CN102354151B - Tangential following interpolation method applied to multilayer shoe leather numerical control cutting machine tool - Google Patents

Abstract

The invention provides a tangential following interpolation method applied to a multilayer shoe leather numerical control cutting machine tool. A multilayer shoe leather high speed cutting processing process comprises high frequency vibration of a sheet shape cutter, plane motion of a cutter, and rotation of the sheet shape cutter in a processing process. A high frequency vibration direction is defined as a Z direction, and directions of the plane motion are defined as X and Y directions. In a process of cutting a straight line, according to a feeding speed F and an equivalent interpolation period T0, wherein, T0=nT, and T represents a unit interpolation period, a contour step l of each interpolation period is calculated, and a relation of F, T0 and l is l=FT0. Since a Z axis angle of linear tangential following interpolation is not changed, a linear tangential following interpolation formula is obtained after transformation. The tangential following interpolation method applied to the multilayer shoe leather numerical control cutting machine tool has the characteristics of high cutting precision and high work efficiency.

Description

A kind of tangential following interpolating method that is applied to multilayer shoe leather numerical control Cutting machine bed

Technical field

The present invention relates to be applied to the control method of multilayer shoe leather numerical control Cutting machine bed.

Background technology

Numerical control is cut out the technology of cutting and is included state-of-the-art mechanical technique, computing machine and the information processing technology, systems technology, automatic control technology, sensing and detection technique, servodrive technology.Along with the development of Numeric Control Technology, numerical control is cut out and is cut technology progressively towards future development open, intelligent, high speed.External leather is cut out the system of cutting and has been developed into integrated and intelligentized CNC integrated system,, although external advanced numerical control leather Cutting machine is powerful, but expensive, and China is taked technical monopoly and sealing policy.

For this technical method, relevant domestic research institution has also carried out certain exploration and research.The Zhang Jianhong of Shanghai University utilizes the mechatronics integration method to complete system to numerical control clothing tailoring machine; Lee of University Of Ningbo national wealth etc. has been studied the Control System Design of numerical control clothing tailoring machine.The Ding Wenjie of Xi'an Communications University has inquired into the Digital Program Control technology secondary development based on lattice cypress cutting.Shen Junjia has adopted and has been optimized, has adopted profile turning based on Bezier to seamlessly transit tailoring technique based on cutter point optimization method under the Cutter of adaptive M MAS ant group algorithm to lower cutter point the excessive turning of curve is processed.The Zhu Nianjun of Zhejiang University has inquired into the cutter Control System Design that is used for leather.When the Zhao Yi of Shanghai University has analyzed at the peak cutter work, the actual complex stressing conditions of Cutter, carried out detailed discussion to Cutter correction problem, and adopt the method for fuzzy control, processes the problem of cutter Cutter deflection angle under different stressing conditions.The Chen Zi of Zhejiang University occasion and Wang Wen in conjunction with the great project for bidding in Zhejiang Province " the quasi-flexible manufacturing technology of leather and fur products exploitation (2003C11023); developed the leather cutting process automation system of a cover, and applied for national inventing patent function integrated numerically controlled automatic leather cutting method (200610155436.3).

Present domestic correlative technology field is mainly studied cutter path planning and speed control, wherein mostly is aimed at individual layer leather sanction and cuts processing.Because the individual layer leather is cut out tapping with technology such as laser, high speed water ions, " cut constantly " for multilayer shoe leather, so production efficiency is extremely low.Cutting die stamping-out technology is the more multilayer shoe leather process technology of present domestic application, but low due to automaticity, deposit the cutting die space and have greatly again certain risk, is therefore eliminated by modern enterprise gradually.Under such technical background condition, the multilayer shoe leather numerical control Cutting machine arises at the historic moment.It is that the sheet cutter of dither is cut out in real time according to planned trajectory multilayer shoe leather and cut that multilayer shoe leather is cut out what cut that control technology adopts.Therefore due to the schistose texture of dither cutter, must guarantee that sanction cuts sheet cutter and sanction in process and cut the path and keep in real time the state that cuts mutually.Otherwise directly cause two kinds of situations: the one, can complete to cut out and cut in process, because Cutter direction of motion and edge direction are inconsistent, but when angle is not again very large, cause sanction to cut precision and efficient reduces greatly; The 2nd, work as Cutter direction of motion and cutting edge angle and reach certain value, when even vertical, can not complete to cut out and cut process, the Cutter tool fractures or twists off.

Summary of the invention

Cut in order to overcome the existing sanction that is applied to multilayer shoe leather numerical control Cutting machine bed cutter path planning technology that precision is lower, ineffective deficiency, the invention provides a kind of sanction and cut that precision is high, the tangential following interpolating method that is applied to multilayer shoe leather numerical control Cutting machine bed of high efficiency.

The technical solution adopted for the present invention to solve the technical problems is:

A kind of tangential following interpolating method that is applied to multilayer shoe leather numerical control Cutting machine bed, described multilayer shoe leather is cut out at a high speed the dither that cuts process and comprise the sheet cutter, the plane motion of Cutter tool and the rotation in sheet tool sharpening process, definition dither direction is the Z direction, and definition plane motion direction is X, Y-direction;

Cut in the process of straight line in sanction, Z axis is independent axes and not linking with the XY axle, and the starting point coordinate of known straight line is p _s(x _s, y _s), terminal point coordinate is p _e(x _e, y _e), the start angle value representation of straight-line segment is (unit for °):

Carry out the drift angle and revise that to obtain final cutter start angle be θ ' _s=θ _s-α.

According to speed of feed F and the equivalent interpolation cycle T in the processing instruction ₀, T ₀=nT, T representation unit interpolation cycle calculates the profile step-length l of each interpolation cycle, and three's relation table is shown: l=FT ₀, the Z axis angle of following interpolation due to rectilinear tangential is constant, so there have rectilinear tangential to follow the interpolation formula to be as follows:

$\left\{\begin{array}{c}\mathrm{\Δx}=l\cos a=l\frac{x_e-x_s}{\sqrt{{(x_e-x_s)}^2+{(y_e-y_s)}^2}}\\ \mathrm{\Δy}=\mathrm{\Δ}x\tan a=\frac{\mathrm{\Δx}(y_e-y_s)}{x_e-x_s}\\ \mathrm{\Δc}=0\end{array}\right.---1-2$

For every section straight line, c is constant, obtains by the relation of x and y, obtains rectilinear tangential through conversion and follows the interpolation formula:

$\left\{\begin{array}{c}{x}_{i+1}=x_i+\mathrm{\Δx}\\ y_{i+1}=y_i+\mathrm{\Δy}\\ c_{i+1}={\mathrm{\θ}}_s^{\′}\end{array}\right.---1-3.$

Further, if the known sanction section of cutting circular arc

Be contrary circular arc, the circular arc starting point is P _s(x _s, y _s, c _s), terminal point is P _e(x _e, y _e, c _e), center of circle O is true origin, and the Z coordinate figure is equivalent to the line in current point and the center of circle and the angle of X-axis forward, and the parametric equation of processed curve can be expressed as:

$\left\{\begin{array}{c}x=R\cos \mathrm{\φ}\\ y=R\sin \mathrm{\φ}\\ c=\mathrm{\φ}+\mathrm{\π}/2\end{array}\right.---1-4$

Wherein R is arc radius, and φ is the line in current point and the center of circle and the angle of X-axis forward.

In the process of cutting out the cyclotomy arc, Z axis will keep making blade constantly consistent with circular arc secant direction with the interlock of XY axle, at first will obtain according to the circular arc starting point corner of cutter starting point, and the starting point coordinate of known arc section is p _s(x _s, y _s), terminal point coordinate is p _e(x _e, y _e), central coordinate of circle is p _o(x _o, y _o), the start angle value representation is:

When contrary circular arc sanction is cut,

When cutting along the circular arc sanction,

If P _i(x _i, y _i, c _i) be cutter current location point, the interpolation calculation requirement arrives the next position P after through an interpolation cycle _i+1(x _i+1, y _i+1, c _i+1), P _iThe coordinate of point is:

$\left\{\begin{array}{c}{x}_i=R\cos {\mathrm{\φ}}_i\\ y_i=R\sin {\mathrm{\φ}}_i\\ c_i={\mathrm{\φ}}_i+\mathrm{\π}/2\end{array}\right.---1-5$

In case equivalent interpolation cycle T during the interpolation of circular arc tangential following ₀Determine with feed line speed V, its interpolation step angle α is:

$\mathrm{\&alpha;}=\frac{\mathrm{\&omega;T}}{n}=\mathrm{\&omega;}{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000081116480000042.png,HDA0000081116480000052.png"\; state="\{\{state\}\}">T</figure-callout>}}_0=\frac{V}{R}{T}_0---1-6$

If in Interpolation Process, the coordinate P of current point _i(x _i, y _i, c _i) known, in order to obtain the feeding increment on two coordinate directions, obtain through next interpolated point P after an interpolation cycle _i+1(x _i+1, y _i+1, c _i+1):

$\left\{\begin{array}{c}{x}_{i+1}=R\cos ({\mathrm{\&phi;}}_i+\mathrm{\&alpha;})\\ y_{i+1}=R\sin ({\mathrm{\&phi;}}_i+\mathrm{\&alpha;})\\ c_{i+1}={\mathrm{\&phi;}}_i+\mathrm{\&alpha;}\end{array}\right.---1-7$

Cutter is along X, Y, C amount of feeding Δ x _i+1, Δ y _i+1, Δ c _i+1For:

$\left\{\begin{array}{c}{\mathrm{\&Delta;x}}_{i+1}=R[\cos ({\mathrm{\&phi;}}_i+\mathrm{\&alpha;})-\cos {\mathrm{\&phi;}}_i]\\ {\mathrm{\&Delta;y}}_{i+1}=R[\sin ({\mathrm{\&phi;}}_i+\mathrm{\&alpha;})-\sin {\mathrm{\&phi;}}_i]\\ {\mathrm{\&Delta;c}}_{i+1}=\mathrm{\&alpha;}\end{array}\right.---1-8$

Formula 1-3 abbreviation is got:

$\left\{\begin{array}{c}{x}_{i+1}=x_i\cos \mathrm{\&alpha;}-y_i\sin \mathrm{\&alpha;}\\ y_{i+1}=y_i\cos \mathrm{\&alpha;}+x_i\sin \mathrm{\&alpha;}\\ c_{i+1}=c_i+\mathrm{\&alpha;}\end{array}\right.---1-9$

Set tan (α/2) ≈ α/2, thereby have:

$\cos \mathrm{\&alpha;}=\frac{1-{\left(\frac{\mathrm{\&alpha;}}{2}\right)}^2}{1+{\left(\frac{\mathrm{\&alpha;}}{2}\right)}^2}=\frac{4-{\mathrm{\&alpha;}}^2}{4+{\mathrm{\&alpha;}}^2}---1-10$

In like manner have:

$\sin \mathrm{\&alpha;}=\frac{4\mathrm{\&alpha;}}{4+{\mathrm{\&alpha;}}^2}---1-11$

Make A _i=cos α, B _i=sin α, data sampling method tangential following interpolation formula is:

$\left\{\begin{array}{c}{x}_{i+1}=A_i{x}_i-B_i{y}_i\\ y_{i+1}=A_i{y}_i+B_i{x}_i\\ c_{i+1}=c_i+\mathrm{\&alpha;}\end{array}\right.---1-12$

The feeding increment of each axle is:

$\left\{\begin{array}{c}{\mathrm{\&Delta;x}}_{i+1}=x_{i+1}-x_i\\ {\mathrm{\&Delta;y}}_{i+1}=y_{i+1}-y_i\\ {\mathrm{\&Delta;c}}_{i+1}=c_{i+1}-c_i\end{array}\right.---1-13.$

Technical conceive of the present invention is: be applied to the multilayer shoe leather numerical control sanction and cut in process, keep in real time the sheet Cutter and cut out the interpolating method that cuts the tangent state in path, comprise: the sanction for straight line path is cut, to cut the path tangent with sanction in real time for Cutter, the interpolation operation that does not therefore need to carry out the tangential following motion.But because the cut leather number of plies may difference namely be cut the gross thickness difference, cutting force increases and increases gradually along with cutting thickness; Even same cutting thickness, cutting force increases gradually along with the increase of cutting speed.Therefore be to guarantee that in the lathe course of work, cutting force equates, and then guarantee that machine tool motion is relatively steady, along with the increase of the number of plies, correspondingly shorten interpolation cycle, namely improve interpolation rate, having reached lathe still can smooth working because of cutting hides number of plies difference, enhances productivity; Be the angle that straight line forms for cutting path, adopt and " griffe the "+rotation mode that angle+" roll setting " mode is processed;

To transition arc, enter the front pre-service reduction of speed mode that adopts of circular arc; Adopt the pre-service accelerated mode before breaking away from circular arc.And adjust according to number of plies acceleration degree, the retarded velocity of pre-treating speed is along with the increase linearity of the number of plies reduces, to improve the stability of lathe.Simultaneously calculate the difference between initial angle and end angle according to two circular arc end points, central coordinate of circle, the synchronism according to feed motion and tangential following motion calculates interpolation rate and derives interpolating method; To initial circular arc, enter and adopt the pre-service accelerated mode after circular arc, adopt the pre-service accelerated mode before breaking away from circular arc, acceleration magnitude also with the linear inverse relation of the number of plies.Simultaneously calculate initial angle and end angle difference according to two circular arc end points, central coordinate of circle, the synchronism according to feed motion and tangential following motion calculates interpolation rate and derives interpolating method; To stopping circular arc, adopt the pre-service ways of deceleration before entering circular arc, adopt pre-service reduction of speed mode before breaking away from circular arc, acceleration magnitude also with the linear inverse relation of the number of plies.Simultaneously calculate initial angle and end angle difference according to two circular arc end points, central coordinate of circle, the synchronism according to feed motion and tangential following motion calculates interpolation rate and derives interpolating method.

For small arc-shaped, introduce lathe minimum process circular arc and define as " critical circular arc ", and have processing " critical circular arc " to replace than its less circular arc; For the super large circular arc, because its curvature is very little, satisfying under the precondition of machining precision, " the replace curve by straight line is repeatedly griffed " mode of employing is cut out and is cut processing.

Beneficial effect of the present invention is mainly manifested in: be directed to numerical control shoe leather Cutting machine and cut out at a high speed in the process of cutting, lathe can make the dither cutter keep cutting mutually state---tangential following interpolation technique with the feed motion rail in real time in feed motion.By this interpolating method, the technician only need cut out according to the footwear leather and cut intensity, the footwear leather is cut out and cut the number of plies and processing technology requirement, inputs and regulate correspondingly technical data, just can complete the multilayer shoe leather sanction high-efficiency high-accuracy and cut work.In addition, this tangential following method can also extend to apparel industries such as processing cloth in the same sanction mode of cutting and promotes.

Description of drawings

Fig. 1 is the schematic diagram of feed motion (X, Y) and tangential following motion (Z rotation).

Fig. 2 is tangential following linear interpolation process flow diagram.

Fig. 3 is tangential following interpolation process flow diagram.

Fig. 4 is tangential following linear interpolation schematic diagram.

Fig. 5 is the tangential schematic diagram of circular arc.

Fig. 6 is all quadrants Z axis angle schematic diagram in contrary circular arc.

Fig. 7 is along all quadrants Z axis angle schematic diagram in circular arc.

Fig. 8 is without tangential following interpolation technique design sketch.

Fig. 9 has tangential following interpolation technique design sketch.

Embodiment

The invention will be further described below in conjunction with accompanying drawing.

With reference to Fig. 1, Fig. 1 is the schematic diagram of feed motion and tangential following motion, shown in this figure: multilayer shoe leather is cut out at a high speed and is cut in process, there is three movement: main motion---the dither (Z direction) of sheet cutter, complete the sanction of multilayer shoe leather and cut motion, realize that cutter cuts the sanction of multilayer shoe leather; Cutter tool moving along CAD stock layout track completed in the plane motion of feed motion---Cutter tool (X, Y-direction); Synkinesia---the rotation (Z in sheet tool sharpening process

Direction), i.e. tangential following motion is completed multilayer shoe leather and is cut out and cut in process the sheet cutter and remain that to cut the track tangential direction consistent with sanction, realizes that cutter cuts out the cutter compensation that cuts to multilayer shoe leather.

Fig. 2 is multilayer shoe leather numerical control Cutting machine tangential following linear interpolation algorithm flow chart.

Cut in the process of straight line in sanction, because the cutter blade direction remains unchanged, Z axis is independent axes and not linking with the XY axle.It is just passable that Z axis only needs to rotate to the straight line direction vector before taking the air line, and straight line unit's number of plies interpolation cycle be multiply by a factor of n (n represents the leather number of plies).Therefore, the key of the tangential following of straight-line segment control is to obtain the corner of cutter starting point.The starting point coordinate of known straight line is p _s(x _s, y _s), terminal point coordinate is p _e(x _e, y _e), the start angle value of straight-line segment can be expressed as (unit for °):

Consider that cutter has alignment error, Cutter may with return the cutter raw bits and be equipped with a drift angle α, to this, can carry out the drift angle and revise that to obtain final cutter start angle be θ ' _s=θ _s-α.

According to speed of feed F and the equivalent interpolation cycle T in the processing instruction ₀(T ₀=nT, T representation unit interpolation cycle), calculate the profile step-length l of each interpolation cycle, three's relation can be expressed as: l=FT ₀The Z axis angle of following interpolation due to rectilinear tangential is constant, so there have rectilinear tangential to follow the interpolation formula to be as follows:

$\left\{\begin{array}{c}\mathrm{\&Delta;x}=l\cos a=l\frac{x_e-x_s}{\sqrt{{(x_e-x_s)}^2+{(y_e-y_s)}^2}}\\ \mathrm{\&Delta;y}=\mathrm{\&Delta;}x\tan a=\frac{\mathrm{\&Delta;x}(y_e-y_s)}{x_e-x_s}\\ \mathrm{\&Delta;c}=0\end{array}\right.---1-2$

For every section straight line, c is constant, can obtain by the relation of x and y.Can obtain rectilinear tangential through conversion and follow the interpolation formula:

$\left\{\begin{array}{c}{x}_{i+1}=x_i+\mathrm{\&Delta;x}\\ y_{i+1}=y_i+\mathrm{\&Delta;y}\\ c_{i+1}={\mathrm{\&theta;}}_s^{\&prime;}\end{array}\right.---1-3$

Fig. 6 is multilayer shoe leather numerical control Cutting machine tangential following arc interpolation process flow diagram.

If known procedure section circular arc

Be contrary circular arc, the circular arc starting point is P _s(x _s, y _s, c _s), terminal point is P _e(x _e, y _e, c _e), center of circle O is true origin, by accompanying drawing 5 as can be known the Z coordinate figure be equivalent to the line in current point and the center of circle and the angle of X-axis forward.The parametric equation of processed curve can be expressed as:

$\left\{\begin{array}{c}x=R\cos \mathrm{\&phi;}\\ y=R\sin \mathrm{\&phi;}\\ c=\mathrm{\&phi;}+\mathrm{\&pi;}/2\end{array}\right.---1-4$

Wherein R is arc radius, and φ is the line in current point and the center of circle and the angle of X-axis forward.

In the process of cutting out the cyclotomy arc, Z axis will keep making blade constantly consistent with circular arc secant direction with the interlock of XY axle.At first to obtain according to the circular arc starting point corner of cutter starting point.The starting point coordinate of known arc section is p _s(x _s, y _s), terminal point coordinate is p _e(x _e, y _e), central coordinate of circle is p _o(x _o, y _o), because Machining Arc is different with the corner that adds counterclockwise the cutter in man-hour clockwise, therefore can discuss respectively.As shown in accompanying drawing 4 and 6, its initial angle

The degree value can be expressed as (unit for °):

Contrary circular arc is cut out when cutting,

When cutting along the circular arc sanction,

Because the secant direction of each point on circular curve is different, therefore, when cutting out the cyclotomy arc, necessary control cutter is synchronous rotary with the motion of XY direction.Ultimate principle according to time-divided method, the Real-time interpolation algorithm that has proposed a kind of circular curve tangential following the step pitch horn cupping such as namely adopts to carry out tangential following and controls, its method is to determine according to the sampling period of default and given speed of feed the step angle that per step is walked, then calculates respectively the amount of feeding of each each axle of unit time; Consider along with the number of plies increases, under the identical condition of angular velocity, moment of torsion also increases gradually, therefore, for guaranteeing moment of torsion in the situation that the number of plies is different, the suffered moment of torsion of cutter is still identical, the interpolation cycle T of tangential following unit reached cutting and steadily taken into account cutting efficiency, therefore multiply by a factor

(n represents the number of plies), therefore establish P in Fig. 5 _i(x _i, y _i, c _i) be cutter current location point, the interpolation calculation requirement arrives the next position P after through an interpolation cycle _i+1(x _i+1, y _i+1, c _i+1), P _iThe coordinate of point is:

$\left\{\begin{array}{c}{x}_i=R\cos {\mathrm{\&phi;}}_i\\ y_i=R\sin {\mathrm{\&phi;}}_i\\ c_i={\mathrm{\&phi;}}_i+\mathrm{\&pi;}/2\end{array}\right.---1-5$

In case equivalent interpolation cycle T during the interpolation of circular arc tangential following ₀Determine with feed line speed V, its interpolation step angle α is:

$\mathrm{\&alpha;}=\frac{\mathrm{\&omega;T}}{n}=\mathrm{\&omega;}{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000081116480000042.png,HDA0000081116480000052.png"\; state="\{\{state\}\}">T</figure-callout>}}_0=\frac{V}{R}{T}_0---1-6$

If in Interpolation Process, the coordinate P of current point _i(x _i, y _i, c _i) known, in order to obtain the feeding increment on two coordinate directions, need to obtain through next interpolated point P after an interpolation cycle _i+1(x _i+1, y _i+1, c _i+1):

$\left\{\begin{array}{c}{x}_{i+1}=R\cos ({\mathrm{\&phi;}}_i+\mathrm{\&alpha;})\\ y_{i+1}=R\sin ({\mathrm{\&phi;}}_i+\mathrm{\&alpha;})\\ c_{i+1}={\mathrm{\&phi;}}_i+\mathrm{\&alpha;}\end{array}\right.---1-7$

16 cutters are along X, Y, C amount of feeding Δ x _i+1, Δ y _i+1, Δ c _i+1For:

$\left\{\begin{array}{c}{\mathrm{\&Delta;x}}_{i+1}=R[\cos ({\mathrm{\&phi;}}_i+\mathrm{\&alpha;})-\cos {\mathrm{\&phi;}}_i]\\ {\mathrm{\&Delta;y}}_{i+1}=R[\sin ({\mathrm{\&phi;}}_i+\mathrm{\&alpha;})-\sin {\mathrm{\&phi;}}_i]\\ {\mathrm{\&Delta;c}}_{i+1}=\mathrm{\&alpha;}\end{array}\right.---1-8$

Formula (1-3) abbreviation is got:

$\left\{\begin{array}{c}{x}_{i+1}=x_i\cos \mathrm{\&alpha;}-y_i\sin \mathrm{\&alpha;}\\ y_{i+1}=y_i\cos \mathrm{\&alpha;}+x_i\sin \mathrm{\&alpha;}\\ c_{i+1}=c_i+\mathrm{\&alpha;}\end{array}\right.---1-9$

In order to save the interpolation computing time of system CPU, cos α and sin α are adopted approximate treatment, the site error of the interpolated point that it causes will be analyzed in the back.Because α/2 are very little, thus tan (α/2) ≈ α/2 are arranged, thereby have:

$\cos \mathrm{\&alpha;}=\frac{1-{\left(\frac{\mathrm{\&alpha;}}{2}\right)}^2}{1+{\left(\frac{\mathrm{\&alpha;}}{2}\right)}^2}=\frac{4-{\mathrm{\&alpha;}}^2}{4+{\mathrm{\&alpha;}}^2}---1-10$

In like manner have:

$\sin \mathrm{\&alpha;}=\frac{4\mathrm{\&alpha;}}{4+{\mathrm{\&alpha;}}^2}---1-11$

Make A _i=cos α, B _i=sin α, data sampling method tangential following interpolation formula is:

$\left\{\begin{array}{c}{x}_{i+1}=A_i{x}_i-B_i{y}_i\\ y_{i+1}=A_i{y}_i+B_i{x}_i\\ c_{i+1}=c_i+\mathrm{\&alpha;}\end{array}\right.---1-12$

The feeding increment of each axle is:

$\left\{\begin{array}{c}{\mathrm{\&Delta;x}}_{i+1}=x_{i+1}-x_i\\ {\mathrm{\&Delta;y}}_{i+1}=y_{i+1}-y_i\\ {\mathrm{\&Delta;c}}_{i+1}=c_{i+1}-c_i\end{array}\right.---1-13$

Formula (1-12) is arranged as can be known, in circular arc tangential following interpolation algorithm each increment of coordinate value of interpolation cycle only with on coordinate figure and the step angle of an interpolated point relevant.After step-length and arc radius are determined, the step-length angle is a normal value in whole arc machining process, at this moment x, y increment of coordinate value are only relevant to the coordinate figure of a upper interpolated point, and the incremental angular of Z axis is the positive negative value at step-length angle, and immobilize in whole section circular interpolation.Can get shown in circular arc tangential following interpolation algorithm process flow diagram accompanying drawing 3 according to formula (1-13).Pair radius is that the circular arc of 40mm carries out the tangential following interpolation, gets the interpolation result of step-length when being 4mm as shown in table 3-1.

Table 3-1 radius is that the circular arc employing Interpolation step-length of 40.000mm is the result that 4.000mm carries out the tangential following interpolation

The step order	X(mm)	Y(mm)	C(°)	△(mm)
					1	40	4	4.50	0.20
2	40	8	9.00	0.80
					3	40	12	13.50	1.76
4	36	12	18.00	2.06
					5	36	16	22.50	0.60
6	36	20	27.00	1.18
					7	32	20	31.50	2.26
8	32	24	36.00	0
					9	32	28	40.50	2.52
10	28	28	45.00	0.40
					11	24	28	49.50	3.13
12	24	32	54.00	0
					13	24	36	58.50	3.27
14	20	36	63.00	1.18
					15	16	36	67.50	0.60
16	12	36	72.00	2.06
					17	12	40	76.50	1.75
18	8	40	81.00	0.79
					19	4	40	85.50	0.20
20	0	40	90	0

Table 3-2 radius is that the circular arc employing Interpolation step-length of 40.000mm is the result that 8.000mm carries out the tangential following interpolation

The step order	X(mm)	Y(mm)	C(°)	△(mm)
					1	40	8	9.00	0.79
2	40	16	18.00	3.08
					3	32	16	27.00	4.23
4	32	24	36.00	0
					5	32	32	45.00	5.24
6	24	32	54.00	0
					7	16	32	63.00	5.78
8	16	40	72.00	3.08
					9	8	40	81.00	0.79
10	0	40	90.00	0

Claims (2)

1. tangential following interpolating method that is applied to multilayer shoe leather numerical control Cutting machine bed, described multilayer shoe leather is cut out at a high speed the dither that cuts process and comprise the sheet cutter, the plane motion of Cutter tool and the rotation in sheet tool sharpening process, it is characterized in that: definition dither direction is the Z direction, and definition plane motion direction is X, Y-direction;

Cut in the process of straight line in sanction, Z axis is independent axes and not linking with the XY axle, and the starting point coordinate of known straight line is p _s(x _s, y _s), terminal point coordinate is p _e(x _e, y _e), the start angle value representation of straight-line segment is:

Carrying out the drift angle revises and to obtain final cutter start angle and be α is Cutter and the drift angle of going back to the cutter original position;

According to speed of feed F and the equivalent interpolation cycle T in the processing instruction ₀, T ₀=nT, T representation unit interpolation cycle calculates the profile step-length l of each interpolation cycle, and three's relation table is shown: l=FT ₀, the Z axis angle of following interpolation due to rectilinear tangential is constant, so there have rectilinear tangential to follow the interpolation formula to be as follows:

$\left\{\begin{array}{c}\mathrm{\&Delta;x}=l\cos a=l\frac{x_e-x_s}{\sqrt{{(x_e-x_s)}^2+{(y_e-y_s)}^2}}\\ \mathrm{\&Delta;y}=\mathrm{\&Delta;}x\tan a=\frac{\mathrm{\&Delta;x}(y_e-y_s)}{x_e-x_s}\\ \mathrm{\&Delta;c}=0\end{array}\right.---1-2$

For every section straight line, c is constant, obtains by the relation of x and y, obtains rectilinear tangential through conversion and follows the interpolation formula:

$\left\{\begin{array}{c}{x}_{i+1}=x_i+\mathrm{\&Delta;x}\\ y_{i+1}=y_i+\mathrm{\&Delta;y}\\ c_{i+1}={\mathrm{\&theta;}}_s^{\&prime;}\end{array}\right.---1-3.$

2. a kind of tangential following interpolating method that is applied to multilayer shoe leather numerical control Cutting machine bed as claimed in claim 1, is characterized in that: if the known sanction section of cutting circular arc

Be contrary circular arc, the circular arc starting point is P _s(x _s, y _s, c _s), terminal point is P _e(x _e, y _e, c _e), the center of circle 0 is true origin, and the Z coordinate figure is equivalent to the line in current point and the center of circle and the angle of X-axis forward, and the parametric equation of processed curve is expressed as:

$\left\{\begin{array}{c}x=R\cos \mathrm{\&phi;}\\ y=R\sin \mathrm{\&phi;}\\ c=\mathrm{\&phi;}+\mathrm{\&pi;}/2\end{array}\right.---1-4$

Wherein R is arc radius, and φ is the line in current point and the center of circle and the angle of X-axis forward;

In the process of cutting out the cyclotomy arc, Z axis will keep making blade constantly consistent with circular arc secant direction with the interlock of XY axle, at first will obtain according to the circular arc starting point corner of cutter starting point, and the starting point coordinate of known arc section is p _s(x _s, y _s), terminal point coordinate is p _e(x _e, y _e), central coordinate of circle is p _o(x _o, y _o), the start angle value representation is:

When contrary circular arc sanction is cut,

When cutting along the circular arc sanction,

If P _i(x _i, y _i, c _i) be cutter current location point, the interpolation calculation requirement arrives the next position P after through an interpolation cycle _i+1(x _i+1, y _i+1, c _i+1), P _iThe coordinate of point is:

$\left\{\begin{array}{c}{x}_i=R\cos {\mathrm{\&phi;}}_i\\ y_i=R\sin {\mathrm{\&phi;}}_i\\ c_i={\mathrm{\&phi;}}_i+\mathrm{\&pi;}/2\end{array}\right.---1-5$

In case equivalent interpolation cycle T during the interpolation of circular arc tangential following ₀Determine with feed line speed V, its interpolation step angle α is:

$\mathrm{\&alpha;}=\frac{\mathrm{\&omega;T}}{n}=\mathrm{\&omega;}{T}_0=\frac{V}{R}{T}_0---1-6$

If in Interpolation Process, the coordinate P of current point _i(x _i, y _i, c _i) known, in order to obtain the feeding increment on two coordinate directions, obtain through next interpolated point P after an interpolation cycle _i+1(x _i+1, y _i+1, c _i+1):

$\left\{\begin{array}{c}{x}_{i+1}=R\cos ({\mathrm{\&phi;}}_i+\mathrm{\&alpha;})\\ y_{i+1}=R\sin ({\mathrm{\&phi;}}_i+\mathrm{\&alpha;})\\ c_{i+1}={\mathrm{\&phi;}}_i+\mathrm{\&alpha;}\end{array}\right.---1-7$

Cutter is along X, Y, C amount of feeding Δ x _i+1, Δ y _i+1, Δ c _i+1For:

$\left\{\begin{array}{c}\mathrm{\&Delta;}{x}_{i+1}=R[\cos ({\mathrm{\&phi;}}_i+\mathrm{\&alpha;})-\cos {\mathrm{\&phi;}}_i]\\ \mathrm{\&Delta;}{y}_{i+1}=R[\sin ({\mathrm{\&phi;}}_i+\mathrm{\&alpha;})-\sin {\mathrm{\&phi;}}_i]\\ \mathrm{\&Delta;}{c}_{i+1}=\mathrm{\&alpha;}\end{array}\right.---1-8$

Formula 1-3 abbreviation is got:

$\left\{\begin{array}{c}{x}_{i+1}=x_i\cos \mathrm{\&alpha;}-y_i\sin \mathrm{\&alpha;}\\ y_{i+1}=y_i\cos \mathrm{\&alpha;}+x_i\sin \mathrm{\&alpha;}\\ c_{i+1}=c_i+\mathrm{\&alpha;}\end{array}\right.---1-9$

Set tan (α/2) ≈ α 2, thereby have:

$\cos \mathrm{\&alpha;}=\frac{1-{\left(\frac{\mathrm{\&alpha;}}{2}\right)}^2}{1+{\left(\frac{\mathrm{\&alpha;}}{2}\right)}^2}=\frac{4-{\mathrm{\&alpha;}}^2}{4+{\mathrm{\&alpha;}}^2}---1-10$

In like manner have:

$\sin \mathrm{\&alpha;}=\frac{4\mathrm{\&alpha;}}{4+{\mathrm{\&alpha;}}^2}---1-11$

Make A _i=cos α, B _i=sin α, data sampling method tangential following interpolation formula is:

$\left\{\begin{array}{c}{x}_{i+1}=A_i{x}_i-B_i{y}_i\\ y_{i+1}=A_i{y}_i+B_i{x}_i\\ c_{i+1}=c_i+\mathrm{\&alpha;}\end{array}\right.---1-12$

The feeding increment of each axle is:

$\left\{\begin{array}{c}\mathrm{\&Delta;}{x}_{i+1}=x_{i+1}-x_i\\ \mathrm{\&Delta;}{y}_{i+1}=y_{i+1}-y_i\\ \mathrm{\&Delta;}{c}_{i+1}=c_{i+1}-c_i\end{array}\right.---1-13.$

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