Development of CAM Software to Design and Grind ... - Springer Link

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 16, No. 5, pp. 869-876 DOI: 10.1007/s12541-015-0114-1

MAY 2015 / 869 ISSN 2234-7593 (Print) / ISSN 2005-4602 (Online)

Development of CAM Software to Design and Grind Indexable Inserts Van-Hien Nguyen1, Sung-Guen Shin1, and Sung-Lim Ko1,# 1 Department of Mechanical Design & Production Engineering, Konkuk University, 120, Neungdong-ro, Gwangjin-gu, Seoul, 143-701, South Korea # Corresponding Author / E-mail: [email protected], TEL: +82-2-450-3465, FAX: +82-2-447-5886 KEYWORDS: Indexable insert, Grinding model, CAM system, Developable surface

This paper provides an analytical method that forms the basis for the development of CAM software for the design, manufacturing, and visualization of an indexable insert. There are four special features relevant to the proposed model. The first is a model of indexable inserts, which allows the insert to be designed parametrically. The second is a method for the determination of the generated contour (flank) surface of the insert based on differential geometry. The third feature presented is a post-processor, which converts the obtained data into a four-axis CNC grinder NC code. The last one includes the flowcharts of tool-path planning and the associated diagram of the developed CAM software. Finally, the results of experiment and simulation are compared to validate the proposed model. Manuscript received: October 17, 2014 / Revised: February 11, 2015 / Accepted: February 17, 2015

NOMENCLATURE (OXYZ)w = workpiece coordinate system (OXYZ)m = machine coordinate system di = distance from Ow to ith edge θi = polar angle to determine points in cutting edge ri = corner radius at ith corner αi = clearance angle at ith edge dL = distance from Ow to a chamfered edge θL = polar angle of a chamfered edge t = insert thickness nP = normal vector of contour surface at point P IG = wheel orientation Rwmin, Rwmax =wheel radii Up = grinding plane passes through point P rM = position vector of an edge α· =∂α/∂θ = first derivative of clearance angle P = points in the cutting edge K = points in the bottom face n = total edge numbers of an indexable insert m = total control point numbers in a corner X, Y, B, C = axes of four-axis CNC grinder MB, MC = rotation matrix about Ym and Zm axes

© KSPE and Springer 2015

1. Introduction The indexable insert is a cutting tool that is machined by the CNC grinder and is widely used in high-speed machining. It is characterized by nine design parameters1-shape, clearance angle, tolerance, thickness, and nose radius among others. The precision of these design parameters greatly influences the cutting performance of the insert and the tolerance of machined parts. Thus, a precise machining model is required. The indexable insert has been well standardized and classified.1 The dynamic behavior of indexable insert have been extensively studied. The effects of both the insert shape and nose geometry to its cutting performance have been studied,2,3 with the choice of these parameters forming the basis for the selection of an appropriate insert for a specific cutting performance. Strategies for grinding of chamfers in order to improve workpiece surface quality and the kinematic relation between the grinding wheel and the flank face of the insert have also been presented.4 An in-depth review on cutting edge geometry, technologies for cutting edge preparation, chip formation, and wear behavior of cutting insert have also been performed.5 However, a comprehensive mathematical model and structure of CAM system required to produce the indexable insert has not been well established. Most of the inserts are machined using MACRO NC programs by a small number of companies. These NC programs are created on a case-by-case basis and require skillful operators. The design process of the insert begins with the design of the cutting

870 / MAY 2015

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 16, No. 5

edge geometry and the distribution of the clearance angle at the corners of the cutting edge. To machine the designed insert, the grinding wheel slides along the cutting edge, with the aim of obtaining the designed clearance angle. Consequently, the contour surface of the insert is generated. Therefore, the contour surface of the insert is formed based on the design of the cutting edge curve and the distribution of clearance angles. In other words, the contour surface of the insert is not a freeform surface and it cannot be designed and machined with the commonly used CAD/CAM systems, but rather it requires a dedicated CAD/CAM system. A CAM system for designing and machining of the indexable insert requires four major functions: a) design of the interface, b) generation of the NC code, c) representation of the machined workpiece, and d) verification of the NC code (simulator). Recently, some attempts have been made to machine and determine the contour surface of the insert. Two-axis and three-axis interpolation algorithms have been proposed to grind the corner surface of the insert.6 A virtual machining system then performs the cutting simulation using Boolean subtraction operations to verify the NC code in the grinding indexable insert.7 A mathematical model to approximate the transaction corner in the case of a constant clearance angle have also been previously presented.8 In cases of a zero-clearance angle, the contour surface of the indexable insert can be considered as the contour surface of a camshaft. A CAM system and related algorithms were developed to machine the contour surface of the plate cam.9 A CAD/CAM system was proposed alternating between three types of interpolation methods: linear, circular, and polar (r-θ), to machine the cam surface.10 A new interpolation method, called the triarc curve fitting, was introduced to optimize the number of control points and improve the quality of the designed cam surface.11 The reviewed studies have provided methods for the generation and optimization of the NC code in grinding the indexable insert. However, a CAM system for manufacturing indexable insert requires a more complete model. Apart from its major function, which is generation of NC code, it must also include an efficient and simple design interface. It also needs a simulator, which allows the user to observe the generated contour surface and examine possible collisions between machine parts, and verify the generated NC code. The aim of this paper is to provide a comprehensive model for the development of CAM software for the design, manufacturing and visualization of the indexable insert. The content of this paper is organized as follows: we first suggest a method to design an indexable insert that is convenient for the development of CAM software. The machined contour surface is determined based on differential geometry. Presented next is a post-processor based on the structure of machine and the extracted information of the designed insert is used to generate the NC code. Afterward the software implementation and its associated algorithms are introduced. Finally, the comparison between design, simulation, and experiment is performed to validate the proposed model.

2. Geometric Model An indexable insert of thickness (t) is composed of a top face where the cutting edge is defined, and a contour surface that is formed as the

Fig. 1 Basic components of the indexable insert

Fig. 2 Corner types of the square insert (a) square type, (b) “r-type”, (c) “Lr-type”, (d) “rL-type”

grinding wheel slides along the cutting edge, as depicted in Fig. 1. In designing an indexable insert, the cutting edge is designed first, followed by the specification of the clearance angle, α, at each point along this cutting edge. In this section, we introduce a design model for the indexable insert. This study also introduces an automatic design model, from which users can design standard indexable inserts with minimum input.

2.1 Design model of the indexable insert An indexable insert is classified by the shape of the cutting edge. Three basic shapes are widely used:1 the regular polygon, the diamond and the parallelogram. For each basic shape, many inserts with different corner types can be created. For example, from a square shape (Fig. 2(a)), three types of inserts can be extended. Namely, the “r-type” is created by rounding each corner basic shape (Fig. 2(b)), the “Lr-type” is created by chamfering the left hand side and then rounding each corner as shown in Fig. 2(c), whereas the “rL-type” is created by chamfering the right hand side and then rounding each corner as shown in Fig. 2(d). From the observation of the commercial indexable insert available in the market, it can be seen that cutting edge can be expressed as a combination of line segments and arc segments (circular arcs). Therefore, this study proposes a method for designing the cutting edge of insert, as shown in Fig. 3. On the top face, containing the cutting edge, choose a point Ow to be the origin of the workpiece coordinate system (OXYZ)w.

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 16, No. 5

MAY 2015 / 871

Table 1 Automatic design model of the regular polygon shape Type di

r di = Ric

θi

θi = ( i – 2 ) 2π -----k

Lr d2i-1 = Ric, d2i = dL θ2i – 1 = ( i – 2 ) 2π -----k

rL d2i-1 = Ric, d2i = dL 2π θ2i – 1 = ( i – 2 ) -----k

2π θ2i = ( i – 2 ) ------ + θL k

2π θ2i = ( i – 2 ) ------ – θL k

αi αi = α α2i-1 = α, α2i = αL α2i-1 = α, α2i = αL ri ri = r r2i-1 = 0, r2i = r r2i-1 = r, r2i = 0 Explanation: k: number of edges of regular polygon insert (k≥3) i: ith edge (i=1, 2, …, k) Ric: inscribed radius dL: distance from the chamfered edge to Ow αL: clearance angle at the chamfered edge Fig. 3 Generalized cutting edge geometry of the indexable insert

Assume that the cutting edge has n line-segments, so it can be considered to be a closed set of n edges and n arc segments in which the ith edge can be defined as follows: Edgei = {di,θ i, αi θ 1 < θ 2 < … < θ n} , i = 1, 2, …, n

(1)

where di is the distance from the center Ow to the ith edge, θ i is the angle between the vector di and the axis Zw, and α i is the clearance angle at the ith edge. The ith arc (corner) of the cutting edge is formed by rounding operation of two consecutive edges, the ith and the (i+1)th with a radius ri, so it can be defined in the coordinate system of the workpiece as Arci = {di, di + 1,θi , θi + 1, ri , αi, αi + 1 dn + 1 =d1, θn + 1 =θ1 +2π }

(2)

In this definition the clearance angle, α, varies smoothly from αi to αi+1. The distribution of clearance angles, α(θ), plays an important role in forming the contour surface. Based on the Eqs. (1) and (2), for a generalized insert geometry it is required to input all parameters (di, θi, αi) to design the insert. However, this study provides an automatic design model of the regular polygon insert, from which parameters (di, θi, αi) are automatically assigned, once a minimum number of design parameters are provided. For example, in designing insert of k-regular polygon (polygon with k edges), by selecting the origin Ow coincident with the center of this regular polygon, an automatic design model for three types of corner shapes is defined, as listed in Table 1. In this case, the minimum number of inputs are as follows: the inscribed circle radius, Ric, the distance of the chamfered edge, dL, the clearance angle at the main edge and at the chamfered edge (α, αL), and the rounding radius at the corner (r). In the same manner, the automatic design of other indexable insert types can be established.

2.2 Geometry of grinding points along the cutting edge To machine the contour surface of the insert, one of the solutions in planning the tool path is to machine consecutively each line and arc segment using the tangential grinding method. To do so, the position and normal vectors of the contour surface need to be determined at the control points along the cutting edge. During the grinding process, there exists a common contact line,

Fig. 4 (a) Schematic illustration of the grinding the contour surface by using the flat end-face of the wheel, (b) Notation of the contour surface to be machined

PK, between the end face of the grinding wheel (Fig. 4(a)) and the contour surface that is to be machined as shown in Fig. 4(b). The tangential grinding principle can be used to determine the engagement between the grinding wheel and the workpiece. The principle is at the contact point P in the cutting edge, the normal vector of the flat face of grinding wheel and the contour surface are inline. In grinding the ith edge, the root of altitude, Mi, from the center Ow to each line segment is selected as the control point. The position and normal vectors of the control points are defined as follows: T ⎧ ⎪ rMi = ( di sinθ i, 0, di cosθ i) ⎨ ⎪ nM = ( cos αi sinθi , sin α i, cos α i cos θi )T ⎩ i

(3)

In grinding the ith arc segment, a current control point P can be defined, associated with a polar angle θ. Therefore, the position and normal vectors of the contour surface at point P can be expressed as

872 / MAY 2015

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 16, No. 5

follows: ⎧θ ∈ [θ , θ ] i i+1 ⎪ ⎪ T ⎛ ( di – ri ) sin θi + ( di – r ) cosθi tan ( ∆θ i ) + ri sinθ , 0,⎞ ⎪ ⎟ ⎨ rP = ⎜ ⎝ ( di – ri ) cosθi + ( di – r )sinθi tan ( ∆θ i ) + ri cos θ ⎠ ⎪ ⎪ ⎪nP = ( cos α sinθ , sin α, cos α cosθ )T ⎩

(4)

where ( di + 1 – ri ) – ( di – ri) cos (θ i + 1 – θ i ) tan ( ∆θ i ) = -------------------------------------------------------------------------( di – ri ) sin (θ i + 1 – θi) The engagement of the grinding wheel and the designed insert using the tangential grinding method is: ⎧ –nMi in grinding line segments IG = ⎨ ⎩ –nP in grinding acr segments

(5)

The position and normal vectors of the contour surface at the grinding points along the cutting edge in Eqs. (3)-(4) will form the basis for the calculation of the contour surface and the NC code generation, as described in the following sections.

3. Determination of the Generated Corner Surface

Fig. 5 Notation for calculation of the contour surface: (a) the grinding wheel slides tangentially along the cutting edge to machine the insert, (b) the common contact line between the wheel and the surface to be machined, (c) the contact line is formed as two neighbor planes passing through the grinding points approach to each other

· Note that the plane UP (θ ) also passes through point P and its normal is the vector n· P (θ ) , which is determined as:

Determination of the generated contour surface of the insert is essential. It allows users to observe the generated shape of the insert without performing a real machining operation, so that the production cost can be reduced. This work can be completed by applying the Boolean difference of the tool swept volume from the stock, using commercial software; however, this is a costly and time-consuming process. This section presents a method to determine directly the generated contour surface from the determined position and normal vectors of the contour surface at the grinding points along the cutting edge. The corner surface is formed by sliding the grinding wheel along the cutting edge tangentially, as shown in Fig. 5(a). Since the end surface of the grinding wheel is planar, the formed corner surface is a developable surface generated as an envelope of a single family of planes (wheel end face) that is well known in differential geometry.12,13 Suppose that the corner between the ith and (i+1)th edge is being ground and that the clearance angle varies smoothly from αi to αi+1 along the corner. The current grinding point P with a position vector rP and a normal vector nP, is ground by the plane UP(θ), which is determined by:

However, to determine the location of end-point K, it is required to compute the edge of regression (K1), defined as the envelope curve generated by the family of contact lines (PK). In other words, K1 is the ·· · intersection of planes UP(θ), UP (θ ) and UP (θ ) , or alternatively, K1(θ) · ·· ·· = UP (θ ) ∩ UP (θ ) ∩ UP (θ ) , where the plane UP (θ ) is determined as follows:

UP (θ ):nP (θ ) ( r – rP (θ ) ) = 0

·· 2 2 UP (θ ):∂ ( nP (θ ) ( r – rP ( θ ) ) )/∂θ

· UP (θ ):∂ ( nP (θ ) ( r – rP ( θ ) ) )/∂θ = n· P (θ ) ( r – rP ( θ ) ) – nP ( θ )r· P (θ ) (7) = n· (θ ) ( r – r ( θ ) ) = 0 P

(8)

The direction vector of the contact line (PK) can then be determined as follows: nPK = nP (θ ) × n· P (θ ) T (9) 2 = ( – α· cosθ – sin α cos α sinθ , cos α , α· sinθ – sin α cos α cosθ ) The position vector of the end point K of the contact line is determined as follows: rK (θ ) = rP (θ ) + nPK (θ )lscale

(6)

The generated corner surface is formed as the envelop of the moving planes UP(θ), with θ ∈ [θi, θi+1]. The contact line PK, as shown in Fig. 5(b), this line is then the intersection of two planes UP(θ) and UP(θ+∆θ) as θ approaches zero, as depicted in Fig. 5(c). In other words, the contact · line ( PK = UP (θ ) ∩ UP (θ ) ) is determined by the intersecting plane · UP(θ) with the first derivative plane, UP (θ ) , expressed by:

P

n· P (θ ) = ( – α· sinα sinθ + cos α cosθ , α· cos α , – α· sinα cos θ – cos α sinθ )

·· sin α + α· 2 cos α = 0 = n··P (θ )r + α

(10)

(11)

and, n··P (θ ) = ·· sinα sinθ – α· 2 cos α sinθ – 2α· sin α cosθ – cos α sinθ , (– α ·· cos α – α· 2 cos α, α

(12)

·· sin α cosθ – α· 2 cos α cosθ + 2α· sin α sinθ – cos α cosθ ) –α ·· It can be seen that the plane UP (θ ) always passes through fixed points, defined by:

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 16, No. 5

MAY 2015 / 873

Table 2 Common design parameters of two inserts Parameters Edge 1 Edge 2 Edge 3 Edge 4

di (mm) 6 6 6 6

θi (deg) -45o 45o 135o 225o

αi (deg) 0o 10o 0o 10o

ri (mm) 2 2 2 2

·· sin α + α· 2 cos α ⎞ ⎛ α -, 0⎟ rPfix (α ) = rCi + ⎜ 0, –------------------------------------·· cos α – α· 2 sin α ⎠ ⎝ α

T

Thus, the equation of this plane can be rewritten as: ·· UP (θ ):n··P (θ ) ( r – rPfix ) = 0

(13)

Fig. 6 The change of corner shape via the change of clearance angle distribution: (a) the clearance angle varies linearly, (b) the clearance angle varies followed a quadratic function

Therefore, the location of point K1 is computed as follows: ( rPfix (α ) – rP (θ ) ) ⋅ n··P (θ ) rK = rP (θ ) + ------------------------------------------------------ nPK (θ ) 1 nPK (θ ) ⋅ n··P (θ )

(14)

If this regression point exists and lies inside the workpiece space, then the point K coincides with the point K1; if not, it will lie on the bottom face. Then, the y-component of the position vector of point K can be obtained as follows: rKy = min {rK1y, t}

(15)

where rK1y is computed from Eq. (14). Substituting the y-component obtained from Eq. (15) into Eq. (10) to find the coefficient lscale based on which the position of point K is determined. Actually, determination of the corner surface is the process of determination of the contact lines. From Eqs. (6)-(15) it can be seen that the shape of the corner depends on the distribution function of the clearance angle, α(θ), along the corners of the cutting edge. To observe the change of the corner shape via the distribution function of the clearance angle, the following example is used to illustrate the principle. Two inserts are designed with geometrical parameters shown in Table 2. The only difference between the two inserts is the distribution of the clearance angle at the corners. Specifically, in insert #1, the clearance angle varies linearly along the cutting edge at its corners, as shown in Fig. 6(a). In insert #2, the clearance angle has a quadratic distribution (α = 15o at θ = 0o, 90o, 180o and 270o) as shown in Fig. 6(b). To estimate the result, the radial angle of each corner θ ∈ [θi, θi+1], are divided equally into 10 segments by 11 points for each. The contact lines are then computed at each of sampling points using Eqs. (6)-(15) and the contour surface is formed by tiling all contact lines consecutively, as shown in Fig. 6. From the result, the influence of the distribution function to the shape or contour surface can be observed.

4. Post-Processor for NC Code Generation for the FourAxis CNC Grinder In this section, a post-processor is developed, which converts the derived data and machine structure into the actual NC code to be used in the four-axis CNC grinder. Assume that a fixed coordinate system, (OXYZ)m, is attached to the machine, as shown in Fig. 7. The insert is machined by a four-axis CNC

Fig. 7 Machine structure of four-axis CNC grinder used to grind the insert

grinder, that allows two linear motions, X and Y, along axes Xm and Ym, respectively, and two rotational motions, B and C, around axes Ym, and Zm, respectively. When there is no movement, the wheel center is located m at the primary point Go (xGo, yGo, 0) of the machine’s coordinate system. The workpiece is held in a clamping system such that rotation axis of B goes through the workpiece center Ow, and the rotational axis of C is located at a distance LC with respect to the workpiece center Ow. The orientation of the grinding wheel is always fixed in the negative direction of the Xm axis. Moreover, from the engagement of the grinding wheel and the workpiece (Eq. (5)), the wheel orientation and the normal of the contour surface at the current grinding point, are always inline. Therefore, while grinding the point P in the cutting edge, the workpiece has to rotate around the axes Ym and Zm with angles B and C, respectively, to ensure that the normal vector nP matches with the positive direction of Xm axis.14 The values of these two angles are determined as follows: ⎧ B = θ + π /2 ⎨ ⎩C = α (θ )

(16)

As a result of these two swiveling movements, the grinding point P as defined in the workpiece coordinates will take a new position in the machine coordinate system. Correspondingly, the position of the grinding

874 / MAY 2015

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 16, No. 5

point in the grinding wheel is determined by: T

m

rPx = MB (θ + π /2 )MC (α ) (rP + ( 0, LC, 0 ) )

(17)

where MB and MC are rotation matrices about Ym, and Zm, respectively. ⎧ ⎪ ⎪ MB (θ ) = ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ MC (θ ) = ⎪ ⎩

cosθ 0 – sinθ

0 sinθ 1 0 0 cosθ

(18)

cos α sinα 0 – sinα cos α 0 0 0 1

To assign the grinding point Pm located at the desired distance RP (Rwmin ≤ RP ≤ Rwmax) from the center G of the grinding wheel, the wheel must translate in the XY plane from the initial position to the current grinding position. Therefore, NC equation of the designed four-axis CNC in absolute mode can be determined as follows: ⎧X = rmPx – xGo ⎪ ⎪ Y = rm ± R – y Px P Go ⎨ ⎪B = θ + π /2 ⎪ ⎩C = α

Fig. 8 Interface for inputting the design parameters of the indexable insert

(19)

Note that, the plus or minus signs in the Eq. (19) correspond with the use of the left or the right sides of the end-face of the wheel for machining the grinding point.

5. Software Implementation Based on the developed model, CAM software that allows grinding of the insert was developed. The Graphical User Interface (GUI) was developed in MATLAB and is shown in Fig. 8. Specified inputs include the insert design (that is, the design parameters in Sec. 2), and the machine settings (machine datum, wheel geometry, intended grinding point radius, offset of C-rotation axis). An NC file and a simulator are generated as outputs. The grinding process is divided into two processes: the edge grinding process and the corner grinding process. The tool path generation schemes of each process are shown in Fig. 9. After receiving the input, a finite number of points along the cutting edge are chosen to be the control points. In the edge grinding process, the intersecting points (Mi) between the altitudes, defined from the origin Ow to the corresponding edges, are chosen as the control points. The position and the normal vector at the control points are then obtained by Eq. (3), and immediately after the NC code is generated based on Eqs. (16)-(19). When grinding the ith corner (ri > 0), m+1 points in that corner are selected as control points, namely {Pi0, Pi1, …, Pim}. The surface roughness mainly depends on the number and the distribution of these control points. When these m-points are divided equally in this corner, the radial angle that is used to determine the position of a point Pij, is determined as follows: j θ ij = θ i + ---- (θ i + 1 – θ i ) m where 1 ≤ i ≤ n and 1 ≤ j ≤ m.

(20)

Fig. 9 Tool path generation schemes for edge and corner grinding of the indexable insert

The position and normal vectors to the contour surface at the control points (Pij) are obtained by Eq. (4), and then the NC code is obtained based on Eqs. (16)-(19). A simulator have also been developed based on the proposed model, using programming language C++ and the OpenGL library, which includes two major components: the machine parts, which are designed

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 16, No. 5

MAY 2015 / 875

Fig. 10 Flow diagram of the developed simulator

Fig. 12 Demonstration of results: (a) designed profile, (b) 3D view of simulated workpiece, (c) machined workpiece, (d) 3D view of machined workpiece

Fig. 11 Illustration of the developed simulator

by the used of commercial CAD software, the NC file and the generated workpiece boundary which includes the top face (set of points Pi), bottom face (set of points Ki) and the contour surface (set of contact lines PiKi) obtained as described in Sec. 3. The simulator operates in accordance to the flowchart shown in Fig. 10, which includes a triangulated mesh file of the machine parts (STL file), and the computed workpiece boundary and an NC file. Initially, simulator renders machine parts and workpiece at the reference position (home position of CNC grinder). It then reads the NC file line by line and interpolates the NC code, followed by the rendering the machine and the workpiece at interpolated positions. The simulator is illustrated in Fig. 11.

6. Model Validity Demonstration In order to demonstrate the validity of the proposed model, a square insert with an “rL-corner” type was designed as follows: inscribed radius, Ric=6.35 mm, distance from the chamfered edge to center Ow, dL=7.07 mm, rounding radius at each corner, r=1 mm. Additionary, the chamfered

edge aligns with the main edge with angle, qL=15o, the clearance angles at the main edges and the chamfered edges are, α=11o, αL=15o, respectively. The clearance angle at the corner varies linearly, and thickness t=3.18 mm. The insert profile is shown in Fig. 12(a). Applying the suggested model and using the automatic design model of Table 1 with k=4, the design parameters were input. The required information for the determination of the machined contour surface of the workpiece was obtained via the procedure described in Sec. 3. The virtually formed workpiece was obtained and rendered as shown Fig. 12(b). The NC code was then generated in accordance to the procedure in Sec. 4. It was then transferred to a fouraxis (AGATHON) CNC grinder to produce the designed insert. The experimental results are shown in Figs. 12(c) and (d). By examining the designed and machined profiles of the insert, as shown in Figs. 12(a) and (c), and the predicted workpiece surface and the machined one, as shown in Figs. 12(b) and 12(d), a very close match between the design, simulation, and experiment can be observed. This close match confirms that the developed model is suitable for the development of CAM software for grinding indexable inserts. After machining the designed insert, measurements were taken to validate the designed insert and machined one. The design parameters were checked with allowed tolerance for length and angle dimensions are ±0.01 and 0.5o, respectively. The measurement data is listed in Table 3, which shows that the maximum error for length dimension is 0.008 that is within the allowed tolerance. The deviation between machined part and virtual one is majorly due to dynamic effect during machining process. However, to control the quality of the product, machine is equipped with a probing system that can inspect the dimensions of the generated design parameters. If the deviation amount exceeds the allowed tolerances, a re-grinding process is automatically executed by shifting X-axis coordinate of machine by an amount of the deviated value. The developed software is capable of designing, manufacturing and visualizing the indexable insert by directly inputting the design parameters (di, θi, αi). For a quick design, the automatic design model

876 / MAY 2015

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 16, No. 5

Table 3 Measurement data of machined workpiece Parameters Sample 1 Sample 2 Sample 3 Sample 4

Ric (mm) 6.352 6.342 6.353 6.346

θL(deg) 15.0 ±0.1 15.0 ±0.1 15.0 ±0.1 15.0 ±0.1

ri(mm) 1.0±0.1 1.0±0.1 1.0±0.1 1.0±0.1

REFERENCES dL(mm) 7.071 7.062 7.072 7.065

1. ISO 1832:2012, “Indexable Inserts for Cutting tools. Designation,” 2012. 2. Petropoulos, P. G., “The Effect of Feed Rate and of Tool Nose Radius on the Roughness of Oblique Finish Turned Surfaces,” Wear, Vol. 23, No. 3, pp. 299-310, 1973. 3. Dogra, M., Sharma, V. S., and Dureja, J., “Effect of Tool Geometry Variation on Finish Turning–A Review,” Journal of Engineering Science and Technology Review, Vol. 4, No. 1, pp. 1-13, 2011. 4. Ventura, C. E. H., Köhler, J., and Denkena, B., “Strategies for Grinding of Chamfers in Cutting Inserts,” Precision Engineering, Vol. 38, No. 4, pp. 749-758, 2014. 5. Denkena, B. and Biermann, D., “Cutting Edge Geometries,” CIRP Annals-Manufacturing Technology, Vol. 63, No. 2, pp. 631-653, 2014. 6. Tian, X. C. and Deng, X. H., “Trajectory Interpolation in CNC Grinding of Indexable Inserts,” Advanced Materials Research, Vols. 97-101, pp. 2007-2010, 2010.

Fig. 13 Some types of inserts: (a) triangular with “Lr-type”, (b) pentagon with “rLr-type”, (c) octagon with “r-type”, (d) diamond shape with “r-rtype”, (e) diamond shape with “r-L-type”, (f) diamond shape with “rLr-type”, (g) parallelogram with “r-r-type”, (h) parallelogram with “rL-rtype”, (i) parallelogram with “r-L-type”

for other insert shapes were developed which allow eight different types of the regular polygon, eight types of diamond, and eight types of parallelogram to be designed and machined. Some inserts with the different types of corner were designed and are illustrated in Fig. 13 to show the capability of the developed software.

7. Conclusion The paper provided an easy and efficient method for the developments of a CAM system in manufacturing an indexable insert. The contributions of this paper can be summarized as follows: 1. A design model of an indexable insert was introduced 2. A method for determining the contact line between the workpiece and grinding wheel was suggested, from which a model for workpiece representation of the indexable insert was proposed 3. A post-processor for generating the NC code of a four-axis CNC grinder was introduced 4. CAM software based on the proposed model is validated by the comparison between simulation and experiment results

ACKNOWLEDGEMENT This work was supported by Konkuk University.

7. Wang, Y. Y., Zhang, C. L., and Zhao, J., “Research of Virtual Grinding Technology for Planar Inserts with Various Linetypes,” Advanced Materials Research, Vols. 452-453, pp. 359-363, 2012. 8. Li, F., Yao, B., Zhang, Z., and Yao, B., “Modeling and Grinding Method of Indexable Inserts,” Proc. of International Conference on Mechanical Engineering and Technology, 2011. 9. Satyanarayana, B., Rao, P., and Tewari, N., “Machining of Plate Cam Profiles on CNC Machine Tools using a Highly Integrated Part Programming System,” The International Journal of Advanced Manufacturing Technology, Vol. 3, No. 4, pp. 105-125, 1988. 10. Yang, M. and Kim, C., “A CAD/CAM System for Precision Cams with Three CNC Interpolation Methods,” The International Journal of Advanced Manufacturing Technology, Vol. 9, No. 2, pp. 87-92, 1994. 11. Yang, M. Y., Shon, T. Y., Lee, T. M., and Lee, T. M., “CAM Profile Machining by Triarc Curve Fitting,” International Journal of Production Research, Vol. 36, No. 7, pp. 1767-1778, 1998. 12. Pottmann, H. and Peternell, M., “Envelopes-Computational Theory and Applications,” Proc. of Spring Conference on Computer Graphics and Its Applications, pp. 3-23, 2000. 13. Bodduluri, R. M. C. and Ravani, B., “Geometric Design and Fabrication of Developable Bézier and B-Spline Surfaces,” Journal of Mechanical Design, Vol. 116, No. 4, pp. 1042-1048, 1994. 14. Feng, X. and Hongzon, B., “CNC Rake Grinding for a Taper BallEnd Mill with a Torus-Shaped Grinding Wheel,” The International Journal of Advanced Manufacturing Technology, Vol. 21, No. 8, pp. 549-555, 2003.