On cutting parameters selection for plunge milling of heat-resistant-super-alloys based on precise cutting geometry

Journal of Materials Processing Technology 213 (2013) 1378–1386

Contents lists available at SciVerse ScienceDirect

Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec

On cutting parameters selection for plunge milling of heat-resistant-super-alloys based on precise cutting geometry Kejia Zhuang, Xiaoming Zhang ∗ , Dong Zhang, Han Ding State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China

a r t i c l e

i n f o

Article history: Received 23 December 2012 Received in revised form 28 February 2013 Accepted 5 March 2013 Available online 15 March 2013 Keywords: Plunge milling Cutting force modeling HRSA Cutting parameter optimization

a b s t r a c t In plunge milling operation the tool is fed in the direction of the spindle axis which has the highest structural rigidity, leading to the excess high cutting efficiency. Plunge milling operation is one of the most effective methods and widely used for mass material removal in rough/semi-rough process while machining high strength steel and heat-resistant-super-alloys. Cutting parameters selection plays great role in plunge milling process since the cutting force as well as the milling stability lobe is sensitive to the machining parameters. However, the intensive studies of this issue are insufficient by researchers and engineers. In this paper a new cutting model is developed to predict the plunge milling force based on the more precise plunge milling geometry. In this model, the step of cut as well as radial cutting width is taken into account for chip thickness calculation. Frequency domain method is employed to estimate the stability of the machining process. Based on the prediction of the cutting force and milling stability, we present a strategy to optimize the cutting parameters of plunge milling process. Cutting tests of heat-resistant-super-alloys with double inserts are conducted to validate the developed cutting force and cutting parameters optimization models. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Nickel-base super alloy, also called heat-resistant-super-alloys (HRSA) containing a niobium age-hardening addition, takes advantages of very high strength, good ductility and anti-fatigue. This alloy can work at temperatures from −217◦ to 700◦ with nonmagnetic, oxidation- and corrosion- resistant (Smithberg, 1987). It is widely used in the components of liquid rockets parts, aircraft turbine engines, metal processing, nuclear power systems, and cryogenic tankage (Galimberti, 1962-1963). There are some characteristics of the poor machinability of HRSA for it has an austenitic matrix, such as high cutting force, cutting tool abrasiveness, low thermal properties leading to high cutting temperatures and stresses, the workpiece surface damage, and also work harden rapidly during machining (Shaw and Nakayama, 1967). Up to date, the machining of HRSA with high-efficiency and low damage remain great challenges and open issues to the public (Choudhury and El-Baradie, 1998). Plunge milling operation exhibits vibration-free comparing with the plane milling and side milling operations for the feed direction along with the spindle axis is the most rigid direction. Plunge milling process is used in cavities and walls in molds and dies,

∗ Corresponding author. Tel.: +86 27 87559842. E-mail address: [email protected] (X. Zhang). 0924-0136/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2013.03.007

aerospace parts for the higher productivity than conventional operations, also this strategy is used in rough machining of hard material such as nickel base super alloys for excess material removal rapidly. Fig. 1 illustrates the sample plunge milling operations, in which there are two types of blades, i.e., integral ones and separate ones engaged to workpiece in plunge milling. Fig. 1(a)–(c) show that the plunge milling can be used in slotting large holes, roughing and enlarging small holes, respectively. There are also many difficulties in plunge milling operations that limits the use of this strategy. Most of the previous works concentrated on the design of cutter geometry and the chatter stability of the plunge milling while how to use this operation, especially the cutting parameters selection to improve the machining efficiency is addressed little. Wakaoka et al. (2002) studied the intermittent plunge milling process to make vertical walls by focusing on the tool geometry and motion. Li et al. (2000) presented a plunge milling method to create complex chamfer patterns and estimated cutting forces while neglecting the structural dynamics of the system. Al-Ahmad et al. (2005) proposed a cutting model that included the determination of tool geometry (radial engagement, chip thickness) and the evaluation of the cutting forces, which was validated experimentally though tests on the 40GrMnMo8 material using end milling. Damir et al. (2011) proposed a horizontal approach to compute the chip area to consider the contribution of the main and side edge in the cutting zone and to deal with any geometric shape of the insert. Altintas and Ko (2006) had proposed frequency domain modeling of mechanics

K. Zhuang et al. / Journal of Materials Processing Technology 213 (2013) 1378–1386

Nomenclature N ji  ae Fq fz stn S(ji ) h0 (i ) Kq Fqd RPM D/R 0 ϕp as a(ji ) st ex h (i ) fMRR q HRSA

number of flutes immersion angle of tooth j spindle speed radial depth of cut cutting force in Cartesian coordinate feed per tooth changeable cutting angle real-time dynamic cutting area(tooth j at time i) regenerative chip thickness cutting coefficients dynamic cutting force rev per minute diameter/radius of the tool rake angle of plunge cut cutter pith angle step of cut real-time uncut width thickness cutting in angle cutting out angle dynamic uncut chip thickness material removal rate dynamic displacement heat-resistant-super-alloys

and dynamics of plunge milling by regenerative the chip thickness, also Ko and Altintas (2007a,b) presented a time domain, chatter stability prediction theory for plunge milling, which can be reduced by increasing the torsional stiffness with strengthened flute cavities. But the previous studies did not take the role of the cutting parameters, like cutting step as well as cutting width into account. However, these parameters play an important role in the model of cutting force of plunge milling, which is confirmed by our cutting experiments. 2. Literature review Metal cutting has been a major machining process in manufacturing industries for decades, and how to improve the productivity and stability of cutting process is still an important problem. The selection of the optimal machining parameters in plunge milling

1379

is a key point of efficient metal cutting condition for the cutting operation. Many researchers have worked on the optimization of machining parameters. However most work done on the optimization of the cutting conditions focuses on flank milling or end milling, while plunge milling has received relatively little attention with regard to the optimization of cutting parameters. High speed machining takes advantages of high material removal rate (MRR), low cutting force and minimal workpiece distortion when machining nickel-based super alloy. The cutting parameters of the plunge milling cutting process determine the cutting force, MRR, distortion and stability in manufacturing. Literatures reviews show that a lot of work has been done on how to select optimal parameters in cutting process. In the efforts made by researchers, different objective functions have been used, including minimum production cost (Wang, 1993), minimum production time (Chua et al., 1993), maximum MRR (Billatos and Tseng, 1991 and Dong, 1992), maximum tool life (Choudhury and Appa Rao, 1999), suitable cutting force, etc. Also many works addressed the optimization solution methods for the problems of machining parameters optimization, such as the approaches of graphical, linear programming, Lagrangian multipliers, dynamic programming, artificial intelligence and Gray-Taguchi. Tolouei-Rad and Bidhendi (1997) described the development and utilization of an optimization system which determines optimum machining parameters for milling operations. Choudhury and Appa Rao (1999) presented an approach for improving the cutting tool life by using optimal values of velocity and feed throughout the cutting process, also an equation of tool life has been established from experimental data and adhesion wear model, however the radial and axial depth of cut were not optimized. Chua et al. (1993) developed a mathematical model for TiN-coated carbide tools and Röchling T4 medium carbon steel based on the design and analysis of machining experiments. Billatos and Tseng (1991) discussed the optimization strategy using a knowledge-based system, developed the intelligent controller, and illustrated a practical machining application that provides on-line direct measurement of tool failure. Dong (1992) presented a unified optimization approach for the selection of the machining parameters that provide the maximum metal removal rate for any specified surface quality and tool life. Juan et al. (2003) constructed an investigation of optimal cutting parameters for minimizing production cost on the rough machining of high speed milling operation. In recent years, the genetic algorithm have been used in optimal the parameters in manufacturing. Wang (1993) presented a neural

Fig. 1. Plunge milling process configuration: (a) plunge milling process for making large hole with blade in integrity, (b) intermittent plunge milling process to make vertical wall or conduct rough cutting, (c) plunge milling process to enlarge a hole.

1380

K. Zhuang et al. / Journal of Materials Processing Technology 213 (2013) 1378–1386

network based approach to multi-objective optimization of cutting parameters. Shunmugam et al. (2000) used a genetic algorithm to optimal the number of passes, depth of cut, speed and feed in facemilling operation to yield minimum total production cost. Wang et al. (2005) presented an approach to select the optimal machining parameters for multi-pass milling which was based on genetic algorithm and simulated annealing approaches. Suresh et al. (2002) dealt with the study and development of a surface roughness prediction model for machining mild steel based on the predict models which used response surface methodology (RSM) and genetic algorithms (GA). In the ref of Kim and Ramulu (2004), a multiple objective linear program approach was used to optimize drilling feed and speed, not only to maximize each hole quality parameter to the greatest extent possible but also to minimize machining cost. Shunmugam et al. (2000) also optimized the machining parameters such as the number of passes, depth of cut in each pass, speed and feed using a GA, to yield minimum total production cost while considering technological constraints such as allowable speed and feed, dimensional accuracy, surface finish, tool wear and machine tool capabilities. A hybrid of GA and SA is presented to use the strengths of GA and SA and overcome their weakness (Wang et al., 2005). Liu and Wang (1999) improved the convergence speed of traditional GA and obtained good results by defining and changing the operating domain of GA. Robust parameter design (RPD) is a methodology for choosing optimum parameters in engineer process, and Taguchi method based on experiment is a key tool for RPD. Kopac et al. (2002) dealt with the issue of optimizing the turning of raw workpieces of low-carbon steel with low cold pre-deformation to achieve acceptable surface roughness by using Taguchi method. The contributions of this paper are that first we develop a precise cutting geometry model for plunge milling operations, and second the cutting parameters optimization strategy in plunge milling process is proposed based on the new cutting geometry model. The cutting geometry reflects the nature of plunge milling process by taking into account the impact of cutting step. The proposed analysis of precise cutting geometry is helpful to understand the plunge milling process intuitively. Based on the proposed precise cutting geometry, the real-time dynamic cutting force model is given, which approaches the experimental results. With the proposed cutting force model, cutting parameters optimization model for plunge milling of HRSA is developed with the help of frequency domain milling stability analysis. In the model the objective is to maximize material removal rate and the constraint conditions are to keep the cutting force under the predefined one and require the cutting process stable. A detailed optimization procedure is presented for solving the cutting parameters optimization equations, which are nonlinear optimization ones. To validate the models given in this study, a series of cutting tests were conducted and the results support the proposed models.

3. Simulation model 3.1. Cutting force model based on new cutting geometry The cutting geometry and parameters of a classic plunge milling cutter are shown in Fig. 2 and the inserts of the plunge cutter have an offset distance from the spindle axis. In plunge milling operation, the feed direction is along the spindle axis z where axes x, y are the horizontal coordinates. In the process, Ff is the feeding force, Ft is the one in the direction of cutting speed which is called tangential cutting force, and Fr is the normal cutting force in the insert of the plunge cutter. The immediately predicted cutting forces (Ft , Fr and Ff ) in plunge milling process, can be transformed into three orthogonal force components (Fx , Fy , Fz ) in Cartesian coordinates of the cutter axes.

Fig. 2. The geometry and parameter of a classic plunge cutter. R = 16 mm, N = 2,  0 = 10◦ .

Fig. 3. Cutting geometry of side milling.

In light of its importance to machine tool design and machining process planning, model of cutting force in plunge milling has received considerable attention for many years. In previous work, the cutter geometry and tool motion were addressed (Wakaoka et al., 2002). Li et al. (2000) developed an analytical model for the cutting forces in multiblade plunge cutting of cylindrical but the structural dynamics of the system was neglected in the cutting model. Altintas and Ko (2006), Ko and Altintas (2007a,b) presented the pioneer work on plunge milling dynamics, although the dynamics model came from the model of side milling and end milling. As shown in Fig. 3, in side milling and end milling, while we calculate the chip load, which is the crucial component in cutting force modeling, the zone ABD is considered, and the zone ABC is normally ignored since the feed rate along the direction from O1 to O2 is smaller enough to be ignored comparing with the radial cutting depth. For a comparison, cutting geometry of plunge milling is shown in Fig. 4, where Y1 and Y2 are the adjacent cutting positions during the plunge milling operations. But in plunge milling, the feed is in the axial direction and the cutting step is as great as the radial cutting depth, so the red area ABC should be taken into account in plunge milling model. For example, with the same cutting parameters given in Table 1, zone ABC has different account of zone ABD in side and plunge milling operations. In plunge milling, the start zone accounts for 25.65% while only 0.15% occupied in side milling.

K. Zhuang et al. / Journal of Materials Processing Technology 213 (2013) 1378–1386

1381

where S(ji ) = a(ji )fz is the real-time dynamic uncut chip area by cutter tooth j. The predicted cutting force given above can be transformed into three orthogonal components in Cartesian coordinates of the cutter axes as follows

⎡

Fxj (ji )

⎤

⎡

− cos ji

⎢ ⎥ ⎢ ⎣ Fyj (ji ) ⎦ = ⎣ sin ji Fzj (ji )

⎤⎡

⎤

− sin ji

0

− cos ji

0 ⎦ ⎣ Frj (ji ) ⎦

0

0

⎥⎢

Ftj (ji )

⎥

(4)

Ffj (ji )

1

The total instantaneous cutting forces on the cutter can be evaluated by

⎡

Fx (i )

⎤

⎡

Fxj (ji )

⎤

⎢ ⎥ ⎢ ⎥ ⎣ Fy (i ) ⎦ = ⎣ Fyj (ji ) ⎦ N

j=1

Fz (i )

Fig. 4. Cutting geometry of plunge milling.

⎡

⎤⎡ ⎤ Kt − cos ji − sin ji 0 N  ⎢ ⎥⎢ ⎥ = ⎣ Kr ⎦ ⎣ sin ji − cos ji 0 ⎦ S(ji )

Table 1 The cutting parameters of side milling and plunge milling.

j=1

Side milling Plunge milling

D

ae

as

fz

32 mm 32 mm

3.5 mm 3.5 mm

– 3.5 mm

0.05 mm/rev 0.05 mm/rev

ji < st , ji > ex

ae − R R− a(ji ) = cos ji ⎪

⎪ ⎩

R−

st ≤ ji ≤ stn



R2 − as 2 · cos2 ji + as · sin ji

stn ≤ ji ≤ ex (1)

In Eq. (1), the boundary of the cutting angle st , stn , ex in plunge milling process can be stated as



st =  − a cos 1 −

 ae



ex =  + a tan

0

0

1

3.2. Stability analysis In plunge milling operation, the cutter is fed into the material in spindle axis direction with fz . The cutter will experience radial (x, y) and axial (z) vibration taking the tool geometry and cutting insert distribution into account. The general formulation of plunge milling process dynamics can be shown as



Mq

       q¨ + Cq

 

q˙ + Kq {q} = Fq {q} = ( qx

qy

qz )

T

(6)

For this cutting process, the vibration in radial direction (x, y) can be transformed into feed direction(z) due to the geometry of the cutting tool. As shown in Fig. 5, the uncut chip of plunge milling is h(i ) = fz +h0 (i ), where h0 (i ) is the real-time dynamic uncut chip and can be stated as h0 (i ) = x sin i tan 0 + y cos i tan 0 + z

(7)

The dynamic cutting forces on the cutting insert are

R

2Rae − ae 2 − as R − ae

stn =  − a tan

Kf

(5)

where N is the teeth number and Kt , Kr and Kf are the cutting coefficients.

So in plunge milling the start area should be taken into account. In this study, we give the detailed analysis of cutting geometry of plunge milling, and treat the cutting step and cutting width as the equally important factors in modeling. In Figs. 3–4, ji is the real-time position of the tooth j and a(ji ) is the dynamic cutting width of the instance cutting angle, in plunge milling process which can be described by

⎧ 0 ⎪ ⎪ ⎨

Fzj (ji )

⎡

(2)

a 

Fxd (i )

⎤

⎡

−Kt cos i − Kr sin i

⎢ ⎥ ⎢ ⎥ ⎣ Fyd (i ) ⎦ = a(i ) ⎣ Kt sin i − Kr cos i ⎦ Kf

Fzd (i )

s

2R



Then the cutting forces in tangential, radial, feed directions of the tooth j at the cutting angle ji are given by Ftj (ji ) = Kt S(ji ) Frj (ji ) = Kr S(ji )

(3)

sin i tan 0

cos i tan 0

⎤ ⎡  x 1 ⎣ y ⎦

(8)

z where  0 is the rake angle of cutter tooth, and the formula can be illustrated in matrix as

  F

Ffj (ji ) = Kf S(ji )

⎤

=

  1 a(i )[A(i )] t 2

(9)

Table 2 The mechanical composition of the workpiece. C

Mn

Si

P

Ni

Cr

Mo

Ti

Nb

Co

B

Al

Fe

0.03

0.02

0.09

0.003

52.48

18.94

3.03

0.98

5.13

0.02

0.003

0.51

Other

1382

K. Zhuang et al. / Journal of Materials Processing Technology 213 (2013) 1378–1386

Then the critical cutting width(ae ) and spindle speed() can be found with the eigenvalues from Eq. (15) as explained in detail by Altintas in (Altintas, 2000). alim = − T=

 R (1 + 2 ), Nf Ktc

1 (ε + 2k), ωC

← =

I sin ωc T = 1 − cos ωc T R

← ε =  − 2 tan−1 ,

→˝=

60 NT

(16)

Then for nth lobe k = 1,2,3,. . .,n the critical depth of cut and corresponding speeds are found and the lobe diagram is plot as explained in (Altintas, 2000). 3.3. Cutting parameters optimization

Fig. 5. Dynamic uncut chip thickness model of plunge milling.

With the frequency domain chatter stability analysis proposed by Ko and Altintas (Ko and Altintas, 2007a,b), the mean values of time directional factor matrix can be evaluated as: [A0 ] =



1 p

ex

A(i )d = st

N [˛] 2

(10)

The cutting process involved in this paper is used for rough milling with large radial engagements at lower spindle speeds where the directional factors do not lead to flip bifurcation of the modes, the mean values of directional factor matrix is suitable. Nevertheless, if any unforeseen application requires the inclusion of higher order Fourier terms, the multi-frequency model of the proposed stability law (Merdol and Altintas, 2004.) or semidiscretization method (Insperger and Stépán, 2002) should be used. The transfer function matrix at the cutter-workpiece contact zone in this paper can be illustrated as

⎡

⎢ ˚(iω) = ⎣

˚xx (iω)

0

0

0

˚yy (iω)

0

0

0

˚zz (iω)

⎤ ⎥ ⎦

(11)

The dynamic regeneration displacement of the operation is (iωc ) =



 



r(iωc ) − r(iω0 )

 

= (1 − e−iωc T )eiωc t [˚(iωc )] F

(12) Substituting Eq. (12) into the dynamic milling equations Eqs. (9)–(10), we have

 

F eiωc t =

  1 N a(i ) [1 − e−iωc T ][˚(iωc )] F eiωc t 2 2

(13)

which has a no-trivial solution if its determinant is zero,



det

[I] −



1 N a(i )[1 − e−iωc T ][˚(iωc )] 2 2

=0

(14)

In Eq. (14), the eigenvalues can be found with real and imaginary parts: = R + i I = −

N aKt (1 − e−iωc T ) 2

(15)

In metal cutting operation, the parameters can be classified as fixed ones and variable ones. The former includes machine tools parameters, cutting tools parameters and characteristics parameters of workpiece, while the latter normally refers to the cutting conditions parameters. Among the parameters that optimized in this paper are as , fz , ae and . The key target that measured in this study is to maximize MRR for it gives the milling efficiency in rough or semi-finish plunge milling operation, and the constraints are that (1) the cutting process should be stability, (2)the maximal cutting force and the spindle speed should meet the upper limitation of the tool-machine system. MRR can be expressed as the product of , fz , ae and as , i.e., fMRR = N˝fz ae as

(17)

The cutting geometry model with the real-time dynamic cutting width is illustrated in Section 3.1 and the dynamics of plunge milling is shown in Section 3.2. From the cutting model shown above, the optimization formulation in plunge milling can be expressed as max fMRR (ae , as , ˝, fz )

⎧ ⎪ ⎨

s.t.

⎪ ⎩

Fi (ae , as ) ≤ Fmax ˝ ≤ ˝0

(18)

max (˚(ae , as , ˝)) ≤ 1

where  ≤ 0 denotes that the spindle speed is limited by the 5axis machining center capability, and Fi (ae , as ) ≤ Fmax illustrates the maximal cutting force should be less than the tolerance of the cutting tool-machine system, and max (˚(ae , as , ˝)) ≤ 1 is to guarantee the milling process stable. Meanwhile the cutting parameters should meet limitation of the cutting tool, i.e. ae ≤ ae max

(17)

as ≤ as max

(18)

where aemax and asmax are the upper limitation of ae and as , respectively. 4. Modeling results and experimental validation In this section, cutting tests are carried out to validate the proposed cutting force and parameters optimization models. First the structural dynamics parameters of the spindle-tool system are identified. Also the recommended cutting parameters are given in machine tool and cutting tool manuals. Then the cutting coefficients of the workpiece-tool system are fitted by a series of cutting experiments. Cutting tests are conducted and the results are used to validate the cutting geometry model and optimized cutting parameters. The optimization results are comparing with the

K. Zhuang et al. / Journal of Materials Processing Technology 213 (2013) 1378–1386

1383

Fig. 6. The schematic diagram of cutting tests.

un-optimization ones, and it says the optimization results greatly improve MRR with a stable cutting process.

Fig. 8. Experiment setup for measurement of the run-out of cutting tool.

4.1. Model parameters identification The cutting system parameters as input variables to the optimization procedure are the structural dynamics parameters, cutting coefficients of plunge milling operation, also the limitation of the tool and machine systems are included in the input variables. First a set of experimental apparatus are combined to obtain the input variables. The schematic diagram of the experiment setup of plunge milling operation is shown in Fig. 6. The material tested in this study is HRSA with the size of rectangle block 85 mm × 70 mm × 30 mm, and the mechanical composition of this material is shown in Table 2. The experiments of plunge milling are performed in MIKRON DURO UCP 800, a 5-axis milling center with a Heidenhain numerical control system. The cutter is a 32 mm Sandvik plunge milling cutter (No.R210-025A32-09 M) with tool holder (No.392.410CGA-63 32 09), as shown in Figs. 7 and 8. A pulse hammer and an acceleration transducer are used to obtain the structural dynamics parameters of tool-machine system, presented in Fig. 7. Fig. 8 shows that the laser sensor is used to

Fig. 9. Experiment setup of plunge milling operation.

measure the run-out of the cutting tool, which should be less than 10 ␮m without external cutting force in this study. Also a noise transducer is used to get the audio signal of the cutting tests as shown in Fig. 9. Cutting forces in three directions x, y, z are measured by a three component dynamometer whose type is Kistler 9257B with an amplifier. All the sensors signals are collected by a NI acquisition instrument, which is connected to an industrial personal computer (IPC). The accuracy of cutting coefficients affects the cutting force in plunge milling operation as side milling. A series of cutting tests at  = 500 rpm but at various feed rates have been conducted to calibrate the cutting coefficients related to the material and the plunge milling cutter that are used in this study. Through the measurement and the linear regression analysis, the cutting coefficients used in Eqs. (3)–(5) are shown in Table 3. The modal parameters of the plunge mill attached to MIKRON machining center are shown in Table 4. The flexible modes of the cutting system can be measured through impact modal tests as Table 3 Identified cutting coefficients in plunge milling of HRSA.

Fig. 7. Experiment setup for acquisition structural dynamic parameters of toolmachine system.

Kt (N/mm2 )

Kr (N/mm2 )

Kf (N/mm2 )

1080

6613

7450

1384

K. Zhuang et al. / Journal of Materials Processing Technology 213 (2013) 1378–1386 1000

Table 4 Modal parameters of plunge milling. No.

Natural frequency (ωn )

Damping ratio ( )

Dynamic stiffness (2k )

x

1 2

540.5 Hz 1180.2 Hz

0.015 0.0047

2.149 (N/␮m) 21.35 (N/␮m)

y

1 2

545.5 Hz 1195.2 Hz

0.018 0.0045

2.349 (N/␮m) 21.55 (N/␮m)

z

1 2

325 Hz 425 Hz

0.042 0.035

20.2 (N/␮m) 58.6 (N/␮m)

z 

1 1

11,908 Hz 11,000 Hz

0.00146 0.00209

0.0635 (N/␮m) 55.76 (N/␮m)

600

Cutting force(N)

400 200 0 -200 -400 -600 -800 -1000 -1200

-8

20

x 10

14 12

8 6 4 2 0 100

200

300

400

500

600

300

400

500

600

700

700

Cutting angle(°) Fig. 10. The dynamic uncut chip with the cutting parameters shown in Table 5.

shown in Fig. 7. The torsional mode   and the torsional-axial mode z are also measured by the same instruments with the accelerometer pasted to the axial direction of the opposing tooth while the hammer impact to the tool. The cutter is flexible in lateral directions more than that in axial direction, and the torsional-axial mode as well as the axial modes exhibits considerably stiffness. 4.2. Plunge milling model verification The cutting forces in plunge milling are predicted by the method mentioned in Section 3.1 with the cutting coefficients shown in Table 3. Fig. 10 shows the real-time dynamic uncut chip in plunge milling process and Fig. 11 shows the predicted and measured cutting forces with the cutting coefficients shown in Table 3 and the cutting parameters given in Table 5. From Figs. 10–11, the predicted and measured cutting forces are in good quantitative agreement, which indicates the correctness of the proposed model in Section 3.1 with the prediction of real-time dynamics uncut chip thickness. 4.3. Optimization procedure In order to improve the performance of plunge milling, an optimization procedure is used to optimize the cutting width ae , cutting step as and spindle speed  in plunge milling process. Optimization model developed in this work (Section 3.3) is a nonlinear, multi-variable model of a complex nature. The objective function

ae 3e-3 mm

1. A cutting tests group is used to calibrate the cutting coefficients and measure the basic structural dynamics parameters of the tool-machine system. 2. Set the initial cutting parameters of the plunge milling operation (ae , as , fz , ) and the optimization interval data (a0 , 0 ). 3. Calculate the maximal cutting widths aem , ae , aen under the given spindle speeds ( + 0 , ,  − 0 ). 4. If ae is not the maximal of aem , ae and aen , then  =  − 0 and go to step 3. 5. Calculate the maximal cutting force(Fmax ) by ae , as , fz . 6. If Fmax > F0 then as = as − a0 , and go to step 5. Output the optimized cutting parameters as , ae and . 4.4. Validation results The experiments of plunge milling optimization are carried out in a 5-axis milling machining center. In Table 6, the conventional cutting parameters in plunge milling come from the tool and machine manual while the optimized cutting parameters are obtained by the proposed model. Note that the cutting speed in cutting HRSA is about 60 m/min and the corresponding speed is 620 rpm, which is relatively small comparing with that in machining of AL 7075, and the maximal cutting force is set as 1500 N for the tool-machine system. When machining the HRSA, the feed-rate should be small than that machining aluminum alloy, so fz is set as 0.05 mm/tooth. In the conventional plunge milling parameters shown in Table 5, MRR is 759.5 mm3 /min while MRR is raised to 2199.8 mm3 /min by using the optimization results, with MRR increasing by 189.6%. Also Table 6 The cutting parameters in plunge milling.

Table 5 Cutting test parameters.

500 rpm

200

is to maximize MRR in plunge milling operation that used in semirough/rough milling, meanwhile the constraints of the procedure are the stability of plunge milling process and the prediction of cutting forces, as well as the cutting parameters should meet the limitation of tool-machine system capability. Then an algorithm is proposed to optimize the radial cutting widths and cutting speed in this operation. The flow chart for optimization procedure is shown in Fig. 12 and can be detailed as follows

10



100

Fig. 11. The predicted and measured cutting forces (pre and exp indicate the predicted and measured ones, respectively) with the cutting parameters shown in Table 5.

16

0

0

Cutting angle(°)

18

Dynamic uncut chip(mm2)

Fx-exp Fy-exp Fz-exp Fx-pre Fy-pre Fz-pre

800

fz 0.05e-3 mm/tooth

as 6.5e-3 mm

Conventional parameters Optimal parameters

ae



as

fz

3.5 mm 6.7 mm

620 rpm 619.5 rpm

3.5 mm 5.3 mm

0.05 mm/tooth 0.05 mm/tooth

K. Zhuang et al. / Journal of Materials Processing Technology 213 (2013) 1378–1386

1385

4

Sound Pressure(s)

3

Tooth pass excitation frequency(20.67Hz)

2 1

0 -1 -2 -3 -4

0

0.5

1

1.5 2 Time(s)

2.5

3

3.5

160

180

Fig. 14. Signal of sound pressure.

0.18

Tooth pass excitation frequency(20.67Hz)

0.16

Fig. 12. The flow chart for optimization procedure.

the cutting process is stable and the maximal cutting force in this operation is required the limitation of tool-machine system. From the sample cutting test, the model was proved useful in maximize MRR in machining HRSA with plunge milling operation. With the optimal cutting parameters above, the sensor signal obtained the frequency domain signal which shows the operation is stable under the machine condition. With the modal parameters given in Tables 3 and 4, we use the semi-discretization method to predict the chatter stability and the resulted stability lobe is given in Fig. 13 to show the comparison from the one obtained by the

Sound pressure(Pa)

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0

0

20

40

60

100

120

140

Frequency(Hz) Fig. 15. FFT analyses of sound pressure.

1500

Fx-pre Fy-pre Fz-pre Fx-exp Fy-exp Fz-exp

1000

Cutting force(N)

500

0

-500

-1000

-1500 0

100

200

300

400

500

600

700

Cutting angle(°) Fig. 13. The predict stability lobes of plunge milling by frequency domain method (red) and semi-discretization method (black). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article).

Fig. 16. The predicted and measured cutting forces (pre and exp indicate the predicted and measured ones, respectively) with the optimal parameters shown in Table 6.

1386

K. Zhuang et al. / Journal of Materials Processing Technology 213 (2013) 1378–1386

the National Science & Technology Pillar Program (2012BAF08B01) and the National Engineering and Research Center for Commercial Aircraft Manufacturing (SAMC12-JS-15-006). References

Fig. 17. The chip formation of plunge milling. L: with conventional cutting parameters; R: with optimized cutting parameters.

time averaging method. It can be seen that the stability lobes are approximate with the parameters given in this paper. Furthermore, the optimized cutting parameters are falling into the stable regions, which are given by the two different stability prediction methods. The Point in Fig. 13 refers the optimal condition and Fig. 14 gives the sound pressure while the FFT analyses of sound pressure are shown in Fig. 15. The sound signal shows that the cutting operation is stable and the tooth pass excitation frequency is 20.67 Hz. Fig. 16 gives the contrast of the predicted and experimental cutting force of the optimal parameters, which are in good agreement. Fig. 17 gives the chip formation of the optimal and conventional parameters. From Fig. 17, we can see that the color and shape of the different chips are similar which confirms that with optimal cutting parameters MRR is improved greatly without the workpiece surface quality deteriorated. 5. Conclusions In this work, a new cutting model of plunge milling is proposed. The cutting step as well as cutting width is used to predict the realtime dynamic cutting width in plunge milling operation. And the cutting parameters optimization procedure is used to optimize the radial cutting width and the spindle speed. Compared to the traditional method in optimization of parameters, the cutting step can be take into account as well as cutting width in the new model of plunge milling operation. Also in the experiment, the cutting force and stability of the system are in the allowable range of machining condition. Test results showed that with the optimization procedure substantial improvement of MRR in plunge milling is obtained, while milling process is stable and workpiece quality is guaranteed. Acknowledgements This work was partially supported by the National Basic Research Program of China (2011CB706804), the National Natural Science Foundation of China (51005087, 51120155001, 51121002),

Altintas, Y., 2000. Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design. Cambridge University Press. Altintas, Y., Ko, J., 2006. Chatter stability of plunge milling. CIRP AnnalsManufacturing Technology 55, 361–364. Billatos, S.B., Tseng, P.C., 1991. Knowledge-based optimization for intelligent machining. Journal of Manufacturing Systems 10, 464–475. Choudhury, S., Appa Rao, I., 1999. Optimization of cutting parameters for maximizing tool life. International Journal of Machine Tools and Manufacture 39, 343–353. Chua, M., Rahman, M., Wong, Y., Loh, H., 1993. Determination of optimal cutting conditions using design of experiments and optimization techniques. International Journal of Machine Tools and Manufacture 33, 297–305. Damir, A., Ng, E.G., Elbestawi, M., 2011. Force prediction and stability analysis of plunge milling of systems with rigid and flexible workpiece. The International Journal of Advanced Manufacturing Technology 54, 853–877. Dong, Y., 1992. A unified optimization model of a machining process for specified conditions of machined surface and process performance. The International Journal of Production Research 30, 647–663. Galimberti, J.M., 1962–1963. Improved metal removal rates for difficult-to-machine alloys. Creative Manufacturing Seminar, ASTME 63-194. Choudhury, I.A., El-Baradie, M.A., 1998. Machinability of nickel-base super alloys: a general review. Journal of Materials Processing Technology 77, 278–284. Juan, H., Yu, S., Lee, B., 2003. The optimal cutting-parameter selection of production cost in HSM for SKD61 tool steels. International Journal of Machine Tools and Manufacture 43, 679–686. Kim, D., Ramulu, M., 2004. Drilling process optimization for graphite/ bismaleimide–titanium alloy stacks. Composite structures 63, 101–114. Ko, J.H., Altintas, Y., 2007a. Dynamics and stability of plunge milling operations. Journal of Manufacturing Science and Engineering 129, 32. Ko, J.H., Altintas, Y., 2007b. Time domain model of plunge milling operation. International Journal of Machine Tools and Manufacture 47, 1351–1361. Kopac, J., Bahor, M., Sokovic, M., 2002. Optimal machining parameters for achieving the desired surface roughness in fine turning of cold pre-formed steel workpieces. International Journal of Machine Tools and Manufacture 42, 707–716. Li, Y., Liang, S., Petrof, R., Seth, B., 2000. Force modelling for cylindrical plunge cutting. The International Journal of Advanced Manufacturing Technology 16, 863–870. Liu, Y., Wang, C., 1999. A modified genetic algorithm based optimisation of milling parameters. The International Journal of Advanced Manufacturing Technology 15, 796–799. Al-Ahmad, M.A.D.A., Lescalier, C., Bomont, O., 2005. Year of conference modelling of cutting forces in plunge milling. In: 7th International Conference on Advanced Manufacturing Systems and Technology, Udine, Italy. Merdol, A., Altintas, Y., 2004. Multi frequency solution of chatter stability for low immersion milling. ASME Journal of Manufacturing Science and Engineering 126, 459–466. Shaw, M., Nakayama, K., 1967. Machining high strength materials. CIRP AnnalsManufacturing Technology 15, 45–59. Shunmugam, M., Bhaskara Reddy, S., Narendran, T., 2000. Selection of optimal conditions in multi-pass face-milling using a genetic algorithm. International Journal of Machine Tools and Manufacture 40, 401–414. Smithberg, D., 1987. Inconel 718 machining manual. Report 6M59-559. Manufacturing Research and Development. Boeing Commercial Airplane Company. Suresh, P., Venkateswara Rao, P., Deshmukh, S., 2002. A genetic algorithmic approach for optimization of surface roughness prediction model. International Journal of Machine Tools and Manufacture 42, 675–680. Insperger, T., Stépán, G., 2002. Semi-discretization method for delayed systems. International Journal for Numerical Methods in Engineering 55, 503–518. Tolouei-Rad, M., Bidhendi, I., 1997. On the optimization of machining parameters for milling operations. International Journal of Machine Tools and Manufacture 37, 1–16. Wakaoka, S., Yamane, Y., Sekiya, K., Narutaki, N., 2002. High-speed and highaccuracy plunge cutting for vertical walls. Journal of Materials Processing Technology 127, 246–250. Wang, J., 1993. Multiple-objective optimisation of machining operations based on neural networks. The International Journal of Advanced Manufacturing Technology 8, 235–243. Wang, Z., Rahman, M., Wong, Y., Sun, J., 2005. Optimization of multi-pass milling using parallel genetic algorithm and parallel genetic simulated annealing. International Journal of Machine Tools and Manufacture 45, 1726–1734.