CN101271326A - Ruled surface impeller tool path planning and processing method - Google Patents

Abstract

A path planning processing method of a ruled surface impeller cutter relates to a cutter path planning processing method. The invention solves the problems of the prior numerical control processing method of an impeller part, the problem are that a whole processing technology for processing a integral type ruled surface impeller is not proposed, the calculating method of the point of a knife centre or the point of a knifepoint is not given, the processing cutting efficiency is low, the operation is complex and the degree of automation is low and the five-axis processing of the ruled surface impeller can not be realized etc. The main steps of the method are the establishment of the calculator assistant manufacturing model CAM of an impeller part, the calculation of the vector of a cutter shaft, the calculation of the point of the knife centre, the planning of whole cutter path and the achievement of the processing of the impeller part. The method of the invention solves the problem of the five-axis processing of the ruled surface impeller and has the advantages of high processing cutting efficiency, easy operation and high degree of automation The ruled surface impeller processed by the method has the characteristics of orderly linage of flow passage, symmetrical structure and the uniform distribution of cutter path at the surface of the flow passage, thus reducing the workload of subsequent polishing processing greatly.

Description

Ruled surface impeller tool path planning and processing method

Technical field

The present invention relates to a kind of cutter path planning job operation, it is specifically related to a kind of cutter path planning job operation of computer-aided manufacturing of monoblock type ruled surface impeller.

Background technology

The digital control processing of impeller part is a bigger technical matters of difficulty in the field of machining.Past is adopted the job operation of a little milling usually to the processing of impeller blade.This method utilizes the end of milling cutter to carry out the cut of blade.Because the contact area of this cutting process cutter and workpiece is little, causes cutting data also smaller, this directly causes impeller cut time lengthening, has reduced working (machining) efficiency.The complex contour of impeller part, be difficult to finish processing with three traditional machining centers, the blade of cutter shaft and impeller can bump in the process, therefore, five processing of impeller part are a kind of inevitable choices, by the control of five machining centers to generating tool axis vector, avoid the generation of colliding, simultaneously also can more rational control cutting-tool angle, finish cutting.Aspect the impeller moulding, there is not the CAD formative method that provides impeller pattern of system in the prior art.Aspect control algolithm, most method has only provided the control algolithm of the generating tool axis vector of ruled surface impeller side milling processing, but do not provide the computing method of cutter heart point or point of a knife point, there is not the calculating of cutter heart point, just can't utilize the bulb of ball head knife partly to process wheel hub surface, can only after processing blade separately, process wheel hub surface more separately, so this patent has also proposed the computing method of cutter heart point.In addition, the algorithm in past is not considered the problem of Impeller Machining technology yet, does not propose the complete processing technology of processing monoblock type impeller.From the angle of technology, finish a complete Impeller Machining, common processing arrangement is to finish according to fluting, expansion groove and the such order of finishing.Most research does not have the clear and definite planing method that provides cutter path, so this patent has also proposed the cutter path planing method of integral wheel processing.At present also not mature enough to the exploitation of the cutter path planning software of integral wheel.The planning complexity of the cutter path of impeller need generate cutter path automatically by computer software, manually can't finish.The main method of domestic present employing is to utilize external business software such as UG, PowerMill to carry out the cutter path planning of impeller.But aforementioned business software costs an arm and a leg, and complicated operation, be difficult to grasp, so we set about having carried out having the exploitation of the Impeller Machining cutter path planning software of independent intellectual property right.

Summary of the invention

The present invention propose for the numerical-control processing method that solves existing impeller part exists processing monoblock type ruled surface impeller complete processing technology, do not provide cutter heart point or point of a knife point computing method, process that stock-removing efficiency is low, complicated operation, automaticity are low, five problems such as processing that can't realize the ruled surface impeller, and then provide a kind of Ruled surface impeller tool path planning and processing method.

The technical scheme that technical solution problem of the present invention is adopted is: a kind of Ruled surface impeller tool path planning and processing method, specifically realize according to following steps:

The foundation of step 1, impeller part computer-aided manufacturing MODEL C AM: read the orderly data point (track data) on the curve of impeller three-dimensional design figure by CAM software, adopt approximate algorithm to carry out the match that approaches of each bar curve on the impeller the orderly data point that reads, obtain the CAM model of impeller part;

The calculating of step 2, generating tool axis vector: set up the mathematical model of calculating generating tool axis vector,

$\left\{\begin{array}{c}\mathrm{\&alpha;}=\arccos \left(\frac{2d{\sin }^2(\mathrm{\&gamma;}/2)}{\sqrt{{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20081006415300151.png"\; state="\{\{state\}\}">L</figure-callout>}}^2+4{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A20081006415300151.png"\; state="\{\{state\}\}">d</figure-callout>}}^2{\sin }^2(\mathrm{\&gamma;}/2)}}\right)\\ d=R/\sin \left(\mathrm{\&alpha;}\right)\end{array}\right.$

In the wherein above-mentioned system of equations, α is a side rake angle, d: offset distance, α and d all are unknown numbers, and L is the ruled surface bus, and R is a tool radius, and γ is the angle of method vector, and L, R and γ all are known numbers;

The calculating of step 3, cutter heart point: the generating tool axis vector in the step 2 is abstracted into the space directed line segment, and the offset surface of impeller wheel surface is abstracted into free form surface, and calculating the free form surface of gained and the intersection point of space directed line segment is exactly the position of cutter heart point;

The planning of step 4, solid tool track: fluting processing, the processing of expansion groove, blade finishing;

Step 5, finish the processing of impeller part.

The present invention has following beneficial effect: the inventive method has proposed the complete processing technology of monoblock type ruled surface impeller, the computing method of cutter heart point or point of a knife point have been provided, solve the problem of five processing of ruled surface impeller, had processing stock-removing efficiency height, easy to operate, advantage that automaticity is high.The ruled surface impeller that utilizes this method to process has the advantages that runner marshalling, structural symmetry, water passage surface cutter path are evenly distributed, and has reduced the workload of follow-up polishing processing significantly.Impeller blade utilizes the one-shot forming of cutter side edge, smooth surface, and shape is accurate.This method adopts the cutter side edge to process in addition, cut with the some milling of processing and to compare with the cutter end, has the big advantage of cutting output, overcome and a little milled the low problem of processing stock-removing efficiency, so this method can improve working (machining) efficiency significantly, this point has also obtained checking in machining experiment.The application of this method will improve the programming efficiency of impeller part by numerical control job sequence greatly.

Description of drawings

Fig. 1 is a process flow diagram of the present invention, Fig. 2 is impeller three-dimensional design figure, Fig. 3 is the SPL figure of CAM software match, Fig. 4 is that ruled surface impeller side milling processing cutter spacing is determined schematic diagram, Fig. 5 is the schematic diagram of asking for of generating tool axis vector, Fig. 6 is the discrete triangular plate schematic diagram of free form surface, Fig. 7 is the structure schematic diagram of fluting auxiliary surface, Fig. 8 is that (dash-dot arrows is represented feed to fluting process principle figure, solid arrow represents that the worker advances, dotted arrow is represented withdrawing), Fig. 9 is actual grooving tool path effects figure, Figure 10 is that (dash-dot arrows is represented feed to expansion groove process principle figure, solid arrow represents that the worker advances, dotted arrow is represented withdrawing), Figure 11 is actual expansion groove cutter path design sketch, Figure 12 is that (dash-dot arrows is represented feed to the finishing schematic diagram, solid arrow represents that the worker advances, dotted arrow is represented withdrawing), Figure 13 is the actual cutter rail of a finishing design sketch, Figure 14 is a leaf basin blade processing track design sketch, Figure 15 is a blade back blade processing track design sketch, Figure 16 is the simulation result figure that VERICUT goes up integral wheel processing, and Figure 17 is a process chart in the Impeller Machining process, and Figure 18 is the impeller figure that adopts after the inventive method is carried out machining.

Embodiment

Embodiment one: as shown in Figure 1, the described Ruled surface impeller tool path planning and processing method of present embodiment is realized according to following steps:

The foundation of step 1, impeller part computer-aided manufacturing MODEL C AM: read the orderly data point (track data) on the curve of impeller three-dimensional design figure by CAM software, adopt approximate algorithm to carry out the match that approaches of each bar curve on the impeller the orderly data point that reads, obtain the CAM model of impeller part;

In engineering, impeller shape generally designs according to aerodynamic force or hydrodynamic performance index, or utilizes three-coordinates measuring machine to measure.No matter adopt which kind of mode, what provide on the drawing generally is the data point of describing the impeller blade curved surface.For blade is the impeller of ruled surface, and the data point that provides usually is shrouding disc curve and the discrete point of reel curve, the shrouding disc curve of pressure face and the discrete point on the reel curve of suction surface.These distribution of data points are very inhomogeneous, again because be discrete point, can not constitute parametric line, the curved surface of describing impeller blade shapes simultaneously, do not have the parametric line curved surface, just can't carry out next step cutter path planning.Therefore, form parametric spline curve, just become a problem that will solve at first of impeller moulding by these discrete point matches.As mentioned above, for the match of these discrete points, traditional way adopts interpolation to realize.But the interpolation algorithm part that comes with some shortcomings in actual applications.In principle, interpolation algorithm makes the data point that passes through of curve, curved surface strictness.Data point measures by digitizer (three-coordinates measuring machine, laser scanner) from surface in kind often.And can there be the zone of some not fairing because of reasons such as processing or wearing and tearing in surface in kind.And also can cause data distortion in the digitized process owing to the device systems error or because of operator's technical merit.Therefore, make interpolation curve, curved surface strictness not only can not guarantee to reduce tested curve, curved surface, also may cause interpolation curve, the serious not fairing of curved surface by data point.In digital control processing, fairness is an important index.The cutter path of fairing can reduce the frequent acceleration and deceleration of each kinematic axis of lathe, makes cutting more steady, smooth, improves the surface quality of part to be processed.And approximate algorithm can well address the above problem, and obtains the SPL of fairing, so we adopt the algorithm that data point is approached to come the match data point.

The calculating of step 2, generating tool axis vector: set up the mathematical model of calculating generating tool axis vector,

$\left\{\begin{array}{c}\mathrm{\&alpha;}=\arccos \left(\frac{2d{\sin }^2(\mathrm{\&gamma;}/2)}{\sqrt{{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20081006415300151.png"\; state="\{\{state\}\}">L</figure-callout>}}^2+4{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A20081006415300151.png"\; state="\{\{state\}\}">d</figure-callout>}}^2{\sin }^2(\mathrm{\&gamma;}/2)}}\right)\\ d=R/\sin \left(\mathrm{\&alpha;}\right)\end{array}\right.$

In the wherein above-mentioned system of equations, α is a side rake angle, d: offset distance, α and d all are unknown numbers, and L is the ruled surface bus, and R is a tool radius, and γ is the angle of method vector, and L, R and γ all are known numbers;

In five coordinate digital control processings, the planning algorithm of cutter path generally includes the computing method of generating tool axis vector, the computing method of cutter heart point (point of a knife point) and the planning algorithm in whole path.

Generating tool axis vector is calculated principle with reference to figure 4 and Fig. 5.As shown in Figure 1, the P that sets up an office ₁Be on the leaf top line w (blade back shrouding disc curve 2, leaf basin shrouding disc curve 4) a bit, the some P ₂Be on the blade root line Q (blade back reel curve 1, leaf basin reel curve 3) a bit, P ₁The per unit system vector of point is n ₁, P ₂The unit vector of point is n ₂, some C ₁It is vector n ₁On a bit, some C ₂It is vector n ₂On a bit.

Order | P ₁P ₂|=L, | P ₁C ₁|=| P ₂C ₂|=d, with reference to figure 5, P ₂C ₂And P ₂C ' ₁Angle be defined as γ,

$\mathrm{\&gamma;}=\arccos \left(\frac{{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="A20081006415300142.png,A20081006415300151.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20081006415300151.png"\; state="\{\{state\}\}">n</figure-callout>}}_2}{\left|{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="A20081006415300142.png,A20081006415300151.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\right|\&CenterDot;\left|{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="A20081006415300151.png"\; state="\{\{state\}\}">n</figure-callout>}}_2\right|}\right)$

At triangle Δ P ₁O ₁C ₁In

d＝R/sinα

At triangle Δ C ₂C ₁P ₁In

$\cos \mathrm{\&alpha;}=\frac{{\left|P_1{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="A20081006415300142.png,A20081006415300151.png"\; state="\{\{state\}\}">C</figure-callout>}}_1\right|}^2+{\left|C_1{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="A20081006415300151.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\right|}^2-{\left|P_1{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="A20081006415300151.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\right|}^2}{2\left|P_1{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="A20081006415300142.png,A20081006415300151.png"\; state="\{\{state\}\}">C</figure-callout>}}_1\right|\left|C_1{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="A20081006415300151.png"\; state="\{\{state\}\}">C</figure-callout>}}_2\right|}$

The above equation of simultaneous can get system of equations and is

$\left\{\begin{array}{c}\mathrm{\&alpha;}=\arccos \left(\frac{2d{\sin }^2(\mathrm{\&gamma;}/2)}{\sqrt{{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="A20081006415300151.png"\; state="\{\{state\}\}">L</figure-callout>}}^2+4{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="A20081006415300151.png"\; state="\{\{state\}\}">d</figure-callout>}}^2{\sin }^2(\mathrm{\&gamma;}/2)}}\right)\\ d=R/\sin \left(\mathrm{\&alpha;}\right)\end{array}\right.$

Wherein α and d are unknown numbers, and all the other all are known numbers.This formula is a Nonlinear System of Equations, and we use Newton method and have found the solution this system of equations.So just can try to achieve generating tool axis vector.

The calculating of step 3, cutter heart point: the generating tool axis vector in the step 2 is abstracted into the space directed line segment, and the offset surface of impeller wheel surface is abstracted into free form surface, and calculating the free form surface of gained and the intersection point of space directed line segment is exactly the position of cutter heart point;

The planning of step 4, solid tool track: fluting processing, the processing of expansion groove, blade finishing;

The basic thought of solid tool method for planning track is: according to opening, expand groove and accurately machined characteristic, automatically construct some auxiliary quadric surfaces (blade back fluting auxiliary quadric surface 10, leaf basin fluting auxiliary quadric surface 11) respectively, these curved surfaces all rotate around blade revolving shaft by processed spoon of blade.Fig. 7 is processed as the structure schematic diagram that example has shown auxiliary quadric surface with fluting, and the auxiliary quadric surface of fluting processing here is selected in the center of impeller channel.The auxiliary quadric surface structure principle that expands groove processing is similar.

For integral wheel, the distribution of blade has geometrical symmetry, so it is just passable only need to cook up the cutter path of a slice blade.The branches such as number that the cutter path of rest blade only need be pressed blade rotate just passable.

To narrate fluting below respectively, expand groove and the accurately machined cutter path planing method of blade (as Fig. 7～shown in Figure 15):

One), fluting processing: the curved surface of the ruled surface blade of impeller being regarded as parameters u, v decision, parameters u at every turn according to from small to large or sequence alternate from big to small change, parameter v at every turn according to from big to small single rule change, just generated " it " font cutter rail (as Fig. 8 and shown in Figure 9) of fluting processing.

Two), expand groove processing: expand groove processing and simply say to be exactly to utilize the side edge similar die cavity that carries out in layer of cutter to mill processing.The method that we adopt is that the side edge penetration of a cutting tool length of every layer of processing all less than the side edge length of cutter, is processed by being divided into multilayer in the way that expands groove processing employing layering on depth of cut direction, finishes the whole process flow that expands groove processing.Aspect the parameter variation, being different from fluting processing, the change direction of parameter v1 is not by the parameter v decision of spoon of blade, but by the parameter v decision of wheel hub curved surface.Turning axle with impeller is a series of auxiliary quadric surface of central configuration, expands the cutter path of groove processing and carries out with regard to relying on this a series of auxiliary quadric surface.Each auxiliary quadric surface has formed a cutter path along parameters u 1 direction (as shown in Figure 10 and Figure 11).

Rely on user's input along the variation of the cutter axis orientation number of plies, layer is processed the whole depth of cut with the spacing between the layer by the expansion groove and is determined divided by the number of plies.In addition, expand groove processing and finishing hereinafter and will notice that direction of feed is to move to outer rim from the center of impeller, can guarantee that like this point of a knife does not head on hub surface and processes.

Three), blade finishing: similar expansion groove is processed, and just do not have the variation of parameter v2 direction, and in order to reach accurately machined effect, the change interval of parameters u 2 also should be littler, to embody accurately machined cutter path planning intention (as Figure 12 and shown in Figure 13).

Step 5, finish the processing of impeller part.

Embodiment two: as shown in Figures 2 and 3, present embodiment is to use least square method to carry out approaching of ruled surface impeller upper curve (blade back reel curve 1, blade back shrouding disc curve 2, leaf basin reel curve 3, leaf basin shrouding disc curve 4, wheel hub section line 5) at approximate algorithm described in the step 1, and concrete steps are as follows:

Step a, with the orderly offset point sequence P on the curve of the impeller three-dimensional design figure that reads _i(i=0 ..., m) be configured to B-spline curves:

$r\left(u\right)=\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{V}_i\&CenterDot;N_{i,k}\left(u\right)$

V wherein _i(i=0 ..., n) be control polygon vertex, N _{I, k}(u) for being defined in knot vector U={u ₀, u ₁..., u _N+k|1On k B spline base function;

Step b, ask for V _i(i=0 ..., n): adopt the least square method formula

Brief note is TV=P

Its least square solution is V=(T ^TT) ^-1TP

T is the basis function matrix in the wherein above-mentioned equation, and V is a control polygon vertex matrix, and P is orderly offset dot matrix;

Step c, the refinement one by one of employing process of iteration: to each t _i, introduce adjustment amount Δ t _i, wherein

$\mathrm{\&Delta;}{t}_i=\frac{|P_i-r\left(t_i\right)|}{\left|r^{\&prime;}\left(t_i\right)\right|}$

Make for real-valued sequence t _iI=0,1 ..., m has the margin of error $e(r,t)=\underset{i=0}{\overset{m}{\mathrm{\&Sigma;}}}\left|\right|P_i-r\left(t_i\right)\left|\right|$ Reach minimum; Real-valued sequence t in the following formula _iI=0,1 ..., m is that data point is corresponding to the parameter value of putting on the curve;

Steps d, in the process of each iteration, all calculate approximate error, if error does not meet the demands, use following formula correction t so _i, iteration once more is till satisfying the approximation accuracy requirement.Other step is identical with embodiment one.In actual applications, often introduce the power of amendment factor, can solve the iteration diverges problem preferably like this.Also introduced maximum iteration time I _MaxWith minimum iterative convergence speed v _MinAbove-mentioned two parameters can solve unlimited iterative problem.

Embodiment three: as Fig. 4 and shown in Figure 6, present embodiment is as follows in the concrete steps of the position calculation of the heart point of cutter described in the step 3:

Step I, elder generation are separated into triangular plate with the offset surface 9 of impeller wheel surface 8, use the position of the algorithm computation intersection point of triangular plate and space directed line segment find intersection, and the position of described intersection point is exactly the position of cutter heart point;

Wherein the offset surface of impeller wheel surface is separated into triangular plate and carries out as follows:

One), according to etc. parametric method calculate each point on the wheel hub section line lead vector n3;

Two), the per unit system vector of leading vector and plane, wheel hub section line place makes multiplication cross, just tried to achieve the method vector n4 of section line;

Three), the method vector of wheel hub section line multiply by the tool radius value, just tried to achieve the point on the skew rear curved surface;

Four), the point on the wheel hub section line is rotated along blade revolving shaft, can generate one group of spatial point cloud;

Five), these clouds are connected into triangular plate in a certain order, just finished offset surface discrete of impeller wheel surface, the offset surface that is about to impeller wheel surface is abstracted into free form surface;

Step I i, utilize the principle of oriented volume to find the solution the intersection point of triangular plate and space directed line segment, the oriented tetrahedron in space is formed on summit of space directed line segment and three summits of triangular plate, utilize oriented tetrahedral cubature formula

$\left[\mathrm{DABC}\right]=\frac{1}{6}\left[\begin{array}{cccc}{x}_a& y_a& z_a& 1\\ x_b& y_b& z_b& 1\\ x_c& y_c& z_c& 1\\ x_d& y_{\mathrm{<figure-callout\; id="1"\; label="d\; z\; d"\; filenames="A20081006415300142.png,A20081006415300151.png"\; state="\{\{state\}\}">d</figure-callout>}}& z_d{}_{}& 1\end{array}\right],$ A (x wherein _a, y _a, z _a), B (x _b, y _b, z _b), C (x _c, y _c, z _c) be the coordinate on three summits of triangular plate, D (x _d, y _d, z _d) apex coordinate of space directed line segment,

Judge whether line segment intersects with triangular plate, if intersect, the equation of simultaneous space directed line segment and triangular plate obtains system of equations again

$\left[\begin{array}{ccc}-d& V_1-V_0& V_2-V_0\end{array}\right]\&CenterDot;\left[\begin{array}{c}t\\ u\\ v\end{array}\right]=[P-V_0]$

D represents directed line segment direction, V ₀, V ₁, V ₂Represent the control vertex of triangular plate, t, u, v represent the parameter of straight line and triangular plate respectively, and P represents the starting point of directed line segment.

Separate this system of equations, just can obtain the coordinate of intersection point, just the coordinate of cutter heart point.

Other step is identical with embodiment one.

Embodiment four: as Figure 16, Figure 17 and and shown in Figure 180, in order to verify correctness with the emulation of the ruled surface impeller of the inventive method processing, we have processed workpiece at reality on B, C turning axle five coordinate lathes, the aluminum cylinder blank that this experiment material therefor is diameter 90mm, the material model is LY11.First being processed on five coordinate lathes at first should be finished the turning processing in blank cross section on numerically controlled lathe, making the blank cross section is circular curve.Then use the computing method of the generating tool axis vector of this patent proposition, the computing method and the solid tool trajectory planning scheme of cutter heart point to carry out the planning of cutter path, give digital control system, just can process the five coordinate numerical control file transfer that generate.The cutter that Milling Process adopted is the circular cutter of diameter 6mm.Because major technique that this patent adopted is a cutter side milling processing scheme, thus the side edge length of cutter also within the scope that will consider, the cutter side edge length that is adopted in the experiment is 8mm.Though the side edge curtailment of 8mm once to finish the side edge milling of whole blade, uses the way of the layered cutting of this patent proposition, divides the two-layer processing that just can finish whole blade.As can be seen, the processing result of Figure 18 and the simulation result of Figure 16 are just the same, have proved the correctness of algorithm and emulation.From the result of processing, the runner marshalling of impeller, structural symmetry.The water passage surface cutter path is evenly distributed, and can significantly reduce the workload of follow-up polishing processing.Impeller blade utilizes the one-shot forming of cutter side edge, smooth surface, and shape is accurate.This method adopts the cutter side edge to process in addition, compares with milling with cutter end processing stand, and cutting output is big, so can improve working (machining) efficiency significantly, this point has also obtained checking in machining experiment.

Claims (3)

1, a kind of Ruled surface impeller tool path planning and processing method is characterized in that it realizes according to following steps:

The foundation of step 1, impeller part computer-aided manufacturing MODEL C AM: read the orderly data point on the curve of impeller three-dimensional design figure by CAM software, adopt approximate algorithm to carry out the match that approaches of each bar curve on the impeller the orderly data point that reads, obtain the CAM model of impeller part;

The calculating of step 2, generating tool axis vector: set up the mathematical model of calculating generating tool axis vector,

$\left\{\begin{array}{c}\mathrm{\&alpha;}=\arccos \left(\frac{2d{\sin }^2(\mathrm{\&gamma;}/2)}{\sqrt{L^2+4d^2{\sin }^2(\mathrm{\&gamma;}/2)}}\right)\\ d=R/\sin \left(\mathrm{\&alpha;}\right)\end{array}\right.$

In the wherein above-mentioned system of equations, α is a side rake angle, d: offset distance, α and d all are unknown numbers, and L is the ruled surface bus, and R is a tool radius, and γ is the angle of method vector, and L, R and γ all are known numbers;

The calculating of step 3, cutter heart point: the generating tool axis vector in the step 2 is abstracted into the space directed line segment, and the offset surface of impeller wheel surface is abstracted into free form surface, and calculating the free form surface of gained and the intersection point of space directed line segment is exactly the position of cutter heart point;

The planning of step 4, solid tool track: fluting processing, the processing of expansion groove, blade finishing;

Step 5, finish the processing of impeller part.

2, Ruled surface impeller tool path planning and processing method according to claim 1 is characterized in that at approximate algorithm described in the step 1 it being to use least square method to carry out approaching of ruled surface impeller upper curve, and concrete steps are as follows:

Step a, with the orderly offset point sequence P on the curve of the impeller three-dimensional design figure that reads _i(i=0 ..., m) be configured to B-spline curves:

$r\left(u\right)=\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{V}_i\&CenterDot;N_{i,k}\left(u\right)$

V wherein _i(i=0 ..., n) be control polygon vertex, N _{I, k}(u) for being defined in knot vector U={u ₀, u ₁..., u _N+k|1On k B spline base function;

Step b, ask for V _i(i=0 ..., n): adopt the least square method formula

Brief note is TV=P

Its least square solution is V=(T ^TT) ^-1TP

T is the basis function matrix in the wherein above-mentioned equation, and V is a control polygon vertex matrix, and P is orderly offset dot matrix;

Step c, the refinement one by one of employing process of iteration: to each t _i, introduce adjustment amount Δ t _i, wherein

$\mathrm{\&Delta;}{t}_i=\frac{|P_i-r\left(t_i\right)|}{\left|r^{\&prime;}\left(t_i\right)\right|}$

Make for real-valued sequence t _iI=0,1 ..., m has the margin of error $e(r,t)=\underset{i=0}{\overset{m}{\mathrm{\&Sigma;}}}\left|\right|P_i-r\left(t_i\right)\left|\right|$ Reach minimum; Real-valued sequence t in the following formula _iI=0,1 ..., m is that data point is corresponding to the parameter value of putting on the curve;

Steps d, in the process of each iteration, all calculate approximate error, if error does not meet the demands, use following formula correction t so _iIteration once more is till satisfying the approximation accuracy requirement.

3, Ruled surface impeller tool path planning and processing method according to claim 1 is characterized in that in the concrete steps of the position calculation of the heart point of cutter described in the step 3 as follows:

Step I, elder generation are separated into triangular plate with the offset surface of impeller wheel surface, use the position of the algorithm computation intersection point of triangular plate and space directed line segment find intersection, and the position of described intersection point is exactly the position of cutter heart point;

Wherein the offset surface of impeller wheel surface is separated into triangular plate and carries out as follows:

One), according to etc. parametric method calculate the vector of leading of each point on the wheel hub section line;

Two), the per unit system vector of leading vector and plane, wheel hub section line place makes multiplication cross, just tried to achieve the method vector of section line;

Three), the method vector of wheel hub section line multiply by the tool radius value, just tried to achieve the point on the skew rear curved surface;

Four), the point on the wheel hub section line is rotated along blade revolving shaft, can generate one group of spatial point cloud;

Five), these clouds are connected into triangular plate in a certain order, just finished offset surface discrete of impeller wheel surface, the offset surface that is about to impeller wheel surface is abstracted into free form surface;

Step I i, the oriented tetrahedron in space is formed on summit of space directed line segment and three summits of triangular plate, utilized the principle of oriented volume to find the solution the intersection point of triangular plate and space directed line segment.

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