CN102581364B - Method for calculating milling load of ball-end milling cutter - Google Patents

Abstract

The invention discloses a method for calculating the milling load of a ball-end milling cutter, and the method comprises the following steps of: obtaining a relative position parameter model of the cutter and a workpiece, and determining all cutter micro-units participating in cutting according to the relative position parameter model of the cutter and the workpiece, calculating the cut-in angle, the cut-out angle and the instantaneous cutting thickness of each side-tilting milling micro-unit participating in cutting, calculating the cut-in angle, the cut-out angle and the instantaneous cutting thickness of each forward-tilting milling micro-unit participating in cutting each involved cutting, superimposing the instantaneous cutting thickness of each side-tilting milling micro-unit and the instantaneous cutting thickness of each forward-tilting milling micro-unit participating in cutting so as to obtain the instantaneous cutting thickness of a cutter micro-unit, and summing the instantaneous cutting thickness of all cutter micro-units participating in cutting so as to obtain the instantaneous milling load of the ball-end milling cutter. With the method of the invention, the instantaneous cutting state of a cutting edge and the workpiece and the cutting thickness can be obtained during side-tilting and forward-tilting milling of the cutter, so that predication about a cutting force during five-axis milling processing can be realized.

Description

Calculate the method for milling load of ball-end milling cutter

Technical field

The present invention relates to computer numerical control processing technique field, be specifically related to calculate in a kind of five-shaft numerical control processing the method for milling load of ball-end milling cutter.

Background technology

Rose cutter five axle millings are the complex-curved accurately machined technical ways of aero-engine impeller, blade space-like curved surface and mould class.Due to the complexity of part, thereby the axis direction that conventionally need to change cutter is avoided interfering.For predicting the cutting force of five axle milling process, reduce distortion and vibration in process, first need to calculate the momentary cutting thick of milling cutter cutting workpiece.

Modeling of Milling Forces for Ball-end Milling Cutter is generally divided into some discoid cutter infinitesimals by cutter along axis direction, by calculating cutting state and the infinitesimal cutting force of infinitesimal, then the cutting force of infinitesimal is superposeed and obtains whole Milling Force.Yet existing model is all generally in the situation that the relative position of cutter and workpiece more special (only have and roll or only lean forward) carries out Milling Force prediction, and adopts vector calculation method to obtain cutting load.Yet this method cannot reflect that infinitesimal cuts workpiece and cut out the true process of workpiece in one-period, also cannot calculate the milling load that rose cutter not only rolls but also leans forward.

Summary of the invention

The object of the invention is to the defect existing in existing milling force modeling, a kind of method of calculating milling load of ball-end milling cutter is provided, it can obtain instantaneous cutting state and the thickness of cutting of cutting edge and the workpiece of cutter when cutter rolls and leans forward milling, thereby realizes the prediction of five axle Milling Forces.

The present invention is achieved by the following technical solutions:

A method of calculating milling load of ball-end milling cutter, comprises the steps:

(1) obtain the relative position parameter model of cutter and workpiece;

(2) according to the relative position parameter model of cutter and workpiece, determine the whole cutter infinitesimals that participate in cutting, cutter infinitesimal comprises inclination milling infinitesimal and leans forward milling infinitesimal;

(3) according to the relative position parameter model of cutter and workpiece, calculate each entrance angle that participates in the inclination milling infinitesimal of cutting, cut out angle and momentary cutting thick;

(4) according to the relative position parameter model of cutter and workpiece, calculate each entrance angle that participates in the milling infinitesimal that leans forward of cutting, cut out angle and momentary cutting thick;

(5) momentary cutting thick of the milling infinitesimal that leans forward of the momentary cutting thick of each inclination milling infinitesimal and each participation cutting is superposeed, to obtain the momentary cutting thick of cutter infinitesimal;

(6) momentary cutting thick that participates in all cutter infinitesimals of cutting is sued for peace, to obtain the Instantaneous Milling load of rose cutter.

The present invention has following advantage and technique effect: by rose cutter working angles is decomposed, disclose the incision of cutter infinitesimal and the process that cuts out workpiece of the different axial locations of cutter, and the thickness of the instantaneous cutting of infinitesimal, obtain the cutting point of instantaneous participation cutting, thereby calculate the thickness of cutting in cutter inclination situation, to predict that five axles process instantaneous cutting force.

Accompanying drawing explanation

Fig. 1 is the flow chart that the present invention calculates the method for milling load of ball-end milling cutter

Fig. 2 is the relative tertiary location schematic diagram of cutter and workpiece.

Fig. 3 (a) is that to Fig. 3 (c) cutter sphere participates in the part of cutting and the relation of direction of feed.

Fig. 4 is the decomposing schematic representation of cutter infinitesimal direction of feed.

Fig. 5 is for rolling milling schematic diagram.

Fig. 6 (a) is the milling schematic diagram that leans forward.

Fig. 6 (b) is to the different milling view of Fig. 6 (e) for the milling infinitesimal that leans forward.

Fig. 7 (a) and (b) the milling load result that adopts the inventive method to calculate is shown.

The specific embodiment

Below in conjunction with drawings and Examples, the scheme of accepting of the present invention is described in further detail, but the present embodiment is not limited to the present invention.

The parameter of the rose cutter that the present invention adopts is as follows: 10 millimeters of diameters, and sword number is 4, helical angle 30 degree, surface to be machined is plane, and cutting way adopts groove milling mode, and cutting depth is 1 millimeter, and per tooth feeding is 0.1 millimeter.

As shown in Figure 1, the method that the present invention calculates milling load of ball-end milling cutter comprises the following steps:

1, obtain the relative position parameter model of cutter and workpiece;

As shown in Figure 2, T is tool axis direction, and cutting direction of feed is identical with X-direction, and the incline direction of cutter and angle are shown in right figure, O is the centre of sphere point of cutter, OA represents tool axis, and α represents tool axis and finished surface normal direction angulation, and φ represents the corner of cutter infinitesimal, be that tool axis is at the angle of finished surface projection and direction of feed X, A ' expression A point, in the projection (as shown in Fig. 3 (a) to (c)) of finished surface, when φ=0, is the milling of leaning forward; When φ=pi/2, for rolling milling.

2, according to the relative position parameter model of cutter and workpiece, determine the whole cutter infinitesimals that participate in cutting, cutter infinitesimal comprises inclination milling infinitesimal and the milling infinitesimal that leans forward, and the feed motion of cutter infinitesimal can be decomposed into the feed motion of inclination milling infinitesimal and lean forward the feed motion of milling infinitesimal;

As shown in Figure 4, the feeding of cutter infinitesimal can be divided into inclination milling feed f in the feed motion of cutter infinitesimal _cwith the milling feed f that leans forward _q, and calculated by following formula (1):

$\left\{\begin{array}{c}{f}_c=f\sin \mathrm{\φ}\\ f_q=f\cos \mathrm{\φ}\end{array}\right.---\left(1\right)$

The feeding that in formula, f is rose cutter.

As shown in Figure 5, θ represents the position angle of cutter infinitesimal, and establishing the region minimum bit angle setting that participates in cutting is θ _s, that maximum is θ _e,

$\left\{\begin{array}{c}{\mathrm{\θ}}_s=\mathrm{\α}-\arccos \frac{\left|\mathrm{OH}\right|}{R}\\ {\mathrm{\θ}}_e=\mathrm{\α}+\arccos \frac{\left|\mathrm{OH}\right|}{R}\end{array}\right.---\left(2\right)$

Work as θ _s< θ < θ _etime, infinitesimal participates in cutting.The radius that wherein R is rose cutter, | OH| represents that centre of sphere O is to the line segment length of intersection point H.

3, according to the relative position parameter model of cutter and workpiece, calculate each entrance angle that participates in the inclination milling infinitesimal of cutting, cut out angle and momentary cutting thick;

Roll milling cross section as shown in Figure 5, direction of feed is outside perpendicular to paper.For the different infinitesimals that participate in cutting, it is not identical that its incision cuts out angle.Position angle is the cutter infinitesimal at θ place, and its radius of clean-up is | AD|, cuts out angle Φ _ex, entrance angle Φ _stexpression formula is:

$\left\{\begin{array}{c}{\mathrm{\&Phi;}}_{\mathrm{st}}=\arccos (-\frac{\left|\mathrm{AC}\right|}{\left|\mathrm{AD}\right|})\\ {\mathrm{\&Phi;}}_{\mathrm{ex}}=2\mathrm{\&pi;}-{\mathrm{\&Phi;}}_{\mathrm{st}}\end{array}\right.---\left(3\right)$

In formula, | AC| with | the value of AD| can be passed through similar Δ BAC and Δ BHO:

$\left\{\begin{array}{c}\left|\mathrm{AC}\right|=\left|\mathrm{OH}\right|\&CenterDot;\frac{\left|\mathrm{AB}\right|}{\left|\mathrm{HB}\right|}=\left|\mathrm{OH}\right|\&CenterDot;\frac{\left|\mathrm{OB}\right|-\left|\mathrm{OA}\right|}{|\mathrm{OH}\&CenterDot;\tan \mathrm{\&alpha;}|}=\frac{|\mathrm{OH}\&CenterDot;\sec \mathrm{\&alpha;}|-|R\&CenterDot;\cos \mathrm{\&theta;}|}{\tan \mathrm{\&alpha;}}\\ \left|\mathrm{AD}\right|=R\&CenterDot;\sin \mathrm{\&theta;}\end{array}\right.---\left(4\right)$

In rolling milling, because tool axis is perpendicular to direction of feed, when the corner of cutter infinitesimal meet time, its thickness of cutting expression formula is:

Due to in variation desirable on the occasion of and negative value, so h _cmay be negative value, now represent that this blade is away from workpiece cutting surface.

4, according to the relative position parameter model of cutter and workpiece, calculate each entrance angle that participates in the milling infinitesimal that leans forward of cutting, cut out angle and momentary cutting thick;

As Fig. 6 (a), in the milling of leaning forward, the position angle of establishing the cutter infinitesimal of current participation cutting is θ, and the cutter infinitesimal position angle at this place of front cutting at one time is θ ', perpendicular to the feed engagement f of cutter axis orientation _θcan be expressed as:

±f _θ＝Rsinθ+f _qcosα-Rsinθ′(6)

Rcosθ＝Rcosθ′+f _qsinα (7)

Be f _θmeet equation with θ:

${(R\sin \mathrm{\&theta;}+f_q\cos \mathrm{\&alpha;}\stackrel{\&OverBar;}{+}{f}_{\mathrm{\&theta;}})}^2+{(R\cos \mathrm{\&theta;}-f_q\sin \mathrm{\&alpha;})}^2=R^2---\left(8\right)$

F in formula _qfor the feed engagement of the milling of leaning forward, in formula (6), in darker regions, get positive sign, in light areas, get negative sign, in formula (8), in contrast.

In the milling mode leaning forward, the instantaneous thickness of cutting of not being out of shape of infinitesimal is as Fig. 6.In Fig. 6 (a), dotted outline is the tooth feeding position of cutter before, the outline position that solid line is current cutting tool.While leaning forward milling, there are four exemplary position, four positions as shown in Fig. 6 (a) 1,2,3,4, Fig. 6 (b), (c), (d), (e) in cutter infinitesimal be A to plane.Position 1, before the corresponding infinitesimal cutting of current cutter, this place's workpiece was not cut by last position knives, and therefore the cutting state of corresponding infinitesimal is as shown in Fig. 6 (b), and hatching is expressed as orthogonal cutting; Position 2, as Fig. 6 (c), dotted line represents to be cut by last position knives, and before the corresponding infinitesimal cutting of current cutter, this place's workpiece was cut by last position knives, but current infinitesimal still can switch to surface of the work, and hatching is expressed as orthogonal cutting; Position 3, the cutting state of corresponding infinitesimal is as shown in Fig. 6 (d), before current corresponding infinitesimal cutting, this place's workpiece was cut by last position knives, but current infinitesimal can not switch to surface of the work, hatching is orthogonal cutting region, and cutter tooth is cut and cut out is negative cutting zone constantly; During position 4, as Fig. 6 (e), current cutter infinitesimal can not switch to workpiece, and cutter tooth is in negative cutting zone.

As shown in Fig. 6 (b), 1 place in position, the angular position theta of cutter infinitesimal meets following formula:

$\arccos \frac{R\cos {\mathrm{\&theta;}}_e+f_q\sin \mathrm{\&alpha;}}{R}\&le;\mathrm{\&theta;}<{\mathrm{\&theta;}}_e$

In formula, θ _eby formula (2), provided.

The O2 that sets up an office is d to horizontal distance _θ, be equal in formula (4) | AC|:

$d_{\mathrm{\&theta;}}=\frac{\left|\mathrm{OH}\right|\&CenterDot;\sec \mathrm{\&alpha;}-R\cos \mathrm{\&theta;}}{\tan \mathrm{\&alpha;}}$

Cutting out angle can be expressed as:

$\left\{\begin{array}{c}{\mathrm{\&Phi;}}_{\mathrm{st}}=\mathrm{\&pi;}-\arccos \frac{d_{\mathrm{\&theta;}}}{R\sin \mathrm{\&theta;}}\\ {\mathrm{\&Phi;}}_{\mathrm{ex}}=\mathrm{\&pi;}+\arccos \frac{d_{\mathrm{\&theta;}}}{R\sin \mathrm{\&theta;}}\end{array}\right.$

When cutter infinitesimal corner meet time, its thickness of cutting expression formula is:

Because be less than zero, so above formula positive sign.

The incision that in like manner can obtain position 2, position 3 and position 4 cutters cuts out angle and momentary cutting thick.

5, the momentary cutting thick of the milling infinitesimal that leans forward of the momentary cutting thick of each inclination milling infinitesimal and each participation cutting is superposeed, to obtain the momentary cutting thick of cutter infinitesimal;

Make α=45 °, φ=45 °, result of calculation is as Fig. 7 (a), and the curve in figure is the rotate a circle state of diverse location cutting workpiece of a blade of cutter, being less than or equal to null representation does not have cutting workpiece, is greater than the momentary cutting thick of null representation cutting workpiece.Visible in figure, the cutting maximum ga(u)ge of infinitesimal occurs in the instantaneous of incision workpiece, and thickness of cutting reduces in time gradually afterwards, until cut out workpiece.Make α=45 °, φ=10 °, result of calculation is as Fig. 7 (b), and the cutting maximum ga(u)ge of infinitesimal occurs in a certain moment after incision workpiece, can calculate the thickness of cutting of arbitrfary point on any time blade simultaneously.

6, the momentary cutting thick that participates in all cutter infinitesimals of cutting is sued for peace, to obtain the Instantaneous Milling load of rose cutter.

Claims (1)

1. a method of calculating rose cutter five axle milling loads, is characterized in that, comprises the steps:

(1) obtain the relative position parameter model of cutter and workpiece, in this step, the cutter centre of sphere point of rose cutter is defined as to O, tool axis is defined as OA, the projection of tool axis OA on finished surface is defined as OA ', between tool axis and finished surface normal direction, angulation is expressed as α, and the described projection OA ' of tool axis on finished surface and the angle between direction of feed are expressed as φ, build in this way the relative position parameter model between cutter and workpiece;

(2) according to the above-mentioned relative position parameter model of cutter and workpiece, determine the whole cutter infinitesimals that participate in cutting, described cutter infinitesimal comprises inclination milling infinitesimal simultaneously and leans forward milling infinitesimal, thus the feed motion of all cutter infinitesimals is decomposed into separately to the inclination milling infinitesimal feed motion and the milling infinitesimal feed motion of leaning forward that by following formula (), are represented:

(1)

Wherein, f _crepresent to roll the feed motion amount of milling infinitesimal, f _qrepresent the to lean forward feed motion amount of milling infinitesimal, the corner that represents each cutter infinitesimal, is also formed angle respectively between the projection of its corresponding tool axis on finished surface and direction of feed, and f represents the total feed of rose cutter;

(3) according to the above-mentioned relative position parameter model of cutter and workpiece calculate described each participate in cutting inclination milling infinitesimal entrance angle and cut out angle, based on following formula (two), calculate the momentary cutting thick h that each rolls milling infinitesimal simultaneously _c:

(2)

Wherein, f _crepresent that each rolls the feed motion amount of milling infinitesimal, its numerical value calculates in step (2);

(4) according to the relative position parameter model of described cutter and workpiece calculate described each participate in cutting the milling infinitesimal that leans forward entrance angle and cut out angle, based on following formula (three) and (four), calculate the momentary cutting thick h of each milling infinitesimal that leans forward simultaneously _q:

(3)

$d_{\mathrm{\&theta;}}=\frac{\left|\mathrm{OH}\right|\&CenterDot;\sec \mathrm{\&alpha;}-R\cos \mathrm{\&theta;}}{\tan \mathrm{\&alpha;}}$ (4)

Wherein, R represents the radius of rose cutter, and θ represents the position angle of each cutter infinitesimal, | OH| represents that the cutter centre of sphere of milling cutter is to the line segment length between its intersection point;

(5) momentary cutting thick of the milling infinitesimal that leans forward of the momentary cutting thick of described each inclination milling infinitesimal and described each participation cutting is superposeed, to obtain the momentary cutting thick of described cutter infinitesimal;

(6) momentary cutting thick that participates in all cutter infinitesimals of cutting is sued for peace, to obtain the Instantaneous Milling load of rose cutter.