CN102248387B - Method for forming annular end tooth edge line of arc-shaped end tooth vertical mill - Google Patents

Abstract

The invention discloses a method for forming an annular end tooth edge line of an arc-shaped end tooth vertical mill. In the method, a tool making unit processes and forms the arc-shaped end tooth vertical mill according to a mathematical model built by a data control unit and parameter data output by the data control unit. The data control unit builds the mathematical model and output the parameter data by the following steps: inputting the diameter and helical angle of the tool; building the mathematical model of the end tooth edge line; building a mathematical model of the annular end tooth edge line by resolving equation of tangent at the end of a peripheral tooth edge line, resolving the intersection point of the extended line of a straight edge and the tangent at the end of the peripheral tooth edge line, determining the plane defined by the straight edge and the tangent at the end of the peripheral tooth edge line, and resolving the intersection line of the plane and an annular surface to form an annular edge line; and finally outputting the parameter data of the annular edge line to the tool manufacturing unit. The invention establishes a method for forming the end tooth straight edge line and annular edge line of a vertical mill, which is used for building the mathematical model of the annular vertical mill and instructing manufacturing and processing in order to ensure the smooth connection of the peripheral tooth edge line and the end tooth straight edge.

Description

The formation method of annular end tooth edge line of arc-shaped end tooth vertical mill

Technical field

The present invention relates to cutlery and make the field, particularly a kind of Circular Nose Cutting Edge line modelling method of the radius end mill for Digit Control Machine Tool processing.

Background technology

Radius end mill is the new structure cutter a kind of commonly used of Digit Control Machine Tool processing curve, in industry extensive application such as mould manufacturing, automobile making, space flight and aviation, the manufacturings of telecommunications product.In the Design and manufacture of radius end mill, the design of edge curve and sharpening processing are most important, because blade has not only determined the profile of cutter, thereby determine the shape (shaping adds man-hour) of finished surface, and cutter cutting ability, crudy are played an important role.In the grinding of traditional endless end tooth slotting cutter was made, owing to there is not the guiding of theoretical annular sword line model, annular end tooth rake face often adopted the mode of direct emery wheel feed to form, and produced easily and interfered, and formed breach at annular sword; In the sharpening of rear knife face, behind the annular sword behind knife face and the Zhou Ren smooth transition of knife face also be difficult to be guaranteed.

Summary of the invention

In view of the shortcoming of prior art, the objective of the invention is the modeling method that the present invention has set up a kind of slotting cutter end tooth straight line sword line and annular sword line, be used for setting up Mathematical Modeling and the controlled working of annular slotting cutter.

The objective of the invention is to realize by following means:

The formation method of annular end tooth edge line of arc-shaped end tooth vertical mill, cutter manufacturing cell is according to the Mathematical Modeling of DCU data control unit foundation and the supplemental characteristic machine-shaping circular arc end tooth slotting cutter of output, in its annular end land line moulding, DCU data control unit adopts following step to set up the supplemental characteristic of Mathematical Modeling and output:

1) input endless knife basic design parameters;

2) set up end tooth sword line Mathematical Modeling;

3) set up annular sword line Mathematical Modeling, comprise sequentially and carry out following steps: find the solution the terminal tangential equation of all land lines; Find the solution the intersection point of the terminal tangent line of straight line sword extended line and all land lines; Determined the terminal tangent plane of straight line sword and all land lines; Plane and anchor ring ask intergrowth to circularize the sword line;

4) output of annular sword line supplemental characteristic.

Adopt method of the present invention, the perfect formation method of annular end tooth edge line of arc-shaped end tooth vertical mill comprises end tooth straight line sword and annular sword.End tooth straight line sword has guaranteed that slotting cutter end tooth tooth partial center amount, tooth cross center amount and leaning angle, and annular sword line adopts plane curve, and itself and straight line sword and all land lines all are smoothly connected.The present invention has considered that also the radius end mill end tooth crosses center amount, and tooth partial center amount and leaning angle, and being smoothly connected of annular sword curve and straight line sword and all land lines are for Design of digital and the manufacturing of circular arc end tooth slotting cutter provides theoretical foundation.

Description of drawings is as follows:

Fig. 1 is general structure flow chart of the present invention.

Fig. 2 is end tooth straight line sword design diagram.Wherein 2a is that end tooth straight line sword left view 2b is end tooth straight line sword front view, and 2c is the partial enlarged drawing of theoretical end tooth straight line sword and actual end tooth straight line sword relation.

Fig. 3 is that annular sword line forms principle schematic.

Fig. 4 is end tooth sword line instance graph.Wherein 4a is end tooth straight line sword left view, and having leaning angle 4b in the end tooth straight line is end tooth straight line sword front view, and the straight line cutlery has tooth partial center amount and tooth to cross the center amount, and 4c is the schematic diagram of end tooth annular sword sword and straight line sword and all land linear light slips.

The specific embodiment:

The invention will be further described below in conjunction with drawings and Examples.

Fig. 1 is general structure flow process of the present invention, mainly comprises four steps:

1. select the endless knife basic design parameters: tool diameter, sword length, helical angle, all tooth cone angles, end tooth leaning angle, tooth partial center amount, tooth are crossed center amount etc.

2. set up the Mathematical Modeling of end tooth straight line sword according to the endless knife basic design parameters, comprise conversion and the actual introversion straight line of the straight line sword sword mathematical modeling of coordinate system;

3. set up the Mathematical Modeling of annular sword line, comprise by finding the solution the terminal tangential equation of all land lines and finding the solution straight line sword extended line and the intersection point of the terminal tangent line of all land lines, and determined the terminal tangent plane of straight line sword and all land lines, final formation plane and anchor ring ask intergrowth to circularize the sword line, realize the smooth transition of annular sword line and straight line sword and all tooth helical edges;

4. the annular sword line model that will obtain is exported to the Geometric Modeling that the cutter geometric modeling system can be supported cutter, outputs it to tool grinding analogue system and cutter manufacturing system, helps to improve the crudy of endless knife.

It specifically is treated to:

Tool diameter and helical angle that input is selected can be set up coordinate system O as shown in Figure 2 _r-X _rY _rZ _rWith local coordinate system O _l-X _lY _lZ _l, two coordinate origins overlap, and Z _lAxle and Z _rAxle overlaps, X _lAxle and X _rThe axle clamp angle is

Shown in the accompanying drawing 2a, end tooth straight line cutlery has leaning angle η, and Fig. 2 c is seen in the position of its end points K.

Among the accompanying drawing 2b, end tooth straight line cutlery has tooth partial center amount h.

Dotted line shown in the accompanying drawing 2c figure is theoretical introversion sword line (1), but because the existence of tooth partial center amount h, actual introversion straight line sword (2) can not conform to theoretical introversion sword line, therefore in the design of straight line sword, for guaranteeing its inclined angle, introversion straight line sword is crossed be positioned at theoretical inner conical surface (3) and ring surface (4) join some J on the circle and and X _lO _lZ _lPlane parallel and at X _lO _lZ _lThe projection line on plane and X _lThe axle clamp angle is theoretical leaning angle η.

According to geometrical relationship, obtain at coordinate system O _r-X _rY _rZ _rThe coordinate figure of mid point J, K is

Thereby obtain at coordinate system O _r-X _rY _rZ _rMiddle introversion sword line L ₁Equation and unit vector be

In the formula, t ₁Be parameter.

Finish the Mathematical Modeling of setting up annular sword line according to above end tooth introversion sword line Mathematical Modeling:

As shown in Figure 3, annular sword line (1) adopts plane sword line, namely obtain by anchor ring is crossing on a plane and the end sword, all be smoothly connected for guaranteeing annular sword and straight line sword and all swords, the tangent line (2) of all land line ends and the extended line (3) of end tooth straight line sword must be crossed in this plane.For this reason, must guarantee straight line L again ₁With straight line L ₂Intersect.Finding the solution mainly of annular sword line may further comprise the steps:

(1) finds the solution the terminal tangential equation of all land lines

The I that sets up an office is the end of all land lines, as shown in Figure 2.According to the definition of generalized helix, at coordinate system O _r-X _rY _rZ _rThe middle sword line tangent line L that crosses some I ₂The unit tangent vector be

$F_{L2}=\left[\begin{array}{c}-\cos \mathrm{\β}\sin \mathrm{\κ}\\ \sin \mathrm{\β}\\ \cos \mathrm{\β}\cos \mathrm{\κ}\end{array}\right]---\left(3\right)$

In the formula

β is the helical angle of all land lines in I point place;

κ is all tooth cone angles, and κ=0 o'clock is cylinder week tooth, and κ ≠ 0 o'clock is band cone angle week tooth.

Thereby can get tangent line L ₂Equation be

$\left\{\begin{array}{c}x=x_{\mathrm{Or}}+r_e\cos \mathrm{\κ}-t_2\cos \mathrm{\β}\sin \mathrm{\κ}\\ y=t_2\sin \mathrm{\β}\\ z=r_e\sin \mathrm{\κ}+t_2\cos \mathrm{\β}\cos \mathrm{\κ}\end{array}\right.---\left(4\right)$

In the formula, t ₂Be parameter

(2) find the solution the intersection point of the terminal tangent line of straight line sword extended line and all land lines

The equation group that must find the solution sword line tangent line and introversion sword line intersection point according to formula (1), (4) is

In the formula, t ₁, t ₂,

Be unknown quantity.

Can be solved by this formula

${\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA0000066828120000022.png"\; state="\{\{state\}\}">t</figure-callout>}}_1=\frac{-B+\sqrt{B^2-4\mathrm{AC}}}{2A}$

$t_2=\frac{B1-{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA0000066828120000022.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\sin \mathrm{\&eta;}}{\cos \mathrm{\&beta;}\cos \mathrm{\&kappa;}}$

In the formula

A＝(sin ²η-cos ²βcos ²κ)

B＝2[(A1sinκsinη+C1cos ²κcosη)cos ²β-B1sin ²βsinη]

C＝[A1 ²-(x _Or-r _esinη) ²cos ²κ]cos ²β+B1 ²sin ²β

A1＝x _Orcosκ+r _e(1-sinκcosη)

B1＝r _e(cosη-sinκ)

$\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HDA0000066828120000022.png"\; state="\{\{state\}\}">C</figure-callout>}1=\sqrt{{(x_{\mathrm{Or}}-r_e\sin \mathrm{\&eta;})}^2-h^2}$

Thereby determined t ₁, t ₂With

Relation between the three.

(3) determined the plane of the terminal tangent line of straight line sword and all land lines

According to known straight line L ₁With L ₂Direction vector, can try to achieve straight line L ₁With L ₂The plane normal vector be

Then cross straight line L ₁With L ₂Plane M equation can be written as

F _Mnx(x-A2)+F _Mny(y-B2)+F _Mnz(z-C2)＝0 (8)

In the formula

C2＝r _ecosη-t ₁sinη

(4) plane and anchor ring ask intergrowth to circularize the sword line

The equation of turning circle anchor ring can be expressed as

$\left\{\begin{array}{c}x=(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})\cos \mathrm{\&phi;}\\ y=(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})\sin \mathrm{\&phi;}(\mathrm{\&kappa;}\&le;\mathrm{\&theta;}\&le;\frac{\mathrm{\&pi;}}{2}+\mathrm{\&eta;},0\&le;\mathrm{\&phi;}<2\mathrm{\&pi;})\\ z=r_e\sin \mathrm{\&theta;}\end{array}\right.---\left(9\right)$

In the formula, θ, φ are variable, and satisfy $(\mathrm{\&kappa;}\&le;\mathrm{\&theta;}\&le;\frac{\mathrm{\&pi;}}{2}+\mathrm{\&eta;},0\&le;\mathrm{\&phi;}<2\mathrm{\&pi;})$

In conjunction with crossing straight line L ₁With L ₂Plane equation, obtain

F _Mnx[(x _Or+r _ecosθ)cosφ-A2]+F _Mny[(x _Or+r _ecosθ)sinφ-B2]+F _Mnz(r _esinθ-C2)＝0

(10)

In the formula, θ, φ are parameter.

In conjunction with sin ²φ+cos ²φ=1 can solve θ, and the relational expression between the φ is

$\left\{\begin{array}{c}\sin \mathrm{\&phi;}=\frac{F_{\mathrm{Mny}}(D-F_{\mathrm{Mnz}}{r}_e\sin \mathrm{\&theta;})\&PlusMinus;F_{\mathrm{Mnx}}\sqrt{(F_{\mathrm{Mnx}}^2+F_{\mathrm{Mny}}^2){(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})}^2-{(D-F_{\mathrm{Mnz}}{r}_e\sin \mathrm{\&theta;})}^2}}{(F_{\mathrm{Mnx}}^2+F_{\mathrm{Mny}}^2)(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})}\\ \cos \mathrm{\&phi;}=\frac{F_{\mathrm{Mnx}}(D-F_{\mathrm{Mnz}}{r}_e\sin \mathrm{\&theta;})m{F}_{\mathrm{Mny}}\sqrt{(F_{\mathrm{Mnx}}^2+F_{\mathrm{Mny}}^2){(x_{\mathrm{or}}+r_e\cos \mathrm{\&theta;})}^2-{(D-F_{\mathrm{Mnz}}{r}_e\sin \mathrm{\&theta;})}^2}}{(F_{\mathrm{Mnx}}^2+F_{\mathrm{Mny}}^2)(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})}\end{array}\right.---\left(12\right)$

In the formula

D＝A2F _Mnx+B2F _Mny+C2F _Mnz

Formula (12) substitution formula (9) is namely got annular sword curvilinear equation is

$\left\{\begin{array}{c}x=\frac{F_{\mathrm{Mnx}}(D-F_{\mathrm{Mnz}}{r}_e\sin \mathrm{\&theta;})m{F}_{\mathrm{Mny}}\sqrt{(F_{\mathrm{Mnx}}^2+F_{\mathrm{Mny}}^2){(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})}^2-{(D-F_{\mathrm{Mnz}}{r}_e\sin \mathrm{\&theta;})}^2}}{(F_{\mathrm{Mnx}}^2+F_{\mathrm{Mny}}^2)}\\ y=\frac{F_{\mathrm{Mny}}(D-F_{\mathrm{Mnz}}{r}_e\sin \mathrm{\&theta;})\&PlusMinus;F_{\mathrm{Mnx}}\sqrt{(F_{\mathrm{Mnx}}^2+F_{\mathrm{Mny}}^2){(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})}^2-{(D-F_{\mathrm{Mnz}}{r}_e\sin \mathrm{\&theta;})}^2}}{(F_{\mathrm{Mnx}}^2+F_{\mathrm{Mny}}^2)}(\mathrm{\&kappa;}\&le;\mathrm{\&theta;}\&le;\frac{\mathrm{\&pi;}}{2}+\mathrm{\&eta;})\\ z=r_e\sin \mathrm{\&theta;}\end{array}\right.---\left(13\right)$

According to formula (10), order

F＝F _Mnx[(x _Or+r _ecosθ)cosφ-A2]+F _Mny[(x _Or+r _ecosθ)sinφ-B2]+F _Mnz(r _esinθ-C2)＝0

According to $\frac{\mathrm{dF}}{\mathrm{d\&theta;}}=0$ Obtain

$\frac{\mathrm{d\&phi;}}{\mathrm{d\&theta;}}=\frac{F_{\mathrm{Mnx}}{r}_e\sin \mathrm{\&theta;}\cos \mathrm{\&phi;}+F_{\mathrm{Mny}}{r}_e\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}-F_{\mathrm{Mnz}}{r}_e\cos \mathrm{\&theta;}}{(F_{\mathrm{Mny}}\cos \mathrm{\&phi;}-F_{\mathrm{Mnx}}\sin \mathrm{\&phi;})}---\left(14\right)$

Obtaining annular sword curve unit tangent vector according to formula (9), (14) is

$\stackrel{\mathrm{ur}}{T}=\left[\begin{array}{c}{T}_x\\ T_y\\ T_z\end{array}\right]=\left[\begin{array}{c}\frac{-(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})\sin \mathrm{\&phi;}\frac{\mathrm{d\&phi;}}{\mathrm{d\&theta;}}-r_e\sin \mathrm{\&theta;}\cos \mathrm{\&phi;}}{\sqrt{{(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})}^2{\left(\frac{\mathrm{d\&phi;}}{\mathrm{d\&theta;}}\right)}^2+r_e^2}}\\ \frac{(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})\cos \mathrm{\&phi;}\frac{\mathrm{d\&phi;}}{\mathrm{d\&theta;}}-r_e\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}}{\sqrt{{(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})}^2{\left(\frac{\mathrm{d\&phi;}}{\mathrm{d\&theta;}}\right)}^2+r_e^2}}\\ \frac{r_e\cos \mathrm{\&theta;}}{\sqrt{{(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})}^2{\left(\frac{\mathrm{d\&phi;}}{\mathrm{d\&theta;}}\right)}^2+r_e^2}}\end{array}\right]$

Embodiment:

Choose the end tooth annular radius and be 3 slotting cutter as design example, its detail parameters is as follows:

Zhou Ren is equal helix angle sword line, helixangleβ=39 °, all tooth cone angle κ=4 °; End tooth leaning angle η=3 °, tooth partial center amount h=1, tooth cross center amount l=2.

The end tooth straight line sword that forms and annular sword are as shown in Figure 4.Shown in accompanying drawing 4a, end tooth straight line cutlery has leaning angle, and Fig. 4 b has showed partial center amount and the center of the mistake amount of straight line sword, the annular sword of end tooth shown in Fig. 4 c and end tooth straight line sword and all land linear light slips.

More than show and described principal character of the present invention, invention essence, basic principle, technological merit; and the specific embodiment; one skilled in the art will appreciate that; embodiment described here is in order to help reader understanding's principle of the present invention; without departing from the spirit and scope of the present invention; the present invention is based on other various changes and modifications that prior art can be known by inference, should be understood in protection scope of the present invention.

Claims (3)

1. the formation method of annular end tooth edge line of arc-shaped end tooth vertical mill, cutter manufacturing cell is according to the Mathematical Modeling of DCU data control unit foundation and the supplemental characteristic machine-shaping circular arc end tooth slotting cutter of output, in its annular end land line moulding, DCU data control unit adopts following step to set up the supplemental characteristic of Mathematical Modeling and output:

1) input tool diameter and helical angle;

2) set up end tooth introversion sword line Mathematical Modeling by the coordinate system conversion;

3) set up annular sword line Mathematical Modeling, comprise sequentially and carry out following steps: find the solution the terminal tangential equation of all land lines; Find the solution the intersection point of the terminal tangent line of straight line sword extended line and all land lines; Determined the terminal tangent plane of straight line sword and all land lines; Anchor ring asks intergrowth to circularize the sword line on described plane and the end sword;

4) output of annular sword line supplemental characteristic.

2. the formation method of described annular end tooth edge line of arc-shaped end tooth vertical mill according to claim 1 is characterized in that, the foundation of described end tooth introversion sword line Mathematical Modeling, and equation and the unit vector of end tooth introversion sword line Mathematical Modeling are after the coordinate system conversion:

In the formula, t ₁Be parameter, h is tooth partial center amount, and η is leaning angle,

Be X _lAxle and X _rThe axle clamp angle, F _L1Be introversion sword line L ₁Unit vector.

3. the formation method of described annular end tooth edge line of arc-shaped end tooth vertical mill according to claim 1 is characterized in that equation and the unit vector of described annular sword line Mathematical Modeling are:

Annular sword curve unit tangent vector $\stackrel{\&RightArrow;}{T}=\left[\begin{array}{cc}{T}_x& \\ T_y& \\ T_z& \end{array}\right]=\left[\begin{array}{c}\frac{-(x_{\mathrm{Or}}+r_c\cos \mathrm{\&theta;})\sin \mathrm{\&phi;}\frac{\mathrm{d\&phi;}}{\mathrm{d\&theta;}}-r_e\sin \mathrm{\&theta;}\cos \mathrm{\&phi;}}{\sqrt{{(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})}^2{\left(\frac{\mathrm{d\&phi;}}{\mathrm{d\&theta;}}\right)}^2+r_e^2}}\\ \frac{(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})\cos \mathrm{\&phi;}\frac{\mathrm{d\&phi;}}{\mathrm{d\&theta;}}-r_e\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}}{\sqrt{{(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})}^2}{\left(\frac{\mathrm{d\&phi;}}{\mathrm{d\&theta;}}\right)}^2+r_e^2}\\ \frac{r_e\cos \mathrm{\&theta;}}{\sqrt{{(x_{\mathrm{Or}}+r_e\cos \mathrm{\&theta;})}^2{\left(\frac{\mathrm{d\&phi;}}{\mathrm{d\&theta;}}\right)}^2+r_e^2}}\end{array}\right]$ ; θ, φ are parameter, and η is leaning angle.

Images