TW200925812A - Method of planning path for curved surface cutting process based on global optimization - Google Patents

Abstract

This invention provides a method of planning path for a curved surface cutting process based on global optimization. Its main characteristic is to convert the problem of motion planning of a cutter in a three-dimensional space into a mathematical planning problem of the corresponding relationship between two independent curved lines so as to obtain the final path for the curved surface cutting process by finding the solution with the global optimization mathematical model. Therefore, it can accurately control the error of the path for the curved surface cutting process and, given that different types of error value conditions are satisfied, automatically generate the best cutter path in order to provide precise and flexible path planning functions. The method of planning path for a curved surface cutting process can greatly improve the processing and manufacturing process capability in such industries as aerospace, automobile, marine, air-conditioning, and mold manufacturing.

Description

200925812 IX. INSTRUCTIONS: TECHNICAL FIELD The present invention relates to a method for path cutting path planning, and more particularly to an innovative designer based on a global optimization method. [Prior Art] According to the continuous development of CAD/CAM technology, free-form surface modeling in response to product aesthetics and ❹ functional requirements is becoming more and more popular, and is widely used in product structures such as aviation, automobiles, shipbuilding parts and consumer electronics. . Take the aerospace and the turbine blades of the refrigeration and air-conditioning industry as an example, and their development capabilities are advanced.

The curved shape of the 〇 turbine blade is highly complex, 'Because of the three-axis numerical processing, it is often regarded as one of the important indicators of industrial technology level. A large amount of research resources are invested in the field; the industry of turbine blades, appearance geometry + method B Small # cutters have a limited range of movement in space, no

Difficult and lacking the aid of automatic calculation methods. The wearing limit can not completely create the five-axis sharpening of the design degree. Because it is used for two kinds of complex geometric shapes, the straight-lined surface has more excellent cutting error control, which is more difficult. 200925812, to the knowledge of the five-axis side sharp path planning method, must first select the knife, * 卩 and other parameters straight 1 line method for (four) 'first must be in the boundary curve ^ and other parameters to obtain discrete points, if the two curves produce points If the numbers are the same, the corresponding points are connected to determine the tool axis. If the number of curve points is different, the motion mode (such as Tangeint〇fan) can be used to generate the complete path. Other rules=such as fixed tool axis, or the normal vector of the specified surface determines the tool data. (1) For the whole song (4), its motion The mode is only—and fixed, and the surface geometry cannot be properly adjusted. The planning methods have no cutting error caused by the machining path, and only the degree of knife density can be changed to produce a very small error improvement. In fact, the tool position is only Can reduce one of the numerical processing atl. a) It is not the planning method of improving the tool brain. How to:: Out: ^: The problem of the conventional cutting processing method, the industry will think again to break through 1;; the innovative design of use, it needs to be related to recklessness The target and direction of the big break. And set =: This needle has been engaged in the manufacture and development of related products for many years - it is practical, after detailed design and prudent evaluation, [Summary] The main purpose of the invention is the surface cutting of the road after the rule = Supply: Based on the global optimization method, how to develop - the most cutting error: the problem to be solved, the more accurate innovation, correction, error control mechanism, the surface of the knife and the processing path planning method for the goal 6 200925812 Cable Breaker; - The technical special path planning method for solving the problem of the present invention includes: · The design institute, two independent geometries in the surface cutting process; the two boundary curves of the surface = curved surface are changed into space Corresponding relationship mathematical machining of the tool movement problem to the mathematical model to solve the problem; the use of the global optimization W Μ post-transmission finally use this innovative unique design to make the Tai, surface cutting path; a new Surface cutting ~ prior to the technology, you can mention... 々U丄 path stroke surface overall cutting error minimized J method, not only can consider the diameter Rules can be based also cut by automatic calculation of the machining tool path adjustment corresponding to the target function, and further to provide a different error defined thereby to provide a very elastic and the curved @ seeking tool path combination, correct the error control mechanism. The sigma path planning method, and the quasi-preferred method, please refer to the first to π 阁μα- > π = the figure is not, which is the preferred method of the surface-cutting process of the invention based on the global optimization method. The examples are for illustrative purposes only and are not limited by this structure in the patent application. The invention focuses on the innovation of the D1 stroke and the tool planning method, and the main concept is to subtly convert the curved road planning problem of the curved surface of the five-axis side milling into the search problem of the correspondence between the independent curves of the space rain. The steps are as follows: The two boundary curves 13 and 14 of the ten curved surface 1 are two independent geometries in space, and the false & 77 has a point corresponding to each of the boundary curves 13, 14 at each position. The endpoint connection represents the best correspondence between the two boundary curves 13, 14, 200925812 The so-called optimal correspondence means that the cutting error generated by the tool from the position to the next position is the smallest. As a result, the actual tool motion planning becomes the boundary curve 13 and the corresponding correspondence. The purpose is to establish a boundary curve between the two boundary curves 13, & point and point to minimize the overall cutting error. By way of illustration (as shown in Figures 1 and 2), the planning of the machining path 1〇, u can be regarded as finding a machining path starting from the starting point and ending at the end point in the two-dimensional matrix 12 The overall (four) error is the smallest, the horizontal axis in the figure represents the parameter value ui of the strip boundary curve 13 , and the vertical (four) is the parameter value of the other strip boundary curve 14 is old. After converting the planning problem into a search problem corresponding to the curve, it can be solved by using the existing global optimization mathematical model (such as dynamic programming, gene algorithm and particle swarm algorithm). In addition, based on the difference in the cutting error requirements of the planner, the optimized mathematical model can adopt a discrete or continuous mathematical representation. If the discrete representation is used, the two boundary curves 13, 14 will be converted into discrete points 15 form, and The establishment of its correspondence is limited to only the discrete points 15. From the matrix diagram on the right side of the 2nd W (a), the horizontal axis and the vertical axis represent the parameter values of the two boundary curves 13, 14 respectively. When the curve correspondence is established by the discrete point 15, the feasible path has only three paths. Direction (horizontal and longitudinal diagonal lines), compared to the continuous optimization mathematical mode (as shown in Figure 2 (b)), the feasible path is not limited to these three directions (horizontal, vertical) The search for the correspondence with the diagonal lines ', ie the boundary curves 13, 14 can be made anywhere on the curve. By transforming the path planning problem of five-axis side milling into a search problem of the correspondence between curves and using the optimized mathematical model to solve, one side 8 200925812 can improve the flexibility of the path planning 'efficiency and accuracy, another On the one hand, planners have better error control mechanisms. Through the optimization calculation process, different tool motion modes are automatically taken into consideration, and the better mode is selected with the local surface geometry to reduce the overall cutting error. The invention automatically sets the σ special tool movement to achieve the purpose of reducing the error. Compared with the conventional five-axis side milling for a single curved surface, the method of using only the fixed path generation method is extremely different, and the invention is a breakthrough innovation.

另一 Another advantage of the present invention is that it provides a high degree of flexibility in path planning's requirements for different error definitions and tolerance ranges for users, correspondingly using different optimized target functions<, and automatically generating the best Tool path group 2, for s, for the same - design surface, with the difference between error accuracy requirements and calculation methods, the optimized tool path will be different. The present invention proposes two different algorithms for optimizing the surface side milling path. "The tool is a dynamic programming with discrete points as the stage and a dynamically planned network map with the specified range as the stage." Dynamic programming (Dynsmic Programming; np, sm * g DP) is a mathematical method used to deal with multi-stage (mUltista ge) decision problems. The idiom system breaks down a huge problem into a series of related and related small questions. ★ H full, ask and then deal with, and the dynamic programming does not have a fixed number of sound grips, .., sub-type. And the invention belongs to the deterministic (determ nnSt1C) dynamic programming, using L + million忐 to produce the best side milling path; and the above two algorithms provide the same moxibustion. Most users choose, the parameters do not have discrete points 'can cross the point, side... line extension ratio and limit Straight-grained green knows 'cross-value. (See Table 1 for description of the parameters of Table 1 9 200925812 Parameter ****·—« -—• Circle describes discrete points (NDPi and secret) and other parameters take point ·· The parameter value takes a point on the boundary curve and takes the same distance to take the point * to equidistant values in the boundary curve --- ~*~--- take the point on the line and can cross the number of points (P& and PS2) in the same boundary curve Up -» once - consecutive points that can be crossed 0 boundary curve extension ratio (control point of ER! and two boundary curves > ER2) correspondingly produces four vectors extending to four vectors according to the extension ratio ___ -- ---- Stretch 9 as a new boundary curve 0 Limit Straight Line Span Value (CS) --- Limit Surface Straight Line Length 〇 Total, Surface

, your Qiongjie curve Αυ, η Γ / | 俯 w H, the factory to side milling of this surface 1, must be in the two boundary curves 13, 14 discrete points, and discrete points are divided into equal parameters and Equidistance takes two points' The invention is mainly applied to equal parameter points. The number of points that can be spanned represents the number of points that can be crossed at a time on a boundary curve. In general, for the side milling program of the transmission, the tool must travel at the point on the boundary curve to cut, so for the MD 1 τ β work, the present invention proposes this parameter to enter =: must pass through each discrete point 15 can span points t so == planning. As shown in Figure 3, there will be a straight line 16 connected, which also represents the discrete point 15 on the line, 13 and 14; and in the third picture (4) the path will pass every ~ discrete points = 2, so the same - strip boundary曲10 200925812 The discrete points at 13 and 14, at most two consecutive points, will not be connected by straight line and i6, which means that the tool path does not have to pass through every discrete point 15, because it is not necessary to pass each discrete point i. 5 will cause the total error amount to be the smallest. Generally, when planning the tool path, the boundary curve of the original design surface is directly taken up, and the tool path is planned to reduce the error amount. The present invention is to follow the boundary curves 13, 14 The corresponding control point vector is extended, and then the extended boundary curves 13 and 14 are discretely taken, and the tool path planning is performed. As shown in Fig. 4, the original boundary curve control point of the object A in the figure is hit, ❹ P2. P3, P4 four points; object B original boundary curve control points are p5, p6, P7, P8 four points. Pi and P5 form V1 vector, ?2 and support form V2 vector, and P7 constitute V3 inward, P4 and P8 constitute V4 vector. Object a new boundary curve control point P1 is followed by P1 The -V1 vector is obtained by multiplying the extension ratio L=〇·5, which is obtained by multiplying the P2/σ-V2 vector by the extension ratio L=〇·5, and p3 is obtained by multiplying the extension ratio L=0.5 along the —μ vector. P4*P4 is obtained by multiplying the vector by the extension ratio L=0·5, and the object B new boundary curve control point p5 is obtained by multiplying p5 along the νι vector by the extension ratio L=0 5, and P6 is multiplied by p6 along the V2 vector. The upper extension® stretch ratio L=〇·5 is obtained, and the Ρ7 is obtained by multiplying Ρ7 along the V3 vector by the extension ratio ^〇5, and P8 is obtained by multiplying P8 along the V4 vector by the extension ratio L=〇·5. The new control point of the A ^ bound curve of the object is the new control point of the boundary curve of the object B, R is the original control point of the A boundary curve, and Pj is the original control point of the boundary curve of the object B, and its 〇si ^ N and 〇s ]·$ N, ER, and 服服11 200925812 respectively, the cutter is used to pass the tool, and the equivalent of the corresponding addition and subtraction is given, such as the boundary curve of the object A and the extension ratio of the object β boundary. The last parameter is to limit the straight line crossing value ((3), the length of the straight line is longer than the _, so the path of the tool plus I must be matched with Planning, because when the tool is very large across the surface, the super: long cutting range will lead to machining failure. As shown in Figure 5, the limit of the straight line is crossed, and the boundary curve is found to be reasonable. Discrete point 19. First calculate the soil variable so that the definition is reasonable (1 i + cs), then according to this

Finding the corresponding discrete point DPi around the boundary curve 18 (υρ2_) is one of the reasonable discrete points. The present invention mainly utilizes dynamic programming for tool path optimization. Before entering the dynamic programming algorithm, the most basic steps must construct a network diagram that conforms to the dynamic programming, which is composed of nodes and paths. "6 Figure does not 'to establish a dynamic plan network program diagram with discrete points as the stage, the construction steps are as follows: In this method, the discrete points on the boundary curve are used as the stage of dynamic planning' The selection of the two boundary curves, and the selection of which does not affect the results of the optimal tool path, because the network diagram established by the two boundary curves has a symmetrical relationship

SteP2: When the user sets the extension boundary curve ratio, it is convenient to take the point on the extended boundary curve; if the extension ratio is not set, the discrete point is only taken on the boundary curve of the original design surface.

Step3: According to the set number of points that can be crossed and the horizontal line value of the straight line, the conditional formula must be satisfied before the dynamic planning network diagram can be constructed. 12 200925812 The present invention defines a node as an I, a straight node, which further includes two forms: = for: _ phase... virtual node. The original node is defined as 〇N;j, such == original node and group straight line, and the virtual I _ p point contains a narration..., that is, the point is defined as (10); In addition, the point only contains - the discrete points on the boundary curve, and η means that the discrete points are - the edges and the η table is not discrete points can be expressed as the ηth point on the Dp line, so the horse muscle, η. In the present invention, only one discrete point is selected as the 线上 ❹ ❹ 绿 绿 . 以 以 以 & & & & & & & & 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界 边界The discrete points on the line are listed in the FDRb n table (1). Search for non-target curves. 2 discrete points that can be connected to form stage s. All the nodes in the node, and then continue to search for the nodes in each phase from the FI, that is, complete an element_node in the dynamic network circle. The explanations are as follows: As shown in Figures 7 and 8, the three-point parameters are taken on the boundary curve 2〇 and the boundary curve 21 respectively, given the parameters (NDPi, NDP2, pSi, 吆, 贶肱,

Under 3,1,0, 0, 0, 2), a discrete point is searched for from the discrete point 22 (FDPw) on the non-target curve, and a set of reasonable corresponding discrete points is obtained. DPu' Dh'2 } ' and the node of the discrete point 22 ( FDPw ) at this stage are arranged as {(muscle, .), (DPu ), ( DPaWv ) , ( D

Pu, DP2, 2), (DP2, d, DPu, DP2, 2) }. In this combination number, the departure point 22 (FDPi, 〇) is the starting point of the ruled line 23 and the corresponding point in the combination number is the end point of the ruled line 23. Therefore, the five combined numbers represent five original nodes ΟΝμ, 0Ν〇, ι, ONo'2, ONo.3, ONm appear in stage & φ ^ τ 0 and the original node ONi.j contains one or more The ruled line is represented as Rab (a represents FDP», the value of n in n; b represents the value of η in the). Completing the discrete points 13 200925812 u ) After all the nodes are counted, the discrete points 24 (FDPu) and the discrete points 25 (FDPi2) are respectively completed by the same procedure. In this way, all the original nodes (10) in the dynamic plan network diagram can be completed. ❹ Ο 卜 A virtual node has only one virtual no-line, not like the original node can contain multiple straight lines, and no straight lines The line is considered to be the straight line connecting the previous stage. As shown in Figure 8, there are six original nodes (10)w, 敝1, (10)L, 〇Nl, 4' chaos 5 in the stage, and each original The node m, muscle "〇m, the last line of the 5th line in the 5th phase has its corresponding virtual no-language point. (Thus, the establishment of the virtual node must be in accordance with the last of all the original nodes in the previous stage. A straight line has a corresponding virtual node in the next stage. If the set can span 2 points, the last straight line for the original save has a corresponding virtual node 35 in the next stage. The next stage of vain, point, will copy the same virtual & node in the next stage.) When constructing the original node hidden in the dynamic programming network diagram and the virtual node d Nu, the final will be added Section '(4), its corresponding virtual node and termination node 3 The start node 30 and the terminating node 31 respectively represent the starting straight line and the ending straight line in the curved surface 2 of the design, and the corresponding (10)u no node is different from the other virtual no nodes, because the virtual benefit section _ does not have any straight line The line takes the first discrete point on the target curve as the starting point and does not divide R (J, D. The description of the symbol in Table 2 is ~ Si —. The first stage of the dynamic programming network diagram is 1~~ 14 200925812 ❹ ❹

Ni, ----~-______________ The i-th section of the j-th stage in the dynamic planning network diagram is black. ONi.: DNi, DP, FDP.

The Ra.l node will be the node node rule rule original node imaginary node η point on the m-th boundary curve------a _ discrete point on the target boundary curve ~~~~~~ -~~ line by Dh , a and w\b (m η) 槿 points ^ — Before applying the dynamic programming algorithm, the relationship between the two adjacent stages must also be determined. In the node, a straight line is recorded as the end point. The end points of the straight line are sorted by the serial number. Therefore, the adjacent two orders can be judged according to the two rules. 1: Use the parameter to cross the number of points (10) to determine if the two nodes are related. If you compare the serial number of the last straight bite line in the node in the previous stage and the serial number of the first straight line in the current stage, compare: the difference between the two numbers and the value of the cross-point can be compared. The number of points 佶(ρς), Β,, J, J will not be related, and there will be no feasible path between J points; if the two orders are equal to the value of the crossing point (ps), then These two points have a feasible path for connection. 2: Avoid the last line in the streak line of the straight line - straight: compare - the intersection of the straight line in the middle stage: the first line in the middle node, that is, between the two nodes will not Will be concerned. There will be no feasible path for the connection. As shown in Figure 9, the style of the _ ', the feasible path between the stages. 15 200925812 ❹ e The steps of constructing a dynamic programming network diagram according to the present invention are as follows: 6. Discrete the points on the boundary curve and represent all the discrete points by symbols such as DP»,n. The original node is established according to the discrete points on the target boundary curve. The start node and the end node are added, and the virtual nodes corresponding to each original node are constructed according to the given parameters.攸Starting node to terminating node' In the two adjacent stages, the node ... judges whether there is a connection relationship according to rules 1 and 2. Dynamically plan the network map from Stepl to step 4. After the dynamic planning of the network diagram is completed, the values are optimized. From the starting node to the termination criteria evaluation path represents - (four) with a path.卩 卩 - - ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( For example, the Ministry of Construction has a dynamic planning program diagram in the orbital stage. The steps are as follows::, to establish the range Stepl: when setting the extension boundary curve ratio, discretely take the point; if no extension boundary curve is set (4), the discrete curve on the boundary curve of the design surface: 贞 is only the original SteP2 : This method uses the scope as the level of dynamic planning, allowing the user to directly specify which range: :: The purpose is to make the messenger more intuitive (4), | Toolpath #. & must go through the 'Step3: According to the user can set the value of the cross-point value to establish a dynamic planning network map '" Straight line across the picture in other words dynamic rules _

Step2 Step3 Step4 Construction Requirement 16 200925812 The size of the road map is controlled according to the parameter limits given by the user. The biggest difference between this method and dynamic programming with discrete points is that each phase has only the original node and no virtual nodes appear. The original node contains only one straight line. As shown in the nth figure, take ten parameters under the boundary curve 35 and the boundary curve 36, respectively, in the given parameters (muscle milk, delete p2, p S!, PS2, ERi, Efe, CS) = (l〇, 1〇, 1,1,〇,〇,丨), and select two stages of 37, 38 basis, one for DBu and 肭3, and the other for Dpi 7 and muscle 6. According to the given parameters (PSl=1 and the upper and lower bounds of the decision phase range 37, 38, taking DPu and Dh, 3 as an example, the upper bound of DPl 3 is DPu, and the lower bound is DPw; above DP2, 3 The boundary is])h 4, and the lower boundary is muscle 2, the region Rp is formed according to the corresponding upper and lower bounds, and the other is DPi 7 and muscle e. The upper boundary of muscle 7 is DPu and the lower boundary is DPl 6; The upper boundary is the muscle 7 and the lower boundary and d

Pu ' forms an area based on the corresponding upper and lower bounds. The first step is to search the boundary curve 合理 from the lower bound DP1, 2 in the region R! according to the parameter (CS=1), and obtain a reasonable corresponding discrete point 丨Dp2 “Dh 2 〇, muscle '3 }, but since the punch 2a is lower than the lower bound DPz 2, it is not included in the reasonable range, so the corresponding reasonable discrete point is (muscle 2, I } two points, then sequentially find DPl, 3 and DPl, 4 reasonable Corresponding to the discrete points. Finally, all the combined numbers will represent the number of nodes in this phase appearing in phase S. As shown in Fig. 12. After the number of f nodes is completed, the same procedure is completed in the heart of the region (stage Sl) the number of all nodes, so that all the original nodes in the dynamic network map can be completed. If DPu Xiaoji 2 is selected as the basis of the stage range, and based on the reference CS=1), search for the edge from DPi, 2 1 α Α I curve on the 5 points that can be connected to discrete points, the result is 17 200925812, so the range of the stage

A set of corresponding discrete points { Dp2,i, DP2.2, DP2,3 } nodes have three, respectively, R2 2, R2 3 D, in the two adjacent stages, Ming went to the sentence · 4 曰 secret rights A Points can be judged according to the two rules to determine whether there is a connection. Rule 1 • Use the parameter to bridge the 4-! ! »« ~ 祆垮 points (PS) to determine if the two nodes are related. If comparing the straight lines in the nodes in the previous stage

For Ra, b and the current ruled line in the node is Rc,d, if [(c-aM

Ο dj3)] > PS B win, then the two nodes will be irrelevant, that is, two

There is no path between the nodes for connection; if [(C-a)-(d-b)] SPS, it means that the two nodes have paths for connection. Rule 2: = Straight: Lines will be interlaced. If the previous order is compared, the straight line in the middle node and the straight line in the node in the current stage are ^, which means that there is no correlation between the two nodes. In other words, there is no path between the two nodes for connection. Then start to construct this network diagram as follows:

Stepl discretely takes points on the boundary curve and symbolizes these discrete points as DPm,n .

Step2 & 疋 | a surrounding basis to establish the upper and lower bounds, and according to the parameters 1 S) down to find all feasible straight lines.

Step3 ··Add the starting node and the ending node.

Step4 'Starting point to terminating node' The nodes in the adjacent two stages determine whether there is a connected relationship according to rules 1 and 2. From Step to Step 4, complete the dynamic planning network diagram. ', 18 200925812 ' Advantages of the invention: 1. ❺ 2. Providing accurate error control mechanism: The conventional curved path planning method generates a type 2 'by reducing the cutting error by trial and error method by changing the tool path'. It is to solve the fundamental error definition target function 'with the rigorous mathematical optimization= to solve the problem, and to generate a feasible solution through the optimization calculation, so it can work accurately. Difference ^ Five-axis side milling plus highly flexible path planning: ❹ If the target function is defined to reduce the "overcutting error", the corresponding tool path is the result of minimizing the overcut error. The plan is highly flexible. If the user wants to limit the "overcutting error value" to a certain range, then the corresponding target function can be optimally solved, and it is judged whether the setting range is feasible by the calculation result. According to this adjustment error range or replacement of the target function, the present invention will be able to meet different error control requirements, and the user will have more choices and planning degrees of freedom in path planning. 3. Integrate different tool motion modes: The present invention does not use the #-tool motion mode to generate the road #, but automatically determines the more suitable mode according to the surface geometry by optimizing the calculation, thereby integrating and matching different tools. Achieve the goal of minimizing the overall error' and make full use of the freedom of five-axis machining. 4. Optimization of Mathematical Methodology: 19 200925812 i'J (mathematical programming) ^ ^ 6 ^ A long time, so when the abstraction of tool motion problems becomes an optimal mathematical problem, it can be applied to development. + > In & The different methodologies for the implementation of the exhibition are not limited to a single calculation method.

The above embodiments are disclosed by way of specific terminology, and the changes and modifications to the changes and modifications of the spirit and principles of the technical field should be covered in the specification. The invention is specifically described, and the specifics of the invention can be used to define the invention, and the scope of the invention is

20 200925812 [Simple description of the diagram] Fig. 1: Schematic diagram of the search for the best correspondence between the curves of the present invention. Figure 2: Discrete and continuous representation of the invention. Figure 3: Schematic diagram of the cross-points of the present invention. Figure 4: Schematic diagram of the extension of the boundary curve of the present invention. Fig. 5 is a schematic view showing the restriction of the ruled line of the present invention. Figure 6: Flow chart 1 of the dynamic programming of the present invention. Figure 7: Figure 1 of the parametric design surface of the present invention. Figure 8 is a schematic view of a node of each state in the curved surface of the present invention. Figure 9: A feasible path diagram between the two phases of the present invention. Figure 1 : Flow chart 2 of the dynamic programming of the present invention. Figure 11: Figure 1 of the parametric design surface of the present invention. Figure 12: Schematic diagram 2 of the nodes of each state in the curved surface of the present invention. [Description of main component symbols] ❹ Object A Object B Area R 1 Area R 2 Surface 1 Λ 2 Boundary curve 1 3 , 1 4 3 5 , 3 6 Machining path 1 0 '1 1 Two-dimensional matrix 1 2 1 7, 1 8 , 2 0, 2 21 200925812 Discrete point 15 Straight line 16 Start point 3 0 End point 3 1 Stage range 3 7 , 19 , 22 , 24 , 25 , 2 3 , 3 8 ❹

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Claims (1)

200925812 X. Patent application scope ···1, based on the global best method, including: : The surface cutting path planning side design The two boundary curves of the surface are space φ Two independent geometries in the surface cutting process The mathematical programming problem of the relationship is that the motion problem is converted into a curve-to-curve pair using the global optimization number. Solution, to obtain the final curve, according to the method of the surface cutting path planning described in the item _1,; == mode = two-axis side sharp addition, the five-axis side =, five free Degrees are respectively in the X direction, γ square...: Thousand degrees of freedom of movement, and two degrees of freedom of rotation and inclination. 3. The method according to the global optimization method for the surface cutting path planning method according to the first aspect of the patent application scope, wherein the correspondence relationship between the curves refers to the correspondence between any two independent curves in the space, which may be Continuous or discrete counterparts. 4. According to the scope of the patent application, the global optimization method based on the surface optimization path planning Wanfa's optimization mathematical model can be selected by dynamic programming, gene algorithm, particle swarm algorithm Wait for one of the optimization calculation methods. 23 200925812 ' 5. The method of path cutting path planning based on the global optimization method according to claim 1 of the patent application scope, wherein the optimized mathematical mode may adopt a discrete or continuous mathematical representation. twenty four