CN103869756A - Method for calculating machinable area of complex plane cavity tool - Google Patents
Method for calculating machinable area of complex plane cavity tool Download PDFInfo
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- CN103869756A CN103869756A CN201410102848.5A CN201410102848A CN103869756A CN 103869756 A CN103869756 A CN 103869756A CN 201410102848 A CN201410102848 A CN 201410102848A CN 103869756 A CN103869756 A CN 103869756A
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Abstract
The invention provides a method for calculating the machinable area of a complex plane cavity tool. The method includes the total implementation procedures that first, crossing arcs of a plane cavity are calculated, wherein all the possible crossing arcs in the plane cavity are calculated; second, the effectiveness of the crossing arcs is judged, wherein a series of judging criteria are formulated according to geometrical and technological knowledge to screen effective crossing arcs; third, contact line chains are constructed, wherein contact edges are calculated and recognized according to the effective crossing arc judgment result, and the contact line chains are constructed at last. With the method, the machinable area of the plane cavity tool can be extracted fast and accurately, and a technological basis is provided for calculation of the machinable area and the remaining area in the automatic programming process.
Description
Technical field
The present invention is that a kind of complex plane die cavity cutter can machining area computing method, and the method is chosen important parameter is provided for process planning stage cutter, also can calculate important evidence is provided for residual region.The method, for specialized, intelligent CAD/CAPP/CAM integrated system " the quick NC Programming System of aircraft complex component " provide basic technology support, belongs to digitizing Technology of NC Programming field.
Background technology
Pocket machining is widely used in the fields such as aviation, automobile, mold manufacturing industry, and flat surface impression processing is again most important in pocket machining, most widely used processing.Wherein, whether reasonable the selection of the cutter in process planning stage is will directly affect crudy, working (machining) efficiency and the processing cost of flat surface impression.And cutter given flat surface impression can machining area be to affect the key factor that cutter is selected, also affect the calculating of residual region simultaneously.At present the following two kinds of methods of main application calculate cutter can machining area: 1) secondary offsetting; 2) build variation Voronoi Mountain.Above-mentioned two methods have shortcoming separately, and biasing algorithm is complicated and can not guarantee that all curves all setover successfully, and cannot guarantee to build variation Voronoi Mountain algorithm stability according to CAD/CAM software engineering at present.Therefore, research and development complex plane die cavity cutter can machining area computing method, for improving numerical control programming intelligent level, to realize the efficient high-quality manufacture of complex plane die cavity significant.It is the core content during cutter can machining area calculates that CNC Machining Tool touches line computation, can build and touch linear chain by touching line computation and identification, and be the composition border that cutter can machining area in flat surface impression and touch linear chain.Therefore, how building tactile linear chain can calculate most important by machining area to cutter.Summary of the invention
The invention provides a kind of complex plane die cavity cutter can machining area computing method, the method by simulate round as a ball in flat surface impression border, roll and be automatically extracted in flat surface impression can machining area border.This result is applied to cutter and chooses the further raising that is conducive to numerical control programming intelligent level with residual region calculating.
The object of the invention is to be achieved through the following technical solutions: a kind of complex plane die cavity cutter can machining area computing method, it is characterized in that: the main-process stream that the method realizes is: 1) flat surface impression calculates across arc; 2) judge across arc validity; 3) touch linear chain structure.
The present invention will adopt biasing algorithm to build can machining area, but the biasing algorithm of meeting non-circular curve is complicated and unstable, can not guarantee that all curves setover successfully, therefore the present invention is separated into one group of straight line by the non-circular curve on all profiles according to certain precision.
The main contents that described step 1) flat surface impression calculates across arc have: contour loop and the serializing of boss ring in (1) flat surface impression; (2) essential information of ring top and point; (3) in Calculation Plane die cavity, exist across arc.
Wherein in (1) flat surface impression, the process of contour loop and the serializing of boss ring is as follows: <1> arranges the positive dirction of contour loop and boss ring: the algorithm that the present invention proposes is for flat surface impression, its mucosal structure can be represented along the position relationship between the ring of the two-dimensional projection of baseplane normal direction and ring by flat surface impression, the ring of outermost is called to contour loop, is designated as l
c, represent that the hole in flat surface impression, ring sagging and fluting are also considered as contour loop, and regulation is counterclockwise contour loop positive dirction.The non-contour loop that contour loop is surrounded is called boss ring, is designated as l
s, definition clockwise direction is the positive dirction of boss ring; <2> is according to encircling positive dirction serializing ring: all rings on sketch are carried out to serializing, by all limits according to same direction sequence ring direction, and according to step <1>, the result of determination of ring is judged to whether each ring serializing direction is correct, if incorrect, serializing in the other direction;
(2) process of the essential information of ring top and point is as follows:
<1> calculates the direction of each relative edge place, limit ring, determine starting point and the terminating point on limit, be specially: judge according to ring serializing direction whether current line segment meets ring direction, if do not meet, need starting point and terminating point switch, finally determine straight-line segment direction and starting point, terminating point coordinate, according to continue before last definite essential information structure each point limit and follow-up side information.Before the continue account form on limit and follow-up limit as follows: for any summit P on ring
i, P
imust be by two limit e
i, e
jintersect and form, remove P from current ring
iouter any point is along ring positive dirction traversal ring sideline, if certain the limit e first traversing
mmeet e
m∈ { e
i, e
j, put P
ibefore the limit of continuing, be designated as e
f, after the limit e that traverses
nmeet e
m∈ { e
i, e
j, be a P
ifollow-up limit, be designated as e
b;
The concavity and convexity on summit in <2> ring;
If summit to be asked is P, the computing method of P concavity and convexity are as follows: V
fwith V
brespectively representative point P before the limit e that continues
fwith follow-up limit e
bin P place tangent vector, define vectorial V
z(x, y, z), makes V
z=V
f× V
bif P is positioned at contour loop l
cupper, meet z<0, title P is salient point, meets z>0, title P is concave point, otherwise, if P is positioned at boss ring l
supper, meet z>0, title P is salient point, meets z<0, claims P
ifor concave point.No matter P
ibe positioned at l
cor l
supper, if z=0 claims P
ifor point of contact;
(3) in Calculation Plane die cavity, exist across arc, its main contents comprise:
By round as a ball and contact point sketch pressed on ring, be called contact, be designated as P
ct.Continuous set of contacts on baseline is closed and is referred to as to touch line, is designated as e
c.In round as a ball motion process, the limit that forces round as a ball direction of motion to change is called and hinders limit, the moment that round as a ball direction of motion changes hinders on limit and the round as a ball point joining, and is called and hinders a little, is designated as P
ob.By being transitioned into from contact along round as a ball direction of motion the circular arc hindering a little, be called across arc.Owing to being connecting terminal across arc and hindering tie a little, regulation also belongs to tactile line across arc.Can be divided into two classes across arc: effectively across arc and invalid across arc.If be one of element that composition can machining area border across arc, be called effectively across arc, be designated as c
v, otherwise be called invalidly across arc, be designated as c
u.
Because non-circular curve is separated into one group of straight-line segment by the present invention, therefore calculate and can be divided into three types across arc:
<1> calculating across arc between points;
Calculating across arc between <2> point and line;
Calculating across arc of <3> etween the lines.
These three kinds are applied to several algorithms most in use across arc computing method: straight-line segment asks friendship, circular arc and circular arc to ask cross, straight line biasing and circular arc biasing algorithm with circle.
Described step 2) have across the main contents of arc validity judgement: set up a series of criterions according to how much with process knowledge and across arc whether effectively to judge; Concrete criterion thes contents are as follows:
A, access criterion: if the maximum inscribed circle radius R of flat surface impression
i<r, and flat surface impression exists across arc c, and c is invalid;
B, distance criterion: any two geometric object a
1with a
2between exist effectively across arc c
vone of necessary condition be a
1with a
2between minor increment d must meet d<R, wherein a
1with a
2can be a little or line;
C, major arc criterion: effectively across arc c
vit must be major arc;
D, homonymy criterion: effectively across arc c
vthe inevitable and round as a ball m in the center of circle
gin position, the same side;
E, salient point criterion: between some P and geometric object a, have one of effective necessary condition across arc: P must be salient point, wherein a can be point or line;
F, bottleneck region criterion: known ring l is upper across arc c, the contact Pct of c and to hinder a Pob to be all positioned at l upper, to traveling through by Pct to all sidelines Pob, has following criterion by v:
If exist on these sidelines of f1 across arc ci and the ci center of circle and c distance of center circle from d<R, ci is invalid;
If exist across arc c on these sidelines of f2
i, c
ithe center of circle and c distance of center circle are from the maximum inscribed circle radius R of the ring of d>=R and these sidelines formation
i<R, c
iinvalid;
G, two intersection principles: if there is intersection point P across arc c and ring
i, and
c is invalid;
H, without Cross Criterion: if touch line e
cupper existence is intersected across arc c
1with c
2if, c
1with c
2meet following two conditions:
(1) intersection point only have one and
all not identical;
(2) c
1with c
2distance of center circle d<R.
C
1with c
2all invalid;
I, edge point are across arc editing criteria: along v to, if limit e
1with limit e
2exist across arc c, e
1only there are an end points and e
2exist across arc set
across arc all meet without Cross Criterion, along current v to c
iinvalid;
J, concurrent are across arc editing criteria: if contact P
ctplace exists multiple across arc c
i, meet without Cross Criterion, as round as a ball m
gwhen relative baseline chain left-hand, the leftmost side c that meets two intersection principles is effective; And work as m
gwhen relative baseline chain dextrad, the rightmost side c that meets two intersection principles is effective.In like manner, if hinder a P
obthere are multiple c in place
i, work as m
gwhen relative baseline chain left-hand, the rightmost side c that meets two intersection principles is effective, and works as m
gwhen relative baseline chain dextrad, the leftmost side c that meets two intersection principles is effective;
The main contents that described step 3) is touched linear chain structure have: according to the Engineering Semantics of touching line representative, the line set of touching in order end to end and that can be merged into a closed-loop is called to tactile linear chain, can be used as and touch linear chain the boundary representation that flat surface impression can machining area; This step can be divided following two little steps:
(1) touch line identification:
<1> is according to effectively calculating and touch line across arc result of determination;
<2> is according to effectively touching line across the screening of arc result of determination;
Touch line screening compliance criterion k: in ring, touch the invalid criterion of line:, at tactile linear chain E
cin construction process, if effectively across arc c
vcontact P
ctwith hinder a P
oball be positioned at contour loop l
cor boss ring l
supper, along v to, l
cor l
son be positioned at P
ctwith P
obbetween sideline be all regarded as building E
cinvalid tactile line, claim this criterion for ring in touch the invalid criterion of line.
<3> according in can machining area across arc geometrical property according to a definite sequence traversal ring, its process is followed criterion l: parity criterion:, along v to, touch putting in order and must meet contact, hinder a little alternate principle across arc on linear chain, claim this be can machining area across the parity criterion of arc;
<4> considers the tactile line of special circumstances extraction omission.
Its process is followed criterion m: the criterion of picking up any lost article from the road, that is, can be combined into one or several closed-loop if the residue sideline of flat surface impression after parity criterion screening is all or part of, and on the composition limit of ring without any effectively across arc, this ring is to touch linear chain, claims this criterion for the criterion of picking up any lost article from the road.
(2) touch linear chain structure
The tactile line obtaining is combined into one or several closed-loop by <1>; To obtain all tactile lines and be combined into one or several orderly closed-loop, its method is similar with ring serializing;
<2> rejects not closed-loop; Whether the ring that judges structure for the result of calculation of aforementioned <1> seals, reject if do not seal, finally remaining tactile linear chain just formed current diameter cutter in flat surface impression can machining area.
Beneficial effect of the present invention: the present invention adopts such scheme, can be according to effectively calculating with identification and touch limit across arc result of determination, and finally structure touches linear chain.Adopt can extract rapidly and accurately in this way flat surface impression cutter can machining area, for the calculating of section's machining area and residual region in automated programming process provides technical foundation.
Accompanying drawing explanation
Fig. 1 is that cutter can machining area calculated population process flow diagram.
Fig. 2 is some concavity and convexity calculating schematic diagram.
Fig. 3 (a) is that point calculates schematic diagram with point across arc.
Fig. 3 (b) is that point calculates schematic diagram with line across arc.
Fig. 3 (c) calculates schematic diagram across arc for line and line.
Fig. 4 (a) is access criterion schematic diagram.
Fig. 4 (b) is bottleneck region criterion schematic diagram.
Fig. 5 (a) is two intersection principle schematic diagram.
Fig. 5 (b) is without Cross Criterion schematic diagram.
Fig. 6 (a) is that edge point is across arc editing criteria schematic diagram.
Fig. 6 (b) is that concurrent is across arc editing criteria schematic diagram.
Fig. 7 is side position criterion schematic diagram.
Fig. 8 is salient point criterion schematic diagram.
Fig. 9 touches line criterion schematic diagram for touching line in ring.
Figure 10 is parity criterion schematic diagram.
Figure 11 is the criterion schematic diagram of picking up any lost article from the road.
Figure 12 is that application algorithm provided by the invention calculates the example schematic that cutter can machining area in flat surface impression.
Figure 13 is that flat surface impression calculates across arc and differentiates result schematic diagram, and wherein heavy line represents effectively across arc, and dotted line represents invalid across arc.
Figure 14 is that cutter can machining area result of calculation schematic diagram.
Embodiment
Below in conjunction with accompanying drawing, embodiment of the present invention is elaborated; this embodiment carries out under take invention technical scheme as prerequisite; the present invention has provided detailed embodiment and concrete implementation procedure, but protection scope of the present invention is not limited to following embodiment.
Figure 1 shows that the idiographic flow that cutter that the present invention proposes can machining area method be realized, implementation step is: 1) flat surface impression calculates across arc; 2) judge across arc validity; 3) touch linear chain structure.
Step 1): flat surface impression calculates across arc
(1) by the contour loop of flat surface impression and the serializing respectively of boss ring, and regulation is contour loop positive dirction counterclockwise, regulation is the positive dirction of boss ring clockwise, and in ring, the relative direction of relative place, every limit ring positive dirction, determines the starting point and the terminating point that encircle upper every limit according to relative direction.
(2) concavity and convexity of putting in ring
The concavity and convexity of introducing point according to front continue limit and follow-up limit calculates:
As Fig. 2, in figure, coordinate meets the right-hand rule, V
fwith V
brespectively representative point P before the limit e that continues
fwith follow-up limit e
bin P place tangent vector, define vectorial V
z(x, y, z), makes V
z=V
f× V
bif P is positioned at contour loop l
cupper, meet z<0, title P is salient point, meets z>0, title P is concave point, otherwise, if P is positioned at boss ring l
supper, meet z>0, title P is salient point, meets z<0, claims P
ifor concave point.No matter P
ibe positioned at l
cor l
supper, if z=0 claims P
ifor point of contact.
(3) between calculation level point across arc
Between <1> point point, need to meet distance criterion across arc;
Between <2> point point, need to meet salient point criterion across arc;
Between <3> point point across arc computing method:
As shown in Fig. 3 (a), respectively with P
1, P
2for the center of circle, be that radius is made auxiliary circle across arc radius r, the intersection point of two circles
be the center of circle of a point across arc, P
1, P
2be contact and hinder a little.
(4) calculate between dotted line across arc
Between <1> dotted line, need to meet distance criterion across arc;
Between <2> dotted line, need to meet salient point criterion across arc;
Between <3> dotted line across arc computing method:
As shown in Figure 3 (b), with P
1point is the center of circle, is that radius is made auxiliary circle, and line e is setovered towards round as a ball orientation across arc radius r, and offset or dish is r, the line e ' after biasing and the intersection point P of auxiliary circle
cbe the center of circle of dotted line across arc, and P
1point be across the contact of arc across the point of contact on the online e of arc and hinder a little.
(5) calculate between line line across arc
Between <1> line line, need to meet distance criterion across arc;
Between <2> line line across arc computing method:
As shown in Figure 3 (c), by limit e
1, e
2towards the biasing of round as a ball orientation, two line intersection points after biasing are the center of circle P across arc respectively
c, and across arc and e
1, e
2point of contact P
1, P
2be across the contact of arc with hinder a little.
Step 2) judge across arc validity
Need meet aforesaid access criterion, distance criterion, major arc criterion, homonymy criterion and salient point criterion herein across the effective necessary condition of arc.
(a) access criterion, as the condition precedent that judges that whether reasonable given tool diameter is, if rolling diameter does not meet this criterion, shows that tool diameter is excessive, must produce and cut with flat surface impression, even exist across arc in flat surface impression, invalid across arc.
(b) distance criterion, if the minor increment between two geometric objects is greater than rolling diameter, shows round as a ball can passing through in this region, inevitable existence across arc.
(c) major arc criterion, known according to the Engineering Semantics of round as a ball representative must be effectively major arc across arc.
(d) homonymy criterion is the round as a ball circular arc border staying after the motion of bottleneck location across arc, across arc certainty and position, round as a ball maintenance the same side.
(e) salient point criterion, according to known across the round as a ball geometrical property in arc place, if some P is concave point, P place is round as a ball inevitable cuts with encircling.Therefore there is one of effective necessary condition across arc: P must be salient point.
Only all effectively across arc according to filtering out across the necessary condition of arc existence, therefore need following several criterion as judging the criterion foundation whether effective across arc:
(f) bottleneck region criterion, is applied to regional area by maximum inscribed circle method, as whether there being the effectively basis for estimation across arc in regional area.
(g), if there is more than three or three intersection point across arc and ring upper sideline, according to producing and cut with ring across arc place is round as a ball across arc definition is known in two intersection principles.
(h) without Cross Criterion, handled situation belongs to common type, and this criterion can be used as the supplementary judgement of bottleneck region criterion.
(i) edge point is across arc editing criteria, and this criterion is applied situation as shown in Figure 6 (a), when limit is positioned at bottleneck region, needs to consider that application edge point filters out partial invalidity across arc across arc editing criteria.
(j) across arc whether effectively concurrent is across arc editing criteria, for a contact or hinder a place to have multiple situations across arc, now need to judge according to the side position of round as a ball relatively current ring and round as a ball velocity reversal.
Step 3): touch linear chain structure
(1) according to criterion k: touch the invalid criterion of line in ring, screen invalid tactile limit;
As Fig. 9, according to effective result of determination across arc, can utilize the tactile invalid criterion of line in ring to filter out the invalid tactile limit of a part.
(2) as Figure 10, according to criterion l: parity criterion, traversal can machining area sideline in certain sequence, and the sideline of traversal is tactile line.
Obtain effectively across arc set
by F
cvadd in contour loop and boss ring sideline, will encircle upper sideline at F
cvin across the contact of arc with hinder a place to be interrupted; Appoint get one not traversal effectively across arc c
vhinder is some starting point P
s; With P
sfor starting point is along round as a ball speed v direction, traversal ring sideline, if traverse across arc contact, take this hindering a little as starting point continues traversal, until get back to P across arc
s; Touch linear chain according to v to building
if successfully select a new not traversal c
vcontinue traversal, otherwise abandon current tactile linear chain, select a new not traversal c
vcontinue traversal; Judge whether to exist and do not travel through c
vif, exist, continue traversal, if do not exist, show that obtaining tactile linear chain by parity criterion finishes, end product is one or several closed-loop.
(3) according to criterion m: the criterion of picking up any lost article from the road, obtain to omit and touch line.
The tactile line only obtaining according to parity criterion can not guarantee successfully to extract all tactile lines, when tool diameter less, or can process completely in boss situation, on contour loop or on boss ring, may not exist any effectively across arc, but this contour loop or boss ring are again effectively to touch linear chain, as Figure 11, now need to formulate the criterion of picking up any lost article from the road and extract the tactile line of omission.
Claims (3)
1. complex plane die cavity cutter can machining area computing method, it is characterized in that: the main-process stream that the method realizes is: 1) flat surface impression calculates across arc; 2) judge across arc validity; 3) touch linear chain structure.
2. a kind of complex plane die cavity cutter according to claim 1 can machining area computing method, it is characterized in that:
The main contents that described step 1) flat surface impression calculates across arc have: contour loop and the serializing of boss ring in (1) flat surface impression; (2) essential information of ring top and point; (3) in Calculation Plane die cavity, exist across arc;
Described step 2) have across the main contents of arc validity judgement: set up a series of criterions according to how much with process knowledge and across arc whether effectively to judge; Concrete criterion thes contents are as follows:
A, access criterion: if the maximum inscribed circle radius R of flat surface impression
i<r, and flat surface impression exists across arc c, and c is invalid;
B, distance criterion: any two geometric object a
1with a
2between exist effectively across arc c
vone of necessary condition be a
1with a
2between minor increment d must meet d<R, wherein a
1with a
2can be a little or line;
C, major arc criterion: effectively across arc c
vit must be major arc;
D, homonymy criterion: effectively across arc c
vthe inevitable and round as a ball m in the center of circle
gin position, the same side;
E, salient point criterion: between some P and geometric object a, have one of effective necessary condition across arc: P must be salient point, wherein a can be point or line;
F, bottleneck region criterion: known ring l is upper across arc c, the contact Pct of c and to hinder a Pob to be all positioned at l upper, to traveling through by Pct to all sidelines Pob, has following criterion by v:
If exist on these sidelines of f1 across arc ci and the ci center of circle and c distance of center circle from d<R, ci is invalid;
If exist across arc c on these sidelines of f2
i, c
ithe center of circle and c distance of center circle are from the maximum inscribed circle radius R of the ring of d>=R and these sidelines formation
i<R, c
iinvalid;
G, two intersection principles: if there is intersection point P across arc c and ring
i, and
c is invalid;
H, without Cross Criterion: if touch line e
cupper existence is intersected across arc c
1with c
2if, c
1with c
2meet following two conditions:
(1) intersection point only have one and
all not identical;
(2) c
1with c
2distance of center circle d<R;
C
1with c
2all invalid;
I, edge point are across arc editing criteria: along v to, if limit e
1with limit e
2exist across arc c, e
1only there are an end points and e
2exist across arc set
across arc all meet without Cross Criterion, along current v to c
iinvalid;
J, concurrent are across arc editing criteria: if contact P
ctplace exists multiple across arc c
i, meet without Cross Criterion, as round as a ball m
gwhen relative baseline chain left-hand, the leftmost side c that meets two intersection principles is effective; And work as m
gwhen relative baseline chain dextrad, the rightmost side c that meets two intersection principles is effective; In like manner, if hinder a P
obthere are multiple c in place
i, work as m
gwhen relative baseline chain left-hand, the rightmost side c that meets two intersection principles is effective, and works as m
gwhen relative baseline chain dextrad, the leftmost side c that meets two intersection principles is effective;
The main contents that described step 3) is touched linear chain structure have: according to the Engineering Semantics of touching line representative, the line set of touching in order end to end and that can be merged into a closed-loop is called to tactile linear chain, can be used as and touch linear chain the boundary representation that flat surface impression can machining area; This step can be divided following two little steps:
(1) touch line identification:
<1> is according to effectively calculating and touch line across arc result of determination;
<2> is according to effectively touching line across the screening of arc result of determination;
Touch line screening compliance criterion k: in ring, touch the invalid criterion of line:, at tactile linear chain E
cin construction process, if effectively across arc c
vcontact P
ctwith hinder a P
oball be positioned at contour loop l
cor boss ring l
supper, along v to, l
cor l
son be positioned at P
ctwith P
obbetween sideline be all regarded as building E
cinvalid tactile line, claim this criterion for ring in touch the invalid criterion of line;
<3> according in can machining area across arc geometrical property according to a definite sequence traversal ring, its process is followed criterion l: parity criterion:, along v to, touch putting in order and must meet contact, hinder a little alternate principle across arc on linear chain, claim this be can machining area across the parity criterion of arc;
<4> considers the tactile line of special circumstances extraction omission;
Its process is followed criterion m: the criterion of picking up any lost article from the road, that is, can be combined into one or several closed-loop if the residue sideline of flat surface impression after parity criterion screening is all or part of, and on the composition limit of ring without any effectively across arc, this ring is to touch linear chain, claims this criterion for the criterion of picking up any lost article from the road;
(2) touch linear chain structure
The tactile line obtaining is combined into one or several closed-loop by <1>; To obtain all tactile lines and be combined into one or several orderly closed-loop, its method is similar with ring serializing;
<2> rejects not closed-loop; Whether the ring that judges structure for the result of calculation of aforementioned <1> seals, reject if do not seal, finally remaining tactile linear chain just formed current diameter cutter in flat surface impression can machining area.
3. a kind of complex plane die cavity cutter according to claim 2 can machining area computing method, it is characterized in that:
In described (1) flat surface impression, the process of contour loop and the serializing of boss ring is as follows: <1> arranges the positive dirction of contour loop and boss ring: the ring of outermost is called to contour loop, is designated as l
c, represent that the hole in flat surface impression, ring sagging and fluting are also considered as contour loop, and regulation is counterclockwise contour loop positive dirction; The non-contour loop that contour loop is surrounded is called boss ring, is designated as l
s, definition clockwise direction is the positive dirction of boss ring; <2> is according to encircling positive dirction serializing ring: all rings on sketch are carried out to serializing, by all limits according to same direction sequence ring direction, and according to step <1>, the result of determination of ring is judged to whether each ring serializing direction is correct, if incorrect, serializing in the other direction;
Described (2) ring top and the essential information of point; Process is as follows:
<1> calculates the direction of each relative edge place, limit ring, determine starting point and the terminating point on limit, be specially: judge according to ring serializing direction whether current line segment meets ring direction, if do not meet, need starting point and terminating point switch, finally determine straight-line segment direction and starting point, terminating point coordinate, according to continue before last definite essential information structure each point limit and follow-up side information; Before the continue account form on limit and follow-up limit as follows: for any summit P on ring
i, P
imust be by two limit e
i, e
jintersect and form, remove P from current ring
iouter any point is along ring positive dirction traversal ring sideline, if certain the limit e first traversing
mmeet e
m∈ { e
i, e
j, put P
ibefore the limit of continuing, be designated as e
f, after the limit e that traverses
nmeet e
m∈ { e
i, e
j, be a P
ifollow-up limit, be designated as e
b;
The concavity and convexity on summit in <2> ring;
If summit to be asked is P, the computing method of P concavity and convexity are as follows: V
fwith V
brespectively representative point P before the limit e that continues
fwith follow-up limit e
bin P place tangent vector, define vectorial V
z(x, y, z), makes V
z=V
f× V
bif P is positioned at contour loop l
cupper, meet z<0, title P is salient point, meets z>0, title P is concave point, otherwise, if P is positioned at boss ring l
supper, meet z>0, title P is salient point, meets z<0, claims P
ifor concave point; No matter P
ibe positioned at l
cor l
supper, if z=0 claims P
ifor point of contact;
In described (3) Calculation Plane die cavity, exist across arc, its main contents comprise:
By round as a ball and contact point sketch pressed on ring, be called contact, be designated as P
ct; Continuous set of contacts on baseline is closed and is referred to as to touch line, is designated as e
c; In round as a ball motion process, the limit that forces round as a ball direction of motion to change is called and hinders limit, the moment that round as a ball direction of motion changes hinders on limit and the round as a ball point joining, and is called and hinders a little, is designated as P
ob; To be transitioned into the circular arc hindering a little from contact along round as a ball direction of motion, be called across arc; Owing to being connecting terminal across arc and hindering tie a little, regulation also belongs to tactile line across arc; Can be divided into two classes across arc: effectively across arc and invalid across arc; If be one of element that composition can machining area border across arc, be called effectively across arc, be designated as c
v, otherwise be called invalidly across arc, be designated as c
u.
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