CN104345687B - A kind of tool sweep volume modeling method - Google Patents

A kind of tool sweep volume modeling method Download PDF

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Publication number
CN104345687B
CN104345687B CN201310347465.XA CN201310347465A CN104345687B CN 104345687 B CN104345687 B CN 104345687B CN 201310347465 A CN201310347465 A CN 201310347465A CN 104345687 B CN104345687 B CN 104345687B
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msub
mrow
sweep volume
beta
point
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CN201310347465.XA
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CN104345687A (en
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郭锐锋
王鸿亮
黄骏
李博
郑飂默
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中国科学院沈阳计算技术研究所有限公司
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05BCONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00Programme-control systems
    • G05B19/02Programme-control systems electric
    • G05B19/18Numerical 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
    • G05B19/19Numerical 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

Abstract

The present invention relates to a kind of tool sweep volume modeling method, more particularly in nc machining simulation application, universal cutter model in cutter frame system is expressed with implicit function, and rigid motion Frame Theory and counter-movement mode are utilized, universal cutter model scanning body is expressed with the four-dimensional implicit function comprising time parameter.The quick position relationship for judging point with sweep volume in machining simulation, to realize that efficient material dispels emulation and interference and collision is detected.

Description

A kind of tool sweep volume modeling method

Technical field

The present invention relates to Numeric Control Technology, and in particular to a kind of tool sweep volume modeling method.

Background technology

For the nc program used first, it is impossible to ensure its correctness and security, it is necessary to which it is verified.Compare Lathe on-line debugging method, the features such as nc machining simulation has efficiently with low cost.The modeling method of tool sweep volume is several One of key technology of machining simulation is controlled, the efficiency of nc machining simulation is largely have impact on.Traditional explicit parametric method exists Problems with is there are in terms of construction tool sweep volume:, need to be every by calculating firstly, for the cutter model with complex outline Moment tool surface normal vector constructs sweep volume surface with the critical line under direction of motion orthogonality condition, and the calculating process is more It is time-consuming;Secondly, in material dispels emulation and interference and collision detection application, the sweep volume and workpiece mould of explicit parament expression are determined The intersecting area of type needs also exist for time-consuming space three-dimensional face and intersects calculating with face.Therefore, explicit parament representation builds cutter Sweep volume time complexity is high.

The content of the invention

For deficiency of the existing explicit parament tool sweep volume construction method on time performance, the present invention considers straight The implicit function expression formula for solving tool sweep volume is connect, the directly quick sky for judging point with sweep volume is realized using the implicit function equation Between position relationship, dispel emulation and interference and collision detection application to realize by the material of sweep volume and workpiece there is provided a kind of efficient Tool sweep volume modeling method.

The technical scheme that is used to achieve the above object of the present invention is:A kind of tool sweep volume modeling method, including with Lower step:

Its implicit function expression formula T (x, y, z)=0 in cutter frame system is calculated according to universal cutter model;According to The Frame Theory and cutter of rigid motion and the counter-movement relation of workpiece, calculate workpiece frame system and cutter frame system Conversion relational expression;State (the x by tool sweep volumes,ys,zs) and done state (xe,ye,ze) and said frame system Between conversion relational expression, calculate the frame system conversion relational expression comprising time parameter t;

By the frame system conversion relational expression comprising time parameter t and universal cutter model implicit function expression formula T (x, y, z) =0, calculate the tool sweep volume four-dimension implicit function S (x, y, z, t)=0 comprising time parameter t;

Test point (the x of workpiece will be belonged tow,yw,zw) the four-dimensional implicit function of affiliated tool sweep volume is assigned to, obtain on t's Equation S (xw,yw,zw, t)=0, the test point (x of workpiece is judged according to equation solution situationw,yw,zw) closed with the position of sweep volume System.

The universal cutter model is specially in the implicit function expression formula T (x, y, z)=0 of cutter frame system:

According to universal cutter model (as shown in Figure 1), implicit function is divided into three parts:Top, middle part and bottom;Wherein, in Portion is divided into outside middle part and in middle part again;

Implicit function expression formula per part revolving body curved surface is as follows.

fTop(x, y, z)=x2+y2-[e+rccosβc+(z+h1-h+rcsinβc)tanβc]2=0,

Wherein, e is the centre of sphere of middle part revolving body parent to the distance of cutter shaft center line, lcutterIt is whole cutter model Length, h1It is distance of the point of a knife point to origin, h is the centre of sphere of middle part revolving body parent to the distance of point of a knife point, rcIt is that middle part is turned round The radius of body parent, αcIt is lower cone bus and the angle of x-axis, βcIt is the element of cone on top and the angle of y-axis.

The counter-movement relation of the cutter and workpiece is specially:

In fixed cutter frame system, workpiece frame system is moved with respect to tooling system framework, the motion and knife Tool is relatively fixed the motion of workpiece reverse motions each other.

The conversion relational expression of the workpiece frame system and cutter frame system is specially:

The relational expression for the coordinate value that point in workpiece frame system is corresponded in cutter frame system, can be represented by the formula.

(xc,yc,zc)=(cXw,cYw,cZw)+(xw,yw,zw)

Wherein, (xc,yc,zc) be cutter frame system in coordinate, (xw,yw,zw) be workpiece frame system in coordinate, (cXw,cYw,cZw) it is workpiece frame system origin coordinate in cutter frame system.

The frame system conversion relational expression comprising time parameter t is specially:

Using linear difference method, the state (x since tool sweep volumes,ys,zs) arrive done state (xe,ye,ze) make with t For the linear difference of parameter, the corresponding coordinate values (x (t), y (t), z (t)) of each variate-value t in two state values centre are provided, it is as follows It is shown.

(x (t), y (t), z (t))=(xs,ys,zs)+[(xe,ye,ze)-(xs,ys,zs)]·t

Wherein, (xs,ys,zs) it is the coordinate that tool sweep volume starts state, (xe,ye,ze) terminate shape for tool sweep volume The coordinate of state, (x (t), y (t), z (t)) is each variate-value t in the middle of the coordinate of the beginning state and the coordinate of done state Corresponding coordinate value.

The tool sweep volume four-dimension implicit function S (x, y, z, t)=0 is specially:

Sweep volume implicit function includes three parts, i.e. top, middle part and bottom, wherein, middle part is divided into outside middle part and middle part again It is interior.It is as follows.

fTop(x, y, z, t)=(x-xs-tΔx))2+(y-ys-tΔy))2-[e+rccosβc+(z-zs-tΔz-h+rcsin βc)tanβc]2=0

fIn middle part(x, y, z, t)=(x-xs-tΔx)2+(y-ys-tΔy)2-(e+rcsinαc)2=0

fBottom(x, y, z, t)=(x-xs-tΔx)2+(y-ys-tΔy)2-ctg2αc(z-zs-tΔz)2=0

Wherein, Δ x=xe-xs, Δ y=ye-ys, Δ z=ze-zs, e is the centre of sphere of middle part revolving body parent to cutter shaft center The distance of line, h1It is distance of the point of a knife point to origin, h is the centre of sphere of middle part revolving body parent to the distance of point of a knife point, rcIt is middle part The radius of revolving body parent, αcIt is lower cone bus and the angle of x-axis, βcIt is the element of cone on top and the angle of y-axis.

Test point (the x that workpiece will be belonged tow,yw,zw) be assigned to the four-dimensional implicit function of sweep volume and obtain equation S on t (xw,yw,zw, t)=0, it is specially:

Test point (xw,yw,zw) the four-dimensional implicit function of sweep volume is assigned to, obtain the equation S (x on tw,yw,zw, t)=0, The quadratic equation with one unknown f on top is obtained after arrangementTopQuadratic equation with one unknown f in (x, y, z, t), middle partIn middle part(x, y, z, t), in Unary biquadratic equation f outside portionOutside middle part(x, y, z, t) and the quadratic equation with one unknown of bottom

fBottom(x, y, z, t)=(x-xs-tΔx)2+(y-ys-tΔy)2-ctg2αc(z-zs-tΔz)2=0

Wherein, Δ x=xe-xs, Δ y=ye-ys, Δ z=ze-zs, e is the centre of sphere of middle part revolving body parent to cutter shaft center The distance of line, αcIt is lower cone bus and the angle of x-axis.

It is described to judge that the position relationship of the point and sweep volume is specially according to equation solution situation:

For the quadratic equation with one unknown on top, in interval [0,1], in the absence of solution, then the point is external in scanning, if in the presence of Two solutions for differing, then the point is in sweep volume, otherwise, and the point is in scanning dignity;

For the quadratic equation with one unknown of bottom, in interval [0,1], in the absence of solution, then the point is external in scanning, if in the presence of Two solutions for differing, then the point is in sweep volume, otherwise, and the point is in scanning dignity;

For the unary biquadratic equation in middle part, in interval [0,1], there is solution, then otherwise the point is examined in sweep volume The quadratic equation with one unknown solution situation surveyed outside middle part.Quadratic equation with one unknown outside for middle part, in interval [0,1], if without solution The point is external in scanning, if in the presence of a solution or four identical solutions, the point is in scanning dignity, and otherwise, the point is in sweep volume It is interior.

The present invention has advantages below and beneficial effect:

1. it is capable of the sweep volume of accurate expression universal cutter model;

2. avoiding sweep volume explicit expression method, the solution to complicated critical line and scanning of a surface, amount of calculation is less;

3. utilizing counter-movement mode, simplify calculating process;

4. using the characteristic of implicit function, directly quickly judge spatial relation of the point with sweep volume, it is to avoid time-consuming Calculating is intersected in space three-dimensional face with face, improves machining simulation efficiency.

5. using above-mentioned quick judgement point and sweep volume position relationship method, it can realize that efficient material dispels emulation and fast The collision of speed detection cutter and workpiece and interference situation.

Brief description of the drawings

Fig. 1 is universal cutter model in cutter frame system;

Fig. 2 is schematic diagram in outer and middle part in the middle part of universal cutter model;

Fig. 3 is cutter and workpiece motion s and the schematic diagram of counter-movement;

Fig. 4 is the situation and point and sweep volume position relationship schematic diagram of quadratic equation with one unknown and unary biquadratic equation solution;

Fig. 5 is the overview flow chart of the present invention;

Fig. 6 is point and implicit function sweep volume position relationship decision flow chart;

Fig. 7 is the judgement schematic diagram of spatial point and implicit function position relationship.

Embodiment

The present invention is elaborated below in conjunction with the accompanying drawings.

The present invention comprises the following steps (as shown in Figure 5):

According to universal cutter model (as shown in Figure 1) calculate cutter cutter frame system implicit function expression formula T (x, Y, z)=0;

The universal cutter model is specially in the implicit function expression formula of cutter frame system:

Universal cutter model implicit function expression formula is divided into three parts, i.e. upper, middle and lower (as shown in Figure 1).Wherein Middle part, which has, to be divided into outside middle part and in middle part (as shown in Figure 2).

According to the Frame Theory and cutter of rigid motion and the counter-movement relation of workpiece.Calculate cutter frame system and workpiece The conversion relational expression of frame system;

The workpiece frame system and cutter frame system are specially:

Workpiece frame system refers to be fixed on frame system static on workpiece, and cutter frame system is integrally fixed on cutter Frame system, and cutter frame system is considered as what is constantly moved in fixed workpiece frame system.

The counter-movement relation of the cutter and workpiece is specially:

The movement relation (as shown in Figure 3) of cutter and workpiece is considered as in workpiece frame system during machining simulation In, the relatively-stationary workpiece frame system of cutter frame system makees motion M.The counter-movement relation of cutter and workpiece is (such as Fig. 3 institutes Show) refer to that above-mentioned motion process can also be regarded as in fixed cutter frame system, workpiece frame system is in cutter frame system Middle work and the motion-M of the above-mentioned reversing of motion.

The conversion relational expression of the cutter frame system and workpiece frame system is specially:

Relational expression refers to the relation for the coordinate value that the point in workpiece frame system is corresponded in cutter frame system.

State (x being moved by tool sweep volumes,ys,zs) and done state (xe,ye,ze) and frame system conversion Relational expression, calculates the frame system conversion relational expression for including time parameter t.

The tool sweep volume motion beginning state and done state are specially:

Sweep volume beginning and end moment three linear axes x, y, z displacement (as shown in Figure 3), the data can be by numerical control Machining code is provided.

The frame system conversion relational expression comprising time parameter t is specially:

Using linear difference method, the state at per moment in beginning and end state is expressed with dotted state and parameter t Value, and represent the frame system conversion relational expression per moment state value.

By the transferring frame relational expression comprising time parameter t and cutter implicit function expression formula T (x, y, z)=0, calculating is included Time t sweep volume four-dimension implicit function S (x, y, z, t)=0.

The sweep volume four-dimension implicit function S (x, y, z, t)=0 is specially:

The implicit function is divided into three parts, i.e. top, middle part and bottom, wherein, middle part is divided into outside middle part and in middle part again.

By the test point (x on workpiecew,yw,zw) bring the four-dimensional implicit function of sweep volume into and obtain S (xw,yw,zw, t)=0, with the party The solution situation of journey judges position relationship of the point with sweep volume.

The sweep volume four-dimension implicit function S (xw,yw,zw, t)=0, its upper and lower part is outside quadratic equation with one unknown, middle part It is quadratic equation with one unknown for unary biquadratic equation, in middle part.

The solution situation with the equation judges that the position relationship of point and sweep volume is specially (as shown in Figure 6):

For the implicit function quadratic equation with one unknown of upper and lower part, in [0,1] is interval, put if without solution external in scanning (such as Fig. 4 P4It is shown), if in the presence of two different Xie Zedian in sweep volume (such as Fig. 4 P1It is shown), if identical in the presence of two Solution or a solution then put on sweep volume surface (such as Fig. 4 P2And P3It is shown).

For the unary biquadratic equation in middle part, in interval [0,1], there is solution, then the point (such as Fig. 4 in sweep volume P5And P6It is shown), otherwise detect the quadratic equation with one unknown solution situation outside middle part.Quadratic equation with one unknown outside for middle part, in area Between in [0,1], the point is external in scanning if without solution, if in the presence of a solution or four identical solutions, the point on scanning is honorable, Otherwise, the point is in sweep volume.

The present invention is described in further detail below.

The implicit function modeling method of curved surface is the relational expression for setting up the point on curved surface between each reference axis, the spy of implicit function Property (as shown in Figure 7) is when point (x, y, z) meets function f (x, y, z)=0 this point on the curved surface, if f (x, y, z)<0 The point is present in the closing space that curved surface is surrounded, if f (x, y, z)>0 point is present in outside the closing space that curved surface is surrounded. Therefore, using this characteristic of implicit function, spatial point and the spatial relation of closing tool sweep volume can quickly be judged, and Solve sweep volume implicit function expression formula and it is quick judge spatial point and sweep volume position relationship be present invention mainly solves One of the problem of.

On the other hand, for complicated cutter model, solving has the cutter model scanning plane of complex outline complex, The present invention considers that cutter is constant all the time using the counter-movement mode of cutter and workpiece, and workpiece is moved relative to cutter, it is to avoid multiple The solution of miscellaneous curved surface, improves sweep volume and builds speed.

The present invention in view of said circumstances and complete, it is therefore intended that improve machining simulation in tool sweep volume structure effect Rate, simplifies the Boolean subtraction calculation of sweep volume and workpiece, and realizes that efficient material dispels emulation and collision, interference detection.

In order to solve described problem and reached purpose, the present invention is according to existing universal cutter model solution model in knife Has the implicit function expression formula of frame system.And using the cutter and the counter-movement mode and existing rigid motion frame of workpiece proposed The change type of frame theoretical calculation workpiece and cutter frame system is transformed into cutter frame so that relative motion to the point in workpiece framework In frame.The cutter for solving the four-dimension using the conversion formula of cutter frame system and the implicit function expression formula of universal cutter model is swept Retouch body implicit function expression formula and position relationship of the point with sweep volume space is judged according to the situation of the expression formula solution.

According to the present invention, the universal cutter model under workpiece framework is initially set up, as shown in Figure 1.The cutter model point Constituted for three parts, i.e. top, middle part and bottom.Wherein, middle part is divided into outside middle part and in middle part again., can because it is revolving body The implicit function expression formula T (x, y, z)=0 of three parts is solved respectively, as shown in formula (1).

Wherein, the implicit function expression formula of three parts is respectively as shown in formula (2), (3), (4) and (5).

fTop(x, y, z)=x2+y2-[e+rccosβc+(z+h1-h+rcsinβc)tanβc]2=0,

According to the present invention, it is contemplated that in machining simulation process, for the relatively-stationary workpiece of cutter with complex outline Move linearly, then the cutter implicit function solved per the moment is more difficult.In order to simplify calculating, the present invention uses workpiece and cutter Counter-movement mode, it is assumed that cutter is motionless, that is, be always implicit function expression formula T (x, y, z) under calculated workpiece framework= 0, workpiece goes out corresponding points of the measuring point to be checked in cutter framework in workpiece with respect to tool motion, then a demand, moves and anti- Move schematic diagram as shown in Figure 2.Frame Theory according to rigid motion is easy to get out the transformational relation of workpiece and cutter frame system Shown in formula such as formula (6).

(xc,yc,zc)=(cXw,cYw,cZw)+(xw,yw,zw) (6)

Wherein, (xc,yc,zc) be cutter frame system in coordinate, (xw,yw,zw) be workpiece frame system in coordinate, (cXw,cYw,cZw) it is workpiece frame system origin coordinate value in cutter frame system.It is to be noted that provided by numerical control code Motion state data (Xaxis,Yaxis,Zaxis) it is positive movement, it is necessary to be converted into counter motion (- Xaxis,-Yaxis,- Zaxis), and draw (cXw,cYw,cZw)=(- Xaxis,-Yaxis,-Zaxis)。

According to the present invention, by linear interpolation method, state (X need to being moved by tool sweep volumes,Ys,Zs) and done state (Xe,Ye,Ze) per moment motion state data (X, Y, Z) is calculated as shown in formula (7).

(X, Y, Z)=(Xs,Ys,Zs)+[(Xe,Ye,Ze)-(Xs,Ys,Zs)]·t (7)

Wherein, Δ x=xe-xs, Δ y=ye-ys, Δ z=ze-zs.Band time ginseng can be calculated by (1), (6) and (7) Number t four-dimensional tool sweep volume implicit function equation S (x, y, z, t)=0.Implicit function equation S top is to be outside formula (8), middle part It is formula (10) in formula (9), middle part, bottom is formula (11).

fTop(x, y, z, t)=(x-xs-tΔx))2+(y-ys-tΔy))2-[e+rccosβc+(z-zs-tΔz-h+rcsin βc)tanβc]2=0 (8)

fIn middle part(x, y, z, t)=(x-xs-tΔx)2+(y-ys-tΔy)2-(e+rcsinαc)2=0 (10)

fBottom(x, y, z, t)=(x-xs-tΔx)2+(y-ys-tΔy)2-ctg2αc(z-zs-tΔz)2=0 (11)

Arrangement formula (8), (10) and (11) respectively obtain quadratic equation with one unknown, arrange formula (9) and obtain unary biquadratic equation.

According to the present invention, measuring point to be checked on workpiece is brought into sweep volume implicit function, the part foundation (2) of affiliated cutter, (3), (4) and (5) are brought into equation.Judge position relationship of the point with sweep volume, tool according to solution situation respectively for three parts Body situation is divided into (as shown in Figure 4):

For upper and lower part, when quadratic equation with one unknown (8) and (11) are interval in [0,1], in the absence of solution, then measuring point to be checked It is external in scanning, if in the presence of two different solutions, in sweep volume, in scanning dignity if in the presence of a solution or two identical solutions On.

For middle part, when quadratic equation with one unknown (10) is interval in [0,1], if there is solution, measuring point to be checked in sweep volume, Otherwise it is when unary biquadratic equation (9) is interval without solution in [0,1], then external in scanning, if a solution or four identical solutions, point In scanning dignity, otherwise inside sweep volume.

According to above-mentioned spatial point and the method for detecting position of sweep volume, it can quickly be determined according to sweep volume implicit function on workpiece Point and tool sweep volume position relationship, realize efficient material dispel emulation or interference, collision detection.

Claims (7)

1. a kind of tool sweep volume modeling method, it is characterised in that comprise the following steps:
Its implicit function expression formula T (x, y, z)=0 in cutter frame system is calculated according to universal cutter model;According to rigid body The Frame Theory and cutter of motion and the counter-movement relation of workpiece, calculate the conversion of workpiece frame system and cutter frame system Relational expression;State (the x by tool sweep volumes,ys,zs) and done state (xe,ye,ze) and said frame system between turn Relational expression is changed, the frame system conversion relational expression comprising time parameter t is calculated;
By the frame system conversion relational expression comprising time parameter t and universal cutter model implicit function expression formula T (x, y, z)=0, Calculate the tool sweep volume four-dimension implicit function S (x, y, z, t)=0 for including time parameter t;
Test point (the x of workpiece will be belonged tow,yw,zw) the four-dimensional implicit function of the tool sweep volume is assigned to, obtain the equation on t S(xw,yw,zw, t)=0, the test point (x of workpiece is judged according to equation solution situationw,yw,zw) closed with the position of tool sweep volume System;
The counter-movement relation of the cutter and workpiece is that workpiece frame system is with respect to cutter system in fixed cutter frame system System framework is taken exercises, and the motion and cutter are relatively fixed the motion of workpiece reverse motions each other.
2. a kind of tool sweep volume modeling method according to claim 1, it is characterised in that the universal cutter model exists The implicit function expression formula T (x, y, z)=0 of cutter frame system is specially:
According to universal cutter model, implicit function is divided into three parts:Top, middle part and bottom;Wherein, middle part be divided into again middle part it is outer and In middle part;
Implicit function expression formula per part revolving body curved surface is as follows:
fTop(x, y, z)=x2+y2-[e+rccosβc+(z+h1-h+rcsinβc)tanβc]2=0,
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mo>-</mo> <mrow> <mo>(</mo> <mi>e</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>cos&amp;beta;</mi> <mi>c</mi> </msub> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>l</mi> <mrow> <mi>c</mi> <mi>u</mi> <mi>t</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>h</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>sin&amp;beta;</mi> <mi>c</mi> </msub> </mrow> <mo>)</mo> <msub> <mi>tan&amp;beta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>e</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>cos&amp;beta;</mi> <mi>c</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>l</mi> <mrow> <mi>c</mi> <mi>u</mi> <mi>t</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>h</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>sin&amp;beta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>tan&amp;beta;</mi> <mi>c</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mo>-</mo> <mrow> <mo>(</mo> <mi>e</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>cos&amp;beta;</mi> <mi>c</mi> </msub> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>l</mi> <mrow> <mi>c</mi> <mi>u</mi> <mi>t</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>h</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>sin&amp;beta;</mi> <mi>c</mi> </msub> </mrow> <mo>)</mo> <msub> <mi>tan&amp;beta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>e</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>cos&amp;beta;</mi> <mi>c</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>l</mi> <mrow> <mi>c</mi> <mi>u</mi> <mi>t</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>h</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>sin&amp;beta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>tan&amp;beta;</mi> <mi>c</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>z</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mi>h</mi> <mo>-</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>sin&amp;beta;</mi> <mi>c</mi> </msub> <mo>,</mo> <msub> <mi>l</mi> <mrow> <mi>c</mi> <mi>u</mi> <mi>t</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein, e is the centre of sphere of middle part revolving body parent to the distance of cutter shaft center line, lcutterIt is the length of whole cutter model, h1It is distance of the point of a knife point to origin, h is the centre of sphere of middle part revolving body parent to the distance of point of a knife point, rcIt is that middle part revolving body is female The radius of body, αcIt is lower cone bus and the angle of x-axis, βcIt is the element of cone on top and the angle of y-axis.
3. a kind of tool sweep volume modeling method according to claim 1, it is characterised in that the workpiece frame system with The conversion relational expression of cutter frame system is specially:
The relational expression for the coordinate value that point in workpiece frame system is corresponded in cutter frame system, can be represented by the formula:
(xc,yc,zc)=(cXw,cYw,cZw)+(xw,yw,zw)
Wherein, (xc,yc,zc) be cutter frame system in coordinate, (xw,yw,zw) be workpiece frame system in coordinate, (cXw ,cYw,cZw) it is workpiece frame system origin coordinate in cutter frame system.
4. a kind of tool sweep volume modeling method according to claim 1, it is characterised in that described to include time parameter t Frame system conversion relational expression be specially:
Using linear difference method, the state (x since tool sweep volumes,ys,zs) arrive done state (xe,ye,ze) make using t as ginseng Several linear differences, provides the corresponding coordinate values (x (t), y (t), z (t)) of each variate-value t in two state values centre, following institute Show:
(x (t), y (t), z (t))=(xs,ys,zs)+[(xe,ye,ze)-(xs,ys,zs)]·t
Wherein, (xs,ys,zs) it is the coordinate that tool sweep volume starts state, (xe,ye,ze) it is tool sweep volume done state Coordinate, (x (t), y (t), z (t)) is corresponding with each variate-value t in the middle of the coordinate of done state for the coordinate of the beginning state Coordinate value.
5. a kind of tool sweep volume modeling method according to claim 2, it is characterised in that the tool sweep volume is four-dimensional Implicit function S (x, y, z, t)=0 is specially:
Tool sweep volume implicit function includes three parts, i.e. top, middle part and bottom, wherein, middle part is divided into outside middle part and middle part again It is interior, it is as follows:
fTop(x, y, z)=x2+y2-[e+rccosβc+(z+h1-h+rcsinβc)tanβc]2=0,
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mo>-</mo> <mrow> <mo>(</mo> <mi>e</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>cos&amp;beta;</mi> <mi>c</mi> </msub> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>l</mi> <mrow> <mi>c</mi> <mi>u</mi> <mi>t</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>h</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>sin&amp;beta;</mi> <mi>c</mi> </msub> </mrow> <mo>)</mo> <msub> <mi>tan&amp;beta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>e</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>cos&amp;beta;</mi> <mi>c</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>l</mi> <mrow> <mi>c</mi> <mi>u</mi> <mi>t</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>h</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>sin&amp;beta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>tan&amp;beta;</mi> <mi>c</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mo>-</mo> <mrow> <mo>(</mo> <mi>e</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>cos&amp;beta;</mi> <mi>c</mi> </msub> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>l</mi> <mrow> <mi>c</mi> <mi>u</mi> <mi>t</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>h</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>sin&amp;beta;</mi> <mi>c</mi> </msub> </mrow> <mo>)</mo> <msub> <mi>tan&amp;beta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>e</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>cos&amp;beta;</mi> <mi>c</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>l</mi> <mrow> <mi>c</mi> <mi>u</mi> <mi>t</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mo>-</mo> <mi>h</mi> <mo>+</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>sin&amp;beta;</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>tan&amp;beta;</mi> <mi>c</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>z</mi> <mo>&amp;Element;</mo> <mo>&amp;lsqb;</mo> <mi>h</mi> <mo>-</mo> <msub> <mi>h</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>r</mi> <mi>c</mi> </msub> <msub> <mi>sin&amp;beta;</mi> <mi>c</mi> </msub> <mo>,</mo> <msub> <mi>l</mi> <mrow> <mi>c</mi> <mi>u</mi> <mi>t</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
fTop(x, y, z, t)=(x-xs-tΔx))2+(y-ys-tΔy))2-[e+rccosβc+(z-zs-tΔz-h+rcsinβc) tanβc]2=0
fIn middle part(x, y, z, t)=(x-xs-tΔx)2+(y-ys-tΔy)2-(e+rcsinαc)2=0
fBottom(x, y, z, t)=(x-xs-tΔx)2+(y-ys-tΔy)2-ctg2αc(z-zs-tΔz)2=0
Wherein, Δ x=xe-xs, Δ y=ye-ys, Δ z=ze-zs, e is the centre of sphere of middle part revolving body parent to cutter shaft center line Distance, h1It is distance of the point of a knife point to origin, h is the centre of sphere of middle part revolving body parent to the distance of point of a knife point, rcIt is that middle part is turned round The radius of body parent, αcIt is lower cone bus and the angle of x-axis, βcIt is the element of cone on top and the angle of y-axis.
6. a kind of tool sweep volume modeling method according to claim 5, it is characterised in that the inspection that workpiece will be belonged to Measuring point (xw,yw,zw) be assigned to the four-dimensional implicit function of tool sweep volume and obtain equation on t
S(xw,yw,zw, t)=0, it is specially:
fTop(x, y, z, t)=(x-xs-tΔx))2+(y-ys-tΔy))2-[e+rccosβc+(z-zs-tΔz-h+rcsinβc) tanβc]2=0
fIn middle part(x, y, z, t)=(x-xs-tΔx)2+(y-ys-tΔy)2-(e+rcsinαc)2=0
fBottom(x, y, z, t)=(x-xs-tΔx)2+(y-ys-tΔy)2-ctg2αc(z-zs-tΔz)2=0
Test point (xw,yw,zw) the four-dimensional implicit function of tool sweep volume is assigned to, obtain the equation S (x on tw,yw,zw, t)=0, The quadratic equation with one unknown f on top is obtained after arrangementTopQuadratic equation with one unknown f in (x, y, z, t), middle partIn middle part(x, y, z, t), in Unary biquadratic equation f outside portionOutside middle part(x, y, z, t) and the quadratic equation with one unknown of bottom
fBottom(x, y, z, t)=(x-xs-tΔx)2+(y-ys-tΔy)2-ctg2αc(z-zs-tΔz)2=0
Wherein, Δ x=xe-xs, Δ y=ye-ys, Δ z=ze-zs, e is the centre of sphere of middle part revolving body parent to cutter shaft center line Distance, αcIt is lower cone bus and the angle of x-axis.
7. a kind of tool sweep volume modeling method according to claim 5, it is characterised in that described according to equation solution feelings Condition judges that the position relationship of the point and tool sweep volume is specially:
fTop(x, y, z, t)=(x-xs-tΔx))2+(y-ys-tΔy))2-[e+rccosβc+(z-zs-tΔz-h+rcsinβc) tanβc]2=0
fIn middle part(x, y, z, t)=(x-xs-tΔx)2+(y-ys-tΔy)2-(e+rcsinαc)2=0
fBottom(x, y, z, t)=(x-xs-tΔx)2+(y-ys-tΔy)2-ctg2αc(z-zs-tΔz)2=0
For the quadratic equation with one unknown on top, in interval [0,1], in the absence of solution, then the point outside tool sweep volume, if in the presence of Two solutions for differing, then the point is in tool sweep volume, otherwise, and the point is on tool sweep volume face;
For the quadratic equation with one unknown of bottom, in interval [0,1], in the absence of solution, then the point outside tool sweep volume, if in the presence of Two solutions for differing, then the point is in tool sweep volume, otherwise, and the point is on tool sweep volume face;
For the unary biquadratic equation in middle part, in interval [0,1], there is solution, then otherwise the point is examined in tool sweep volume The quadratic equation with one unknown solution situation surveyed outside middle part;Quadratic equation with one unknown outside for middle part, in interval [0,1], if without solution The point is outside tool sweep volume, if in the presence of a solution or four identical solutions, the point is on tool sweep volume face, otherwise, the point In tool sweep volume.
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US5208763A (en) * 1990-09-14 1993-05-04 New York University Method and apparatus for determining position and orientation of mechanical objects
CN101870073A (en) * 2010-06-11 2010-10-27 华中科技大学 Multi-axis numerical control machining tool motion planning method based on process system rigidity characteristic
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CN102809364A (en) * 2012-07-09 2012-12-05 天津大学 Method for determining complex curved surface profile error

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5208763A (en) * 1990-09-14 1993-05-04 New York University Method and apparatus for determining position and orientation of mechanical objects
CN101870073A (en) * 2010-06-11 2010-10-27 华中科技大学 Multi-axis numerical control machining tool motion planning method based on process system rigidity characteristic
CN102402198A (en) * 2011-10-24 2012-04-04 华中科技大学 Universal post processing method for multi-axis numerical control machine tool
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