CN106227153A - A kind of cutter positioning method being applicable to the non-extended straight-line surface of Flank machining - Google Patents

A kind of cutter positioning method being applicable to the non-extended straight-line surface of Flank machining Download PDF

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CN106227153A
CN106227153A CN201610872912.7A CN201610872912A CN106227153A CN 106227153 A CN106227153 A CN 106227153A CN 201610872912 A CN201610872912 A CN 201610872912A CN 106227153 A CN106227153 A CN 106227153A
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point
cutter
vector
straight
line
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CN106227153B (en
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莫艽
关立文
王立平
陈晃
李铁民
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Tsinghua University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • 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
    • G05B19/402—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 control arrangements for positioning, e.g. centring a tool relative to a hole in the workpiece, additional detection means to correct position
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/36—Nc in input of data, input key till input tape
    • G05B2219/36359—As function of tool location

Abstract

The present invention relates to a kind of cutter positioning method being applicable to the non-extended straight-line surface of Flank machining, its step: choose the non-extended straight-line surface of part to be processed, up-and-down boundary curve is C1(u) and C2(u)；Choose any one straight edge line S on ruled surface1S2, corresponding parameter value is u0；At straight edge line S1S2Near choose unknown parameter u1And u2, coboundary curve is at P1The unit tangent vector of point is T1(u1), lower boundary curve is at P2The unit tangent vector of point is T2(u2), at P1The unit vector of the principal normal of point is N1(u1), the unit vector of binormal is B1(u1), at P2The unit vector of the principal normal of point is N2(u2), the unit vector of binormal is B2(u2)；Determine about putting M on tool axis1、M2With a P1、P2Relation equation；After equation adds two constraintss, solve four unknown quantity u1、u2, θ andAnd then calculate M1And M2Value, then the generating tool axis vector obtaining cutter is, in conjunction with point of a knife point M2, determine the pose of cutter；All parameters are traveled through with suitable parameter space from small to large ord until completing the location attitude of the cutter of whole ruled surface along boundary curve.

Description

A kind of cutter positioning method being applicable to the non-extended straight-line surface of Flank machining
Technical field
The present invention relates to a kind of cutter positioning method, especially with regard to a kind of application suitable in Digit Control Machine Tool manufacture field Cutter positioning method for the non-extended straight-line surface of Flank machining.
Background technology
At present, each point as it is shown in figure 1, non-extended straight-line surface is different from extended straight-line surface, on the same straight edge line of curved surface The size and Orientation of normal vector is not quite similar, and there is twist angle (as shown in Figure 2), due to the existence of twist angle so that cutter without The most complete coating surface of this kind of extended straight-line surface of image of Buddha conical side surface, cylindrical side, and and plane tangent.Determine in any case , always there is the errors of principles in location attitude of the cutter, the method calculating location attitude of the cutter of existing a series of mathematics accurate Analysis is (the most single Point offsetting, 2 offsettings, 3 phase pressure methods etc.) all there is some problems: single-point offsetting, the method such as 2 offsettings is by mistake Difference is excessive, and 3 phase pressure methods are the most sensitive for initial value, and calculates the hugest, and inefficiency is the most all unfavorable for Processing faster and better on Digit Control Machine Tool has the part of non-extended straight-line surface feature.
Summary of the invention
For the problems referred to above, it is an object of the invention to provide a kind of cutter being applicable to the non-extended straight-line surface of Flank machining and determine Method for position, the method can reduce the errors of principles (compared with single-point offsetting and 2 offsettings) of more than 90%, and phase For 3 phase pressure methods can reduce more than 62% the calculating time.
For achieving the above object, the present invention takes techniques below scheme: one is applicable to the non-extended straight-line surface of Flank machining Cutter positioning method, it is characterised in that the method comprises the following steps: 1) choose the non-extended straight-line surface of part to be processed, The up-and-down boundary curve of this non-extended straight-line surface is C1(u) and C2(u)；2) any one straight edge line on non-extended straight-line surface is chosen S1S2, this straight edge line S1S2Corresponding parameter value is u=u0；3) at straight edge line S1S2Near choose unknown parameter u1And u2, u1Corresponding Coboundary curve C1Point P on (u)1, u2Corresponding lower boundary curve C2Point P on (u)2, coboundary curve C1U () is at P1The list of point Position tangent vector is T1(u1), lower boundary curve C2U () is at P2The unit tangent vector of point is T2(u2), at P1The unit of the principal normal of point Vector is N1(u1), the unit vector of binormal is B1(u1), in like manner at P2The unit vector of the principal normal of point is N2(u2), secondary method The unit vector of line is B2(u2)；4)M1M2For 2 point on tool axis, junction point M1With P1Point, junction point M2With P2Point, makes them Meet vector (M1-P1) at N1(u1) and B1(u1) in the plane that determines, with N1(u1) into θ angle, and its mould is equal to tool radius R； In like manner, vector (M2-P2) at N2(u2) and B2(u2) in the plane that determines, with N2(u2) becomeAngle, its mould is equal to tool radius R；? To about putting M on tool axis1、M2With a P1、P2Relation equation；Wherein, some M2For point of a knife point, put M1Pacify for point of a knife point and cutter A bit between decorateeing；5) to step 4) in equation add first constraints: (M1-M2)·(M1-P1)=(M1-M2)· (M2-P2)=0；6) to step 4) in equation add second constraints: second constraints is M0M1M2Three point on a straight line, M0It is M1M2Midpoint；7) equation obtained after adding two constraintss constitutes the equation group containing four equations, solves four Unknown quantity u1、u2, θ and8) according to step 7) in solving result calculate M1And M2Value, then the generating tool axis vector obtaining cutter is (M1-M2), in conjunction with point of a knife point M2, determine the pose of cutter；Generate the location attitude of the cutter NC instruction on this straight edge line；9) basis Step 1)～8) press parameter order traversal from small to large all straight edge lines sequence along boundary curve, until having calculated whole straight burr The location attitude of the cutter in face determines.
Further, described step 4) in, tool axis is put M1、M2With a P1、P2Relation equation is:
M1-P1=Rcos (θ) N1(u1)+Rsin(θ)B1(u1),
Further, described step 5) in, obtain after adding first constraints:
a1cos(θ)+b1Sin (θ)+R=0,
Wherein:
a2=(M1-M2)N2(u2)-RB1(u1)·N2(u2)sinθ+RN1(u1)·N2(u2) cos θ,
b2=(M1-M2)B2(u2)-RB1(u1)·B2(u2)sinθ+RN1(u1)·B2(u2)cosθ。
Further, described step 6) in, obtain after adding second constraints:
M 0 x - M 1 x M 2 x - M 1 x = M 0 y - M 1 y M 2 y - M 1 y = M 0 z - M 1 z M 2 z - M 1 z ;
In formula, M0x、M0y、M0zRepresent M respectively0X, y, z coordinate value；M1x、M1y、M1zRepresent M respectively1X, y, z coordinate Value；M2x、M2y、M2zRepresent M respectively2X, y, z coordinate value.
Further, described step 9) in, straight edge line sequence is according to total arc length equal decile up-and-down boundary directrix, in directrix Obtain the series of points that arc length interval is equal, the corresponding straight edge line of each point in these points, thus by these some correspondences Straight edge line constitutes straight edge line sequence.
Due to the fact that and take above technical scheme, it has the advantage that the present invention passes through the upper of non-extended straight-line surface Point on point on lower boundary curve and tool axis sets up equation group, and solve after adding two constraintss corresponding the most not The amount of knowing u1、u2, θ andAnd then determine the pose of cutter.Therefore, present invention achieves effectively determining location attitude of the cutter, it is possible to Effectively complete the Flank machining to non-extended straight-line surface part, reduce mismachining tolerance, promote working (machining) efficiency.
Accompanying drawing explanation
Fig. 1 is non-extended straight-line surface schematic diagram in prior art；
Fig. 2 is twist angle schematic diagram in prior art；
Fig. 3 is the location attitude of the cutter schematic diagram of the present invention；
Fig. 4 a is that extended straight-line surface part non-for same uses single-point offsetting to calculate error map；
Fig. 4 b is that extended straight-line surface part non-for same uses 2 offsettings to calculate error map；
Fig. 4 c is that extended straight-line surface part non-for same uses 3 phase pressure methods to calculate error map；
Fig. 4 d is that extended straight-line surface part non-for same uses inventive algorithm to calculate error map.
Detailed description of the invention
With embodiment, the present invention is described in detail below in conjunction with the accompanying drawings.
As it is shown on figure 3, the present invention provides a kind of cutter positioning method being applicable to the non-extended straight-line surface of Flank machining, its bag Include following steps:
1) choosing the non-extended straight-line surface of part to be processed, the up-and-down boundary curve of this non-extended straight-line surface is C1(u) and C2 (u)。
2) any one straight edge line S on non-extended straight-line surface is chosen1S2, this straight edge line S1S2Corresponding parameter value is u=u0。
3) in step 2) in straight edge line S1S2Near choose unknown parameter u1And u2, u1Corresponding coboundary curve C1On (u) Some P1, u2Corresponding lower boundary curve C2Point point P on (u)2, coboundary curve C1U () is at P1The unit tangent vector of point is T1 (u1), lower boundary curve C2U () is at P2The unit tangent vector of point is T2(u2), at P1The unit vector of the principal normal of point is N1(u1), The unit vector of binormal is B1(u1), in like manner at P2The unit vector of the principal normal of point is N2(u2), the unit vector of binormal For B2(u2)。
4)M1M2For 2 point on tool axis, junction point M1With P1Point, junction point M2With P2Point, makes them meet vector (M1- P1) at N1(u1) and B1(u1) in the plane that determines, with N1(u1) into θ angle, and its mould is equal to tool radius R；In like manner, vector (M2-P2) at N2(u2) and B2(u2) in the plane that determines, with N2(u2) becomeAngle, its mould is equal to tool radius R.Therefore two are obtained Individual equation:
M1-P1=Rcos (θ) N1(u1)+Rsin(θ)B1(u1),
Wherein, some M2Exactly point of a knife point, puts M1For a bit between point of a knife point and Cutting tool installation manner point.
5) to step 4) in equation add first constraints: vector (M1-P1) and vector (M2-P2) all with (M1- P1) vertical, so constraints is (M1-M2)·(M1-P1)=(M1-M2)·(M2-P2)=0, therefore obtains:
a1cos(θ)+b1Sin (θ)+R=0,
Wherein:
a2=(M1-M2)N2(u2)-RB1(u1)·N2(u2)sinθ+RN1(u1)·N2(u2) cos θ,
b2=(M1-M2)B2(u2)-RB1(u1)·B2(u2)sinθ+RN1(u1)·B2(u2)cosθ。
6) to step 4) in equation add second constraints: S0It is S1S2Midpoint, M0It is M1M2Midpoint, (M0- S0) it is N1(u1) and N2(u2) angular bisector direction, its mould be equal to tool radius R, second constraints is M0M1M23 altogether Line, obtains equation:
M 0 x - M 1 x M 2 x - M 1 x = M 0 y - M 1 y M 2 y - M 1 y ,
M 0 y - M 1 y M 2 y - M 1 y = M 0 z - M 1 z M 2 z - M 1 z ;
In formula, M0x、M0y、M0zRepresent M respectively0X, y, z coordinate value；M1x、M1y、M1zRepresent M respectively1X, y, z coordinate Value；M2x、M2y、M2zRepresent M respectively2X, y, z coordinate value.
7) by step 5) and step 6) in equation constitute containing the equation group of four equations, solve four unknown quantity u1、u2、θ With
8) according to step 7) in solving result calculate M1With point of a knife point M2Value, then the generating tool axis vector obtaining cutter is (M1-M2), in conjunction with point of a knife point M2, determine the pose of cutter；Generate the location attitude of the cutter NC instruction on this straight edge line；
9) according to step 1)～8) press parameter order traversal from small to large all straight edge lines sequence along boundary curve, until meter The location attitude of the cutter having calculated whole ruled surface determines；Wherein, straight edge line sequence is according to total arc length equal decile up-and-down boundary directrix (or arbitrary height directrix), obtains the series of points that arc length interval is equal in directrix, and in these points, each point is at straight burr On unique straight edge line on face, the therefore corresponding straight edge line of each point, thus be made up of directly the straight edge line that these points are corresponding Bus sequence.
Above-mentioned steps 7) in, the equation group constituted due to four equations is transcendental equations, so needing to use iterative method Solve, u1、u2, θ andIterative initial value can be chosen as u0、u0, 0,0, it is also possible to select other initial values as required.
Above-mentioned steps 8) in, along tool axis direction, point of a knife point can suitably be adjusted, reach preferably to process Purpose.
Above-mentioned steps 9) in, arc length interval is to have certain reasonable value scope, and this reasonable value scope is for set in advance Determine scope, in this span, have upper boundary values, arbitrarily change, less than what the arc length of this upper boundary values was spaced, the principle caused Range of error (maximum error-minimum error) variation is all without less than 10%, if arc length interval is more than this upper boundary values, then The scope of the errors of principles can be caused beyond 10%.It should be understood that the least calculating in interval of (1) arc length is the longest, the most in advance The coboundary of the reasonable value scope first arranged is optimum.(2) the 10% of this errors of principles mobility scale can be according to reality Suitably variation is made in errors of principles required precision.(3) upper boundary values of the errors of principles and the processing ruled surface shape of part and make Relevant with the diameter of cutter, it is different in varied situations, should determine according to results of calculation and mobility scale percentage ratio.
Embodiment: as shown in Fig. 4 a～Fig. 4 d, for a kind of specific S-shaped part, the cutter positioning method of the present invention is relative The errors of principles of more than 90% can be reduced, as shown in table 1 in existing single-point offsetting and 2 offsettings.
Several distinct methods of table 1 efficiency comparative under MATLAB emulates
As shown in table 1, for a kind of specific S-shaped part, the cutter positioning method of the present invention is relative to 3 phase pressure method energy Enough reduce the calculating time of more than 62%.
It follows that the present invention is in use, based on the actual application requirements, it is possible to effectively complete non-extended straight-line surface The processing of part, and generate corresponding location attitude of the cutter NC instruction.
The various embodiments described above are merely to illustrate the present invention, the structure of each parts, size, arrange position and shape is all permissible Be varied from, on the basis of technical solution of the present invention, all improvement individual part carried out according to the principle of the invention and etc. With conversion, the most should not get rid of outside protection scope of the present invention.

Claims (5)

1. the cutter positioning method being applicable to the non-extended straight-line surface of Flank machining, it is characterised in that the method includes following Step:
1) choosing the non-extended straight-line surface of part to be processed, the up-and-down boundary curve of this non-extended straight-line surface is C1(u) and C2(u)；
2) any one straight edge line S on non-extended straight-line surface is chosen1S2, this straight edge line S1S2Corresponding parameter value is u=u0；
3) at straight edge line S1S2Near choose unknown parameter u1And u2, u1Corresponding coboundary curve C1Point P on (u)1, u2Under correspondence Boundary curve C2Point P on (u)2, coboundary curve C1U () is at P1The unit tangent vector of point is T1(u1), lower boundary curve C2(u) At P2The unit tangent vector of point is T2(u2), at P1The unit vector of the principal normal of point is N1(u1), the unit vector of binormal is B1(u1), in like manner at P2The unit vector of the principal normal of point is N2(u2), the unit vector of binormal is B2(u2)；
4)M1M2For 2 point on tool axis, junction point M1With P1Point, junction point M2With P2Point, makes them meet vector (M1-P1) N1(u1) and B1(u1) in the plane that determines, with N1(u1) into θ angle, and its mould is equal to tool radius R；In like manner, vector (M2-P2) At N2(u2) and B2(u2) in the plane that determines, with N2(u2) becomeAngle, its mould is equal to tool radius R；Obtain about tool axis Upper some M1、M2With a P1、P2Relation equation；Wherein, some M2For point of a knife point, put M1For between point of a knife point and Cutting tool installation manner point Point；
5) to step 4) in equation add first constraints:
(M1-M2)·(M1-P1)=(M1-M2)·(M2-P2)=0；
6) to step 4) in equation add second constraints: second constraints is M0M1M2Three point on a straight line, M0It is M1M2Midpoint；
7) equation obtained after adding two constraintss constitutes the equation group containing four equations, solves four unknown quantity u1、 u2, θ and
8) according to step 7) in solving result calculate M1And M2Value, then obtain the generating tool axis vector of cutter for (M1-M2), in conjunction with cutter Cusp M2, determine the pose of cutter；Generate the location attitude of the cutter NC instruction on this straight edge line；
9) according to step 1)～8) press parameter order traversal from small to large all straight edge lines sequence along boundary curve, until having calculated The location attitude of the cutter becoming whole ruled surface determines.
A kind of cutter positioning method being applicable to the non-extended straight-line surface of Flank machining, its feature exists In: described step 4) in, tool axis is put M1、M2With a P1、P2Relation equation is:
M1-P1=Rcos (θ) N1(u1)+Rsin(θ)B1(u1),
A kind of cutter positioning method being applicable to the non-extended straight-line surface of Flank machining, its feature exists In: described step 5) in, obtain after adding first constraints:
a1cos(θ)+b1Sin (θ)+R=0,
Wherein:
a2=(M1-M2)N2(u2)-RB1(u1)·N2(u2)sinθ+RN1(u1)·N2(u2) cos θ,
b2=(M1-M2)B2(u2)-RB1(u1)·B2(u2)sinθ+RN1(u1)·B2(u2)cosθ。
A kind of cutter positioning method being applicable to the non-extended straight-line surface of Flank machining, its feature exists In: described step 6) in, obtain after adding second constraints:
M 0 x - M 1 x M 2 x - M 1 x = M 0 y - M 1 y M 2 y - M 1 y = M 0 z - M 1 z M 2 z - M 1 z ;
In formula, M0x、M0y、M0zRepresent M respectively0X, y, z coordinate value；M1x、M1y、M1zRepresent M respectively1X, y, z coordinate value；M2x、 M2y、M2zRepresent M respectively2X, y, z coordinate value.
A kind of cutter positioning method being applicable to the non-extended straight-line surface of Flank machining, its feature exists In: described step 9) in, straight edge line sequence is according to total arc length equal decile up-and-down boundary directrix, obtains arc length interval in directrix Equal series of points, the corresponding straight edge line of each point in these points, thus be made up of directly the straight edge line that these points are corresponding Bus sequence.
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