Proposal of a tool path generation method for rough

Bulletin of the JSME

Journal of Advanced Mechanical Design, Systems, and ManufacturingVol.15, No.2, 2021

© 2021 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2021jamdsm0019]Paper No.20-00170

Proposal of a tool path generation method

for rough machining of complex shapes

based on topology optimization

Maho KUMANOTANI*, Hitoshi KUSHINO* and Keiichi NAKAMOTO* *Tokyo University of Agriculture and Technology

2-24-16 Nakacho, Koganei-shi, Tokyo 184-8588, JAPAN

E-mail: [email protected]

1. Introduction

Recently, the demand of complex shape parts has increased mainly in the aircraft and medical industry. In these

parts machining, the displacement and vibration of workpiece that strongly affect the machining efficiency are induced

as a result of the heavy change of the unmachined workpiece shape and stiffness while rough machining. Though these

problems may be avoided by selecting proper cutting conditions and so on, it is difficult to automatically determine the

manufacturing information even by using a commercial CAM system because there is a large number of combinations.

There are many researches and various strategies regarding complex parts machining such as optimization of cutting

conditions, novel workpiece fixturing and tool path modification. Yan maximized the depth of cut for semi-finish and

finishing machining (Yan et. al., 2018). Through physical experiments, the allowable maximum normal cutting force

and the maximum depth of cut are determined in each cutter contact point to satisfy the maximum cutting force.

Ringgaard optimized cutting conditions by maximizing the material removal rate that is the function of radial depth of

cut, axial depth of cut, feed per tooth, number of flutes and spindle speed (Ringgaard, et. al., 2019). In order to restrict

vibration amplitude, the cost function that incorporates the deflection and chatter stability constraints is adapted. Ozturk

proposed novel workpiece fixturing in milling process using a robot (Ozturk, et. al., 2018). Li proposed an analytical

approach to optimize the fixturing scheme for variable stiffness structures that have flexible and rigid parts in one

structure (Li, et. al., 2019). The variable stiffness structure is categorized into 3 regions according to the deformation

Received: 2 April 2020; Revised: 18 June 2020; Accepted: 17 August 2020

Abstract Recently, the demand of complex shape parts has increased mainly in the aircraft and medical industries. In these parts machining, the displacement and vibration of workpiece that strongly affect the machining efficiency are induced as a result of the heavy change of the unmachined workpiece shape and stiffness while rough machining. On the other hand, it is difficult to automatically determine the manufacturing information by using a commercial CAM system because there is a large number of combinations. Thus, in order to improve the machining efficiency of complex shape parts, the authors have proposed a determination method of workpiece transition shapes during a rough machining operation based on topology optimization. However, tool paths are not generated automatically to create the obtained workpiece transition shapes in the previous study. Therefore, in this study, a tool path generation method is proposed considering both static stiffness of workpiece and machining efficiency. The proposed method supposes 5-face milling and in the machining the tool orientation is determined to minimize the change of tool orientations by using the obtained parameters in topology optimization. The tool paths are continuously generated based on not only the design variables of topology optimization but also geometric feature of machining area, target shape, final support. A case study assuming rough machining of complex shape parts is conducted to confirm the effectiveness of the proposed method.

Keywords : Tool path generation, Topology optimization, Computer aided manufacturing, Operation planning, Rough machining

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2© 2021 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2021jamdsm0019]

Kumanotani, Kushino and Nakamoto, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.15, No.2 (2021)

induced by the fixturing. Finally, the fixturing scheme is built to minimize the total deformation of these 3 regions

using genetic algorithm. Wan integrated the three type errors into the deviation of cutting tool respect to workpiece:

location error of fixturing datum, elastic deformation of workpiece by the fixturing and machine tool (Wan et. al, 2011).

The cutter location data generated by CAM software is modified based on the deviation of cutting tool. Li modified the

tool paths to minimize the machining errors based on predicted deformation of workpiece and cutting tool (Li and Zhu,

2019). The deformation of cutting tool is predicted using a cantilever beam model and the workpiece deformation is

predicted by finite element model. However, these strategies are heavily affected by the tool paths and may result in the

deterioration of machining efficiency when the improper tool paths are generated. Therefore, this paper focuses on the

tool path generation considering workpiece static stiffness.

In general, tool paths are generated based on the geometric feature of workpiece and target shape (for example

Takasugi and Asakawa, 2018), and the workpiece stiffness is not usually considered. Smith indicated the possibility of

high speed milling of thin webs that are structures created at the face of end mill by optimizing the tool paths (Smith

and Dcorak, 1998). Nassehi proposed a tool path generation and optimization method that can be applied to various

optimization objectives (Nassehi, et. al., 2015). The study superimposes several points in reticular pattern and the

machining sequence of points are determined to satisfy the optimization objectives using genetic algorithm. However,

the assumed objective functions do not contain the properties in terms of workpiece stiffness. Wang proposed a

determination algorithm of machining sequence to reduce the workpiece deformation (Wang, et. al, 2017). In this

algorithm, the workpiece is divided into some blocks and the removal sequence of each block is determined

considering the workpiece deformation. However, this algorithm assumes simple contour-line tool paths and the

effectiveness of the algorithm is confirmed only against the simple thin-walled part.

In order to improve the machining efficiency of complex shape parts, the authors have proposed a determination

method of workpiece transition shapes during a rough machining operation based on topology optimization (Takahashi

and Nakamoto, 2017). However, the tool paths are not generated automatically to create the obtained workpiece shapes.

Thus, in this study, a tool path generation method considering both workpiece stiffness and machining efficiency is

proposed. The proposed method supposes 5-face milling and in the machining the tool orientation is determined to

minimize the change of tool orientations by using the obtained parameters in topology optimization. The tool paths are

continuously generated based on not only the calculation results of topology optimization but also geometric feature of

machining area, target shape and final support.

The remainder of this paper is organized as follows. The basic theory of topology optimization applied to

workpiece is explained in Chapter 2, and the proposed tool path generation method is described in Chapter 3. A

conducted case study for confirming the effectiveness of the proposed method is shown in Chapter 4. Finally, the

conclusion of this study is given in Chapter 5.

2. Topology optimization to calculate workpiece transition shapes

Topology optimization is one of the structural optimization methods. The feature of this optimization method is

introduction of the changeable fixed design domain D and discretized characteristic function 𝜒Ω which describes the

existence of material with 1 or 0. By introducing the fixed design domain and characteristic function, a structural

optimization problem can be converted to an optimal material distribution problem. The optimal material distribution is

determined in order to maximize or minimize the objective function while satisfying a series of constraints. However,

since 𝜒Ω is a discretized function and discretized structures are obtained, it is required to relax the design space.

Typical relaxation methods of design space are the homogenization method that obtains general material characteristics

using microstructures (Bendsøe and Kikuchi, 1988), the density method that utilizes the normalized density from 0 to1

(Mlejnek and Schirrmacher, 1993, Yang and Chuang, 1994) and the level set method that treats the characteristic

function as the function of level set variables (Yamada et. al., 2010). In this study, topology optimization is used to

maximize the static stiffness of workpiece and operated based on SIMP method that is one of the density methods.

The followings are explanations regarding the topology optimization for maximizing static stiffness based on SIMP

method using the shape imitating “J”. In SIMP method, the normalized density is utilized as the design variable and the

homogenized elastic tensor EH is described using normalized density ρ as follows:

𝑬𝑯 = 𝑬𝜌𝑝 (0 ≤ 𝜌 ≤ 1), (1)

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where E is an elastic tensor and p is a penalty factor that is utilized to avoid the state of gray scale where the element

has an intermediate value of design variable.

In general, when the penalty factor is above 2 or 3, it is less likely to occur gray scale. The design variables are

normalized densities and the values of design variables are determined based on optimization algorithms. For

maximizing the static stiffness of workpiece, the mean compliance l (ρ) that indicates flexibility is utilized as the

objective function and the workpiece volume 𝑣0 is limited as a constraint condition in this study. Thus, the topology

optimization problem for maximizing workpiece stiffness is formulated as follows:

minimize 𝑙(𝜌) = 𝑼𝑻𝑲𝑼,

subject to 𝑣𝑙𝑜𝑤 ≤ 𝑣0 ≤ 𝑣𝑢𝑝𝑝𝑒𝑟 ,

(2)

where U, K, 𝑣𝑙𝑜𝑤 and 𝑣𝑢𝑝𝑝𝑒𝑟 are a nodal displacement vector, a global stiffness matrix, lower and upper limits of

volume, respectively.

Figure 1 (a) shows the calculation flow of the topology optimization for maximizing static stiffness of workpiece

Fig. 1 Outline of obtainment of workpiece transition shapes based on topology optimization. (a) shows the

calculation flow of topology optimization for maximizing static stiffness of workpiece shape. CAD

models of target shape and workpiece shape are converted to voxel models as shown in (b). The

workpiece shape is defined as the design domain and the boundary conditions of finite element

method are set as shown in (c). (d) indicates design variable of each element in the design domain.

Input data

Definition of design domain

Setting of design variables

Setting of boundary conditions

Calculation of finite element method

Calculation of objective function

and total volume

Update of design variables

based on optimization algorithm

Converge?

Binarization of design variables

Acquisition of optimized shape

(c) Definition of design domain and boundary conditions

(d) Setting of design variable in each element

Design variable

Workpiece

(design domain)

Fixed domain

Loads Target shape

(Non design domain)

Original model Voxel model

(b) Conversion of CAD model to voxel model

(a) Calculation flow of topology optimization for maximizing static stiffness

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shape based on SIMP method. Firstly, the basic information such as material parameters is input. In this study, CAD

models of target shape and workpiece shape are converted to voxel models to prepare input data as shown in Fig. 1 (b).

The boundary conditions such as fixed domain and load and the design domain are set as shown in Fig. 1 (c). In the

calculation of transient workpiece shapes, the design domain is the workpiece shape except for the target shape. The

design variable is set for each element in the design domain as shown in Fig. 1 (d). The objective function and the total

volume are calculated by using finite element method. When the variation of objective function exceeds a threshold

value, the design variables are updated based on the optimization algorithm. In this study, CONLIN (Cho and Lee,

2011) that is one of the sequential convex programming methods is utilized as the optimization algorithm. On the other

hand, when the variation of objective function is below the threshold value, the calculation of updating of design

variables is finished. The design variables that have larger value are converted to 1 and the other design variables are

converted to 0. Finally, the materials are arranged according to the elements where the values of design variable are 1.

As it can be seen from the above description, the elements that are important for maintaining stiffness have large value

of design variables. Thus, in this study, the elements that have smaller value of design variables are machined as

preferentially as possible.

3. Tool path generation method for rough machining of complex shapes

3.1 Assumed rough machining

In the previous study, based on topology optimization, the workpiece transient shapes are obtained by dividing a

rough machining operation according to the unmachined volume rate as shown in Fig. 2. This study aims to generate

the tool path to create each optimized workpiece shape. In the proposed method, the final workpiece shape that contains

final supports is firstly obtained and the final supports are left for finishing of target complex shape. 5-face milling with

contour-line tool paths are assumed for rough machining in this study. The tool orientation in the machining is

determined to minimize the change of tool orientations by using obtained parameters in topology optimization. Cutting

Fig. 2 Workpiece transition shapes while rough machining. These workpiece shapes are determined according

to unmachined volume rate based on topology optimization. Final supports are left for finishing of target

complex shape.

Fig. 3 Loads applied to target shape for calculation of topology optimization. Target shape receives only the

loads normal to the voxel surface from the side of end mill.

Cutting tool

Loads

Target shape

100% 50% 30%

20% 10% Final workpiece shape

Final support Unmachined volume rate

Target shape

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loads in the direction normal to the element surfaces are given from the side of end mill to voxels indicating the target

shape for the calculation of topology optimization as shown in Fig. 3

3.2 Determination of tool orientation

In this study, tool orientation is defined as the relative orientation between workpiece and cutting tool as shown in

Fig. 4. The tool orientation is assumed to be normal to workpiece faces in 5 faces milling. In order to decrease the

orientation change in 5-face milling, the tool orientations are determined as shown in Fig. 5. The elements that should

be removed to create the optimized shape are obtained from the above calculation results as shown in Fig. 5 (a). The

obtained elements are hereinafter called as removal elements. This study utilizes design variables to generate tool paths.

In the determination process of workpiece transition shapes, the design variables have close values to either 0 or 1 due

to the penalty factor, and the differences among removal elements are extremely small. Therefore, the calculation of

topology optimization is operated again with the penalty factor that causes an intentional gray scale to obtain

Fig. 4 Definition of tool orientation. Tool orientation is the relative orientation between workpiece and cutting tool. In this study, only the orientations that are normal to the face of 5face milling are considered.

Cutting tool

Workpiece

Tool orientations

Fig. 5 Determination procedure of tool orientation in 5-face milling. (a) shows acquisition of removal

elements using workpiece transition shapes. (b) shows tool orientations. Orientation A and C are

essential to machine removal elements and the orientations are called as essential orientations. The

other tool orientations are determined using the elements that cannot be machined from essential

orientation as shown in (c).

(a) Acquisition of removal elements

Removal elements

(c) Determination of tool orientation except essential orientation

(b) Tool orientations

B A

C

D

E Initial workpiece shape

Essential orientation

E

D Removal elements machined from D or E

Workpiece faces

55



differences of the design variables and the following procedure is operated based on these design variables. In this

calculation that generates intentional gray scale, the design domain contains only removal elements.

Firstly, essential orientations that some removal elements cannot be machined in other tool orientations, are

detected among 5 tool orientations perpendicular to 5 faces. If the all removal elements can be machined in the

essential orientations, the essential orientations are adopted as the tool orientations and all removal elements are

machined in only these tool orientations. Otherwise, in order to minimize the change of tool orientations, the following

procedure is applied. For example, when the tool orientation A and C are essential orientations as shown in Fig. 5 (b), it

is judged whether the remained removal elements can be machined in only one orientation such as B, D or E. In the

case shown in Fig. 5 (c), there are some elements that cannot be machined in the essential orientations and these

elements are can be machined in D or E. Thus, the tool orientations are determined as the essential orientation A and C,

and arbitrary orientations D and E. If it is impossible that the remained removal elements are machined in only one

orientation, the combinations of B and D, B and E, or D and E are tried to machine the remained removal elements. The

elements unmachinable in any tool orientation are excluded from the removal elements.

Once the tool orientations are obtained, the tool orientation sequences are determined by using design variables. In

each orientation, the average value of design variables is calculated using the elements can be machined in the

orientation. Then, the orientation having the minimum average value is selected as the first tool orientation. In order to

machine a lot of elements in one orientation, the whole machinable elements are machined in the first tool orientation

and the assigned elements to the orientation are not changed. The average values of design variables are calculated

once again for the remained removal elements, and the orientation having the minimum average value is selected as the

second tool orientation. This calculation of average value is conducted until all orientation sequences are determined. In

this average calculation, the orientation sequences are changed in ascending order of the average values to

preferentially machine the elements that have small design variable values. The tool orientations in which no elements

are machined are not utilized to conduct a rough machining operation. Contour-line tool paths are generated in each

tool orientation.

Orientation A

Machining area 1

Machining area 2

Fig. 6 Acquisition of machining area. Adjacent removal elements are grouped in each tool orientation as one

machining area and tool paths are generated for each machining area.

Orientation C

Machining area 3

Fig. 7 Modification of machining sequence. (a) shows original machining sequence determined based on the

average of design variables. In this case, the interference may be occurred between a cutting tool and a

machining area. (b) shows the machining sequence modified to avoid the interference.

Machining sequence change Machining area 1

Machining area 2

Tool orientation

Machining sequence

Interference

(a) Original machining sequence (b) Modified machining sequence

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3.3 Generation of contour-line tool paths in each tool orientation

In each tool orientation, the adjacent removal elements are grouped as one machining area as shown in Fig. 6. The

average value of design variables is calculated in each machining area. Similar to the determination of tool orientation,

the machining sequence of machining areas is basically determined based on the average value of design variables.

However, when there is an interference between a cutting tool and a machining area as shown in Fig. 7 (a), the

machining sequence is modified to avoid the interference as shown in Fig. 7 (b).

Contour-line tool paths for each machining area are generated based on the geometric features of machining area,

target shape and final support. The machining area is divided by planes normal to the tool orientation as shown in Fig.

8. Then, the boundary elements that are adjacent to un-machined elements that consist of the target shape elements,

final support elements and workpiece elements except for removal elements are obtained to generate a continuous tool

path as shown in Fig. 9. The removal elements adjacent to boundary elements are also obtained as the next boundary

Tool path

Target shape

Final support

Boundary element Machining area

Fig. 8 Division of machining area. Machining area is

divided by planes normal to tool orientation.

Tool paths are generated for each divided

machining area.

Machining area

Tool orientation

Fig. 9 Tool path generation for first boundary elements.

Boundary elements that are adjacent to the

un-machined elements that consist of target

elements, final support elements and workpiece

elements except for removal elements are

obtained. Continuous tool path is generated along

the boundary elements.

(a) Overlapped elements among tool paths

Final support

Target shape Overlapped element

Tool path

(b) Assignment of overlapped elements

Area 1 (average: 0.5)

Area 2 (average: 0.2)

Area 1

Overlapped element

Area 2 0.3

0.3

0.5

0.5

Fig. 10 Assignment of overlapped elements. (a) shows overlapped elements that can be machined by some tool

paths. The average value of design variables is calculated except for the overlapped elements in each

area. Then, the overlapped elements are assigned to the area having the closer average value of design

variables as shown in (b).

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elements and a tool path is generated along the new boundary elements. This procedure is repeated until the tool paths

are generated for all removal elements contained in the machining area. If there are overlapped elements that can be

machined by some tool paths as shown in Fig. 10, the average value of design variables is calculated except for the

overlapped elements in each area. Then, the overlapped elements are assigned to the area having the closer average

value of design variables, respectively.

After the tool paths are generated, approach and evacuation points are added following similar procedures. Thus,

the addition method of approach points is described in here. In this study, the liner motion is assumed for the tool

approach. If there is a hollow area, the approach point is placed in the hollow area to avoid the feed direction change

after the tool approach because the immediately direction change is undesirable for machine tools. For example, as

shown in Fig. 11 (a), approach point 1 is adopted because the feed direction change is required immediately in case of

approach point 2. If there is no hollow area, the approach point is placed above the element that are machined firstly as

shown Fig. 11 (b).

As noted above, a tool path is generated along preceding tool path, except for the first tool path. In rough

machining, the cutting tool motions are added to move from the evacuation point of a tool path to the approach point of

the preceding tool path.

4. Case study

In order to confirm the feasibility of the proposed method, a case study assuming rough machining of complex

shape parts is conducted. Figure 12 shows the original CAD model of target shape that imitates a leaf of ginkgo and the

converted voxel model that the element size is 4 mm. In this case study, the rough machining operation is divided by

two steps according to unmachined volume rate: 30 % and 5 %. Figure 13 shows the workpiece transition shapes and

the final support determined based on topology optimization using commercial CAE software (Altair optistruct). The

fixed domain is the area where Z coordinate is lower than 20 mm and the other area is prepared as the design domain.

In this case study, the second step of rough machining from 30 % to 5 % of the unmachined volume rate is focused

because the workpiece has relatively high static stiffness during the first step from 100 % (initial workpiece shape) to

30 %. Additionally, the tool paths generated by the proposed method are compared with tool paths generated by a

commercial CAM software (DP Technology, ESPRIT) in terms of machining efficiency and accuracy. In case of using

the commercial CAM software, the tool orientations, orientation sequences and machining sequence are determined in

Tool path

Approach point 1

Approach point 2

Tool path

Element machined firstly

Hollow area

Tool path

Fig. 11 Setting of approach points. (a) shows approach point setting in hollow area. Approach point is placed in

the hollow area to realize a liner motion to avoid the feed direction change after the tool approach. (b)

shows the case that there is no hollow area. Approach point is placed above the element that are

machined firstly.

(a) Approach point setting in hollow area

(b) Approach point above an element machined firstly

Tool path

Element machined firstly

Approach point

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descending order of machinable volume. The rough machining operation of both the proposed method and comparison

case are conducted by down cutting. Tool path pattern of comparison case is a circular pattern from the inside to the

outside because this circular pattern is utilized to realize stable down cutting.

Table 1 shows the workpiece material and cutting conditions, that used in both the proposed method and

comparison case, and the machine tool utilized in this case study is Takumikun (UNITECH SYSTEM). Figure 14

shows an example of generated tool paths and Fig. 15 shows the machined shape based on the proposed method. It is

found that continuous tool paths are generated along un-machined elements. In order to avoid the occurrence of thin

unmachined portion, the radial depth of cut is basically equal to radius of cutting tool except for the case that slotting is

required. In the proposed method, the machining sequence of tool orientations is A, B, C and D in Fig. 13. In the

comparison case, the machining sequence is A, C, B, E and D. The machining times of the proposal method and

Original CAD model Voxel model

Fig. 12 Original CAD model and converted voxel model of target shape for case study. The shape of original

CAD model imitates a leaf of ginkgo and the voxel element size is 4 mm.

100 % 30 % 5 %

Unmachined volume rate

Fig. 13 Workpiece transition shapes and final support determined based on topology optimization. The workpiece

shape size is 80 mm x 40 mm x 80 mm. The area where Z coordinate is lower than 20 mm is utilized as

the fixed domain and the other area is prepared as the design domain. Arrows A to E displayed in

unmachined volume rate 30% are tool orientation in 5-face milling.

Target shape Final support

A

B

C D

E

Tool orientation 80

60

40

X

Y

Z 20

Fixed domain

Design domain

Table 1 Material of workpiece and cutting conditions in case study. These cutting parameters are utilized in the

machining from 30 % to 5 % of the unmachined volume rate. Both the proposed method and

comparison case are operated using these cutting conditions.

Material

Cutting tool diameter [mm]

Number of cutting tooth

Spindle speed [min-1]

Feed rate [mm/min]

Depth of cut (radial) [mm]

Depth of cut (axial) [mm]

ABS

4

2

4800

700

2

2

99



comparison case are 43.0 min and 37.3 min, respectively. The proposed method requires longer machining time than

that of comparison case because the tool paths for approach and evacuation are not optimized in the proposed method.

In order to verify the machining accuracy, the machined workpieces are measured using a non-contact 3D

coordinate measuring machine (KEYENCE, VL-300) and the measurement results are compared to the original CAD

model. From this measurement, it is found that in the comparison case, the area away from the fixed domain is

deformed about 0.25 mm in Y direction. On the other hand, in the proposed method, the deformation is decreased to 0.1

Tool path

Target shape

Final support

Fig. 14 Example of generated tool paths. These tool paths are utilized in machining in orientation A.

Continuous tool paths are generated along un-machined elements that consist of target shape

elements and final support elements and workpiece elements except for removal elements.

Front view Rear view

Fig. 15 Result of experimental machining by the proposed method. The calculated shape by topology

optimization is obtained by rough machining.

Target shape

Final support

Tool path

Deformed area

Fig. 16 Example of tool path generated in comparison case, and machining simulation in the CAM software. (a)

shows example of tool paths in comparison case. (b) shows the machining simulation in CAM software.

From these figures, it is recognized that the area far from fixed domain is machined after a lot of material

is removed and the workpiece stiffness becomes low due to the circular tool path pattern from the inside

to the outside, and these tool paths induce the deformation to Y direction.

Z

X

Z

X Y

(a) Example of tool path in comparison case. (b) Machining simulation in CAM software

Machined surface

Cutting tool

Fixed domain Fixed domain

10



mm. The deformations are induced while the machining in the orientation A and B. In the comparison case, the area far

from fixed domain is machined after a lot of material is removed and the workpiece stiffness becomes low, due to the

circular tool path pattern from the inside to the outside as shown in Fig. 16. As a result, the larger deformation to Y

direction is induced in the comparison case. Additionally, in the proposed method, it is thought that the elements

machined in tool orientation C is an important role for securing static stiffness than the elements machined in tool

orientation B. On the other hand, in the comparison case, the tool orientation C is utilized before the tool orientation B.

From these results, it is recognized that the traditional tool paths based on only geometric feature using commercial

CAM software cause comparatively large deformation than that of proposed method under the same cutting parameters.

Therefore, the effectiveness and feasibility of tool path generated by the proposed method is confirmed though the

deformation is still left even in the proposed method. In addition, there are some bent parts at right angles in the

generated tool paths. Therefore, the optimization of cutting conditions and tool paths are also required to realize

efficient rough machining in the future.

5. Conclusion

In complex shape parts machining, the workpiece shape and stiffness heavily change, and the displacement and

vibration of workpiece are easily induced. Thus, this study aims to propose a tool path generation method considering

both workpiece stiffness and machining efficiency to improve the machining efficiency of complex shape parts

machining based on the topology optimization. The proposed method assumes 5-face milling and the tool orientation is

determined to minimize the change of tool orientations and the machining sequence is assigned using the available of

design variables. In each tool orientation, the continuous contour-line tool paths are generated along the unmachined

elements that consist of target shape elements, final support elements and workpiece elements except for removal

elements. Moreover, an experimental machining is conducted and the machined result is compared with the case using

a commercial CAM software. From the results, the effectiveness of proposed method is confirmed. In future work, a

tool path generation method that contains the optimization of cutting conditions and tool paths would be proposed.

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Proposal of a tool path generation method for rough