ARTICLES

ORIGINAL ARTICLE

Detecting re-design area for increasing manufacturability of drilling and three-axis pocketing operations

Hesam Samarghandy & Ye Li

Received: 12 October 2012 /Accepted: 19 April 2013 /Published online: 10 May 2013 # Springer-Verlag London 2013

Abstract The intensive competition has forced the manufacturing industry to improve product quality and pro- duction efficiency, and meanwhile reduce production cost. Detecting potential manufacturability problems in early de- sign stages would prevent unnecessary cost involved in re- work and/or re-design activities at later manufacturing stages. This paper presents an algorithm for determining re-design areas to feedback the designer when the design model involves machining holes and pockets using a three- axis computer numerical control machine. The algorithm takes into account the various sizes of tools and tool holders, and therefore allows a designer to test the manufacturability of their available cutters on their design models. A color- based obstacle-detecting method, based on layer-slicing of re-design areas, helps a designer to re-evaluate a design model for increasing manufacturability. Practical examples are provided as the output of the process.

Keywords Re-design . DFM (design for manufacturing) .

Visibility . Manufacturability . Obstacle feature

1 Introduction

Currently, there is an intensive competition among manu- facturers to obtain production processes with increased pro- ductivity, quality and reduced costs and time. This competition is significantly dependent on the effectiveness of product design. It has been reported that 70–80 % of

product costs are directly affected by product design [1–3]. On the other hand, it has been shown that almost 90 % of the designers do not have deep understanding of manufacturing processes [4]. Therefore, it will be necessary to make a good connection between designers and manufacturers. In order to close this gap, design for manufacturability (DFM) has been developed since 1970s [5]. By associating design with manufacturing, DFM is able to avoid design defects in manufacturing stages, and therefore leads to reduced cost and production time that may be incurred in the forms of defects and re-work. With DFM implemented, design models are continuously evaluated and revised from early design stages so that the design problems can be minimized prior to manufacturing. This has made DFM well received in both industry and academia.

In order to make design models manufacturable, one solu- tion is to define manufacturing features and then design by those predefined manufacturing features. However restricting designers with predefined manufacturing features tend to nar- row down the designers’ creativity and freedom [4, 6, 7]. For eliminating this restriction, feature recognition method for manufacturability analysis has been used [8]. Barari et al. [9] presented a platform through which the accuracy of sculptured surfaces on the final machined part could be predicted for the available machines. This would be helpful to designers in evaluating the choices for allocating tolerances. Mikola Lysenko et al. [10] conducted image-based machinability analysis based on the accessibility of surface by tool with the largest diameter. Visibility is also one of the most impor- tant factors to be considered in manufacturability analysis. Yang et al. [11] analyzed feasible tool approach directions for sculptured surface machining based on visibility map. Li and Frank [12] computed machinability for flat-end milling cutters with specific diameters based on the concept of configuration-space (C-space). Previous researchers also reported on the evaluation of manufacturing process costs

H. Samarghandy : Y. Li (*) Department of Industrial & Manufacturing Engineering & Technology, Bradley University, Peoria, IL 61625, USA e-mail: [email protected]

H. Samarghandy e-mail: [email protected]

Int J Adv Manuf Technol (2013) 69:337–349 DOI 10.1007/s00170-013-5023-9

for conceptual design [3, 13]. Sharma and Gao [14] developed a knowledge-based system for the evaluation of manufac- turability according to the criteria of time and cost along with parametric variation in design.

The manufacturability of a machine tool is directly relat- ed to the number of simultaneously controlled axes. Five- axis milling offers better accessibility than three-and four- axis machines. However, it requires a much more compli- cated CAD/CAM system which must be operated by an experienced person. Moreover, proper fixturing and colli- sion detection is a challenging task in five-axis milling machine set-up. It requires more design evaluation and process simulation than three-axis milling. On the contrary, a three-axis machine has been shown to be the most popular and economically affordable manufacturing equipment. Not only because it is a relatively easily programmable equip- ment, but also the investment in a three-axis machine is much lower than that in a four- or five-axis machine.

This paper intends to detect obstacle features and deter- mine the re-design areas that prevent the design models from being accomplished by three-axis machines. The focus of this paper is on drilling operations for making hole features and milling operations for machining pocket fea- tures. The re-design areas corresponding to these two fea- tures can be detected based on user’s input tooling parameters. Most hole and pocket features require the cut- ting tool to approach along a single direction in the machin- ing process. The hole and pocket features are considered in this research because some designs may have surfaces or features above them along the tool approaching direction; this will cause tool accessibility problem if not corrected. When this happens, more costly manufacturing machines such as five-axis machines will become necessary for mak- ing such kind of parts. By eliminating the overlapping areas, using a three-axis machine then become feasible, and con- sequently the machining cost is reduced.

In order to make a design model free of machining accessibility problems, a procedure is needed in early design stages for determining the surface accessibility. For milling processes, it can start with checking visibility which is an approximation of the actual accessibility, and then detect the re-design areas for increasing visibility and hence the ma- chinability. The detected re-design areas will guide the designer to change the target features or surfaces according- ly so that they can be properly machined. This paper presented an algorithm through which the minimum re- design area for increasing the visibility along the tool approaching direction can be detected for drilling and pocketing operations. The minimum re-design area is based on the selected cutter dimension and the tool holder dimen- sion. Detection of minimum re-design area can help de- signers to modify their designs for better manufacturability with reduced cost and time in early design stages.

This paper is organized as follows: Section 2 shows the algorithm for detecting the re-design area and determining the order of obstacle features’ priority over the target area. Each step of the algorithm is then explained in details in Section 3. Examples of drilling and pocketing operations are presented in Section 5, and Section 6 provides the conclusion.

2 Overview of the method

This paper presents a general algorithm to detect re-design areas and to obtain the boundaries on the obstacle features. With this algorithm, designers will be assisted in making changes for increasing visibility and consequently machin- ability. The objective is to make it possible to utilize a single set-up of three-axis milling machine for drilling and pocketing operations. Through this algorithm, the features layout according to their order over the machining area is attained as well.

Figure 1 shows the flowchart for analyzing re-design areas according to the dimensions of cutter and tool holder. It starts with the selection of machining area by the designer, followed by checking the local visibility over the area for the accessibility along the tool approaching direction. If the normal accessibility is available, then there is no need for further analysis; otherwise the algorithm will detect the re- design areas that block the normal accessibility through geometric operations of projection, extrusion and intersec- tion. After the re-design areas are determined, the sequence of obstacle features above the machining area is also iden- tified. This is accomplished by assigning a color to each feature and detecting the combinations of colors on 2D images through a slicing procedure.

3 Methodology

With Fig. 1 showing the flowchart of the proposed algo- rithm, this section will explain each step of flow chart in details.

3.1 Tool approaching direction

One unique feature in drilling and pocketing operations is the tool approaching direction. In drilling operations, the cutter needs to maintain aligned with the hole axis, while in pocketing operations the cutter is required to be perpendic- ular to the bottom of the pocket. In order for the cutter to have a full coverage over the machining features, tool approaching direction should be normally visible to the machining area. Otherwise, machines with more than three simultaneously controlled axes will be required; hence,

338 Int J Adv Manuf Technol (2013) 69:337–349

machining cost will increase. Therefore, the first step in the algorithm is to find the tool approaching direction and then detect the obstacle features above its boundary normally.

For drilling processes, the approaching direction is the axis of the hole feature. Figure 2 shows an example of finding tool approach direction in drilling. For pocketing processes, most of pocket features in CAD models have flat bottoms. This type of pocket feature is defined as flat- bottom pocket in this paper, and the tool approaching direc- tion is normal to the pocket bottom surface. The normal vector is usually normalized and denoted as N. Figure 3 gives an example of flat-bottom pocket. However some CAD models do have free-formed bottom surface, particu- larly for mold and die industry. Such kind of pocket is defined as free-formed bottom pocket. Figure 4 shows a pocket with curved bottom surface.

In order to find the tool approaching direction for free- form bottom pocket, local visibility is used in this paper. Visibility is a useful concept in different applications in manufacturing research. In design and manufacturing, visi- bility describes the accessibility of line of sight to an area. It can be used to evaluate the cutting tool direction and work- piece set-up planning in computer numerical control ma- chining [12, 15, 16]. Geometrically, visibility is usually represented as visibility cones [12, 17]. In this paper, we used visibility cone to determine the tool approaching di- rection for milling free-formed bottom pockets. A visibility cone for free-form bottom pocket is the collection of di- rections from which the tool can cut the pocket bottom without having collisions with pocket wall.

Since the scope of this paper is limited to the pocketing area of a CAD model, local visibility is computed only for the pocketing area; the surfaces and features other than the pocket feature on the CAD model are neglected. The input file used in this work is STL file of a CAD model. An STL file is composed of triangular facets, and each facet has its normal direction and hence its local visibility cone. The normal direction of each facet can be used to calculate the local visibility cone which is a hemisphere with the normal of the facet as the pole. Figure 5 shows the visibility cone of a facet on the surface of a sample CAD model. The local visibility cone is a complete hemisphere aligned with the normal direction of the facet. The same process can be used to compute the local visibility of each facet comprising the

Tool approach direction

Fig. 2 Tool approach direction in drilling process

Fig. 3 Tool approach direction of pocket with flat bottom

Select hole feature or pocket feature

Find the tool approaching direction

Construct bounding sphere and projection plane

Obtain tool movement boundary

Extrude to obtain tool and tool holder work spaces from projection plane

Check visibility

Obtain tool holder boundary

Insert the tool and tool holder parameters: heights and

diameters

Bottom-up slicing along tool approaching

direction

Obtain sequence of obstacle features over machining area

Obtain re-design areas by intersection

Fig. 1 Re-design algorithm

Int J Adv Manuf Technol (2013) 69:337–349 339

pocket feature. The intersection of all hemispheres will result in the overall local visibility cone which gives the feasible tool approaching direction set for machining the pocket. The overall local visibility may contain more than one possible approaching direction. In this case, the direc- tion parallel to the machine Z-axis is selected in order to avoid complex machine set-up or fixturing devices.

Figure 6 shows an example of determining tool approaching direction for a free-formed bottom pocket. The pocket surface is represented as an STL model. A local visibility hemisphere was created for each facet of the pock- et with different colors (Fig. 6a and b). The surface of a pocket feature can be divided into pocket wall and pocket bottom. The visibility hemispheres in these two areas were overlapped. For better clarification, Fig. 6c shows the overlapped visibility of those hemispheres in pocket wall area, and Fig. 6d shows the overlapped visibility of those hemispheres in pocket bottom area. Figure 6e shows the overall visibility of the pocket feature which has all visibil- ity hemisphere overlapped, including those on the pocket wall and those on pocket bottom. Overall visibility is the set of visible directions along which the cutting tool can ap- proach the pocket bottom. In this example, Z-axis exists in this set. So the best tool approaching direction is along the Z-axis of a three-axis machine. It should be noted that the accuracy of visibility analysis depends on the number of facets selected on the wall and bottom of the pocket. For more accurate result, tessellation granularity should be re- duced, which will render more facets on the pocket feature.

3.2 Bounding sphere

A bounding sphere is an imaginary sphere that can completely encompass an object. It is defined by its center and radius. In this paper, we use the Gravity Center of a CAD model as the center of a bounding sphere. The radius is then defined as the maximum distance from the center of the sphere to vertexes on the object. Although the radius of the sphere could not be said minimized, the generated sphere will enclose the CAD model and satisfy the need of finding the re-design area. By using a bounding sphere, another concept, projection plane, is defined to be tangent to the bounding sphere and perpendicular to the chosen tool approaching direction. Machining areas will be projected on the projection plane and an extrusion process will be used to locate the re-design area. This will be discussed in more detail in following sections. The purpose of using bounding sphere and projection plane is to generate a starting point of the extrusion process (to be discussed in Section 3.5) and to guarantee that there is no collision and interference between the cutting tool, tool holder and the CAD model before extrusion.

With a CAD model consisting of n vertices Pi (xi, yi, zi) , i=1,2,3,…,n, the Euclid distance between the Center of Gravity Qcg (xcg, ycg, zcg) and each vertex of the CAD model can be calculated using Eq. (1).

di Distance between point Piand Qcg � �

¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Px � Qxð Þ2 þ Py � Qy

� �2 þ Pz � Qzð Þ2 q

ð1Þ

After the distance di for each vertex Pi is calculated, the maximum distance is chosen as the radius of the bounding sphere. An example of bounding sphere is shown in Fig. 7.

3.3 Projection of the machining boundary

In order to determine the re-design area for increased ma- chinability, the machining boundary needs to be determined. A machining boundary is a containment boundary in ma- chining a pocket feature. This step intends to obtain a machining boundary for a pocket feature through 3D pro- jection, where a hole or pocket feature is projected onto a

AX+BY+CZ+D=0 (A,B,C)=(Nx,Ny,Nz)

Fig. 5 A unit hemisphere of a facet on the surface of a designed part

N

Fig. 4 Tool approach direction of pocket with free-formed bottom

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a

Unit Hemispheres of the facets

Pocketing

Obstacle

b

c d e

A single direction A visibility cone A single direction

Fig. 6 a A sample CAD model, b unit hemispheres of the facets on wall and bottom of the pocket, c overlapped visibility cones on pocket wall region, d overlapped visibility cones on pocket

bottom, e overall visibility is a single point that represents the tool approaching direction

Int J Adv Manuf Technol (2013) 69:337–349 341

plane, called projection plane. A projection plane is used to obtain machining boundary of pocket feature after the bounding sphere is determined. In this paper a projection plane is defined using two the constraints. The first con- straint is the alignment with the tool approaching direction of the pocket bottom surface, which will make the re-design area corresponding to the actual tool approaching direction. The second one is the tangency to the bounding sphere, which will make the following extrusion process start at a point free of collision.

Prospective projection and parallel projection are two major methods of projection used in engineering field. In this paper, orthogonal projection which belongs to parallel projection is applied for our objective. An orthographic projection is a parallel projection for which the direction of the projection is perpendicular to the projection plane [18, 19]. The required parameters for orthographic projection are projection plane and the direction of projection. In this research the projection direction is the same as the tool approaching direction. Thus, if the projection plane vector is n=(n1, n2, n3, n4) then the center of projection is V (−n1, −n2, −n3, 0). The projection matrix is

M ¼ n22 þ n23 �n1n2 �n1n3 0 �n1n2 n21 þ n23 �n2n3 0 �n1n3 �n2n3 n21 þ n22 0 �n4n3 �n4n2 �n4n3 n21 þ n22 þ n23

2 664

3 775 ð2Þ

For instance, the projection matrix for an orthographic projection onto the plane z=0 (for which n=(0, 0, 1, 0) and V (0, 0, 1, 0)) is

M ¼ 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1

2 664

3 775 ð3Þ

After a hole or pocket feature is projected onto the projection plane through an orthographic projection, a ma- chining boundary is obtained. Figure 8 illustrates this

projection. The obtained machining boundary will be offset to accommodate tool diameter and tool holder diameter. The two offset boundaries will be extruded opposite to the pro- jection direction to determine the re-design area. This will be discussed in Section 3.5.

3.4 Offset of the boundary

Projecting the machining area onto the projection plane will produce a boundary on the projection plane within which tool is moving. Such a boundary is used to derive re-design area so that tool collision can be avoided in the re-designed product geometry. In addition to tool collision, tool holder collision is also an aspect to be considered in early design stages. Since the diameter of tool holder is different from that of the cutter, a new boundary describing the boundary of tool holder movement should be defined to prevent tool holder collision during machining. The 2D projection area on the projection plane is offset in order to obtain tool holder movement boundary.

Offset operation moves boundary of an area along its normal by a selected amount. Depending on the offset direc- tion, offset operation needs to handle the issue of curve intersection and gap generation (Fig. 9). The original shape is shown in Fig. 9a–c show the outward offset and inward offset respectively. In outward offset, gaps are generated be- tween adjacent geometric entities on the original geometry,

Q: Center of Gravity

P: The vertex that gives the maximum distance from Center of Gravity

R: Radius of the bounding sphere

Fig. 7 Bounding sphere of a CAD model

Fig. 8 Parallel projection of a surface on a projection plane

Fig. 9 Offset boundaries of a selected feature

342 Int J Adv Manuf Technol (2013) 69:337–349

while curve intersection will occur when the original geome- try is under inward offset. Mathematically, if the boundary of the cutter is given by a curve C(t)=(x(t), y(t)) on the projection plane with unit normal n(t) along the boundary, the offset curve for tool holder is expressed as Od(t)=C(t)+d·n(t), where d is called offset distance [18]. The offset distance d in this paper is equal to:

d ¼ Dh � Dt 2

ð4Þ

Where Dh is tool holder diameter and Dt is tool diameter. In order to avoid the issues of curve intersection and gap

generation, Minkowski sum is used in this paper to obtain offset boundaries. Assuming that sets A and B have been positioned in a coordinate system, Minkowski sum will calculate the vector summations of each element from sets A and B:

A þ B ¼ x þ y x 2 A; y 2 Bjf g In this research, in order to calculate boundary of tool

holder, set A is the cutter boundary projected on the projec- tion plane, and set B is a circle with the diameter equal to (Dh−Dt)/2. In Fig. 10, set A is denoted in solid line describ- ing the boundary of tool movement, set B is a circle with diameter to be (Dh−Dt)/2, and the boundary in centerline is the tool holder boundary after the Minkowski sum of set A with set B [20, 21].

3.5 Extrusion of tool and tool holder boundaries

In order to improve the manufacturability of a CAD model, the volume on the model that needs to be re-designed should be determined. Since the cutting tool and the tool holder are restricted to the tool boundary and tool holder boundary respectively, the volume for re-design can be obtained from extrusion of these boundaries. Extrusion is a way of creating

3D geometry from translating a 2D cross-section along a user-defined trajectory [22]. For this research, the extrusion will start from the two boundaries on the projection plane, one for the cutting tool and the other for the tool holder. The extrusion direction is normal to the projection plane, and points opposite to the projection direction. The extruded volume is the volumetric space within which the cutting tool and tool holder are moving, and therefore it can be used to check the collision between the cutting tool, tool holder and geometric features on the CAD model. The extrusion distances for the cutting tool and tool holder are different. For the boundary of the cutting tool, extrusion will go all the way to touch the bottom of the hole feature or pocket feature, while the extrusion distance for the tool holder will be shorter by the amount of tool length.

Figure 11 shows the parameters used in extruding the two boundaries mentioned above. Parameter h0 is the initial position of the cutting tool above the pocket bottom prior to the machining operation. This initial position should be above the projection plane along the tool approaching di- rection. H denotes tool holder height, and h denotes tool length. The extrusion distance of the tool boundary is equal to h1, the distance from the projection plane to the bottom of the hole or pocket feature, and the extrusion distance of the tool holder boundary is h1−h.

4 Slicing process to determine obstacle sequence

Although the previous sections are able to detect the features on the CAD model that have collisions with tool and tool holder movement, they cannot present a designer with the information on the sequence of the obstacle feature sequence. In order to obtain the obstacle sequence

Fig. 10 Minkowski sum to obtain tool holder boundary

Projection Plane

h0

h

H

d

D h1

Fig. 11 Tool and tool holder parameters with respect to machining area

Int J Adv Manuf Technol (2013) 69:337–349 343

information, relationship among obstacle features along the tool approaching direction need to be revealed. This section intends to use a slicing approach to accomplish the objective of determining obstacle sequence. A set of slicing planes are used to interrogate the obstacle features within the extruded volumes from the previous section. The slicing process produces a set of 2D images at each slicing positions along the tool approaching direction. A color and image process- ing approach is then used to analyze the images on each slicing position.

In order to implement this color and image processing based approach, the obstacle features of a CAD model are assigned with different colors. They are also assigned trans- parent property as obstacle features may have overlap area along the tool approaching direction. In case where overlap area exists, the overlaps will be represented by the combi- nation of the colors of the overlapping obstacle features. Figure 12 shows that the CAD model has two obstacle features above the pocket, which are assigned to be red and blue respectively. The tool approaching direction is perpendicular to the pocket bottom. The image is taken from the projection plane level. The overlap area takes pink color, which is the combination of red and blue. The combination color in Fig. 12a suggests that the red obstacle feature is above the blue feature, as the combination color is closer to red. The combination color in Fig. 12b suggests that the blue obstacle feature is above the red feature, as the combination color is closer to blue.

In order to interrogate the sequence of obstacle features, a set of slicing planes are created parallel to the projection plane with a fixed spacing apart. In this way, a set of images are obtained at each corresponding position of the slicing planes. The same CAD model is sliced in Fig. 13. The slicing spacing is selected as 5 mm starting from the level on top of the plate feature. The images at each slicing position are analyzed for the overlapping area.

As the slicing plane moves up, the overlap area starts to merge at the level with Z=25 mm (Fig. 13f). For this example, it is apparent that the red feature is above the blue one along the tool approaching direction because the over- lap area color is pink and is closer to red in color space. The flow chart of finding obstacle features is summarized in Fig. 14.

5 Examples

In this section, two geometric models are presented as examples for drilling and pocketing milling operations re- spectively. Both of them have been evaluated through the algorithm presented in this paper, and their results on the re- design areas are presented in this section as well. Table 3 shows the CAD models and the steps of obtaining re-design areas. The dimensions of cutting tools and tool holders used for these two examples are given in Tables 1 and 2.

Part (a) of Table 3 shows the original CAD models for these parts. Part (b) of Table 3 demonstrates the bounding spheres that enclose these two models and center at their Centers of Gravity. The hole feature and pocket feature are projected on the projection planes which are tangent to the bounding spheres. The projected machining boundaries and the offset tool holder boundaries are presented in part (c) of Table 3. In order to determine the re-design areas for these part models, the machining boundaries and tool holder boundaries are extruded towards the hole feature and pocket feature, creating working spaces of cutting tools (part (d) of Table 3). In order to distinguish cutters and tool holders, the working spaces for cutters and tool holders are painted in green and red, respectively. These two working spaces are converted into solid models (Part (e) of Table 3), and their intersections with the original CAD models are determined. Part (f) of Table 3 represents the intersections of cutters with

Projection Plane

a b

Projection Plane Fig. 12 Color of overlapping obstacle features

344 Int J Adv Manuf Technol (2013) 69:337–349

the original CAD models, and part (g) of Table 3 shows the contours of the intersections. Similarly, part (h) of Table 3 represents the intersections of the tool holders with the

original CAD models, and part (i) of Table 3 shows the contours of the intersections. The unions of intersections of cutters and tool holders work spaces with the CAD models are displayed in part (j) of Table 3, and they represent the re-design areas for increasing machinabil- ity. In order to show what the current machine set-up can accomplish on the original CAD models, the work space volumes of the cutter and tool holder are subtracted from the obstacle features on the original CAD models. These subtracted obstacle feature geome- tries are displayed in part (k) of Table 3.

The procedure presented in Table 3 is able to evaluate initial designs and help a designer to visualize the actual manufacturability of their products. The result will also give the designer suggestions to modify current design models since the re-design areas are identified. It should be noted that such a process will iterate during the design stages, and intend to engage the designer in the downstream manufacturing process planning.

To demonstrate the practical application of this method- ology, an example part was machined using a three-axis milling machine as shown in Fig. 15. The stock material was a polyamide plastic workpiece with the dimension of 76.2 mm×101.6 mm×50.8 mm (3 in.×4 in.×2 in.). A 12.7 mm diameter (0.5 in.) flat-end milling cutter with

Assign different colors for obstacle features

Start slicing process from a selected machining surface

Save images at each slicing level

Process images for color blending detection

Determine sequence of obstacle features

Fig. 14 Slicing flowchart

Table 1 Drilling cutter and tool holder

Drilling Diameter Length

Tool 12 mm 108 mm

Tool holder 50 mm 25 mm

Z=0

Top view (Tool approach direction)

Z=5mm

Z=10mm

Z=15mm

Z=20mm

Z=25mm

Z=30mm

Z=35mm

a

b

c

d

e

f

g

h Fig. 13 Finding order of the obstacle features over the machining area

Int J Adv Manuf Technol (2013) 69:337–349 345

45.7 mm (1.8 in.) tool length was used to machine the pocket area, and MasterCAM software was used to generate the pocketing toolpath. Figure 15a shows the machined part. It can be seen that part of the wall feature was mistakenly

cut, which was due to its collision with the cutter while the pocket was being machined. Figure 15b and c show the side view and top view of machining simulation in MasterCAM environment, where the cutter movement has intersection with the wall feature geometry. The methodology presented in this paper was applied to detect the re-design area on the example part CAD model. The previously mentioned pro- cedure (parts (a) to (k) in Table 3) has been implemented to evaluate the design model. The analysis results show that the tool holder movement does not have collision with the part model while the tool movement does have. Figure 16

Table 3 Implementation examples

Drilling process Pocket milling process

a) CAD model of original design

b) Bounding sphere

d) Work space for tool and tool holder

Table 2 Flat-end milling cutter and tool holder for pocketing

Milling Diameter Length

Tool 12 mm 108 mm

Tool holder 50 mm 25 mm

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Table 3 (continued)

e) Converted CAD model combined with work spaces for tool and tool

holder

f) Intersection of CAD models with cutter work space

g) Contour of intersection of CAD models with cutter work space

h) Intersection of CAD models with tool holder work space

i) Contour of intersection of CAD models with tool holder work space

j) Union of intersections of cutters and tool holders work spaces with the

CAD models

k) Obstacle feature geometries with cutters and tool holders work spaces

subtracted

Int J Adv Manuf Technol (2013) 69:337–349 347

shows the detected intersection volume between tool move- ment and the wall feature geometry from the presented methodology. The corresponding intersection volume on the machined part is measured and displayed in Fig. 17. Clearly there is a deviation between the dimensions of the detected intersection volume and its corresponding volume measured on the machined part although both the geome- tries and dimensions of these two volumes are close as shown in Figs. 16 and 17. Possible causes leading to the deviation include set-up and fixturing errors, plastic work- piece deformation during machining and the machining errors in creating other features before pocketing, etc.

6 Conclusion

This paper presents a method for detecting potential manufac- turability problems in early design stages that need drilling and pocketing processes. The method is able to determine re- design areas on the original CAD models. The re-design areas are determined through using tool movement bound- aries; therefore they represent the minimum spaces that need to be re-designed. The dimensions of both cutting tools and tool holders are treated as input parameters to the algorithm; therefore the method allows designers to test a variety of cutters on their designs. Moreover,

Fig. 15 Machining example, a machined part, b side view of tool collision with workpiece during pocketing, c topview of tool collision with workpiece during pocketing

Fig. 16 Detected intersection volume (units: in millimeter) Fig. 17 Intersection volume on the machined part (units: in millimeter)

348 Int J Adv Manuf Technol (2013) 69:337–349

color-based evaluation of the re-design areas also deter- mined the sequence of obstacle features.

The intention of this paper is to involve designers in manufacturability evolution from early design stages as it will reduce cost and waste in the downstream manufacturing stages. Although the current approach is dedicated to ana- lyzing drilling and pocketing processes, the authors will extend it to determine re-design areas of products that need four- or five-axis machine tools. Another branch of future research is to extend the current approach to assembly process that needs the accessibility.

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