CN104287858A - Method for cutting bracket-free invisible appliance - Google Patents

Method for cutting bracket-free invisible appliance Download PDF

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Publication number
CN104287858A
CN104287858A CN201410505449.3A CN201410505449A CN104287858A CN 104287858 A CN104287858 A CN 104287858A CN 201410505449 A CN201410505449 A CN 201410505449A CN 104287858 A CN104287858 A CN 104287858A
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cutter
coordinate system
axis
point
rotating shaft
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CN104287858B (en
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吕建明
肖遂
陈飞舟
朱彤
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HANGZHOU YIYA DIGITAL DENTAL Co Ltd
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HANGZHOU YIYA DIGITAL DENTAL Co Ltd
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Abstract

The invention discloses a method for cutting a bracket-free invisible appliance. The method comprises the following steps: generating a cutting track curve on a tooth model, wherein the tooth model comprises a gum model and a dentition model; taking a coordinate system of the cutting track curve as a workpiece coordinate system SYHE, sampling the cutting track curve, wherein the number of sampling points is N, and direction vectors epsilon x, epsilon y and epsilon z and coordinates (X, Y) are formed in each sampling point; and generating a tool path of a five-axis processing center by virtue of the cutting track curve. The method disclosed by the invention has the advantages that the cutting track curve is automatically generated by scanning boundary points of the gum and dental crown on the tooth model, and the method is high in generating speed, high in stability, high in repeatability and high in accuracy.

Description

A kind of cutting method without bracket invisible orthotic device
Technical field
The present invention relates to a kind of cutting method of the sideline without bracket invisible orthotic device.
Technical background
Be a kind of transparent elastic material movable correcting device by computer-aided design and manufacture without bracket invisible orthotic device, it is a series of continuous print orthotic devices, by constantly among a small circle moving teeth reach the object of orthodontic.
At present, the manufacture method without bracket invisible orthotic device is: the tooth former model first obtaining patient; Use thermoplastic and Gypsum Fibrosum filling molding on tooth former model, obtain patient's tooth jaw physical model, wherein gum portion is made up of thermoplastic, and dental part is made up of Gypsum Fibrosum; Heat in described tooth jaw physical model and treat that the thermoplastic at straightening of teeth position makes it soften, then moved to target and correct position; Cooling treats that the thermoplastic at straightening of teeth position makes it harden, and adopt correction sheet with tooth jaw physical model now for master mold obtains invisible orthotic device, target is corrected position and obtained by computer-aided design; After thermoplastic hardening by cooling, by workman with hand-held live invisible orthotic device and tooth former model, then invisible orthotic device cuts down along its sideline from tooth former model by craft cutting grinding wheel or shears.The shortcoming existed by workman's hand cut appliance is: cutting route is generated by experience by workman, and the experience of each workman is different, and the cutting route therefore obtained is also different; Even and same person cuts, each cutting route is not identical yet; Therefore, the shape disunity in appliance sideline is caused, the poor stability of cutting route and poor accuracy.
Summary of the invention
There is cutting route need repeatedly to design to overcome existing appliance cutting method, the shortcoming of the poor stability of cutting route, the invention provides a kind of cutting route only need design once, the good stability of cutting route, the cutting method without bracket invisible orthotic device that accuracy is good.
Without the cutting method of bracket invisible orthotic device, comprise the following steps:
1), on tooth model, generate cutting track curve, tooth model comprises gingival model and dental arch model:
(1.1) obtain every upper teeth hat and the point that several are put and each gingival papilla is corresponding of the contact of gingiva, these points are connected successively, connects with straight line between consecutive points;
(1.2) form level and smooth curve to the smoothing process of broken line formed in step (1.1), the principle of smoothing processing is: lines do not depart from corona summit as far as possible, but lines can encase gingival papilla, and this level and smooth curve is as cutting track curve;
2), using the coordinate system of cutting track curve as workpiece coordinate system SYHE, sample to cutting track curve, the quantity of sampled point is N, and each sampled point has direction vector ε x, ε y, ε z and coordinate (X, Y);
3) Tool route of Five-axis NC Machining Center, is generated by cutting track curve:
(3.1) determine Cutter coordinate system: be first positioned on lathe by tooth model, using the anchor point of tooth model as the initial point of X-direction and Y direction, using the baseplane of tooth model as the initial point of Z-direction, Cutter coordinate system CSO determines;
(3.2) using the nearest point of distance Cutter coordinate system initial point on appliance cutting track curve as playing a cutter point;
(3.3) Five-axis NC Machining Center Tool route is determined:
(3.3.1) suppose: workpiece coordinate is that the zero of OwXYZ, OwXYZ is on Z axis; It is the rotating shaft with cutter that rotating shaft B and rotating shaft C and X-coordinate direction form OrXYZ, rotating shaft B, and rotating shaft B is parallel with Y-axis or overlapping; Rotating shaft C is the output shaft of PTO, and rotating shaft C is parallel with Z axis or overlapping, and the zero of OrXYZ is the intersection point of rotating shaft B and rotating shaft C; OwXYZ initial point is H to OrXYZ initial point distance; The known cutter heart and generating tool axis vector ask the coordinates of motion value of workpiece under lathe coordinate system; Lathe coordinate system is the coordinate system determined by the mechanical switch of lathe itself and system;
(3.3.2) set generating tool axis vector ε as free vector or unit vector, the starting point of generating tool axis vector moved on to the initial point of workpiece coordinate system, generating tool axis vector by rotation transformation forward to+Z-direction is consistent;
The rotation of cutter shaft is converted into the swing of cutter relative to workpiece, first makes cutter opposite piece be rotated counterclockwise C angle around Z axis, then make cutter opposite piece rotate to be B angle around Y-axis;
When , time, ;
When time, ;
When time, ;
When time, ;
When time, ;
When time, ;
When time, ;
(3.3.3) position of cutter heart Co after workpiece rotates in lathe coordinate system OrXYZ is determined, the coordinates of motion X of lathe, Y, Z;
The transformation matrix that cutter spacing moves to lathe coordinate system OrXYZ from workpiece coordinate system OwXYZ is
Workpiece rotates-C angle around Z axis, and transformation matrix is
=(Xco, Yco, Zco 1) T1 T2 can be obtained (X, Y, Z, 1)
Launched:
(X, Y, Z) cutter location coordinate figure for providing in actual processing.
Further, in step 1), the generation step of cutting track curve comprises:
(1.1) select the contact point of tooth corona and gingiva, according to corona and gingiva border naturally move towards sort, generation sorted points;
(1.2) Laplace algorithm is adopted to carry out fairing to sorted points;
(1.3) sorted points between adjacent two gingival papilla is fitted to B-spline curves;
(1.4) eliminate the sharpened areas at gingival papilla summit place, adopt lead angle algorithm, level and smooth gingival papilla region;
(1.5) line smoothing that all B-spline curves and lead angle generate is spliced into B-spline curves, splicing ensures that curve is continuous, thus obtains cutting track curve.
Further, when tool motion, on the basis of the Five-axis NC Machining Center Tool route obtained in step 3) by cutter, to the direction away from appliance, cutter is departed from the distance of a tool radius.
The invention has the advantages that: the gingiva on cutting track curve negotiating scanning tooth model and the boundary point of corona generate automatically, and its formation speed is fast, and good stability, reproducible, accuracy is high.
Accompanying drawing explanation
Fig. 1 is schematic diagrams of several points in the contact of corona and gingiva.
Fig. 2 connects with straight line the schematic diagram that each point forms broken line.
Fig. 3 be by smoothing processing of discounting after schematic diagram.
Fig. 4 is the schematic diagram determining workpiece coordinate system SYHE.
Fig. 5 is schematic diagram generating tool axis vector starting point being moved to OrXYZ initial point.
Fig. 6 is that cutter opposite piece is rotated counterclockwise C angle around Z axis and selects the schematic diagram at B angle around Y-axis.
Detailed description of the invention
Without the cutting method of bracket invisible orthotic device, comprise the following steps:
1), on tooth model, generate cutting track curve, tooth model comprises gingival model and dental arch model:
(1.1) obtain every upper teeth hat and the point that several are put and each gingival papilla is corresponding of the contact of gingiva, these points are connected successively, connects with straight line between consecutive points; As depicted in figs. 1 and 2;
(1.2) level and smooth curve is formed to the smoothing process of broken line formed in step (1.1), the principle of smoothing processing is: lines do not depart from corona summit as far as possible, but lines can encase gingival papilla, this level and smooth curve as cutting track curve, as shown in Figure 3.In smoothing process, lines can not depart from corona minimum point as far as possible, but should offset downward along gingival papilla as far as possible, because stress so not only can be avoided to concentrate, the sectional area that appliance is stressed can also be increased, enable appliance produce larger Orthodontic force, the reduction of mean stress can delay the generation of stress relaxation equally.
The specific algorithm process of step 1) is as follows:
(1.1) select the contact point of tooth corona and gingiva, according to corona and gingiva border naturally move towards sort, generation sorted points;
(1.2) Laplace algorithm is adopted to carry out fairing to sorted points;
(1.3) sorted points between adjacent two gingival papilla is fitted to B-spline curves;
(1.4) eliminate the sharpened areas at gingival papilla summit place, adopt lead angle algorithm, level and smooth gingival papilla region;
(1.5) line smoothing that all B-spline curves and lead angle generate is spliced into B-spline curves, splicing ensures that curve is continuous, thus obtains cutting track curve.
2), step 1) generates the cutting track curve of appliance, the coordinate of this cutting track curve is workpiece coordinate system SYHE, as Fig. 4, again this cutting track curve is sampled, take out several key points, each point has direction vector ε x, ε y, ε z(perpendicular to the territory, face at this place) and coordinate figure X, Y, Z form;
3), again by the Tool route of cutting track curve generation Five-axis NC Machining Center, detailed process is as follows:
1) lathe coordinate system is determined
First when generating 3D and printing the mathematical model of tooth model, two dowel holes are added in the baseplane of model, these two pin-and-holes will on the fixture that model is installed to Five-axis NC Machining Center time implementation model location, the fixture of Five-axis NC Machining Center has a circular pegs, the rhombus pin of a chamfered edge.Select the initial point of center as X, Y direction in the hole that tooth model coordinates with circular pegs, select the initial point of lower plane as Z-direction of tooth model.The Cutter coordinate system of such invisible orthotic device has just been decided, as Fig. 4 coordinate system CSO.Coordinate system SYHE in Fig. 4 is then workpiece coordinate system, and the cutter location under workpiece coordinate system also will be transformed into lathe coordinate system by the later stage, correctly could generate processor.
2) cutter point has been determined
The point that on appliance cutting track curve, distance Cutter coordinate system initial point is nearest is selected to be cutter point, as the A point of Fig. 4.
3) Five-axis NC Machining Center Tool route (postpositive disposal) is determined
That is to say Post-processing Algorithm, determine the coordinate figure of each key point in Five-axis NC Machining Center processor, and whole processor.For main shaft single oscillation, single turntable type Five-axis NC Machining Center, then need X, Y, Z, B, C five coordinate figures determining each key point:
1. the Fundamentals of Mathematics of Post-processing Algorithm
In figure procedure for displaying, in general, need to carry out the basic geometric transformation operation such as translation, Scalable, rotation to figure.The translation of image, Scalable, rotation are all mathematically geometric propertieses " conversion ", therefore are referred to as again the geometric transformation of figure.The conversion of this class is mainly achieved by the homogeneous transform matrix method in matrix algebra.
Here mainly introduce the basic coordinates conversion of 3-D graphic, comprise transformation of scale, symmetry transformation, translation transformation and rotation transformation, when carrying out the conversion of 3-D graphic, some homogeneous coordinates are expressed as , transformation matrix adopts 4*4 rank matrix below.
(formula 1)
In formula, for producing the conversion such as ratio, symmetry, rotation; for producing the translation transformation along three axis; for producing full scale conversion; for producing perspective projection transformation.
Transformation of scale:
3 d scale conversion be exactly by each summit of solid figure by regulation scale amplifying or reduce.Element a, e, j effect on leading diagonal in (formula 1) is exactly make figure produce transformation of scale.Transformation matrix is namely
Wherein, a, e, j are respectively the zoom factor in X, Y, Z tri-directions.
Symmetry transformation:
Almost symmetry converts the symmetry transformation comprised zero, coordinate axes and coordinate plane.Mainly introduce the simplify factor to coordinate plane below.
The symmetry transformation of XOY plane, except the Z coordinate of each point in solid becomes except opposite number, X, Y-coordinate are constant, therefore homogeneous transform matrix is
namely
The symmetry transformation of XOZ plane, homogeneous transform matrix is:
namely
The symmetry transformation of YOZ plane, homogeneous transform matrix is:
namely
Translation transformation:
Translation transformation refers to that solid moves a certain distance along X, Y, Z tri-directions in space, and does not change three-dimensional shape own and size.Homogeneous transform matrix is:
namely
Rotation transformation:
Basic rotation transformation refers to that space multistory rotates to an angle around a certain axle, and the positive and negative of each anglec of rotation is determined by right-hand rule: right hand thumb points to the forward of rotating shaft, and the sensing of all the other 4 fingers is anglec of rotation forward.
Introduce below respectively around X, Y, Z axis spin matrix.
θ angle is rotated around X-axis.
Three-dimensional when X-axis rotates, the X-axis coordinate on each summit is constant, just Y, Z changes in coordinates, and transformation matrix is:
(formula 2)
θ angle is rotated around Y-axis.
Three-dimensional when Y-axis rotates, the Y-coordinate on each summit is constant, just X, Z changes in coordinates, and transformation matrix is:
(formula 3)
When Z axis rotates, the Z coordinate on each summit is constant, just X, Y-coordinate change, and transformation matrix is
(formula 3)
The research of Post-processing Algorithm
Five Axis CNC System comprises basic parameter input, Path calculates and postpositive disposal three subsystems, wherein the process that the cutter spacing source file that pre-process produces generates the numerical control program that instruction number controlled machine can perform is called postpositive disposal.Postpositive disposal comprises movement instruction conversion and control instruction conversion, wherein movement instruction conversion comprises the calculating of linear axis coordinate and the calculating of rotating shaft coordinate, namely the cutter spacing anglec of rotation calculates and coordinate transform, and coordinate transform be core technology in postpositive disposal owing to calculating cutter path time, adopt be workpiece coordinate system as Fig. 4 coordinate system CSO(and workpiece motionless, cutter is relative to workpiece motion s), and in reality processing, use lathe coordinate system as Fig. 4 coordinate system SYHE(and cutter motionless, workpiece is relative to tool motion).Assuming that: workpiece coordinate is OwXYZ, and initial point is on the rotating shaft of Z axis; It is the rotating shaft with cutter that rotating shaft B and rotating shaft C and X-coordinate direction form OrXYZ, rotating shaft B, and rotating shaft B is parallel with Y-axis or overlapping; Rotating shaft C is the output shaft of PTO, and rotating shaft C is parallel with Z axis or overlapping, and the zero of OrXYZ is the intersection point of rotating shaft B and rotating shaft C; OwXYZ initial point is H to OrXYZ initial point distance; The known cutter heart and generating tool axis vector ask the coordinates of motion value of workpiece under lathe coordinate system; Lathe coordinate system is the coordinate system determined by the mechanical switch of lathe itself and system; As shown in Figure 5 and Figure 6.
From mathematical angle, cutter heart point transformation, mainly by the coordinate transform of figure, after each coordinate in the cutter location file under workpiece coordinate system is rotated by the rotating shaft in lathe coordinate system, is become the coordinate under lathe coordinate system by postpositive disposal.Postpositive disposal solves and is divided into: calculate position X, Y, Z value of anglec of rotation coordinate figure B, C and cutter heart Co after workpiece rotates in coordinate system OrXYZ.
L calculates anglec of rotation B, C
If generating tool axis vector ε is free vector (unit vector), the starting point of generating tool axis vector is moved on to the initial point of workpiece coordinate system, as shown in Figure 5.Because the major axes orientation of lathe is parallel with Z axis, and point to-Z-direction, so target is exactly that generating tool axis vector is consistent with Z-direction by forwarding to after rotation transformation.
From lathe running parameter:
B axle pivot angle meets :-150 °≤B≤30 °
C Shaft angle meets: 0 °≤C≤360 °
First by generating tool axis vector ε ON in Z axis dextrorotation gyration C to (+X) (+Z) plane, turn clockwise angle B to OM again around Y-axis, consistent with Z-direction, generating tool axis vector is horizontal circular arc around the movement locus that Z axis rotates, and is semi arch around the movement locus that Y-axis rotates.
The rotation of cutter shaft is converted into the swing of cutter relative to workpiece, first makes cutter opposite piece be rotated counterclockwise C angle around Z axis, then make cutter opposite piece rotate to be B angle around Y-axis, as shown in Figure 6.
When , time, generating tool axis vector ε ON, angle C in Z axis dextrorotation gyration C to (+X) (+Z) plane are equal to the ∠ C on XOY plane, due to , can obtain such as formula 4
(formula 4)
When when span is different, as used above-mentioned reasoning, can obtain formula 5,6,7.
(formula 5)
(formula 6)
(formula 7)
Then, when time, generating tool axis vector ε turns clockwise angle B to OM around Y-axis, and namely rotate to OM from ON, angle B is equal to the ∠ NOM in XOZ plane, and the radius of circle rotated around Z axis is , then , formula 8. can be obtained
(formula 8)
When when span is different, as above-mentioned reasoning, formula 9,10. can be obtained (formula 9) (formula 10)
These formulas meet B=-150 ° ~ 30 °, C=0 ° ~ 360 °, because the coordinates of motion convert with the change of the anglec of rotation, determine coordinates of motion X, Y, Z below by anglec of rotation B, C.
The determination of l linear axis X, Y, Z value
The coordinate rotated is realized by cutter oscillation, work motionless relative to its coordinate system, namely B axle rotates does not affect work coordinate system, so only need consider the coordinate transform that work table rotation causes, its coordinate figure, around work table rotation central rotation angle C, tries to achieve postrotational coordinate figure by coordinate transform.
The position of cutter heart Co after workpiece rotates in lathe coordinate system OrXYZ is discussed, i.e. the coordinates of motion X of lathe, Y, Z. below
By the transformation matrix that cutter spacing moves to lathe coordinate system OrXYZ from workpiece coordinate system OwXYZ be
(formula 11)
Workpiece rotates-C angle around Z axis, and transformation matrix is
(formula 12)
=(Xco, Yco, Zco 1) T1 T2 can be obtained (XYZ1)
Launched:
(formula 13)
So far the cutter location coordinate figure that should provide in actual processing has been tried to achieve.
It is worthy of note that the machine tool motion coordinate of five-axis machine is the coordinate of cutter relative to machine tool motion coordinate system, instead of cutter is relative to the coordinate of workpiece coordinate system.Given by cutter location file is Working position (3 coordinates) and generating tool axis vector (3 coordinates) totally 6 parameters, and 5-axis machining center is 5 coordinate machines, three the coordinate X namely processed, and Y, Z and cutter oscillation B, workbench rotate C.The postpositive disposal process of this lathe, converts coordinates of motion X, Y, Z, B, C of lathe to by cutter heart Co coordinate Xco, Yco, the Zco in cutter spacing source file and generating tool axis vector ε coordinate ε x, ε y, ε z.
In order to not destroy appliance edge, when tool motion, then the distance offseting tool radius to the direction away from appliance edge can obtain the cutting tool route of final Five-axis NC Machining Center.
The invention has the advantages that: the gingiva on cutting track curve negotiating scanning tooth model and the boundary point of corona generate automatically, and its formation speed is fast, and good stability, reproducible, accuracy is high.
Content described in this description embodiment is only enumerating the way of realization of inventive concept; protection scope of the present invention should not be regarded as being only limitted to the concrete form that embodiment is stated, protection scope of the present invention also and conceive the equivalent technologies means that can expect according to the present invention in those skilled in the art.

Claims (3)

1., without the cutting method of bracket invisible orthotic device, comprise the following steps:
1), on tooth model, generate cutting track curve, tooth model comprises gingival model and dental arch model:
(1.1) obtain every upper teeth hat and the point that several are put and each gingival papilla is corresponding of the contact of gingiva, these points are connected successively, connects with straight line between consecutive points;
(1.2) form level and smooth curve to the smoothing process of broken line formed in step (1.1), the principle of smoothing processing is: lines do not depart from corona summit as far as possible, but lines can encase gingival papilla, and this level and smooth curve is as cutting track curve;
2), using the coordinate system of cutting track curve as workpiece coordinate system SYHE, sample to cutting track curve, the quantity of sampled point is N, and each sampled point has direction vector ε x, ε y, ε z and coordinate (X, Y);
3) Tool route of Five-axis NC Machining Center, is generated by cutting track curve:
(3.1) determine Cutter coordinate system: be first positioned on lathe by tooth model, using the anchor point of tooth model as the initial point of X-direction and Y direction, using the baseplane of tooth model as the initial point of Z-direction, Cutter coordinate system CSO determines;
(3.2) using the nearest point of distance Cutter coordinate system initial point on appliance cutting track curve as playing a cutter point;
(3.3) Five-axis NC Machining Center Tool route is determined:
(3.3.1) suppose: workpiece coordinate is that the zero of OwXYZ, OwXYZ is on Z axis; It is the rotating shaft with cutter that rotating shaft B and rotating shaft C and X-coordinate direction form OrXYZ, rotating shaft B, and rotating shaft B is parallel with Y-axis or overlapping; Rotating shaft C is the output shaft of PTO, and rotating shaft C is parallel with Z axis or overlapping, and the zero of OrXYZ is the intersection point of rotating shaft B and rotating shaft C; OwXYZ initial point is H to OrXYZ initial point distance; The known cutter heart and generating tool axis vector ask the coordinates of motion value of workpiece under lathe coordinate system; Lathe coordinate system is the coordinate system determined by the mechanical switch of lathe itself and system;
(3.3.2) set generating tool axis vector ε as free vector or unit vector, the starting point of generating tool axis vector moved on to the initial point of workpiece coordinate system, generating tool axis vector by rotation transformation forward to+Z-direction is consistent;
The rotation of cutter shaft is converted into the swing of cutter relative to workpiece, first makes cutter opposite piece be rotated counterclockwise C angle around Z axis, then make cutter opposite piece rotate to be B angle around Y-axis;
When , time, ;
When time, ;
When time, ;
When time, ;
When time, ;
When time, ;
When time, ;
(3.3.3) position of cutter heart Co after workpiece rotates in lathe coordinate system OrXYZ is determined, the coordinates of motion X of lathe, Y, Z;
The transformation matrix that cutter spacing moves to lathe coordinate system OrXYZ from workpiece coordinate system OwXYZ is
Workpiece rotates-C angle around Z axis, and transformation matrix is
=(Xco, Yco, Zco 1) T1 T2 can be obtained (X, Y, Z, 1)
Launched:
(X, Y, Z) cutter location coordinate figure for providing in actual processing.
2., as claimed in claim 1 without the cutting method of bracket invisible orthotic device, it is characterized in that: in step 1), the generation step of cutting track curve comprises:
(1.1) select the contact point of tooth corona and gingiva, according to corona and gingiva border naturally move towards sort, generation sorted points;
(1.2) Laplace algorithm is adopted to carry out fairing to sorted points;
(1.3) sorted points between adjacent two gingival papilla is fitted to B-spline curves;
(1.4) eliminate the sharpened areas at gingival papilla summit place, adopt lead angle algorithm, level and smooth gingival papilla region;
(1.5) line smoothing that all B-spline curves and lead angle generate is spliced into B-spline curves, splicing ensures that curve is continuous, thus obtains cutting track curve.
3. as claimed in claim 2 without the cutting method of bracket invisible orthotic device, it is characterized in that: when tool motion, on the basis of the Five-axis NC Machining Center Tool route obtained in step 3) by cutter, to the direction away from appliance, cutter is departed from the distance of a tool radius.
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