}_2\left(\mathrm{\α}\right)=m_{1}p+c\frac{p}{2\mathrm{\π}}(\mathrm{\α}-2\mathrm{\π})+C_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3+D_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3(\mathrm{\α}-4\mathrm{\π})\\ +E_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3{(\mathrm{\α}-4\mathrm{\π})}^2\end{array};$

2 π≤α≤4 π in formula,C is screw rod Vacuum pump compression ratio, p is exhaust section screw rod helical pitch, m₂For interlude screw rod helical pitch parameter, α is the winding angle of spiral curve；

The axial parametric equation of circular helix of exhaust section is

4 π≤α≤(2+n) 2 π, m in formula₁For inspiratory limb screw rod helical pitch parameter, m₂For interlude screw rod helical pitch parameter, p is exhaust section screw rod helical pitch, and α is the winding angle of spiral curve.

Compared with prior art, this screw vacuum pump self-balancing screw rotor is according to the screw vacuum pump needed for actual condition Compression ratio c, pumping speed and compression effectiveness adjust c, m neatly₁、m₂And progression, in a word, the screw rod designed by above-mentioned strategy Rotor is suitable for different actual condition demands.

Accompanying drawing explanation

Fig. 1 is screw rotor front view and the axially expanded figure of circular helix, and this expanded view represents screw rotor axle position Put the relation of z and looping angle α.

Fig. 2 is screw rotor pitch change curve, and this change curve represents the pass of screw rotor shaft position z' and looping angle α System.

Fig. 3 is the screw rotor pitch change curve with actual parameter.

Detailed description of the invention

The following is the specific embodiment of the present invention and combine accompanying drawing, technical scheme is further described, But the present invention is not limited to these embodiments.

As it is shown in figure 1, for the constant screw rotor of profile, its axial screw line is circular helix Γ, permissible It is expressed as

$\left\{\begin{array}{c}{r}_i\left(\mathrm{\α}\right)=x_i\left(\mathrm{\α}\right)i+y_i\left(\mathrm{\α}\right)j+z_i\left(\mathrm{\α}\right)k\\ x_i\left(\mathrm{\α}\right)=R\cos \left(\mathrm{\α}\right)\\ y_i\left(\mathrm{\α}\right)=R\sin \left(\mathrm{\α}\right)\\ z_i\left(\mathrm{\α}\right)=P_i\left(\mathrm{\α}\right)\end{array}\right.,i=1,2,3;$

In formula, i=1,2,3 represent the helix of inspiratory limb, interlude and exhaust section respectively；

α is helix variable, represents the winding angle of helix；R is circular helix radius；P_i(α) it is cylindrical screw Bobbin, to parametric equation, represents the change of helix axial length；Corresponding P_i' (α) be pitch parametric equation, represents pitch Change.

Set constraints P₁' (0)=ap, then the axial parametric equation of the circular helix of inspiratory limb is

$P_1\left(t\right)=m_{1}p+c\frac{p}{2\mathrm{\π}}(\mathrm{\α}-{\mathrm{\α}}_1)+C_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^3+D_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^3\mathrm{\α}+E_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^3{\mathrm{\α}}^2,$

0≤α≤α in formula₁,

The axial parametric equation of circular helix of interlude is

$\begin{array}{c}{P}_2\left(\mathrm{\α}\right)=m_1\frac{p}{2\mathrm{\π}}{\mathrm{\α}}_1+c\frac{p}{2\mathrm{\π}}(\mathrm{\α}-{\mathrm{\α}}_1)+C_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^3+D_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^3(\mathrm{\α}-{\mathrm{\α}}_2)\\ +E_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^3{(\mathrm{\α}-{\mathrm{\α}}_2)}^2\end{array},$

α in formula₁≤α≤α₂,

The axial parametric equation of circular helix of exhaust section is

α in formula₂≤α≤α₃；

In the axial parametric equation of above-mentioned circular helix, p is the minimum pitch calculating reference value of screw rod；A is that head screw rises The varying pitch parameter of beginning position；C is end and the varying pitch parameter of interlude screw rod original position of inspiratory limb screw rod；B is row The uniform pitch parameter of gas section screw rod；m₁For inspiratory limb screw rod helical pitch parameter, m₂For interlude screw rod helical pitch parameter.

In the range of inspiratory limb, the parametric equation of pitch curve is

$P_1^{\′}\left(\mathrm{\α}\right)=c\frac{p}{2\mathrm{\π}}+3C_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^2+3D_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^2\mathrm{\α}+D_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^3+3E_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^2{\mathrm{\α}}^2+2E_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^3\mathrm{\α}$

0≤α≤α in formula₁,

In the range of interlude, the parametric equation of pitch curve is

$\begin{array}{c}{P}_2^{\′}\left(\mathrm{\α}\right)=c\frac{p}{2\mathrm{\π}}+3C_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^2+3D_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^2(\mathrm{\α}-{\mathrm{\α}}_2)+3D_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^3\\ +3E_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^2{(\mathrm{\α}-{\mathrm{\α}}_2)}^2+2E_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-{\mathrm{\α}}_1)}^3(\mathrm{\α}-{\mathrm{\α}}_2)\end{array},$

α in formula₁≤α≤α₂,

In the range of exhaust section, the parametric equation of pitch curve isα in formula₁≤α≤α₂；

In the parametric equation of above-mentioned pitch curve, p is the minimum pitch calculating reference value of screw rod；A is head screw start bit The varying pitch parameter put；C is end and the varying pitch parameter of interlude screw rod original position of inspiratory limb screw rod；B is exhaust section The uniform pitch parameter of screw rod；m₁For inspiratory limb screw rod helical pitch parameter, m₂For interlude screw rod helical pitch parameter.

As it is shown on figure 3, the improvement of the screw vacuum pump compression performance of interior compression, a key factor is how to optimize design Internal compression, sets axial whole helical pitch number (progression) value of screw rotor less than or equal to 8；Inspiratory limb screw rod and interlude screw rod It it is all 1 helical pitch；Screw rotor so can be made to obtain good balance and reduce screw rod progression.So, above-mentioned cylindrical screw Bobbin α in parametric equation and in above-mentioned pitch curve parametric equation₁=2 π, α₂=4 π, α₃=(2+n) 2 π, n=0,1, 2,3,4,5,6。

Set a=b=1, and for avoid the occurrence of less pitch, set 1 ＜ m₁＜ c, 1 ＜ m₂＜ c, a ＜ c；Then c is Screw vacuum pump compression ratio, 1 ＜ c≤10；P is exhaust section screw rod helical pitch,In formula, L is that screw rotor is total Length.

Reset between screw vacuum pump compression ratio and inspiratory limb screw rod helical pitch parameter and interlude screw rod helical pitch parameter true Fixed equation is m₁p+m₂P=(c+1) p, i.e. m₁+m₂=c+1.Pitch curve and spiral shell in the range of interlude in the range of inspiratory limb It is unsymmetric structure away from curve, the parametric equation P of pitch curve in the range of inspiratory limb₁' pitch curve in the range of (α) and interlude Parametric equation P₂' (α) meet following formula relation: P₂' (α)=p (c+1)-P₁' (α-2 π), in formula, p is exhaust section screw rod helical pitch, c For screw vacuum pump compression ratio, α is the winding angle of spiral curve.

Such as c=5 in Fig. 3, m₁=3.4, m₂=2.6 or m₁=3.25, m₂=2.75 or m₁=2.7, m₂=3.3；m₁Value The biggest, then screw vacuum pump pumping speed is the biggest；If m₂Value is the biggest, then screw vacuum pump compression effectiveness is more excellent.Designing in a word Cheng Zhong, selects screw vacuum pump compression ratio numerical value according to screw rotor total length in actual screws vacuum pump and applying working condition, m₁Numerical value, m₁Numerical value and progression, be calculated p value, more corresponding parameter substituted into the axial parametric equation of above-mentioned circular helix Obtaining required equation with above-mentioned pitch curve parametric equation, design screw rotor, this screw rotor realizes the static state of 100% Balance and at least up to more than 80% dynamic equilibrium.

Designing screw rotor processing according to above-mentioned to obtain screw rotor in kind, dynamic balance running uses the hard of Shen gram, Shanghai Type balancing machine, model YYW-300A, the screw design stage had good dynamic balancing, amount of unbalance mainly by processing, The uneven of material causes, and overall amount of unbalance is the least, actual measured value left end 0.653g, right-hand member 1.71g, meets ISO1940 dynamic balance level.In the case of or requirement for dynamic balance higher at rotating speed is higher, in order to allow screw vacuum pump can adapt to Severe working environment, only need to change the geometry at screw rotor end improves dynamic equilibrium；At both ends of the surface eccentric position A little weight is removed in boring.This screw rotor, without at crest top land auxiliary transverse alignment, i.e. keeps the complete of screw rod tooth top body structure surface Property, adapt to bad working environments, have again self dynamically balanced screw rod good, increase the service life and reduce maintenance cost.

Claims (7)

1. a screw vacuum pump self-balancing screw rotor, this screw rotor has the asymmetric contrate tooth profile that position of centre of gravity is eccentric And the change pitch relevant with looping angle；When the winding number of turns is 2 circle, pitch starts the end face toward interlude from the end face of inspiratory limb Direction and inspiratory limb increase, interlude reduce；When winding number of turns ＞ 2 is enclosed, pitch starts toward aerofluxus from the end face of inspiratory limb Section end face direction and inspiratory limb increase, interlude reduce, exhaust section maintain an equal level；When being wound around a circle, pitch arrives maximum Value, when being wound around two circles, pitch arrives minima；It is characterized in that, in the range of inspiratory limb pitch curve with in interlude scope Interior pitch curve is unsymmetric structure, the screw vacuum pump compression ratio c that by total looping angle, determines, the inspiratory limb screw rod determined Helical pitch parameter m₁, interlude screw rod helical pitch parameter m that determines₂, the pitch curve that determines and the screw vacuum pump compression determined Than c and inspiratory limb screw rod helical pitch parameter m determined₁With interlude screw rod helical pitch parameter m determined₂Between equation, calculate realize The static equilibrium of 100% and at least up to more than 80% dynamic equilibrium, and by changing the geometry at screw rotor end Improve dynamic equilibrium.

Screw vacuum pump self-balancing screw rotor the most according to claim 1, it is characterised in that described inspiratory limb screw rod is led Journey parameterP in formula₁For inspiratory limb screw rod helical pitch, p is exhaust section screw rod helical pitch；Interlude screw rod helical pitch parameterP in formula₂For interlude screw rod helical pitch, p is exhaust section screw rod helical pitch.

Screw vacuum pump self-balancing screw rotor the most according to claim 2, it is characterised in that described exhaust section screw rod is led JourneyL is the length of screw rotor, m₁For inspiratory limb screw rod helical pitch parameter, m₂Join for interlude screw rod helical pitch Number, n is exhaust section progression, 0≤n≤6.

Screw vacuum pump self-balancing screw rotor the most according to claim 1, it is characterised in that described screw vacuum is pumped Contract than c and inspiratory limb screw rod helical pitch parameter m₁With interlude screw rod helical pitch parameter m₂Between equation be

m₁+m₂=c+1；M in formula₁≠m₂, 1 ＜ m₁＜ c, 1 ＜ m₂＜ c.

Screw vacuum pump self-balancing screw rotor the most according to claim 1, it is characterised in that in the range of described inspiratory limb The parametric equation P of pitch curve₁' the parametric equation P of pitch curve in the range of (α) and interlude₂' (α) meet following formula relation:

P₂' (α)=p (c+1)-P₁' (α-2 π), in formula, p is exhaust section screw rod helical pitch, and c is screw vacuum pump compression ratio, and α is spiral The winding angle of curve.

Screw vacuum pump self-balancing screw rotor the most according to claim 5, it is characterised in that in the range of described inspiratory limb The parametric equation P of pitch curve₁' (α) be

$\begin{array}{c}{P}_1^{\′}\left(\mathrm{\α}\right)=c\frac{p}{2\mathrm{\π}}+3C_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^2+3D_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^2\mathrm{\α}+D_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3\\ +3E_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^2{\mathrm{\α}}^2+2E_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3\mathrm{\α}\end{array},0\≤\mathrm{\α}\≤2\mathrm{\π};$

In formula

C is screw vacuum pump compression ratio, and p is exhaust section screw rod helical pitch, m₁For inspiratory limb screw rod helical pitch parameter, α is spiral curve Winding angle；

The parametric equation P of pitch curve in the range of described interlude₂' (α) be

$\begin{array}{c}{P}_2^{\′}\left(\mathrm{\α}\right)=c\frac{p}{2\mathrm{\π}}+3C_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^2+3D_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^2(\mathrm{\α}-4\mathrm{\π})+3D_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^2\\ +3E_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^2{(\mathrm{\α}-4\mathrm{\π})}^2+2E_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3(\mathrm{\α}-4\mathrm{\π})\end{array},2\mathrm{\π}\≤\mathrm{\α}\≤4\mathrm{\π};$

In formulaC is screw vacuum pump compression ratio, p For exhaust section screw rod helical pitch, m₂For interlude screw rod helical pitch parameter, α is the winding angle of spiral curve.

7. according to the screw vacuum pump self-balancing screw rotor described in Claims 2 or 3 or 4 or 5, it is characterised in that screw rod turns The axial parametric equation of circular helix of son:

The circular helix axial parametric equation P of inspiratory limb₁(t) be

$P_1\left(t\right)=m_{1}p+c\frac{p}{2\mathrm{\π}}(\mathrm{\α}-2\mathrm{\π})+C_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3+D_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3\mathrm{\α}+E_1\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3{\mathrm{\α}}^2;$

0≤α≤2 π in formula,

C is screw vacuum pump compression ratio, and p is exhaust section screw rod helical pitch, m₁For inspiratory limb screw rod helical pitch parameter, α is spiral curve Winding angle；

The circular helix axial parametric equation P of interlude₂(t) be

$\begin{array}{c}{P}_2\left(\mathrm{\α}\right)=m_{1}p+c\frac{p}{2\mathrm{\π}}(\mathrm{\α}-2\mathrm{\π})+C_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3+D_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3(\mathrm{\α}-4\mathrm{\π})\\ +E_2\frac{p}{2\mathrm{\π}}{(\mathrm{\α}-2\mathrm{\π})}^3{(\mathrm{\α}-4\mathrm{\π})}^2\end{array};$

2 π≤α≤4 π in formula,C is screw vacuum Pump compression ratio, p is exhaust section screw rod helical pitch, m₂For interlude screw rod helical pitch parameter, α is the winding angle of spiral curve；

The circular helix axial parametric equation P of exhaust section₃(t) be

4 π≤α≤(2+n) 2 π, m in formula₁For inspiratory limb screw rod helical pitch parameter, m₂For Interlude screw rod helical pitch parameter, p is exhaust section screw rod helical pitch, and α is the winding angle of spiral curve.