CN107247444B - It is a kind of for generate curved surface without interference five-axis robot track projection algorithm - Google Patents
It is a kind of for generate curved surface without interference five-axis robot track projection algorithm Download PDFInfo
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- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
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- G—PHYSICS
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract
It is a kind of for generate curved surface without interference five-axis robot track projection algorithm, belong to Milling Process technical field, it is therefore intended that guarantee that final cutter-contact point is located on original workpiece curved surface, raising machining accuracy simultaneously guarantee preferable machined surface quality.The present invention chooses cutter and is projected in the cutter-contact point on triangle model as initial point；Calculate corresponding points of the initial point to the shortest distance of curve surface of workpiece and on curve surface of workpiece；Established tangent plane of the corresponding points on curve surface of workpiece；It executes cutter to project to tangent plane, obtains the subpoint in tangent plane；To convergence concussion problem, adjustment step-size in search algorithm is executed；Meet the subpoint of error as cutter-contact point in output tangent plane.The present invention is inspired by Newton-Raphson algorithm, using the method based on the continuous iteration of tangent plane, guarantees that cutter-contact point on original workpiece curved surface, improves the computational accuracy of cutter-contact point.
Description
Technical field
The invention belongs to numerical control milling methods, and in particular to one kind is for generating curved surface without interference five-axis robot track
Projection algorithm.
Background technique
Common complex curved surface parts have airframe, propeller blade, phone mould appearance curved surface, turbine blade,
Body of a motor car etc. is widely used in the fields such as Aeronautics and Astronautics, navigation, mold, the energy, traffic.It is processed compared to three-axis numerical control,
Five-shaft numerical control processing can guarantee preferable surface quality and higher processing efficiency, and current complex-curved class part utilizes five mostly
Shaft and NC Machining Test processing.
Projection algorithm is one of the effective ways for planning tool sharpening track, as shown in Figure 1, projection algorithm is divided into two steps
Rapid: driving point is chosen in 1. planning driving track；2. the driving o'clock of selection is projected on curve surface of workpiece along a projecting direction,
Generate tool sharpening track.
It is of the invention for ease of understanding, combine Fig. 2 to explain the related concept in planning tool sharpening track first:
Cutter-contact point, abbreviation CC point are tangent with curve surface of workpiece and cutter curved surface during referring to Tool in Milling curve surface of workpiece
Location point；
Cutter location, abbreviation CL point refer to that the positioning datum point of cutter generally takes tool axis for various milling cutters
With the intersection point of cutter bottom end.
Lathe coordinate system, is right-handed Cartesian coordinate system, and coordinate origin is intrinsic on lathe after the completion of scheduling and planning
Point, specific location are accurately adjusted on each feed shaft with limit switch by machine tool manufacturer, and coordinate value has inputted number
It controls in device, in actual operation, after each lathe powers on, presses each axis reset button, lathe is just automatically found machine origin,
Lathe coordinate system ZJAxis is parallel to machine tool chief axis axis, and forward direction is the direction far from workpiece, XJAxis be it is horizontal, forward direction is
The direction on the right, Y are directed toward in terms of from machine tool chief axis to workpieceJAxis is determined by right-handed Cartesian coordinate system.
Workpiece coordinate system (WCS, Workpiece Coordinate System) is right-handed Cartesian coordinate system, to guarantee
The consistency of programming and machine tooling, the geometry of workpiece, workpiece coordinate system origin are the edge of workpiece for ease of description
A bit of place optionally, XWAxis, YWAxis and ZWThe X of axis and lathe coordinate systemJAxis, YJAxis and ZJAxis is consistent.
During calculating tool sharpening track, need to calculate the point of contact of cutter curved surface and curve surface of workpiece to determine that knife touches
The position of point.But the point of contact of direct solution cutter and curve surface of workpiece is relatively difficult, therefore curve surface of workpiece is usually separated into three
Cornual plate model will be converted to the point of contact for solving triangular plate of the cutter curved surface with curve surface of workpiece after discrete the problem of determining cutter-contact point.
Application number 201611205764X, entitled " a kind of projection algorithm of the five-axis robot track for no interference "
Patent of invention calculates the cutter-contact point and machining locus of the discrete triangle model of curve surface of workpiece using projection algorithm, such as Fig. 4 institute
Show comprising following step: curve surface of workpiece (a) being separated into triangle model first；(b) as shown in Figure 1, planning driving rail
Mark includes m driving point on track altogether；(c) cutter at i-th of driving point is projected along projecting direction to triangle model,
Projecting direction is the opposite direction of normal vector of the driving point in drive surface；(d) as shown in figure 3, screening cutter is along above-mentioned projection
N triangular plate of direction covering；(e) cutter is projected along above-mentioned projecting direction to j-th of triangular plate；(f) it calculates and is located at j-th three
Subpoint and projector distance on cornual plate, subpoint be along projecting direction cutter curved surface and the tangent point of triangular plate, step (e) with
(f) n times are recycled, the subpoint and projector distance on n triangular plate are obtained；(g) the corresponding subpoint of most short projector distance is chosen
As the cutter-contact point that the cutter at i-th of driving point is projected to triangle model, step (c) to step (f) is recycled m times, obtains m
A cutter-contact point positioned at triangle model；(h) the output m cutter-contact points positioned at triangle model, are finally calculated by cutter-contact point and are added
Work track.
Projection algorithm in foregoing invention patent has the following problems: first is that the computational accuracy and computational efficiency of cutter-contact point it
Between contradiction, if the density of triangular plate is inadequate, will lead to practical cutter-contact point and ideal cutter-contact point has certain error, computational accuracy
It is lower；, can be more because of triangular plate quantity if the density of triangular plate is larger, cause computational efficiency low.Second is that being located in Discrete Surfaces
Cutter-contact point makes the machining locus generated and cutter axis orientation single order discontinuous, to influence processing quality.
Summary of the invention
The present invention provides a kind of for generating curved surface without the projection algorithm for interfering five-axis robot track, for the prior art
The above defects or improvement requirements, using the method based on the continuous iteration of tangent plane of similar Newton-Raphson, it is therefore intended that
Guarantee that final cutter-contact point is located on original workpiece curved surface, improve machining accuracy and guarantees preferable machined surface quality.
It is provided by the present invention a kind of for generating projection algorithm of the curved surface without interference five-axis robot track comprising following
Step:
(1) the number of iterations variable c is set1=1, maximum number of iterations M is set1It is 20~100, convergence precision ε1It is 1.0-3
~1.0-6, choose cutter and be projected in the cutter-contact point on triangular plate as initial point P0；The cutter is projected in the knife on triangular plate
Contact is the corresponding subpoint of cutter most short projector distance along multiple triangular plates that projecting direction covers；
(2) initial point P is calculated at workpiece coordinate system WCS0To the shortest distance D of curve surface of workpiece0And on curve surface of workpiece
D0Corresponding points Q0Coordinate；
(3) judge whether D0≤ε1, it is then by initial point P0It exports, terminates as cutter-contact point；Otherwise step (4) are carried out；
(4) judge whether c1≥M1, it is then by initial point P0It exports, terminates as cutter-contact point；Otherwise step (5) are carried out；
(5) it is established under workpiece coordinate system and passes through point Q0Curve surface of workpiece tangent plane, carry out step (6)；
(6) cutter is projected to the tangent plane, obtains subpoint P of the cutter in tangent plane1Coordinate, carry out step
(7)；
(7) the subpoint P in the tangent plane is calculated1To the shortest distance D of curve surface of workpiece1And the D on curve surface of workpiece1
Corresponding points Q1, carry out step (8)；
(8) judge whether D1≤ε1, it is then by subpoint P1It exports, terminates as cutter-contact point；Otherwise step (9) are carried out；
(9) by the corresponding points Q on curve surface of workpiece0Coordinate and shortest distance D1It is respectively put into a container Pnt and apart from container
In Dis, judge whether that the number of element in two containers is equal to 2, is to carry out step (10), otherwise by corresponding points Q1Seat
Mark assigns corresponding points Q0, by c1+ 1 value assigns c1, go to step (4)；
Described container Pnt and be the sequential memory that can accommodate 2 elements apart from container Dis, point container Pnt are first
The element being stored in afterwards is respectively the first point element Pnt [0] and the second point element Pnt [1], the member being successively stored in apart from container Dis
Element is respectively first distance element Dis [0] and second distance element Dis [1]；
(10) judge whether Dis [1] > Dis [0], be to carry out step (11)；Otherwise respectively from container Pnt and a distance
Pnt [0] and Dis [0] are taken out in container Dis, by corresponding points Q1Coordinate assign corresponding points Q0, by c1+ 1 value assigns c1, turn step
Suddenly (4)；
(11) the first point element Pnt [0] and the second point element Pnt [1] are obtained using adjustment step-size in search algorithm
The point Q of misconvergence concussion on curve surface of workpiecenew, respectively from container Pnt and in container Dis take out Pnt [0] and
Dis [0], by point QnewCoordinate assign corresponding points Q0, by c1+ 1 value assigns c1, go to step (4)；
In above steps, the meaning that certain point is exported as cutter-contact point is defeated as cutter-contact point coordinate for the coordinate for putting certain
Out；The meaning for calculating or obtaining certain point is the coordinate for calculating or obtaining certain point.
In the step (2), when curve surface of workpiece is made of s surface composition, initial point P is calculated0Arrive curve surface of workpiece
Shortest distance D0When, initial point P is found out respectively0To the shortest distance L of s curved surfacekAnd the L on curve surface of workpiecekCorresponding points Rk
Coordinate, wherein k=1,2 ... s, initial point P0To the shortest distance D of curve surface of workpiece0=min { Lk, the D on curve surface of workpiece0
Corresponding points be Q0。
Step (6) cutter is projected to tangent plane, including following sub-step:
(6.1) tool coordinate system (CCS, Cutter Coordinate System) is established, is right-handed Cartesian coordinate system,
Coordinate origin is cutter location CL0(0,0,0), the cutter axis orientation T of cutterAFor Z axis, point Q is crossed0Curve surface of workpiece on tangent plane
Normal vector and Z axis determine that XOZ plane, X-axis are located in XOZ plane and perpendicular to Z axis, and Y-axis is orthogonal with X-axis and Z axis；
(6.2) point Q will be passed through under workpiece coordinate system WCS0Curve surface of workpiece tangent plane normal vector NTIt is transformed into cutter
Under coordinate system；
(6.3) the normal vector N of tangent plane is calculatedTWith the intersection point of cutter curved surface, as cutter-contact point CC0, obtain tool offset
Vector O is from cutter location CL0(0,0,0) it is directed toward cutter-contact point CC0Vector；
(6.4) it calculates and crosses cutter-contact point CC along projecting direction0Straight line with pass through point Q0Curve surface of workpiece tangent plane intersection point
Coordinate obtains being located at subpoint P in tangent plane under tool coordinate system1Coordinate；
(6.5) subpoint P in tangent plane will be located under tool coordinate system CCS1Coordinate transformation be workpiece coordinate system WCS under
Coordinate.
The cutter-contact point of step (8) output is subpoint P of the cutter in tangent plane1Rather than it is located at the point on curved surface
Q1, it is on the one hand to guarantee that the cutter location line of cutter projection front and back is parallel with projecting direction, so that cutter be avoided to cut
Cutter shaft fluctuation during curve surface of workpiece, on the other hand in order to guarantee that cutter and curve surface of workpiece are cut or owe to cut without mistake, to avoid
Cause the interference between cutter and curve surface of workpiece.
The step (10), when Dis [1] [0] > Dis, when showing to search for cutter-contact point using the method based on tangent plane,
Convergence reforming phenomena when similar Newton-Raphson rooting is produced between point Pnt [0] and Pnt [1], and adjustment is called to search
Rope step length algorithm can be searched for and occur less than the case where optimal cutter-contact point to avoid due to convergence concussion.
The step (11) includes following sub-step:
(11.1) cycle-index variable c is set2=1, maximum cycle M is set2It is 20~100, terminates precision ε2For
1.0-3~1.0-6, with symbol QaIt indicates Pnt [0], symbol QbIt indicates Pnt [1]；
By the point Q in workpiece coordinate systemaAnd QbBe converted to the correspondence parameter Q in parameter spacepa(ua, va) and Qpb(ub,
vb)；
(11.2) Q is calculatedpa(ua, va) and Qpb(ub, vb) between two parameter Qpa1(ua1, va1) and Qpa2(ua2, va2):
Qpa1(ua1, va1)=Qpb(ua, vb)-λ(Qpb(ua, vb)-Qpa(ua, va)),
Qpa2(ua2, va2)=Qpa(ua, va)+λ(Qpb(ua, vb)-Qpa(ua, va))；
In formula, constant λ=0.618；
(11.3) by the parameter Q in parameter spacepa1(ua1, va1) and Qpa2(ua2, va2) be converted in workpiece coordinate system space
Corresponding points Qa1And Qa2, and calculate Da1=f (Qa1) and Da2=f (Qa2)；
Da1=f (Qa1) indicate will point Qa1Coordinate assign corresponding points Q0, then carry out step (5), step (6) and step (7)
Afterwards, shortest distance D is obtained1, assign its value to Da1；
Da2=f (Qa2) indicate will point Qa2Coordinate assign corresponding points Q0, then carry out step (5), step (6) and step (7)
Afterwards, shortest distance D is obtained1, assign its value to Da2；
(11.4) judge whether c2≥M2, it is, it will point Qa1Coordinate assign point Qnew, export Qnew, terminate；Otherwise it carries out
Sub-step (11.5)；
(11.5) judge whether Da1≥Da2, it is to carry out sub-step (11.6), otherwise rotor step (11.9)；
(11.6) judge whether Da2≤ε2, it is, it will point Qa2Coordinate assign point Qnew, export Qnew, terminate；Otherwise it carries out
Sub-step (11.7)；
It (11.7) will point Qa1Coordinate assign Qa, point Qa2Coordinate assign Qa1, distance Da2Value assign Da1, calculate Qpa
(ua, va) and Qpb(ub, vb) between parameter Qpa2(ua2, va2):
Qpa2(ua2, va2)=Qpa(ua, va)+λ(Qpb(ua, vb)-Qpa(ua, va)): it carries out sub-step (11.8)；
(11.8) by the parameter Q in parameter spacepa2(ua2, va2) be converted to corresponding points Q in workpiece coordinate systema2, calculate
Da2=f (Qa2), by c2+ 1 value assigns c2, rotor step (11.4)；
(11.9) judge whether Da1≤ε2, it is, it will point Qa1Coordinate assign point Qnew, export Qnew, terminate；Otherwise it carries out
Sub-step (11.10)；
It (11.10) will point Qa2Coordinate assign Qb, point Qa1Coordinate assign Qa2, distance Da1Value assign Da2, calculate Qpa
(ua, va) and Qpb(ub, vb) between parameter Qpa1(ua1, va1):
Qpa1(ua1, va1)=Qpb(ub, vb)-λ(Qpb(ua, vb)-Qpa(ua, va))；It carries out sub-step (11.11)；
(11.11) by the parameter Q in parameter spacepa1(ua1, va1) be converted to corresponding points Q in workpiece coordinate systema1, calculate
Da1=f (Qa1), by c2+ 1 value assigns c2, rotor step (11.4).
Above-mentioned adjustment step-size in search algorithm, similar Fibonacci method look for extreme value, indicate to restrain at two in order to clearer
The process that adjustment step-size in search is constantly searched between point Pnt [0] and Pnt [1] is shaken, with symbol QaIt indicates Pnt [0], symbol QbTable
Show Pnt [1].When adjusting step-size in search, need to calculate point QaWith point QbBetween two o'clock Qa1And Qa2, to find misconvergence concussion
Point.The Q linearly calculated in workpiece coordinate systema1And Qa2Not on curve surface of workpiece, in order to guarantee Qa1And Qa2On curve surface of workpiece,
Using the point in workpiece coordinate system and the one-to-one relationship of the parameter in parameter space, first by the point Q in workpiece coordinate systema
And QbThe correspondence parameter Q being converted into parameter spacepa(ua, va) and Qpb(ub, vb)；Then in parameter space, two are calculated
Parameter Qpa1And Qpa2；Finally by Qpa1And Qpa2It is transformed into workpiece coordinate system, obtains point Qa1And Qa2。
As parameter space, curve surface of workpiece vector parameters equation is the two-dimensional Cartesian coordinate system formed using parameter u and vRespectively correspond workpiece coordinate system sky
Between in point Q (x, y, z) X, Y, Z coordinate, the parameter in point Q (x, y, z) and parameter space in workpiece coordinate system space
Mapping relations are Q (x, y, z)=Qp(u, v)；
Curve surface of workpiece vector parameters equation is indicated with B-spline surface vector parameters equation are as follows:
In formula, dI, j(i=0,1 ... m；J=0,1 ... n) be control point, the number of parameter u and v are respectively k and l, NI, k
(u) (i=0,1 ... m) and NJ, l(v) (j=0,1 ... n) is B-spline base；K, l, m, n are respectively positive integer；
B-spline base NI, k(u) (i=0,1 ... m) may be expressed as:
B-spline base NJ, 1(v) (j=0,1 ... n) may be expressed as:
As any one parameter Q in given parameters space on curve surface of workpiecep(u, v) it is bent can be directly substituted into above-mentioned B-spline
Face vector parameters equation, and parameter Q is acquired using De Boor algorithmpThe corresponding points Q (x, y, z) of (u, v) in workpiece coordinate system,
Specific calculating process see middle work " Computer-aided Geometric Design and non-uniform rational B-spline " of excuting a law (Higher Education Publishing House,
In September, 2013) one section of B-spline surface in 253-255 pages.When the calculating process is realized in software, Open can be directly utilized
The function interface Geom_Surafce:+gp_Pnt Value (u, v) provided in CASCADE is by the arbitrary parameter in parameter space
Qp(u, v) is converted into the corresponding points Q (x, y, z) in workpiece coordinate system space；
Any point Q (x, y, z), the corresponding points Q being converted into parameter space in given workpiece coordinate systemp(u, v)
When, objective function are as follows:
Min { Q (x, y, z)-Qp(u, v) }2
The corresponding parameter Q of above-mentioned objective function is solved using iterative algorithmpmin(umin, vmin), parameter QpminAs point Q (x,
Y, z) correspondence parameter Q in parameter spacep(u, v), specific calculating process see excute a law it is middle write " Computer-aided Geometric Design with
Non-uniform rational B-spline " in 493-494 pages by putting one section of inverse evaluation of parameters on curve, curved surface.The calculating process is real in software
Now, it can directly utilize the function interface GeomLibTool:+parameter (Surface) provided in Open CASCADE will
Any point Q (x, y, z) in workpiece coordinate system space is converted into corresponding parameter Q in parameter spacep(u, v)；
As shown in figure 5, Newton-Raphson method seeks the root of function of a single variable f (x)=0, appoints take a point F first0As first
Initial point makees point F0To the vertical line of curve f (x), point G is obtained0, and cross point G0Make the tangent line of f (x), hands over x-axis in F1Point, point F1Along vertical
Directly in the direction projection of x-axis to curve f (x), point G is obtained1, and cross point G1The tangent line for making f (x) obtains point F2, repeatedly, most
It can level off to the root of Equation f (x)=0 eventually.Cutter is to curved surface accurate projection algorithm, as shown in fig. 6, first with cutter to triangle
Piece, which projects, determines initial point P0, then calculate point P0To the shortest distance of curve surface of workpiece, point Q is obtained0, establish point Q0In workpiece song
Then cutter is projected along projecting direction to tangent plane, obtains the subpoint P in tangent plane by the tangent plane on face1, calculate and throw
Shadow point P1To the shortest distance of curve surface of workpiece, the subpoint Q on curve surface of workpiece is obtained1, to subpoint Q1Tangent plane is established, is held
Row cutter is projected to tangent plane, obtains subpoint P2.Repeatedly, cutter and the tangent subpoint of curved surface are eventually found, as
Cutter-contact point.
The present invention is in 201611205764X, a kind of entitled " projection calculation of the five-axis robot track for no interference
After the step of on the basis of the patent of invention of method ", being further improved to it, the patent of invention can be loaded on (g).
Inspiration of the present invention by Newton-Raphson iteration rooting, it is resulting to triangle model projection using cutter
Cutter-contact point using establishing tangent plane and implementing the method that cutter projects to tangent plane, utilizes adjustment step-size in search as initial point
Algorithm solves the problems, such as the convergence occurred when similar Newton-Raphson rooting concussion, compared with prior art, it is ensured that
Cutter-contact point improves the computational accuracy of cutter-contact point on original workpiece curved surface.
Detailed description of the invention
Fig. 1 is the schematic diagram of projection algorithm principle；
Fig. 2 is the definition schematic diagram of coordinate system, cutter-contact point and cutter location parameter；
Fig. 3 is the cutter triangle model perspective view discrete to curve surface of workpiece；
Fig. 4 is the existing cutter triangle model projection algorithm flow diagram discrete to curve surface of workpiece；
Fig. 5 is Newton-Raphson iteration rooting algorithm schematic diagram；
Fig. 6 is that the present invention is based on the projection algorithm schematic diagrames of the continuous iteration of tangent plane；
Fig. 7 is flow diagram of the embodiment of the present invention；
Fig. 8 is cutter to tangent plane projection algorithm schematic diagram.
Fig. 9 is adjustment step-size in search algorithm flow chart.
Figure 10 is the mapping relations schematic diagram of workpiece coordinate system space and parameter space.
Figure 11 is to utilize the improved cutter of the present invention to curve surface of workpiece accurate projection algorithm flow chart.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention further illustrates.
The embodiment of the present invention is as shown in fig. 7, comprises following steps:
The number of iterations variable c is arranged in step (1)1=1, maximum number of iterations M is set1It is 30, convergence precision ε1It is 1.0-6,
It chooses cutter and is projected in the cutter-contact point on triangular plate as initial point P0；It is knife that the cutter, which is projected in the cutter-contact point on triangular plate,
The corresponding subpoint of tool most short projector distance along multiple triangular plates that projecting direction covers；
Step (2) calculates initial point P at workpiece coordinate system WCS0To the shortest distance D of curve surface of workpiece0And in workpiece
D on curved surface0Corresponding points Q0Coordinate:
When curve surface of workpiece is made of 4 surface compositions, initial point P is calculated0To the shortest distance D of curve surface of workpiece0When, point
Initial point P is not found out0To the shortest distance L of 4 curved surfaceskAnd the L on curve surface of workpiecekCorresponding points RkCoordinate, wherein k=
1,2 ... 4, initial point P0To the shortest distance D of curve surface of workpiece0=min { Lk, the D on curve surface of workpiece0Corresponding points be Q0；
Step (3), judges whether D0≤ε1, it is then by initial point P0It exports, terminates as cutter-contact point；Otherwise step is carried out
(4)；
Step (4), judges whether c1≥M1, it is then by initial point P0It exports, terminates as cutter-contact point；Otherwise step is carried out
(5)；
Step (5) is established under workpiece coordinate system and passes through point Q0Curve surface of workpiece tangent plane, carry out step (6)；
(5.1) point Q is found0Normal vector N on curve surface of workpiece0；
(5.2) point Q is utilized0And its normal vector N0It establishes and passes through point Q0Curve surface of workpiece tangent plane；
Step (6) obtains the subpoint P in tangent plane as shown in figure 8, cutter is projected to tangent plane1, go to step
(7)；
(6.1) tool coordinate system (CCS, Cutter Coordinate System) is established, is right-handed Cartesian coordinate system,
Coordinate origin is cutter location CL0(0,0,0), the cutter axis orientation T of cutterAFor Z axis, point Q is crossed0Curve surface of workpiece on tangent plane
Normal vector and Z axis determine that XOZ plane, X-axis are located in XOZ plane and perpendicular to Z axis, and Y-axis is orthogonal with X-axis and Z axis；
(6.2) point Q will be passed through under workpiece coordinate system WCS0Curve surface of workpiece tangent plane normal vector NTIt is transformed into cutter
Under coordinate system；
(6.3) the normal vector N of tangent plane is calculatedTWith the intersection point of cutter curved surface, as cutter-contact point CC0, obtain tool offset
Vector O is from cutter location CL0(0,0,0) it is directed toward cutter-contact point CC0Vector；
(6.4) it calculates and crosses cutter-contact point CC along projecting direction0Straight line with pass through point Q0Curve surface of workpiece tangent plane intersection point
Coordinate obtains being located at subpoint P in tangent plane under tool coordinate system1Coordinate；
(6.5) subpoint P in tangent plane will be located under tool coordinate system CCS1Coordinate transformation be workpiece coordinate system WCS under
Coordinate.
Step (7) calculates the subpoint P in the tangent plane1To the shortest distance D of curve surface of workpiece1And in curve surface of workpiece
Upper D1Corresponding points Q1, carry out step (8)；
Step (8), judges whether D1≤ε1, it is then by subpoint P1It exports, terminates as cutter-contact point；Otherwise step is carried out
(9)；
Step (9), by the corresponding points Q on curve surface of workpiece0Coordinate and shortest distance D1Be respectively put into a container Pnt and away from
2 are equal to from the number in container Dis, judging whether element in two containers, is to carry out step (10), otherwise by corresponding points
Q1Coordinate assign corresponding points Q0, by c1+ 1 value assigns c1, go to step (4)；
Described container Pnt and be the sequential memory that can accommodate 2 elements apart from container Dis, point container Pnt are first
The element being stored in afterwards is respectively the first point element Pnt [0] and the second point element Pnt [1], the member being successively stored in apart from container Dis
Element is respectively first distance element Dis [0] and second distance element Dis [1]；
Step (10) judges whether Dis [1] > Dis [0], is to carry out step (11)；Otherwise respectively from a container Pnt
With Pnt [0] and Dis [0] are taken out in container Dis, by corresponding points Q1Coordinate assign corresponding points Q0, by c1+ 1 value assigns
c1, go to step (4)；
Step (11), for the first point element Pnt [0] and the second point element Pnt [1], using adjustment step-size in search algorithm,
Obtain the point Q of the misconvergence being located on curve surface of workpiece concussionnew, Pnt is taken out from container Pnt and in container Dis respectively
[0] and Dis [0], by point QnewCoordinate assign corresponding points Q0, by c1+ 1 value assigns c1, go to step (4)；
As shown in figure 9, adjustment step-size in search algorithm specifically comprises the following steps:
(11.1) cycle-index variable c is set2=1, maximum cycle M is set2It is 20, terminates precision ε2It is 1.0-6, with
Symbol QaIt indicates Pnt [0], symbol QbIt indicates Pnt [1]；
As shown in Figure 10, by the point Q in workpiece coordinate systemaWith point QbBe converted to the correspondence parameter Q in parameter spacepa(ua,
va) and Qpb(ub, vb)；
(11.2) Q is calculatedpa(ua, va) and Qpb(ub, vb) between two parameter Qpa1(ua1, va1) and Qpa2(ua2, va2):
Qpa1(ua1, va1)=Qpb(ua, vb)-λ(Qpb(ua, vb)-Qpa(ua, va)),
Qpa2(ua2, va2)=Qpa(ua, va)+λ(Qpb(ua, vb)-Qpa(ua, va))；
In formula, constant λ=0.618；
(11.3) by the parameter Q in parameter spacepa1(ua1, va1) and Qpa2(ua2, va2) be converted to pair in workpiece coordinate system
It should point Qa1And Qa2, and calculate Da1=f (Qa1) and Da2=f (Qa2)；
Da1=f (Qa1) indicate will point Qa1Coordinate assign corresponding points Q0, then carry out step (5), step (6) and step (7)
Afterwards, shortest distance D is obtained1, assign its value to Da1；
Da2=f (Qa2) indicate will point Qa2Coordinate assign corresponding points Q0, then carry out step (5), step (6) and step (7)
Afterwards, shortest distance D is obtained1, assign its value to Da2；
(11.4) judge whether c2≥M2, it is, it will point Qa1Coordinate assign point Qnew, export Qnew, terminate；Otherwise it carries out
Sub-step (11.5)；
(11.5) judge whether Da1≥Da2, it is to carry out sub-step (11.6), otherwise rotor step (11.9)；
(11.6) judge whether Da2≤ε2, it is, it will point Qa2Coordinate assign point Qnew, export Qnew, terminate；Otherwise it carries out
Sub-step (11.7)；
It (11.7) will point Qa1Coordinate assign Qa, point Qa2Coordinate assign Qa1, distance Da2Value assign Da1, calculate Qpa
(ua, va) and Qpb(ub, vb) between parameter Qpa2(ua2, va2):
Qpa2(ua2, va2)=Qpa(ua, va)+λ(Qpb(ua, vb)-Qpa(ua, va)): it carries out sub-step (11.8)；
(11.8) by the parameter Q in parameter spacepa2(ua2, va2) be converted to corresponding points Q in workpiece coordinate systema2, calculate
Da2=f (Qa2), by c2+ 1 value assigns c2, rotor step (11.4)；
(11.9) judge whether Da1≤ε2, it is, it will point Qa1Coordinate assign point Qnew, export Qnew, terminate；Otherwise it carries out
Sub-step (11.10)；
It (11.10) will point Qa2Coordinate assign Qb, point Qa1Coordinate assign Qa2, distance Da1Value assign Da2, calculate Qpa
(ua, va) and Qpb(ub, vb) between parameter Qpa1(ua1, va1):
Qpa1(ua1, va1)=Qpb(ub, vb)-λ(Qpb(ua, vb)-Qpa(ua, va))；It carries out sub-step (11.11)；
(11.11) by the parameter Q in parameter spacepa1(ua1, va1) be converted to corresponding points Q in workpiece coordinate systema1, calculate
Da1=f (Qa1), by c2+ 1 value assigns c2, rotor step (11.4).
The present embodiment is in 201611205764X, a kind of entitled " projection calculation of the five-axis robot track for no interference
On the basis of the patent of invention of method ", it is further improved, after step (g) shown in Fig. 4 being loaded on, is constituted shown in Figure 11
The step of process (h), (i), (j).
Claims (4)
1. it is a kind of for generate curved surface without interference five-axis robot track projection algorithm, which is characterized in that itself the following steps are included:
(1) the number of iterations variable c is set1=1, maximum number of iterations M is set1It is 20~100, convergence precision ε1It is 1.0-3~
1.0-6, choose cutter and be projected in the cutter-contact point on triangular plate as initial point P0；The cutter is projected in the touching of the knife on triangular plate
Point is the corresponding subpoint of cutter most short projector distance along multiple triangular plates that projecting direction covers；
(2) initial point P is calculated at workpiece coordinate system WCS0To the shortest distance D of curve surface of workpiece0And the D on curve surface of workpiece0's
Corresponding points Q0Coordinate；
(3) judge whether D0≤ε1, it is then by initial point P0It exports, terminates as cutter-contact point；Otherwise step (4) are carried out；
(4) judge whether c1≥M1, it is then by initial point P0It exports, terminates as cutter-contact point；Otherwise step (5) are carried out；
(5) it is established under workpiece coordinate system and passes through point Q0Curve surface of workpiece tangent plane, carry out step (6)；
(6) cutter is projected to the tangent plane, obtains subpoint P of the cutter in tangent plane1Coordinate, carry out step (7)；
(7) the subpoint P in the tangent plane is calculated1To the shortest distance D of curve surface of workpiece1And the D on curve surface of workpiece1Pair
It should point Q1, carry out step (8)；
(8) judge whether D1≤ε1, it is then by subpoint P1It exports, terminates as cutter-contact point；Otherwise step (9) are carried out；
(9) by the corresponding points Q on curve surface of workpiece0Coordinate and shortest distance D1It is respectively put into a container Pnt and apart from container Dis
In, judge whether that the number of element in two containers is equal to 2, is to carry out step (10), otherwise by corresponding points Q1Coordinate
Assign corresponding points Q0, by c1+ 1 value assigns c1, go to step (4)；
Described container Pnt and be the sequential memory that can accommodate 2 elements apart from container Dis, point container Pnt are successively deposited
The element entered is respectively the first point element Pnt [0] and the second point element Pnt [1], the element being successively stored in apart from container Dis point
It Wei not first distance element Dis [0] and second distance element Dis [1]；
(10) judge whether Dis [1] > Dis [0], be to carry out step (11)；Otherwise respectively from container Pnt and apart from container
Pnt [0] and Dis [0] are taken out in Dis, by corresponding points Q1Coordinate assign corresponding points Q0, by c1+ 1 value assigns c1, go to step
(4)；
(11) the first point element Pnt [0] and the second point element Pnt [1] are located at using adjustment step-size in search algorithm
The point Q of misconvergence concussion on curve surface of workpiecenew, Pnt [0] and Dis are taken out from container Pnt and in container Dis respectively
[0], by point QnewCoordinate assign corresponding points Q0, by c1+ 1 value assigns c1, go to step (4)；
In above steps, the meaning that certain point is exported as cutter-contact point is exported for the coordinate for putting certain as cutter-contact point coordinate；
The meaning for calculating or obtaining certain point is the coordinate for calculating or obtaining certain point.
2. as described in claim 1 for generating projection algorithm of the curved surface without interference five-axis robot track, it is characterised in that:
In the step (2), when curve surface of workpiece is made of s surface composition, initial point P is calculated0To the most short distance of curve surface of workpiece
From D0When, initial point P is found out respectively0To the shortest distance L of s curved surfacekAnd the L on curve surface of workpiecekCorresponding points RkCoordinate,
Wherein k=1,2 ... s, initial point P0To the shortest distance D of curve surface of workpiece0=min { Lk, the D on curve surface of workpiece0Corresponding points
For Q0。
3. as claimed in claim 1 or 2 for generating projection algorithm of the curved surface without interference five-axis robot track, feature exists
In:
Step (6) cutter is projected to tangent plane, including following sub-step:
(6.1) tool coordinate system (CCS, Cutter Coordinate System) is established, is right-handed Cartesian coordinate system, coordinate
Origin is cutter location CL0(0,0,0), the cutter axis orientation T of cutterAFor Z axis, point Q is crossed0Curve surface of workpiece on tangent plane normal direction
Vector and Z axis determine that XOZ plane, X-axis are located in XOZ plane and perpendicular to Z axis, and Y-axis is orthogonal with X-axis and Z axis；
(6.2) point Q will be passed through under workpiece coordinate system WCS0Curve surface of workpiece tangent plane normal vector NTIt is transformed into tool coordinate
Under system；
(6.3) the normal vector N of tangent plane is calculatedTWith the intersection point of cutter curved surface, as cutter-contact point CC0, obtain tool offset vector
O is from cutter location CL0(0,0,0) it is directed toward cutter-contact point CC0Vector；
(6.4) it calculates and crosses cutter-contact point CC along projecting direction0Straight line with pass through point Q0Curve surface of workpiece tangent plane intersection point sit
Mark obtains being located at subpoint P in tangent plane under tool coordinate system1Coordinate；
(6.5) subpoint P in tangent plane will be located under tool coordinate system CCS1Coordinate transformation be workpiece coordinate system WCS under seat
Mark.
4. as claimed in claim 1 or 2 for generating projection algorithm of the curved surface without interference five-axis robot track, feature exists
In:
The step (11) includes following sub-step:
(11.1) cycle-index variable c is set2=1, maximum cycle M is set2It is 20~100, terminates precision ε2It is 1.0-3~
1.0-6, with symbol QaIt indicates Pnt [0], symbol QbIt indicates Pnt [1]；
By the point Q in workpiece coordinate systemaWith point QbBe converted to the correspondence parameter Q in parameter spacepa(ua, va) and Qpb(ub, vb)；Institute
Stating parameter space is the two-dimensional Cartesian coordinate system being made of parameter u and v；
(11.2) calculating parameter Qpa(ua, va) and Qpb(ub, vb) between two parameter Qpa1(ua1, va1) and Qpa2(ua2, va2):
Qpa1(ua1, va1)=Qpb(ua, vb)-λ(Qpb(ua, vb)-Qpa(ua, va)),
Qpa2(ua2, va2)=Qpa(ua, va)+λ(Qpb(ua, vb)-Qpa(ua, va))；
In formula, constant λ=0.618；
(11.3) by the parameter Q in parameter spacepa1(ua1, va1) and Qpa2(ua2, va2) be converted to corresponding points in workpiece coordinate system
Qa1And Qa2, and calculate Da1=f (Qa1) and Da2=f (Qa2)；
Da1=f (Qa1) indicate will point Qa1Coordinate assign corresponding points Q0, then after carrying out step (5), step (6) and step (7), obtain
To shortest distance D1, assign its value to Da1；
Da2=f (Qa2) indicate will point Qa2Coordinate assign corresponding points Q0, then after carrying out step (5), step (6) and step (7), obtain
To shortest distance D1, assign its value to Da2；
(11.4) judge whether c2≥M2, it is, it will point Qa1Coordinate assign point Qnew, export Qnew, terminate；Otherwise sub-step is carried out
(11.5)；
(11.5) judge whether Da1≥Da2, it is to carry out sub-step (11.6), otherwise rotor step (11.9)；
(11.6) judge whether Da2≤ε2, it is, it will point Qa2Coordinate assign point Qnew, export Qnew, terminate；Otherwise sub-step is carried out
Suddenly (11.7)；
It (11.7) will point Qa1Coordinate assign Qa, point Qa2Coordinate assign Qa1, distance Da2Value assign Da1, calculate Qpa(ua, va)
And Qpb(ub, vb) between parameter Qpa2(ua2, va2):
Qpa2(ua2, va2)=Qpa(ua, va)+λ(Qpb(ua, vb)-Qpa(ua, va)): it carries out sub-step (11.8)；
(11.8) by the parameter Q in parameter spacepa2(ua2, va2) be converted to corresponding points Q in workpiece coordinate systema2, calculate Da2=f
(Qa2), by c2+ 1 value assigns c2, rotor step (11.4)；
(11.9) judge whether Da1≤ε2, it is, it will point Qa1Coordinate assign point Qnew, export Qnew, terminate；Otherwise sub-step is carried out
Suddenly (11.10)；
It (11.10) will point Qa2Coordinate assign Qb, point Qa1Coordinate assign Qa2, distance Da1Value assign Da2, calculate Qpa(ua,
va) and Qpb(ub, vb) between parameter Qpa1(ua1, va1):
Qpa1(ua1, va1)=Qpb(ub, vb)-λ(Qpb(ua, vb)-Qpa(ua, va))；It carries out sub-step (11.11)；
(11.11) by the parameter Q in parameter spacepa1(ua1, va1) be converted to corresponding points Q in workpiece coordinate systema1, calculate Da1=
f(Qa1), by c2+ 1 value assigns c2, rotor step (11.4).
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| CN110362039B (en) * | 2018-04-11 | 2021-02-12 | 华中科技大学 | Five-axis machining workpiece placement posture optimization method |
| CN110450150B (en) * | 2018-05-07 | 2022-10-21 | 苏州睿牛机器人技术有限公司 | Trajectory tracking control method and trajectory tracking system |
| CN110455272B (en) * | 2018-05-07 | 2023-05-12 | 苏州睿牛机器人技术有限公司 | Sensor system in a track following system |
| CN110096034B (en) * | 2019-04-26 | 2020-06-09 | 华中科技大学 | Reconstruction method of three-axis tool path curved surface transverse information based on projection algorithm |
| CN110221575B (en) * | 2019-05-31 | 2020-07-10 | 华中科技大学 | Thin-wall part robot machining path generation method based on machining parameters |
| CN110394487A (en) * | 2019-07-30 | 2019-11-01 | 哈尔滨理工大学 | A kind of hardened steel free form surface test specimen and milling process |
| CN110727246B (en) * | 2019-10-29 | 2021-03-19 | 江苏长虹智能装备股份有限公司 | Tool and workpiece instantaneous contact contour extraction method based on tool position file |
| CN112734830B (en) * | 2020-12-30 | 2022-05-03 | 无锡祥生医疗科技股份有限公司 | Point cloud data-based pose control method, device, equipment and storage medium |
| TWI742981B (en) | 2021-01-06 | 2021-10-11 | 財團法人工業技術研究院 | Method for analyzing overcutting defect of machining path |
| CN113377066B (en) * | 2021-05-25 | 2022-09-09 | 北京工业大学 | Rapid interference detection method for NURBS curved surface five-axis machining cutter path |
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