CN102354157A - Radius compensation algorithm for convex contour closed-angle linear and circular arc composite transitional cutting tool - Google Patents

Abstract

The invention discloses a tool radius compensation algorithm for a convex profile, sharp angle, straight line and circular arc compound transition, that is, D tool compensation, which includes the following steps: using line segment BC, circular arc CD and line segment DE as the compensation method for the tool radius of the linear arc compound transition tool Tool center trajectory; calculation of transition point coordinates; establishment and cancellation of tool compensation. Because the present invention extends the center track of the tool at the transition point of the sharp corner of the cam profile, so that the tool is no longer in constant contact with point A, effectively solving the problem that the B tool compensation stays at the sharp corner for too long and causes burns at the sharp corner. Because the present invention adopts circular arc transition at the sharp angle transition of the cam profile, the tool center trajectory is smooth and continuous, which effectively solves the problem of frequent acceleration and deceleration caused by the transition of the C tool compensation broken line, and it is difficult to increase the processing speed. The length of the tool center track of the D tool compensation of the present invention is slightly longer than that of the B tool compensation tool center track, and shorter than that of the C tool compensation tool center track.

Description

The compound transition cutter radius compensation of a kind of cam contour wedge angle Straight Line and Arc algorithm

Technical field

The present invention relates to a kind of novel numerical control process technology, the compound transition cutter radius compensation of particularly a kind of cam contour wedge angle Straight Line and Arc algorithm.

Background technology

The wedge angle transition problem is a traditional problem in the digital control processing, and present most digital control system cutter radius compensation adopts Type B cutter radius compensation (being called for short the B cutter mends) or C type cutter radius compensation (being called for short the C cutter mends).

The Type B cutter radius compensation calculates the movement locus of center cutter according to parts profile size and tool radius in the program segment; Intersection point with adjacent programs section cam contour is the center of circle, is the corresponding central track of cutter of circular arc linker section profile of radius with the tool radius, and the junction must be tangent.Through after the arc transition, the central track of cutter transient curve has single order continuation property at least, can reduce the acceleration and deceleration frequency of utilization effectively, can improve working (machining) efficiency well.But, add man-hour carrying out the cam contour wedge angle, because the cam contour sharp corner is in cutting state all the time, the manufacturability of wedge angle processing is just poor, and this is especially outstanding in grinding, and the wedge angle of being processed tends to occur burn and is processed to little fillet.In addition, the Type B cutter radius compensation adopts and reads one section, calculates one section, one section the control method of going further when confirming central track of cutter, so just can't estimate owing to the influence to the generation of this section machining locus of hypomere machining locus that tool radius caused.The principal feature of C type cutter radius compensation adopts straight transitions exactly.After straight transitions, cutter leaves workpiece at the cam contour sharp corner, can well avoid the long-time problem that causes the cam contour burn and form little circular arc that contacts with workpiece of cutter.But no matter be the elongation type that calculates the wide central track of cutter extending line intersection point of two adjacent cams; Still after the wide central track of cutter of two adjacent cams being extended a tool radius separately; Insert the insert type of straight line section; Cutting tool path is broken line, when high-speed cutting, need constantly carry out acceleration and deceleration, in High-speed NC Machining, will certainly have influence on the speed and the quality of processing.Therefore, all there are certain problem in Type B and C type Cutter Radius Compensation Method in the high-speed cutting of cam contour transition line.

Summary of the invention

For solving the problems referred to above that prior art exists; The present invention will propose the advantage of a kind of abundant combination Type B Cutter Radius Compensation Method and C type Cutter Radius Compensation Method; Both can solve the Type B Cutter Radius Compensation Method causes wedge angle burn, the frequent acceleration and deceleration of needs that can avoid the transition of C type Cutter Radius Compensation Method broken line to cause again to cause being difficult to improving the compound transition cutter radius compensation of the cam contour wedge angle Straight Line and Arc algorithm of the problem of process velocity at the sharp corner overstand.

To achieve these goals, technical scheme of the present invention is following: the compound transition cutter radius compensation of a kind of cam contour wedge angle Straight Line and Arc algorithm may further comprise the steps:

A, cutter are mended Algorithm Analysis

A1, known cam contour wedge angle programming track are OA, AF; Tool radius is r; The central track of cutter of JB for OA being setovered behind the tool radius r; The central track of cutter of EK for AF being setovered behind the tool radius r, AB, AE are called the tool radius vector, and B and E point are respectively the starting point and the terminal point of B cutter benefit or C cutter benefit;

A2, cross B point prolongs a δ along the JB direction distance, arrive a D along the distance that the opposite direction of EK prolongs a δ with reason E point to a some C; The δ value is chosen according to fabrication process condition, generally gets δ=0.1～1mm;

A3, cross the parallel lines that some C makes AB, cross the parallel lines that some D makes AE, two parallel lines intersect at a N;

A4, be the center of circle with N, | NC| or | ND| is a radius, is that C, terminal point are the circular arc of D as starting point;

A5, line segment BC, circular arc C D and line segment DE are the central track of cutter of the compound transition Cutter Radius Compensation Method of Straight Line and Arc, are called for short the D cutter and mend;

A6, when the cam contour wedge angle is the obtuse angle, the extended line of central track of cutter JB and EK meets at the I point, the equal in length of BI and EI, its length is represented with λ; If λ is not more than δ, then to adopt with the A point be the center of circle for this sharp corner, and tool radius r is that the circular arc BE of radius makes the B cutter and makes amends for one's faults and cross, and crosses otherwise adopt above-mentioned D cutter to make amends for one's faults;

B, transit point coordinate Calculation

AB, AF are the tool radius vector, and formula (1) and formula (2) are then arranged:

OB＝OA+AB (1)

OE＝OA+AE (2)

If α is the deflection of programming vector OA, β is the deflection of programming vector AF; Known A point coordinate is (X _a, Y _a), the coordinate of then putting B and E can be calculated by formula (3) and formula (4) respectively:

(3)

Y _b＝Y _a±r?cosα

(4)

Y _e＝Y _a±r?cosβ

The left cutter added time is got top symbol, the right cutter added time side's of taking off symbol in the formula;

Can get by the vector summation:

OC＝OB+BC (5)

OD＝OE+ED (6)

Because | BC|=|ED|=δ, can be calculated by formula (7) and formula (8) respectively so extend the coordinate of some C and D:

X _c＝X _b+δcosα

(7)

Y _c＝Y _b+δsinα

X _d＝X _e-δcosβ

(8)

Y _d＝Y _e-δsinβ

Calculate the coordinate of transition arc center of circle N below, because:

ON＝OC+CN (9)

ON＝OD+DN (10)

If the radius of transition arc is r ', promptly | CN|=|DN|=r can be got by formula (9) and (10):

$r^{\′}=\±\frac{X_c-X_d}{\sin \mathrm{\β}-\sin \mathrm{\α}}=\±\frac{Y_c-Y_d}{\cos \mathrm{\α}-\cos \mathrm{\β}}---\left(11\right)$

The left cutter added time is got top symbol, the right cutter added time side's of taking off symbol in the formula;

Therefore, can get the N point coordinate by formula (9) and formula (10):

X _n＝X _c-r′sinα＝X _d-r′sinβ (12)

Y _n＝Y _c+r′cosα＝Y _d+r′cosβ

C, cutter are reconstructed upright and cancellation

C1, cutter are reconstructed immediately, are the center of circle with cam contour wedge angle A point, and tool radius r is that radius is drawn circle, crosses the tangent line OB that the O point is made circle, and B is the point of contact;

Central track of cutter behind C2, the profile AF that will the programme biasing tool radius r is EK, and AB, AE are the tool radius vector, and B and E point then are respectively starting point and the terminal point that cutter is reconstructed upright transition section;

C2, cross B point prolongs a δ along the OB direction distance, arrive a D along the distance that the opposite direction of EK prolongs a δ with reason E point to a some C; The δ value is chosen according to fabrication process condition, generally gets δ=0.1～1mm;

C3, cross the parallel lines that some C makes AB, cross the parallel lines that some D makes AE, two parallel lines intersect at a N;

C4, be the center of circle with N, | NC| or | ND| is a radius, is that C, terminal point are the circular arc of D as starting point;

C5, line segment OB, line segment BC, circular arc C D and line segment DE are the cutter of the compound transition Cutter Radius Compensation Method of Straight Line and Arc and reconstruct central track of cutter immediately;

C6, when the cam contour wedge angle is the obtuse angle, the extended line of central track of cutter OB and EK meets at the I point, the equal in length of BI and EI, its length is represented with λ; If λ is not more than δ, be the center of circle then with the A point, tool radius r is that radius is made circular arc BE; Line segment OB, circular arc BE and line segment EK are the cutter of the compound transition Cutter Radius Compensation Method of Straight Line and Arc and reconstruct central track of cutter immediately;

Central track of cutter when C7, the cancellation of cutter benefit is identical with the central track of cutter that cutter is reconstructed immediately, but in the opposite direction.

Compared with prior art, the present invention has following beneficial effect:

1, because the present invention at cam contour wedge angle transition position, has extended central track of cutter, makes cutter no longer contact all the time, solved B cutter benefit effectively and caused the wedge angle burn at the sharp corner overstand with the A point.

2, because the present invention has adopted arc transition at cam contour wedge angle transition position, make central track of cutter smoothly continuous, solved the C cutter effectively and mended the frequent acceleration and deceleration of needs that the broken line transition causes, be difficult to improve the problem of process velocity.

3, the central track of cutter length of D cutter benefit of the present invention is long slightly than B cutter benefit central track of cutter, and it is short to mend central track of cutter than the C cutter.

Description of drawings

4 in the total accompanying drawing of the present invention, wherein:

Fig. 1 is that cutter of the present invention is mended Algorithm Analysis figure.

Fig. 2 is an obtuse angle of the present invention corner cutter complement.

Fig. 3 is that cutter of the present invention is reconstructed upright figure.

Fig. 4 is a cutter profile envelope diagram of the present invention.

Embodiment

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

Fig. 1 has represented the B cutter is mended, the C cutter is mended and the D cutter is mended algorithm and central track of cutter.Line segment JB, radius are the circular arc BE of r and the central track of cutter that line segment EK mends for the B cutter; Line segment JB, line segment BC, radius are the central track of cutter that circular arc C D, line segment DE and the line segment EK of r ' mends for the D cutter; The central track of cutter that line segment JB, line segment BG, line segment GH, line segment HE and line segment EK mend for the C cutter.

Cutter when Fig. 2 has represented that the cam contour wedge angle is the obtuse angle corner is mended Algorithm Analysis.Line segment JB, line segment BI, line segment IE and line segment EK mend central track of cutter for the C cutter; Line segment JB, circular arc BE and line segment EK mend central track of cutter for the B cutter.

Fig. 3 has represented that cutter of the present invention reconstructs upright process, and tool radius vector AB is vertical with BC with line segment OB, and line segment BC and circular arc C D are tangent.Line segment OB, line segment BC, circular arc C D, line segment DE and line segment EK are the cutter of the compound transition Cutter Radius Compensation Method of Straight Line and Arc and reconstruct central track of cutter immediately.

Fig. 4 has represented the envelope diagram of the cutter profile of D cutter added time; From figure, find out; When center cutter motion when the B point is between the track that E order, the cutter profile has broken away from programming profile cusp A and has contacted, and has solved the problem that B cutter benefit causes wedge angle to burn at the sharp corner overstand.

Claims (1)

1. A tool radius compensation algorithm for cam profile sharp angle linear arc compound transition, characterized in that: comprising the following steps: A. Analysis of tool compensation algorithm A1. It is known that the programmed trajectory of the sharp corner of the cam profile is OA, AF, the tool radius is r, JB is the tool center trajectory after OA is offset by tool radius r, EK is the tool center trajectory after AF is offset by tool radius r, AB and AE are called tool radius vectors, B and E points are the starting point and end point of B tool compensation or C tool compensation respectively; A2. After point B, extend a distance of δ along the direction of JB to point C, and for the same reason, point E extends a distance of δ along the opposite direction of EK to point D; the value of δ is selected according to the processing technology conditions, generally δ = 0.1 ~ 1mm ; A3. Make a parallel line to AB through point C, and a parallel line to AE through point D, and the two parallel lines intersect at point N; A4. With N as the center and |NC| or |ND| as the radius, make an arc with the starting point C and the ending point D; A5. The line segment BC, arc CD and line segment DE are the tool center trajectory of the straight line arc compound transition tool radius compensation method, referred to as D tool compensation; A6. When the sharp angle of the convex profile is an obtuse angle, the extension line of the tool center trajectory JB and EK intersects at point I, and the lengths of BI and EI are equal, and the length is represented by λ; if λ is not greater than δ, the sharp angle is used Take point A as the center of the circle, and the arc BE of the tool radius r as the radius, make B tool compensation transition, otherwise use the above-mentioned D tool compensation transition; B. Calculation of transfer point coordinates AB and AF are tool radius vectors, then there are formulas (1) and (2): OB＝OA+AB (1) OE＝OA+AE (2) Let α be the orientation angle of the programming vector OA, and β be the orientation angle of the programming vector AF; given that the coordinates of point A are (Xa, Ya), then the coordinates of points B and E can be obtained by formula (3) and formula (4) respectively calculate:

(3) Y _b ＝ Y _a ± r cos α

(4) Y _e =Y _a ±r cosβ In the formula, the upper symbol is used for the left tool compensation, and the lower symbol is used for the right tool compensation; From vector summation we get: OC＝OB+BC (5) OD＝OE+ED (6) Since |BC|=|ED|=δ, the coordinates of extension points C and D can be calculated by formula (7) and formula (8) respectively: X _c ＝X _b +δcosα (7) Y _c ＝ Y _b + δ sin α X _d =X _e -δcosβ (8) Y _d ＝Y _e -δ sin β The coordinates of the center N of the transition arc are calculated below, because: ON＝OC+CN (9) ON＝OD+DN (10) Let the radius of the transition arc be r′, that is, |CN|=|DN|=r, from formulas (9) and (10): ${\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&PlusMinus;</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; \&PlusMinus;</span>\frac{{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}{\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$ In the formula, the upper symbol is used for the left tool compensation, and the lower symbol is used for the right tool compensation; Therefore, the coordinates of point N can be obtained from formula (9) and formula (10): X _n = X _c -r'sinα = X _d -r'sinβ (12) Y _n =Y _c +r'cosα= _Yd +r'cosβ C. Tool compensation establishment and cancellation C1. When tool compensation is established, draw a circle with point A at the sharp corner of the cam profile as the center, tool radius r as the radius, and draw the tangent line OB of the circle passing through point O, and B is the tangent point; C2. The tool center trajectory after the programmed contour AF is offset by the tool radius r is EK, AB and AE are the tool radius vectors, and B and E are the starting point and end point of the tool compensation establishment transition section respectively; C2. Pass point B and extend a distance of δ along the direction of OB to point C. For the same reason, point E extends a distance of δ along the opposite direction of EK to point D; the value of δ is selected according to the processing technology conditions, generally δ = 0.1 ~ 1mm ; C3. Make a parallel line to AB through point C, and a parallel line to AE through point D, and the two parallel lines intersect at point N; C4. With N as the center and |NC| or |ND| as the radius, make an arc with the starting point C and the ending point D; C5, line segment OB, line segment BC, arc CD and line segment DE are the tool center trajectory when the tool compensation is established in the straight line arc compound transition tool radius compensation method; C6. When the sharp angle of the convex profile is an obtuse angle, the extension line of the tool center trajectory OB and EK intersects at point I, and the lengths of BI and EI are equal, and the length is represented by λ; if λ is not greater than δ, point A is the center of the circle , the tool radius r is the radius for the arc BE; the line segment OB, arc BE and line segment EK are the tool center trajectory when the tool compensation is established in the straight line arc compound transition tool radius compensation method; C7. The tool center track when the tool compensation is canceled is the same as the tool center track when the tool compensation is established, but the direction is opposite.

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