CN102722137A - Five-axis plunge milling machining method for ruled surface impeller - Google Patents

Abstract

The invention discloses a five-axis plunge milling machining method for a ruled surface impeller. The method comprises the following steps of: generating a boundary vector, interpolating the boundary vector, calculating the row pitch and step pitch, calculating a cutter center point, and planning a cutter path until machining of a ruled surface impeller part is finished. By the method, the defect of low rough machining efficiency in the prior art is overcome, the material removal rate and machining efficiency of the plunge milling are guaranteed, and the method is applicable to popularization and application.

Description

Ruled surface impeller five coordinates are inserted milling method

Technical field

The invention belongs to the digital control processing field, relate generally to a kind of impeller and insert milling method, particularly relate to a kind of ruled surface impeller five coordinates and insert milling method.

Background technology

Slotting milling is called z axle milling method again, and its working method is similar to drilling, and cutter is done feed motion along major axes orientation, utilizes the cutting edge of bottom to bore, mill the combination cutting, and is as shown in Figure 1.

The slotting processing method of milling is that complex-curved metal cutting realizes the most effectively one of job operation of high resection rate, is applied in widely on the Cutting Parts with vertical sidewall.The working (machining) efficiency of inserting milling is higher than conventional method for milling far away, and when needs excised a large amount of metal material fast, milling is inserted in employing can make shorten significantly process time.In addition, insert and to mill processing and also have the following advantages: 1) side force is little, has reduced part deformation; 2) it is lower to act on the radial cutting force of milling machine in the processing, the not high lathe of main axis stiffness still can be used and does not influence the crudy of workpiece; 3) the cutter length that overhangs is bigger, is fit to the surface of workpiece deep trouth is carried out Milling Process and prolonged cutter life, and is applicable to hard-cutting materials such as high temperature alloy are carried out grooving processing.

Though insert and to mill processing and have many advantages, in the past and the optimization problem of current research when mainly concentrating on the use side milling cutter and processing sculptured surface to Milling Process.Seldom can see the research of milling process tool route planning to inserting.

Document EL-MIDANY T T; ELKERAN A; TAWFIK H.Optimal CNC plunger selection and toolpoint generation for roughing sculptured surfaces cavity [j] .Journal of Manufacturing Science and Engineering.; 2006,128 (4): 1025-1029 is that the document that mills process tool route planning is inserted in the research that minority is published.The document has proposed overlapping filling circle, and (over-lapped circles filling, Ocfill) algorithm generates and inserts the cutter path of milling processing, preferably resolves the slotting generation problem of milling process tool route in the 2D zone.But this algorithm can not be controlled (can only be applied in the processing of three-dimensional lathe) to cutter shaft, can't generate to insert to the part with distortion die cavity to mill machining path.Document KO J H; ALTINTAS Y.Time domain model of plunge milling operation [J] .Machine Tools & Manufacture.; 2007; 47 (9): 1351-1361, the plug in machinery and a dynamics time domain model of processing of milling has been proposed, still also only be applied on the three-dimensional Milling Process.

In commercial production, there is one type of part to necessarily require could process it with five coordinate lathes, impeller class part is exactly typical case's representative.

Traditional Impeller Machining process planning scheme generally comprises fluting, expands groove and finishing.Wherein slot, expand slot part and be equivalent to the general roughing stage.Most of taper rose cutter that adopts; Slot at the center section of runner earlier; Adopt side milling method mind-set both sides from runner progressively to expand then,, adopt side milling or some milling to accomplish the finishing of blade at last again until reach till the rough machined surplus requirement of blade.Have data to show, at fluting, to expand the material removal amount in groove stage very big, is about 60% ~ 90%, therefore, the quality of rough machined efficient and technology is to the shortening process-cycle and cut down finished cost and have great importance.

The problem that comprehensive impeller part roughing is faced is milled machining characteristics with inserting, and slotting milling is the rough machined first-selected bill of impeller class part.But; Because the runner (die cavity) complex-shaped usually (as shown in Figure 2) of impeller class part; Thereby when generating cutter path, require CAM software very high to the control ability of cutter shaft, and should guarantee to insert milling path and evenly distribute, guarantee that again the different blade surfaces of cutter interfere.How therefore plug in milling cutter generates collisionless cutter axis orientation and optimization in the multi-coordinate digital control processing cutter spacing track is one of hot issue of current research.

Document HU Chuangguo, ZHANG Dinghua, REN Junxue; Et al.Research on the plunge milling of blisk tunnel [J] .China Mechanical Engineering, 2007,18 (2): (in Chinese) [Hu Chuanguo p.153-155.; Zhang Dinghua appoints and learns military affairs, etc. open type integral leaf dish passage is inserted and is milled roughing Study on Technology [J]. Chinese mechanical engineering; 2007,18 (2): 153-155], carried out the slotting roughing Study on Technology of milling of passage of open type integral leaf dish; Utilize ruled surface to approach the blade profile curved surface of impeller,, plan cutter path through connecting the corresponding point on the cutter heart and the cutter shaft.But this method is not considered the calculation criterion of line-spacing, step pitch, can't guarantee to insert to mill material processed clearance and working (machining) efficiency (cutter path of generation is not necessarily the shortest), and is unfavorable to the research of inserting the profound level of milling processing.

In addition, insert and mill the job operation that processing is a kind of comparison novelty, also be in conceptual phase at present.Usually common slotting milling method can only be accomplished to insert on the three-dimensional lathe and mill processing, and it is powerless usually that needs big to narrow runner, leaf curling as the impeller and dark die cavity could be accomplished the workpiece of processing with five coordinate lathes.

Summary of the invention

Goal of the invention

To the variety of issue that above-mentioned prior art exists, the present invention inserts milling method to complex-shaped surface mould and studies, and has proposed a kind of ruled surface impeller five coordinates and has inserted milling method, efficiently solves the problems referred to above.

Technical scheme

The present invention realizes through following technical scheme:

A kind of ruled surface impeller five coordinates are inserted milling method; It is characterized in that: according to the skew boundary vector of ruled surface blade; Utilize the hypercomplex number interpolation method calculate to insert to mill the generating tool axis vector of processing, propose and confirmed that five coordinates insert line-spacing, the step pitch of milling processing, cook up the cutter machining locus; Thereby workpiece is processed, and these method concrete steps are following:

The generation of a, boundary vector:

In engineering, the expression way of the parametric equation of ruled surface is:

P(u,v)＝(1-v)Q(u)+vW(u) （1）

Wherein W (u) and Q (u) are respectively ruled surface vane top line and blade root line, u, v be respectively u to v to parameter; By leg-of-mutton geometric relationship, the mathematical model of setting up the computation bound vector gets following system of equations:

$\left\{\begin{array}{c}\mathrm{\&alpha;}=\arccos \left(\frac{2d{\sin }^2(\mathrm{\&gamma;}/2)}{\sqrt{{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">L</figure-callout>}}^2+4{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">d</figure-callout>}}^2{\sin }^2(\mathrm{\&gamma;}/2)}}\right)\\ d=R/\sin \left(\mathrm{\&alpha;}\right)\end{array}\right.---\left(2\right)$

R is a tool radius in the formula, and L is middle P ₁P ₂Length, γ is P ₁C ₁And P ₂C ₂Angle, α is P ₁C ₁And C ₁C ₂Angle, d is the offset distance of the relative blade of cutter; This system of equations is a non-linear equation with two unknowns group, and wherein α and d are unknown number; α that the group of solving an equation is tried to achieve and the value of d, calculating the vector that departs from the ruled surface distance to a declared goal is boundary vector;

The interpolation of b, boundary vector:

Be between boundary vector, to fill (interpolation) vector uniformly as plugging in the cutter shaft orientation of milling processing; Like this; Generated at above-mentioned steps a under the situation of boundary vector, through reasonably boundary vector being carried out interpolation, the final processing of accomplishing the die cavity that boundary vector surrounded;

Rotatablely move and adopt the Quaternion Representation mode; Generate the cutter path of even excision amount with the hypercomplex number method of interpolation; Guarantee that working engagement of the cutting edge keeps even always in the slotting process of milling; Mill the generating tool axis vector employing spherical coordinates linear interpolation arithmetic (Spherical Linear Interpolation is called for short Slerp) that processing generates interpolation to inserting, the interpolation formula of Slerp is:

Slerp(q ₀,q ₁,h)＝q ₀(q ₀ ^-1·q ₁) ^h （4）

In the formula, h is an interpolation parameter, q ₀, q ₁---represent hypercomplex number;

---represent the inverse of hypercomplex number, its computing formula is:

$q_0^{-1}=\frac{q_0^{*}}{{\left|\right|q_0\left|\right|}^2}---\left(5\right)$

In the formula, ---represent the conjugation of hypercomplex number; || q ₀||---represent the mould of hypercomplex number;

The calculating of c, line-spacing, step pitch:

Owing to the variation of cutter shaft angle between the adjacent slotting milling cutter path, causing the cutting scope is an irregular conical region in the processing of five coordinates, and making the coordinate of the cutter heart point in two adjacent slotting millers steps is O ₁, O ₂, the die cavity upper surface is L to the line distance of cutter heart point, the intersection point at the cutter edge in two adjacent slotting miller steps is B, crosses the B point and does the vertical line of generating tool axis vector and give P mutually with generating tool axis vector ₁, P ₂Point, then

BP ₁＝BP ₂＝R （6）

In the formula, R---be tool radius,

With BP ₁O ₁O ₂P ₂The pentagon that forms that surrounds extracts, and makes that C is O ₁O ₂The mid point of line, cross C and be BP ₁Vertical line meet at the D point, cross O ₁The vertical line that point is CD meets at the E point, and the angle of the generating tool axis vector of name adjacent process steps is the inclination angle distance, representes with β; Make the long L of being of BC, O ₁O ₂Long for H, because BD+DP ₁=R is at Δ CBD and Δ CO ₁Among the E,, can obtain equality according to the triangle geometric relationship:

$L\sin \frac{\mathrm{\&beta;}}{2}+\frac{\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">H</figure-callout>}}{2}\cos \frac{\mathrm{\&beta;}}{2}=R---\left(7\right)$

According to the interpolation principle, the angle that makes each row bound vector is A, and the distance between the boundary vector cutter heart point is H ₀, obtain equality:

$\frac{\mathrm{\&beta;}}{A}=\frac{H}{H_0}---\left(8\right)$

Simultaneous equality (7) and (8) obtain a binary nonlinear system of equations

$\left\{\begin{array}{c}L\sin \frac{\mathrm{\&beta;}}{2}+\frac{\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">H</figure-callout>}}{2}\cos \frac{\mathrm{\&beta;}}{2}=R\\ \frac{\mathrm{\&beta;}}{A}=\frac{H}{H_0}\end{array}\right.---\left(9\right)$

Wherein L, R, A and H ₀Be known number, β and H are unknown number, adopt the quasi-Newton method in the numerical analysis to calculate the result; After trying to achieve the value of β and H, obtain average step pitch and inclination angle distance, confirm interpolation result at line direction;

At the interpolation result of column direction, just the calculating principle of line-spacing is identical with the computing method of step pitch, just is not the boundary vector of each row by the vector of interpolation, but the boundary vector at blade two ends, H ₀Length also should be blade wheel hub surface length of a curve;

The calculating of d, cutter heart point:

Boundary vector is abstracted into space line, and the intersection point of the offset plane of computation bound vector and wheel hub surface is the coordinate position of cutter heart point;

E, cutter path planning: fluting processing, the processing of expansion groove, the finishing of ruled surface impeller;

The processing of f, completion ruled surface impeller part.

Among the step a, the generation of boundary vector will be calculated through the tool radius that squints according to suction surface and pressure face, in order to leave surplus to finishing, and on the basis of skew tool radius, the process redundancy that squints again, surplus is 0.1mm.

The calculating of cutter heart point in the steps d, promptly the intersection algorithm of boundary vector and wheel hub surface is following:

The wheel hub cross section of ruled surface impeller is a circular cross-section, calculates intersection point with analytic geometry method, and circular cross-section can be expressed as around the postrotational surface equation of Z axle:

$f(x,y,z)={(\sqrt{x^2+y^2}-x_0)}^2$

$+{(z-z_0)}^2-{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">R</figure-callout>}}^2=$ （10）

$x^2+y^2-2x_0\sqrt{x^2+y^2}$

$+x_0^2+z^2-2z_{0}z+z_0^2-{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">R</figure-callout>}}^2$

The equation of the space line that boundary vector is abstracted into is:

$\left\{\begin{array}{c}x=(1-t)x_1+{\mathrm{tx}}_2\\ y=(1-t)y_1+{\mathrm{ty}}_2\\ z=(1-t)z_1+t{z}_2\end{array}\right.---\left(11\right)$

Equation (11) is brought in the equation (10), can obtains following One-place 2-th Order nonlinear equation

$f\left(t\right)={[(1-t)x_1+{\mathrm{tx}}_2]}^2+{[(1-t)y_1+{\mathrm{ty}}_2]}^2$

$-2x_0\sqrt{{[(1-t)x_1+{\mathrm{tx}}_2]}^2+{[(1-t)y_1+{\mathrm{ty}}_2]}^2}---\left(12\right)$

$+x_0^2+{[(1-t)z_1+{\mathrm{tz}}_2]}^2-2[(1-t)z_1+{\mathrm{tz}}_2]z_0$

$+z_0^2-{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">R</figure-callout>}}^2=0$

This equation is the quadratic equation with one unknown about parametric t, and the bisection method in the applied numerical analysis is tried to achieve its t as a result, brings t into formula (11), tries to achieve the offset plane of wheel hub surface and the intersection point of boundary vector, is to plug in the cutter heart point coordinate position of milling this work step of processing.

For blade shape is the impeller of free form surface, and free form surface is fitted to ruled surface, processes again.

Advantage and effect

The present invention provides a kind of ruled surface impeller five coordinates to insert milling method, has following advantage and beneficial effect:

The present invention has greatly improved the rough machined working (machining) efficiency of impeller, can save the roughing time significantly; Simultaneously, the process redundancy when having reduced impeller finishing to improving the accurately machined machining precision of last impeller, also can play certain booster action.

Description of drawings

Fig. 1 mills process principle figure for inserting;

Fig. 2 is processed impeller part model figure;

Fig. 3 is the boundary vector schematic diagram calculation;

Fig. 4 is boundary vector result of calculation figure;

Fig. 5 is that Lerp and Slerp interpolation algorithm compare;

Fig. 6 inserts for multi-coordinate and mills the irregular conical region schematic diagram of processing;

Fig. 7 is line-spacing, step pitch schematic diagram calculation;

Fig. 8 mills the cutter path that processing generates for inserting;

Fig. 9 mills processing for cutter lifting in the machining simulation with inserting.

Description of reference numerals

S, step pitch, α _θ, working engagement of the cutting edge, 1, runner, 2, the ruled surface blade, 3, wheel hub surface, 4, the offset plane of wheel hub surface, 5, pressure face, 6, suction surface, 7, the skew boundary vector, 8, cutter path.

Embodiment

Below in conjunction with accompanying drawing the present invention is done further explanation:

The present invention is that a kind of ruled surface impeller five coordinates are inserted milling method; It is characterized in that: according to the skew boundary vector of ruled surface blade; Utilize the hypercomplex number interpolation method calculate to insert to mill the generating tool axis vector of processing, propose and confirmed that five coordinates insert line-spacing, the step pitch of milling processing, cook up the cutter machining locus; Thereby workpiece is processed, and these method concrete steps are following:

The generation of a, boundary vector:

For blade shape is the impeller of free form surface, can adopt and recklessly create the way that proposes in " open type integral leaf dish passage is inserted and milled the roughing Study on Technology " that state etc. delivers, and free form surface is fitted to ruled surface.Therefore, the present invention only discusses the generation of the boundary vector of ruled surface impeller.

In inserting milling method; The generation of boundary vector has crucial meaning; Boundary vector both can guarantee that cutter and spoon of blade did not interfere and over-cutting (is that the biasing surface of using the blade ruled surface generates in the present invention; So can not interfere), simultaneously be again the interpolation algorithm of boundary vector carry out interpolation institute foundation with reference to vector, so extremely important.Its ultimate principle is following:

In engineering, the expression way of the parametric equation of ruled surface is:

P(u,v)＝(1-v)Q(u)+vW(u) （1）

Wherein W (u) and Q (u) are respectively ruled surface vane top line and blade root line, u, v be respectively u to v to parameter, can be with reference to Siemens PLM Software.UG NX help file [EB/OL] .http: //www.ugs.com.cn, 2008 and Fig. 3; By leg-of-mutton geometric relationship, the mathematical model of setting up the computation bound vector gets following system of equations:

$\left\{\begin{array}{c}\mathrm{\&alpha;}=\arccos \left(\frac{2d{\sin }^2(\mathrm{\&gamma;}/2)}{\sqrt{{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">L</figure-callout>}}^2+4{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">d</figure-callout>}}^2{\sin }^2(\mathrm{\&gamma;}/2)}}\right)\\ d=R/\sin \left(\mathrm{\&alpha;}\right)\end{array}\right.---\left(2\right)$

R is a tool radius in the formula, and L is P among Fig. 3 ₁P ₂Length, γ is P ₁C ₁And P ₂C ₂Angle, α is P ₁C ₁And C ₁C ₂Angle, d is the offset distance of the relative blade of cutter; This system of equations is a non-linear equation with two unknowns group; Wherein α and d are unknown number, about the detailed derivation step of this system of equations, and can be with reference to Siemens PLM Software.UG NX help file [EB/OL] .http: //www.ugs.com.cn; 2008, repeat no more at this; α that the group of solving an equation is tried to achieve and the value of d, just can calculate the vector that departs from the ruled surface distance to a declared goal is boundary vector.

The generation of boundary vector will be calculated through the tool radius that squints according to suction surface and pressure face among the present invention, simultaneously in order to leave surplus to finishing, and on the basis of skew tool radius, the process redundancy that squints again, this surplus can be 0.1mm; Boundary vector according to said method obtains is as shown in Figure 4.

The interpolation of b, boundary vector:

Key component of the present invention is to carry out interpolation to the boundary vector that obtains among the step a; Promptly between boundary vector, fill (interpolation) vector uniformly as plugging in the cutter shaft orientation of milling processing; Like this, generated at step a under the situation of boundary vector, through reasonably boundary vector being carried out interpolation; Finally just can accomplish the processing of the die cavity (is exactly runner to impeller) that boundary vector is surrounded, the key in the key is that the interpolation of boundary vector is wanted rationally.

This be because, uniformly to mill processing very important to inserting for the excision amount, inserts that to mill be to lean on the edge of cutter to gnaw from top to bottom along the direction of Z axle to cut, can to guarantee to insert the working engagement of the cutting edge that mills in the processing constant, as shown in Figure 1 in distribution uniformly between the interpolation vector.

In order to solve the problem that generates even working engagement of the cutting edge; The present invention is on the basis that has contrasted multiple interpolation method; The hypercomplex number method of interpolation is incorporated into slotting milling in the cutter path planing method of impeller channel; Preferably resolve to insert and mill the problem that even excision amount cutter path generates in the process, will introduce the cutter path that the hypercomplex number method generates even excision amount in detail below.

Insert at five coordinates and to mill in the process tool orbit generation method, the most important thing is to control generating tool axis vector, and generating tool axis vector has been represented sense of rotation, so in fact be a kind of interpolation method of rigid body rotation according to the interpolation of border generating tool axis vector.As previously mentioned, Spin Control even more, it is also just even more to insert the bite of milling in the process.

In theoretical circles, the multiple expression mode that rotatablely moved is like Eulerian angle definition mode, rotation matrix definition mode and hypercomplex number mode.

Usually using orthogonal matrix to represent Eulerian angle to describe traditionally rotatablely moves; This is because rigid body is simple and be widely used around the rotation matrix form of X, Y and Z axle; Can be to use the mode of Eulerian angle and rotation matrix to define to rotatablely move and have following defective: (1) lacks intuitive, intuitively goes up the orientation of finding out object that Eulerian angle and rotation matrix can not be clear and definite; (2) Universal lock problem, Eulerian angle and rotation matrix can lost one degree of freedom in some cases, corresponding a plurality of rotations of direction in this case, thus produce the Universal lock problem; (3) realize relatively difficulty of interpolation, (4) are indeterminate to the expression of rotation, and a given rotation matrix can't instead be asked the rotation of its representative; (5) there is redundancy in expression-form, has redundant data in the expression way like the quadrature rotation matrix.

Hypercomplex number has exactly remedied the deficiency of Eulerian angle and rotation matrix: (1) geometric properties is obvious; (2) independence and coordinate system; (3) interpolation algorithm is simple; (4) expression-form is compact; (5) there is not the Universal lock problem; (6) the combination rotation (only needs two hypercomplex numbers are multiplied each other) easily.Just because of there is above-mentioned advantage in hypercomplex number,, the present invention rotatablely moves so adopting hypercomplex number to describe.

The definition of hypercomplex number comprises a scalar component and a 3D component, usually scalar component is designated as w, and the note component of a vector is single v or the x that separates, y and z.Be expressed as [w, x, y, z] or [w, v].People have defined the standard operation that adds, subtracts, takes advantage of and remove of hypercomplex number.In the present invention, it is spherical coordinates linear interpolation (Spherical Linear Interpolation is called for short Slerp) to inserting the most useful computing of generating tool axis vector of milling processing generation interpolation.Slerp can carry out level and smooth interpolation between two hypercomplex numbers (representative rotation, in the present invention just generating tool axis vector), this is common interpolation, and institute is out of the question like linear interpolation (Linear interpolation is called for short Lerp).For Lerp and Slerp are compared, provide its formula below:

Common linear interpolation formula is: Lerp (q ₀, q ₁, h)=q ₀(1-h)+q ₁H (3)

The interpolation formula of Slerp is: Slerp (q ₀, q ₁, h)=q ₀(q ₀ ^-1Q ₁) ^h(4)

In the formula, h is an interpolation parameter, q ₀, q ₁---represent hypercomplex number;

---represent the inverse of hypercomplex number, its computing formula is:

$q_0^{-1}=\frac{q_0^{*}}{{\left|\right|q_0\left|\right|}^2}---\left(5\right)$

In the formula,

---represent the conjugation of hypercomplex number; || q ₀||---represent the mould of hypercomplex number; Conjugation, mould and other algorithms about hypercomplex number can be with reference to DAM E B, KOCH M, LILLHOLM M.Quaternions, Interpolation and Animation [R] .Copenhagen:University of Copenhagen, 1998.Planar, utilize formula (3) and (4), as shown in Figure 5 to the result of Lerp interpolation and Slerp interpolation.Can find out more evenly (having divided equally whole circular arc) of the interpolation result distribution of Slerp, this just can guarantee to insert, and working engagement of the cutting edge keeps even always in the process of milling.

The calculating of c, line-spacing, step pitch:

After having confirmed the interpolation of boundary vector, if the interpolation of boundary vector is too sparse, so insert mill processing after, the residual metal level in the runner can be excessive, even can appear at the situation of the towering kish of appearance between two adjacent slotting milling cutter paths; But simultaneously, the generating tool axis vector of interpolation can not be too dense, if too dense, mills finished surface though can access to insert preferably, because the feed number of times is too many, inserts the advantage of milling this high efficiency processing mode and also just exhausted.So confirming of line-spacing, step pitch also is vital.

Insert in traditional three-dimensional and to mill in the processing, as shown in Figure 1, line-spacing and step pitch phasing contrast really are easier to, and in the processing of five coordinates, definite difficulty that just becomes of line-spacing and step pitch.Mainly be because the variation of cutter shaft angle between the adjacent slotting milling cutter path causes the cutting scope to be an irregular conical region, as shown in Figure 6.

As shown in Figure 6, making the coordinate of the cutter heart point in two adjacent slotting miller steps is O ₁, O ₂, the die cavity upper surface is L to the line distance of cutter heart point, the intersection point at the cutter edge in two adjacent slotting miller steps is B, crosses the B point and does the vertical line of generating tool axis vector and intersect at P with generating tool axis vector ₁, P ₂Point, then

BP ₁＝BP ₂＝R （6）

In the formula, R---be tool radius,

With BP ₁O ₁O ₂P ₂The pentagon that forms that surrounds extracts, and is as shown in Figure 7, makes that C is O ₁O ₂The mid point of line, cross C and be BP ₁Vertical line meet at the D point, cross O ₁The vertical line that point is CD meets at the E point, and the angle of the generating tool axis vector of name adjacent process steps is the inclination angle distance, representes with β; Make the long L of being of BC, O ₁O ₂Long for H, because BD+DP ₁=R is at Δ CBD and Δ CO ₁Among the E,, can obtain equality according to the triangle geometric relationship:

$L\sin \frac{\mathrm{\&beta;}}{2}+\frac{\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">H</figure-callout>}}{2}\cos \frac{\mathrm{\&beta;}}{2}=R---\left(7\right)$

According to the interpolation principle, as shown in Figure 4, the angle that makes each row bound vector is A, and the distance between the boundary vector cutter heart point is H ₀, because interpolation algorithm will evenly carry out interpolation between boundary vector, promptly step pitch is identical, and the inclination angle is apart from also identical, and the two is proportional, so can obtain equality:

$\frac{\mathrm{\&beta;}}{A}=\frac{H}{H_0}---\left(8\right)$

Simultaneous equality (7) and (8) obtain a binary nonlinear system of equations

$\left\{\begin{array}{c}L\sin \frac{\mathrm{\&beta;}}{2}+\frac{\mathrm{<figure-callout\; id="2"\; label="H"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">H</figure-callout>}}{2}\cos \frac{\mathrm{\&beta;}}{2}=R\\ \frac{\mathrm{\&beta;}}{A}=\frac{H}{H_0}\end{array}\right.---\left(9\right)$

Wherein L, R, A and H ₀Be known number, β and H are unknown number, because this is a binary nonlinear system of equations, can't try to achieve its result by hand, can only adopt the quasi-Newton method in the numerical analysis can calculate the result;

After trying to achieve the value of β and H, just obtained average step pitch and inclination angle distance, just confirmed at the interpolation result of line direction so.

At the interpolation result of column direction, just the calculating principle of line-spacing is identical with the computing method of step pitch, just is not the boundary vector of each row by the vector of interpolation, but the boundary vector at blade two ends, H ₀Length also should be blade wheel hub surface length of a curve.

The calculating of d, cutter heart point:

It also is very important inserting the calculating of milling cutter heart point in the process tool trajectory planning at five coordinates.If there is not the calculating of cutter heart point, just can't obtain inserting the slotting degree of depth of milling of milling processing, also can not be applied in the engineering reality.

Cutter heart point principle of calculating is that boundary vector (being generating tool axis vector) is abstracted into space line; The intersection point of the offset plane (this example is the offset plane of circular cross-section wheel hub surface) of generating tool axis vector (space line) and wheel hub surface is asked in calculating, is the coordinate position of cutter heart point;

In the computational geometry field, the computing method of find intersection have a variety of, because the wheel hub cross section of impeller of the present invention is a circular cross-section, so adopt analytic geometry method to calculate intersection point.

The calculating of cutter heart point among the above-mentioned steps d, promptly the intersection algorithm of generating tool axis vector and wheel hub surface is following:

According to the ultimate principle of computational geometry, a circular cross-section can be expressed as around the postrotational surface equation of Z axle:

$f(x,y,z)={(\sqrt{x^2+y^2}-x_0)}^2$

$+{(z-z_0)}^2-{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">R</figure-callout>}}^2=$ （10）

$x^2+y^2-2x_0\sqrt{x^2+{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}$

$+x_0^2+z^2-2z_{0}z+z_0^2-{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">R</figure-callout>}}^2$

The equation of the space line that generating tool axis vector is abstracted into is:

$\left\{\begin{array}{c}x=(1-t)x_1+{\mathrm{tx}}_2\\ y=(1-t)y_1+{\mathrm{ty}}_2\\ z=(1-t)z_1+t{z}_2\end{array}\right.---\left(11\right)$

Equation (11) is brought in the equation (10), can obtains following One-place 2-th Order nonlinear equation:

$f\left(t\right)={[(1-t)x_1+{\mathrm{tx}}_2]}^2+{[(1-t)y_1+{\mathrm{ty}}_2]}^2$

$-2x_0\sqrt{{[(1-t)x_1+{\mathrm{tx}}_2]}^2+{[(1-t)y_1+{\mathrm{ty}}_2]}^2}---\left(12\right)$

$+x_0^2+{[(1-t)z_1+{\mathrm{tz}}_2]}^2-2[(1-t)z_1+{\mathrm{tz}}_2]z_0$

$+z_0^2-{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="120629121100.png,120629121121.png"\; state="\{\{state\}\}">R</figure-callout>}}^2=0$

Though this equation form more complicated; But because be quadratic equation with one unknown about parametric t; So the bisection method in the simple applied numerical analysis just can be tried to achieve its t as a result; Bring t into formula (11), can be and plug in the cutter heart point coordinate that mills this work step of processing in the hope of the intersection point of the offset plane and the generating tool axis vector of wheel hub surface.

E, cutter path planning: fluting processing, the processing of expansion groove, the finishing of ruled surface impeller;

The processing of f, completion ruled surface impeller part.

Emulation and experiment processing checking:

Utilize this ruled surface impeller five coordinates of the present invention to insert milling method, can directly generate the slotting process tool track that mills of five coordinates of impeller class part.Fig. 4 and Fig. 8 utilize the moulding result of the inventive method to impeller.

The foliage leaf wheel-class parts has geometrical symmetry, as long as generate the cutter path of a runner, the cutter path of all the other runners can and be duplicated generation through rotation.So the present invention only generates cutter path according to a runner, all the other are just passable through duplicating.According to slotting milling cutter method for planning track proposed by the invention, the cutter path that calculates is as shown in Figure 8.

Because five coordinates processing more complicated is cut and interference problem in order to prevent in reality processing, to cause.On lathe, carry out actual first being processed, carry out the simulating, verifying of cutter path usually by computer software, whether the inspection cutter path is correct with rearmounted processing.The cutter path that adopts the VERICUT software verification to generate, as shown in Figure 9.

Owing to insert the singularity mill processing, utilize VERICUT to carry out emulation to the shear action between cutter and the machined material and effect merely in addition, that must carry out that actual cutting experiment can verify this paper slottingly mills whether process algorithm feasible., a turning axle carried out actual cut experiment on being five coordinate lathes of B, C axle, shown in the photo in other documentary evidences 1, photo 2 for this reason.The cutter that adopts is the rose cutter of diameter 6mm.

Photo 1 is inserted for last runner and is milled a work step in the processing, and photo 2 is for inserting the impeller part that mills after roughing is accomplished.Be different from the conventional milling cutting method, insert the impeller wheel surface that mills after machining and present cataphracted tool marks, rather than be the nemaline track of radiation.

Be about 30 minutes the process time of a runner of this impeller, adds the accurately machined time, is no more than 50 minutes.And use conventional methods, on this lathe, identical cutter, identical speed of feed needs 1 hour at least.It is thus clear that this slotting milling method of the present invention has improved working (machining) efficiency to a certain extent.

Conclusion: the present invention proposes a kind of ruled surface impeller class part five coordinates and insert milling method, use hypercomplex number spherical coordinates interpolation method and obtained five coordinates and insert and mill the interpolation generating tool axis vector in the processing; Emphasis has solved multi-coordinate and has inserted and mill the definite of line-spacing and step pitch in the processing; Set up the slotting process tool track that mills of impeller part; Remedied prior art and inserted the deficiency of milling aspect the working ability, improved the roughing efficient of integral wheel, guaranteed to insert and milled material processed clearance and working (machining) efficiency at five coordinates; Simultaneously in VERICUT machining simulation software, carried out the machining simulation checking, and on five coordinate lathes of B, C turning axle, carried out actual inserting and milled machining experiment.Emulation and machining experiment prove that slotting milling method of the present invention has been taken into account rough machined material removing rate of impeller part and working (machining) efficiency, for the roughing technology of impeller part provides new selection scheme.

Claims (4)

1. ruled surface impeller five coordinates are inserted milling method; It is characterized in that: according to the skew boundary vector of ruled surface blade; Utilize the hypercomplex number interpolation method calculate to insert to mill the generating tool axis vector of processing, propose and confirmed that five coordinates insert line-spacing, the step pitch of milling processing, cook up the cutter machining locus; Thereby workpiece is processed, and these method concrete steps are following:

The generation of a, boundary vector:

In engineering, the expression way of the parametric equation of ruled surface is:

P(u,v)＝(1-v)Q(u)+vW(u) （1）

Wherein W (u) and Q (u) are respectively ruled surface vane top line and blade root line, u, v be respectively u to v to parameter; By leg-of-mutton geometric relationship, the mathematical model of setting up the computation bound vector gets following system of equations:

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

R is a tool radius in the formula, and L is middle P ₁P ₂Length, γ is P ₁C ₁And P ₂C ₂Angle, α is P ₁C ₁And C ₁C ₂Angle, d is the offset distance of the relative blade of cutter; This system of equations is a non-linear equation with two unknowns group, and wherein α and d are unknown number; α that the group of solving an equation is tried to achieve and the value of d, calculating the vector that departs from the ruled surface distance to a declared goal is boundary vector;

The interpolation of b, boundary vector:

Be between boundary vector, to fill (interpolation) vector uniformly as plugging in the cutter shaft orientation of milling processing; Like this; Generated at above-mentioned steps a under the situation of boundary vector, through reasonably boundary vector being carried out interpolation, the final processing of accomplishing the die cavity that boundary vector surrounded;

Rotatablely move and adopt the Quaternion Representation mode; Generate the cutter path of even excision amount with the hypercomplex number method of interpolation; Guarantee that working engagement of the cutting edge keeps even always in the slotting process of milling; Mill the generating tool axis vector employing spherical coordinates linear interpolation arithmetic Spherical Linear Interpolation that processing generates interpolation to inserting, be called for short Slerp, the interpolation formula of Slerp is:

Slerp(q ₀,q ₁,h)＝q ₀(q ₀ ^-1·q ₁) ^h （4）

In the formula, h is an interpolation parameter, q ₀, q ₁---represent hypercomplex number;

---represent the inverse of hypercomplex number, its computing formula is:

$q_0^{-1}=\frac{q_0^{*}}{{\left|\right|q_0\left|\right|}^2}---\left(5\right)$

In the formula,

---represent the conjugation of hypercomplex number; || q ₀||---represent the mould of hypercomplex number;

The calculating of c, line-spacing, step pitch:

Owing to the variation of cutter shaft angle between the adjacent slotting milling cutter path, causing the cutting scope is an irregular conical region in the processing of five coordinates, and making the coordinate of the cutter heart point in two adjacent slotting millers steps is O ₁, O ₂, the die cavity upper surface is L to the line distance of cutter heart point, the intersection point at the cutter edge in two adjacent slotting miller steps is B, crosses the B point and does the vertical line of generating tool axis vector and give P mutually with generating tool axis vector ₁, P ₂Point, then

BP ₁＝BP ₂＝R （6）

In the formula, R---be tool radius,

With BP ₁O ₁O ₂P ₂The pentagon that forms that surrounds extracts, and makes that C is O ₁O ₂The mid point of line, cross C and be BP ₁Vertical line meet at the D point, cross O ₁The vertical line that point is CD meets at the E point, and the angle of the generating tool axis vector of name adjacent process steps is the inclination angle distance, representes with β; Make the long L of being of BC, O ₁O ₂Long for H, because BD+DP ₁=R is at △ CBD and △ CO ₁Among the E,, can obtain equality according to the triangle geometric relationship:

$L\sin \frac{\mathrm{\&beta;}}{2}+\frac{H}{2}\cos \frac{\mathrm{\&beta;}}{2}=R---\left(7\right)$

According to the interpolation principle, the angle that makes each row bound vector is A, and the distance between the boundary vector cutter heart point is H ₀, obtain equality:

$\frac{\mathrm{\&beta;}}{A}=\frac{H}{H_0}---\left(8\right)$

Simultaneous equality (7) and (8) obtain a binary nonlinear system of equations

$\left\{\begin{array}{c}L\sin \frac{\mathrm{\&beta;}}{2}+\frac{H}{2}\cos \frac{\mathrm{\&beta;}}{2}=R\\ \frac{\mathrm{\&beta;}}{A}=\frac{H}{H_0}\end{array}\right.---\left(9\right)$

Wherein L, R, A and H ₀Be known number, β and H are unknown number, adopt the quasi-Newton method in the numerical analysis to calculate the result; After trying to achieve the value of β and H, obtain average step pitch and inclination angle distance, confirm interpolation result at line direction;

At the interpolation result of column direction, just the calculating principle of line-spacing is identical with the computing method of step pitch, just is not the boundary vector of each row by the vector of interpolation, but the boundary vector at blade two ends, H ₀Length also should be blade wheel hub surface length of a curve;

The calculating of d, cutter heart point:

Boundary vector is abstracted into space line, and the intersection point of the offset plane of computation bound vector and wheel hub surface is the coordinate position of cutter heart point;

E, cutter path planning: fluting processing, the processing of expansion groove, the finishing of ruled surface impeller;

The processing of f, completion ruled surface impeller part.

2. ruled surface impeller five coordinates according to claim 1 are inserted milling method; It is characterized in that: among the step a; The generation of boundary vector will be calculated through the tool radius that squints according to suction surface and pressure face, in order to leave surplus to finishing, on the basis of skew tool radius; The process redundancy that squints again, surplus is 0.1mm.

3. ruled surface impeller five coordinates according to claim 1 are inserted milling method, it is characterized in that: the calculating of cutter heart point in the steps d, and promptly the intersection algorithm of boundary vector and wheel hub surface is following:

The wheel hub cross section of ruled surface impeller is a circular cross-section, calculates intersection point with analytic geometry method, and circular cross-section can be expressed as around the postrotational surface equation of Z axle:

$f(x,y,z)={(\sqrt{x^2+y^2}-x_0)}^2$

$+{(z-z_0)}^2-R^2=$ （10）

$x^2+y^2-2x_0\sqrt{x^2+y^2}$

$+x_0^2+z^2-2z_{0}z+z_0^2-R^2$

The equation of the space line that boundary vector is abstracted into is:

$\left\{\begin{array}{c}x=(1-t)x_1+t{x}_2\\ y=(1-t)y_1+{\mathrm{ty}}_2\\ z=(1-t)z_1+t{z}_2\end{array}\right.---\left(11\right)$

Equation (11) is brought in the equation (10), can obtains following One-place 2-th Order nonlinear equation

$f\left(t\right)={[(1-t)x_1+t{x}_2]}^2+{[(1-t)y_1+{\mathrm{ty}}_2]}^2$

$-2x_0\sqrt{{[(1-t)x_1+{\mathrm{tx}}_2]}^2+{[(1-t)y_1+{\mathrm{ty}}_2]}^2}---\left(12\right)$

$+x_0^2+{[(1-t)z_1+{\mathrm{tz}}_2]}^2-2[(1-t)z_1+{\mathrm{tz}}_2]z_0$

$+z_0^2-R^2=0$

This equation is the quadratic equation with one unknown about parametric t, and the bisection method in the applied numerical analysis is tried to achieve its t as a result, brings t into formula (11), tries to achieve the offset plane of wheel hub surface and the intersection point of boundary vector, is to plug in the cutter heart point coordinate position of milling this work step of processing.

4. insert milling method according to claim 1,2 or 3 described ruled surface impeller five coordinates, it is characterized in that: for blade shape is the impeller of free form surface, and free form surface is fitted to ruled surface, processes again.

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