Automatic 3D Spiral Toolpath generation for SPIF.p

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详细说明：三维空间上单点渐进成形轨迹的开发自动生成策略描述。Top contour Lofted surface surace Fig. 2 Points generated on the contour toolpath Bottom Cotour Fig. 2), so that the 3D spiral toolpath(Fig. 3) can be subsequently generated by linear interpolation between consecutive contours Fig 4 Schematic of volumetric error calculation Sec.2.2) 2.2 Generation of 3D Spiral Toolpath. A methodology simi- lar to that used by Lee [14] was used in this work to generate 3D Surtace model between the two contours, closing the top and bot- spiral loolpaths fron contour loolpaths. A 3D helix is generaled tom surfaces. and then calculating the volume of the solid thus between two successive contours by interpolating linearly be- tween corresponding points(Eq.(1)on the two contours. The The shaded region in fiy. 4 is the difterence between the lofted same operation is performed for all pairs of consecutive contours and actual solids between two successive contours. Volumetr to generate a continuous 3D spiral toolpath for the entire compo- error(vol_error) is calculated as nent, abs(part volume - lofted volume) voi error ×100(2 =S1+(-S)p (1) part_ volume here Figure 5 shows a profile view of the actual semicircular tool profile curves for a 3D spiral toolpath. The profile of the tool is generated at a number of points on each piecewise generated 3D P+1-p spiral path, and the intersection between consecutive tool profile curves in the z direction is obtained. as shown in Fig. 5. the distance between this intersection point and the shortest normal D+1-P projection of this point onto the CAD surface is the scallop height at that here pr is the lth point on the ith slice, pi is the /th point on the 2.3.2 Insertion of Slices. The insertion of slices is carried out (i-1)th slice, and N is the number of points on each contour slice. based on two measures, namely, volumetric error and scallop The 3D spiral toolpath is generated until this step assumes that height. Values of maximum tolerable volumetric error (vol_error the region of the component between two consecutive slices is a_max), maximum tolerable scallop height(scallop_max),and uled surface. It is quite possible that this is not true, especially minimum incremental depth allowed (z- min) are required when the toolpath is generated with a certain constant Az for a puts. The value of z_min incorporates constraints on the reso freeform component. In such cases, the 3D spiral toolpath may lie lution in the z direction for the CNC heing used. A contour is outside the envelope of the actual component. Sec. 2.3 will ad- inserted at half the z distance between two existing co dress how the newly developed methodology avoids this problen. if either one of the following two conditions are met is if the 2.3 Adaptive slicing procedure volumetric error between two contours is found to be greater than vol_error_max. The other is if the scallop height at any point is 2.3.1 Calculation of Volumetric Error and Scallop Heights. found to be greater than scallop_max. However, if such a prospec Volumetric error (vol error) is calculated between two consecu- tive insertion of a contour causes the slice thickness between any Live contour paths(Sec. 2.1)according to Ey.(2). The lofted_vol- two consecutive contours to be reduced to below z_min, then the ume term is the volume of the solid obtained by lofting the bottom insertion does not occur In the case that a confict arises between contour onto the top contour and closing the top and bottom faces. the criteria for insertion and noninsertion of a slice, priority can be The part_ volume term is obtained by extracting the region of the explicitly given to the volumetric and scallop height criteria or to the z_min criterion depending on the importance of each in the final desired function of the component. If slice insertion, the adaptive slicing criteria are re-evaluated to see if further slice Tool、 profile profile Scallop height calculated Fig3 3D spiral toolpath generated from contour toolpath Fig 5 Schematic of scallop heights calculation Journal of Manufacturing Science and Engineering DECEMBER2010,Vo.132/0610033 xer Input CAD ITMlel, alop max, vol error_ maky/ ate Datin, initial slices with AFz max To Top contour Top contour 7m.mn翼 Paint on 3D Inserted Points on contour 3D spiral 3D spiral toolpath Ifi≤M Bottom b (c) Evaluatevol error and scallop height between slices i and (i+1 Fig. 8 Schematic illustrating adaptive slicing for 3D spiral toolpath generation vol errorvol emor max OR Scallophts >scallop max (Figs. 8(b) and &(c) the points on the 3D spiral toolpath move closer to the intended geometry. This effect becomes even more important when the component is large and consists of one or more asymmetric and symmetric surfaces. Insert slice at half the z distance between slices and(i+ 1h update N, To understand why trapezoidal build edges are used for volu- update the array containing the slice metric error determination instead of rectangular build edges. a heights part consisting only of planar faces, as shown in Fig 9, is consid ered. The difference between trapezoidal and rectangular build edges [14] is illustrated in Fig. 10. As stated earlier, from the geometric accuracy point of view, slice insertion is not required ig. 6 Flowchart showing slice insertion methodology used In such cases, using rectangular build edges will result in nonzero volumetric error between two consecutive slices which may exceed vol_error_max, leading to unwanted slice in- insertion is required. Insertion of slices between any two slices is Sertion. The use of trapezoidal build edges ensures that the volu carried out until the volumetric error between the two slices be metric error between two slices in such cases is always zero comes lesser than vol_error_ max and the scallop height is lesser thereby avoiding unwanted slice insertion or deletion than scallop_max. A flowchart of this process is shown in Fig. 6 The scallop height calculation used in this work(Sec. 2.3. 1)is Geometric error is calculated on a global basis between the two a conservative estimate of the scallop height in a local region of consecutive contours by using volumetric error measure presented the component. It does not account for stretching of material be- as chordal deviation would require discretization of each of the scallop heights of the component actually formed to a value bele n Sec. 2.3. 1. Using a local measure of geometric deviation such tween two successive helixes during forming, which may reduc contours into smaller corresponding intervals along which the the calculated value. Therefore, the scallop height calculated is the maximum possible scallop height in that local region of the com- tionally very expensive, especially for larger components. The ponent for a particular combination of incremental depth and tool volumetric error criterion ensures that the geodesic on the surface size. Using this kind of a conservative scallop height criterion of the component between any point on the top slice and the ensures that the maximum possible scallop heights in any region closest corresponding point on the bolon slice is as close lo a of the component are below the maximum specified scallop height straight line as required to achieve a specified level of geometric (scallop_ max) accuracy. For example, contour toolpaths generated without adap- 2.3.3 Deletion of Slices. The extra slices are removed, which tive slicing with a constant Az of 2 mm are shown in Fig. 7(6). will not adversely affect the accuracy of the forned componenL. If Some features of the component that are omitted are highlighted. the volumetric error percentage between slice n and slice(n+1)is These features are not omitted when the same component is adap- found to be lesser than a predefined value (vol_error min)and the tively sliced, as shown in Fig. 7(c) difference in z-height belween slice n and slice (n+2) is noL As stated in Sec. 2.2, for some components, the 3D spiral tool greater than the predefined value (z max), then slice (n+1)is path may lie outside the envelope of the component's geometry deleted. The value of vol error min allows a lower limit on the when a constant incremental depth is used. Even though a very volumetric error and may or may not be used depending on the small 4z may make the 3D) spiral toolpath accurate enough, it application ould also increase forming time in most cases unnecessarily Adaptive slicing is indispensable for ensuring that the 3D spiral 2.4 Generation of Tool Size Compensated Toolpaths. The toolpath lies on the surface of the component to be formed with- 3D spiral path shown in Fig 3 consists of the points at which the out increasing forming time unnecessarily In Fig. 8(a), the 3D hemispherical ended forming tool should make contact with the spiral point is generated between two corresponding points on the sheet. In Fig. ll, Ice is the center of the hemispherical part of the top and bottom contours when no adaptive slicing is done tool, Ten is the point on the tool at which the tool should contact As the number of contours increases due to adaptive slicing the sheet (obtained from the 3D spiral toolpath calculated in Sec Fig. 7 (a) Part to be formed, (b) contour path generated without adaptive slicing and(c)contour path generated with adaptive slicing 0610034/Vo.132, DECEMBER2010 Transactions of the asme Wall angle(e) Fig 12 (a) CAD model of the pyramid formed to examine the surface finish and(b) schematic of the incremental forming p used Fig 9 Component consisting of planar surfaces Step 5: If a new contour is inserted, then repeat steps 2-4 for the newly inserted contour and the corresponding top contour Otherwise, move onto the next pair of contours and perform 2.2), n is the unit vector normal to the surface of the component at steps 1-4 again until all the contours are processed Tcp, and Ttip is the tip of the hemispherical end of the forming Step 6: Perform slice deletion(Sec. 2.3.3)to get the final set of contour slices tool. Assuming that a three-axis milling machine is being used for forming the component and R is the radius of the forming tool Step 7 Generate the final 3D) spiral toolpath(Sec. 2.2) from the contour slices in step 6 toolpath compensation is applied according to Eqs. (3)and (4). In Step 8: Perform tool size compensation(Sec. 2. 4)to generate case a hive-axis machine is being used, compensation has to be toolpaths for a three-axis CNC applied differently as the tool can have additional rotational de grees of freedom and can be oriented along the normal to the 3 Experiments urfa All the experiments were performed using AA5052 blank ma Tce=ten+ rn (3) terial. Tool feed was 250 mm/min: tool rotation was absent and high pressure lubricant was used between the blank and the tool tip=Ice-Rk (4) The capability of the developed methodology to achieve the scal lop heights below the specified value and to achieve good geo 2.5 Summary of Toolpath Generation Procedure. The metric accuracy were evaluated by forming square pyramids and overall algorithm for 3D spiral toolpath generation combines the freeform components using 3D spiral toolpaths. The square pyra procedures described in above sections and the sequence in which mids were chosen to test the capability for forming components they are used is presented below (details can be seen in Ref. [17J). with scallop heights less than scallop_max since scallop heights Step 1: Generate contour toolpaths(Sec. 2. 1)with a constant are easier to measure on flat surfaces. Since pyramids have the incremental depth z_max same slope throughout, constant scallop heights are generated by Step 2: Generate 3D spiral toolpaths from the contours(Sec. uSing the adaptive slicing criterion. Three pyramids with wall angles of 20 deg, 40 deg, and 60 deg(Fig. 12)were formed using Step 3: Calculate volumetric errors and scallop heights (Sec three tools of 4 mm. 6 mm. and 8 mm diameter for two values of 2.3.1) maximum permissible scallop heights(scallop_max) of 10 um Step 4: Use the adaptive slicing criterion(Sec. 2.3. 2) to evalu and 50 um. The scallop heights were measured using a white ate if a new contour needs to be inserted light interferometer(MicroXAM Surface mapping microscope, resolution 10 nm in the z direction) and each experiment was repeated twice. The CAD model of the pyramid component and the schematic of the setup used are shown on Figs. 12(a)and 12(b), respectively. The list of experiments for forming the pyra- mids is shown in table 1 The freeform component shown in Fig. 13 has a depth of 15 mm and the Cad model was made in solidworks by lofting Trapezoidal build Rectangular a circle onto a rectangle along a spline guide curve. The guide curve was drawn freehand so that along the guide curve the com- build edges ponent has a truly freeform shape. Therefore, the results obtained by forming this shape can be regarded as applicable to symmetric Fig 10 Schematic showing the difference between trapezoidal and asymmetric shapes. This component was formed using a 3D and rectangular built edges spiral toolpath generated by the toolpath generation methodology developed during the present work, with zmax=1.0 mm Z Tool centre vol error max=1.0%, vol error min=0.50%, scallop max =0.5 mm, and z min=0.001 mm. The same component was also formed using the 3D spiral toolpath generaled by the milling mod- ule in a commercial CAM package with constant Az values of 0.5 Tool tip (Ttp) 0.375 (i.e.,30,40,and50si Tool contact point T tively). All the freeform components were formed using a 9.5 mm Current sheet hemispherical ended tool. The geometry of the formed compo- Configuration nents was measured using a Brown and Sharpe Microval coordi nate measuring machine (CMM). To the best of our knowledge, Final sheet Configuration no module of any commercial CAm package is able to take input in terms of required geometric accuracy or scallop heights to gener ate a 3D spiral toolpath for the component shown in Fig. 13 Fig 11 Schematic of tool radius compensation Various machining modules of commercial CAM packages were Journal of Manufacturing Science and Engineering DECEMBER2010,Vo.132/061003-5 Table 1 List of experiments performed for testing scallop heights criterion Scallop height Standard Wall angle Tool dia Scallop_max from code deviation (o xp. NO (mm) (m) (experiments) 20 50 2 40 1234567890123 2 888444666888444666 11153 21 0.76 0.54 0.37 00000000000 0.93 0.90 20 40 2226663 1.24 0.47 0.56 0.61 0.33 14 40 10 0.54 15 8.3 0.74 16 10 0.99 0.16 10 0.78 tried out with the scallop height requirement as an input but the scallop height of 50 um. In this case, the actual scallop heights CAM module always failed to generate a 3D spiral toolpath for the are qualitatively similar to the calculated scallop heights but quan Fig 13 titatively there is derable diffe The effect of the tool size becomes more apparent by compar 4 Results and discussion ing the scallop heights for the three pyramids with different wall angles formed using three different tool sizes(figs. 16 and 17). In This section shows experimental results which confirm that the Figs. 16(a)and 16(b)(4 mm and 6 mm tool diameters, respec- methodology developed in this work is capable of generating 3D spiral toolpaths for SPIF such that the scallop heights of the tively), it can be seen that for all three pyramids formed with a formed components are below scallop-max. Moreover, the profile scallo of the component is as close or closer to the required geometry as Ote rofile scallop_max of 10 um, the actual scallop heights and the scallop heights calculated from the code are qualitatively and quantita- compared with the formed profile generated by commercial CAM tively in good agreement packages without unnecessarily increasing the forming time. Sec However, Fig. 16(c) shows that under the same conditions us tion 4. I deals with the scallop heights criterion and Sec. 4.2 deals ing a larger tool( 8 mm diameter) results in considerable quanti with the geometric accuracy and forming time tative difference between the formed and the calculated scallop heights. Figure 17 shows that when scallop max is 50 um, no 4.1 Scallop Heights Criterion. The scallop heights criterion, matter which size of tool was used for all three pyramids, there is Is described in Sec. 2, was tested by forming pyramids having considerable qualilative and quantitative deviation belween three different wall angles with three different tools and two dif- formed and calculated scallop heights. Figures 14-17 indicate that Terenl maximun allowable scallop height(scallop_max)values. the toolpath generation methodology developed during the present Figure 14 shows the comparison between the measured scallop work can be used effectively to limit the scallop heights of the heights. the scallop heights calculated from the developed code formed component to lower than the maximum scallop height and the maximum allowable scallop heights(10 um here)for all (scallop_max)specified as input. three pyramids However, since the forming tool has surface contact, it also It can be seen that the maximum deviation between the mea- stretches the material between consecutive helixes (as mentioned sured and calculated values is for the 8 mm diameter tool. Al- earlier in Sec. 2.3.2). As a result, the scallop height between con- though there is a quantitative difference at other two tool diam- secutive helixes reduces as well. Effect of stretching between con- ters,the values at those diameters are qualitatively and secutive helixes in a 3D spiral toolpath is going to increase with quantitatively more closely in agreement with the values calcu- tool diameter as larger tools have greater contact area as compared lated from the developed methodology presented in this paper. with smaller tools. This agrees with the experimental results in Figure 15 shows a similar comparison for a maximum allowable Figs. 15 and 16i.e, using the 8 mm tool results in greater discrep (b) Fig. 13(a) Isometric view and (b) side view of freeform component formed to examine the geo metric accuracy and forming time 0610036/Vo.132, DECEMBER2010 Transactions of the asme 2 兰 -----. ↓= Ea- 5 7 Tool Diameter(mm Tool Diameter mm (b) 10 scallop heights 兰 6 k scallop hieghts c alculated from 十+- c ode Enom measured scallop heights 78 9 Tool Diameter(mm) Fig. 14 Comparison between scallop heights, measured, calculated from code, and maximum specified (10 um) for (a)20 deg pyramid,(b )40 deg pyramid, and (c)60 deg pyramid, each formed with three different tool sizes ancy between the desired and the actual scallop heights than using corresponding scallop heights calculated from the developed the 4 mm and 6 mm tools. This stretching effect may also be methodology are higher as well. The stretching effect does not responsible for the scallop heights being much lesser than the allow the formed scallop heights to rise close enough to the higher calculated scallop heights when a scallop_max of 50 um is speci- calculated scallop heights for any of the tools sizes used in this fied(Figs. 15 and 17). When the scallop_ max value is higher, the work. Since the methodology developed in this work calculates 50 } 20 10 4567 6 89 Tool D a neter(mm) Tool Dameter(mm (b) MaXimum scallop heights Dec ified E40 上 scallop hieghts calculated fr code -e.measured scallop heights 3 Tool Diameler(mmk c Fig. 15 Comparison between scallop heights, measured, calculated from code, and maximum specified (50 um) for(a)20 deg pyramid,(b)40 deg pyramid, and (c)60 deg pyramid, each formed with three different tool sizes Journal of Manufacturing Science and Engineering DECEMBER2010,Vo.132/0610037 12 10 8 6 59E兰录 4 2 0 1020 405060 Wa le(degree wallAngle(degrees) maximum scallop heights 5oE· 8 A scallop hieghts calculated from code easured scallop heights 70 Wal Angle【 degrees (c) Fig. 16 Comparison between scallop heights, measured, calculated from code, and maximum specified(10 um) for(a)4mm tool,(b)6 mm tool, and(c)8 mm tool for all three pyramidal components 50 20 10 0 3 10 20 Wall Angle(Deg rees) WalAngke(Degrees) (a) (b) maximum b scallop heights 毛 spec ified r scallop hieghts 一-- calculated from …==1= 4· measured scallop heights Wall Angle(Degrees Fig. 17 Comparison between scallop heights, measured, calculated from code, and maximum specified(50 um) for(a) 4mm tool,(b)6 mm tool, and (c)8 mm tool for all three pyramidal components 061003-8/Vo.132, DECEMBER2010 Transactions of the asme …-4 UG (30 slices constant) 6 -UG(50 slices consta) 了到 12 -14 Fig 20 Components formed using 3D spiral toolpaths gener ated by the developed methodology Fig. 18 Comparison of cross-sectional profiles between CAD component and components formed using developed method- ology(adaptive slicing) and commercial CAM software nent formed by using toolpath generated with the proposed meth odology is as close or closer to the desired Cad geometry as scallop heights without taking into account this stretching effect, compared with the proti le of the component formed using CAM module generated toolpaths. In addition, the forming time is there is a discrepancy between the actual and calculated scallop higher by a percentage of 15.6%, 43. 75%, and 106.25%o for the heights. However, the scallop heights of the actual component are components formed using Cam, as shown in the table 2. There esser than the maximum specified(scallop max) for all the pyra fore, the 3D spiral toolpath generated using the developed meth- mids formed, which in addition to being one of the goals of this odology is able to achieve better or similar geometrical accuracy ne in mo with lesser forming times than the 3D spiral toolpath generated by 4.2 Geometric Accuracy. To evaluate the developed toolpath commercial CAM package generation methodology in terms of geometric accuracy and form Furthermore, it can be seen in Fig. 19 that the base of the ing time, the freeform component shown in Fig. 13 was formed components formed using the 3D spiral toolpath generated by using the 3D spiral toolpath generated from the developed meth- CAM is not flat. However, the base of the component formed using odology. The same component was also formed using the 3D spi- the toolpath generated by the developed methodology is fat and ral toolpath generated by the CAM module with three constant conforming to the caD geometry. This indicates that there may incremental depths also be a problem with the tool compensation methodology used Figure 18 shows a comparison between the measured geom- in commercial CAM packages. It should be noted here that all the etries for these component and the four formed components are component geometries were measured without cutting them out shown in Fig. 19. Table 2 shows the forming times for the com- fron the unformed blank but unclamped ron the fixture the ponents formed by a 3D spiral toolpath generated using CAM with cutting operation induces an additional geometric inaccuracy al- constant incremental depths and for the component formed by a though an important consideration is outside the scope 3D spiral toolpath generated using the methodology developed in paper. The methodology described in this work was also used to this work. It can be seen in Fig. 18 that the profile of the compo- generate 3D spiral toolpaths for other freeform components, and some components formed using the same methodology are shown Fig. 20 5 Conclusions SPIf has attracted researchers due to its flexi bility and high formability. However, it has not been widely adopted hy the in dustry due to long process time and the lack of geometric accu racy. Here, an attempt has been made to resolve these issues from a toolpath generation point of view. Currently, 3D spiral toolpaths for SPif are generated based on commercial CAM nodules and are not capable of using specified constraints on both geometric ac curacy and maximum scallop heights as inputs to generate a 3D spiral toolpath that simultaneously minimizes the forming time The methodology developed in this work is dedicated to tool path generation for single point incremental forming and deals with tradeoffs that exist between geometric accuracy, surface fin- Fig. 19 Freeform components formed using toolpath from(a) ish, and forming time. The use of variable incremental depths CAM(30 slices),(b) CAM(40 slices ),(C)CAM(50 slices), and (a) based on the local geometry of the component and constraints on developed methodology geometric accuracy and surface finish naturally minimizes the forming time. Experiments conducted have shown that this meth Table 2 Comparison between forming times for the freeform odology can form components with better or similar geometric component formed using 3D spiral toolpath generated by CAM accuracy as compared with commercial CAM Loulpaths with much modules and by the methodology developed in this work lesser forming time. Experiments also show that by using a scal- lop height criterion that uses rigorous computation instead of em Forming time pirical formulae, the scallop heights of the formed components Method used ln can be constrained to be lower than the specified maximum per CAM 0.5 (constant) missible scallop height (scallop_max). In summary, the developed CAM 0.375(constant) methodology is able to automatically generate 3D spiral toolpaths CAM 0.3 (constant) 66 for forming asymmetric(freeform) and symmetric shapes with Developed code Variable 32 similar or better geometric profiles than the commercial CAM tool- paths and with scallop heights lesser than a user specified maxi- Journal of Manufacturing Science and Engineering DECEMBER2010,Vo.132/061003-9 mum limit while simultaneously minimizing the forming time Incremental Forming, "Proc. Inst. Mech. Eng, Part B, 218(11), pp. 1453 1459 6 Future Work [5]Hirt, G, Ames, J, Bambach, M, and Kopp, R. 2004. "Forming Strategies and Process Modelling for CNC Incremental Sheet Forming, "CIRP Ann., 53(1), Notice that the developed approach is purely based on part pp.203-206 eometry and a process mechanics based toolpath generation [G Kopac, J, and Kampus, Z, 2005, "Incremental Sheet Metal Forming on CNC Milling Machine-Tool, Mater. Process. Technol., 162-163, pp 622-628 methodology with the methodology developed in this work as a [7] Attanasio, A, Cerei, E, and Giardini, C, 2006, "Optimization of Tool Path foundation needs to be developed. SPif inherently does not give in Two Points Incremental Forming, J. Mater. Process. Technol., 177, pp very good geometrical accuracy and the geometric accuracy may 409-412 be further improved by using a supporting tool. Moreover, the [8]Bambach, M, Ames, J, Azaouzi, M, Campagne, L, Hirt, G, and Batoz, L 2005, Initial Experimental and Numerical Investigation Into a Class of New geometric inaccuracy that is induced in the part after it is cut out Stratcgics for Single Point Incremental Shcct Forming(SPIF), Procccdings of from the sheet needs to be investigated. To make the scallop the rapid prototyping and rapid tooling esa form 2005 Conference. pp height criterion more accurate, the mechanics of deformation be 671-674 Tween successive toolpath notions needs lo be Modeled so that [9 Skjoedt, M, Hancock, M. H, and Bay, N 2007, "Creating 3D Spiral Tool forming times can be potentially reduced even further Paths Tor Single Point Incremental Forming, "Key Eng. Mater. 344. pp. 583- [10 Verbert, J, Duflou, J.R., and Lauwers, B, 2007. "Feature Based Approach for Acknowledgment Increasing the Accuracy of the SPIf Process, "Key Eng. Mater, 344, Pp This work has been supported by Department of Science and [11] Hagen, E, and Jcswict, J, 2004, "Analysis of Surface Roughness for Parts Technology, New Delhi, India and National Science Foundation Formed by CNc Incremental Forming, Proc. Inst Mech. Eng, Part B, 21 19 Authors also thank Indo-US Science and Technology Forum. New Delhi, for supporting the exchange visits. The authors would like [12] Ham, M, Powers, B. Brown, C.A., Jeswiet. J, and Hamilton. K. 2009. o thank ankit Surti and Samarjit Singh for their help Roughness Evaluation of Single Point Incrementally Formed Surfaces Trans. NAMRI/SME, 37, pp. 411-4I8 [13] All wood, J M., Music, O, Raithathna, A, and Duncan, S.R., 2009."Closed References Feedback Control of product Pro Flexible Metal Forming cesses With Mobile Tools. "CIRP Ann, 58 (1), pp 287-290 [1] Jeswiet, J, Micari, F, Hirt, G, Bramley, A, Duflou, J, and Allwood, J, 2005, [14] Lee, E, 2003, Contour Offset Approach to Spiral Toolpath Generation With Asymmetric Incremental Sheet Forming, Adv Mater Res, 6-8, pp 35-58 Constant Scallop Height, "Comput.-Aided Des, 35, pp 511-518 [2] Filice, L. Fratini, L, and Micari, F, 2002, "Analysis of Material Formability [15] Pandey, P. M, Reddy, N. V, and Dhande, S. G, 2003, "Slicing Procedures in in Incremental Forming, "CIRP Ann, 51(1), pp. 199-202 Layered Manufacturing, " Rapid Prototyping J, 9(5), pp. 274-288 [3]kim,T.J.,andYang,D.Y.,2000,imprOvementofFormabilityfortheIncre-[16www.opencascade.drg mental Sheet Metal Forming Process, "Int J Mech. Sci., 42, pp. 1271-1286. [17] Malhotra, R, 2008, "Automatic Tool Path Generation for Single Point Incre [4 Young, D and Jcswict, J., 2004, "Wall Thickncss Variations in Singlc-Point mental Forming, MS thesis, Indian Institutc of Tcchnology Kanpur, India 061003-10/vo.132, DECEMBER2010 Transactions of the asme

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