STL表面的螺旋路径渐进成形使用非确定性技术和球形工具获得用于加工J.L. Huertas-Talo

文件名称: STL表面的螺旋路径渐进成形

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详细说明：使用非确定性技术和球形工具获得用于加工STL表面的螺旋路径渐进成形J.L. Huertas-Talon et al. Computer-Aided Design 50(2014)41-50 Triangle i Side il, 12, 13 Triangle A Sidej1,j2, j3 Side side Ik Contour side sid∈2△→ no contour yes Store side i, as contour Fig 2. Condition of one side to be the contour Initial profile 1 Successive profiles: 2, 3, c g xmax, min n Fig 3. Obtaining profiles prior to the spiral. to the interior(though later, rearrangement is possible to change out with respect to the gravity centre at each point a displacement the machining order) is applied the coordinates are actually multiplied by a scale) the Initially, the machining runs are"parallel"profiles which are distances of this point to each coordinated axis are taken into obtained as shown in Fig 3, displacing each point a certain amount account. For example towards the interior of the profile in the direction of axis OX and if the point is in the first quadrant, the scales in the direction another in the direction of axis oy, the same as if a scale was carried out but variable in each direction. The entry datum is the distance OX and oY, in function of some certain runs, Px and py in each direction which will be looked at later are d between homologous points but measured in a certain direction which depends on the position of the point Px The position of the point is classified by quadrants originated by e maX g a system of coordinates. This system of coordinates can be chosen in function of various parameters. The origin has been taken as the p gravity centre of the series of initial points ym y Nith this, it is possible to calculate the coordinates of the trans- (1) formed point in the chosen system of universal coordinates This system of coordinates classifies the plane in four quadrants(L. xp=(x-xeg)ex+xcg Il, Ill and Iv). To classify each point, its difference is simply carried yp yeg)·ey+yg J.L. Huertas-talon et al. Computer-Aided Design 50(2014)41-50 Fig. 6. Smoothing a profile Fig 4. Pitch calculation Contour(red) Added points :875 points added t 228 Spiral path(black) ………,,…… Fig. 5. Spiral 2D tool-path Fig. 7. Additional points to increase precision On this occasion, the runs in x and y, Px and py take the same value, given by the expression obtained in Fig 4 in function of the ra 2 dius of the spherical tool and the roughness crestf if, supposedly milling was in the horizontal plane. Other cases(concave and con- vex surfaces)can be consulted[24 (r-f)2+ (4) Fig. 8. Tool radius and surface curvature for a section The process is repeated for each new profile but taking the maxi- mum coordinates that correspond to the previous profile as maxi- the one hand should the profile be too abrupt, it is smoothed over mum values to enter into(2). Fig. 6. The criteria can be very varied: to carry out the average of Finally, worth noting is that the points which change quadrant next points or to optimize trajectories to a minimum number of with respect to the first of the line of points of the initial contour points [ 26, among other possibilities cannot change due to the previous transformation. therefore, a Once smoothing has been carried out according to the precision filter is used if the point changes to another quadrant; this filter of the stl lattice the addition of more points may be required This reduces to zero the coordinate that causes this change is done depending on a step or interpolation precision(distance In order to transform the previous points into a spiral, the between two consecutive points), in the direction of the spiral orbit process consists of working with the equivalent points of a profile from one point to the next. Therefore, one or more intermediate of those obtained previously and the following profile. This is done points can be added between two points, Fig. 7. Some authors considering that initially all the profiles have the same number of described the application of adaptive tool-paths[27]with excellent points.A formula is used for this purpose which brings the points results in the surface finish: but in our case the tool-path follows a of a profile closer to those of the following profile: the first point is more uniform direction, so less acceleration milling is required to the next to profile p-1, and the last point next to profile p obtain precise results Again, the algorithms for smoothing can be applied to this new x=X,P1+(x-x2-n) spiral path with added points. yi=yi -1+(vi. -yi.p-1) 2.4. Projection of the spiral path points onto the surface where, i is the current point of profile, p is the current profile, and The previously obtained spiral path 2D points are transformed n is the number of profile points into the 3d path by projecting the 2d points onto the StL surface, Fig 5 shows the results obtained In this figure, a high value has but also taking tool size into consideration been taken in expression (4) for the height of the roughness crest, Tool size is extremely important. Fewer runs can be made using f, to obtain few profiles and so be able to illustrate the process The large diameter tools, see expression (4). But the inconvenience is contour forms part of the tool path to calculate the first or last cut, that the smallest curvature radius possible on the surface is that of according to whether start-up is made from the outside inwards or the tool tip radius, as unmachined hollows can remain, Fig. 8 ce versa For this choice between the tool radius and that of the surface curvature, the coordinate z of the tool contact point with the 2.3. Algorithms to smooth the profile surface must be determined. This point is not necessarily the projection of the coordinates(x, y)on the surface This is due to the The use of processes of smoothing is not new and has been used fact that the surface curvature can cause the tool to make contact in different fields [25]. These algorithms have a dual purpose On with another upper z coordinate Fig. 8 right J.L. Huertas-Talon et al. Computer-Aided Design 50 (2014)41-50 Cell side tool radius Fig. 9. Zone classification by means of a grid y≥mx+b P3 P3 Fig. 10. Situation of a point with regard to a triangle The projection on the stl surface can be made once the triangle To obtain the projection of a point onto a particular triangle, containing the coordinates(x, y) is known. In order to locate the best results are obtained using the normal plane equation, as the triangle where the tool is situated classification is carried out by plane director vector containing the triangle is known zones, Fig 9, to speed up the result of the algorithm as, once the point(x, y) is assigned to a zone, it is only necessary to work x cos c t y cos p+ 2 CoSy=q with the triangles of that zone and find the triangle containing the where, Fig. 11, a, B and y are the angles of the director vector of projection of the point(x, y) the plane of each coordinate axis and the distance of the origin According to the directions of the axes x and y, the number of of the coordinates of the plane. The director cosines are data of the grids is StL file maximum- minimum The value of parameter g is obtained by substituting the nx×= roundnessupper radius coordinates of a vertex, for example, the first(according to the too matrix used maximum- minimum roundness q= xy cos a+yo cos B t zu cos y radius To locate the zone where the tool point(x, y) is situated we apply The coordinate z of the projection point can now be obtained zone x whole part x- minimum o cos a+yu Cos B+ Zu cos y-xs cos a- ys cos B radluStool (6b) COSy zone= whole part/y-minimum radius It can be seen that, when the plane is vertical, Cos y=0, there no projectin Within the zone a search is made to find the triangle that contains the tool tip a triangle consists of three points(vertices)which, wher 2.5. Calculation of the final tool-path x, y, z using non-deterministic grouped into two, form three straights (sides Each side of the techniques triangle is viewed to see whether the point we want to check and the opposite vertex are on the same half-plane, this means sharing To calculate the 3D tool-path, the 2D path of Fig. 5 is projected the same sign when we substitute the coordinates of the points in onto the surface, Fig. 13, but, taking into account the three the normal line equation conditioners, Fig. 14 half_plane sign axQ+byo +c (a close to the contour of the surface position z lower than the tool, is the point where it is tangential to the surface(point of intersection with the surface): sign(axo + byo +c) (b) the initial position z of each pair of x, y coordinates is the upper Fig. 10 Shows that both points p and Q comply with this condition part of the billet block for the first side(Plp2)but, on checking the following side(P1P3). (c)the final position z of each pair of x, y coordinates is that which P is outside the triangle holds the tool in tangential contact with the surface J.L. Huertas-Talon et al. Computer-Aided Design 50(2014) 41-50 RA(. 10.z0) y Fig. 11. Angle of the director vector of the plane that contains an Stl triangle with coordinate axis T& oP Fig. 15. Successive approaches. (a) Tool descends making contact with the surface Fig. 12. Coordinates of tool tip centre s. tangent point t and returns to the previous step (b)The tool descends again but with smaller step sizes. This process continues until the increase is less than the required value. Th tool always remains in the previous position tool returns to the previous step and the process is repeated with a reduction in the step size This process ceases(Fig. 15) when the step size is less than a predetermined value of tolerance and the final value of the vertical position is the third coordinate Fig. 16 shows the flowchart of the method applied in Fig. 15 This method always starts from the same coordinate z, so it is not necessary to use the eq (10). However it is also possible to start from the position given by Eq. (10) and raise the position following the same routine until the intersection with the triangles disappears, descending again with a smaller increment The variation of the membership function for the descending stage (b) of Fig. 16 can be observed in the following figure Fig. 13. XY route for projection on the stl surface (Fig. 17). The tolerance of this function decreases when there is a collision with any triangle in the influence area of the tool tip. The number of tolerance variations is not very high: three changes previous projection is not carried out using any mathemat are typically enough, e. g. 1,0. 1, and 0.01 mm. If the acceptable cal calculation. Only the condition"the tool touches the surface"is tolerance increases these values could change slightly, e.g. 1, 0.1 used, and which is analysed following the application of a tool de- and 0.02 mm, i. e 0.01 mm more than in the previous case. In the scent function from position (b) in Fig. 14 first case the maximum theoretical distance between the nomina The descent can be carried out in several ways [14, but in and the milling surfaces is 0.01 mm vs the 0.02 mm of the second this case a lineal function with a maximum of ten steps has been case, in which the required time decreases(obviously, mechanical chosen. Once contact is made between the tool and the surface, the tolerances should also be considered). C Fig. 14. Limit posilions of the Lool on the OZ axis J.L. Huertas-Talon et al. Computer-Aided Design 50 (2014)41-50 i=i+1 Fig. 19. Case A Touch triangle? YES YES △z=△z Fig. 16. Flowchart of the tool descending stage(b, where t"is the tolerance, which can be up(b), centred(c)or down(d). Fig. 20. Case B Membership function for the first 4z Last membership Az. Fig 21. Case c Fig. 17. Evolution of several membership functions with the tolerance the surface occurs That is in this situation the distance from the vertex to the sphere centre is less than the tool tip radius. This distance is checked for each of the j vertices(i=0, 1, 2)of each triangle-i-under study in the tool tip influence zone (see fig 9). If the distance then (Xc-X)2+(yc-y)2 the tool tip position must be corrected Study case B, Fig. 20: if the projection of the sphere centre on the lane(less perpendicular distance) is within of the triangle, an intersection occurs. Should this point fall outside the triangle there may be an intersection, as in cases a and C. In fact, the only real case could be b under certain conditions Study case C, Fig. 21: if any of the sides of the triangle cross the sphere and its points of intersection, M and N, are contained on this side. It should then be checked to see if these two points are between the vertices of the side. If only one point is inside, we are faced with case a Fig 18. Relative positions of the tool tip sphere and the triangles that compose the 3. Results: comparison with three commercial cam packages TL surface So et al. [28 compared their method with commercial To correct the tool position given in (10) several cases of CAD-CAM software in order to check the results of the proposed tool interference with the surface [1 1] have been studied Fig. 18 algorithm. In a similar way, three experts on different commercial shows the case that can happen. As mentioned before, this can CAM packages were contacted to apply the spiral tool-path using be solved either in a deterministic way [11 or by correcting the their software so it was possible to compare their results with displacement of the tool by means of successive approaches within those obtained in this study under the same machining conditions a certain tolerance (roughness, feed rate and speed) Study case A, Fig. 19: if any one of the three triangle vertices is To avoid influencing the results, we did not participate in the contained within the sphere an intersection of the tool tip with process of obtaining the nc program with the commercial Cam J.L. Huertas-talon et al / Computer-Aided Design 50(2014)41-50 Table 1 Empty cells are filled to apply the addition 1 1) correctly 46.796 5074 57.870 -46.796 5.074 57.995 ZZz 304 XXxX 57995 58.120 5497 58.120 YyYY 46.796 46.796 ZZZZ 5.304 5.497 59815 47546 5598 59815 -47.546 5.598 Fig 22. Machining with"WinUnisoft "simulator for the two crest heights (Left: roughing with 10 mm tool tip. Right: finishing with 3 mm tool tip and 0.02 mm cre height y Table 2 Comparison of tool-path lengths and numbers of points. Tool-path length(mm Number of points CAM A 45675 43088 CAM B 37797 34567 CAM C 68728 148005 New algorithm 31524 36412 packages. Thus, this task was performed by a technical expert on each CAM package, so their results could be considered optimal The conditions and materials given to each expert were exactly the same as listed below (a) stl file with the geometry to be machined. This file was exactly the same that was used to test our method as shown in this paper (b)maximum roughness: 20 um (c the followed tool- path is the same from the inside to the outside and vice versa: (a) each expert had to obtain the nc program of just one complete Fig 23. Roughing process( tool tip diameter= 10 mm) and machined piece(cycle path with a spherical tool tip with diameter=3 mm saddle before finishing(tool diameter= 3 mm) (e) the machining conditions (advance and cut-speed )were also defined by us in order to be the same as we used, although they obtained using each commercial CAM package and, in the last are not really relevant in this stud f)lineal interpolation was the only one to be used, so the list of arrow, using our method coordinates(x, y, z) was preceded by go1 As the distance between points is very small, the applied addition( 11) gives a good approximation to the tool-path length The compared parameters are the tool-path length and the and the machining time can be obtained dividing the total length cxact number of interpolation points. The followed method is by the advance speed For that reason, the shorter tool-path will be explained below. Other studies [29]use roughness as a parameter described in less time to compare results, but we considered that the tool-path length The number of points influences the time needed by the no clearly indicated the required machining time and the number of machine to read all the information. If this number is too high in a interpolation points is related to the processing time of the nc[ 26]. tool-path, the buffer of the look-ahead function will be full and the The tool-path length has been obtained using the following lower numberof will be lower [26]. This is why tool-paths with Eq (11), taking all the coordinates from an Excel spreadsheet. As said before the followed method by each commercial CAI package and the routine presented in this paper has not been =∑(x-x-12+0y-y-1)2+(z-z-1)2) (11) compared, because commercial CAM packages are oriented to general purposes. This means that the steps that must be followed The interpolation points in which a coordinate has been omitted to achieve the same result, will be very similar to this algorithm because it was equal to the previous one have been completed, so steps; but in this case, those steps have been automated for the the previous summation(11)could be correctly applied, as shown type of surfaces used in this paper. This is why it is only needed in table 1 to load the stl file. In the case of commercial CAm software Table 2 has been obtained applying the previous addition. This the developer can provide the customized macro, if required, to table compares the tool-path lengths and the number of points perform the same operation in just one step J.L. Huertas-Talon et al. Computer-Aided Design 50(2014 41-50 The spherical cavities were used to position the horizontal plane of reference and to orientate the coordinate axes as shown in Fig. 25. A longitudinal nominal profile is represented in Fig. 26, which also includes its measured profile, obtained by a linear interpolation of the measurement spiral points. The deviation in the measured points has always been smaller than the chosen tolerance value of 0.05 mm As shown in Table 2, the presented algorithm generates tool paths with a length that makes possible to improve the machining time compared with commercial CAM packages Finally, the surface roughness was measured using confocal microscopy, obtaining the results shown in Fig. 27. These results displayed a maximum roughness below the programmed value, 20 um in this case, in both the wide and the narrow areas of the pIece Fig. 24. Verifying the piece with a coordinate-measuring machine. Acknowledgements 4. Conclusions The present work corresponds to a part of the innovation With the algorithms presented it is possible to mill STl surfaces, project titled" Knowledge as a development engine in mechanical Figs. 22 and 23, providing that they comply with certain conditions manufacturing", financed by the education ministry of Spain and thereby obtaining regular profiles and with a quality of finish very the european social fund close to that required Surface measurements (Fig. 27) have been performed al The dimensional results(Fig. 24)are within the programmed the surfaces and Coatings Characterization service at CEQMA margin of error for this piece(0.05 mm), providing enough quality (CSIC-Universidad de zaragoza Our thanks go to fellows of the Integrated College of Technical for manufacturing different custom-made objects, such as the cycle Training"Corona de aragon " from Zaragoza (Spain), francisco saddle shown in this example or different types of ergonomic Valdivia Calvo and Juan Jose garde barace, for their assistance in components, among other applications the preparation of parts and field work The measurement path was obtained from the points used in We are grateful to the english teacher richard ]. Stephenson, for the milling process of the workpiece, but increasing their separa the english correction tion, i.e., decreasing the number of points( Fig. 25). The points were This paper could not be the same without the help of three collected in a spreadsheet and, after that, exported to cad to com- anonymous experts of leader CAM companies. Thank you very pare them with the nominal surface. In order to evaluate the re- much for making possible the comparison for the third part of this sults, the surface was cut into longitudinal and transversal sections. paper. Blue: Measured curve Grey: Projected cu Fig. 25. Measurenent prucess Measured point Nominal profile Fig. 26. Longiludinal section Lhal shows the Measured profile vs the nominal J.L. Huertas-Talon et al / Computer-Aided Design 50(2014) 41-50 Fig. 27. Images of the piece surface obtained with confocal microscopy (Left narrow area. Right: wide area References [15 Azaouzi M, Lebaal N Tool path optimization for single point incremental sheet forming using response surface method Simul. Modell. Pract. Theory 2012: 24 I1 Chen T, Ye PQ. A tool path generation strategy for sculptured surfaces 116| Sun Y-W. Guo D-M Jia Z-Y Spiral cutting operation strategy for machining of sculptured surfaces by conformal map approach. Mater Process Technol [2]Chen T, Shi Z A tool path generation strategy for three-axis ball-end milling of 2006;180:74-82. free-form surfaces. J Mater Process Technol 2008: 208: 259-63 [17 Popov K, Petkov P Layer based micro-machining -new approach for tool-path [3 Hsieh H-T, Chu C-H Improving optimization of tool path planning in 5-axis generation CIRP J Manuf Sci Technol 2011: 4: 370-5 flank milling using advanced PSO algorithms. Robot Comput-Integr Manuf[18 Dweiri F, Al-Jarrah M, Al-Wedyan H Fuzzy surface roughness modeling of CNc 2013;29:3-11. down milling of Alumic-79. Mater Process Technol 2003; 133: 266-75 [4] Quinsat Y, Sabourin L Optimal selection of machining direction for three-axis [ 19] Lo S-P. An adaptive-network based fuzzy inference system for prediction of milling of sculptured parts. Int J Adv Manuf Technol 2007: 33: 684-92 workpiece surface roughness in end milling. J Mater Process Technol 2003 5 Held M, Spielberger C A smooth spiral tool path for high speed machining of 42:665-75 2D pockets. Comput-Aided Des 2009: 41: 539-50 [20Ip RWL, Lau HCW, Chan FTS. An economical sculptured surface machining [6 Hu Shen H, Zeng S, Wang Y B-spline tool offset of a free-form curve in the approach using fuzzy models and ball-nosed cutters. Mater Process technol shoe last high-speed machining CNC system. IntJ Adv Manuf Technol 2006 2000;138:579-85 [21 Iqbal A, He N, Li L, Dar NU. A fuzzy expert system for optimizing parameters 0:864-9 [7]Lee RT, Cheng WS. A multizone scaling method for CAd in shoe sole design. Int and predicting performance measures in hard-milling process. Expert Syst Appl.2007;32:1020-7 Adv Manuf technol 2002: 19: 313-7 [8 Vijayaraghavan A, Sodemann A, Hoover A, Mayor JR, Dornfeld D. Trajectory 22] Hoa W-H, Tsai J-T, Lin B-T, Chou J-H Adaptive network-based fuzzy inference rstem for prediction of surface roughness in end milling process using hybrid generation in high-speed high-precision micromilling using subdivision Taguchi-genetic learning algorithm. Expert Syst. Appl curves. Int J Mach Tools Manuf 2010; 50: 394-403 [23 Petzolda R, Zeilhoferb H-F, Kalendera WA Rapid prototyping technology in 9] Banerjee A, Feng H-Y, Bordatchev EV Process planning for Floor machining of medicine-basics and applications. Comput. Med Imaging Graph. 1999; 23 2 1/2D pockels based on d morphed spiral loul path pattern. CoInpuL Ind. Eng 277-84 2012:63:971_9 124 Choi Y-K, Banerjee A Tool path generation and tolerance analysis for free-form 10 Boujelbene M, Moisan A, Tounsi N, Brenier B Productivity enhancement in dies Irfaces. Int J Mach Tools Manuf 2007: 47: 689-96 and molds manufacturing by the use of C(1)continuous tool path. Int J Mach [25 MCMaster RB. The integration of simplification and smoothing algorithms in Tools manuf 2004: 44: 101-7 line generalization Cartographica 1989: 26: 101-21 [11 Kayal P. Offset error analysis of ball-end mill for cutter-path generation from [26 Huertas Talon J L, Gella Marin, Garcia- Hernandez C, et al. Generation of point-based surfaces. Int Adv Manuf Technol 2008: 36: 1133-44 mechanizing trajectories with a minimum number of points. Int J Adv manuf [12 Chen ZC, Fu Q A practical approach to generating steepest ascent tool-paths Technol2013;69(1-4):361-74 for three-axis finish milling of compound NUrbS surfaces. Comput-Aided Des [27] Vijayaraghavan A, Hoover AM, Hartnett J, Dornfeld DA. Improving endmilling urface finish by workpiece rotation and adaptive toolpath spacing. Int J Mach 007:39:964-74. Tools manuf 2009: 49: 89-98 [13 Szilvasi-Nagy M, Matyasi G Analysis of STL files. Math. Comput. Modelling 128] So BS, Jung YH, Kurfess TR, Hwang SM 5-Axis machining speed enhancement 2003:38:945-60 14 Lu B, Chen J, Ou H, Cao J. Feature-based tool path generation approach Ro, by step length optimization. J Mater Process Technol 2007: 187-188: 2-5 [29 Quinsat Y, Sabourin L, Lartigue C Surface topography in ball end millin for incremental sheet forming process. I Mater Process Technol 2013; 213 process ription of a 3D surface roughness parameter J Mater Proder 1221-33 Technol2008:195:135-43

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