Micro texture fabrication by a non-resonant vibration generator

Journal of Manufacturing Processes 45 (2019) 732–745

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Technical Paper

Micro texture fabrication by a non-resonant vibration generator a,b,⁎

Yanjie Yuan a b

a

a

b

, Dawei Zhang , Xiubing Jing , Jian Cao , Kornel F. Ehmann

b

T

Key Laboratory of Advanced Ceramics and Machine Technology of Ministry of Education, Tianjin University, China Department of Mechanical Engineering, Northwestern University, USA

ARTICLE INFO

ABSTRACT

Keywords: Vibration surface texturing Non-resonant vibration generator Double frequency surface texturing

Surface texturing with designed micro-structures exhibits numerous novel functional characteristics and features as compared to ordinary smooth surfaces or surfaces generated by the conventional customary manufacturing processes. Though several micro-scale surface textures generating techniques have been used to fabricate surface textures, most of these techniques are either of low efficiency or lack the flexibility to fabricate sophisticated surface topographies. In this study, a non-resonant vibration generator was used to control the micro surface texturing generation process. The principles of this vibration assisted surface texturing process are analyzed. Furthermore, surface generation models for both the cylindrical and flat surfaces of a cylinder are formulated to serve as a vehicle for generating the desired surface topography. Finally, surface texturing experiments were conducted, and complex micro textured topographies were successfully fabricated.

1. Introduction Textured surfaces can enhance the functionality and performance of industrial components and are widely used in various industries for applications including self-cleaning [1], tribology [2], optics [3], solar energy technology [4], and bioengineering [5], to mention a few. To promote the broad use of structured surfaces, high-performance manufacturing technologies for the fabrication of micro structures with arbitrary complex geometric features are critically required. Currently, several micro-scale surface texturing techniques are in use to generate textured surfaces. Focused ion beam, electron beam machining and lithography are favorable for generating micro/nano structures with straight sidewalls, yet they are not economical for generating textured surfaces with large heights due to their time-consuming nature [6]. Although laser ablation can improve machining efficiency and can be applied to most materials, the surface properties machined by the laser may change due to the heat-affected-zone and material re-deposition. Micro-rolling generally offers the highest production rates among most manufacturing operations. Since this texturing process is based on the material’s plastic deformation, it is impractical to generate textures on brittle materials. In addition, the geometrical shape must be pre-textured on the roll. This inevitably increases the cost when used for small-scale production. To generate accurate surface textures, ultra-precision diamond cutting is still one of the most promising approaches due to its flexibility and high geometric accuracy. Traditional diamond cutting is generally

⁎

implemented on multi-axis machines to create the desired texture patterns [7]. However, machine tool characteristics such as large inertia, backlash and friction, impose barriers on the ability to accurately and efficiently generate the desired micro-scale surface textures [8]. In addition, extremely high chemical tool wear occurs when machining hard materials by traditional diamonds cutting processes. To solve this problem, Shamoto et al. [9] developed an elliptical vibration cutting (EVC) method by superimposing a vibration on the cutting tool tip. In the EVC process, the tip of the tool periodically separates from the workpiece. This has numerous benefits including lower cutting forces, extended tool life, burr elimination and better surface finish to mention a few [10]. Numerous intractable materials such as ceramics, tungsten carbide, hardened steel, etc. were successfully machined using the EVC method. Inspired by the idea of the EVC method, Guo et al. [11] designed a 2D ultrasonic vibrator and used it for surface texturing. Later, a surface generation model was built for this elliptical vibration texturing process (EVT) based on the analysis of the cutting mechanics of surface generation [12]. Furthermore, Suzuki et al. [13] developed an advanced amplitude control system for the EVT process. Ultra-precision micro-groove structures were also successfully generated on hardened steel using this method. However, these proposed methods encounter two vital problems that need to be solved. Firstly, the frequencies of these tertiary vibration devices are fixed since they work in the device’s resonant mode, which obviously hinders their broad application in generating diverse and sophisticated surface textures [14]. Secondly, they also have shortcomings in terms of low stiffness or small vibration

Corresponding author at: Key Laboratory of Advanced Ceramics and Machine Technology of Ministry of Education, Tianjin University, China. E-mail address: [email protected] (Y. Yuan).

https://doi.org/10.1016/j.jmapro.2019.08.010 Received 30 May 2018; Received in revised form 9 February 2019; Accepted 5 August 2019 1526-6125/ © 2019 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

Journal of Manufacturing Processes 45 (2019) 732–745

Y. Yuan, et al.

amplitudes, which restrict surface texture fabrication at larger height scales. To overcome the above-mentioned problems, non-resonant vibration generators offer a good choice. He et al. [15] designed a one dimensional (1D) non-resonant vibration generator to generate micro dimples on cylindrical surfaces. In our previous work, a new two dimensional (2D) flexure-based non-resonant vibration generator was developed [16]. It can generate considerably larger vibration amplitudes over a range of frequencies than the resonant devices. Another advantage of this device is that it can use not only a single frequency but also multiple frequencies at the same time to generate arbitrary trajectories. Here we further explore the feasibility of using this nonresonant vibration generator for complex surface texture fabrication. The principles of double or multiple frequency surface texturing process on cylindrical surfaces for complex surface texture fabrication are discussed in detail. Furthermore, the principle of uniform surface texture fabrication on the face of a cylinder is also analyzed. Surface generation models both for the cylindrical and the face surfaces of a cylinder are established to provide guidelines for generating the desired surface topography. The organization of the paper is shown as follows: Firstly, the design and analysis of the non-resonant vibration generator is conducted and provided in Section 2. The fundamental principles of the vibration assisted texturing method are described in Section 3. In Section 4 surface generation models for both cylindrical and flat surfaces are presented. The experimental setup, equipment and procedures are described in Section 5. A variety of complex textures are generated and compared to the simulation results in Section 6, followed by conclusions in Section 7.

Fig. 2. Experimental setup.

DOC directions will correspondingly change, resulting in an arbitrary 2D trajectory defined by these two directions. The vibration trajectories were measured using two Micro-Sense capacitance sensors which were orthogonally arranged in normal and tangential directions. The measuring range of the capacitance sensors is 100 μm with a 100 kHz bandwidth and sub-nanometer resolution. The measuring setup is shown in Fig. 2. Two sinusoidal signals were generated in LabVIEW software and sent to a data acquisition card (NI PCIe-6361, USA) as drive signals. The signals were then input into the piezo-amplifier (Trek PZD350A, USA), with a rapid response rate of 500 V/μs. Two amplified sinusoidal signals (peak to valley 400 V) with phase differences ranging from 0 to 180 deg in 30 deg intervals were used to excite the piezoelectric actuators. The measured vibration displacements were collected at a sampling frequency of 10 kHz using the same data acquisition card. The measured results are shown in Fig. 3(a). It is clearly shown that the vibration locus changes with varying input phase difference. When the input voltage phase difference is 0 deg and 180 deg, the locus narrows into a line. For other conditions, perfect eclipses can be acquired. When the input voltage phase difference is 60 deg, the variation of the displacement (peak to valley) with voltage is shown in Fig. 3(b). It should be noted that the output displacements will be different with different preload forces of the piezoelectric actuators. In both directions, the vibration amplitude increases with increasing voltage. Therefore, different vibration amplitudes and vibration loci can be obtained by controlling the input voltage amplitude and phase shift. In addition, since this device works in the non-resonant mode, it can use not only a single frequency but also multiple frequencies at the same time. Therefore, arbitrary complex surface textures can be generated in one step by summing several different sinusoidal signals.

2. 2D non-resonant vibration generator The schematic of the designed non-resonant vibration generator is shown in Fig. 1(a) [16]. Two compound bridge mechanisms and piezoelectric actuators are symmetrically configured on two sides of a Zshaped flexure hinge mechanism. The kinematic scheme of the flexures in their deformed and undeformed configuration is shown in Fig. 1(b). When two periodic voltages are input to the piezoelectric actuators, driving forces occur between the compound bridge and the piezoelectric actuators. The middle mass block will periodically move in the cutting direction due to the parallel-kinematic configuration of the device. The outputs of the compound bridge mechanisms serve as the inputs of the Z-shaped flexure hinge mechanism. In response, the bending of the flexible beams outputs a displacement at the tool tip in the depth of cut (DOC) direction. With different input voltage waveform amplitudes and phase shifts, the tool tip motions in the cutting and

Fig. 1. Schematic of (a) the designed non-resonant vibration generator and (b) flexure kinematics. 733

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Fig. 3. Measured trajectories of the non-resonant tertiary motion generator: (a) as a function of phase and (b) as a function of input voltage.

Fig. 4. Schematics of vibration-assisted cutting and vibration-assisted surface texturing process: (a) EVC, (b) EVT and (c) DEVT processes.

3. Principles of surface texturing

speed ratio, is defined as the ratio of the nominal cutting velocity over the maximum periodic vibration velocity component as:

The schematic diagrams of the tool tip motion in the EVC, EVT and a double frequency surface texturing process (DEVT) are shown in Fig. 4. By setting the cutting direction as the x-axis, and the DOC direction as the y-axis, both the EVC and the EVT process can be expressed in a Cartesian coordinate system. The position of the cutting tool relative to workpiece in the EVC and EVT processes can be expressed as:

x1 (t ) = A cos(

0t

+ ) + Vc t

y1 (t ) = B cos(

0 t)

=

(1)

where x1 and y1 are displacements in the cutting and DOC directions, respectively, A and B are the tool vibration amplitudes, respectively, the angular frequency ω0 is defined by the vibration frequency f as ω0 = 2πf, φ denotes the phase shift and Vc is the nominal cutting velocity. Based on Eqs. (1) and (2), the cutting tool velocities relative to the workpiece are given as:

A sin(

0t

y 1 (t ) =

B sin(

0 t)

+ ) + Vc

(5)

Generally, the speed ratio λ in EVC processes is low (λ≤1). As shown in Fig. 4(a), the tool tip will periodically separate from the workpiece under this condition due to the reverse motion of the cutting tool. This behavior brings many benefits, e.g., reduced cutting force, improved surface finish, extended tool life, etc. [10]. The EVT process originates from the EVC process, however, a relatively higher speed ratio (λ﹥1) is used in EVT, the interrupted cutting phenomenon disappears, and the tool tip vibration in the DOC direction results in a relative motion between the cutting tool and the workpiece. Consequently, periodic micro dimples are generated on the workpiece as shown in Fig. 4(b). When several frequencies are used, the tool tip trajectories become more complex. Taking two frequencies as an example, a complex micro structure can be generated on the workpiece surface in the DEVT process as shown in Fig. 4(c). The relative displacement of the tool tip, in this case, can be described as:

(2)

x 1 (t ) =

Vc A

(3) (4)

The velocities of the tool tip relative to workpiece in the cutting direction of the EVC and EVT processes are no longer a constant value according to Eq. (3). They consist of a periodic vibration velocity component (-Asin(ωt+φ)) and a constant cutting speed (Vc) component. To characterize the EVC and EVT processes, a parameter, λ, the

x2 (t ) = A1 cos(

1t

+

y2 (t ) = B1 cos(

1t)

1)

+ A2 cos(

+ B2 cos(

2t

+

2)

(6)

+ Vc t

(7)

2 t)

while the tool tip velocities in the cutting and DOC directions is given by:

x 2 (t ) = 734

A1

1 sin( 1 t

+

1)

+ A2

2

sin(

2t

+

2)

+ Vc

(8)

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Fig. 5. Clearance angle.

y 2 (t ) =

B1

1 sin( 1 t )

B2

2

sin(

(9)

2 t)

3.1. Influence of the clearance angles on the texture generation process In the dimple generation process, shown in Fig. 5, the insert first moves downward to the bottom of the dimple and then moves upward. To avoid interference of the machined surface with the tool flank surface, the clearance angle should be correctly selected. The slope along the tool path is defined as the angle between the tangent to the tool path and the x-axis as:

(t ) =

y 2 (t ) x 2 (t )

Fig. 6. Dimple pattern geometry definition on a cylindrical surface.

(10)

When the insert moves downward, to avoid interference of the machined surface with the tool flank surface, the clearance angel should satisfy:

max [ (t )]

Lc =

Lf =

=

(12)

ft 2 =

2 R0

(17)

fz × N

(18)

60

where fz is feed per revolution. Then, the distance between the workpiece center and the tool tip can be derived as:

r = r0

(13)

(19)

ft 2 t

The nominal instantaneous cutting velocity, in turn, can be expressed as:

where K is the integer part, and υ is the fractional part which decides the phase shift ξ. The phase shift distance ξ between two adjacent revolutions in the cutting direction is calculated as:

=

Lf

For the face surface of a cylinder, as the workpiece rotates, and the cutting tool approaches the workpiece center, the tool tip trajectory is an Archimedean spiral without the superimposed vibration as shown in Fig. 7. The federate of the insert in the radial direction can be calculated as:

where R0 is the radius of workpiece and N denotes the spindle speed (rev/min). A typical micro dimple structure on a cylindrical surface can be defined with the aid of Fig. 6. The number of dimples generated on the workpiece within one revolution is:

60f =K+ N

(16)

3.3. Dimple pattern geometry definition on the face surface of a cylinder

For a cylindrical surface, the nominal cutting velocity Vc can be expressed as:

=

ft N

where ft is the feed rate (mm/min). The phase shift distance δ between two adjacent dimples in one revolution in the feed direction can be calculated as:

3.2. Dimple pattern geometry definition on a cylindrical surface

2 R0 N 60

(15)

while the dimple interval length in the feed direction is the same as the feed per revolution, i.e.:

(11)

It should be noted that in Fig. 5, the cutting tool is assumed to have a perfectly sharp edge. However, in actual situations, the cutting-edge radius is in range of 0.5–5 μm while the DOC is in the range of dozens of microns. Therefore, even when the clearance angel satisfies the above condition, a part of the flank surface will still contact the machined surface and ploughing phenomena occur. A part of the material will elastically recovery after this ploughing process [17]. This elastical recovery effect will be considered in the surface generation models.

Vc =

Vc f

vc = rws = 2 (r0

(20)

ft 2 t ) N /60

When the spindle speed and the vibration frequency are constant, the dimple length Ll is:

(14)

The dimple interval length between two adjacent dimples in one revolution in the cutting direction is:

Ll = 735

t + tcut t

vc dt =

tcut 0

2 (r0

ft 2 t ) N /60dt

(21)

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Fig. 7. Dimple pattern geometry definition on the face surface of a cylinder.

where tcut is the tool engagement time given by:

tcut = t2

t1 =

cos

1 1 f

of material spring back is included in the model. However, how to calculate the spring back rate was not discussed in detail in their work. In addition, there is a lack of an accurate surface texturing model for the face surface of the cylinder. In this work, a surface texture generation model for both the cylindrical and the face surfaces of the cylinder are developed. The material removal mechanism in this surface texture generation process is analyzed, the spring back rate of the material is calculated and is included in the surface generation model.

1 DOC Az

(22)

where Az denotes the tool vibration amplitude in the DOC direction as shown in Fig. 7(b). If the spindle speed and the vibration velocity are constant, the number of dimples generated in one revolution is constant. In this case, the dimple length Ll decreases from the outer to inner diameters due to the decreasing cutting velocity. The phase shift angle between two adjacent machining passes is given by:

=2

4.1. Surface texture generation model on the cylindrical surface To accurately describe the vibration-assisted surface texturing process, three coordinate systems are defined as illustrated in Fig. 8. The machining coordinate system (Om-Xm Ym Zm) is defined with its origin set at the bottom face of the cylindrical workpiece and its Zm-axis in axial direction of the cylinder. The Ym-axis coincides with the cutting velocity direction at the initial contact point. The Xm-axis is determined by the right-hand rule. The workpiece coordinate system (Om-Xw Yw Zw) is a moving frame, which rotates around the Zw-axis at a constant speed ωt. The initial workpiece coordinate system is coincident with the machining coordinate system. To describe the tool geometry, a local tool coordinate system (Ot-Xt Yt Zt) is established on the rake face of the tool with its origin located at the tool nose arc center and its Xt-, Yt- and Zt-axes are coincident with the machining coordinate system. The geometry of a standard turning insert was adopted for the process model formulation as shown in Fig. 8. To simplify the modeling process, the following assumptions were made: (a) the cutting tool is

(23)

/

while the angular spacing can be calculated as:

=

tcut 0

2 N /60dt

(24)

The space between two adjacent dimples can be written as: t 2

Ll =

t 1

vc dt =

t 2 t 1

2 (r0

ft 2 t ) N /60dt

(25)

To fabricate uniform textures on the face surface, the ratio of the cutting velocity over the vibration frequency should be kept constant during the entire process, i.e.:

=

vc f

(26)

Based on Eq. (26), there are two ways to generate a uniform texture: one is to control the spindle speed, another is to control the vibration frequency. Since, the spindle speed is quite slow, it is hard to continuously control the spindle speed. In contrast, the vibration texturing system is easily controlled by LabVIEW software. To maintain δ as a constant, the vibration frequency needs to decrease from the workpiece’s outer diameter to its center by satisfying the following relationship:

f=

2 (r0

ft 2 t ) N 60

(27)

4. Surface texture generation models in vibration assisted texturing A surface texture generation model is useful for predicting the surface topography before the machining process and provide guidance in the selection of specific machining parameters to obtain the desired surface texture rather than using costly experiments. Therefore, an accurate surface generation model is vitally significant to reduce the overall machining cost. In a previous study, Guo et al. [12] built a surface texturing model for the cylindrical surface texture generating process, where the effect

Fig. 8. The coordinate systems on the cylindrical surface. 736

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Y. Yuan, et al.

radially symmetric with a nose radius, Rn, (b) the flank surface is a curved surface with a constant clearance angle and the rake surface is a planar surface, (c) the cutting-edge arc is the intersecting space curve of flank surface and rake surface. According to the definition in Guo’s work [12], the cutting tool geometry is defined by parametric equations (l, θ) in the local tool coordinate system (Ot-Xt Yt Zt) as:

Xt (l, ) = (Rn Yt (l, ) = (Rn

l sin t ) sin cos t l cos t sin t l sin t ) sin sin t + l cos t cos t ,

Zt (l, ) = (Rn

l sin

t)

[

min ,

mesh girds based on the specific spatial resolution ζ in the simulation process. The angular resolution, ν, is specified as the ratio of ζ over the workpiece radius R0. The mathematical expression of the cylindrical workpiece can be expressed in cylindrical form, i.e., as:

(L ,

max ]

(28) where γt and αt are the rake angle and clearance angle, respectively, θ is the angle between NOt and the Zt axis within a minimum, θmin, and a maximum, θmax, angle of the angular boundary of the cutting edge as shown in Fig. 8. When the l > 0, the parametric functions describe the flank face of the cutting tool while when l < 0, the parametric functions describe the rake face of cutting tool. Specifically, for l = 0 one obtains the equations defining cutting edge, i.e.:

[

min ,

L (l , , t ) L˜ w (l, , t ) = round w

max ]

by:

+

t ) T (X0

cos t sin t 0 0 sin t cos t 0 0 0 0 1 0 0 0 0 1

1 0 0 0

0 1 0 0

0 X0 DOC 0 H0 1 L0 + ft t 0 1

Xv (t ) Xt (l, ) Yt (l, ) Yv (t ) + Zt (l, ) Z v (t ) 1 0

Xw (l, , t ) Yw (l, , t ) = Rz ( Z w (l, , t ) 1

(31)

For faster calculation of the intersection of the cutting-edge and the workpiece, the tool coordinates with the superimposed vibrations need to be expressed in cylindrical form, i.e., as [18]:

L w (l , , t ) w (l , , t ) = w (l , , t )

=

Z w (l , , t ) Yw (l, , t ) Xw (l, , t )

t ) T (R 0

cos t sin t 0 0 sin t cos t 0 0 0 0 1 0 0 0 0 1

1 0 0 0

0 1 0 0

ft t , H0,

Z0 + DOC ) Ry (

0 R0 ft t 0 H0 1 Z0 + DOC 0 1

0 0 1 0

0 1 0 0

1 0 0 0

2 0 0 0 1

)

Xt (l, ) Xv (t ) Yt (l, ) Yv (t ) + Z v (t ) Zt (l, ) 1 0 Xt (l, ) Yt (l, ) + Zt (l, ) 1

Xv (t ) Yv (t ) Z v (t ) 0

(36)

Xw2 (l, , t ) + Yw2 (l, , t ) arctan

(35)

, t)

To develop the model three coordinate systems on the face surface of the cylinder are defined as shown in Fig. 10. The machining and the workpiece coordinate system are the same as the coordinate systems defined in Section 4.1. The workpiece coordinate system is established on the rake face of the tool with its origin located at the tool nose arc center with its Xt-, Yt- and Zt-axes coincident with the Zm-, Ym- and Xmaxes of the machining coordinate system. In the local tool coordinate system, the cutting tool is also defined by Eq. (28). The transformation between the local tool coordinate system and machining coordinate system is a pure translation T (R0 ft t , H0, Z0 + DOC ) and a rotation transformation Ry ( /2) , where Z0 is the initial contact position. Similarly, the coordinate transform relationship between the machining coordinate system and the workpiece coordinate system is also determined by a pure rotation transformation, which is defined by matrix Rz(-ωt). The tertiary motion of the tool tip for the case of two frequencies is defined by Eq. (30). Finally, the coordinates of the cutting tool coupled with the vibrations in the workpiece coordinate system can be written as:

2)

Xv (t ) Xt (l, ) Yt (l, ) Yv (t ) + Zt (l, ) Z v (t ) 1 0

w (l ,

4.2. Surface texture generation model on the face surface of the cylinder

(30)

DOC , H0, L 0 + ft t )

(34)

tn = (L˜ w (l, , t ), ˜w (l, , t ))

the tool tip vibrations in the workpiece coordinate system are given

Xw (l, , t ) Yw (l, , t ) = Rz ( Z w (l, , t ) 1

=

2t

, t)

For given points on the cutting-edge (specify parameter values l and θ) that intersect the workpiece, the nominal instantaneous chip thickness is the difference between the nearest workpiece surface height and the corresponding cutting-edge point in the radial direction, which can be calculated as:

To calculate the interaction points between the cutting tool and workpiece, the coordinate position (Xt, Yt, Zt) of any arbitrary cuttingedge point needs to transformed into the workpiece coordinate frame (Om-Xw Yw Zw). Firstly, the transformation between the local tool coordinate system and the machining coordinate system can be realized by a pure translation, which is defined by the matrix T (X0 DOC , H0, L0 + ft · t ) . X0 is the initial contact position, H0 denotes the initial shift in the Ym- direction, ft denotes the feedrate and L0 denotes the initial tool displacement in the feed direction. Secondly, with the obtained coordinate position (Xm, Ym, Zm) in the machining coordinate system, a further transformation is needed to transform the coordinate position in the workpiece frame, which is defined by a rotation transformation matrix Rz(-ωt). Based on the above, the tool coordinates with superimposed vibrations in the workpiece coordinate system can be determined. For example, for tool tip vibrations taking place at two frequencies expressed in the local tool coordinate system as:

Xv (t ) = A1 cos( 1 t + 1) + A2 cos( Yv (t ) = B1 cos( 1 t ) + B2 cos( 2 t ) Z v (t ) = 0

w (l ,

˜w (l, , t ) = round

(29)

Zt (l, ) = Rn cos

(33)

= R0

where the length L is discretized according to spatial resolution ζ, the azimuth θw is discretized based on angular resolution, ν, while the radial displacement component ρ is constant. Correspondingly, the cutting-edge is discretely described by the parametric variables l and θ. The schematic diagram of the discretized cutting tool and workpiece are shown in Fig. 9. At each time step, the coordinates of the cutting tool will be updated in cylindrical form in the workpiece coordinate system based on Eq. (32), which include both the cutting-edge and the flank face. The length coordinates and the azimuth of the cutting tool are rounded to the nearest workpiece mesh point. The corresponding mesh points on the workpiece are calculated based on the following equation [12]:

cos

Xt (l, ) = Rn sin cos t Yt (l, ) = Rn sin sin t ,

w)

Similarly, the tool coordinates with superimposed vibrations in Eq. (36) is also expressed in cylindrical form based on Eq. (32). To find the nearest workpiece points corresponding to the tool coordinates, the workpiece and the cutting edge are also discretized into specific mesh girds. The mathematical expression of the face surface of the cylinder

(32)

To find the nearest workpiece points corresponding to the tool coordinates, both the workpiece and the cutting edge are discretized into 737

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For given points on the cutting-edge (specified parameter values l and θ) that intersect the workpiece at a given time t, the nominal instantaneous chip thickness is the difference between the nearest workpiece surface height and the corresponding cutting-edge point in axial direction as:

L ( ˜w (l, , t ), ˜w (l, , t ))

tn = L w (l, , t )

(39)

4.3. Surface generation mechanism In micro machining processes, spring back is a crucial factor that must be considered in process modeling. Surface texture generation falls into this category of processes because the minimum chip thickness, hmin, is of a similar dimension as the cutting-edge radius. When the chip thickness exceeds the hmin, the cutting process is a shearing dominated process. Otherwise, ploughing is dominant. The minimum chip thickness in diamond cutting processes is related to the cuttingedge radius re as [19]:

Fig. 9. Schematic of the nominal instantaneous chip thickness calculation.

workpiece can be expressed in cylindrical form, i.e.:

L( ,

w)

(37)

=0

where the radial distance component ρ and the azimuth θw are discretized to the desired spatial and angular resolutions (ζ and ν), while the length L is set equal to 0. The cutting tool are discretely described by the parametric variables l and θ. The cutting tool coordinates are updated in the workpiece coordinate system and expressed in cylindrical form at each time step. The coordinates of points on the cutting tool are rounded to the closest mesh points on the workpiece. The corresponding points on the workpiece are calculated based on following equation:

˜w (l, , t ) = round ˜w (l, , t ) = round

w (l ,

, t)

w (l ,

, t)

(40)

h min = cre

where c is in the range of 0.3 to 0.4, and a c value of 0.35, refer to [20], is used in this study. The spring back mechanism in material removal processes is illustrated in Fig. 11 [20]. The normal stress at point P locating at the contact interface between the tool flank surface and the machined workpiece surface can be formulated as [21]: n

H E

=k H

(41)

where kσ is chosen as 3.5 [20], and H and E are the hardness and elastic modulus of material, respectively. The shear stress τs at point P can be derived according to the normal stress σn as:

(38)

s

=µ

(42)

n

where μ denotes the friction coefficient chosen as 0.2 [22] in this work. The minimum principal stress σp can be used to evaluate the true stress at point P [22]: p

=

n

n

2

2

+

2 s

(43)

As shown in Fig. 11, the normal stress and the shear stress will compress and stretch the workpiece, respectively. Generally, the principal stress is far larger than the yield stress in metal cutting processes. Based on the elasto-plastic deformation theory, the true stress-strain can be expressed as a piecewise function [23]:

E e, t

y n

= y

1+

, y

>

y

(44)

where the true stress, σt, is equal to the principal, σp, σy is the yield stress, εy is the yield strain, ε is the total effective strain and the n is the strain hardening coefficient. In the tool-workpiece contact area, the total effective strain ε consist of the elastic and plastic strain components. During the micro-texturing process, a small amount of material will slightly recover due to the elastic deformation. Thus, the plastic strain εp is calculated as: p

=

y

(45)

where the yield strain εy is a linearly related to the yield strength, σy, and elastic modulus, E, as σy/E. Assuming that the plastic stress is uniformly distributed on the machined workpiece surface under the tool flank surface and remains constant after friction occurs [24]. Then, the material’s spring back, Rs, is given by [20]:

Fig. 10. Definition of coordinate systems on face surface of the cylinder. 738

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Table 1 Material properties of aluminum alloy Al 6061 [20]. Parameter

H (GPa)

E (GPa)

kσ

σy (MPa)

n

Value

1

70

3.5

300

0.11

coordinates with vibrations in the workpiece frame will be calculated based on Eq. (36). Then, the corresponding points on the workpiece are calculated based on Eq. (38). Finally, the axial coordinates of workpiece are also updated with the calculated chip thickness (Eq. (39)) and spring back ((Eq. (47)). The new axial coordinates of flat surface of the cylinder are updated in accordance with:

L ( ˜w (l, , t ), ˜w (l, , t )) = L w (l , , t ) Fig. 11. Illustration of material spring back mechanism in the material removal process [20].

Rs = (1

The texturing experiments were conducted on a CNC HAAS milling machining center. The experimental setup is displayed in Fig. 14. For cylindrical surface texturing, the configuration of the experimental setup is provided in Fig. 14(a). The vibration generator is fixed on the Y-axis table. The workpiece material is Aluminum 6061 with a diameter of 10.4 mm. For face surface texturing, the vibration generator was set on the bottom at the workpiece as shown in Fig. 14(b). Commercially available diamond inserts were used in both texturing processes, the nose radius of the insert was 200 μm, the rake angle 10 deg and clearance angle 7 deg. Before the surface texturing experiments, a premachining step was used to remove the effects caused by the eccentricity of the spindle and workpiece geometrical errors. The cutting parameters used in the pre-machining process were: depth of cut 20 μm, spindle speed 1000 rpm and feed rate 5 μm/rev. Surface texturing was performed on the cylindrical surface and the face surface of the cylinder. The cutting and vibration parameters are given in Table 2. In the cylindrical surface texture generation process, in Case 1 and Case 2, a single excitation frequency was used with an input voltage amplitude of 400 V (peak to valley) and a phase difference of 60 deg. In Case 3, two frequencies were used with an input voltage amplitude for each frequency of 400 V and with phase shifts, φ1 and φ2, of 60 deg according to Eqs. (6) and (7). In the face surface texturing experiments, Case 4, the input voltage was set to 100 V and the phase difference to 60 deg, while in Cases 5–7, the input voltage was set to 100 V with a phase difference of 60 deg. However, continuously changing frequencies were used in these cases.

In this study, aluminum alloy Al 6061 is used as the workpiece. The material properties of Al 6061 are provided in Table 1 to calculate the spring back. The cutting-edge radius was measured by an optical microscope (Alicona, Austria). The result is shown in Fig. 12. Five positions on the cutting edge were selected for evaluation, one of the profiles along the tool’s cutting-edge is shown in Fig. 12(b). The average of five evaluations yields a cutting-edge radius of 2.71 μm. Using the material properties listed in Table 1, the plastic strain, εp, is calculated to be 0.1156, yielding a minimum chip thickness, hmin, of 0.84 μm. In this study, the material is assumed to undergo full recovery if the nominal chip thickness, tn, is smaller than the material’s elastic deformation limit, te, which is chosen to be 0.01 μm [12]. If the nominal chip thickness, tn, increases beyond the elastic deformation limit but remains smaller than hmin, the material experiences elasto-plastic deformation under these conditions and the material partially elastically recovers. The maximum value of material recovery is obtained when the nominal chip thickness, tn, is equal to hmin. If the nominal chip thickness, tn, is larger than hmin, the cutting process becomes a shear dominated process. Instead of considering spring back to be zero in the shear dominated process, as assumed in a previous study [25], spring back is assumed to be a constant value equal to te [22]. Concluding the analysis above, spring back, δt, is then expressed as a piecewise function of the nominal chip thickness, tn, as [22]:

t=

tn (1 te

p ) h min

h min

te

(tn

tn < te te ) + te te tn < h min tn h min

6. Results and discussion Based on above experiments, the experimental results both on the cylindrical surface and the face surface of the cylinder are discussed in the following sections.

(47)

Based on Eq. (47), the spring back of the material is plotted in Fig. 13. Considering the spring back effect, the new radial coordinates of the cylindrical surface in Section 4.1 will be updated in the workpiece mesh grids. The material update process is calculated as follows. Firstly, the tool coordinates with vibrations at any point on the cutting-edge in the workpiece frame are calculated based on Eq. (31). Secondly, the corresponding nearest points on the workpiece are calculated based on Eq. (34). Thirdly, the radius of the workpiece is renewed with the calculated chip thickness (Eq. (35)) and spring back ((Eq. (47)). Finally, the workpiece can be expressed in the resulting radial coordinates based on the following equation:

(L˜ w (l, , t ), ˜w (l, , t )) =

w (l ,

, t) + t

(49)

5. Experimental setup

(46)

p ) h min

t

6.1. Generated surface texturing on the cylindrical surface After the experiments, the workpieces were measured using a whitelight interferometer (Zygo Newview 7300). The measured results and simulation results corresponding to Case 1 are shown in Fig. 15. The simulation results show a close agreement with the experimental results. In addition, since the frequency (10 Hz) is low, the dimples are overlaid in the cutting direction and a micro channel-like texture is generated. The profiles extracted across the channel from the simulations and the experiments are shown in Fig. 15(c). The profiles are again in close agreement. When the vibration frequency increases to 30 Hz, the machined dimple pattern shown in Fig. 16(a) is obtained along with the corresponding simulation results shown in Fig. 16(b). The comparison of the two figures again suggests a close consistency. A better quantitative

(48)

The new axial coordinates of the flat surface of the cylinder in Section 4.2 are also renewed in the workpiece mesh arrays. The tool 739

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Fig. 12. Measured tool cutting edge radius (a)3D topography of the tool (b) 2D profile of the tool cutting edge.

the material spring back compensation used in the model. To reduce the effect of cutting-edge radius, the use of a single crystal diamond (SCD) tool would be a good choice. Previous studies, e.g., [12], indicate that high-accuracy surface textures can be generated using SCD tools whose cutting-edge radius is normally within hundreds of nanometers [21] as opposed to the 2.71 μm of radius used in the current work. In addition, employing a higher cutting speed to avoid the formation of a built-up edge would be helpful to improve machining quality. Additional plausible reasons leading to the discrepancy are: (a) tool mounting errors leading to rake angle and clearance angle variations, (b) the open-loop operation of the vibration generators leading to variations of the vibration amplitudes from their nominal values due to the cutting resistance when the cutting tool is engaged with the workpiece and (c) the hysteresis characteristic of the piezo actuators. The latter two reasons can be alleviated by the use of a closed loop position control system for the tool, while the former with potentially better models that account for tool edge radius effects in the process. When a sum of frequencies (10 + 30 Hz) is used, hybrid features can be generated in one step as shown in Figs. 17(a) and (b), which can be considered as surface texturing by two single frequencies added together. In general, the experimental results show reasonable similarities. For example, valley-like structures are generated on the top of the surface. The profile extracted across the valley-like structure is shown in Fig. 17(c). According to a previous study [27], such structures can significantly improve the hydrophobic properties of workpieces. Also, there are some differences between the experimental results and the simulation results. Except for the above-mentioned reasons, the small amplitudes on the machined surface might be caused by damaging of the sharp tops of the features at the micron level. From the above examples, it is clearly seen that different textured

Fig. 13. Spring back, δt, with respect to the normal chip thickness.

assessment of the differences between the experimental results and the simulation results is provided by comparing the sectional profiles in Fig. 16(c). In spite of the close agreement, there are obvious discrepancies which can, to a certain extent, be explained by the mechanics of micro-cutting operations. According to the discussion in Section 4.3, the tool cutting-edge radius is 2.71 μm while the theoretical minimum chip thickness is around 0.84 μm. However, the cutting speed in this machining process is very low. The low cutting speed results in the formation of the built-up edge, which increases the cutting-edge radius of cutting tool [26]. During the machining process, part of the material removal mechanism changes from a shearing to a ploughing process. Thus, large elastic deformations and recovery occur leading to the deviations of the final profile from the simulation result even with

Fig. 14. Experimental setup(a) Cylindrical surface texturing process (b) Face surface texturing process. 740

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Table 2 Vibration and cutting parameters. Case

N (rpm)

fz (μm/rev)

DOC (μm)

f (Hz)

Cylindrical surface

1 2 3

23 23 23

60 60 60

10 10 10

10 30 10 + 30

Flat surface

4 5 6 7

7 7 7 7

250 250 250 250

0 0 0 10

10 From 30 Hz to 1 Hz From 45 Hz to 1.5 Hz From 30 Hz to 1 Hz

Fig. 15. Measured and simulated textured surface (Case 1): (a) Measured texture, (b) Simulated texture and (c) Sectional profile.

Fig. 16. Measured and simulated textured surface (Case 2): (a) Measured texture, (b) Simulated texture and (c) Sectional profile.

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Fig. 17. Measured and simulated textured surface (Case 3): (a) Measured texture, (b) Simulated texture and (c) Sectional profile.

Fig. 18. Measured and simulated textured surface (Case 4): (a) Measured texture, (b) Simulated texture, (c) Detailed measured results from the outer to the inner diameters and (d) Generated dimples with scale-bars.

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Fig. 19. Measured textured surface (Case 5): (a) Detailed measured results from the outer to the inner diameters, (b) Simulated texture and (c) Sectional profile.

Fig. 20. Measured textured surface corresponding to different frequencies: (a) Case 5 (b) Case 6.

surfaces can be generated in accordance with the designed machining parameters. In addition, sophisticated micro textured surfaces can be fabricated with carefully selecting the input voltage. Such surfaces with designed patterns on cylindrical surfaces can be, for example, applied in friction reduction in the bearings.

Fig. 18(c). The details of the machined surface obtained by the Zygo white-light interferometer at the inner to outer diameters is shown in Fig. 18(d). It should be noted that due to the existence of burrs (circled in white), the total height is different in the three figures resulting in different colors in the images. Therefore, the color bar for each figure is provided in Fig. 18(d). As shown in the figures, the machining process forms concentric dimples arranged along an Archimedean spiral on the face of the workpiece. The generated surface dimples are inconsistent when progressing from the outer to the inner diameters. It is clearly shown that the length of the dimples decreases from the outer to the inner due to the decreasing circumferential velocity with decreased distance from the center. To generated uniform surface textures on the face of the cylindrical surface, the ratio δ in Eq. (26) should be a constant. As discussed above, there are two ways to generate uniform textures, one is the control of

6.2. Generation of surface textures on the face surface of a cylinder The generated surface texture corresponding to Case 4 in Table 2 is shown in Fig. 18(a), where a constant frequency was used. The simulation results based on the proposed surface generation model is provided in Fig. 18(b). Comparing Fig. 18(a) and (b), similar feature patterns are observed. To observe the overall dimple pattern, the machined surface was further captured and stitched by a variable focus optical microscope (Alicona, Austria). The measured result is illustrated in 743

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Fig. 21. Measured textured surface corresponding to Case 7.

the spindle speed, and another is the control of the vibration frequency. Since, the spindle speed is quite slow, it is hard to continuously control it. In contrast, the vibration texturing system is easily controlled by LabVIEW software. The necessary variation of the frequency is determined by Eq. (27). The obtained textures measured by the infinite focus optical microscope (Alicona, Austria) corresponding to Case 5 in Table 2 is shown in Fig. 19(a). Three positions on the machined surface were selected and measured by the Zygo white-light interferometer. The measured results are shown in Fig. 19(b). From Fig. 19(b), it can be observed that uniform dimples are generated on the face surface of the cylinder by controlling the variation of the vibration frequency. The simulation results are illustrated in Fig. 19(c), while cross sectional profiles, both from the experimental and the simulation results, are provided in Fig. 19(d). Generally, the maximal depth and wavelength along the indicated sections of the experimental results are close to the theoretical values. As an additional example, the effects of the vibration frequencies on texture generation are shown in Fig. 20. The measured results corresponding to Case 5 and Case 6 are shown in Fig. 20(a) and (b), respectively, indicating the expected outcome that with increasing vibration frequency, the number of dimples per unit area increases. The effect of the DOC on the texture pattern is also studied. As shown in Fig. 7(b), when the DOC is smaller than Az, the cutting tool will periodically separate from the workpiece. Consequently, periodic micro dimples can be generated on the workpiece surface as shown in Case 5. Otherwise, when the DOC is larger than Az, the tool will remain in contact with the workpiece all the time. Then a blended texture of channels and dimples can be generated in one step. Taking a DOC of 10 μm (Case 7) as an example, the generated texture is shown in Fig. 21(a). The simulation results are illustrated in Fig. 21(b). As it can be seen the basic pattern features are consistent between the experimental and the simulation results. However, due to the fact that the tool vibrations are not synchronized with the spindle rotation, it is hard to control the relative position of the texture features in the two adjacent passes/rotations. Hence, only experimental profiles in three adjacent passes are provided in the figure. The addition of an encoder to the spindle would allow a precise control of the relation of texture features in adjacent passes.

7. Conclusion In this paper, a non-resonant vibration generator was used for textured surface fabrication. The performance of this vibration generator was tested by capacitance sensors. The results have shown that different vibration amplitudes and vibration loci can be obtained by controlling the input voltage amplitude and phase shift. The principles of this vibration assisted surface texturing process both on the cylindrical and face surfaces of a cylinder were analyzed. Concurrently, surface generation models were established. The predictive accuracy of the proposed surface generation models was ascertained through a series of experiments. In addition, the experimental results also verified the flexibility of the vibration generator for textured surface fabrication. The cylindrical surface texturing experiments have verified that arbitrary complex surface textures can be generated in one step by summing several different sinusoidal vibration signals. The face surface texturing experiments demonstrated that uniform surface textures can be generated by controlling the variation of the vibration frequencies. Acknowledgement The authors would like to thank the National Natural Science Foundation of China (Grant No. 51675367). References [1] Callies M, Chen Y, Marty F, Pépin A, Quéré D. Microfabricated textured surfaces for super-hydrophobicity investigations. Microelectron Eng 2005;78:100–5. [2] Zhu W-L, Xing Y, Ehmann KF, Ju B-F. Ultrasonic elliptical vibration texturing of the rake face of carbide cutting tools for adhesion reduction. Int J Adv Manuf Technol 2016;85:2669–79. [3] Yang Y, Pan Y, Guo P. Structural coloration of metallic surfaces with micro/nanostructures induced by elliptical vibration texturing. Appl Surf Sci 2017;402:400–9. [4] Yang J, Luo F, Kao TS, Li X, Ho GW, Teng J, et al. Design and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing. Light Sci Appl 2014;3:e185. [5] Miyoshi H, Adachi T, Ju J, Lee SM, Cho DJ, Ko JS, et al. Characteristics of motilitybased filtering of adherent cells on microgrooved surfaces. Biomaterials 2012;33:395–401. [6] Zhang J, Cui T, Ge C, Sui Y, Yang H. Review of micro/nano machining by utilizing elliptical vibration cutting. Int J Mach Tools Manuf 2016;106:109–26.

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