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Determining the effect of tool posture on cutting force in a turn milling process using an analytical prediction model
Journal Pre-proof Determining the effect of tool posture on cutting force in a turn milling process using an analytical prediction model Koji Utsumi, Shoki Shichiri, Hiroyuki Sasahara PII:
S0890-6955(19)30490-0
DOI:
https://doi.org/10.1016/j.ijmachtools.2019.103511
Reference:
MTM 103511
To appear in:
International Journal of Machine Tools and Manufacture
Received Date: 1 May 2019 Revised Date:
24 November 2019
Accepted Date: 25 November 2019
Please cite this article as: K. Utsumi, S. Shichiri, H. Sasahara, Determining the effect of tool posture on cutting force in a turn milling process using an analytical prediction model, International Journal of Machine Tools and Manufacture (2019), doi: https://doi.org/10.1016/j.ijmachtools.2019.103511. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
Determining the effect of tool posture on cutting force in a turn milling process using an analytical prediction model
Koji UTSUMIa, Shoki SHICHIRIb, Hiroyuki SASAHARAb
a Research
& Development Group, Hitachi, Ltd., 292 Yoshida-cho, Totsuka-ku,
Yokohama-shi, Kanagawa, 244–0817, JAPAN
b Department
of Mechanical Systems Engineering, Tokyo University of Agriculture and
Technology, 2-24-16 Naka-cho, Koganei-shi, Tokyo 184–8588, JAPAN
Corresponding author: Koji Utsumi E-mail address of the corresponding author: [email protected]
1
Determining the effect of tool posture on cutting force in a turn milling process using an analytical prediction model Koji UTSUMIa, Shoki SHICHIRIb, Hiroyuki SASAHARAb a Research
& Development Group, Hitachi, Ltd., 292 Yoshida-cho, Totsuka-ku,
Yokohama-shi, Kanagawa, 244–0817, JAPAN b Department
of Mechanical Systems Engineering, Tokyo University of Agriculture and
Technology, 2-24-16 Naka-cho, Koganei-shi, Tokyo 184–8588, JAPAN Corresponding author: Koji Utsumi E-mail address of corresponding author: [email protected] Abstract Turn milling is a key technique that can be used to achieve high-efficiency machining and improve life of tools used for difficult-to-cut materials because intermittent cutting with multiple cutting edges can suppress a rise in temperature compared with conventional turning. However, the contact condition between the rotary tool and the cylindrical workpiece varies significantly depending on the tool posture, which is defined by the tool axis inclination angles against the workpiece: namely, lead and tilt angles. Thus, clarifying the effect of the lead and tilt angles on cutting forces in turn milling is essential for determining the optimal tool posture. In this paper, we propose a simulation model to predict the cutting force for 5-axis turn milling considering the contact behavior between the tool and workpiece depending on the tool posture. The workpiece is modeled as a point cloud and any points that interfere with the tool volume are removed when the tool edge passes the surface of the workpiece. We examined the simulated cutting forces using a radius end mill as a linear function of the uncut chip thickness and found that the predicted cutting forces were in agreement with the experimental results for several combinations of tool postures and feed rates. We also clarified that the tool posture significantly affects the maximum cutting force, which varies even if the material removal rate is maintained at a constant value in the turn milling process. Keywords: Turn milling, Machining simulation, Cutting force, Tool posture
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1
Introduction Machining productivity when working with difficult-to-cut materials such as super
heat-resistant alloys used in the industrial fields of aeronautics, nuclear power, and medicine is generally low because of the short tool life caused by high cutting temperatures, high cutting forces, and low chip disposability [1]. Turn milling, which can generate separated chips due to its interrupted cutting, has attracted interest as a relatively new machining strategy. In this process, tool wear and cutting temperature are decreased by using multiple cutting edges with interrupted cuts, which results in small chips and a low tool temperature [2]. Moreover, turn milling can be applied to machine free-form surfaces such as turbine blades because it has a higher degree of freedom in the cutting tool posture motion. In an academic study started in the 1990s by Schulz et al. [3], two categories of turn milling operations were introduced: orthogonal and axial turn milling. This study also investigated surface quality in the high-speed turn milling of the roller bearing components made of steel; the results showed that surface quality obtained by turn milling is better than that obtained by conventional turning. In another study, kinematic conditions and their influence on tool design and choice of technological parameters were investigated [4]. Another study regarding surface finish quality was conducted by Vedat et al. [5], who analyzed the surface roughness in tangential turn milling and found that it achieved a high-precision surface comparable to grinding. Considering the efficiency of the material removal rate (MRR), Kopac et al. [6] found that it was possible to achieve a thirty times higher MRR by turn milling with a small radius end mill than with the recommended cutting conditions in turning. Choudhury et al. [7] studied the effect of parameters such as spindle speed and feed rate on the surface quality and found that a ten times better surface quality could be achieved by turn milling compared to conventional turning. They also investigated the effect of various parameters such as the end mill tool shape, axial depth of cut, and workpiece rotational speed on surface quality in tangential turn milling and found that a higher quality surface could be achieved by turn milling than by the conventional milling process [8]. With respect to simulation research, Yuan and Zheng developed a geometric model of turn milling operation to predict the surface roughness and studied the effects of various turn milling parameters [9]. Filho et al. proposed a numerical cutting simulation model of turn milling and validated it through a comparison of the simulation and experimental test results [10]. Karaguzel et al. and Kara et al.
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investigated a simulation model for orthogonal, tangential, and co-axial turn milling operations to predict the cutting force and verified the model using experiments. Specifically, the cutting force calculated by the proposed model was in accordance with the simulation results, with an error of less than under different cutting parameter conditions [11][12]. Zhu et al., H. O. Ortega et al., and U. Karaguzel et al. also proposed another simulation model based on the formulation of an uncut chip shape considering various kinematics in orthogonal turn milling [13][23][24]. Comak et al. proposed an approach to predict cutting force, torque, and consumption power based on a model of generalized chip thickness distribution as a function of linear feed drive motions, tool, and workpiece spindle rotations [14]. Sun et al. proposed a stability model for orthogonal turn milling that could obtain stability lobe diagrams using a complete discretization technique based on the Eulerian method [15]. In another approach for surface finish prediction, Kaibu et al. proposed a simulation method for cutting textures with 3D-CAD considering the tool lead and tilt angle. Here, the tilt angle was considered to be the inclination of the tool axis around the y-axis and the lead angle was considered the inclination around the z-axis, as shown in Fig. 1 [22]. They investigated the effect of the machining feed rate and tool shape on the texture shape and found that the prediction results were comparable with experimental results [16]. As stated above, although extensive research has been conducted on turn milling, the machining kinematics of the turn milling process are not yet fully understood because of the complicated contact condition between the tool and workpiece defined by various parameters such as the tool workpiece shape, lead and tilt angles of the milling tool axis, and cutting conditions. Most recent research has focused on kinematics in orthogonal turn milling processes; however, there are a very few published studies on the effect of both the lead and tilt angles of the milling tool axis on the cutting forces. It is important to predict the change in cutting force with respect to variation in the lead and tilt angles. In this paper, we propose a new simulation model with the point cloud method considering the lead and tilt angles of the tool. This model can be adapted to any workpiece shape and can analyze the complex contact area between the tool and workpiece along with the transition of the cutting force in the turn milling process using a radius end mill. The proposed model is experimentally validated by a cutting test under the condition that both the tilt and lead angle are simultaneously applied. We also investigated the effect of the tool posture on the change in cutting forces and demonstrated that the tool posture significantly affects the average and maximum cutting force, which varies even if the MRR is maintained at a constant value in the
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turn milling process on the basis of the proposed simulation.
Fig. 1 Definition of lead and tilt angles in turn milling. 2
Identification of cutting force and validation validation of face milling model
First, to predict the cutting force in turn milling, we measured the cutting force coefficients by a face milling test, as shown in Fig. 2. A dynamometer (KISTLER, 9257B) was attached to a 3-axis vertical machine tool and the cutting forces were measured by a grooving test using a block material of stainless steel SUS304 with a round indexable insert (5-mm radius, rake angle ranging from 5° through 8°, helix angle of 10°, ACM300 PVD coated) attached to a radius end mill with a diameter of 32 mm with one flute based on fluid cooling. The experimental conditions are listed in Table 1. The inclined dynamometer was reset to zero before each experiment in order to cancel the gravity effect.
Fig. 2 Experimental setup for identification of cutting coefficients by radius end mill. Table 1 Face milling test conditions.
S [rpm]
fr
ap
(V [m/min])
[mm/tooth]
[mm]
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1990 (200)
0.1–0.3
0.5, 1.0, 1.5
In order to obtain the cutting force coefficient, a time-average cutting force method that could be adapted not only to a square end mill but also to a ball end mill and radius end mill has been proposed [17]–[20]. However, this method considers the average cutting force including noise caused by unstable uncut chip thickness when the tool edge starts cutting or exits from the workpiece [21]. This makes it difficult to accurately identify cutting force coefficients for use in the simulation model to predict maximum forces that significantly affect tool breakage and wear. Therefore, because of the significance of predicting the maximum cutting force, an additional algorithm based on the time average cutting force model that considers the radius of the nose shape has been proposed. In this algorithm, only the cutting force waveform in the vicinity of the maximum cutting forces Fx, Fy, and Fz are extracted from the measured force time-domain data in the x, y, and z directions. Then, the cutting force coefficients are identified at each moment, along with the extracted data. The noise caused by the unstable uncut chip thickness when the tool edge starts cutting or exits from the workpiece can be ignored, which enables us to identify the cutting coefficient in the stable region accurately. The method used to obtain the coefficients and the analysis model used for cutting force identification are described as follows. Figure 3(a) provides an overview of the analytical model of the cutting coefficients for a radius end mill with one flute in grooving, and Fig. 3(b) shows the differential cutting force dFi (i = t, r, a) acting on each discretized cutting edge of the mill. The instantaneous uncut chip thickness fr’ at point P on the tool edge is defined as ′ = cos
(1)
where fr0 is the feed per tooth, and φ and κ are the radial and axial immersion angles, respectively. The differential cutting forces acting on the discretized cutting edge segment in the tool edge coordinate system are defined as in previous research [17–20]. , k , k = ′ ∙ + , k
(2)
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where Kic and Kie (i = t,r,a) are the cutting and edge force coefficients, respectively, and
= "# ∙ is the edge length of each segment. Using Eqs. (2) and (1), the differential cutting force dFi’ in the rotating tool coordinate system is formulated as
$ , k 1 0 0 $ , k = 0 '( − sin 0 sin cos $ , k
(3)
Using Eq. (3), the differential cutting forces (dFx, dFy, dFz) acting on the edge in a work-piece coordinate system can be formulated as , , k '( 0 ′ - , k = − '( 0 ′ . , k 0 0 1 ′
'( '( − sin = −'( '( '( sin 0 sin '(
(4)
From the above equation, the differential cutting forces on each segment are obtained by substituting Eqs. (2) and (1) into Eq. (4) as , , k '( − '( - , k = − '( '( '( 0 − '( − . , k '( '( − sin + −'( '( '( sin / 0 sin '(
=
01 2
(5)
34 ∙ + "# ∙ 35
where A1 and A2 are 2 2 '( 31 = 2 1 − '( 2 '( 0
1 − '( 2 1 + '( 2 − 2 1 + '( 2 2 2
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− 1 − '( 2 2 2 2 1 + '( 2
(6a)
'( 32 = sin( ) 0
cos () −'(( ) cos() sin()
−( ) sin() cos ( ) () cos()
(6b)
Here, by assuming that the cutting force coefficient does not depend on the position of the cutting edge, the instantaneous cutting forces Fx, Fy, and Fz can be obtained by integrating Eqs. (5), (6a), and (6b) for κ as , ( ) "# - ( ) = 84 / + "# ∙ 85 / 4 . ( )
(7)
where B1 and B2 are 84 = 9
:/5
<=
34
@ 2sin(2 ) sin() ? = ? 2(1 − cos(2 )) () ? 0 > where A = K + (2)L 4
85 = 9
cos( ) 35 = sin( ) 0
:/5
<=
5
(1 − cos(2 ))A − (2 ) A
− ( ) cos (2) sin( ) sin() −cos( ) sin() − cos()
EIJ H:/5 1 (1 − cos(2 ))cos (2)D 2 C 1 − sin(2 ) cos(2) C C 2 2 ( ) A BE H< FG
sin( ) cos() IJ − cos( ) cos() sin() E H< E
FG
(8a)
=
H:/5
(8b) =
The maximum axial immersion angle km is determined by using the axial depth of cut
ap as M = N4 K1 −
OP L "#
(9)
Equation (7) indicates the instantaneous cutting forces in the X, Y, and Z directions that can be measured using a dynamometer as shown in Fig. 2. {R } = {R } + {R }
(10)
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Using Eq. (10), the measured cutting force Fi can be converted into a linear expression relating to the feed rate fr0. Therefore, the cutting coefficients can be calculated by combining Eqs. (10) and (7) as 2 = 01 84N4 {R }
4 = 01 85N4 QR S
(a) Cutting force simulation model with radius end mill
(b) Differential cutting force model on the cutting edge at point P Fig. 3 Cutting force analytical model of the radius end mill.
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11
Figure 4(a) shows the measured cutting force on each feed rate (fr0 = 0.1, 0.2, 0.3 mm/t) during the tool rotation and Fig. 4(b) indicates the measured cutting force converted into a linear expression relating to the feed rate calculated by Eq. (10). For example, the extracted points indicated by circles and triangles at φ0, φ1 in Fig. 4(a) are expressed as a linear regression line, as shown in Fig. 4(b). The slope and intercept of the line signify the first and second terms of the right side of Eq. (10), respectively. Then, the cutting coefficients can be calculated by Eq. (11). Figure 5 shows the calculation results of the cutting coefficients at ap = 0.5 mm from the measurement data shown in Fig. 4(a). Here, to avoid noise owing to unstable uncut chip thickness when the tool edge starts cutting or exits from the workpiece, the cutting force coefficients are identified using the average coefficients when φ = 30
150°, as
shown in the figure. As these coefficients depend on the axial depth of the cut, they are determined as a function of the maximum axial depth of the cut: TRU = V ∙ OWM, V4
(i = t,r,c, j = c,e),
(12)
where C0 and C1 are linear regression constants determined by each cutting coefficient at ap = 0.5, 1.0, and 1.5 mm (Table 2).
(a) Measured cutting force
(b) Linear regression of measured cutting force
Fig. 4 Calculation of cutting force coefficient (e.g., ap = 0.5 mm).
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Fig. 5 Identification of cutting force coefficient (e.g., ap = 0.5 mm). Table 2 Cutting force coefficients.
Krc
Ktc
Kac
Kre
Kte
Kae
N/m2
N/m2
N/m2
N/m
N/m
N/m
C0
–483.2
–266.7
58.8
–12.0
8.2
20.8
C1
936.2
2310.6
616.8
52.7
23.4
20.7
3
Point cloud simulation model to predict the cutting force in face milling
3.1 Point cloud simulation model We validated the identified coefficients by comparing the cutting test results in groove milling on a flat surface, as shown in Fig. 3(a). Here, a point cloud simulation model that expresses the tool and workpiece as points was used to predict the cutting force. This simulation method can not only analyze a flat surface but also analyze a 3D curved surface with a simple vector analysis. Therefore, it is easy to analyze any freeform shape by placing the point cloud in the initial material shape. Moreover, it is suitable for time-domain analysis with a short time interval. Figure 6(a) shows the point cloud simulation model in face milling and a schematic view of the contact area between the tool and workpiece. The material, which has a thickness Hw, width Ww, and length Lw, is equally divided by the grid using dxw, dyw, and dzw along the x, y, and z directions of the material, respectively. The points of a point cloud are generated at the divided grid points such that the workpiece shape is expressed by the point cloud model. The cutting edge profile of the radius end mill is a circle with radius RI, and the cutting edge is equally divided by a minute angle dκ. Then, 10 / 29
the inserted body is represented using a point cloud with a thickness of dφ. Interferences between the tool body and the removing part are judged on the basis of the vector calculation, as shown in Fig. 6(b), where points Aj and Bj constitute the point cloud model of the workpiece and the point arranged at an equal interval on the tool edge, respectively. When calculating the uncut chip thickness fr, if the cutting edge of the rotating tool enters the workpiece point cloud and causes interference between the tool and workpiece, a pair of points (Aj in the workpiece and Bj on the cutting edge) is identified
YYYYYZX can then be expressed using the (described later). The uncut chip thickness vector
normalized vector YYYZ, [ which is a unit vector normal to the cutting edge at each point Bj ,
3X 8X , which is a vector connecting point Aj on the workpiece and the interfered vector YYYYYYYYZ
surface and point Bj on the cutting edge, as YYYYYYYYYZ YYYYZ)a \]YYZ^ = (_ = c, d, e … ^ `^ ∙ a ^ YYYYZ b ^
(13)
The detailed steps to determine the pair of points Aj and Bj, and the uncut chip thickness, are as follows (see Fig. 6(b)). First, the nearest point Bj on the tool edge to the interfered point Aj of the workpiece is searched by comparing the distance between the two points. The idea here is to find candidates for the pair Aj and Bj to define the uncut chip thickness. For instance, points Aj1, Aj2, and Aj3 are selected as candidates to pair with Bj in this case. Next, as shown in Eq. (13), vector calculation is conducted for each pair, and the uncut chip thicknesses YYYYYYYYYYZg, g YYYYYYYYYYZg, and g YYYYYYYYYYZg are obtained. The largest one is the nearest approximation to the g X4
X5
Xh
YYYYYYYYYYZg at Aj2; it is chosen as the uncut chip thickness at Bj actual uncut chip thickness g X5
in this case. This process is repeated for each point of the cutting edge to determine the distribution of the uncut chip thickness along the cutting edge. Differential cutting forces on each tool edge point in face milling can be determined
YYYZ and Eq. (5), and the time-series differential cutting force of the radius end mill using
can be calculated by considering the sum of the differential cutting forces in each time step. In this simulation, the resolution of the point cloud needs to be configured properly because accuracy and efficiency are in a trade-off relationship. Thus, the division size of
dxw, dyw on the tool rotation plane should be set to less than the feed per tooth, and the resolution size of dzw should be set to less than at least 1/10th of the axial depth of the cut.
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(a) Overview of face milling simulation geometry with the point cloud method
(b) Point cloud simulation model and methodology for calculating uncut chip thickness Fig. 6 Cutting force simulation model using point cloud method for face milling with a corner radius end mill. 3.2 Validation of the cutting force coefficient and simulation model Figure 7(a) compares the predicted cutting forces to the measured forces at ap =1.0 mm, fr0 = 0.1 mm/tooth, and 0.3 mm/tooth. Here, because this experiment was conducted under the one flute condition, the effect of tool run-out was generally negligible. Fig. 7(b) shows the maximum and average cutting forces on each axis under the conditions shown in Table 1. The results of the analysis of the cutting force are in accordance with the experimental results. Moreover, the maximum and average cutting forces under several conditions are also in accordance with the experimental results shown in Fig. 7(b), which demonstrates that the proposed identification method and the identified cutting force coefficients in Table 2 are suitable for the simulation. The
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coefficients obtained here and the proposed simulation model are used in a turn milling simulation, as discussed in the next section.
(a) Measured and predicted cutting force (e.g. ap = 1.0 mm, fr0 = 0.1 mm/t)
(b) Predicted and measured maximum and average cutting forces for the conditions given in Table 1 Fig. 7 Comparison of analytical cutting force and measured cutting force.
4
Analytical prediction model for turn milling simulation
4.1 Turn milling simulation model In the turn milling process, several parameters are determined by the tool and workpiece geometrical shape, tool posture, and cutting conditions, as shown in Fig. 8. Parameters such as tool rotation speed St, workpiece rotation speed Sw, tool axis lead and tilt angle α, β, and tool feed rate FRz directly affect the cutting situation. Here, we
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define an axial depth of the cut (ap) and radial depth of the cut (ar), as shown in the figure. The feed speed of the tool on the Z-axis per workpiece rotation is defined as FRz =
ap /sin(β ). The angle between the center point of the tool and the rotational center point of the workpiece is defined as the lead angle α, which is determined by the tool offset e. The clockwise and counter-clockwise rotations of the workpiece from the view of the end face of the workpiece are defined as CW and CCW.
Fig. 8 Schematic view and parameters of turn milling. Figure 9(a) shows the simulation model used with the point cloud method. In this analysis, we defined various parameters of turn milling, including lead angle α, tilt angle β, cutting speed V (rotational speed St), and tool feed rate fr0. The lead angle α is the tool inclination angle against the line connecting the workpiece center and the tool tip center along the xy plane. The tilt angle β is the tool inclination angle along the xz plane. These parameters correspond to the settings of the machining conditions and the machine tool. As the tool axis cannot be inclined along the xy plane on the equipment used in the experiment, the tool offset e in the y direction was used to establish the same situation in order to set the tool lead angle α. Here, the lead angle is expressed as
i = tan l /m by using the tool center y coordinate and the tool offset.
The point cloud model of the workpiece and tool in this analysis is established using
the same method as that for the face milling model, as shown in Fig. 6. The work material is defined to be of a cylinder with a diameter D0. Point clouds are arranged on grids divided into small angles dφw in the circumferential direction and small lengths
dzw in the axial direction to express the surface shape of the cylindrical material. Here, the changes to the work material shape after machining are determined by placing a new point cloud on the machined surface after passing the tool edge. The tool insert
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shape is defined using the same rule as that shown in Fig. 6. Figure 9(b) shows the contact area between the tool and the workpiece during turn milling, along with a schematic view of the uncut chip thickness determined using the point cloud model. One of the special features of turn milling is that the contact state between the tool and the work material changes significantly during one rotation of the tool, and it also largely depends on the tool posture, namely, the tilt angle and lead angle. As the contact state changes significantly in the turn milling process, it is challenging to express the transition of the contact state analytically based on geometrical relationships. According to the analytical method using the point cloud model, it is easy to express the complex contact state between the tool and the workpiece, as well as the uncut chip thickness at each simulation step in the turn mill process, by means of only the normalized normal vector and the interfered vector (Eq. (13)). Moreover, the machined surface shape can be determined more accurately compared with the general voxel model because a new point cloud is set on the machined surface along the tool path after passing the tool edge. These are the advantages of the proposed point cloud model. In addition, this method can be applied not only to a simple cylindrical workpiece shape shown here but also to freeform surface shapes such as turbine blades because the point cloud model can be tailored to the initial material shape. The tool and workpiece coordinates are as follows: no ′ = pqo$
ro$
so$ tu ,
nv ′ pqv rv svtu
(14)
where Xt and Xw are the coordinates of the tool and workpiece at the original coordinate
O at t = 0 [s], respectively. After coordinate conversion, the tool and workpiece coordinates in turn milling at time t [s] are as follows no w, x yo]zo ∙ y{ ∙ y| ∙ n$o }o ,
nv w, x yv]zo ∙ nv ′
where Rtrot, Ra, Rb, and Rwrot are the rotational matrices defined as
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(15)
yo]zo
1 0 0 = 0 cos x )sin x , 0 sin x cos x
cos i )sin i 0 y| sin i cos i 0 , 0 0 1
yv]zo
cos x~ )sin x~ 0 sin x~ cos x~ 0 0 0 1
(16)
cos 0 )sin 1 0 y{ 0 sin 0 cos
The workpiece rotation speed is defined as no w, x yo]zo ∙ y{ ∙ y| ∙ n$o }o ,
nv w, x yv]zo ∙ nv ′
(17)
where it is necessary to obtain the tool center position Ot (xt0, yt0, zt0) in advance to satisfy the tool posture (lead and tilt angles α, β), the axial depth of cut ap, and the radial depth of cut ar. However, contact between the inclined tool and the cylindrical surface of the workpiece is complex, which makes it difficult to obtain a coordinate Ot uniquely. Therefore, the tool center coordinate Ot is calculated by convergent calculation, which moves Ot from an initial position Ot'(xt0, yt0, zt0) to a position at which the tool outer face comes into contact with the workpiece outer face, as shown in Fig. 9(c). In this study, we evaluate the validity of the proposed simulation method by comparing the simulated cutting forces with the experimental forces when the lead angle α and the tilt angle β are given simultaneously. In addition, we clarify the optimal tool posture for ensuring minimum resultant force.
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(a) Overview of turn milling simulation geometry
(b) Point cloud simulation model and methodology for turn milling
(c) Definition of initial tool center position by convergent calculation Fig. 9 Turn milling simulation model using the point cloud method.
4.2 Experimental validation of the turn milling simulation model Figure 10(a) provides an overview of the experimental setup, featuring a one flute radius end mill with a 50-mm diameter attached to a 10-mm diameter round insert, for the turn milling of a cylindrical stainless steel SUS304 workpiece. The workpiece was attached to a MAZAK INTEGREX i-200 multi-tasking machine. The cutting forces on each axis in the tool coordinate system were measured using a Kistler 9125 rotary dynamometer under several cutting conditions (listed in Table 3(I)). The axial depth of cut ap and the radial depth of cut ar are defined based on the milling, and they were set as 0.5 mm and 25 mm, respectively. Then, the finished workpiece diameter after turn milling differs based on β.
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(a) Setup for cutting force validation
(b) Cutting tool and insert geometry
Fig. 10 Experimental setup for validation of turn milling with the tool given a lead and tilt angle simultaneously.
Table 3 Turn milling conditions; (I)Experimental conditions for cutting force validation, (II)Simulation conditions for evaluation of the effect of the tool posture.
Workpiece material Number of flutes
V
fr0
depth
SUS304
SUS304
1
5
5
5
200
200
mm
Cutting velocity
Axial
(II)
Nt
Nose radius r
Feed rate
(I)
m/min mm/tooth
of
cut
ap Radial depth of cut ar
(a)0.129, (b)0.204 (c)0.311, (d)0.516
0.1
mm
0.5
0.5
mm
25
25
Down
Down
Cutting direction Work diameter D
mm
100
100
Tool diameter
mm
50
50
°
-35
-35, -45, -60
Lead angle
α
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Tilt angle
β
°
(a)15, (b)30, (c)45, (d)60
15, 30, 45, 60
The validation results of the predicted cutting forces are provided in Fig. 11. In this experiment, we evaluate the resultant forces Fxy, Fxyz, and a tool rotational axis force Fz, as these forces are not related to the attached insert position against the tool rotary coordinate system. The predicted and experimentally measured cutting forces with several different tool postures are in agreement with each other, as shown in the figure, despite the fact that the cutting force coefficients were assumed to be constant, as mentioned in section 2. It follows that the effect of the tool radius on the cutting force in the turn mill with the corner radius end mill was small, because the center of the cutting tool is not used in the corner radius end mill, unlike that of the ball-end mill; as such, the changes in the cutting speed on the tool edge were small. Here, the cutting force must become zero during the air cut, but the measured cutting forces in Fxy and Fxyz were not zero. This is because the low stiffness of the long tool holder, due to a limitation of the dynamometer structure, caused the tool to vibrate in only the XY plane of the tool rotary coordinate system after the tool insert exited from the workpiece. This vibration affected the cutting forces in Fx and Fy during the air cut period, as shown in Fig. 12; as a result, Fxy and Fxyz were not zero. However, no chatter vibration occurred while the tool was in contact with the workpiece because normal finishing surfaces were obtained, as shown in Fig. 13; thus, stable cutting could be implemented in this cutting test. The validity of the proposed method was confirmed from the above cutting force test results. In the next section, the effect of the tool posture when varying the lead angle α and tilt angle β using the proposed simulation method for the cutting force is discussed.
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Fig. 11 Measured and predicted cutting force at different inclination angles β under the conditions given in Table 3(I).
Fig. 12 Vibration of measured cutting force at (d) α = 35°, β = 60°, as shown in Fig. 11.
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Fig. 13 Machined surface with turn milling. 4.3 Effect of the tool posture on cutting force In this evaluation, we examined the effect of the tool posture on the cutting forces Fz,
Fxy, and Fxyz while varying the lead and tilt angles as shown in Table 3(II); other cutting conditions were the same and the MRR was kept constant. Both the average and maximum cutting forces were evaluated as the average cutting forces affect the roughness and stability limit of the chatter vibration and the maximum cutting forces affect tool wear and failure. Figure 14 shows the average cutting forces ((1) ~ (3)) and the maximum cutting forces ((4) ~ (6)) extracted from the time-dependent simulated force. The absolute average axial force |Fz| did not change when the tool lead and tilt angle were varied, while, in contrast, the average resultant forces Fxy and Fxyz did change with the tool lead angle. At the same time, under the conditions of both minimum P1 and maximum P2 values of |Fz|, Fxy and Fxyz in Fig. 14(b), the opposite tendency against Fig. 14(a) occurred. The predicted forces under P1 and P2 are shown in Fig. 15. As shown in Fig. 15(P1), |Fz|,
Fxy and Fxyz have trapezoidal wave shapes, presumably because the tool always comes into contact with the workpiece as the cutting force does not return to zero. The transitions of the contact area between tool and workpiece during a tool rotation under conditions P1 and P2 are shown in Fig. 16. Here, the horizontal and vertical axis represent tool rotation angle φ and the contact angle κ between the tool and the workpiece, respectively. According to Fig. 16 (P1; trapezoidal shape), the tool first comes into contact with the workpiece at around φ=45°, and the contact area gradually increases from φ =60° to about 110°. Then, the area suddenly reduces until the end of contact at about φ =125°. In addition, the contact rotation angle φP1 (=80°) is larger than the cutter pitch angle (=72°). Thus, the tool always comes into contact with the workpiece because the cutting force with a trapezoidal shape does not return to zero. Therefore, the cutting forces have trapezoidal wave shapes under P1. In contrast, Fxy and Fxyz under P2 have sharp triangular wave shapes and return to zero after reaching the maximum force, as shown in Fig. 15(P2). In Fig. 16 (P2;
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triangular shape), the tool first comes into contact with the workpiece at around φ=75°, and the contact area exponentially increases to about 117°. Then, the area suddenly reduces until the end of a contact at approximately φ =125°. In addition, φP2 (=50°) under P2 was smaller than the cutter pitch angle, such that each tool edge disengaged after cutting as the cutting force with the triangular shape returned to zero. Therefore, the cutting forces have triangular wave shapes under P2. Therefore, the average resultant cutting force Fxyz under P1 is higher than that in intermittent cutting at P2 because continuous cutting is conducted under P1 and the cutting force does not become zero, but the maximum cutting force under P1 is smaller than that under P2. Specifically, the maximum Fxyz under P2 is approximately 1.7 times higher than that under P1. Moreover, as an overall tendency, the average resultant cutting force Fxyz decreases with an increase of the lead angle, but the tilt angle does not have a big effect on the forces. In contrast, the maximum resultant cutting force Fxyz increases with an increase of the lead angle. This is because the contact area between the tool and the workpiece moves from the bottom side to the outer side on the cutting edge of the round insert as the lead angle increases. Therefore, the axial cutting force coefficients kac and kae increase in proportion to the axial depth of cut ap as shown in Eq. (12). As a result, the maximum axial cutting force Fz under P2 increases as shown in Fig. 15(P2). According to these results, the tool posture defined by the lead and tilt angles of the cutting tool has a strong effect on the cutting forces on each axis in the turn milling process; this is particularly true in the case of the lead angle. In addition, the average and maximum cutting forces change depending on the tool posture even though the efficient does not change.
(a) Average cutting force
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(b) Maximum cutting force Fig. 14 Effect of tool posture on cutting force in several tool postures under the conditions given in Table 3(II).
(P1) Cutting force (α =35°, β = 15°)
(P2) Cutting force (α =60°, β = 15°) Fig. 15 Comparison of maximum and minimum cutting forces under conditions P1 and P2 in Fig. 14.
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Fig. 16 Transition of contact area between the tool and workpiece during tool rotation under P1 and P2 shown in Fig. 14.
5
Conclusion Turn milling with a 5-axis multi-tasking machine significantly differs from
conventional face milling due to the complicated contact state between the tool and workpiece, where the tool rotational axis is inclined against the workpiece rotational axis and both the inclined cutter and workpiece are rotated simultaneously. Particularly, in this case, it is more difficult to predict cutting forces in several tool postures with the tool given a lead and a tilt angle simultaneously compared with the case of orthogonal turn milling, as reported in previous papers. This study developed a flexible simulation methodology for turn milling based on the interference between the tool and point cloud of the workpiece, that can predict cutting forces in various tool postures with lead and tilt angles. It can also consider the involvement of multiple cutting edge at the same time. Experiments with several different tool postures were performed to evaluate the predicted cutting forces. The main results are summarized as follows. (1) In the proposed point cloud method, an uncut chip thickness in the turn mill can be defined by means of a simple vector calculation with the normal vector of the tool edge and the interfered vector that is directed from the interfered work piece surface point to the point on the cutting edge. Moreover, the machined surface shape can be redefined more accurately and compared with the general voxel simulation model because a new point cloud is set on the machined surface along the tool path after passing the tool edge. (2) According to the experimental results of the validation test, the predicted cutting forces were in agreement with the experimental forces against the change in lead and tilt angles. The cutting force in 5-axis turn milling was accurately predicted
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using the simple calculation of an uncut chip thickness and the proposed identification method for cutting coefficients. (3) From the simulation results with several tool postures under various lead and tilt angles and feed rates, it was clarified that both the average and maximum cutting forces vary even if the material removal rate is kept constant. In the case of turn milling with a small lead angle, the average resultant cutting forces Fxy and Fxyz were larger than those in the case with a large lead angle. In contrast, the maximum resultant cutting forces Fxy and Fxyz became smaller when the lead angle decreased. This is because the cutting force wave form at small lead angles is trapezoidal, presumably because the cutting force does not return to zero as the tool maintains contact with the workpiece. In contrast, the cutting force wave form at the large lead angle resembles a sharp triangle and returns to zero after every cutting edge exit from the workpiece. According to these results, the tool posture defined by the lead and tilt angles of the cutting tool has a strong effect on the cutting forces in the turn milling process; this phenomenon is especially evident in the case of the lead angle. In addition, the average and maximum cutting forces change depending on the tool posture even though the cutting efficiency remains the same. In our future work, we will apply the proposed simulation method to more complicated work materials (such as turbine blades) and investigate the effect of tool posture on tool wear and chatter vibration.
Nomenclature S, V
Spindle and cutting speed
C 0, C 1
Constants of the linear regression
fr0
Feed per tooth
Aj
Point on the tool
ft
Uncut chip thickness
Bj
Point on the workpiece
ap
Axial depth of cut
djw
Division size of workpiece (j=x,y,z)
φ, κ
Radial and axial immersion angles
St
Tool rotation speed
dκ
Angle of discrete element
Sw
Workpiece rotation speed
dS
Differential edge length
FRz
Axial feed rate
Kic, Kie Cutting and edge force coefficients (i = t,r,a) ar
Radius depth of cut
α, β
Lead and tilt angle
e
Tool offset
dFi(j)
Differential cutting force (j=x,y,z)
D 0, D 1
Diameter
of
unmachined
machined workpiece
25 / 29
and
RI
Radius of rounded insert
Xt, Xw
Km
Maximum axial immersion angle
Rkrot, Rl Rotational matrix (k=t,w)(l=a,b)
κst, κex
Angular engagement limit
Ot
Tool and workpiece coordinates
Tool center position
References [1] A. Shokrani, V. Dhokia, and S.T. Newman, Environmentally conscious machining of difficult-to-machine materials with regard to cutting fluids, Int. J. Mach. Tools Manuf. 57 (2012) 83–101. [2] U. Karaguzel, U. Olgun, E. Budak, and M. Bakkal, High performance turning of high temperature alloys on multi-tasking machine tools, New Production Technologies in Aerospace Industry (2014) 1–9. [3] H. Schulz and G. Spur, High speed turn-milling: A new precision manufacturing technology for the machining of rotationally symmetrical workpieces, CIRP Ann. Manuf. Technol. 39 (1990) 107–109. [4] H. Schulz and G. Spur, Turn-milling of hardened steel: An alternative to turning, CIRP Ann. Manuf. Technol. 43 (1994) 93–96. [5] S. Vedat and C. Ozay, Analysis of the surface roughness of tangential turn-milling for machining with end milling cutter, J. Mater. Process. Technol. 186(1) (2007) 279–283. [6] J. Kopac and M. Pogacnik, Theory and practice of achieving quality surface in turn milling, Int. J. Mach. Tools Manuf. 37(5) (1997) 709–715. [7] S.K. Choudhury and K.S. Mangrulkar, Investigation of orthogonal turn milling for the machining of rotationally symmetrical workpieces. J. Mater. Process. Technol. 99 (2000) 120–128. [8] S.K. Choudhury and J.B. Bajpai, Investigation in orthogonal turn-milling towards better surface finish, J. Mater. Process. Technol. 170 (3) (2005) 487–493. [9] S.M. Yuan and W.W. Zheng, The surface roughness modeling on turn-milling process and analysis of influencing factors, Appl. Mech. Mater. 117 (2012) 1614– 1620. [10] C. Filho and J. Martins, Prediction of cutting forces in mill turning through process simulation using a five-axis machining center, Int. J. Adv. Manuf. Technol. 58(1–4) (2012) 71–80. [11] U. Karagüzel, E. Uysal, E. Budak, and M. Bakkal, Analytical modeling of turn-milling process geometry, kinematics and mechanics, Int. J. Mach. Tools Manuf. 91 (2015) 24–33. 26 / 29
[12] M. E. Kara and E. Budak, Optimization of Turn-milling Processes, Procedia CIRP 33 (2015) 476–483. [13] L. Zhu, H. Li, and C. Liu, Analytical modeling on 3D chip formation of rotary surface in orthogonal turn-milling, Archives of Civil and Mechanical Eng. 16(4) (2016) 590–604. [14] A. Comak and Y. Altintas, Mechanics of turn-milling operations, Int. J. Mach. Tool. Manuf. 121 (2017) 2–9. [15] T. Sun, L. Qin, Y. Fu, and J. Hou, Chatter stability of orthogonal turn-milling analyzed by complete discretization method. Prec. Eng. 3 (2018). [16] S. Kaibu, A. Ikeda, and Y. Ihara, Study on Cutting Marks by Turn Mill Process, Procedia CIRP. 77 (2018) 251–254. [17] J. Gradisek, M. Kalveram, and K. Weinert, Mechanistic identification of specific force coefficients for a general endmill. Int. J. Mach. Tools Manuf. 44 (2004) 401– 414. [18] G. Ge, W. Baohai, Z. Dinghua, and L. Ming, Mechanistic identification of cutting force coefficients in bull-nose milling process, C. J. Aero. 26 (2013) 823–830. [19] P. Lee and Y. Altintaş, Prediction of ball-end milling forces from orthogonal cutting data, Int. J. Mach. Tools Manuf. 36 (1996) 1059–1072. [20] E. Layegh, I. Lazoglu, A New Identification Method of Specific Cutting Coefficients for Ball End Milling, Procedia CIRP, 14 (2014) 182–187. [21] T. Özel and X. Liu, Investigations on Mechanics-Based Process Planning of Micro-End Milling in Machining Mold Cavities, Mater. Manuf. Process. 24(2009) 1274–1281. [22] E. Ozturk, L. T. Tunc, E. Budak, Investigation of lead and tilt angle effects in 5-axis ball-end milling processes, Int. J. Mach. Tools Manuf. 49 (2009) 1053–1062. [23] U. Karaguzel, E. Uysal, E. Budak and M. Bakkal, Effects of tool axis offset in turn-milling process, J. Mater. Process. Technol. 231 (2016) 239–247. [24] H. O. Ortega, P. A. Osoro and P. J. A. Arriola, Analytical modeling of the uncut chip geometry to predict cutting forces in orthogonal centric turn-milling operations. Int. J. Mach. Tools Manuf. 144 (2019) 103428.
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List of figures Fig. 1 Definition of lead and tilt angles in turn milling Fig. 2 Experimental setup for identification of cutting coefficients by radius end mill. Fig. 3 Cutting force analytical model of the radius end mill. (a) Cutting force simulation model with radius end mill (b) Differential cutting force model on the cutting edge at point P Fig. 4 Calculation of cutting force coefficient (e.g., ap = 0.5 mm). (a) Measured cutting force (b) Linear regression of measured cutting force Fig. 5 Identification of cutting force coefficient (e.g., ap = 0.5 mm). Fig. 6 Cutting force simulation model using point cloud method for face milling with a corner radius end mill. (a) Overview of face milling simulation geometry with the point cloud method (b) Point cloud simulation model and methodology for calculating uncut chip thickness Fig. 7 Comparison of analytical cutting force and measured cutting force. (a) Measured and predicted cutting force (e.g. ap = 1.0 mm, fr0 = 0.1 mm/t) (b) Predicted and measured maximum and average cutting forces for the conditions given in Table 1 Fig. 8 Schematic view and parameters of turn milling. Fig. 9 Turn milling simulation model using the point cloud method. (a) Overview of turn milling simulation geometry (b) Point cloud simulation model and methodology for turn milling (c) Definition of initial tool center position by convergent calculation Fig. 10 Experimental setup for validation of turn milling with the tool given a lead and tilt angle simultaneously. (a) Setup for cutting force validation
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(b) Cutting tool and insert geometry Fig. 11 Measured and predicted cutting force at different inclination angles β under the conditions given in Table 3(I). Fig. 12 Vibration of measured cutting force at (d) α = 35°, β = 60°, as shown in Fig. 11. Fig. 13 Machined surface with turn milling. Fig. 14 Effect of tool posture on cutting force in several tool postures under the conditions given in Table 3(II). (a) Average cutting force (b) Maximum cutting force Fig. 15 Comparison of maximum and minimum cutting forces under conditions P1 and P2 in Fig. 14. (P1) Cutting force (α =35°, β = 15°) (P2) Cutting force (α =60°, β = 15°) Fig. 16 Transition of contact area between the tool and workpiece during tool rotation under P1 and P2 shown in Fig. 14.
29 / 29
We would like to show my greatest appreciation to members of our laboratory whose comments and suggestions were of inestimable value for my study.
1
Table 1 Face milling test conditions.
S [rpm]
ft [rpm]
(V [m/min]) 1990
ap [mm] 0.5, 1.0,
0.1–0.3
(200)
1.5
Table 2 Cutting force coefficients.
Krc
Ktc
Kac
Kre
Kte
Kae
N/m2
N/m2
N/m2
N/m
N/m
N/m
C0
–483.2
–266.7
58.8
–12.0
8.2
20.8
C1
936.2
2310.6
616.8
52.7
23.4
20.7
Table 3 Experimental conditions for cutting force validation.
Workpiece material Number of flutes
Nt
Nose radius r
mm
Cutting velocity Feed rate Axial
V
fr0
depth
m/min mm/tooth
of
cut
ap Radial depth of cut ar
(I)
(II)
SUS304
SUS304
1
5
5
5
200
200
(a)0.129, (b)0.204 (c)0.311, (d)0.516
0.1
mm
0.5
0.5
mm
25
25
Down
Down
Cutting direction Work diameter D
mm
100
100
Tool diameter
mm
50
50
°
-35
-35, -45, -60
α
Lead angle Tilt angle
β
°
(a)15, (b)30, (c)45, (d)60
1
15, 30, 45, 60
Fig. 1 Definition of the lead and tilt angle in turn milling
Fig. 2 Experimental setup for identification of cutting coefficient by radius end mill.
(a) Cutting force simulation model with radius end mill
1
(b) Differential cutting force model on the cutting edge at point P Fig. 3 Cutting force analytical model of the radius end mill.
(a) Measured cutting force
(b) Linear regression of measured cutting force
Fig. 4 Calculation of cutting force coefficient (e.g., ap = 0.5 mm).
2
Fig. 5 Identification of cutting force coefficient (e.g., ap = 0.5 mm).
(a) Overview of face milling simulation geometry with the point cloud method
3
(b) Point cloud simulation model and methodology for calculating uncut chip thickness Fig. 6 Cutting force simulation model using point cloud method for face milling with a corner radius end mill.
(a) Measured and predicted cutting force (e.g. ap = 1.0 mm, fr0 = 0.1 mm/t)
4
(b) Predicted and measured maximum and average cutting forces for the conditions given in Table 1 Fig. 7 Comparison of analytical cutting force and measured cutting force.
Fig. 8 Schematic view and parameters of turn milling.
(a) Overview of turn milling simulation geometry 5
(b) Point cloud simulation model and methodology for turn milling
(c) Definition of initial tool center position by convergent calculation Fig. 9 Turn milling simulation model using the point cloud method.
(a) Setup for cutting force validation
(b) Cutting tool and insert geometry
Fig. 10 Experimental setup for validation of turn milling with the tool given a lead and tilt angle simultaneously.
6
Fig. 11 Measured and predicted cutting force at different inclination angles β under the conditions given in Table 3(I).
Fig. 12 Vibration of measured cutting force at (d) α = 35°, β = 60° in Fig. 11.
7
Fig. 13 Machined surface with turn milling.
(a) Average cutting force
(b) Maximum cutting force Fig. 14 Effect of tool posture on cutting force in several tool postures under the conditions given in Table 3(II).
8
(P1) Cutting force (α =35°, β = 15°)
(P2) Cutting force (α =60°, β = 15°) Fig. 15 Comparison of maximum and minimum cutting forces under conditions P1 and P2 in Fig. 14.
Fig. 16 Transition of contact area between the tool and workpiece during tool rotation under P1 and P2 shown in Fig. 14.
9
Highlights
A turn milling simulation method to predict the cutting force by using a point cloud modeling was proposed.
The predicted cutting forces in turn milling at various tool postures with lead and tilt angles agreed with experimental results.
Cutting force in turn milling can be minimized by selecting appropriate tool posture keeping MRR.
S0890-6955(19)30490-0
DOI:
https://doi.org/10.1016/j.ijmachtools.2019.103511
Reference:
MTM 103511
To appear in:
International Journal of Machine Tools and Manufacture
Received Date: 1 May 2019 Revised Date:
24 November 2019
Accepted Date: 25 November 2019
Please cite this article as: K. Utsumi, S. Shichiri, H. Sasahara, Determining the effect of tool posture on cutting force in a turn milling process using an analytical prediction model, International Journal of Machine Tools and Manufacture (2019), doi: https://doi.org/10.1016/j.ijmachtools.2019.103511. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
Determining the effect of tool posture on cutting force in a turn milling process using an analytical prediction model
Koji UTSUMIa, Shoki SHICHIRIb, Hiroyuki SASAHARAb
a Research
& Development Group, Hitachi, Ltd., 292 Yoshida-cho, Totsuka-ku,
Yokohama-shi, Kanagawa, 244–0817, JAPAN
b Department
of Mechanical Systems Engineering, Tokyo University of Agriculture and
Technology, 2-24-16 Naka-cho, Koganei-shi, Tokyo 184–8588, JAPAN
Corresponding author: Koji Utsumi E-mail address of the corresponding author: [email protected]
1
Determining the effect of tool posture on cutting force in a turn milling process using an analytical prediction model Koji UTSUMIa, Shoki SHICHIRIb, Hiroyuki SASAHARAb a Research
& Development Group, Hitachi, Ltd., 292 Yoshida-cho, Totsuka-ku,
Yokohama-shi, Kanagawa, 244–0817, JAPAN b Department
of Mechanical Systems Engineering, Tokyo University of Agriculture and
Technology, 2-24-16 Naka-cho, Koganei-shi, Tokyo 184–8588, JAPAN Corresponding author: Koji Utsumi E-mail address of corresponding author: [email protected] Abstract Turn milling is a key technique that can be used to achieve high-efficiency machining and improve life of tools used for difficult-to-cut materials because intermittent cutting with multiple cutting edges can suppress a rise in temperature compared with conventional turning. However, the contact condition between the rotary tool and the cylindrical workpiece varies significantly depending on the tool posture, which is defined by the tool axis inclination angles against the workpiece: namely, lead and tilt angles. Thus, clarifying the effect of the lead and tilt angles on cutting forces in turn milling is essential for determining the optimal tool posture. In this paper, we propose a simulation model to predict the cutting force for 5-axis turn milling considering the contact behavior between the tool and workpiece depending on the tool posture. The workpiece is modeled as a point cloud and any points that interfere with the tool volume are removed when the tool edge passes the surface of the workpiece. We examined the simulated cutting forces using a radius end mill as a linear function of the uncut chip thickness and found that the predicted cutting forces were in agreement with the experimental results for several combinations of tool postures and feed rates. We also clarified that the tool posture significantly affects the maximum cutting force, which varies even if the material removal rate is maintained at a constant value in the turn milling process. Keywords: Turn milling, Machining simulation, Cutting force, Tool posture
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1
Introduction Machining productivity when working with difficult-to-cut materials such as super
heat-resistant alloys used in the industrial fields of aeronautics, nuclear power, and medicine is generally low because of the short tool life caused by high cutting temperatures, high cutting forces, and low chip disposability [1]. Turn milling, which can generate separated chips due to its interrupted cutting, has attracted interest as a relatively new machining strategy. In this process, tool wear and cutting temperature are decreased by using multiple cutting edges with interrupted cuts, which results in small chips and a low tool temperature [2]. Moreover, turn milling can be applied to machine free-form surfaces such as turbine blades because it has a higher degree of freedom in the cutting tool posture motion. In an academic study started in the 1990s by Schulz et al. [3], two categories of turn milling operations were introduced: orthogonal and axial turn milling. This study also investigated surface quality in the high-speed turn milling of the roller bearing components made of steel; the results showed that surface quality obtained by turn milling is better than that obtained by conventional turning. In another study, kinematic conditions and their influence on tool design and choice of technological parameters were investigated [4]. Another study regarding surface finish quality was conducted by Vedat et al. [5], who analyzed the surface roughness in tangential turn milling and found that it achieved a high-precision surface comparable to grinding. Considering the efficiency of the material removal rate (MRR), Kopac et al. [6] found that it was possible to achieve a thirty times higher MRR by turn milling with a small radius end mill than with the recommended cutting conditions in turning. Choudhury et al. [7] studied the effect of parameters such as spindle speed and feed rate on the surface quality and found that a ten times better surface quality could be achieved by turn milling compared to conventional turning. They also investigated the effect of various parameters such as the end mill tool shape, axial depth of cut, and workpiece rotational speed on surface quality in tangential turn milling and found that a higher quality surface could be achieved by turn milling than by the conventional milling process [8]. With respect to simulation research, Yuan and Zheng developed a geometric model of turn milling operation to predict the surface roughness and studied the effects of various turn milling parameters [9]. Filho et al. proposed a numerical cutting simulation model of turn milling and validated it through a comparison of the simulation and experimental test results [10]. Karaguzel et al. and Kara et al.
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investigated a simulation model for orthogonal, tangential, and co-axial turn milling operations to predict the cutting force and verified the model using experiments. Specifically, the cutting force calculated by the proposed model was in accordance with the simulation results, with an error of less than under different cutting parameter conditions [11][12]. Zhu et al., H. O. Ortega et al., and U. Karaguzel et al. also proposed another simulation model based on the formulation of an uncut chip shape considering various kinematics in orthogonal turn milling [13][23][24]. Comak et al. proposed an approach to predict cutting force, torque, and consumption power based on a model of generalized chip thickness distribution as a function of linear feed drive motions, tool, and workpiece spindle rotations [14]. Sun et al. proposed a stability model for orthogonal turn milling that could obtain stability lobe diagrams using a complete discretization technique based on the Eulerian method [15]. In another approach for surface finish prediction, Kaibu et al. proposed a simulation method for cutting textures with 3D-CAD considering the tool lead and tilt angle. Here, the tilt angle was considered to be the inclination of the tool axis around the y-axis and the lead angle was considered the inclination around the z-axis, as shown in Fig. 1 [22]. They investigated the effect of the machining feed rate and tool shape on the texture shape and found that the prediction results were comparable with experimental results [16]. As stated above, although extensive research has been conducted on turn milling, the machining kinematics of the turn milling process are not yet fully understood because of the complicated contact condition between the tool and workpiece defined by various parameters such as the tool workpiece shape, lead and tilt angles of the milling tool axis, and cutting conditions. Most recent research has focused on kinematics in orthogonal turn milling processes; however, there are a very few published studies on the effect of both the lead and tilt angles of the milling tool axis on the cutting forces. It is important to predict the change in cutting force with respect to variation in the lead and tilt angles. In this paper, we propose a new simulation model with the point cloud method considering the lead and tilt angles of the tool. This model can be adapted to any workpiece shape and can analyze the complex contact area between the tool and workpiece along with the transition of the cutting force in the turn milling process using a radius end mill. The proposed model is experimentally validated by a cutting test under the condition that both the tilt and lead angle are simultaneously applied. We also investigated the effect of the tool posture on the change in cutting forces and demonstrated that the tool posture significantly affects the average and maximum cutting force, which varies even if the MRR is maintained at a constant value in the
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turn milling process on the basis of the proposed simulation.
Fig. 1 Definition of lead and tilt angles in turn milling. 2
Identification of cutting force and validation validation of face milling model
First, to predict the cutting force in turn milling, we measured the cutting force coefficients by a face milling test, as shown in Fig. 2. A dynamometer (KISTLER, 9257B) was attached to a 3-axis vertical machine tool and the cutting forces were measured by a grooving test using a block material of stainless steel SUS304 with a round indexable insert (5-mm radius, rake angle ranging from 5° through 8°, helix angle of 10°, ACM300 PVD coated) attached to a radius end mill with a diameter of 32 mm with one flute based on fluid cooling. The experimental conditions are listed in Table 1. The inclined dynamometer was reset to zero before each experiment in order to cancel the gravity effect.
Fig. 2 Experimental setup for identification of cutting coefficients by radius end mill. Table 1 Face milling test conditions.
S [rpm]
fr
ap
(V [m/min])
[mm/tooth]
[mm]
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1990 (200)
0.1–0.3
0.5, 1.0, 1.5
In order to obtain the cutting force coefficient, a time-average cutting force method that could be adapted not only to a square end mill but also to a ball end mill and radius end mill has been proposed [17]–[20]. However, this method considers the average cutting force including noise caused by unstable uncut chip thickness when the tool edge starts cutting or exits from the workpiece [21]. This makes it difficult to accurately identify cutting force coefficients for use in the simulation model to predict maximum forces that significantly affect tool breakage and wear. Therefore, because of the significance of predicting the maximum cutting force, an additional algorithm based on the time average cutting force model that considers the radius of the nose shape has been proposed. In this algorithm, only the cutting force waveform in the vicinity of the maximum cutting forces Fx, Fy, and Fz are extracted from the measured force time-domain data in the x, y, and z directions. Then, the cutting force coefficients are identified at each moment, along with the extracted data. The noise caused by the unstable uncut chip thickness when the tool edge starts cutting or exits from the workpiece can be ignored, which enables us to identify the cutting coefficient in the stable region accurately. The method used to obtain the coefficients and the analysis model used for cutting force identification are described as follows. Figure 3(a) provides an overview of the analytical model of the cutting coefficients for a radius end mill with one flute in grooving, and Fig. 3(b) shows the differential cutting force dFi (i = t, r, a) acting on each discretized cutting edge of the mill. The instantaneous uncut chip thickness fr’ at point P on the tool edge is defined as ′ = cos
(1)
where fr0 is the feed per tooth, and φ and κ are the radial and axial immersion angles, respectively. The differential cutting forces acting on the discretized cutting edge segment in the tool edge coordinate system are defined as in previous research [17–20]. , k , k = ′ ∙ + , k
(2)
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where Kic and Kie (i = t,r,a) are the cutting and edge force coefficients, respectively, and
= "# ∙ is the edge length of each segment. Using Eqs. (2) and (1), the differential cutting force dFi’ in the rotating tool coordinate system is formulated as
$ , k 1 0 0 $ , k = 0 '( − sin 0 sin cos $ , k
(3)
Using Eq. (3), the differential cutting forces (dFx, dFy, dFz) acting on the edge in a work-piece coordinate system can be formulated as , , k '( 0 ′ - , k = − '( 0 ′ . , k 0 0 1 ′
'( '( − sin = −'( '( '( sin 0 sin '(
(4)
From the above equation, the differential cutting forces on each segment are obtained by substituting Eqs. (2) and (1) into Eq. (4) as , , k '( − '( - , k = − '( '( '( 0 − '( − . , k '( '( − sin + −'( '( '( sin / 0 sin '(
=
01 2
(5)
34 ∙ + "# ∙ 35
where A1 and A2 are 2 2 '( 31 = 2 1 − '( 2 '( 0
1 − '( 2 1 + '( 2 − 2 1 + '( 2 2 2
6 / 29
− 1 − '( 2 2 2 2 1 + '( 2
(6a)
'( 32 = sin( ) 0
cos () −'(( ) cos() sin()
−( ) sin() cos ( ) () cos()
(6b)
Here, by assuming that the cutting force coefficient does not depend on the position of the cutting edge, the instantaneous cutting forces Fx, Fy, and Fz can be obtained by integrating Eqs. (5), (6a), and (6b) for κ as , ( ) "# - ( ) = 84 / + "# ∙ 85 / 4 . ( )
(7)
where B1 and B2 are 84 = 9
:/5
<=
34
@ 2sin(2 ) sin() ? = ? 2(1 − cos(2 )) () ? 0 > where A = K + (2)L 4
85 = 9
cos( ) 35 = sin( ) 0
:/5
<=
5
(1 − cos(2 ))A − (2 ) A
− ( ) cos (2) sin( ) sin() −cos( ) sin() − cos()
EIJ H:/5 1 (1 − cos(2 ))cos (2)D 2 C 1 − sin(2 ) cos(2) C C 2 2 ( ) A BE H< FG
sin( ) cos() IJ − cos( ) cos() sin() E H< E
FG
(8a)
=
H:/5
(8b) =
The maximum axial immersion angle km is determined by using the axial depth of cut
ap as M = N4 K1 −
OP L "#
(9)
Equation (7) indicates the instantaneous cutting forces in the X, Y, and Z directions that can be measured using a dynamometer as shown in Fig. 2. {R } = {R } + {R }
(10)
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Using Eq. (10), the measured cutting force Fi can be converted into a linear expression relating to the feed rate fr0. Therefore, the cutting coefficients can be calculated by combining Eqs. (10) and (7) as 2 = 01 84N4 {R }
4 = 01 85N4 QR S
(a) Cutting force simulation model with radius end mill
(b) Differential cutting force model on the cutting edge at point P Fig. 3 Cutting force analytical model of the radius end mill.
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11
Figure 4(a) shows the measured cutting force on each feed rate (fr0 = 0.1, 0.2, 0.3 mm/t) during the tool rotation and Fig. 4(b) indicates the measured cutting force converted into a linear expression relating to the feed rate calculated by Eq. (10). For example, the extracted points indicated by circles and triangles at φ0, φ1 in Fig. 4(a) are expressed as a linear regression line, as shown in Fig. 4(b). The slope and intercept of the line signify the first and second terms of the right side of Eq. (10), respectively. Then, the cutting coefficients can be calculated by Eq. (11). Figure 5 shows the calculation results of the cutting coefficients at ap = 0.5 mm from the measurement data shown in Fig. 4(a). Here, to avoid noise owing to unstable uncut chip thickness when the tool edge starts cutting or exits from the workpiece, the cutting force coefficients are identified using the average coefficients when φ = 30
150°, as
shown in the figure. As these coefficients depend on the axial depth of the cut, they are determined as a function of the maximum axial depth of the cut: TRU = V ∙ OWM, V4
(i = t,r,c, j = c,e),
(12)
where C0 and C1 are linear regression constants determined by each cutting coefficient at ap = 0.5, 1.0, and 1.5 mm (Table 2).
(a) Measured cutting force
(b) Linear regression of measured cutting force
Fig. 4 Calculation of cutting force coefficient (e.g., ap = 0.5 mm).
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Fig. 5 Identification of cutting force coefficient (e.g., ap = 0.5 mm). Table 2 Cutting force coefficients.
Krc
Ktc
Kac
Kre
Kte
Kae
N/m2
N/m2
N/m2
N/m
N/m
N/m
C0
–483.2
–266.7
58.8
–12.0
8.2
20.8
C1
936.2
2310.6
616.8
52.7
23.4
20.7
3
Point cloud simulation model to predict the cutting force in face milling
3.1 Point cloud simulation model We validated the identified coefficients by comparing the cutting test results in groove milling on a flat surface, as shown in Fig. 3(a). Here, a point cloud simulation model that expresses the tool and workpiece as points was used to predict the cutting force. This simulation method can not only analyze a flat surface but also analyze a 3D curved surface with a simple vector analysis. Therefore, it is easy to analyze any freeform shape by placing the point cloud in the initial material shape. Moreover, it is suitable for time-domain analysis with a short time interval. Figure 6(a) shows the point cloud simulation model in face milling and a schematic view of the contact area between the tool and workpiece. The material, which has a thickness Hw, width Ww, and length Lw, is equally divided by the grid using dxw, dyw, and dzw along the x, y, and z directions of the material, respectively. The points of a point cloud are generated at the divided grid points such that the workpiece shape is expressed by the point cloud model. The cutting edge profile of the radius end mill is a circle with radius RI, and the cutting edge is equally divided by a minute angle dκ. Then, 10 / 29
the inserted body is represented using a point cloud with a thickness of dφ. Interferences between the tool body and the removing part are judged on the basis of the vector calculation, as shown in Fig. 6(b), where points Aj and Bj constitute the point cloud model of the workpiece and the point arranged at an equal interval on the tool edge, respectively. When calculating the uncut chip thickness fr, if the cutting edge of the rotating tool enters the workpiece point cloud and causes interference between the tool and workpiece, a pair of points (Aj in the workpiece and Bj on the cutting edge) is identified
YYYYYZX can then be expressed using the (described later). The uncut chip thickness vector
normalized vector YYYZ, [ which is a unit vector normal to the cutting edge at each point Bj ,
3X 8X , which is a vector connecting point Aj on the workpiece and the interfered vector YYYYYYYYZ
surface and point Bj on the cutting edge, as YYYYYYYYYZ YYYYZ)a \]YYZ^ = (_ = c, d, e … ^ `^ ∙ a ^ YYYYZ b ^
(13)
The detailed steps to determine the pair of points Aj and Bj, and the uncut chip thickness, are as follows (see Fig. 6(b)). First, the nearest point Bj on the tool edge to the interfered point Aj of the workpiece is searched by comparing the distance between the two points. The idea here is to find candidates for the pair Aj and Bj to define the uncut chip thickness. For instance, points Aj1, Aj2, and Aj3 are selected as candidates to pair with Bj in this case. Next, as shown in Eq. (13), vector calculation is conducted for each pair, and the uncut chip thicknesses YYYYYYYYYYZg, g YYYYYYYYYYZg, and g YYYYYYYYYYZg are obtained. The largest one is the nearest approximation to the g X4
X5
Xh
YYYYYYYYYYZg at Aj2; it is chosen as the uncut chip thickness at Bj actual uncut chip thickness g X5
in this case. This process is repeated for each point of the cutting edge to determine the distribution of the uncut chip thickness along the cutting edge. Differential cutting forces on each tool edge point in face milling can be determined
YYYZ and Eq. (5), and the time-series differential cutting force of the radius end mill using
can be calculated by considering the sum of the differential cutting forces in each time step. In this simulation, the resolution of the point cloud needs to be configured properly because accuracy and efficiency are in a trade-off relationship. Thus, the division size of
dxw, dyw on the tool rotation plane should be set to less than the feed per tooth, and the resolution size of dzw should be set to less than at least 1/10th of the axial depth of the cut.
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(a) Overview of face milling simulation geometry with the point cloud method
(b) Point cloud simulation model and methodology for calculating uncut chip thickness Fig. 6 Cutting force simulation model using point cloud method for face milling with a corner radius end mill. 3.2 Validation of the cutting force coefficient and simulation model Figure 7(a) compares the predicted cutting forces to the measured forces at ap =1.0 mm, fr0 = 0.1 mm/tooth, and 0.3 mm/tooth. Here, because this experiment was conducted under the one flute condition, the effect of tool run-out was generally negligible. Fig. 7(b) shows the maximum and average cutting forces on each axis under the conditions shown in Table 1. The results of the analysis of the cutting force are in accordance with the experimental results. Moreover, the maximum and average cutting forces under several conditions are also in accordance with the experimental results shown in Fig. 7(b), which demonstrates that the proposed identification method and the identified cutting force coefficients in Table 2 are suitable for the simulation. The
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coefficients obtained here and the proposed simulation model are used in a turn milling simulation, as discussed in the next section.
(a) Measured and predicted cutting force (e.g. ap = 1.0 mm, fr0 = 0.1 mm/t)
(b) Predicted and measured maximum and average cutting forces for the conditions given in Table 1 Fig. 7 Comparison of analytical cutting force and measured cutting force.
4
Analytical prediction model for turn milling simulation
4.1 Turn milling simulation model In the turn milling process, several parameters are determined by the tool and workpiece geometrical shape, tool posture, and cutting conditions, as shown in Fig. 8. Parameters such as tool rotation speed St, workpiece rotation speed Sw, tool axis lead and tilt angle α, β, and tool feed rate FRz directly affect the cutting situation. Here, we
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define an axial depth of the cut (ap) and radial depth of the cut (ar), as shown in the figure. The feed speed of the tool on the Z-axis per workpiece rotation is defined as FRz =
ap /sin(β ). The angle between the center point of the tool and the rotational center point of the workpiece is defined as the lead angle α, which is determined by the tool offset e. The clockwise and counter-clockwise rotations of the workpiece from the view of the end face of the workpiece are defined as CW and CCW.
Fig. 8 Schematic view and parameters of turn milling. Figure 9(a) shows the simulation model used with the point cloud method. In this analysis, we defined various parameters of turn milling, including lead angle α, tilt angle β, cutting speed V (rotational speed St), and tool feed rate fr0. The lead angle α is the tool inclination angle against the line connecting the workpiece center and the tool tip center along the xy plane. The tilt angle β is the tool inclination angle along the xz plane. These parameters correspond to the settings of the machining conditions and the machine tool. As the tool axis cannot be inclined along the xy plane on the equipment used in the experiment, the tool offset e in the y direction was used to establish the same situation in order to set the tool lead angle α. Here, the lead angle is expressed as
i = tan l /m by using the tool center y coordinate and the tool offset.
The point cloud model of the workpiece and tool in this analysis is established using
the same method as that for the face milling model, as shown in Fig. 6. The work material is defined to be of a cylinder with a diameter D0. Point clouds are arranged on grids divided into small angles dφw in the circumferential direction and small lengths
dzw in the axial direction to express the surface shape of the cylindrical material. Here, the changes to the work material shape after machining are determined by placing a new point cloud on the machined surface after passing the tool edge. The tool insert
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shape is defined using the same rule as that shown in Fig. 6. Figure 9(b) shows the contact area between the tool and the workpiece during turn milling, along with a schematic view of the uncut chip thickness determined using the point cloud model. One of the special features of turn milling is that the contact state between the tool and the work material changes significantly during one rotation of the tool, and it also largely depends on the tool posture, namely, the tilt angle and lead angle. As the contact state changes significantly in the turn milling process, it is challenging to express the transition of the contact state analytically based on geometrical relationships. According to the analytical method using the point cloud model, it is easy to express the complex contact state between the tool and the workpiece, as well as the uncut chip thickness at each simulation step in the turn mill process, by means of only the normalized normal vector and the interfered vector (Eq. (13)). Moreover, the machined surface shape can be determined more accurately compared with the general voxel model because a new point cloud is set on the machined surface along the tool path after passing the tool edge. These are the advantages of the proposed point cloud model. In addition, this method can be applied not only to a simple cylindrical workpiece shape shown here but also to freeform surface shapes such as turbine blades because the point cloud model can be tailored to the initial material shape. The tool and workpiece coordinates are as follows: no ′ = pqo$
ro$
so$ tu ,
nv ′ pqv rv svtu
(14)
where Xt and Xw are the coordinates of the tool and workpiece at the original coordinate
O at t = 0 [s], respectively. After coordinate conversion, the tool and workpiece coordinates in turn milling at time t [s] are as follows no w, x yo]zo ∙ y{ ∙ y| ∙ n$o }o ,
nv w, x yv]zo ∙ nv ′
where Rtrot, Ra, Rb, and Rwrot are the rotational matrices defined as
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(15)
yo]zo
1 0 0 = 0 cos x )sin x , 0 sin x cos x
cos i )sin i 0 y| sin i cos i 0 , 0 0 1
yv]zo
cos x~ )sin x~ 0 sin x~ cos x~ 0 0 0 1
(16)
cos 0 )sin 1 0 y{ 0 sin 0 cos
The workpiece rotation speed is defined as no w, x yo]zo ∙ y{ ∙ y| ∙ n$o }o ,
nv w, x yv]zo ∙ nv ′
(17)
where it is necessary to obtain the tool center position Ot (xt0, yt0, zt0) in advance to satisfy the tool posture (lead and tilt angles α, β), the axial depth of cut ap, and the radial depth of cut ar. However, contact between the inclined tool and the cylindrical surface of the workpiece is complex, which makes it difficult to obtain a coordinate Ot uniquely. Therefore, the tool center coordinate Ot is calculated by convergent calculation, which moves Ot from an initial position Ot'(xt0, yt0, zt0) to a position at which the tool outer face comes into contact with the workpiece outer face, as shown in Fig. 9(c). In this study, we evaluate the validity of the proposed simulation method by comparing the simulated cutting forces with the experimental forces when the lead angle α and the tilt angle β are given simultaneously. In addition, we clarify the optimal tool posture for ensuring minimum resultant force.
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(a) Overview of turn milling simulation geometry
(b) Point cloud simulation model and methodology for turn milling
(c) Definition of initial tool center position by convergent calculation Fig. 9 Turn milling simulation model using the point cloud method.
4.2 Experimental validation of the turn milling simulation model Figure 10(a) provides an overview of the experimental setup, featuring a one flute radius end mill with a 50-mm diameter attached to a 10-mm diameter round insert, for the turn milling of a cylindrical stainless steel SUS304 workpiece. The workpiece was attached to a MAZAK INTEGREX i-200 multi-tasking machine. The cutting forces on each axis in the tool coordinate system were measured using a Kistler 9125 rotary dynamometer under several cutting conditions (listed in Table 3(I)). The axial depth of cut ap and the radial depth of cut ar are defined based on the milling, and they were set as 0.5 mm and 25 mm, respectively. Then, the finished workpiece diameter after turn milling differs based on β.
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(a) Setup for cutting force validation
(b) Cutting tool and insert geometry
Fig. 10 Experimental setup for validation of turn milling with the tool given a lead and tilt angle simultaneously.
Table 3 Turn milling conditions; (I)Experimental conditions for cutting force validation, (II)Simulation conditions for evaluation of the effect of the tool posture.
Workpiece material Number of flutes
V
fr0
depth
SUS304
SUS304
1
5
5
5
200
200
mm
Cutting velocity
Axial
(II)
Nt
Nose radius r
Feed rate
(I)
m/min mm/tooth
of
cut
ap Radial depth of cut ar
(a)0.129, (b)0.204 (c)0.311, (d)0.516
0.1
mm
0.5
0.5
mm
25
25
Down
Down
Cutting direction Work diameter D
mm
100
100
Tool diameter
mm
50
50
°
-35
-35, -45, -60
Lead angle
α
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Tilt angle
β
°
(a)15, (b)30, (c)45, (d)60
15, 30, 45, 60
The validation results of the predicted cutting forces are provided in Fig. 11. In this experiment, we evaluate the resultant forces Fxy, Fxyz, and a tool rotational axis force Fz, as these forces are not related to the attached insert position against the tool rotary coordinate system. The predicted and experimentally measured cutting forces with several different tool postures are in agreement with each other, as shown in the figure, despite the fact that the cutting force coefficients were assumed to be constant, as mentioned in section 2. It follows that the effect of the tool radius on the cutting force in the turn mill with the corner radius end mill was small, because the center of the cutting tool is not used in the corner radius end mill, unlike that of the ball-end mill; as such, the changes in the cutting speed on the tool edge were small. Here, the cutting force must become zero during the air cut, but the measured cutting forces in Fxy and Fxyz were not zero. This is because the low stiffness of the long tool holder, due to a limitation of the dynamometer structure, caused the tool to vibrate in only the XY plane of the tool rotary coordinate system after the tool insert exited from the workpiece. This vibration affected the cutting forces in Fx and Fy during the air cut period, as shown in Fig. 12; as a result, Fxy and Fxyz were not zero. However, no chatter vibration occurred while the tool was in contact with the workpiece because normal finishing surfaces were obtained, as shown in Fig. 13; thus, stable cutting could be implemented in this cutting test. The validity of the proposed method was confirmed from the above cutting force test results. In the next section, the effect of the tool posture when varying the lead angle α and tilt angle β using the proposed simulation method for the cutting force is discussed.
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Fig. 11 Measured and predicted cutting force at different inclination angles β under the conditions given in Table 3(I).
Fig. 12 Vibration of measured cutting force at (d) α = 35°, β = 60°, as shown in Fig. 11.
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Fig. 13 Machined surface with turn milling. 4.3 Effect of the tool posture on cutting force In this evaluation, we examined the effect of the tool posture on the cutting forces Fz,
Fxy, and Fxyz while varying the lead and tilt angles as shown in Table 3(II); other cutting conditions were the same and the MRR was kept constant. Both the average and maximum cutting forces were evaluated as the average cutting forces affect the roughness and stability limit of the chatter vibration and the maximum cutting forces affect tool wear and failure. Figure 14 shows the average cutting forces ((1) ~ (3)) and the maximum cutting forces ((4) ~ (6)) extracted from the time-dependent simulated force. The absolute average axial force |Fz| did not change when the tool lead and tilt angle were varied, while, in contrast, the average resultant forces Fxy and Fxyz did change with the tool lead angle. At the same time, under the conditions of both minimum P1 and maximum P2 values of |Fz|, Fxy and Fxyz in Fig. 14(b), the opposite tendency against Fig. 14(a) occurred. The predicted forces under P1 and P2 are shown in Fig. 15. As shown in Fig. 15(P1), |Fz|,
Fxy and Fxyz have trapezoidal wave shapes, presumably because the tool always comes into contact with the workpiece as the cutting force does not return to zero. The transitions of the contact area between tool and workpiece during a tool rotation under conditions P1 and P2 are shown in Fig. 16. Here, the horizontal and vertical axis represent tool rotation angle φ and the contact angle κ between the tool and the workpiece, respectively. According to Fig. 16 (P1; trapezoidal shape), the tool first comes into contact with the workpiece at around φ=45°, and the contact area gradually increases from φ =60° to about 110°. Then, the area suddenly reduces until the end of contact at about φ =125°. In addition, the contact rotation angle φP1 (=80°) is larger than the cutter pitch angle (=72°). Thus, the tool always comes into contact with the workpiece because the cutting force with a trapezoidal shape does not return to zero. Therefore, the cutting forces have trapezoidal wave shapes under P1. In contrast, Fxy and Fxyz under P2 have sharp triangular wave shapes and return to zero after reaching the maximum force, as shown in Fig. 15(P2). In Fig. 16 (P2;
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triangular shape), the tool first comes into contact with the workpiece at around φ=75°, and the contact area exponentially increases to about 117°. Then, the area suddenly reduces until the end of a contact at approximately φ =125°. In addition, φP2 (=50°) under P2 was smaller than the cutter pitch angle, such that each tool edge disengaged after cutting as the cutting force with the triangular shape returned to zero. Therefore, the cutting forces have triangular wave shapes under P2. Therefore, the average resultant cutting force Fxyz under P1 is higher than that in intermittent cutting at P2 because continuous cutting is conducted under P1 and the cutting force does not become zero, but the maximum cutting force under P1 is smaller than that under P2. Specifically, the maximum Fxyz under P2 is approximately 1.7 times higher than that under P1. Moreover, as an overall tendency, the average resultant cutting force Fxyz decreases with an increase of the lead angle, but the tilt angle does not have a big effect on the forces. In contrast, the maximum resultant cutting force Fxyz increases with an increase of the lead angle. This is because the contact area between the tool and the workpiece moves from the bottom side to the outer side on the cutting edge of the round insert as the lead angle increases. Therefore, the axial cutting force coefficients kac and kae increase in proportion to the axial depth of cut ap as shown in Eq. (12). As a result, the maximum axial cutting force Fz under P2 increases as shown in Fig. 15(P2). According to these results, the tool posture defined by the lead and tilt angles of the cutting tool has a strong effect on the cutting forces on each axis in the turn milling process; this is particularly true in the case of the lead angle. In addition, the average and maximum cutting forces change depending on the tool posture even though the efficient does not change.
(a) Average cutting force
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(b) Maximum cutting force Fig. 14 Effect of tool posture on cutting force in several tool postures under the conditions given in Table 3(II).
(P1) Cutting force (α =35°, β = 15°)
(P2) Cutting force (α =60°, β = 15°) Fig. 15 Comparison of maximum and minimum cutting forces under conditions P1 and P2 in Fig. 14.
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Fig. 16 Transition of contact area between the tool and workpiece during tool rotation under P1 and P2 shown in Fig. 14.
5
Conclusion Turn milling with a 5-axis multi-tasking machine significantly differs from
conventional face milling due to the complicated contact state between the tool and workpiece, where the tool rotational axis is inclined against the workpiece rotational axis and both the inclined cutter and workpiece are rotated simultaneously. Particularly, in this case, it is more difficult to predict cutting forces in several tool postures with the tool given a lead and a tilt angle simultaneously compared with the case of orthogonal turn milling, as reported in previous papers. This study developed a flexible simulation methodology for turn milling based on the interference between the tool and point cloud of the workpiece, that can predict cutting forces in various tool postures with lead and tilt angles. It can also consider the involvement of multiple cutting edge at the same time. Experiments with several different tool postures were performed to evaluate the predicted cutting forces. The main results are summarized as follows. (1) In the proposed point cloud method, an uncut chip thickness in the turn mill can be defined by means of a simple vector calculation with the normal vector of the tool edge and the interfered vector that is directed from the interfered work piece surface point to the point on the cutting edge. Moreover, the machined surface shape can be redefined more accurately and compared with the general voxel simulation model because a new point cloud is set on the machined surface along the tool path after passing the tool edge. (2) According to the experimental results of the validation test, the predicted cutting forces were in agreement with the experimental forces against the change in lead and tilt angles. The cutting force in 5-axis turn milling was accurately predicted
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using the simple calculation of an uncut chip thickness and the proposed identification method for cutting coefficients. (3) From the simulation results with several tool postures under various lead and tilt angles and feed rates, it was clarified that both the average and maximum cutting forces vary even if the material removal rate is kept constant. In the case of turn milling with a small lead angle, the average resultant cutting forces Fxy and Fxyz were larger than those in the case with a large lead angle. In contrast, the maximum resultant cutting forces Fxy and Fxyz became smaller when the lead angle decreased. This is because the cutting force wave form at small lead angles is trapezoidal, presumably because the cutting force does not return to zero as the tool maintains contact with the workpiece. In contrast, the cutting force wave form at the large lead angle resembles a sharp triangle and returns to zero after every cutting edge exit from the workpiece. According to these results, the tool posture defined by the lead and tilt angles of the cutting tool has a strong effect on the cutting forces in the turn milling process; this phenomenon is especially evident in the case of the lead angle. In addition, the average and maximum cutting forces change depending on the tool posture even though the cutting efficiency remains the same. In our future work, we will apply the proposed simulation method to more complicated work materials (such as turbine blades) and investigate the effect of tool posture on tool wear and chatter vibration.
Nomenclature S, V
Spindle and cutting speed
C 0, C 1
Constants of the linear regression
fr0
Feed per tooth
Aj
Point on the tool
ft
Uncut chip thickness
Bj
Point on the workpiece
ap
Axial depth of cut
djw
Division size of workpiece (j=x,y,z)
φ, κ
Radial and axial immersion angles
St
Tool rotation speed
dκ
Angle of discrete element
Sw
Workpiece rotation speed
dS
Differential edge length
FRz
Axial feed rate
Kic, Kie Cutting and edge force coefficients (i = t,r,a) ar
Radius depth of cut
α, β
Lead and tilt angle
e
Tool offset
dFi(j)
Differential cutting force (j=x,y,z)
D 0, D 1
Diameter
of
unmachined
machined workpiece
25 / 29
and
RI
Radius of rounded insert
Xt, Xw
Km
Maximum axial immersion angle
Rkrot, Rl Rotational matrix (k=t,w)(l=a,b)
κst, κex
Angular engagement limit
Ot
Tool and workpiece coordinates
Tool center position
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List of figures Fig. 1 Definition of lead and tilt angles in turn milling Fig. 2 Experimental setup for identification of cutting coefficients by radius end mill. Fig. 3 Cutting force analytical model of the radius end mill. (a) Cutting force simulation model with radius end mill (b) Differential cutting force model on the cutting edge at point P Fig. 4 Calculation of cutting force coefficient (e.g., ap = 0.5 mm). (a) Measured cutting force (b) Linear regression of measured cutting force Fig. 5 Identification of cutting force coefficient (e.g., ap = 0.5 mm). Fig. 6 Cutting force simulation model using point cloud method for face milling with a corner radius end mill. (a) Overview of face milling simulation geometry with the point cloud method (b) Point cloud simulation model and methodology for calculating uncut chip thickness Fig. 7 Comparison of analytical cutting force and measured cutting force. (a) Measured and predicted cutting force (e.g. ap = 1.0 mm, fr0 = 0.1 mm/t) (b) Predicted and measured maximum and average cutting forces for the conditions given in Table 1 Fig. 8 Schematic view and parameters of turn milling. Fig. 9 Turn milling simulation model using the point cloud method. (a) Overview of turn milling simulation geometry (b) Point cloud simulation model and methodology for turn milling (c) Definition of initial tool center position by convergent calculation Fig. 10 Experimental setup for validation of turn milling with the tool given a lead and tilt angle simultaneously. (a) Setup for cutting force validation
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(b) Cutting tool and insert geometry Fig. 11 Measured and predicted cutting force at different inclination angles β under the conditions given in Table 3(I). Fig. 12 Vibration of measured cutting force at (d) α = 35°, β = 60°, as shown in Fig. 11. Fig. 13 Machined surface with turn milling. Fig. 14 Effect of tool posture on cutting force in several tool postures under the conditions given in Table 3(II). (a) Average cutting force (b) Maximum cutting force Fig. 15 Comparison of maximum and minimum cutting forces under conditions P1 and P2 in Fig. 14. (P1) Cutting force (α =35°, β = 15°) (P2) Cutting force (α =60°, β = 15°) Fig. 16 Transition of contact area between the tool and workpiece during tool rotation under P1 and P2 shown in Fig. 14.
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We would like to show my greatest appreciation to members of our laboratory whose comments and suggestions were of inestimable value for my study.
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Table 1 Face milling test conditions.
S [rpm]
ft [rpm]
(V [m/min]) 1990
ap [mm] 0.5, 1.0,
0.1–0.3
(200)
1.5
Table 2 Cutting force coefficients.
Krc
Ktc
Kac
Kre
Kte
Kae
N/m2
N/m2
N/m2
N/m
N/m
N/m
C0
–483.2
–266.7
58.8
–12.0
8.2
20.8
C1
936.2
2310.6
616.8
52.7
23.4
20.7
Table 3 Experimental conditions for cutting force validation.
Workpiece material Number of flutes
Nt
Nose radius r
mm
Cutting velocity Feed rate Axial
V
fr0
depth
m/min mm/tooth
of
cut
ap Radial depth of cut ar
(I)
(II)
SUS304
SUS304
1
5
5
5
200
200
(a)0.129, (b)0.204 (c)0.311, (d)0.516
0.1
mm
0.5
0.5
mm
25
25
Down
Down
Cutting direction Work diameter D
mm
100
100
Tool diameter
mm
50
50
°
-35
-35, -45, -60
α
Lead angle Tilt angle
β
°
(a)15, (b)30, (c)45, (d)60
1
15, 30, 45, 60
Fig. 1 Definition of the lead and tilt angle in turn milling
Fig. 2 Experimental setup for identification of cutting coefficient by radius end mill.
(a) Cutting force simulation model with radius end mill
1
(b) Differential cutting force model on the cutting edge at point P Fig. 3 Cutting force analytical model of the radius end mill.
(a) Measured cutting force
(b) Linear regression of measured cutting force
Fig. 4 Calculation of cutting force coefficient (e.g., ap = 0.5 mm).
2
Fig. 5 Identification of cutting force coefficient (e.g., ap = 0.5 mm).
(a) Overview of face milling simulation geometry with the point cloud method
3
(b) Point cloud simulation model and methodology for calculating uncut chip thickness Fig. 6 Cutting force simulation model using point cloud method for face milling with a corner radius end mill.
(a) Measured and predicted cutting force (e.g. ap = 1.0 mm, fr0 = 0.1 mm/t)
4
(b) Predicted and measured maximum and average cutting forces for the conditions given in Table 1 Fig. 7 Comparison of analytical cutting force and measured cutting force.
Fig. 8 Schematic view and parameters of turn milling.
(a) Overview of turn milling simulation geometry 5
(b) Point cloud simulation model and methodology for turn milling
(c) Definition of initial tool center position by convergent calculation Fig. 9 Turn milling simulation model using the point cloud method.
(a) Setup for cutting force validation
(b) Cutting tool and insert geometry
Fig. 10 Experimental setup for validation of turn milling with the tool given a lead and tilt angle simultaneously.
6
Fig. 11 Measured and predicted cutting force at different inclination angles β under the conditions given in Table 3(I).
Fig. 12 Vibration of measured cutting force at (d) α = 35°, β = 60° in Fig. 11.
7
Fig. 13 Machined surface with turn milling.
(a) Average cutting force
(b) Maximum cutting force Fig. 14 Effect of tool posture on cutting force in several tool postures under the conditions given in Table 3(II).
8
(P1) Cutting force (α =35°, β = 15°)
(P2) Cutting force (α =60°, β = 15°) Fig. 15 Comparison of maximum and minimum cutting forces under conditions P1 and P2 in Fig. 14.
Fig. 16 Transition of contact area between the tool and workpiece during tool rotation under P1 and P2 shown in Fig. 14.
9
Highlights
A turn milling simulation method to predict the cutting force by using a point cloud modeling was proposed.
The predicted cutting forces in turn milling at various tool postures with lead and tilt angles agreed with experimental results.
Cutting force in turn milling can be minimized by selecting appropriate tool posture keeping MRR.