CN103577636A - Unified discretization method for blade curved surfaces based on curvature characteristics - Google Patents

Abstract

The invention discloses a unified discretization method for blade curved surfaces based on curvature characteristics. The unified discretization method comprises the following steps: firstly, selecting a section line r, and determining central points B1 and B2 of an arc section; secondly, working out longitudinal curvature lines L2 and L6 from the points B1 and B2; thirdly, finding four points V1, V2, V3 and V4 from the two sides of the points B1 and B2; fourthly, working out longitudinal curvature lines L1, L3, L5 and L7 passing through the four points at the two ends of a blade; fifthly, taking the longitudinal curvature lines L1, L2 and L3 as isoparametric lines, parameterizing a region between the longitudinal curvature lines L1 and L3, and determining boundary lines l1 and l3; taking the longitudinal curvature lines L5, L6 and L7 as isoparametric lines, parameterizing a region between the longitudinal curvature lines L5 and L7, and determining boundary lines l5 and l7; sixthly, respectively determining arc central points M1 and M2 on the section line r; seventhly, determining longitudinal curvature lines L4 and L8 passing through the arc central points M1 and M2; eighthly, taking the longitudinal curvature lines L2, L4, L6 and L8 and the boundary lines l1, l3, l5 and l7 as isoparametric lines of a new parameter region, and re-parameterizing; ninthly, carrying out non-uniform discretization on curved surfaces according to new parameters.

Description

A kind of spoon of blade based on curvature feature is unified discrete method

Technical field

The invention provides a kind of spoon of blade based on curvature feature and unify discrete method, it is a kind of discrete method of the curve surface of workpiece of drawing for cutter track gauge for wide row digital control processing, it relates to the choosing method of discrete cutter location in a kind of wide row digital control processing, belongs to Surface NC Machining technical field.

Background technology

Etc. parameter collimation method, be one of cutter rail planing method conventional in digital control processing, the method is mainly to allow cutter move along a parametric direction of curve surface of workpiece.Etc. parameter collimation method, depend on the parametrization of curved surface.

In conventional CAM system, what surface modeling generally adopted is arc length parameterized, and this kind of parametric method do not considered the crooked situation of curved surface, therefore may produce the situation of parameter line distortion or fluctuation, is unfavorable for actual processing.And parametric method based on mesh of curvature curves can be good at taking into account the local bending feature of curved surface, but when reality complex-curved, the local sculpt error of curved surface can have influence on the overall tendency of the line of curvature, thereby is difficult to obtain believable line of curvature grid.

In the wide row machining prgraming system of reality, generally first to curve surface of workpiece, carry out discrete.In traditional curved surface discrete method, evenly discrete method is directly to choose even parametric grid, and non-uniform discrete method is mainly the density that the local feature (as arc angle changes) by curved surface is adjusted discrete grid block.Above-mentioned traditional curved surface discrete method all carries out discrete based on the existing parameter of curved surface, do not solve the problem of bringing of Surface Parameters line distortion.

The parameter line distortion of general spoon of blade generally occurs near intake and exhaust limit, and intake and exhaust limit near arc transition center position line of curvature tendency because of two principal curvatures gap greatly generally more stable, be subject to the error effect of surface modeling less, and the line of curvature at this place generally can not be distorted and cross the situation of leaf basin blade back, there is the feature of leaf basin blade back " separatrix ".Present patent application has been considered the situation of Surface Parameters line distortion, in conjunction with the above-mentioned feature of spoon of blade, proposes a kind of Reparameterization method based on limited the line of curvature.And be given on the basis of Reparameterization curved surface is carried out to discrete process.

Summary of the invention

1, object: the object of this invention is to provide a kind of spoon of blade based on curvature feature and unify discrete method, in order to solve near the cutter rail fluctuation problem that parameter line distortion causes blade intake and exhaust limit.

2, technical scheme: the present invention is mainly achieved through the following technical solutions.

A kind of spoon of blade based on curvature feature of the present invention is unified discrete method, and it comprises the following steps:

Step 1 is selected a representational section line r, determines the central point B of intake and exhaust limit arc section on it ₁, B ₂position.Detailed process is as follows:

A certain of selected blade is waited parameter line S (u, v ₀) as one section of molded line (as being labeled with in Fig. 2 as shown in section molded line a little) of blade, calculate the curvature distribution of this section of molded line

$k\left(u\right)=\frac{L(u,v_0)}{E(u,v_0)},$

L (u, v wherein ₀)=S _uu(u, v ₀) n (u, v ₀), E (u, v ₀)=S _u(u, v ₀) S _u(u, v ₀), n (u, v ₀) be that curved surface is at point (u, v ₀) per unit system located vows.As shown in Figure 4, function k (u), along with the meeting from small to large of u is by two sudden changes, might as well establish

given threshold value coefficient F, definition is as k (u)>=F * k ₀time, u is within sudden change position.Record respectively the reference position U of first sudden change _1swith final position U _1e, the reference position U of second sudden change _2swith final position U _2e.Definition computing

$\mathrm{std}\left(a\right)=\left\{\begin{array}{c}a+1,a<0;\\ a-1,a>1;\\ a,0\&le;a\&le;1.\end{array}\right.$

$\mathrm{Add}(a,b)=\left\{\begin{array}{c}a+b,a\&le;b;\\ a+b+1,a>b.\end{array}.\right.$

Order

${\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2=\mathrm{std}\left(\frac{\mathrm{Add}(U_{1s},U_{1e})}{2}\right),$

$U_6=\mathrm{std}\left(\frac{\mathrm{Add}(U_{2s},U_{2e})}{2}\right).$

U ₂and U ₆be the center of arc transition.

If do not add explanation in present patent application, have v ₀=0; Std (a) computing has guaranteed that result drops in the field of definition of parameter; Add (a, b) is the situation of considering leap parameter field border, Sudden change region; k ₀in fact represent to cut the mean curvature of molded line; General corresponding the crook of cutting molded line, the center of arc transition; U ₂and U ₆determine also can cut molded line by choosing many, blade, by above-mentioned steps, calculate respectively, then average and obtain; U ₂and U ₆determined the some B in Fig. 3 ₁, B ₂.

Step 2 is from B ₁, B ₂point out and be sent to blade two ends and obtain through a B ₁, B ₂two longitudinal curvature line L ₂, L ₆.Detailed process is as follows:

Make u _2,1=U ₂, u _6,1=U ₆, v ₁=0.

If oneself knows i point on the line of curvature, the parameter value of any under first definite second line of curvature.Calculate spoon of blade at point (u _{2, i}, v _i) locate the principal direction D close with V direction _{2, i}, lower some P2 _{, i+1}=S (u _{2, i}, v _i)+step * D _{2, i}, wherein step is given step-length, its size affects the discrete precision of V direction.Calculation level P again _{2, i+1}parameter value (the u of correspondence on curved surface _{2, i+1}, v _i+1).When vi+1 >=1, above-mentioned steps stops.

For j=6, determine that spoon of blade is at point (u _{j, i}, v _i) locate the principal direction d close with V direction _{j, i},

$u_{j,i+1}=u_{j,i}+(v_{i+1}-v_i)\&times;\frac{\left|S_u(u_{j,i},v_i)\right|}{\left|S_v(u_{j,i},v_i)\right|}\&times;d_{j,i},$

Thereby the parameter value of i+1 point of the j bar line of curvature is (u _{j, i+1}, v _i+1).

For i=2,6, note U _ithe corresponding line of curvature is L _i.

Illustrate: the line of curvature is to represent by a series of discrete points to fixed step size; Also can choose other lines of curvature and determine v _i+1value; Computation process has guaranteed that two lines of curvature are consistent at the V parameter value of i point; Principal direction D _{2, i}for the vector in three dimensions, and d _{j, i}it is the ratio value representation of a direction on curved surface.

Step 3 is representing on section line r, from B ₁, B ₂2 are set out, and find 4 specified point V respectively within the scope of this intake and exhaust limit, both sides circular arc ₁, V ₂, V ₃, V ₄.

Given distance value dis ₁, dis ₂, calculate U ₁, U ₃, U ₅, U ₇, make

${\mathrm{dis}}_1=\left\{\begin{array}{c}{\&Integral;}_{U_1}^{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}\&GreaterEqual;{\mathrm{dis}}_1;\\ {\&Integral;}_{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA0000399835250000012.png"\; state="\{\{state\}\}">U</figure-callout>}}_1}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}+{\&Integral;}_0^{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}<{\mathrm{<figure-callout\; id="1"\; label="dis"\; filenames="HDA0000399835250000012.png"\; state="\{\{state\}\}">dis</figure-callout>}}_1\end{array}\right.$

${\mathrm{dis}}_1=\left\{\begin{array}{c}{\&Integral;}_{U_2}^{{\mathrm{<figure-callout\; id="5"\; label="U"\; filenames="HDA0000399835250000031.png"\; state="\{\{state\}\}">U</figure-callout>}}_5}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}^0\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}\&GreaterEqual;{\mathrm{dis}}_1;\\ {\&Integral;}_{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}+{\&Integral;}_0^{{\mathrm{<figure-callout\; id="5"\; label="U"\; filenames="HDA0000399835250000031.png"\; state="\{\{state\}\}">U</figure-callout>}}_5}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}<{\mathrm{<figure-callout\; id="1"\; label="dis"\; filenames="HDA0000399835250000012.png"\; state="\{\{state\}\}">dis</figure-callout>}}_1\end{array}\right.$

${\mathrm{dis}}_2=\left\{\begin{array}{c}{\&Integral;}_{U_5}^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}\&GreaterEqual;{\mathrm{dis}}_2;\\ {\&Integral;}_{{\mathrm{<figure-callout\; id="5"\; label="U"\; filenames="HDA0000399835250000031.png"\; state="\{\{state\}\}">U</figure-callout>}}_5}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}+{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}<{\mathrm{<figure-callout\; id="2"\; label="dis"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">dis</figure-callout>}}_2\end{array}\right.$

${\mathrm{dis}}_2=\left\{\begin{array}{c}{\&Integral;}_{U_6}^{U_7}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}\&GreaterEqual;{\mathrm{dis}}_2;\\ {\&Integral;}_{U_6}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}+{\&Integral;}_0^{U_7}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}<{\mathrm{<figure-callout\; id="2"\; label="dis"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">dis</figure-callout>}}_2\end{array}\right.$

U ₁, U ₃, U ₅, U ₇be V on required circular arc ₁, V ₂, V ₃, V ₄position.

When solving integration, there is U ₁, U ₃, U ₄, U ₆with the U in step 1 _1s, U _1e, U _2s, U _2emeaning is different.Actual spoon of blade generally can be more disorderly in the curvature tendency of arc transition edge, so need to pass through parameter d is ₁, dis ₂adjust U ₁, U ₃, U ₄, U ₆value, make through point (U ₁, v ₀), (U ₃, v ₀), (U ₄, v ₀), (U ₆, v ₀) four lines of curvature consistent with blade shape construction direction locating stablize credible.

Step 4 is from V ₁, V ₂, V ₃, V ₄set out and obtain and pass through respectively V to blade two ends ₁, V ₂, V ₃, V ₄four longitudinal curvature line L ₁, L ₃, L ₅, L ₇.

u _1，1＝U ₁，u _3，1＝U ₃，u _5，1＝U ₅，u _7，1＝U ₇。

Oneself knows i point on the line of curvature, for j=1, and 3,5,7, determine that spoon of blade is at point (u _{j, i}, v _i) locate the principal direction d close with V direction _{j, i},

$u_{j,i+1}=u_{j,i}+(v_{i+1}-v_i)\&times;\frac{\left|S_u(u_{j,i},v_i)\right|}{\left|S_v(u_{j,i},v_i)\right|}\&times;d_{j,i},$

Thereby the parameter value of i+1 point of the j bar line of curvature is (u _{j, i+1}, v _i+1).

For i=1,3,5,7, note U _ithe corresponding line of curvature is L _i.

Step 5 is L ₁, L ₂, L ₃as waiting parameter line, to L ₁, L ₃reparameterization is carried out in middle region, determines the parameter field boundary line l after Reparameterization ₁, l ₃; L ₅, L ₆, L ₇as waiting parameter line, to L ₅, L ₇reparameterization is carried out in middle region, determines the parameter field boundary line l after Reparameterization ₅, l ₇.

If the average transition arc arc length on blade intake and exhaust limit is ArcL,

Definition

$m(a.b)=\left\{\begin{array}{c}a-b-1,a>b;\\ a-b,a\&le;b.\end{array}\right.;$

$M(a,b)=\left\{\begin{array}{c}a-b+1,c<b;\\ a-b,a\&GreaterEqual;b.\end{array}\right..$

Order

$u_{1,i}=\mathrm{std}(\frac{\mathrm{ArcL}\&times;m(u_{1,i},u_{2,i})}{2{\mathrm{<figure-callout\; id="1"\; label="dis"\; filenames="HDA0000399835250000012.png"\; state="\{\{state\}\}">dis</figure-callout>}}_1}+u_{2,i});$

$u_{3,i}=\mathrm{std}(\frac{\mathrm{ArcL}\&times;M(u_{3,i},u_{2,i})}{2{\mathrm{<figure-callout\; id="1"\; label="dis"\; filenames="HDA0000399835250000012.png"\; state="\{\{state\}\}">dis</figure-callout>}}_1}+u_{2,i});$

$u_{5,i}=\mathrm{std}(\frac{\mathrm{ArcL}\&times;m(u_{5,i},u_{6,i})}{{2\mathrm{<figure-callout\; id="2"\; label="dis"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">dis</figure-callout>}}_2}+u_{6,i});$

$u_{7,i}=\mathrm{std}(\frac{\mathrm{ArcL}\&times;M(u_{7,i},u_{6,i})}{{2\mathrm{<figure-callout\; id="2"\; label="dis"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">dis</figure-callout>}}_2}+u_{6,i});$

Thereby L ₁, L ₃, L ₅, L ₇toward moving to new parameter field border away from intake and exhaust edge direction (as shown in the arrow in Fig. 6).The curve obtaining after note translation is respectively l ₁, l ₃, l ₅, l ₇.

Error due to moulding, actual spoon of blade plays the line of curvature tendency of stub area at intake and exhaust limit transition arc can be more disorderly, generally can not pass through the line of curvature in this region by direct solution, step 4 is that the line of curvature in this outside, region is moved by distance proportion, thereby obtains the approximate line of curvature through this region; l ₁, l ₃, l ₅, l ₇by the some P in Fig. 3 ₁, P ₂, P ₃, P ₄.

Step 6 is determined respectively the central point M of the upper leaf basin blade back circular arc of section line r ₁, M ₂.

Order $U_{}$ ${}_4=\mathrm{std}\left(\frac{\mathrm{Add}(U_6,U_5)}{2}\right),{\mathrm{<figure-callout\; id="8"\; label="U"\; filenames="HDA0000399835250000031.png"\; state="\{\{state\}\}">U</figure-callout>}}_8=\mathrm{std}\left(\frac{\mathrm{Add}(U_7,U_1)}{2}\right).$

U ₄, U ₈recorded some M ₁, M ₂position.

Step 7 is determined through M ₁, M ₂two longitudinal curvature lines or etc. parameter line L ₄, L ₈.

L ₄, L ₈the line of curvature if, solution procedure is as follows:

Oneself knows i point on the line of curvature, for j=4, and 8, determine that spoon of blade is at point (u _{j, i}, v _i) locate the principal direction d close with V direction _{j, i},

$u_{j,i+1}=u_{j,i}+(v_{i+1}-v_i)\&times;\frac{\left|S_u(u_{j,i},v_i)\right|}{\left|S_v(u_{j,i},v_i)\right|}\&times;d_{j,i},$

Thereby the parameter value of i+1 point of the j bar line of curvature is (u _{j, i+1}, v _i+1).

For i=4,8, note U _ithe corresponding line of curvature is L _i.

If L ₄, L ₈for waiting parameter line, for j=4,8, u _{j, i+1}=U _j.

Step 8 is with L ₂, L ₄, L ₆, L ₈and l ₁, l ₃, l ₅, l ₇the parameter line that waits under new argument territory, carries out Reparameterization to curved surface.

If the curved surface expression formula after Reparameterization is S ' (u ', v ').

Regard eight lines as the new U ' parameter line that waits, first determine the U ' coordinate u ' of j bar line correspondence under new argument _j.Make u ' ₁=0,

u′ _j＝u′ _j-1+M(U _j，U _j-1)，j＝2，…，8.

Note u ' ₉=1.

Given U ' V ' coordinate (u ', v _i), its corresponding UV coordinate is

$(\mathrm{std}(\frac{(u^{\&prime;}-{u^{\&prime;}}_j)M(u_{j+1,i},u_{j,i})}{{u^{\&prime;}}_{j+1}-{u^{\&prime;}}_j}+u_{j,i}),v_i),$

Wherein j meets u ' _j≤ u '≤u ' _j+1.

Article eight, line L ₂, L ₄, L ₆, L ₈and l ₁, l ₃, l ₅, l ₇be actually and approach eight lines consistent with V direction on Fig. 2 Leaf curved surface, these eight lines of curvature have been cut apart eight regions relatively stably according to the bending features of curved surface spoon of blade, thereby can guarantee that the parameter line in every region all there will not be excessive distortion.

Step 9 is carried out non-uniform discrete according to new argument to curved surface.

The discrete of V ' direction determined by step 2, therefore only the discrete of U ' direction need be discussed.The discrete bow height of given U ' direction is GgU, and maximum discrete interval is Offset, and note the discrete of V ' direction counted as vnum.If current U ' parameter position is U ' _i, for 1≤j≤vnum, calculation level (U ' _i, v _j) parameter under UV coordinate, thereby determine the curvature uQL along U ' direction at this some place _ij.Order $r_{i,j}=\frac{1}{\left|\mathrm{uQ}{L}_{i,j}\right|},$

${\mathrm{OS}}_{i,j}=\frac{2\&times;\sqrt{r_{i,j}^2-{(r_{i,j}-\mathrm{GgU})}^2+\mathrm{<figure-callout\; id="2"\; label="Gg\; U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">Gg</figure-callout>}{U}^{}{}^2}\&CenterDot;}{{\mathrm{uLen}}_j}$

ULen wherein _jrepresent the curve V=v on curved surface _jarc length.

Make offset _i=min{min _joS _{i, j}, Offset}, next discrete location is U ' _i+1=U ' _i+ offset _i.

Illustrate: maximum discrete interval Offset has limited discrete maximum step-length, to prevent the occurring situation that step-length is excessive when the more flat regions such as discrete blade back leaf basin; The high meaning of discrete bow as shown in Figure 5; The divergent density of U direction is subject to the impact of curved surface local curvature, therefore be non-uniform discrete; The discrete step-length in three dimensions of V direction is determined, can be similar to and think for evenly discrete.

Blade cut molded line generally by leaf pelvic part divide, blade back part and transition arc small in ends form.Wherein the center of spoon of blade moulding arc transition is the mid point of little transition arc.As shown in Figure 1.

Wherein longitudinally refer to blade shape construction direction, refer to that blade cuts the parametric direction of the arrangement of molded line, is generally V direction.As shown in Figure 2.

3, advantage and effect:

The invention provides a kind of spoon of blade based on curvature feature and unify discrete method, the method has been considered the modelling feature of blade, take eight curves as benchmark is to being divided into spoon of blade in the smooth region consistent with line of curvature tendency, eight borders, respectively Reparameterization is carried out in each region again, the border that makes each region is the parameter line that waits under new argument territory, solved near blade serious situation of parameter line distortion intake and exhaust limit, thereby the cutter rail fairing that realizes blade intake and exhaust processing is stable, reduced on the one hand the requirement of blade processing to lathe acceleration and lathe interlock, improved on the other hand the surface quality of blade intake and exhaust limit processing.In addition, the present invention adopts discrete method heterogeneous in the more crooked direction of blade, on the basis that guarantees discrete precision, has greatly saved storage space, has reduced calculated amount.The present invention simultaneously has advantages of that compatibility is strong, it is low to realize cost.

Accompanying drawing explanation

Fig. 1: blade cuts molded line and forms schematic diagram.Can find out, blade cut molded line generally by leaf pelvic part divide, blade back part and transition arc small in ends form.

Fig. 2: blade structure direction explanation.Spoon of blade is generally that the molded line that cuts arranging by several generates, and claims that cutting with blade the parametric direction that the direction of arrangement of molded line is consistent is blade shape construction direction, longitudinal also referred to as blade.For simplicity, in present patent application instructions, it is generally acknowledged that blade shape construction direction is V direction.

Fig. 3: blade cuts molded line subregion point schematic diagram.Point P ₁, P ₂, P ₃, P ₄, M ₁, M ₂, B ₁, B ₂cutting a molded line, be divided into eight sections, these eight sections cut molded line naturally correspondence eight spoon of blade regions.Its mid point P ₁, P ₂, P ₃, P ₄a section molded line has been divided into curvature and has changed uniform four sections, the spoon of blade intra-zone curvature that these four sections of lines are corresponding changes comparatively even, and the parameter line character after Reparameterization has been played to Main Function.

Fig. 4: blade cuts the curvature distribution schematic diagram of molded line.Blade cuts molded line curvature function two obvious peak values, and corresponding blade cuts the position of two transition arcs of molded line respectively.

Fig. 5: the high schematic diagram of discrete bow.If current point is P ₁, can, using 2L as discrete steps, obtain the coordinate of next discrete point.Because meet the requirement that discrete bow is high, now P ₁the discrete steps at some place can not be greater than 2L.

Fig. 6: the subregion schematic diagram of spoon of blade under new parameter field.Can find out line of curvature L ₂, L ₄, L ₆, L ₈with approximate line of curvature l ₁, l ₃, l ₅, l ₇for the parameter line that waits under new argument territory, and these eight waited parameter line naturally blade to be divided into eight regions.

Fig. 7: the unified discrete flow process of spoon of blade.

Code name in figure, symbol description are as follows:

M ₁, M ₂the mid point in corresponding leaf basin blade back region on-section molded line.

B ₁, B ₂the mid point of intake and exhaust limit transition arc on-section molded line

V ₁, V ₂, V ₃, V ₄-cutting on molded line, from B ₁set out, in specified scope, determine some V ₁, V ₂; From B ₂set out, in specified scope, determine some V ₃, V ₄.

P ₁, P ₂, P ₃, P ₄-cutting on molded line V ₁, V ₂, V ₃, V ₄according to specified rule translation, obtain a P ₁, P ₂, P ₃, P ₄.

U ₂, U ₆-corresponding point B ₁, B ₂u direction parameter value.

U ₁, U ₃, U ₅, U ₇-corresponding point V ₁, V ₂, V ₃, V ₄u direction parameter value.

U ₄, U ₈-corresponding point M ₁, M ₂u direction parameter value.

P _ion-curved surface, certain is a bit.

R _ij-P _ipoint place is along the r of discrete direction _ijcurvature.

GgU-is discrete, and bow is high.

L-P _ihalf of point discrete steps.

L ₁, L ₂, L ₃, L ₄, L ₅, L ₆, L ₇, L ₈a process point V on the corresponding curved surface of-difference ₁, B ₁, V ₂, M ₁, V ₃, B ₂, V ₄, M ₂the line of curvature.

L ₁, l ₃, l ₅, l ₇process curve L on the corresponding curved surface of-difference ₁, L ₃, L ₅, L ₇a process point P who obtains after moving with ad hoc rules ₁, P ₂, P ₃, P ₄curve.

Embodiment

The present invention proposes a kind of spoon of blade based on curvature feature and unifies discrete method.Blade cut molded line generally by leaf pelvic part divide, blade back part and transition arc small in ends form.Wherein the center of spoon of blade moulding arc transition is the mid point of little transition arc.As shown in Figure 1.Flow process of the present invention as shown in Figure 7.

Embodiment is as follows:

The moulding parametric direction that might as well establish blade is V direction, and the parametric equation of spoon of blade is S (u, v), 0≤u wherein, v≤1.

Step 1 is selected a representational section line r, determines the central point B of intake and exhaust limit arc section on it ₁, B ₂position.Detailed process is as follows:

A certain of selected blade is waited parameter line S (u, v ₀) as one section of molded line (as being labeled with in Fig. 2 as shown in section molded line a little) of blade, calculate the curvature distribution of this section of molded line

$k\left(u\right)=\frac{L(u,v_0)}{E(u,v_0)},$

L (u, v wherein ₀)=S _uu(u, v ₀) n (u, v ₀), E (u, v ₀)=S _u(u, v ₀) S _u(u, v ₀), n (u, v ₀) be that curved surface is at point (u, v ₀) per unit system located vows.As shown in Figure 4, function k (u), along with the meeting from small to large of u is by two sudden changes, might as well establish

given threshold value coefficient F, definition is as k (u)>=F * k ₀time, u is within sudden change position.Record respectively the reference position U of first sudden change _1swith final position U _1e, the reference position U of second sudden change _2swith final position U _2e.Definition computing

$\mathrm{std}\left(a\right)=\left\{\begin{array}{c}a+1,a<0;\\ a-1,a>1;\\ a,0\&le;a\&le;1.\end{array}\right.$

$\mathrm{Add}(a,b)=\left\{\begin{array}{c}a+b,a\&le;b;\\ a+b+1,a>b.\end{array}.\right.$

Order

${\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2=\mathrm{std}\left(\frac{\mathrm{Add}(U_{1s},U_{1e})}{2}\right),$

$U_6=\mathrm{std}\left(\frac{\mathrm{Add}(U_{2s},U_{2e})}{2}\right).$

U ₂and U ₆be the center of arc transition.

Illustrate: for convenience of explanation, if do not add explanation in present patent application, have v ₀=0; Std (a) computing has guaranteed that result drops in the field of definition of parameter; Add (a, b) is the situation of considering leap parameter field border, Sudden change region; k ₀in fact represent to cut the mean curvature of molded line; General corresponding the crook of cutting molded line, the center of arc transition; U ₂and U ₆determine also can cut molded line by choosing many, blade, by above-mentioned steps, calculate respectively, then average and obtain; U ₂and U ₆determined the some B in Fig. 3 ₁, B ₂.

Step 2 is from B ₁, B ₂point out and be sent to blade two ends and obtain through a B ₁, B ₂two longitudinal curvature line L ₂, L ₆.

Detailed process is as follows:

Make u _2,1=U ₂, u _6,1=U ₆, v ₁=0.

If oneself knows i point on the line of curvature, the parameter value of any under first definite second line of curvature.Calculate spoon of blade at point (u _{2, i}, v _i) locate the principal direction D close with V direction _{2, i,}lower some P _{2, i+1}=S (u _{2, i}, v _i)+step * D _{2, i}, wherein step is given step-length, its size affects the discrete precision of V direction.Calculation level P again _{2, i+1}parameter value (the u of correspondence on curved surface _{2, i+1}, v _i+1).Work as v _i+1>=1 o'clock, above-mentioned steps stopped.

For j=6, determine that spoon of blade is at point (u _{j, i}, v _i) locate the principal direction d close with V direction _{j, i},

$u_{j,i+1}=u_{j,i}+(v_{i+1}-v_i)\&times;\frac{\left|S_u(u_{j,i},v_i)\right|}{\left|S_v(u_{j,i},v_i)\right|}\&times;d_{j,i},$

Thereby the parameter value of i+1 point of the j bar line of curvature is (u _{j, i+1}, v _i+1).

For i=2,6, note U _ithe corresponding line of curvature is L _i.

Illustrate: the line of curvature is to represent by a series of discrete points to fixed step size; Also can choose other lines of curvature and determine v _i+1value; Computation process has guaranteed that two lines of curvature are consistent at the V parameter value of i point; Principal direction D _{2, i}for the vector in three dimensions, and d _{j, i}it is the ratio value representation of a direction on curved surface.

Step 3 is representing on section line r, from B ₁, B ₂2 are set out, and find 4 specified point V respectively within the scope of this intake and exhaust limit, both sides circular arc ₁, V ₂, V ₃, V ₄.

Given distance value dis ₁, dis ₂, calculate U ₁, U ₃, U ₅, U ₇, make

${\mathrm{dis}}_1=\left\{\begin{array}{c}{\&Integral;}_{U_1}^{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}\&GreaterEqual;{\mathrm{dis}}_1;\\ {\&Integral;}_{{\mathrm{<figure-callout\; id="1"\; label="U"\; filenames="HDA0000399835250000012.png"\; state="\{\{state\}\}">U</figure-callout>}}_1}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}+{\&Integral;}_0^{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}<{\mathrm{dis}}_1\end{array}\right.$

${\mathrm{dis}}_1=\left\{\begin{array}{c}{\&Integral;}_{U_2}^{{\mathrm{<figure-callout\; id="5"\; label="U"\; filenames="HDA0000399835250000031.png"\; state="\{\{state\}\}">U</figure-callout>}}_5}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}^0\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}\&GreaterEqual;{\mathrm{dis}}_1;\\ {\&Integral;}_{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}+{\&Integral;}_0^{{\mathrm{<figure-callout\; id="5"\; label="U"\; filenames="HDA0000399835250000031.png"\; state="\{\{state\}\}">U</figure-callout>}}_5}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">U</figure-callout>}}_2}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}<{\mathrm{dis}}_1\end{array}\right.$

${\mathrm{dis}}_2=\left\{\begin{array}{c}{\&Integral;}_{U_5}^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}\&GreaterEqual;{\mathrm{dis}}_2;\\ {\&Integral;}_{{\mathrm{<figure-callout\; id="5"\; label="U"\; filenames="HDA0000399835250000031.png"\; state="\{\{state\}\}">U</figure-callout>}}_5}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}+{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}<{\mathrm{dis}}_2\end{array}\right.$

${\mathrm{dis}}_2=\left\{\begin{array}{c}{\&Integral;}_{U_6}^{U_7}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}\&GreaterEqual;{\mathrm{dis}}_2;\\ {\&Integral;}_{U_6}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}+{\&Integral;}_0^{U_7}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}<{\mathrm{dis}}_2\end{array}\right.$

U ₁, U ₃, U ₅, U ₇be V on required circular arc ₁, V ₂, V ₃, V ₄position.

Illustrate: when solving integration, occur U ₁, U ₃, U ₄, U ₆with the U in step 1 _1s, U _1e, U _2s, U _2emeaning is different.Actual spoon of blade generally can be more disorderly in the curvature tendency of arc transition edge, so need to pass through parameter d is ₁, dis ₂adjust U ₁, U ₃, U ₄, U ₆value, make through point (U ₁, v ₀), (U ₃, v ₀), (U ₄, v ₀), (U6 _,v ₀) four lines of curvature consistent with blade shape construction direction locating stablize credible.

Step 4 is from V ₁, V ₂, V ₃, V ₄set out and obtain and pass through respectively V to blade two ends ₁, V ₂, V ₃, V ₄four longitudinal curvature line L ₁, L ₃, L ₅, L ₇.

u _1，1＝U ₁，u _3，1＝U ₃，u _5，1＝U ₅，u _7，1＝U ₇。

Oneself knows i point on the line of curvature, for j=1, and 3,5,7, determine that spoon of blade is at point (u _{j, i}, v _i) locate the principal direction d close with V direction _{j, i},

$u_{j,i+1}=u_{j,i}+(v_{i+1}-v_i)\&times;\frac{\left|S_u(u_{j,i},v_i)\right|}{\left|S_v(u_{j,i},v_i)\right|}\&times;d_{j,i},$

Thereby the parameter value of i+1 point of the j bar line of curvature is (u _{j, i+1}, v _i+1).

For i=1,3,5,7, note U _ithe corresponding line of curvature is L _i.

Step 5 is L ₁, L ₂, L ₃as waiting parameter line, to L ₁, L ₃reparameterization is carried out in middle region, determines the parameter field boundary line l after Reparameterization ₁, l ₃; L ₅, L ₆, L ₇as waiting parameter line, to L ₅, L ₇reparameterization is carried out in middle region, determines the parameter field boundary line l after Reparameterization ₅, l ₇.

If the average transition arc arc length on blade intake and exhaust limit is ArcL,

Definition

$m(a.b)=\left\{\begin{array}{c}a-b-1,a>b;\\ a-b,a\&le;b.\end{array}\right.;$

$M(a,b)=\left\{\begin{array}{c}a-\mathrm{<figure-callout\; id="1"\; label="b\; +"\; filenames="HDA0000399835250000012.png"\; state="\{\{state\}\}">b</figure-callout>}+1,c<b;\\ a-b,a\&GreaterEqual;b.\end{array}\right..$

Order

${\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000399835250000012.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1,i}=\mathrm{std}(\frac{\mathrm{ArcL}\&times;m({\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000399835250000012.png"\; state="\{\{state\}\}">u</figure-callout>}}_{1,i},{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">u</figure-callout>}}_{2,i})}{2{\mathrm{<figure-callout\; id="1"\; label="dis"\; filenames="HDA0000399835250000012.png"\; state="\{\{state\}\}">dis</figure-callout>}}_1}+{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">u</figure-callout>}}_{2,i});$

${\mathrm{<figure-callout\; id="3"\; label="u"\; filenames="HDA0000399835250000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_{3,i}=\mathrm{std}(\frac{\mathrm{ArcL}\&times;M({\mathrm{<figure-callout\; id="3"\; label="u"\; filenames="HDA0000399835250000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_{3,i},{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">u</figure-callout>}}_{2,i})}{2{\mathrm{<figure-callout\; id="1"\; label="dis"\; filenames="HDA0000399835250000012.png"\; state="\{\{state\}\}">dis</figure-callout>}}_1}+{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">u</figure-callout>}}_{2,i});$

${\mathrm{<figure-callout\; id="5"\; label="u"\; filenames="HDA0000399835250000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_{5,i}=\mathrm{std}(\frac{\mathrm{ArcL}\&times;m({\mathrm{<figure-callout\; id="5"\; label="u"\; filenames="HDA0000399835250000031.png"\; state="\{\{state\}\}">u</figure-callout>}}_{5,i},u_{6,i})}{{2\mathrm{<figure-callout\; id="2"\; label="dis"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">dis</figure-callout>}}_2}+u_{6,i});$

$u_{7,i}=\mathrm{std}(\frac{\mathrm{ArcL}\&times;M(u_{7,i},u_{6,i})}{{2\mathrm{<figure-callout\; id="2"\; label="dis"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">dis</figure-callout>}}_2}+u_{6,i});$

Thereby L ₁, L ₃, L ₅, L ₇toward moving to new parameter field border away from intake and exhaust edge direction (as shown in the arrow in Fig. 6).The curve obtaining after note translation is respectively l ₁, l ₃, l ₅, l ₇.

Illustrate: due to the error of moulding, actual spoon of blade plays the line of curvature tendency of stub area at intake and exhaust limit transition arc can be more disorderly, generally can not pass through the line of curvature in this region by direct solution, step 4 is that the line of curvature in this outside, region is moved by distance proportion, thereby obtains the approximate line of curvature through this region; l ₁, l ₃, l ₅, l ₇by the some P in Fig. 3 ₁, P ₂, P ₃, P ₄.

Step 6 is determined respectively the central point M of the upper leaf basin blade back circular arc of section line r ₁, M ₂.

Order $U_{}$ ${}_4=\mathrm{std}\left(\frac{\mathrm{Add}(U_6,U_5)}{2}\right),{\mathrm{<figure-callout\; id="8"\; label="U"\; filenames="HDA0000399835250000031.png"\; state="\{\{state\}\}">U</figure-callout>}}_8=\mathrm{std}\left(\frac{\mathrm{Add}(U_7,U_1)}{2}\right).$

U ₄, U ₈recorded some M ₁, M ₂position.

Step 7 is determined through M ₁, M ₂two longitudinal curvature lines or etc. parameter line L ₄, L ₈.

L ₄, L ₈the line of curvature if, solution procedure is as follows:

Oneself knows i point on the line of curvature, for j=4, and 8, determine that spoon of blade is at point (u _{j, i}, v _i) locate the principal direction d close with V direction _{j, i},

$u_{j,i+1}=u_{j,i}+(v_{i+1}-v_i)\&times;\frac{\left|S_u(u_{j,i},v_i)\right|}{\left|S_v(u_{j,i},v_i)\right|}\&times;d_{j,i},$

Thereby the parameter value of i+1 point of the j bar line of curvature is (u _{j, i+1}, v _i+1).

For i=4,8, note U _ithe corresponding line of curvature is L _i.

If L ₄, L ₈for waiting parameter line, for j=4,8, u _{j, i+1}=U _j.

Step 8 is with L ₂, L ₄, L ₆, L ₈and l ₁, l ₃, l ₅, l ₇the parameter line that waits under new argument territory, carries out Reparameterization to curved surface.

If the curved surface expression formula after Reparameterization is S ' (u ', v ').

Regard eight lines as the new U ' parameter line that waits, first determine the U ' coordinate u ' of j bar line correspondence under new argument _j.Make u ' ₁=0,

u′ _j＝u′ _j-1+M(U _j，U _j-1)，j＝2，…，8.

Note u ' ₉=1.

Given U ' V ' coordinate (u ', v _i), its corresponding UV coordinate is

$(\mathrm{std}(\frac{(u^{\&prime;}-{u^{\&prime;}}_j)M(u_{j+1,i},u_{j,i})}{{u^{\&prime;}}_{j+1}-{u^{\&prime;}}_j}+u_{j,i}),v_i),$

Wherein j meets u ' _j≤ u '≤u ' _j+1.

Illustrate: eight line L ₂, L ₄, L ₆, L ₈and l ₁, l ₃, l ₅, l ₇be actually and approach eight lines consistent with V direction on Fig. 2 Leaf curved surface, these eight lines of curvature have been cut apart eight regions relatively stably according to the bending features of curved surface spoon of blade, thereby can guarantee that the parameter line in every region all there will not be excessive distortion.

Step 9 is carried out non-uniform discrete according to new argument to curved surface.

The discrete of V ' direction determined by step 2, therefore only the discrete of U ' direction need be discussed.The discrete bow height of given U ' direction is GgU, and maximum discrete interval is Offset, and note the discrete of V ' direction counted as vnum.If current U ' parameter position is U ' _i, for 1≤j≤vnum, calculation level (U ' _i, v _j) parameter under UV coordinate, thereby determine the curvature uQL along U ' direction at this some place _{i, j}, order $r_{i,j}=\frac{1}{\left|\mathrm{uQ}{L}_{i,j}\right|},$

${\mathrm{OS}}_{i,j}=\frac{2\&times;\sqrt{r_{i,j}^2-{(r_{i,j}-\mathrm{GgU})}^2+\mathrm{<figure-callout\; id="2"\; label="Gg\; U"\; filenames="HDA0000399835250000021.png"\; state="\{\{state\}\}">Gg</figure-callout>}{U}^{}{}^2}\&CenterDot;}{{\mathrm{uLen}}_j}$

ULen wherein _jrepresent the curve V=v on curved surface _jarc length.

Make offset _i=min{min _joS _{i, j}, Offset}, next discrete location is U ' _i+1=U ' _i+ offset _i.

Illustrate: maximum discrete interval Offset has limited discrete maximum step-length, to prevent the occurring situation that step-length is excessive when the more flat regions such as discrete blade back leaf basin; The high meaning of discrete bow as shown in Figure 5; The divergent density of U direction is subject to the impact of curved surface local curvature, therefore be non-uniform discrete; The discrete step-length in three dimensions of V direction is determined, can be similar to and think for evenly discrete.

The approach that realizes of the present invention is coding, obtains the information of curve surface of workpiece by the second development interface of CAM system, by said process, curved surface is carried out to curvature feature splitting, and the curved surface after discrete can further be processed by secondary development program.

Claims (1)

1. the spoon of blade based on curvature feature is unified a discrete method, it is characterized in that: it comprises the following steps:

Step 1 is selected a representational section line r, determines the central point B of intake and exhaust limit arc section on it ₁, B ₂position; Detailed process is as follows:

A certain of selected blade is waited parameter line S (u, v ₀) as one section of molded line of blade, calculate the curvature distribution of this section of molded line

$k\left(u\right)=\frac{L(u,v_0)}{E(u,v_0)},$

L (u, v wherein ₀)=S _uu(u, v ₀) n (u, v ₀), E (u, v ₀)=S _u(u, v ₀) S _u(u, v ₀), n (u, v ₀) be that curved surface is at point (u, v ₀) per unit system located vows, function k (u), along with the meeting from small to large of u is by two sudden changes, establishes

given threshold value coefficient F, definition is as k (u)>=F * k ₀time, u is within sudden change position; Record respectively the reference position U of first sudden change _1swith final position U _1e, the reference position U of second sudden change _2swith final position U _2e; Definition computing

$\mathrm{std}\left(a\right)=\left\{\begin{array}{c}a+1,a<0;\\ a-1,a>1;\\ a,0\&le;a\&le;1.\end{array}\right.$

$\mathrm{Add}(a,b)=\left\{\begin{array}{c}a+b,a\&le;b;\\ a+b+1,a>b.\end{array}.\right.$

Order

$U_2=\mathrm{std}\left(\frac{\mathrm{Add}(U_{1s},U_{1e})}{2}\right),$

$U_6=\mathrm{std}\left(\frac{\mathrm{Add}(U_{2s},U_{2e})}{2}\right).$

U ₂and U ₆be the center of arc transition;

If do not add explanation, have v ₀=0; Std (a) computing has guaranteed that result drops in the field of definition of parameter; Add (a, b) is the situation of considering leap parameter field border, Sudden change region; k ₀in fact represent to cut the mean curvature of molded line; General corresponding the crook of cutting molded line, the center of arc transition; U ₂and U ₆determine by choosing many, blade and cut molded line, by above-mentioned steps, calculate respectively, then average and obtain; U ₂and U ₆determined some B ₁, B ₂;

Step 2 is from B ₁, B ₂point out and be sent to blade two ends and obtain through a B ₁, B ₂two longitudinal curvature line L ₂, L ₆; Detailed process is as follows:

Make u _2,1=U ₂, u _6,1=U ₆, v ₁=0

If oneself knows i point on the line of curvature, the parameter value of any under first definite second line of curvature; Calculate spoon of blade at point (u _{2, v}v _i) locate the principal direction D close with V direction _{2, i}, lower some P _{2, i+1}=S (u _{2, i}, v _i)+step * D _{2, i}, wherein step is given step-length, its size affects the discrete precision of V direction; Calculation level P again _{2, i+1}parameter value (the u of correspondence on curved surface _{2, i+1}, v _i+1), work as v _i+1>=1 o'clock, above-mentioned steps stopped;

For j=6, determine that spoon of blade is at point (u _{j, i}, v _i) locate the principal direction d close with V direction _{j, i},

$u_{j,i+1}=u_{j,i}+(v_{i+1}-v_i)\&times;\frac{\left|S_u(u_{j,i},v_i)\right|}{\left|S_v(u_{j,i},v_i)\right|}\&times;d_{j,i},$

Thereby the parameter value of i+1 point of the j bar line of curvature is (u _{j, i+1}, v _i+1);

For i=2,6, note U _ithe corresponding line of curvature is L _i;

Step 3 is representing on section line r, from B ₁, B ₂2 are set out, and find 4 specified point V respectively within the scope of this intake and exhaust limit, both sides circular arc ₁, V ₂, V ₃, V ₄;

Given distance value dis ₁, dis ₂, calculate U ₁, U ₃, U ₅, U ₇, make

${\mathrm{dis}}_1=\left\{\begin{array}{c}{\&Integral;}_{U_1}^{U_2}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_2}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}\&GreaterEqual;{\mathrm{dis}}_1;\\ {\&Integral;}_{U_1}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}+{\&Integral;}_0^{U_2}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_2}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}<{\mathrm{dis}}_1\end{array}\right.$

${\mathrm{dis}}_1=\left\{\begin{array}{c}{\&Integral;}_{U_2}^{U_5}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_{U_2}^0\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}\&GreaterEqual;{\mathrm{dis}}_1;\\ {\&Integral;}_{U_2}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}+{\&Integral;}_0^{U_5}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_{U_2}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}<{\mathrm{dis}}_1\end{array}\right.$

${\mathrm{dis}}_2=\left\{\begin{array}{c}{\&Integral;}_{U_5}^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}\&GreaterEqual;{\mathrm{dis}}_2;\\ {\&Integral;}_{U_5}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}+{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}<{\mathrm{dis}}_2\end{array}\right.$

${\mathrm{dis}}_2=\left\{\begin{array}{c}{\&Integral;}_{U_6}^{U_7}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}\&GreaterEqual;{\mathrm{dis}}_2;\\ {\&Integral;}_{U_6}^1\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}+{\&Integral;}_0^{U_7}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du},{\&Integral;}_0^{U_6}\left|S^{\&prime;}(u,v_0)\right|\mathrm{du}<{\mathrm{dis}}_2\end{array}\right.$

U ₁, U ₃, U ₅, U ₇be V on required circular arc ₁, V ₂, V ₃, V ₄position;

When solving integration, there is U ₁, U ₃, U ₄, U ₆with the U in step 1 _1s, U _1e, U _2s, U _2emeaning is different, and actual spoon of blade generally can be more disorderly in the curvature tendency of arc transition edge, so need to pass through parameter d is ₁, dis ₂adjust U ₁, U ₃, U ₄, U ₆value, make through point (U ₁, v ₀), (U ₃, v ₀), (U ₄, v ₀), (U ₆, v ₀) four lines of curvature consistent with blade shape construction direction locating stablize credible;

Step 4 is from V ₁, V ₂, V ₃, V ₄set out and obtain and pass through respectively V to blade two ends ₁, V ₂, V ₃, V ₄four longitudinal curvature line L ₁, L ₃, L ₅, L ₇;

u _1，1＝U ₁，u _3，1＝U ₃，u _5，1＝U ₅，u _7，1＝U ₇；

Oneself knows i point on the line of curvature, for j=1, and 3,5,7, determine that spoon of blade is at point (u _{j, i}, v _i) locate the principal direction d close with V direction _{j, i},

$u_{j,i+1}=u_{j,i}+(v_{i+1}-v_i)\&times;\frac{\left|S_u(u_{j,i},v_i)\right|}{\left|S_v(u_{j,i},v_i)\right|}\&times;d_{j,i},$

Thereby the parameter value of i+1 point of the j bar line of curvature is (u _{j, i+1}, v _i+1); For i=1,3,5,7, note U _ithe corresponding line of curvature is L _i;

Step 5 is L ₁, L ₂, L ₃as waiting parameter line, to L ₁, L ₃reparameterization is carried out in middle region, determines the parameter field boundary line l after Reparameterization ₁, l ₃; L ₅, L ₆, L ₇as waiting parameter line, to L ₅, L ₇reparameterization is carried out in middle region, determines the parameter field boundary line l after Reparameterization ₅, l ₇;

If the average transition arc arc length on blade intake and exhaust limit is ArcL,

Definition

$m(a.b)=\left\{\begin{array}{c}a-b-1,a>b;\\ a-b,a\&le;b.\end{array}\right.;$

$M(a,b)=\left\{\begin{array}{c}a-b+1,c<b;\\ a-b,a\&GreaterEqual;b.\end{array}\right..$

Order

$u_{1,i}=\mathrm{std}(\frac{\mathrm{ArcL}\&times;m(u_{1,i},u_{2,i})}{2{\mathrm{dis}}_1}+u_{2,i});$

$u_{3,i}=\mathrm{std}(\frac{\mathrm{ArcL}\&times;M(u_{3,i},u_{2,i})}{2{\mathrm{dis}}_1}+u_{2,i});$

$u_{5,i}=\mathrm{std}(\frac{\mathrm{ArcL}\&times;m(u_{5,i},u_{6,i})}{{2\mathrm{dis}}_2}+u_{6,i});$

$u_{7,i}=\mathrm{std}(\frac{\mathrm{ArcL}\&times;M(u_{7,i},u_{6,i})}{{2\mathrm{dis}}_2}+u_{6,i});$

Thereby L ₁, L ₃, L ₅, L ₇toward moving to new parameter field away from intake and exhaust edge direction; The curve obtaining after note translation is respectively l ₁, l ₃, l ₅, l ₇; Error due to moulding, actual spoon of blade plays the line of curvature tendency of stub area at intake and exhaust limit transition arc can be more disorderly, generally can not pass through the line of curvature in this region by direct solution, step 4 is that the line of curvature in this outside, region is moved by distance proportion, thereby obtains the approximate line of curvature through this region;

Step 6 is determined respectively the central point M of the upper leaf basin blade back circular arc of section line r ₁, M ₂;

Order $U_4=\mathrm{std}\left(\frac{\mathrm{Add}(U_6,U_5)}{2}\right),U_8=\mathrm{std}\left(\frac{\mathrm{Add}(U_7,U_1)}{2}\right),$ U ₄, U ₈recorded some M ₁, M ₂position;

Step 7 is determined through M ₁, M ₂two longitudinal curvature lines or etc. parameter line L ₄, L ₈;

L ₄, L ₈the line of curvature if, solution procedure is as follows: oneself knows i point on the line of curvature, for j=4,8, determine that spoon of blade is at point (U _{j, i}, v _i) locate the principal direction d close with V direction _{j, i},

$u_{j,i+1}=u_{j,i}+(v_{i+1}-v_i)\&times;\frac{\left|S_u(u_{j,i},v_i)\right|}{\left|S_v(u_{j,i},v_i)\right|}\&times;d_{j,i},$

Thereby the parameter value of i+1 point of the j bar line of curvature is (u _{j, i+1}, v _i+1); For i=4,8, note U _ithe corresponding line of curvature is L _iif, L ₄, L ₈for waiting parameter line, for j=4,8, u _{j, i+1}=U _j;

Step 8 is with L ₂, L ₄, L ₆, L ₈and l ₁, l ₃, l ₅, l ₇the parameter line that waits under new argument territory, carries out Reparameterization to curved surface;

If the curved surface expression formula after Reparameterization is S ' (u ', v '), regard eight lines as the new U ' parameter line that waits, first determine j bar line corresponding U ' coordinate u ' under new argument _j, make u ' ₁=0,

u′ _j＝u′ _j-1+M(U _j，U _j-1)，j＝2，…，8.

Note u ' ₉=1;

Given U ' V ' coordinate (u ', v _i), its corresponding UV coordinate is

$(\mathrm{std}(\frac{(u^{\&prime;}-{u^{\&prime;}}_j)M(u_{j+1,i},u_{j,i})}{{u^{\&prime;}}_{j+1}-{u^{\&prime;}}_j}+u_{j,i}),v_i),$

Wherein j meets u ' _j≤ u '≤u ' _j+1, eight line L ₂, L ₄, L ₆, L ₈and l ₁, l ₃, l ₅, l ₇be actually and approach eight lines consistent with V direction on spoon of blade, these eight lines of curvature have been cut apart eight regions relatively stably according to the bending features of curved surface spoon of blade, thereby can guarantee that the parameter line in every region all there will not be excessive distortion;

Step 9 is carried out non-uniform discrete according to new argument to curved surface;

The discrete of V ' direction determined by step 2, therefore only the discrete of U ' direction need be discussed; The discrete bow height of given U ' direction is GgU, and maximum discrete interval is Offset, and note the discrete of V ' direction counted as vnum; If current U ' parameter position is U ' _i, for 1≤j≤vnum, calculation level (U ' _i, v _j) parameter under UV coordinate, thereby determine the curvature uQL along U ' direction at this some place _{i, j}, order $r_{i,j}=\frac{1}{\left|\mathrm{uQ}{L}_{i,j}\right|},$

${\mathrm{OS}}_{i,j}=\frac{2\&times;\sqrt{r_{i,j}^2-{(r_{i,j}-\mathrm{GgU})}^2+\mathrm{Gg}{U}^2}\&CenterDot;}{{\mathrm{uLen}}_j}$

ULen wherein _jrepresent the curve V-v on curved surface _jarc length;

Make 0ffset _i=min{min _joS _{i, j}, Offset}, next discrete location is U ' _i+1=U ' _i+ offset _i.

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