CN107065770B - High-speed machining cutter shaft method for fairing based on cutter shaft discretization feasible zone - Google Patents
High-speed machining cutter shaft method for fairing based on cutter shaft discretization feasible zone Download PDFInfo
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- 239000013598 vector Substances 0.000 claims abstract description 25
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- 238000010586 diagram Methods 0.000 description 6
- 238000003801 milling Methods 0.000 description 3
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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
- 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
- G05B19/19—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
- 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
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Abstract
The invention discloses a kind of High-speed machining cutter shaft method for fairing based on cutter shaft discretization feasible zone.It is constant with top rake first to be20 0 Method generate initial cutter path, establish the boundary condition and object function of generating tool axis vector；Then the cutter shaft feasible zone of point of contact in cutter track is carried out to equidistant discrete, the composition feasible domain model of discretization；Secondly each euclidean distance between node pair on adjacent feasible arc is calculated, and penalty is applied to the length of side more than threshold value；Most short cutter path finally is found using digraph method, fairing is carried out to cutter path.This method combination machine tool motion configuration carries out generating tool axis vector fairing, it is excessive to avoid lathe shaft rotary corner, extruding cutting curved surface, influences Forming Quality, corner total journey of the lathe shaft in High-speed machining process is reduced, and largely reduces the calculation amount of computer.
Description
Technical Field
The invention belongs to the field of milling, and particularly relates to a high-speed cutter shaft smoothing method based on a cutter shaft discretization feasible region.
Background
For complex five-axis end milling, tool path planning is often limited to how to avoid interference and obtain the maximum processing bandwidth, but when a single rotation angle of a cutter shaft is too large, a discontinuous rotation phenomenon can be generated, machine tool vibration is caused, excessive extrusion is caused on a forming surface, and functional profiles of workpieces are extremely easy to scrap and tool interference is caused. When the direction vector of the cutter shaft is collinear with the normal vector of the workpiece, the processing point is called a singular point, the area near the singular point is called a singular area, when the cutter shaft passes through the singular area, the rotation angle of the cutter shaft is sharply increased, the phenomenon is called a singular point phenomenon, and the phenomenon is included when the single rotation angle of the cutter shaft is too large.
Luo Ming and the like (reported in mechanical engineering, 2009, 45 (9): 158-163) indicate a monotonous mapping relation between a rotating shaft of the machine tool and a front rake angle of a cutter by combining the mechanism characteristics of the machine tool, optimize a cutter shaft vector on a single track, and realize cutter shaft vector fairing under the limitation of the angular speed, the machining interference and the angular acceleration of the machine tool. Zhang Yongnian and the like (journal of mechanical engineering, 2012, 48 (5): 180-186) comprehensively consider factors such as processing quality, material removal rate, cutter shaft smoothness and the like, establish smoothness measurement indexes of adjacent cutter shafts, use the weighting of the normalization measurement indexes as target parameters of cutter shaft vector optimization, and convert the multi-aspect influence of the cutter shaft vectors on the processing quality into a multi-spring mechanical equilibrium point problem in a Gaussian sphere. And (3) equating the cutting quality evaluation parameters to be spring potential energy, equating the controlled mass point coordinates to be an optimal solution, and seeking an arbor vector optimization scheme under the influence of multiple factors. CN 102528554A uses the average value of the cutter shaft vectors of the non-singular areas before and after the singular area to replace the cutter shaft vector of the singular area, so as to achieve the purpose of secondary optimization of the cutter path of the singular area; however, the arbor vector of the singular region obtained by this method is not necessarily within the arbor feasible region.
Most of the existing processing methods are based on the optimization of cutter shaft vector sequences given by the kinematic level of a machine tool, and some methods solve the problem of singular points through polynomial interpolation, but the calculation amount is directly increased, and the calculation time is increased; some methods solve the problem of singular points through secondary optimization, but other limiting conditions such as the feasible region of a cutter shaft and the like are not considered, so that the processing quality and efficiency cannot be guaranteed well. In addition, most of the existing cutter axis vector optimization methods are continuous cutter path optimization without additional conditions, and a large amount of calculation cost is wasted.
Disclosure of Invention
The invention provides a high-speed cutter shaft fairing method based on a cutter shaft discretization feasible region, which aims to solve the problems of high computation cost of singular points and cutter shaft vector sequences in milling processing and the like.
A high-speed machining cutter shaft smoothing method based on a cutter shaft discretization feasible region comprises the following steps:
1) Generating an initial tool path by a method of keeping a rake angle constant at 20 degrees;
2) Establishing a boundary condition and an objective function of a cutter axis vector;
3) Equidistantly dispersing the feasible regions of the cutter shaft of each cutting contact on the cutter path to form a discretized feasible region model;
4) Calculating the distance between any two nodes on the adjacent feasible arcs, and then applying a penalty function to the edges larger than the threshold value;
5) And finding the shortest tool path by using a directed graph method.
The specific conditions for establishing the boundary condition and the objective function of the cutter-axis vector in the step 2) are as follows:
a) Establishing boundary conditions, cutting tool tracks with n number of tangential contacts, regarding the feasible region of the tool at any tangential contact as an arc, and describing the feasible region of the tool shaft as [ tau ] min ,τ max ]Wherein tau is the included angle between the feasible arc and the tangent contact normal vector;
b) An objective function: defining the distance D between the ith and the (i + 1) th cutting contact points i When the machine tool rotates from the ith contact point to the (i + 1) th contact point, the A axis and the C axis rotate by an angle R Ai And R Ci Wherein, i is more than or equal to 1 and less than or equal to n is the number of any contact:
D i ＝max(R Ai ,R Ci )，
wherein the content of the first and second substances,
R Ci ＝|A i+1 -A i |，
C i and C i+1 Respectively is the included angle between the cutter shaft and the C shaft of the machine tool at the ith and (i + 1) th cutting contact points,
A i and A i+1 Respectively forming included angles between the ith and (i + 1) th cutting contacts of the cutter shaft and the axis A of the machine tool,
setting an objective function as
Step 4) calculating the distance between any two nodes on the adjacent feasible arcs, and applying a penalty function to the edges larger than the threshold, specifically as follows:
c) Calculating the distance from the kth node on the ith contact point to the jth node on the (i + 1) th contact pointAccording to machine tool parametersSetting a threshold value
d) If it isThen pairApplying a penalty function of
Substitutiont is a penalty intensity coefficient, t>1。
The step 5) of finding the shortest tool path by using the directed graph method specifically comprises the following steps:
e) Assigning a value to each node on the feasible arc of each contact point on the tool track, wherein the value means the shortest distance from the initial contact point to the node on the contact point, and for the jth node of the (i + 1) th contact pointIs a setMinimum value of (1);
f) In the above assignment process, the track corresponding to the node with the smallest value, i.e. the shortest tool track, is obtained on the feasible arc of all the contact points.
The method solves the problem of singular points existing in the tool path by applying a penalty function, ensures the surface quality of the workpiece, and finds the shortest tool path by a directed graph method, thereby ensuring the processing efficiency of the workpiece. Meanwhile, the feasible space is dispersed, and the continuous cutter path optimization problem is converted into the discrete cutter path optimization problem, so that the calculation cost of the cutter path is reduced to a great extent, and the calculation efficiency is improved.
Drawings
FIG. 1 is a schematic diagram of a discretized feasible domain model of a cutter shaft;
FIG. 2 is a schematic diagram of finding the shortest tool path using a directed graph method;
FIG. 3 is a view of the arbor angle calculated by the method of applying a constant rake angle of 20 °;
FIG. 4 is an optimal corner view of a cutter shaft under the condition of applying the method without adding a penalty function;
FIG. 5 is a diagram illustrating setting the penalty function parameter to α max Knife axis angle diagram of =2 °, n = 2.
Detailed Description
The method of the present invention will be described in further detail with reference to the accompanying drawings.
The method is used to machine a 40 x 40 workpiece using a radius cutter of 8mm diameter and a chamfer radius of 1mm. The model of the machine tool is JDVT600, and the relevant parameters are as follows:
maximum rotation speed of machine tool C axis: n is a radical of C ＝20r/min，
Interpolation period: t is t p ＝1.8ms，
Machine tool allowable feed speed: m C ∈[850mm/min,10000mm/min]，
Tool path step length: s =0.25mm and is,
the maximum rotation angle of the single interpolation is: n is c ＝N C ·t p ＝0.216°，
The single step maximum machining time was: t is 0 ＝S/M Cmin ＝0.01764s＝17.64ms，
Single step maximum interpolation times: n = T 0 /t p =17.64ms/18ms =9.8, n =10,
maximum rotation of single step feed of machine toolAngle phi max ＝n·n c ＝2.16°，
To simplify the calculation and to make the angle of rotation less than phi max Get it
Generating an initial tool path by a method with a constant 20 degree rake angle, resulting in the tool path numbered P in FIG. 1 1 P 2 P 3 P 4 …, the tool path has 160 contact points, and the corresponding corner diagram of the knife shaft is shown in fig. 3. It can be seen from the figure that the cumulative rotational angle of the tool path is close to 180 °, and the problem of excessive rotational angle of the cutter shaft exists locally. (ii) a
Determining the cutter shaft feasible region [ tau ] of each contact point by using a discrete point cloud method min ,τ max ]For each contact point, the feasible region of the cutter shaft is the allowable rotation space of the cutter shaft, namely the boundary condition of the cutter shaft, wherein tau is the included angle between the feasible arc and the normal vector of the contact point; .
Since the time of a single rotation of the machine tool is determined by the largest rotation angle of the two shafts A, C, the distance D between the ith and (i + 1) th contact points is defined here i When the machine tool rotates from the ith contact point to the (i + 1) th contact point, the A axis and the C axis rotate by an angle R Ai And R Ci Wherein, i is more than or equal to 1 and less than or equal to n, and the number of any contact is as follows:
D i ＝max(R Ai ,R Ci )，
wherein:
R Ci ＝|A i+1 -A i |，
C i and C i+1 Respectively is the included angle between the cutter shaft and the C shaft of the machine tool at the ith and (i + 1) th cutting contact points,
A i and A i+1 Respectively forming included angles between the ith and (i + 1) th cutting contacts of the cutter shaft and the axis A of the machine tool,
and setting an objective function to minimize the total turning angle of the machine tool, namely:
equidistantly dispersing the feasible region of the tool axis to form a feasible region model, for example, P in FIG. 1 1 The corresponding feasible arcs are dispersed into 4 nodes;
calculating the distance from the kth node on the ith contact point to the jth node on the (i + 1) th contact pointSetting thresholds according to machine tool parametersTaking t =2;
if it isThen pairApplying a penalty function, setting the penalty function as
t is a penalty intensity coefficient, t>1，
By replacing corresponding by ESmoothing the tool path.
When the axial vector of the cutter shaft is collinear with the normal vector of the workpiece, the machining point becomes a singular point, and a region near the singular point is called a singular region. The singular point phenomenon refers to the phenomenon that the rotating angle of the cutter shaft is sharply increased when the cutter shaft passes through a singular area, and the singular point problem is solved because the singular point phenomenon can solve the problem that all single-time cutter shaft rotating angles are too large in the implementation process.
And assigning each node on the feasible arc of each contact point on the tool track by using a directed graph method, wherein the value means the shortest distance from the initial contact point to the node on the contact point. FIG. 2 is a schematic diagram of finding the shortest tool path using a directed graph method, P 0 Is the initial position of the tool, P 1 The first point of contact on the workpiece. The following contact point P can be found by applying the method 0 To the contact point P 2 The shortest path ofAnd at this time:
in the above assignment process, the track corresponding to the node with the smallest value, i.e. the shortest tool track, is obtained on the feasible arc of all the contact points.
Fig. 4 shows a graph of cumulative tool rotation angle and minimum tool path rotation angle obtained by applying the method without adding penalty function under the initial tool path. As can be seen from the figure, the accumulated rotation angle of the cutter can be greatly reduced by the method, the total rotation angle is about 115 degrees, but the problem of overlarge rotation angle of the cutter shaft still exists at certain contact points of the cutter shaft.
As shown in FIG. 5, for us to use an optimization algorithm with penalty function added, the maximum tool angle variation is limited by weighting method, so that large turning angle is not selected, settingI.e. the maximum distance of adjacent knife axis vectors is limited to less than 2 deg.. The final accumulated rotation angle is 128.10, and although the accumulated rotation angle of the cutter is increased relative to the algorithm without the penalty function, the singular point problem is solved. Therefore, the method finally ensures the processing quality of the workpiece, and the final tool corner total distance is far less than the constant inclination of the cutter shaft although the corner total distance of some cutters is sacrificedThe method is effective because the method of 20 ° results in a total rotational angle of the tool path.
Claims (2)
1. A high-speed machining cutter shaft smoothing method based on a cutter shaft discretization feasible region is characterized by comprising the following steps of:
1) Generating an initial tool path by a method of keeping a rake angle constant at 20 degrees;
2) Establishing a boundary condition and an objective function of a cutter axis vector;
3) Equidistantly dispersing the feasible regions of the cutter shaft of each cutting contact on the cutter path to form a discretized feasible region model;
4) Calculating the distance between any two nodes on the adjacent feasible arcs, and then applying a penalty function to the edges larger than the threshold value;
5) Searching the shortest cutter path by using a directed graph method;
the specific conditions for establishing the boundary condition and the objective function of the cutter axis vector in the step 2) are as follows:
a) Establishing boundary conditions, cutting tool tracks with n number of tangential contacts, regarding the feasible region of the tool at any tangential contact as an arc, and describing the feasible region of the tool shaft as [ tau ] min ,τ max ]Wherein tau is the included angle between the feasible arc and the tangent contact normal vector;
b) An objective function: defining the distance D between the ith and the (i + 1) th cutting contact points i When the machine tool rotates from the ith contact point to the (i + 1) th contact point, the A axis and the C axis rotate by an angle R Ai And R Ci Wherein, i is more than or equal to 1 and less than or equal to n is the number of any contact:
D i ＝max(R Ai ,R Ci )，
wherein the content of the first and second substances,
R Ci ＝|A i+1 -A i |，
C i and C i+1 Respectively at the ith and the th of the cutter shaftThe included angle between the i +1 contact points and the C axis of the machine tool,
A i and A i+1 Respectively forming included angles between the ith and (i + 1) th cutting contacts of the cutter shaft and the axis A of the machine tool,
setting an objective function to
Step 4) calculating the distance between any two nodes on the adjacent feasible arcs, and applying a penalty function to the edges larger than the threshold, specifically as follows:
c) Calculating the distance from the kth node on the ith contact point to the jth node on the (i + 1) th contact pointSetting thresholds according to machine tool parameters
d) If it isThen pairApplying a penalty function of
Substitutiont is a penalty intensity coefficient, t>1。
2. The method according to claim 1, wherein the step 5) of finding the shortest tool path by applying the directed graph method is as follows:
e) Assigning a value to each node on the feasible arc of each contact point on the tool track, wherein the value means the shortest distance from the initial contact point to the node on the contact point, and for the jth node of the (i + 1) th contact pointIs a setMinimum value of (1);
f) In the above assignment process, the track corresponding to the node with the minimum value, i.e. the shortest tool track, is obtained on the feasible arc of all the last contact points.
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| CN110456731B (en) * | 2019-08-13 | 2022-06-14 | 成都飞机工业（集团）有限责任公司 | Method for extracting characteristics of numerical control cutting geometric tool path |
| CN110658783B (en) * | 2019-09-24 | 2020-10-16 | 华中科技大学 | Solving method and system for feasible region of five-axis machining cutter shaft |
| CN112051803B (en) * | 2020-09-17 | 2022-02-08 | 华南理工大学广州学院 | Small line segment fairing method based on space plane normal vector |
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| CN100588487C (en) * | 2008-05-14 | 2010-02-10 | 北京航空航天大学 | Multi-coordinate end milling process tool position optimization method using longitude line division tool bit |
| CN102608952B (en) * | 2011-12-19 | 2014-03-26 | 华中科技大学 | Method of smoothening five-axis-linkage machine tool machining path by using ball-end cutter |
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