CN106767606A - Quimby pump rotor interference detection method based on rigging error - Google Patents

Abstract

The invention discloses a kind of Quimby pump rotor interference detection method based on rigging error, comprise the following steps：A. by coordinate transform will produce rigging error driving screw rod and driven screw rotor curved surface respectively from moving coordinate system o₁x₁y₁z₁With moving coordinate system o₂x₂y₂z₂It is converted into the quiet coordinate system OXYZ being consolidated on the pump housing；B. the contact line of the driving screw rod and driven screw helicoid is solved；C. the driving screw rod is distributed with the inter-lobe clearance of driven screw under solving rigging error according to the contact line；D. the minimum value of the minimum value according to the gap distribution and given gap band, judge whether driving screw rod and driven screw produce interference in the presence of rigging error, the method can detect screw rotor locus and inter-lobe clearance changes in distribution under the true operating condition of rigging error, so as to quantify the leakage rate of screw pump, and the change that various position deviation lower rotor part inter-lobe clearances are distributed is calculated, for the work such as housing, rotor machining and bearing apolegamy provide accurate quantizating index.

Description

Quimby pump rotor interference detection method based on rigging error

Technical field

It is dry the present invention relates to screw pump interference detection field, more particularly to a kind of Quimby pump rotor based on rigging error Relate to detection method.

Background technology

Screw pump is divided into single-screw (single screw) pump, Quimby pump, three screw pump, five-screw pump etc. by the difference of screw rod radical.Wherein Quimby pump is mainly manifested in rational in infrastructure, energy-conserving and environment-protective due to its superior performance, and screw rotor is not in single-edge grinding Damage, leakage point is few, and leakage rate is low, effectively reduce influence of the greasy dirt to environment.By theoretical tooth Shape Design cutter, it is processed, will The screw rod with the theoretical flank of tooth (i.e. very close to each other) for obtain that a pair of rotor axis are parallel, contacting with each other, but reality processing goes out Screw rotor often due to inevitably manufacture, alignment error (axis not parallel etc.), stress deformation during operating is heated swollen It is swollen, and parts the factor such as abrasion, and can not run well, or even the thing such as cause rotor to abrade due to rotor interference, kill Therefore.

Accordingly, it would be desirable to a kind of Quimby pump rotor interference detection method based on rigging error, the method can be in assembling Screw rotor locus and inter-lobe clearance changes in distribution are detected under the true operating condition of error, so as to quantify letting out for screw pump Leakage quantity, and the change of various position deviation lower rotor part inter-lobe clearance distributions is calculated, it is housing, rotor machining and bearing apolegamy etc. Work provides accurate quantizating index.

The content of the invention

In view of this, it is an object of the invention to provide a kind of Quimby pump rotor interference detection side based on rigging error Method, the method can detect that screw rotor locus and inter-lobe clearance distribution become under the true operating condition of rigging error Change, so as to quantify the leakage rate of screw pump, and calculate the change of various position deviation lower rotor part inter-lobe clearance distributions, be shell The work such as body, rotor machining and bearing apolegamy provide accurate quantizating index.

Quimby pump rotor interference detection method based on rigging error of the invention, comprises the following steps：A. by sitting Mark becomes the driving screw rod of generation rigging error of changing commanders and the rotor curved surface of driven screw respectively from moving coordinate system o₁x₁y₁z₁With dynamic seat Mark system o₂x₂y₂z₂It is converted into the quiet coordinate system OXYZ being consolidated on the pump housing；

In order to consider that the whole of Quimby pump rotor turns assembling process, OXYZ, o are set up respectively₁x₁y₁z₁、o₂x₂y₂z₂Three Coordinate system (as shown in Figure 1), if MN is the screw shaft of the optional position in quiet coordinate system OXYZ, the coordinate of M is (M_X, M_Y, M_Z),_NThe coordinate of point is (N_X, N_Y, N_Z), by following coordinate transform find OXYZ respectively with o₁x₁y₁z₁、o₂x₂y₂z₂Coordinate close System (as shown in Figure 2)：

(1) the quiet coordinate system OXYZ on the screw pump pump housing is fixedly arranged at；

(2) the moving coordinate system o in driving screw rod is fixedly arranged at₁x₁y₁z₁；

(3) the moving coordinate system o on driven screw is fixedly arranged at₂x₂y₂z₂；

1. M points are overlapped through coordinate translation conversion with O points, its transformation matrix of coordinates is P；

The coordinate that can be tried to achieve is：

2. MN after translation is projected to the anglec of rotation α that it is obtained in OXY planes around X-axis, and Then around the rotation transformation square R of X-axis_XFor：

3.-β angles will be rotated around Y-axis around the postrotational MN of X-axis, and will cause moving coordinate system o₁x₁y₁z₁With quiet coordinate system OXYZ It is completely superposed.Wherein

Then around the rotational transformation matrix R of Y-axis_YFor：

The step of summary three, obtains the moving coordinate system o in driving screw rod₁x₁y₁z₁On any point sitting quietly on the pump housing The coordinate of mark system OXYZ；Similarly can obtain the moving coordinate system o on driven screw₂x₂y₂z₂On any point sitting quietly on the pump housing The coordinate of mark system OXYZ.

[X Y Z 1]=[x₁ y₁ z₁ 1]·R₁

B. the contact line of the driving screw rod and driven screw helicoid is solved；

When setting up face line equation, first have to set up the curvilinear equation of screw rod contrate tooth profile, and derive by end-tooth The helical tooth flank equation that shape is formed, then simultaneous mesh equation and screw spiral tooth surface equation, you can obtain given angle position When instantaneous face line equation.

(1) known active, the parametric equation of a certain group of tooth curve of driven screw rotor end-face molded line are respectively：

Then driving screw rod left-turn spiral face equation is：

Driven screw right hand helix face equation is：

In formula, τ is parameter, represents the angle that bus is turned over about the z axis from original position.Looked along Z axis, with side clockwise It is just to rotating.P=S/2 π, S are screw rod helical pitch.

(2) screw spiral curved surface can represent with vector r [x (t, τ), y (t, τ), z (t, τ)], then any one on helicoid The normal vector of point is n；

(3), in order to try to achieve expression of the speed of related movement in driving screw rod coordinate system, the quiet coordinate system of driving screw rod is set up O₁X₁Y₁, the quiet coordinate system O of driven screw₂X₂Y₂, as shown in figure 3, all adding same angular speed-ω to two rotors₂, then two rotor Mutual movement relation it is constant, but now driven screw transfixion, driving screw rod makees compound motion, i.e., with-ω₂Around Z₂Axle Transport motion and with ω₁Around Z₁The relative motion of axle.

Obtained according to dynamics compound motion：

Such as make ω₁Size be a unit, i.e., | ω₁|=1rad/s, have no effect on the side of driven screw relative velocity v To.ThenIn quiet coordinate system O₁X₁Y₁In, the expression formula of each vector is respectively：

Make 1+i=k

Substitute into：

Obtaining expression formula of the relative velocity in driving screw rod moving coordinate system through coordinate transform is：

According to two meshing conditions of rotor,The meshing condition formula that driving screw rod can be obtained is：

The meshing condition formula of driven screw is similarly can obtain, it is one and contains three parametersOrIt is hidden Function expressionOrSuch as give oneOrValue, then can be solved some by meshing condition formula Group (t, τ), the tooth surface equation formula of rotor is substituted into these (t, τ), you can obtain hereinOrDuring position, one of two flank of tooth Contact line.

C. the driving screw rod is distributed with the inter-lobe clearance of driven screw under solving rigging error according to the contact line；

As shown in Figure 4, it is known that P₁For main screw rotor face line a bit,It is P₁The normal vector of point, normal vector prolongs Line long with intersect at P from screw tooth surface₂Point, can try to achieve P₁P₂Distance be inter-lobe clearance.

D. the minimum value according to the gap distribution and the minimum value of given gap band, judge driving screw rod and driven screw Whether interference is being produced in the presence of rigging error.

Quimby pump rotor space rigging position as shown in figure 5,1-4 be bearing position, due to manufacture, assembling During can produce axle center offset equal error, use δ_x、δ_y、δ_zTo represent (as shown in Figure 6).Can be by the coordinate at driving screw rod two ends It is expressed as Similarly the coordinate at driven screw two ends is By above-mentioned coordinate transformation method, the rotor curved surface in arbitrary load error can be unified in Studied under quiet coordinate system, further obtain and be distributed along the inter-lobe clearance of contact line based on master and slave screw rod under rigging error.And it is actual During gap band in practice is evolved into due to the presence of inter-lobe clearance, theoretic contact line, give the minimum of gap band Value d_min, when the minimum value of the gap distribution tried to achieve is less than given d_min, i.e., principal and subordinate's screw rod is in the product in the presence of rigging error Raw interference.

The beneficial effects of the invention are as follows：Quimby pump rotor interference detection method based on rigging error of the invention, energy It is enough that screw rotor locus and inter-lobe clearance changes in distribution are detected under the true operating condition of rigging error, so as to quantify spiral shell The leakage rate of bar pump, and the change of various position deviation lower rotor part inter-lobe clearance distributions is calculated, it is housing, rotor machining and axle Hold the work such as apolegamy and accurate quantizating index is provided.

Brief description of the drawings

The invention will be further described with reference to the accompanying drawings and examples：

Fig. 1 is the installation diagram schematic diagram of Quimby pump；

Fig. 2 is the coordinate transform schematic diagram of screw shaft in the present invention；

Fig. 3 is the schematic diagram of screw rotor helical tooth flank coordinate system relative motion in the present invention；

Fig. 4 is the face line normal distance schematic diagram of two screw rods rotor in the present invention；

Fig. 5 is screw axis locus schematic diagram in assembly of the present invention；

Fig. 6 is the skew schematic diagram of screw rod in assembly of the present invention；

Fig. 7 is the schematic diagram of mobile jib contrate tooth profile curve in the present embodiment；

Fig. 8 is the schematic diagram in the present embodiment from rod end surface tooth curve；

Fig. 9 is the schematic diagram of Quimby pump space contact line in the present embodiment；

Figure 10 is the clearance inspection schematic diagram in the present embodiment during simulation assembling ideally；

Driving and driven screw rod distance of shaft centers reduces δ when Figure 11 is assembled to be simulated in the present embodiment_yClearance inspection schematic diagram；

Master and slave screw axis spatial intersecting clearance inspection schematic diagram Figure 12 is to simulate assembling in the present embodiment when.

Specific embodiment

Calculating is analyzed with A type tooth forms in the present embodiment, it is known that A type screw rod contrate tooth profile curvilinear equations, by above institute Method simultaneous spiral camber equation and mesh equation are stated, face space of lines curve is obtained, and consider ideal situation, principal and subordinate's spiral shell Bar distance of shaft centers reduces, principal and subordinate's screw axis spatial intersecting (distance of shaft centers is constant) three kinds of assembling situations try to achieve inter-lobe clearance, wherein The gap length for setting ideally is 0.12mm, axle center skew δ_x、δ_y、δ_zValue is 0.02mm.Edge connects theoretical calculation respectively The inter-lobe clearance minimum value for touching line is 0.120mm, 0.091mm, 0.063mm.

The geometric parameter of the master and slave screw rod of Quimby pump

Known A types driven screw contrate tooth profile curve is made up of prolate epicycloid, involute, curtate epicycloid, wherein, gradually Involute curve equation is as follows：

Curtate epicycloid is as follows：

Prolate epicycloid curvilinear equation is as follows, as calculating point by taking the point on prolate epicycloid as an example：

Wherein, r_j1=42, r_j2=63,Φ₁=0.250, H₁=2/3；

It is then (17.3592,29.0663) by the coordinate of any on end face epicycloid can be obtained after above-mentioned Coordinate Conversion.

Expression formula of the relative velocity in driving screw moving coordinate system be：

Calculating is then made a concrete analysis of with the situation of principal and subordinate's screw rod distance of shaft centers reduction, through coordinate transform, it is considered to after rigging error Contact line on coordinate be (17.3592,29.0463,75.231), tried to achieve along between its normal vector by inter-lobe clearance calculating method Gap size is 0.091mm.

In order to prove the reliability of the method, certain assembling mistake is given during software Virtual assemble principal and subordinate's screw rod Difference, then carry out interference, clearance inspection (as shown in figs. 10-12) between principal and subordinate's screw rod, most required at last result with it is empty Intend interference, the clearance inspection Comparative result in assembling process, it was demonstrated that the need for the method computational accuracy disclosure satisfy that engineering design, The complete inter-lobe clearance distribution situation of the two screw rods flank of tooth under different rigging errors can be obtained, different inter-lobe clearances can be quantified and obtained The influence that the method for obtaining is distributed to inter-lobe clearance, so as to for the size that screw pump assembles theoretical gap provides certain foundation, enter one Step improves the service behaviour and reliability of screw pump.

Finally illustrate, the above embodiments are merely illustrative of the technical solutions of the present invention and it is unrestricted, although with reference to compared with Good embodiment has been described in detail to the present invention, it will be understood by those within the art that, can be to skill of the invention Art scheme is modified or equivalent, and without deviating from the objective and scope of technical solution of the present invention, it all should cover at this In the middle of the right of invention.

Claims (4)

1. a kind of Quimby pump rotor interference detection method based on rigging error, it is characterised in that comprise the following steps：

A. by coordinate transform will produce rigging error driving screw rod and driven screw rotor curved surface respectively from moving coordinate system o₁x₁y₁z₁With moving coordinate system o₂x₂y₂z₂It is converted into the quiet coordinate system OXYZ being consolidated on the pump housing；

B. the contact line of the driving screw rod and driven screw helicoid is solved；

C. the driving screw rod is distributed with the inter-lobe clearance of driven screw under solving rigging error according to the contact line；

D. the minimum value according to the gap distribution and the minimum value of given gap band, judge driving screw rod and driven screw in dress With whether producing interference in the presence of error.

2. the Quimby pump rotor interference detection method based on rigging error according to claim 1, it is characterised in that step Include in rapid b, the step of solve the contact line:

B1. the contrate tooth profile curvilinear equation of the driving screw rod and driven screw is set up；

B2. the helical tooth flank equation of driving screw rod and driven screw is formed according to the contrate tooth profile curvilinear equation；

B3. simultaneous mesh equation and the helical tooth flank equation, obtain instantaneous face line equation during given angle position.

3. the Quimby pump rotor interference detection method based on rigging error according to claim 1, it is characterised in that step Include in rapid c, the step of solve the inter-lobe clearance：

C1. a point P is chosen in the contact line of the driving screw rod rotor flank of tooth₁；

C2. by P₁The normal vector of pointExtend to and intersect at P with the driven screw flank of tooth₂Point, P₁P₂Distance be the between cog between Gap.

4. the Quimby pump rotor interference detection method based on rigging error according to claim 1, it is characterised in that step In rapid a, the transformation matrix R of the coordinate transform is：

$R={\mathrm{PR}}_X{R}_Y=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ M_X& M_Y& M_Z& 1\end{array}\right]\·\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& \cos \mathrm{\α}& sin\mathrm{\α}& 0\\ 0& -\sin \mathrm{\α}& \cos \mathrm{\α}& 0\\ 0& 0& 0& 1\end{array}\right]\·\left[\begin{array}{cccc}cos\mathrm{\β}& 0& -sin\mathrm{\β}& 0\\ 0& 1& 0& 0\\ sin\mathrm{\β}& 0& \cos \mathrm{\β}& 0\\ 0& 0& 0& 1\end{array}\right]$

Wherein, MN is the screw shaft that driving screw rod or driven screw are located in quiet coordinate system.