Int J Adv Manuf Technol DOI 10.1007/s00170-015-7127-x

ORIGINAL ARTICLE

Influence of dynamic effects on surface roughness for face milling process Shi Zhenyu 1 & Liu Luning 1 & Liu Zhanqiang 1

Received: 18 September 2014 / Accepted: 6 April 2015 # Springer-Verlag London 2015

Abstract In face milling processes, the surface roughness of the machined part reflects the cutting performance of face milling cutter. Surface roughness depends on different factors including feed direction, axial and radial run-out errors, and cutting tool geometry. In this paper, an algorithm considering the effects of static and dynamic factors on surface roughness for predicting the surface roughness is proposed. This work is focusing on straight-edged square insert. The dynamic characteristics of the milling process are also introduced. An electronic impact hammer is used to identify the dynamic parameters of the cutting system. Milling experiments are conducted to validate the prediction model. Results show that the prediction model can estimate the surface roughness of the machined parts after face milling. This paper provides an in-depth understanding of the relationship between machined surface roughness and process conditions especially for axial and radial run-out errors induced by static deformation and Z-axial relative displacement induced by forced vibration. The outcome of this research will lead to methodologies for costeffective monitoring and surface roughness control.

Keywords Static surface roughness roughness . High-speed face milling

. Dynamic surface . Straight-edged insert

* Liu Zhanqiang [email protected] 1

Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Shandong University, Ministry of Education, Jinan, People’s Republic of China

1 Introduction Workpiece surface quality can reflect the cutting performance of face milling cutter. Evaluation of the surface roughness is an important indicator of the quality of the workpiece surface [1, 2]. In face milling processes, since the forced and selfexcited vibration generated by centrifugal force and dynamic cutting force has significant effect on milling stability and surface quality, modeling of the surface roughness in face milling is more challenging than that in turning operations. Mansour and Abdalla [3] pointed out that there are many factors which influence the evaluation of surface roughness. They developed a surface roughness model for the end milling EN32N by considering the effects of cutting speed, federate, and axial depth of cut. Results show that an increase in either the feed or the axial depth of cut increases the surface roughness, while an increase in the cutting speed decreases the surface roughness. However, they did not consider the effect of dynamic motions of the cutting process. Wang and Chang [4] researched the surface roughness by taking slot end-milling experiments. Results show that the dry-cut roughness was reduced by applying cutting fluid, and the significant factors affecting the dry-cut model were the cutting speed, feed, concavity, and axial relief angles. Twardowski et al. [5] analyzed the surface roughness of hardened steel after high-speed milling and elaborated a surface roughness model considering the effects of milling parameters and cutter displacements. The analysis of surface profile charts from the point of view of vibrations and cutting force components is also involved. The researchers keep using theoretical or experimental methods to study the effect of different factors on the surface roughness and trying to give a reasonable explanation. Benardos and Vosniakos [6] presented and discussed various methodologies and strategies that are adopted by researchers in order to predict surface roughness. They pointed

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out that the majority of the existing literatures study this problem in terms of tool features, cutting parameters, cutting phenomenon, tools, fixtures, and workpiece characteristics. Ehmann and Hong [7] introduced a method called “surfaceshaping system” to represent the surface generation process. The system is considering two aspects: one is the kinematics of the machine tool, and the other is the cutting tool geometry. Kim and Chu [8] pointed out that the surface roughness could be determined by the maximum height of the effective scallop including the effects of cutter marks and conventional scallops. The run-out effects were included to make the predicted surface roughness agree with the actual surface roughness. Baptista and Antune Simoes [9] analyzed the effects of three- and five-axis milling of sculptured surface on surface finish and introduced the effects of step over and feed direction on surface roughness. Results showed that lower surface roughness can be obtained by using the end mill inclined in feed direction. Cui and Zhao [10] conducted high-speed face milling of AISI H13 hardened steel and found that with the increment of cutting speed, surface roughness decreased first and then increased rapidly and lowest surface roughness can be obtained at the cutting speed of about 1500 m/min. But, the effects of other parameters of surface roughness are not discussed in their paper. Sai and Bouzid [11] proposed an experimental system method to analyze the evolution of surface roughness in connection with cutting parameters including cutting speed and feed/tooth. Effects of other parameters are not considered in their research. Franco et al. [12] established a surface roughness model for face milling cutter with round blade, considering the cutting parameters (feed rate, depth of cut, etc.), tool geometry (tool teeth, blade diameter, etc.), the tool axis, and radial run-out errors. Milling experiments are also made to verify the validity of the model, and the discrepancies between the experimental and theoretical surface profiles are assumed to be a consequence of different factors such as the variation in undeformed chip thickness along the surface profile. Dae et al. [13] studied surface roughness formation mechanism for face milling cutter with square blade. He found out the surface roughness of the workpiece depending on the tool nose radius and feed/tooth, etc. and established a surface roughness model

to optimize the workpiece feed rate. However, this model does not carry out the statistical analysis of tool errors and does not represent the sensitivity of surface roughness to variations in these errors. Lee et al. [14] developed a theoretical model considering the effects of cutting tool axis inclination on surface roughness in high-speed face milling cutting process. However, the model did not consider the defects in the location of the cutting tool teeth. Cui et al. [15] researched the effect of chip temperature on surface roughness in highspeed face milling of hardened steel and found that the thermal softening effects induced by higher chip temperature led to lower cutting force and more stable cutting process which was beneficial for the better surface roughness. Lela et al. [16] examined the influence of cutting speed and depth of cut on surface roughness in face milling process by adopting three different modeling methodologies namely regression analysis (RA), support vector machines (SVM), and Bayesian neural network (BNN). All three models show that the feed/tooth has the largest effects on surface roughness. But, the tool errors are not considered in their paper. From above analysis, it can be seen that to predict the surface roughness for face milling process, it is necessary to develop a model that includes the influence of cutting conditions, tool errors, and cutting tool geometry. However, the models that have deduced until now have only considered some of these factors. In this paper, a surface roughness prediction model was developed by considering that all these factors including tool tip characteristics consist of shape of tooth, radius of nose, and inherent rake angle; cutter characteristics consist of number of teeth, amount of axial, and radial run-out; process characteristics consist of feed, cutting speed, and machine behavior under operating conditions.

2 Influence factors for surface roughness 2.1 Effects of feed direction Eysion and Liu [17] pointed out that during face milling process, when it is down milling and the milling width is two

Fig. 1 Effect of feed direction on surface roughness Minimum value for surface roughness

Minimum value of feed/tooth

Rotation direction

Machined surface

Maximum value for surface roughness

Maximum value of feed/tooth

Feed direction

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thirds of the tool diameter, it is more favorable for the milling process. Since the angle between the cutting teeth and feed direction is always changing, the cutting force in tangential and radial direction also varies which, in turn, introduces different feed textures. As shown in Fig. 1, when cutting teeth and feed direction are parallel, the actual feed/tooth becomes to be maximum and the surface roughness can reach maximum value. When cutting teeth cuts out of workpiece, the actual feed/tooth becomes to be minimum and the surface roughness can get minimum value. Hence, the surface roughness prediction model should build on the direction when it is parallel to feed direction. 2.2 Effect of cutting tool geometry Figure 2 shows the effects of cutting insert geometry on surface roughness with the same feed/tooth 0.6 mm/Z. Figure 2a shows a small rounded insert with a radius tip of 0.10 mm. It can be seen that the surface roughness is bigger than others; Fig. 2b shows big rounded insert with a radius of tip 0.8 mm. It can be seen that the surface roughness significantly reduced, and Fig. 2c shows a straight-edged insert with straight edge 3.51 mm. The surface roughness can realize minimum when feed/tooth keeps length of insert edge or less. 2.3 Axial and radial run-out error effects on surface roughness

feed/tooth, cutting velocity, and depth of cut were optimizated and the axial and radial run-out errors of each cutting tooth will be the main factors affecting the surface roughness. In this paper, 100B08RS75SD12DG cutting system with six teeth from KENNAMETAL as shown in Fig. 3 was used. Figure 4 shows general view of the effects of axial and radial run-out of the six teeth of the face milling cutter on surface roughness in milling process. Even though feed/tooth is fixed during cutting process, due to the effect of axial and radial run-out errors, the distance between the adjacent two cutting teeth is not exactly the same. There are deviations in axial and radial direction for each cutting tooth. Some teeth involved in cutting process will not affect the workpiece surface roughness, because its trace will be removed by the following cutting teeth. Some cutting teeth even do not have the chance to participate in cutting. Hence, the final surface morphology is decided by the combined effect of axial and radial run-out of each cutting tooth which, in turn, affects the workpiece surface roughness. It can be seen that the axial and radial run-out of the straight-edged insert is the main factor affecting surface roughness, which has bigger effect than feed/tooth.

3 Prediction model of surface roughness 3.1 Analysis of face milling process

During the manufacturing and installation process of cutting tool insert, there are actually three separate errors that affect surface finish. The first one is cutter quality issues relating to the accuracy of the pockets, etc., the second is the tool setup errors, and the third is the machine behavior under load. Hence, after face milling cutter was installed on spindle of machine tool, there are axial and radial run-out errors for each tooth caused by the three separate error sources. After machine tools, face milling cutter, and workpiece have been decided, cutting parameters such as

Face milling system is shown in Fig. 5. The upward direction along the common axis of “spindle-handle-face milling cutter” is set to be Z-axis. Direction opposite to the feed direction of the workpiece is set to be X-axis. Y-axis is set in a direction perpendicular to the X- and Z-axes, pointing to the side where the cutter cuts out. It can be seen that the maximum value of surface roughness is in the direction of X. θі is the angular rotation of the ith tooth that rotates from the entry point Ts to X, and ti is the time needed from Ts to X. D is

Fig. 2 Cutting tool geometry effect on surface roughness. a Small round insert. b Big rounded insert. c Straight-edged insert

R0.8mm

R0.1mm

15嘙 3.51mm

fz 0.6mm/Z

a

Small round insert

fz 0.6mm/Z

b

Big rounded insert

fz 0.6mm/Z

c Straight-edged insert

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Rotation direction Z 1 2:1

Workpiece

Te

Y

Xt

Machined

Fig. 3 Face milling cutter

surface

the cutting tool diameter and V is the feed rate. The displacement in X direction Xi is determined by the following: D⋅θi ⋅π Xi ¼ 360

ð1Þ

O θt

Xn The i+1 th tooth

θn

X The i-th tooth TS

θi Xi

Feed direction

ti can be calculated as follows: ti ¼

Xi V

ð2Þ

Xn and tn show distance and time needed between the adjacent two cutting teeth. D⋅θn ⋅π 360 Xn tn ¼ V

ð3Þ

Xn ¼

ð4Þ

Xt and tt show distance and time needed from Ts to Te. D⋅θt ⋅π 360 Xt tt ¼ V

ð5Þ

Xt ¼

ð6Þ

It can be seen that the cutting teeth simultaneously participated into cutting process should no bigger than the ratio of tt and tn. nZ ≤

tt tn

ð7Þ

The i-1 th tooth Fig. 5 Procedure analysis for face milling

Because the axial and radial cutting forces are different for the simultaneously participated cutting teeth, the axial and radial run-out errors are not the same, which, in turn, have effect on relative displacement in Z direction. Hence, it is necessary to consider that the dynamic cutting force induced by multiteeth participated in cutting and forced vibration’s effect on surface roughness. In this paper, both static and dynamic effects on surface roughness are considered.

3.2 The static model of surface roughness During cutting process, when face milling cutter is mounted on machine spindle, the axial and radial run-out errors for each

Z

x(i)

D

Actual orbit of the Feed/tooth

Nose radius

Tooth 1 Tooth 2 Tooth 3 Tooth 4 Tooth 5 Tooth 6

i-th tooth M[x(i,j), z(i,j)]

O

l

C r

M

fz

B

the i-th tooth

Cutting edge angle

Straight edge of cutting insert

j r

O O

a=1 A

s

A

D

D

Theory orbit of

z(i)

C

B

C B

X

Theory orbit of the i+1th tooth

Fig. 4 Effect of axial and radial run-out errors on surface roughness

Fig. 6 Cutting edge trajectory of the cutting teeth

Int J Adv Manuf Technol Z GT

KT

MT ZT (t)

Fig. 9 Structure diagram for cutting insert

FT Z FW Z MW

KW

In the X-axis sampling length, the measurement data point is n, the face milling cutter tooth is zt, and the X-axial incremental value of each data point is

ZW (t)

Δx ¼

GW

zt ⋅f z n

ð8Þ

Fig. 7 Vibration model in Z direction for face milling

The X-axial coordinate value of the jth data point on the cutting edge contour line of the ith tooth is determined by Eq. 9:

tooth have been decided. The model built on the axial and radial run-out errors is considered to be static surface roughness model. The static model is built in the direction of X-axis which is parallel to feed direction, for surface roughness obtained the maximum value in the direction. Figure 6 shows the cutting edge trajectory curves for straight-edged insert when ith cutting tooth was involved in cutting. As shown in Fig. 6, the cutting edge trajectory included a straight line AB, a nose section BC, and the other line CD. Due to the effect of runout errors, the cutting edge trajectory moves from ABCD to A′B′C′D′. The center point of the trajectory moves from O to O′. M[x(i,j),z(i,j)] is a casual point in this trajectory. The distance between the (i+1)th and the ith tooth is fz. The radial run-out error for the ith tooth is εx(i), and the axial run-out error is εz(i).

xði; jÞ ¼ j⋅Δx−εx ðiÞ

ði ¼ 1; …; zt ; j ¼ 1; …; nÞ

Equation 9 can also be expressed as follows: xði; jÞ ¼

zt ⋅f z ⋅j−εx ðiÞ n

ði ¼ 1; …; zt ; j ¼ 1; …; nÞ

ð10Þ

The starting point A′ on the cutting edge contour of the ith tooth is assumed to be located at the jth data point in the radial direction, and the amount of data point a=1, and then, the coordinates of point A′ marked as x(i,a) and z(i,a) can be expressed as xði; aÞ ¼ j⋅Δx−εx ðiÞ ¼ a⋅Δx−εx ðiÞ

ð11Þ

zði; aÞ ¼ εz ðiÞ

ð12Þ

The length of the line segments A′B′ on the cutting edge contour line is assumed to be s, and then, the coordinates of the endpoint B′ marked as x(i,b) and z(i,b) can be expressed as

Fig. 8 Modal test system for face milling system

Spindle

Holder

Face milling cutter

Acceleration sensor Signal PC

ð9Þ

FFT

amplifier

Electronic impact hammer

Int J Adv Manuf Technol Parameters for straight-edged insert D

S

L10

BS

Table 3 Rε

hm

Cutting edge

xði; bÞ ¼ j⋅Δx þ s−εx ðiÞ ¼ b⋅Δx−εx ðiÞ

ð13Þ

zði; bÞ ¼ εz ðiÞ

ð14Þ

Thus, the amount of data point b of the endpoint B′ on the straight line A′B′ is j⋅Δx þ s Δx

ð15Þ

The nose radius of blade is assumed to be r, and then, the coordinates of center point B′ marked as x(i,b) and z(i,b) on the nose curve can be expressed as xði; oÞ ¼ b⋅Δx

ð16Þ

zði; oÞ ¼ εz ðiÞ þ r

ð17Þ

The main lead angle is assumed to be γ, and then, the coordinates of endpoint C′ marked as x(i,c) and z(i,c) on the nose curve can be expressed as xði; cÞ ¼ j⋅Δx þ s−εx ðiÞ þ rsinγ ¼ c⋅Δx

ð18Þ

zði; cÞ ¼ εz ðiÞ þ rð1−cosγ Þ

ð19Þ

Thus, the amount of data point c of the endpoint C′ on the nose curve is j⋅Δx þ s−εx ðiÞ þ rsinγ c¼ Δx

ð20Þ

Axial depth of cut of blade is assumed to be az, and the length l of the line segment C′D′ on the cutting edge contour line is l ¼ az =sinγ

−0.002 0.001

−0.002 0.002

−0.020 0.012

−0.010 0.002

Thus, the amount of data point c of the endpoint D′ on the line segment C′D′ is d¼

j⋅Δx þ s−εx ðiÞ þ rsinγ þ lcosγ Δx

xði; d Þ ¼ j⋅Δx þ s−εx ðiÞ þ rsinγ þ lcosγ ¼ Δx⋅d

ð22Þ

zði; d Þ ¼ εz ðiÞ þ rð1−cosγ Þ þ lsinγ

ð23Þ

Recommended feed/tooth for cutting insert

zði; jÞ ¼ εz ðiÞ

ð25Þ

When b≤j
ð26Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi zði; jÞ ¼ r2 −½xði; jÞ−b⋅Δx2 þ εz ðiÞ þ r

ð27Þ

When c≤j
fz (mm/Z)

20 %

30 %

40 %

50 %

100 %

0.33

0.23

0.19

0.16

0.15

0.10

ð28Þ

zði; jÞ ¼ tanγ ½xði; jÞ−ð j⋅Δx þ s−εx ðiÞ þ rsinγ Þ þ εz ðiÞ þ rð1−cosγ Þ

ð29Þ At this time, the trajectory of point M on each contour of the cutting edge can be calculated according to the formulas (25), (27), and (29). In the direction of the maximum value of the surface roughness, the surface roughness of the workpiece is obtained by superimposing on each tooth point trajectory.

Ratio of cutting width and cutting tool diameter 10 %

ð24Þ

When 1≤j
ð21Þ

Therefore, the coordinates of endpoint D′ marked as x(i,d) and z(i,d) on the line segment C′D′ can be expressed as

Table 2

Tooth 1 Tooth 2 Tooth 3 Tooth 4 Tooth 5 Tooth 6 Axial run-out −0.001 0.005 error Radial run-out −0.026 0.026 error

SDPT1204EDERGB 12.70 4.76 12.70 3.51 0.8 0.10 4

b¼

Measured axial and radial run-out errors (unit: mm)

Surface roughness (µm)

Table 1

-10

0 Machined distance (mm)

Fig. 10 Simulated surface orbits

According to the analysis above, it can be seen that radial run-out errors εx(i), axial run-out error εz(i), feed/tooth fz, teeth Zt, cutting edge length s, nose radius r, main lead angle γ, axial depth of cut az, and the X-axial total amount of measurement data point are directly related to the surface roughness. Among them, radial run-out errors εx(i) and axial run-out error εz(i) are the main affecting factors.

Dynamic axial displacement (µm)

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3.3 Dynamic model of surface roughness

Machined distance (mm)



8 9    < ˙˙  =  F TZ ði; t i Þ K T þ jGT MT Z T ði; t i Þ Z T ði; t i Þ ¼ þ ˙˙ Z W ði; t i Þ F WZ ði; t i Þ MW : K W þ jGW ; Z M ði; t i Þ

ð30Þ F TZ ði; t i Þ ¼ − F WZ ði; t i Þ

ð31Þ

Based on modal parameters of the face milling system, Z-axial exciting force and acceleration signals can be measured by milling experiment. Based on vibration differential equations of the face milling system (23) and (24), Z-axial relative displacement between the cutter and workpiece can be calculated under the stable cutting condition. That is to say, at ti moment, Z-axial relative dynamic displacement ZDR(i,ti) between the ith teeth and the workpiece excited by forced vibration can be gained by the instantaneous displacement ZT(i,ti) of the face

Fig. 11 Simulated dynamic axial displacement between workpiece and cutter

milling cutter and instantaneous displacement ZW(i,ti) of the workpiece. Z DR ði; t i Þ ¼ Z T ði; t i Þ þ Z W ði; t i Þ

ð32Þ

3.4 Prediction model of surface roughness According the analysis above, workpiece surface roughness is the result of various factors such as the axial and radial run-out errors of each cutting tooth, dynamic milling force, forced vibration, and workpiece feed speed. In the maximum direction of the surface roughness, the prediction model of workpiece surface roughness in high-speed face milling is established according to the formulas (25), (27), (29), and (32). On the location of the jth data point within the sampling length on the X-axis, Z-axial instantaneous relative displacement ZR(i,j,ti) between the ith tooth and the workpiece can be represented as Z R ði; j; t i Þ ¼ zði; jÞ þ Z DR ði; t i Þ

ð33Þ

When using the model to predict workpiece surface roughness, the first step is to get the static prediction value of surface roughness by measuring axial and radial run-out errors of each tooth and calculating the blade trajectory with Matlab software. The second step is to get the dynamic prediction value of surface roughness by determining the modal parameters of

12 10 8 6 4 2 0 -2 -4 -6 -8 -10 0

Surface roughness (μm)

Maciej et al. [18] pointed out that the forced vibration generated in high-speed face milling process will worsen the workpiece surface quality. Despite that the self-excited vibrations also affect the surface texture, regenerative chatter generally occurs under heavy-duty cutting conditions, and thus, the effects of self-excited vibrations on the surface roughness can be ignored. The effect on surface roughness of the Z-axial relative displacement between the workpiece and teeth caused by forced vibration will be the only factor to be considered. As shown in Fig. 7, Z-axial single degree of freedom system for cutter and workpiece is respectively built up to establish their own vibration differential equation. Modal mass, modal stiffness, and modal damping of the face milling cutter are MT, KT, and GT, respectively. Modal mass, modal stiffness, and modal damping of the workpiece are MW, KW, and GW, respectively. At ti moment, the Z-axial interaction force on the ith blade tip point of the face milling cutter is respectively FTZ(i,ti) and FWZ(i,ti), of equal magnitude but opposite direction. Z-axial relative displacement ZR(i,ti) between the workpiece and teeth can be obtained according to the instantaneous displacement ZT(i,ti) of the cutter and instantaneous displacement ZW(i,ti) of the workpiece. In this way, the differential equation for vibration of the Zaxial face milling system can be expressed as follows:

0.5

1.0 1.5 2.0 Machined distance (mm)

Fig. 12 Simulated surface profile

2.5

3.0

Surface roughness (µm)

Int J Adv Manuf Technol 10 8 6 4 2 0 -2 -4 -6 -8 -10

4.2 Face milling experiments

0

0.5

1.0 1.5 2.0 Machined distance (mm)

2.5

3.0

Fig. 13 Measured surface profile

face milling system through the modal experiment, measuring the Z-axial milling force component through the milling experiment and solving the vibration differential equation to obtain the Z-axial instantaneous dynamic relative displacement between the cutter and workpiece. The final step is to predict the surface roughness of the workpiece by combining the static and dynamic prediction values.

4 Experimental procedure

In this paper, 100B08RS75SD12DG was chosen as a face milling cutter, as shown in Fig. 9, cutting inserts were straight-edged square inserts, and workpiece was Al 7050. Table 1 shows the cutting insert parameters, where hm is the chip thickness. According to the user’s manual, the recommended feed/tooth is shown in Table 2. For the milling width is two thirds of the cutting tool diameter is the best choice for face milling, during cutting process, feed/tooth fz is chosen as 0.14 mm/Z. The cutting velocity is 150 m/min. Figure 9 shows the diagram of straight-edged square insert. The experiments were conducted on VMC0540d. Cutting tool presetting tools were used to fix face milling cutter, and the axial and radial run-out errors were measured. The results are shown in Table 3. For several teeth contribute to the surface finish, the surface profile has to be calculated considering tool errors, cutting conditions, etc. The measured axial and radial run-out errors are used in Eqs. (25), (27), (29), and (32) to get the static prediction value of surface roughness.

4.1 Modal test for face milling system

5 Results and discussion The identification of the parameters of the cutting system is necessary in order to model the dynamic characteristics of surface roughness. For the workpiece is clamped directly on the table of the milling machine, the vibration behavior tested includes the cutting tool system, workpiece, and the table of the milling machine. These can be obtained by tests of impact to the tool and workpiece. The principle of the modal test is shown in Fig. 8. The modal tests were conducted on VMC0540d vertical machine center which is installed with HSK63A holder and face milling cutter as shown in Fig. 8. Force and the acceleration signals in the Z direction are from the measurement of the modal test. The natural frequency and damping ratio of the tool were estimated as 2029 Hz and 0.0947.

12 Surface roughness (µm)

Fig. 14 Contrast between simulated results and experimental results

By using Eqs. (25), (27), and (29), each insert orbit can be simulated, as shown in Fig. 10. According to the modal parameters and milling force in Z direction, the instantaneous dynamic relative displacement induced by the forced vibration between workpiece and cutting tool is shown in Fig. 11. According to the surface roughness prediction model, by combining the results of Figs. 10 and 11, the prediction surface roughness profile can be made by trimming lines above the intersection point, as shown in Fig. 12. Figure 13 shows the surface profile of the machined surface measured by a stylus surface profiler.

10 8 6 4 2 0 -2

Experimental results Ave Ra:3.81µm Simulated results Ave Ra:4.07µm

-4 -6 -8 -10 0

0.5

1.0

1.5

2.0

Machined distance (mm)

2.5

3.0

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Figure 14 shows the comparison results between the prediction model and measured surface roughness. The average surface roughness for experimental results is 3.81 μm, and the average surface roughness for simulated results is 4.07 μm. The deviation is 6 %. It can be seen that the prediction results coincide well with the real surface texture. The difference between the two results is coming from the measurement errors of runout, cutting force, and, simply, the vibration differential equations. From above results, it can be concluded that the surface roughness is affected by both the dynamic relative displacement and the static deformation of the axial and radial run-out errors. The prediction model proposed in this paper is especially suitable for the situation of multitooth that participated in face milling process.

References 1.

2.

3.

4.

5.

6. 7.

6 Conclusions

8.

From the developed model for surface roughness and the cutting experiments, the following conclusions can be obtained:

9. 10.

1. The prediction surface roughness model can predict surface texture of face milling. The models are established in the direction of the maximum value of surface roughness which considered the effects of radial and axial run-out error, feed/tooth, nose radius, and axial depth of cut. 2. The surface roughness is affected more by the axial and radial run-out errors than the cutting parameters such as feed/tooth.

11. 12.

13. 14.

15. Acknowledgments This work was supported by grants from Tai Shan Scholar Foundation. The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (51375272, U1201245), the Major Science and Technology Program of High-end CNC Machine Tools and Basic Manufacturing Equipment (2014ZX04012-014), the Specialized Research Fund for the Doctoral Program of Higher Education (20130131120032), China Postdoctoral Science Foundation (2013M540544), the Scientific Research Foundation of Shandong Province Outstanding Yong Scientist Award (BS2013ZZ003), and Independent Innovation Foundation of Shandong University.

16.

17. 18.

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