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Rotary spatial vibration-assisted diamond cutting of brittle materials
Accepted Manuscript Title: Rotary spatial vibration-assisted diamond cutting of brittle materials Author: Zhiwei Zhu Suet To Gaobo Xiao Kornel F. Ehmann Guoqing Zhang PII: DOI: Reference:
S0141-6359(15)00227-5 http://dx.doi.org/doi:10.1016/j.precisioneng.2015.12.007 PRE 6328
To appear in:
Precision Engineering
Received date: Revised date: Accepted date:
25-10-2015 19-12-2015 23-12-2015
Please cite this article as: Zhu Z, To S, Xiao G, Ehmann KF, Zhang G, Rotary spatial vibration-assisted diamond cutting of brittle materials, Precision Engineering (2015), http://dx.doi.org/10.1016/j.precisioneng.2015.12.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights:
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1. Rotary spatial vibration assisted diamond cutting is proposed for better processing brittle materials;
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2. The non-resonant vibration along the three translational directions is adopted to gain more flexibility;
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3. Consistent cutting performance can be always guaranteed even when processing large areas;
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4. Feasibility and superiority of this new technique is demonstrated by fabricating micro-grooves on single-crystal silicon.
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te
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5. Characteristics of the machined surface and the cutting force are detailed.
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Rotary spatial vibration-assisted diamond cutting of brittle materials
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Zhiwei Zhu1, Suet To1,*, Gaobo Xiao1, Kornel F. Ehmann2, and Guoqing Zhang1
(S. To)
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* Corresponding author: [email protected]
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1. State Key Laboratory of Ultra-precision Machining Technology, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, China 2. Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA
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Abstract: In the present study, a novel process, namely rotary spatial vibration (RSV) assisted diamond cutting, is introduced to overcome cutting velocity induced cutting
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parameter inconsistencies as well as the cutting direction induced insufficient
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utilization of vibration assistance in vibration-assisted turning and milling of brittle
the
rotation
of
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materials. In RSV-assisted diamond cutting, a rotary motion component, generated by the
machine’s
spindle,
is
superimposed
onto
the
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three-degrees-of-freedom translational vibrations of the diamond tool. The resulting complex motions of the diamond tool assure the possibility of consistent cutting performance that is always guaranteed even when processing arbitrarily large areas. In practice, the feasibility and superiority of this technique for processing brittle materials is well demonstrated by fabricating a set of circular micro-grooves on monocrystalline silicon wafers with gradually varying depth-of-cut.
Key words: Diamond cutting; Rotary spatial vibration; Monocrystalline silicon; Cutting forces.
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1. Introduction For decades, the manufacturing of structured complex surfaces on optical brittle
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materials has attracted considerable attention for a variety of applications in the infrared optics and electronics industries [1-3]. However, the inherent low fracture
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toughness of the materials used imposes great machining challenges in obtaining
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optically qualified surfaces featuring ultra-smooth roughness and a minimal amount of sub-surface micro-cracks. Compared with the commonly adopted abrasive
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machining methods (including grinding and polishing), which are generally
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time-consuming [4, 5], diamond cutting techniques, dominated by the use of fast or slow tool servos (FTS/STS) [6, 7] and by multi-axis diamond milling [3, 8], are
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widely regarded as more promising for better fulfilling the requirements for
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processing brittle materials with complex shapes due to their capability for achieving
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ultra-precision form accuracy. In diamond cutting, small feedrates and cutting depths are commonly required to allow machining in the ductile region [6, 9] or to restrict the penetration of cracks into the finished surfaces [7, 8]. However, these operations generally lead to extremely low efficiency in practical applications.
To improve the machining performance in diamond cutting, various methods were proposed to enhance the machinability of brittle materials, including ion implantation modification [10, 11], laser-assisted cutting [12, 13] and vibration-assisted machining (VAM) [14-16] to mention a few. Ion implantation modification was reported to be beneficial in reducing cutting forces, increasing the critical depth of cut (DoC) and 3
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enhancing tool life [10, 11]. Generally, the modified layer is very thin in the subsurface of the material. However, laborious serial processes and expensive facilitates are required to implement this modification-assisted cutting method. Laser
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assistance utilizes thermal effects for material softening and the activation of plastic
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flow. This effect is effective for improving the machinability of brittle materials in
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cutting without leaving undesirable defects on the finished surface [12, 13]. However, the unavoidable thermal deformations deteriorate the machining accuracy of the
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desired components. It is also difficult to process surfaces with intricate shapes due to the poor capability for tracking the focal spot of the laser on the surface. Due to its
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low cost and high efficiency, VAM that uses mechanical energy to facilitate material
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of brittle materials [14].
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removal is regarded as a superior machining process for enhancing the machinability
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In general, VAM can be classified into 1-D, 2-D and 3-D machining according to the employed number of vibration directions. The 1-D and 3-D VAM processes are dominated by the resonant ultrasonic cutting mode of operation [17, 18], while 2-D VAM mainly involves both the resonant and non-resonant cutting modes [15, 19, 20]. Compared with the 1-D VAM, the overlapping elliptical tool loci in 2D/3D VAM offer an essential beneficial advantage for automatically generating much thinner chips [14]. Furthermore, it was reported that spatial elliptical vibrations in 3-D VAM are more flexible in machining sculptured surfaces [17, 21]. No matter which kind of VAM is adopted, the horizontal speed ratio (HSR) and duty cycle (DC) are two essential
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parameters, significantly influencing the critical brittle-ductile transition as well as tool wear behavior in machining [14, 22]. By adopting a small enough HSR, the critical DoC was reported to increase several times, offering significantly improved
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economics for processing brittle materials [14, 16, 22]. Nonetheless, it is still
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challenging for VAM to practically facilitate diamond cutting of complex surfaces.
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For instance, to facilitate diamond turning, a progressively increased vibration frequency is obligatorily required to guarantee effective HSR and DC values in view
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of the ever-increasing rotational distance of the cutting points. However, limited by the dynamics of the mechatronic systems, it is not sufficient for VAM to assist in
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turning surfaces with large apertures. As for VAM working in the resonant mode, the vibration frequency and amplitude are non-adjustable. The fixed vibration parameters
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d
lead to time-varying cutting parameters (HSR and DC), due to the variation of the relative distance between the cutter location and spindle axis. Therefore, variable
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cutting conditions will dominate the process, highly deteriorating machining performance. In diamond micro-milling operations, planar 2-D vibrations are mainly superimposed on the workpiece to achieve vibration assistance [23, 24]. In milling, the cutting edge commonly operates at a constant cutting velocity attributed to the constant distance between the cutting edge and the corresponding rotational axis, resulting in a constant HSR when using vibrations with fixed amplitudes and frequencies. However, the rotation of the cutting edge would induce time-varying changes in the cutting directions. Thus, the unchanged vibration plane leads to extremely low utilization of the effective vibration assistance. Besides, since the
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workpiece is vibrated during the process, small workpieces are essentially required in this configuration to achieve high vibration frequencies and for effective cutting. To use VAM for facilitating the generation of micro-structured surfaces, translational
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raster motions instead of rotations were commonly adopted to guarantee homogenous
cr
machining conditions, i.e., consistent HSR and DC [25, 26]. However, the inevitable
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acceleration and deceleration processes in the discontinuous rater feeding motions
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lead to a much lower machining efficiency of the sculpturing process.
Facing the above-listed dilemmas, a novel rotary spatial vibration (RSV) assisted
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diamond cutting technique is proposed and demonstrated in this paper for practically facilitating diamond cutting of brittle materials. With RSV-assisted diamond cutting, a
te
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single point diamond tool is vibrated by piezo-actuators along three translational directions on a rotating spindle, resulting in a rotary vibration assisted cutting process.
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It is noteworthy that rotary vibrations have recently been also introduced for the purpose of FTS-milling [27, 28] and rotary ultrasonic machining (RUM) for drilling as well as milling operations [29-31]. With FTS-milling and RUM, unidirectional vibrations are commonly added to the rotary tool along its axial direction, which introduces new functionalities into the machining process. However, the unidirectional vibrations are more suitable for drilling operations and significantly restrict machining flexibility, especially for processing sculptured surfaces.
In this paper, the employment of 3-D non-resonant rotary vibrations with a constant
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rotational distance of the diamond tool offers the following advantages of the RSVassisted diamond cutting system:
velocity;
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(a) Consistent cutting conditions (HSR and DC) induced by the constant cutting
(b) The capability for large-scale processing of surfaces without limitations of system
dynamics
and
workpiece
size
when
compared
to
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the
vibration-assisted diamond turning;
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(c) Continuously effective vibration assistance due to the rotary vibrations when compared to vibration-assisted milling;
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(d) The potential for tuning the orientation of the vibration plane to achieve optimal cutting with respect to different materials and surface shapes by combining the three-axial vibrations;
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(e) The capability for ultra-precision generation of intricately shaped surfaces
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processes.
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by adopting servo-controlled motions inherited from the FTS/STS
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2. Principle of RSV-assisted diamond cutting of brittle materials 2.1 System configuration for RSV-assisted diamond cutting
The configuration of the RSV-assisted diamond cutting system is illustrated in Fig. 1.
The single point diamond tool is attached to the end-effector of a piezo-actuated compliant spatial vibrator (CSV) that generates spatial vibrations along three translational directions. By means of a vacuum chuck, the CSV is fixed to the spindle and rotated with it (c-axis) as shown in the photograph of the system in Fig. 1(a),
resulting in rotary vibrations of the diamond tool. The spindle, in turn, mounted on the
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x-axis slide of the machine tool, follows motions in the side-feeding direction. The workpiece is clamped on the z-slide of the machine tool to facilitate the generation of surfaces with intricate shapes [32]. A slip ring is employed to transmit the command
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d
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cr
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signals from the stationary command generator to the three rotating piezo-actuators.
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Fig. 1. System configuration of the RSV-assisted diamond cutting system, (a) photograph of the system, and (b) photograph of the CSV.
The CSV was designed to guide the motions of the piezo-actuators and work on the rotating spindle. Special considerations for a high rotational symmetry and a highly compact structure were given during the design of this three-degrees-of-freedom (3-DoF) compliant mechanism. To obtain high machining efficiency and accuracy, a wide working bandwidth and decoupled output motions were also required. Under these considerations, a parallel configuration of the mechanism was employed. The photograph of the CSV is schematically illustrated in Fig. 1(b). Three piezo-actuators 8
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in an orthogonal configuration were employed to generate the three-axial vibrations. L-shaped flexure hinges (LFH) [33, 34] were used as the basic elements for motion guidance to create a highly compact structure with multiple DoFs. In the CSV, four
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sets of LFHs were adopted with symmetric configuration to decouple the output
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cr
motions.
During cutting, the diamond tool rotates on the spindle with a fixed and tunable
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rotational distance/radius, resulting in a diamond fly cutting like arrangement with constant cutting velocity for material removal. Concurrently, the diamond tool
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undergoes spatial vibrations along three translational directions. Unlike the conventional 2-D elliptical vibration cutting (EVC) process, the third vibratory
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d
motion, along the xv-axis direction is introduced into the RSV system to extend the
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tool’s vibrations from the 2-D to the 3-D spatial domain [17, 21].
2.2 Kinematics for processing brittle materials
For process analysis, a local Cartesian coordinate system, ov-xvyvzv, fixed to the
rotating spindle of the machine tool, is defined. Axes ovxv, ovyv and ovzv are aligned
with the three vibration directions generated by the three piezoelectric actuators of the CSV as shown in Fig. 1, while axis ovzv is coincident with the rotational axis of the spindle. The diamond tool is installed on the end-effector of the CSV along the xv-axis, with an offset value of Rd. The kinematic equations of the motions of the diamond tool in the ov-xvyvzv coordinate system are given by: 9
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xv a sin(2 ft x ) Rd yv b sin(2 ft y ) zv c sin(2 ft z )
ip t
(1)
where a, b, and c denote the vibration amplitudes along the xv-, yv- and zv-axis
are the phase angles along the
cr
directions, respectively, x , y and z
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corresponding directions, f is the vibration frequency, and Rd is the offset distance of
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the diamond tool in the xv-direction.
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In the RSV-assisted diamond cutting process, the loci of the diamond tool constitute a set of ellipses in 3-D space [17, 21]. However, in the ov-xvyvzv system, the elliptical
sin(z y )
sin( x y ) Rd cos y sin(z x ) Rd cos z xv yv zv 0 (2) b ab c ac
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a
te
d
vibrations are taking place in a vibration plane expressed by:
Since Eq. (1) only describes the elliptical trajectories in the plane given by Eq. (2) of the rotating ov-xvyvzv system, a stationary coordinate system, ot-xtytzt, is introduced to
express the rotation induced cutting velocity and the relationships between sequential elliptical tool trajectories. Coordinate system ot-xtytzt is defined such that plane ot-ytzt coincides with the tangential plane ST to the rotational motion. Its origin, ot, is set to coincide with point [Rd, 0, 0] in the ov-xvyvzv system at time tk, assumed to coincide with the beginning of the kth cutting cycle (ellipse), while axes otyt and otzt are aligned
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with ovyv and ovzv also at time tk as shown in Fig. 2(a). During the following cutting cycles, the system ot-xtytzt, as stated above, remains stationary.
Therefore, the
current and consequential ellipses can be described in the system ot-xtytzt. Without loss
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of generality, the subsequent analyses will be conducted within two consecutive
(a)
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cutting cycles, i.e., from time t=tk to t=2/f+ tk.
(b) S’
z'
s
pL
xv
yt
o'
ST
te
0.5 pL
ov Spindle
hc,max
to
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n Rd 30
d
Tool Position
d
vC (t )
tm
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Diamond tool
Cutting duration
y'
an
yv
(k+1)th
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kth
ST
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te
Fig. 2 Schematic of (a) the rotary tool motion and (b) the relative tool loci in the orthogonal cutting planes.
Since the ov-xvyvzv system is rotating around the spindle axis, by setting t ' t tk , the
vibratory motions described in Eq. (1) can be transformed to the ot-xtytzt system as:
R cos nt ' Rd 30 d x R v d xt yt yv Rd sin nt ' 30 zt z v 0
(3)
0 0 1
(4)
where
cos nt ' 30
cos nt ' 30 R z sin nt ' 30 0
sin nt '
0
30
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To obtain a closed-form description of the critical cutting parameters for the better understanding of the machining process, the cutting loci are simplified as a set of
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overlapping ellipses [14] under the assumption that x y 0 and z / 2 .
cr
Thus, the vibrations in the ot-xtytzt system under these assumptions are taking place in
with respect to the
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an inclined plane S’ that is inclined by an angle
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ot-xtzt plane as shown in Fig. 2(b).
To simplify the analysis of the vibrations form 3-D space to a 2-D plane, a new local
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coordinate system o ' x ' y ' z ' who’s o ' y ' z ' plane coincides with the plane S’ is introduced. The new system can be obtained by just rotating the coordinate system . By expressing the equations of motion given
d
ot-xtytzt around the zt axis by the angle
te
by Eq. (3) in the o ' x ' y ' z ' system under the small angle assumption nt '
30
,
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the tool loci described in the system o ' x ' y ' z ' from time t = tk to t = 2/f + tk are
given by:
cos sin 0 x t x ' y ' sin cos 0 yt z ' 0 1 z t 0 nRd at ' 30 a 2 b 2 2 nRd t 2 a b sin(2 ft ') 30 c cos(2 ft ')
(5)
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where
b a b2 2
is defined as the projection ratio of the cutting velocity along the
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y ' -axis direction.
Since the vibration frequency is much higher than the rotational frequency, namely
30 a 2 b 2
in Eq. (5) given that t '
cr
nRd at '
can be
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, the quantity
neglected. This suggests that the ellipses in two consecutive cutting cycles can be
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approximately regarded as taking place in the vibration plane S’ as shown in Error! Reference source not found.(b). Thereby, the tool loci in the cutting zones for the kth
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and (k+1)th cutting cycles in the vibration plane S’ can be described by:
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te
d
y '2 z 'k c 1 2 k 2 a b 2 y 'k 1 pL z 'k 1 c 1 a2 b2 pL n Rd 30 f
(6)
where pL denotes the pitch between any two successive ellipses as shown in Fig. 2(b), and the subscripts k and k+1 denote the kth and (k+1)th ellipses.
As shown in Error! Reference source not found.(b), at time to the diamond tool enters the workpiece to remove material. From then on, the cutting depth increases until time tm at which point the cutting depth reaches its maximal value. After that, the
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cutting depth gradually decreases due to the appearance of the upper flat surface, and at time te, the diamond tool moves out of the workpiece. By setting y 'k y 'k 1 yo and z 'k z 'k 1 zo , the position and time at the entry point with respect to the (k+1)th
cr
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cutting cycle can be determined from:
pL
a b2 2
(7)
(8)
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pL yo 2 2 zo c 1 0.5 1 arcsin 0.5 to 2 f f
d
where is the forward feeding ratio defining the ratio between the pitch pL and the a 2 b 2 along the cutting direction. It is commonly much less
than 1, namely
.
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te
vibration amplitude
At point tm, corresponding to the maximal depth of cut (DoC), the requirement
z 'k ,m (c h) should be satisfied, leading to the following relationships:
y ' a2 b2 1 2 k ,m 2 1 arcsin 1 tm f 2 f
ch h 1 c c
(9)
(10)
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where the subscripts k and m denote the kth ellipse and the time tm, respectively; h is the nominal DoC, 1 is the cutting ratio defining the relationship between the
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nominal DoC and the vibration amplitude along the cutting direction.
cr
By calculating the difference between the zv-axis values of the to-be-machined surface
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and the cutting point at time tm, the maximal DoC is obtained as:
2
(11)
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an
hc, max h c z k 1 ( yk ,m ) =c 1 1 2
te
expressed as:
d
By omitting the second order small term, 2 , in Eq. (7), the maximal DoC can be
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hc,max c 2 2 1 2
(12)
At time te, when the diamond tool moves out of the workpiece, the following relationship can be obtained by satisfying the requirement z 'k 1,e (c h) :
2 2 2 y' k 1,e pL a b 1 2 1 arcsin 1 te f 2 f
(13)
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Thus, the DC can be written as:
2
(14)
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DC (te to ) f
arcsin 1 2 arcsin 0.5
n Rd 30 f 2
(15)
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HSR
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cr
and HSR is given by [14]:
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The instantaneous DoC is described by the piecewise function:
(16)
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te
d
z y t z y t , t t tm h(t ) k k 1 k 1 k 1 o h c zk 1 yk 1 t , tm t te
With consideration of the velocity changes along the y’- and z’-axis directions, the instantaneous cutting direction relative to the workpiece can be written as [14]:
60 fc sin(2 ft ) (t ) arctan 60 f a 2 b 2 cos(2 ft ) nR d
(17)
and the effective rake and clearance angles relative to the workpiece expressed by [14]:
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(t ) 0 (t )
(18)
(t ) 0 (t )
(19)
values are two distinctly important
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Remark: The newly defined and
cr
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where 0 and 0 were the nominal rake face and clearance angles, respectively.
parameters directly determining the maximum DoC and the parameters DC and HSR
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in cutting as shown by Eqns. (11), (13) and (14).
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In vibration-assisted turning, the increase of the rotational distance Rd would lead to an increase of . It would further lead to an increase of the maximal DoC and HSR
te
d
deriving from the relationships shown by Eqns. (11) and (14), highly deteriorating,
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thereby, the performances in cutting of brittle materials [14, 16, 22].
In vibration-assisted milling, as reported in [23, 24], the ratio cos nt would 30
periodically change between 0 and 1 and, accordingly, result in a periodic changes of
between 0 to max . It is suggested by Eqns. (10), (13) and (14) that the effects of
the vibrations on material removal would also periodically vary between invalid and normal phases.
With the RSV-assisted diamond cutting system, the two parameters, and , appear to have no relationship to the cutting position, suggesting that a consistent 17
Page 17 of 36
material removal operation can always be achieved, even when processing large-scale
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samples.
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3. Experimental setup
Experiments were performed on an ultra-precision lathe (Moore Nanotech 350FG,
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USA) shown in Fig. 1(a). The CSV made of aluminum alloy 6061 was driven by three
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piezoelectric stack actuators (P-880.51, Polytec PI, Inc., Germany) with three power amplifiers (PI E617.001). A Power PMAC control board (Delta Tau Data Systems,
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Inc., USA) was used for signal communication and control of the vibrator. The amplitudes of the command signals were set to 0 V, 4 V, and 3 V at a frequency of 2
d
kHz for the piezo-actuators in the CSV along the xv-, yv- and zv-aixs directions,
te
respectively. By using a set of capacitive displacement sensors (Elite, Lion Precision,
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USA) in an off-line arrangement, the displacements of the end-effector along each of the three directions were captured and illustrated in Fig. 3(a), while the spatial ellipses formed by the three-axial vibrations are given in Fig. 3(b). As shown in Fig. 3(a), the amplitudes of the vibrations along the three directions were 0.5 μm, 4.8 μm and 2.4 μm, respectively. Since there was no command signal given for the x-axis motion, the
harmonic vibrations were induced by the dynamic coupling effects which would be detailed in future work.
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(a)
1
1 0
0 -0.5 -1 2 1
-2
0
y / μm
2.5
3
3.5 Time / s
4
4.5
5 x 10
-1
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-1.5
-1
-3 2
(b)
0.5
-2
0 0.2 -0.2 x / μm
cr
Displacement / μm
2
a
1.5
z y x
z / μm
3
-3
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Fig. 3. Tool vibrations: (a) vibrations in the time-domain and (b) the synthesized spatial ellipse.
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A natural single crystal diamond tool (Contour Fine Tooling Inc., UK) with a round edge of radius of 0.104 mm and 0o rake face angle was used. To measure the cutting
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force in the process, a three directional dynamometer (9255b, Kistler Group, Germany) was installed on the slide with the workpiece on it. Micro-grooving experiments on
te
d
monocrystalline silicon 〈001〉 were conducted using diamond cutting both with and without RSV assistance. During grooving, the sample was obliquely mounted on the
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slide with a preset inclination angle relative to the end-face of the spindle. Therefore, during one revolution of the diamond tool, it cut in and out of the workpiece with gradually varying DoC. To investigate the cutting performance with larger depths, side-feeding towards the direction with a higher slope was adopted using a feedrate of 0.1 mm/rev along the x-axis of the machine tool. The rotational distance of the diamond tool and the spindle speed were about 1.25 mm and 2 rpm, respectively. After cutting, the surfaces were cleaned with ultrasonic assistance in alcohol. An optical microscope (BX60, Olympus Corporation, Japan) was used to capture photographs of the machined surfaces. In addition, the Nexview 3-D Optical Surface
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Profiler (Zygo Corporation, USA) was employed to capture the 3-D topographies of the corresponding surfaces.
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With the above-stated machining parameters, the theoretically obtained transient
cr
DoCs with respect to the nominal DoCs of 0.2 μm, 0.5 μm and 0.8 μm are illustrated
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with respect to time in one cutting cycle in Fig. 4. For a small nominal DoC, the transient DoC shows an approximately linear relationship with respect to time in the
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two cutting stages. With an increase of the nominal DoC, the nonlinearity of the transient DoC becomes apparent, showing an exponential dependence on time. The
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HSR has no relationship with the nominal DoC, and it is about 0.01 in this case.
-4
d
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m m / uct of ht p e D
x 10
h=0.8 m
te
2
1
0 0
0.2
h=0.5 m h=0.2 m 0.4
0.6 Time / s
0.8
1
1.2 -4 x 10
Fig. 4. Evolution of estimated transient DoC in one cycle.
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4. Experimental results and discussion 4.1 Characteristics of the machined surface
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Without RSV assistance, a micro-groove was firstly fabricated using the same spindle
cr
speed and rotational distance as employed in the cutting with RSV assistance to have a comparison of the machining performance, resulting in the optical microscopic
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image shown in Fig. 5(a). A short distance after the entrance of the tool, a large
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number of cracks is formed on the bottom of the micro-groove as characterized by the dark spots in Fig. 5(a). By means of the Zygo optical surface profiler, the surface
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micro-topography of the micro-groove at the entrance position was further obtained as shown in Fig. 5(b). The cross-sectional profile along the cutting direction was also
d
extracted and shown in Fig. 5(c). It can be seen that the critical DoC at which
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ductile-brittle transition occurs is about 58 nm without RSV assistance. This critical
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DoC is much smaller than the commonly reported values (about 100 nm). This is attributed to the small radius and zero rake face angle of the diamond tool adopted in the present work [1, 35]. From the micro- topography shown in Fig. 5(b), the generated cracks are relatively small in size at the initial stage. With further increase of the nominal DoC, particles with relatively large volume are being intermittently removed, leaving randomly distributed micro-pits on the machined surface. From the profile shown in Fig. 5(c), the depth of the pit is even much larger than the DoC, e.g., cutting with a 200 nm DoC induced a pit depth larger than 250 nm.
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ip t cr us an M
te
d
Fig. 5. Characteristics of the surface topography obtained without RSV assistance: (a) optical microscopic image, (b) projected surface micro-topography captured by the optical surface profiler and (c) extracted cross-sectional profile.
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The images at the initial entrance locations and the location with the maximal DoC for micro-grooves generated with RSV assistance, as captured by the optical microscope, are illustrated in Fig. 6(a) and Fig. 6(b), respectively. As shown in Fig. 6(a), the surface of each groove at the entrance location shows a bright part of a much larger length, indicating ductile mode cutting at this location. As shown in Fig. 6(b), although the machined surfaces with the maximal DoC in the two micro-grooves are full with cracks, the density of the breakages of the surfaces and the borders of the two micro-grooves are much slighter than those generated in cutting without RSV assistance (even at places with much smaller nominal DoC). To have a quantitative
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analysis of the generated surfaces, regions A and B, marked in Fig. 6a and Fig. 6b, were further measured by the optical surface profiler, resulting in the projected 2-D micro-topographies shown in Fig. 6(c) and Fig. 6(e), and the cross-sectional profiles
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shown in Fig. 6(d), and Fig. 6(f). From the surface shown in Fig. 6(c), region A, close
cr
to the brittle-ductile transition point, is seen to be very smooth with no cracks, and the
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profile in Fig. 6(d) further suggests that the critical DoC reached a value of about 744 nm, which was about 12.8 times of that obtained in conventional diamond cutting
an
without RSV assistance.
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As shown in Fig. 6(e), the bottom of the generated micro-groove with the maximal DoC of about 2.4 μm featured a hybrid status of micro-cracks and a small volume of
te
d
micro-pits in zone B. The profile in Fig. 6(f) suggests that a relatively smooth curve with small fluctuations was achieved, which was probably induced by micro-cracks
Ac ce p
and micro-pits generated in cutting. Although brittle cutting with a DoC of about 2.4 μm dominated the process in RSV assisted diamond cutting, the resulting density of
micro-pits was much lower than that generated with a much smaller DoC (200 nm) in cutting without RSV assistance as shown in Fig. 5. This phenomenon is reasonable due to the fact that cracks generated in the cutting zone were partially removed in successive cutting passes in RSV-assisted cutting [14].
By removing the best-fitted curved surface via the analysis system of the Zygo software Mx, the surface micro-topographies at the two regions A and B are illustrated
23
Page 23 of 36
in Fig. 7(a) and Fig. 7(b), respectively. The regional roughness of the surface in region A, featuring almost only the vibration marks was about Sa = 4.3 nm, while that in region B was about Sa = 66.2 nm, attributed to the micro-cracks and micro-pits
ip t
formed on the machined surface after cutting. The results suggest that diamond
cr
cutting with RSV assistance is also very promising for rough machining of brittle
us
materials with large DoC and feedrates while resulting in acceptable surface
Ac ce p
te
d
M
an
roughness and micro-defects.
Fig. 6. Characteristics of surface topography obtained with RSV assistance: (a) and (b) optical microscopic images of the surface at the entrance and middle positions in the micro-grooves, (c) projected micro-topography, (d) cross-sectional profile with a DoC of about 744 nm captured by optical surface profiler, (e) projected micro-topography, and (f) cross-sectional profile with a DoC of about 2.403 μm captured by optical surface profiler.
24
Page 24 of 36
(a)
cr
ip t
(b)
us
Fig. 7. Micro-topographies of the surfaces generated with RSV assistance after removing the best-fitted curved micro-groove structure with DoC of (a) 744 nm and (b) 2.403 μm.
an
4.2 Characteristics of the cutting forces in RSV-assisted diamond cutting
M
Cutting force components along the three directions, namely the x-, y- and z-axis of the machine tool system shown in Fig. 1(a) were collected using the dynamometer in
d
the diamond cutting processes both with and without RSV assistance. The obtained
te
cutting forces with RSV assistance are illustrated in Fig. 8(a), while an enlarged view
Ac ce p
of the forces is shown in Fig. 8(b). As shown in Fig. 8(a), the amplitude of the cutting force components increases with the increase of the nominal DoC, and vice versa. Although the workpiece, together with the dynamometer did not move in the cutting process, the periodic interaction between the diamond tool and the workpiece generated forced vibrations of the workpiece, resulting in impact forces which were strongly coupled with the original cutting force components along all the three directions as shown in Fig. 8(a) and Fig. 8(b). Furthermore, with the cutting force in one vibration cycle of the RSV, the periodic variation of the DoC as shown in Fig. 4(a) also induced multi-frequency vibrations of the system. From the forces shown in Fig.
25
Page 25 of 36
8(b), it can be seen that there are about three fluctuation peaks in one vibration cycle for the cutting force along the y-axis direction, and two fluctuation peaks in one
ip t
vibration cycle along both the x- and z-axis directions.
cr
By employing a Chebyshev low-pass filter with a cut-off frequency of 1 kHz, the
us
cutting forces in the process with RSV-assistance were extracted and shown in Fig. 8(c). In general, the cutting forces are directly related to the nominal DoC with
an
imposition of small bursts which are induced by the intermit formation of micro-cracks and micro-chippings in the brittle removal mode of silicon. The
M
maximal cutting forces along the y- and z-axis were about 0.06 N and 0.015 N, respectively. Meanwhile, the three directional cutting forces obtained in cutting
te
d
without RSV assistance are also illustrated in Fig. 8(d) using the same filtering method as mentioned above. As shown in Fig. 8(d), the cutting forces along the y- and
Ac ce p
z-axis directions are approximately symmetric with respect to cutting time, and an
imposition of much larger bursts was also observed, attributing to the chipping in brittle mode removal. The maximal cutting forces along the y- and z-axis are about 0.3
N and 0.025 N, respectively. On the other hand, the force bursts along each of the direction were much larger than those obtained in the RSV-assisted diamond cutting system. For example, the maximal force bursts along the y-axis direction were about 0.012 N and 0.036 N for the processes with and without RSV assistance, respectively. This suggested that much stronger cracking and chipping were taking place in cutting without RSV assistance. This could also be demonstrated from the obtained
26
Page 26 of 36
micro-topographies of the machined surfaces.
(a)
-0.8 0
2
4
Time / s
6
8
0.012 N
Fz Fy Fx
-0.06 4
Time / s
6
8
ip t 5.0005
0.1 0 -0.1
-0.3
-0.4 0
10
5.001 5.0015 Time / s
5.002
5.0025
(d)
-0.2
M
Cutting force / N
-0.02
2
-0.4
(c)
0
-0.08 0
0
-0.8 5
10
0.02
-0.04
0.4
cr
-0.4
Fy Fz Fx
us
0
(b)
One cycle
an
0.4
0.8
Cutting force / N
Fy Fz Fx
Cutting force / N
Cutting force / N
0.8
0.036 N
2
4
Fz Fy Fx 6 Time / s
8
10
12
Ac ce p
te
d
Fig. 8. Characteristics of the three directional cutting force components: (a) original forces in the process with RSV assistance, (b) enlarged view of the original cutting forces, (c) the filtered force components after removing the high frequency components, and (d) the original forces obtained without RSV assistance.
5. Conclusions
The concept of rotary spatial vibration (RSV) method was introduced in the present study for practically facilitating the removal of brittle materials in diamond cutting. The superposition of the rotary motion and of 3D non-resonant vibrations of the diamond tool offers the cutting system the unique capability to overcome some inherent defects and limitations in conventional vibration-assisted cutting. Taking monocrystalline silicon for a case study, circular micro-grooves with varying depths of cut (DoC) were machined. The main conclusions can be drawn as follows:
27
Page 27 of 36
(i) Two key parameters, namely the forward feeding ratio ratio
,
and the vertical cutting
were defined. They closely relate the machine tool and the spatial
vibration system’s parameter. Accordingly, closed-form descriptions of some of
ip t
the critical parameters and the evolution of the DoC during the process were
cr
obtained to give a better understandings of the cutting process and to guide
us
parameter selection.
an
(ii) Experiments on the generation of circular micro-grooves with varying DoC were conducted both with and without RSV assistance. The critical DoC was about
M
745 nm for the RSV-assisted cutting, which was about 12.8 times that obtained without RSV assistance. Surface roughness of Sa = 4.3 nm and Sa = 66.2 nm was
te
d
achieved with nominal DoCs of 744 nm and 2.403 μm in RSV-assisted diamond
Ac ce p
cutting, respectively.
(iii) The cutting forces in the process with RSV assistance mainly featured nominal DoC dependent trends with the superposition of high frequency inertia forces as well as transient DoC-induced force variations. Due to the much smaller maximal DoC, the trend in cutting with RSV assistance obtained by using low-pass filtering was much smaller than that obtained in cutting without RSV assistance. Furthermore, the smoother features with much smaller force bursts suggested a less brittle way of material removal in RSV-assisted diamond cutting.
28
Page 28 of 36
(iv) Compared to vibration-assisted turning, the constant rotational distance in the RSV-assisted cutting system facilitates consistent cutting parameters for
ip t
processing arbitrarily large areas, including cutting speed, horizontal speed ratio
cr
and duty cycle which significantly dominate cutting performance. On the other
us
hand, benefiting from the resulting complex spatial vibratory motions, effective vibration assistance in material removal can be always guaranteed in
an
RSV-assisted cutting when compared with vibration-assisted milling.
M
Although the feasibility of using the rotary vibration in diamond cutting of brittle materials was demonstrated, the following aspects are required to optimally process
te
d
intricate structures on brittle materials: i) to determine the optimal vibration plane with respect to a given material and the desired surface shape, which requires the
Ac ce p
proper selection of the three directional vibrations; ii) to synthesize motions of the vibration system and of the machine tool to have a coordinated operation for ultra-precision generation of the intricately shaped surfaces.
Acknowledgment The work described in this paper was supported by the Research Committee of The Hong Kong Polytechnic University (RTJZ).
29
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References: [1] G. Xiao, S. To, E. Jelenković, Effects of non-amorphizing hydrogen ion implantation on anisotropy in micro cutting of silicon, Journal of Materials
ip t
Processing Technology, 225 (2015) 439-450.
[2] S. Goel, X. Luo, P. Comley, R.L. Reuben, A. Cox, Brittle–ductile transition during
us
Machine Tools and Manufacture, 65 (2013) 15-21.
cr
diamond turning of single crystal silicon carbide, International Journal of
[3] J. Owen, M. Davies, D. Schmidt, E. Urruti, On the ultra-precision diamond
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machining of chalcogenide glass, CIRP Annals-Manufacturing Technology, 64 (2015) 113-116.
M
[4] Q. Zhao, B. Guo, Ultra-precision grinding of optical glasses using mono-layer nickel electroplated coarse-grained diamond wheels. Part 2: Investigation of
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profile and surface grinding, Precision Engineering, 39 (2015) 67-78.
te
[5] H. Zhu, C. Huang, J. Wang, Q. Li, C. Che, Experimental study on abrasive
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waterjet polishing for hard–brittle materials, International Journal of Machine Tools and Manufacture, 49 (2009) 569-578.
[6] J. Yan, K. Maekawa, J.i. Tamaki, T. Kuriyagawa, Micro grooving on single-crystal germanium for infrared Fresnel lenses, Journal of micromechanics and microengineering, 15 (2005) 1925.
[7] D. Yu, Y. Wong, G. Hong, Ultraprecision machining of micro-structured functional surfaces on brittle materials, Journal of micromechanics and microengineering, 21 (2011) 095011. [8] B.S. Dutterer, J.L. Lineberger, P.J. Smilie, D.S. Hildebrand, T.A. Harriman, M.A. Davies, T.J. Suleski, D.A. Lucca, Diamond milling of an Alvarez lens in germanium, Precision Engineering, 38 (2014) 398-408. 30
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[9]
F.
Fang,
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Ultra-precision
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ip t
crystal
Annals-Manufacturing Technology, 60 (2011) 527-530.
cr
[11] S. To, H. Wang, E. Jelenković, Enhancement of the machinability of silicon by
hydrogen ion implantation for ultra-precision micro-cutting, International Journal
us
of Machine Tools and Manufacture, 74 (2013) 50-55.
an
[12] D. Ravindra, M.K. Ghantasala, J. Patten, Ductile mode material removal and high-pressure phase transformation in silicon during micro-laser assisted
M
machining, Precision engineering, 36 (2012) 364-367.
[13] H. Mohammadi, D. Ravindra, S.K. Kode, J.A. Patten, Experimental work on
d
micro laser-assisted diamond turning of silicon (111), Journal of Manufacturing
te
Processes, 19 (2015) 125-128.
[14] D. Brehl, T. Dow, Review of vibration-assisted machining, Precision Engineering,
Ac ce p
32 (2008) 153-172.
[15] N. Suzuki, M. Haritani, J.-b. Yang, R. Hino, E. Shamoto, Elliptical vibration cutting
of
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Annals-Manufacturing Technology, 56 (2007) 127-130.
[16] C. Nath, M. Rahman, K.S. Neo, Machinability study of tungsten carbide using PCD tools under ultrasonic elliptical vibration cutting, International Journal of Machine Tools and Manufacture, 49 (2009) 1089-1095. [17] E. Shamoto, N. Suzuki, E. Tsuchiya, Y. Hori, H. Inagaki, K. Yoshino, Development of 3 DOF ultrasonic vibration tool for elliptical vibration cutting of sculptured surfaces, CIRP Annals-Manufacturing Technology, 54 (2005)
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321-324. [18] T. Moriwaki, E. Shamoto, K. Inoue, Ultraprecision ductile cutting of glass by applying ultrasonic vibration, CIRP Annals-Manufacturing Technology, 41 (1992)
ip t
141-144. [19] G.D. Kim, B.G. Loh, Characteristics of elliptical vibration cutting in micro-V
cr
grooving with variations in the elliptical cutting locus and excitation frequency,
us
Journal of micromechanics and microengineering, 18 (2008) 025002.
[20] T. Moriwaki, E. Shamoto, Ultrasonic elliptical vibration cutting, CIRP
an
Annals-Manufacturing Technology, 44 (1995) 31-34.
[21] E. Shamoto, N. Suzuki, R. Hino, Analysis of 3D elliptical vibration cutting with
M
thin shear plane model, CIRP Annals-Manufacturing Technology, 57 (2008) 57-60.
d
[22] C. Nath, M. Rahman, Effect of machining parameters in ultrasonic vibration
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965-974.
te
cutting, International Journal of Machine Tools and Manufacture, 48 (2008)
[23] H. Ding, R. Ibrahim, K. Cheng, S.-J. Chen, Experimental study on machinability improvement of hardened tool steel using two dimensional vibration-assisted micro-end-milling, International Journal of Machine Tools and Manufacture, 50 (2010) 1115-1118.
[24] G.-L. Chern, Y.-C. Chang, Using two-dimensional vibration cutting for micro-milling, International Journal of Machine Tools and Manufacture, 46 (2006) 659-666. [25] B. Brocato, T. Dow, A. Sohn, Micromachining using elliptical vibration-assisted machining, in, MS thesis, North Carolina State University, 2005 1 mm, 2005. [26] J. Zhang, N. Suzuki, Y. Wang, E. Shamoto, Ultra-precision nano-structure 32
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fabrication by amplitude control sculpturing method in elliptical vibration cutting, Precision Engineering, 39 (2015) 86-99. [27] J. Köhler, A. Seibel, FTS-based face milling of micro structures, Procedia CIRP,
ip t
28 (2015) 58-63. [28] H. Yoshioka, H. Shinno, H. Sawano, A newly developed rotary-linear motion
cr
platform with a giant magnetostrictive actuator, CIRP Annals-Manufacturing
us
Technology, 62 (2013) 371-374.
[29] Z.C. Li, Y. Jiao, T.W. Deines, Z.J. Pei, C. Treadwell, Rotary ultrasonic machining
an
of ceramic matrix composites: feasibility study and designed experiments, International Journal of Machine Tools and Manufacture, 45 (2005) 1402-1411.
M
[30] Z. Pei, P. Ferreira, An experimental investigation of rotary ultrasonic face milling, International Journal of Machine Tools and Manufacture, 39 (1999) 1327-1344.
d
[31] D. Geng, D. Zhang, Y. Xu, F. He, D. Liu, Z. Duan, Rotary ultrasonic elliptical
te
machining for side milling of CFRP: Tool performance and surface integrity,
Ac ce p
Ultrasonics, 59 (2015) 128-137.
[32] Z. Zhu, S. To, S. Zhang, Theoretical and experimental investigation on the novel end-fly-cutting-servo diamond machining of hierarchical micro-nanostructures, International Journal of Machine Tools and Manufacture, 94 (2015) 15-25.
[33] L.L. Howell, S.P. Magleby, B.M. Olsen, Handbook of compliant mechanisms, John Wiley & Sons, 2013.
[34] N.-H. Nguyen, M.-Y. Lee, J.-S. Kim, D.-Y. Lee, Compliance Matrix of a Single-Bent Leaf Flexure for a Modal Analysis, Shock and Vibration, 2015 (2015). [35] J. Yan, T. Asami, H. Harada, T. Kuriyagawa, Fundamental investigation of subsurface damage in single crystalline silicon caused by diamond machining, 33
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Ac ce p
te
d
M
an
us
cr
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Precision engineering, 33 (2009) 378-386.
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Figure captions:
cr
photography of the system, and (b) photography of the CSV.
ip t
Fig. 1. System configuration of the RSV assisted diamond cutting system, (a)
us
Fig. 2 Schematic of (a) the rotary tool motion and (b) the relative tool loci in the
an
orthogonal cutting planes.
Fig. 3. The used tool vibration in cutting, (a) the vibrations in the time-domain and (b)
M
the synthesized spatial ellipse.
d
Fig. 4. Evolution of estimated transient DoC in one cycle.
te
Fig. 5. Characteristics of surface topography obtained without assistance of the RSV,
Ac ce p
(a) the optical microscopic image, (b) the projected surface micro-topography captured by the optical surface profiler and (c) the extracted cross-sectional profile.
Fig. 6. Characteristics of surface topography obtained with assistance of the RSV, (a) and (b) optical micro-scopic images of the surface at the entrance and middle positions in the micro-grooves, (c) the projected micro-topography and (d) the cross-sectional profile with DoC of about 744 nm captured by optical surface profiler, (e) the projected micro-topography and (d) the cross-sectional profile with DoC of about 2.403 μm captured by optical surface profiler. 35
Page 35 of 36
Fig. 7. Micro-topographies of the surfaces generated with assistance of the RSV after removing the best-fitted curved micro-groove structure with DoC of (a) 744
ip t
nm and (b) 2.403 μm.
Fig. 8. Characteristics of the three directional cutting forces, (a) original forces in the
cr
process with RSV assistance, (b) enlarged view of the original cutting forces,
us
(c) the extracted tendency component of the force by removing the high frequency component, and (d) the original forces obtained without RSV
Ac ce p
te
d
M
an
assistance.
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Page 36 of 36
S0141-6359(15)00227-5 http://dx.doi.org/doi:10.1016/j.precisioneng.2015.12.007 PRE 6328
To appear in:
Precision Engineering
Received date: Revised date: Accepted date:
25-10-2015 19-12-2015 23-12-2015
Please cite this article as: Zhu Z, To S, Xiao G, Ehmann KF, Zhang G, Rotary spatial vibration-assisted diamond cutting of brittle materials, Precision Engineering (2015), http://dx.doi.org/10.1016/j.precisioneng.2015.12.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights:
ip t
1. Rotary spatial vibration assisted diamond cutting is proposed for better processing brittle materials;
cr
2. The non-resonant vibration along the three translational directions is adopted to gain more flexibility;
us
3. Consistent cutting performance can be always guaranteed even when processing large areas;
an
4. Feasibility and superiority of this new technique is demonstrated by fabricating micro-grooves on single-crystal silicon.
Ac ce p
te
d
M
5. Characteristics of the machined surface and the cutting force are detailed.
1
Page 1 of 36
Rotary spatial vibration-assisted diamond cutting of brittle materials
ip t
Zhiwei Zhu1, Suet To1,*, Gaobo Xiao1, Kornel F. Ehmann2, and Guoqing Zhang1
(S. To)
us
* Corresponding author: [email protected]
cr
1. State Key Laboratory of Ultra-precision Machining Technology, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, China 2. Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA
an
Abstract: In the present study, a novel process, namely rotary spatial vibration (RSV) assisted diamond cutting, is introduced to overcome cutting velocity induced cutting
M
parameter inconsistencies as well as the cutting direction induced insufficient
d
utilization of vibration assistance in vibration-assisted turning and milling of brittle
the
rotation
of
te
materials. In RSV-assisted diamond cutting, a rotary motion component, generated by the
machine’s
spindle,
is
superimposed
onto
the
Ac ce p
three-degrees-of-freedom translational vibrations of the diamond tool. The resulting complex motions of the diamond tool assure the possibility of consistent cutting performance that is always guaranteed even when processing arbitrarily large areas. In practice, the feasibility and superiority of this technique for processing brittle materials is well demonstrated by fabricating a set of circular micro-grooves on monocrystalline silicon wafers with gradually varying depth-of-cut.
Key words: Diamond cutting; Rotary spatial vibration; Monocrystalline silicon; Cutting forces.
2
Page 2 of 36
1. Introduction For decades, the manufacturing of structured complex surfaces on optical brittle
ip t
materials has attracted considerable attention for a variety of applications in the infrared optics and electronics industries [1-3]. However, the inherent low fracture
cr
toughness of the materials used imposes great machining challenges in obtaining
us
optically qualified surfaces featuring ultra-smooth roughness and a minimal amount of sub-surface micro-cracks. Compared with the commonly adopted abrasive
an
machining methods (including grinding and polishing), which are generally
M
time-consuming [4, 5], diamond cutting techniques, dominated by the use of fast or slow tool servos (FTS/STS) [6, 7] and by multi-axis diamond milling [3, 8], are
d
widely regarded as more promising for better fulfilling the requirements for
te
processing brittle materials with complex shapes due to their capability for achieving
Ac ce p
ultra-precision form accuracy. In diamond cutting, small feedrates and cutting depths are commonly required to allow machining in the ductile region [6, 9] or to restrict the penetration of cracks into the finished surfaces [7, 8]. However, these operations generally lead to extremely low efficiency in practical applications.
To improve the machining performance in diamond cutting, various methods were proposed to enhance the machinability of brittle materials, including ion implantation modification [10, 11], laser-assisted cutting [12, 13] and vibration-assisted machining (VAM) [14-16] to mention a few. Ion implantation modification was reported to be beneficial in reducing cutting forces, increasing the critical depth of cut (DoC) and 3
Page 3 of 36
enhancing tool life [10, 11]. Generally, the modified layer is very thin in the subsurface of the material. However, laborious serial processes and expensive facilitates are required to implement this modification-assisted cutting method. Laser
ip t
assistance utilizes thermal effects for material softening and the activation of plastic
cr
flow. This effect is effective for improving the machinability of brittle materials in
us
cutting without leaving undesirable defects on the finished surface [12, 13]. However, the unavoidable thermal deformations deteriorate the machining accuracy of the
an
desired components. It is also difficult to process surfaces with intricate shapes due to the poor capability for tracking the focal spot of the laser on the surface. Due to its
M
low cost and high efficiency, VAM that uses mechanical energy to facilitate material
te
of brittle materials [14].
d
removal is regarded as a superior machining process for enhancing the machinability
Ac ce p
In general, VAM can be classified into 1-D, 2-D and 3-D machining according to the employed number of vibration directions. The 1-D and 3-D VAM processes are dominated by the resonant ultrasonic cutting mode of operation [17, 18], while 2-D VAM mainly involves both the resonant and non-resonant cutting modes [15, 19, 20]. Compared with the 1-D VAM, the overlapping elliptical tool loci in 2D/3D VAM offer an essential beneficial advantage for automatically generating much thinner chips [14]. Furthermore, it was reported that spatial elliptical vibrations in 3-D VAM are more flexible in machining sculptured surfaces [17, 21]. No matter which kind of VAM is adopted, the horizontal speed ratio (HSR) and duty cycle (DC) are two essential
4
Page 4 of 36
parameters, significantly influencing the critical brittle-ductile transition as well as tool wear behavior in machining [14, 22]. By adopting a small enough HSR, the critical DoC was reported to increase several times, offering significantly improved
ip t
economics for processing brittle materials [14, 16, 22]. Nonetheless, it is still
cr
challenging for VAM to practically facilitate diamond cutting of complex surfaces.
us
For instance, to facilitate diamond turning, a progressively increased vibration frequency is obligatorily required to guarantee effective HSR and DC values in view
an
of the ever-increasing rotational distance of the cutting points. However, limited by the dynamics of the mechatronic systems, it is not sufficient for VAM to assist in
M
turning surfaces with large apertures. As for VAM working in the resonant mode, the vibration frequency and amplitude are non-adjustable. The fixed vibration parameters
te
d
lead to time-varying cutting parameters (HSR and DC), due to the variation of the relative distance between the cutter location and spindle axis. Therefore, variable
Ac ce p
cutting conditions will dominate the process, highly deteriorating machining performance. In diamond micro-milling operations, planar 2-D vibrations are mainly superimposed on the workpiece to achieve vibration assistance [23, 24]. In milling, the cutting edge commonly operates at a constant cutting velocity attributed to the constant distance between the cutting edge and the corresponding rotational axis, resulting in a constant HSR when using vibrations with fixed amplitudes and frequencies. However, the rotation of the cutting edge would induce time-varying changes in the cutting directions. Thus, the unchanged vibration plane leads to extremely low utilization of the effective vibration assistance. Besides, since the
5
Page 5 of 36
workpiece is vibrated during the process, small workpieces are essentially required in this configuration to achieve high vibration frequencies and for effective cutting. To use VAM for facilitating the generation of micro-structured surfaces, translational
ip t
raster motions instead of rotations were commonly adopted to guarantee homogenous
cr
machining conditions, i.e., consistent HSR and DC [25, 26]. However, the inevitable
us
acceleration and deceleration processes in the discontinuous rater feeding motions
an
lead to a much lower machining efficiency of the sculpturing process.
Facing the above-listed dilemmas, a novel rotary spatial vibration (RSV) assisted
M
diamond cutting technique is proposed and demonstrated in this paper for practically facilitating diamond cutting of brittle materials. With RSV-assisted diamond cutting, a
te
d
single point diamond tool is vibrated by piezo-actuators along three translational directions on a rotating spindle, resulting in a rotary vibration assisted cutting process.
Ac ce p
It is noteworthy that rotary vibrations have recently been also introduced for the purpose of FTS-milling [27, 28] and rotary ultrasonic machining (RUM) for drilling as well as milling operations [29-31]. With FTS-milling and RUM, unidirectional vibrations are commonly added to the rotary tool along its axial direction, which introduces new functionalities into the machining process. However, the unidirectional vibrations are more suitable for drilling operations and significantly restrict machining flexibility, especially for processing sculptured surfaces.
In this paper, the employment of 3-D non-resonant rotary vibrations with a constant
6
Page 6 of 36
rotational distance of the diamond tool offers the following advantages of the RSVassisted diamond cutting system:
velocity;
ip t
(a) Consistent cutting conditions (HSR and DC) induced by the constant cutting
(b) The capability for large-scale processing of surfaces without limitations of system
dynamics
and
workpiece
size
when
compared
to
cr
the
vibration-assisted diamond turning;
us
(c) Continuously effective vibration assistance due to the rotary vibrations when compared to vibration-assisted milling;
an
(d) The potential for tuning the orientation of the vibration plane to achieve optimal cutting with respect to different materials and surface shapes by combining the three-axial vibrations;
M
(e) The capability for ultra-precision generation of intricately shaped surfaces
te
processes.
d
by adopting servo-controlled motions inherited from the FTS/STS
Ac ce p
2. Principle of RSV-assisted diamond cutting of brittle materials 2.1 System configuration for RSV-assisted diamond cutting
The configuration of the RSV-assisted diamond cutting system is illustrated in Fig. 1.
The single point diamond tool is attached to the end-effector of a piezo-actuated compliant spatial vibrator (CSV) that generates spatial vibrations along three translational directions. By means of a vacuum chuck, the CSV is fixed to the spindle and rotated with it (c-axis) as shown in the photograph of the system in Fig. 1(a),
resulting in rotary vibrations of the diamond tool. The spindle, in turn, mounted on the
7
Page 7 of 36
x-axis slide of the machine tool, follows motions in the side-feeding direction. The workpiece is clamped on the z-slide of the machine tool to facilitate the generation of surfaces with intricate shapes [32]. A slip ring is employed to transmit the command
te
d
M
an
us
cr
ip t
signals from the stationary command generator to the three rotating piezo-actuators.
Ac ce p
Fig. 1. System configuration of the RSV-assisted diamond cutting system, (a) photograph of the system, and (b) photograph of the CSV.
The CSV was designed to guide the motions of the piezo-actuators and work on the rotating spindle. Special considerations for a high rotational symmetry and a highly compact structure were given during the design of this three-degrees-of-freedom (3-DoF) compliant mechanism. To obtain high machining efficiency and accuracy, a wide working bandwidth and decoupled output motions were also required. Under these considerations, a parallel configuration of the mechanism was employed. The photograph of the CSV is schematically illustrated in Fig. 1(b). Three piezo-actuators 8
Page 8 of 36
in an orthogonal configuration were employed to generate the three-axial vibrations. L-shaped flexure hinges (LFH) [33, 34] were used as the basic elements for motion guidance to create a highly compact structure with multiple DoFs. In the CSV, four
ip t
sets of LFHs were adopted with symmetric configuration to decouple the output
us
cr
motions.
During cutting, the diamond tool rotates on the spindle with a fixed and tunable
an
rotational distance/radius, resulting in a diamond fly cutting like arrangement with constant cutting velocity for material removal. Concurrently, the diamond tool
M
undergoes spatial vibrations along three translational directions. Unlike the conventional 2-D elliptical vibration cutting (EVC) process, the third vibratory
te
d
motion, along the xv-axis direction is introduced into the RSV system to extend the
Ac ce p
tool’s vibrations from the 2-D to the 3-D spatial domain [17, 21].
2.2 Kinematics for processing brittle materials
For process analysis, a local Cartesian coordinate system, ov-xvyvzv, fixed to the
rotating spindle of the machine tool, is defined. Axes ovxv, ovyv and ovzv are aligned
with the three vibration directions generated by the three piezoelectric actuators of the CSV as shown in Fig. 1, while axis ovzv is coincident with the rotational axis of the spindle. The diamond tool is installed on the end-effector of the CSV along the xv-axis, with an offset value of Rd. The kinematic equations of the motions of the diamond tool in the ov-xvyvzv coordinate system are given by: 9
Page 9 of 36
xv a sin(2 ft x ) Rd yv b sin(2 ft y ) zv c sin(2 ft z )
ip t
(1)
where a, b, and c denote the vibration amplitudes along the xv-, yv- and zv-axis
are the phase angles along the
cr
directions, respectively, x , y and z
us
corresponding directions, f is the vibration frequency, and Rd is the offset distance of
an
the diamond tool in the xv-direction.
M
In the RSV-assisted diamond cutting process, the loci of the diamond tool constitute a set of ellipses in 3-D space [17, 21]. However, in the ov-xvyvzv system, the elliptical
sin(z y )
sin( x y ) Rd cos y sin(z x ) Rd cos z xv yv zv 0 (2) b ab c ac
Ac ce p
a
te
d
vibrations are taking place in a vibration plane expressed by:
Since Eq. (1) only describes the elliptical trajectories in the plane given by Eq. (2) of the rotating ov-xvyvzv system, a stationary coordinate system, ot-xtytzt, is introduced to
express the rotation induced cutting velocity and the relationships between sequential elliptical tool trajectories. Coordinate system ot-xtytzt is defined such that plane ot-ytzt coincides with the tangential plane ST to the rotational motion. Its origin, ot, is set to coincide with point [Rd, 0, 0] in the ov-xvyvzv system at time tk, assumed to coincide with the beginning of the kth cutting cycle (ellipse), while axes otyt and otzt are aligned
10
Page 10 of 36
with ovyv and ovzv also at time tk as shown in Fig. 2(a). During the following cutting cycles, the system ot-xtytzt, as stated above, remains stationary.
Therefore, the
current and consequential ellipses can be described in the system ot-xtytzt. Without loss
ip t
of generality, the subsequent analyses will be conducted within two consecutive
(a)
cr
cutting cycles, i.e., from time t=tk to t=2/f+ tk.
(b) S’
z'
s
pL
xv
yt
o'
ST
te
0.5 pL
ov Spindle
hc,max
to
vM
n Rd 30
d
Tool Position
d
vC (t )
tm
M
Diamond tool
Cutting duration
y'
an
yv
(k+1)th
us
kth
ST
Ac ce p
te
Fig. 2 Schematic of (a) the rotary tool motion and (b) the relative tool loci in the orthogonal cutting planes.
Since the ov-xvyvzv system is rotating around the spindle axis, by setting t ' t tk , the
vibratory motions described in Eq. (1) can be transformed to the ot-xtytzt system as:
R cos nt ' Rd 30 d x R v d xt yt yv Rd sin nt ' 30 zt z v 0
(3)
0 0 1
(4)
where
cos nt ' 30
cos nt ' 30 R z sin nt ' 30 0
sin nt '
0
30
11
Page 11 of 36
To obtain a closed-form description of the critical cutting parameters for the better understanding of the machining process, the cutting loci are simplified as a set of
ip t
overlapping ellipses [14] under the assumption that x y 0 and z / 2 .
cr
Thus, the vibrations in the ot-xtytzt system under these assumptions are taking place in
with respect to the
us
an inclined plane S’ that is inclined by an angle
an
ot-xtzt plane as shown in Fig. 2(b).
To simplify the analysis of the vibrations form 3-D space to a 2-D plane, a new local
M
coordinate system o ' x ' y ' z ' who’s o ' y ' z ' plane coincides with the plane S’ is introduced. The new system can be obtained by just rotating the coordinate system . By expressing the equations of motion given
d
ot-xtytzt around the zt axis by the angle
te
by Eq. (3) in the o ' x ' y ' z ' system under the small angle assumption nt '
30
,
Ac ce p
the tool loci described in the system o ' x ' y ' z ' from time t = tk to t = 2/f + tk are
given by:
cos sin 0 x t x ' y ' sin cos 0 yt z ' 0 1 z t 0 nRd at ' 30 a 2 b 2 2 nRd t 2 a b sin(2 ft ') 30 c cos(2 ft ')
(5)
12
Page 12 of 36
where
b a b2 2
is defined as the projection ratio of the cutting velocity along the
ip t
y ' -axis direction.
Since the vibration frequency is much higher than the rotational frequency, namely
30 a 2 b 2
in Eq. (5) given that t '
cr
nRd at '
can be
us
, the quantity
neglected. This suggests that the ellipses in two consecutive cutting cycles can be
an
approximately regarded as taking place in the vibration plane S’ as shown in Error! Reference source not found.(b). Thereby, the tool loci in the cutting zones for the kth
M
and (k+1)th cutting cycles in the vibration plane S’ can be described by:
Ac ce p
te
d
y '2 z 'k c 1 2 k 2 a b 2 y 'k 1 pL z 'k 1 c 1 a2 b2 pL n Rd 30 f
(6)
where pL denotes the pitch between any two successive ellipses as shown in Fig. 2(b), and the subscripts k and k+1 denote the kth and (k+1)th ellipses.
As shown in Error! Reference source not found.(b), at time to the diamond tool enters the workpiece to remove material. From then on, the cutting depth increases until time tm at which point the cutting depth reaches its maximal value. After that, the
13
Page 13 of 36
cutting depth gradually decreases due to the appearance of the upper flat surface, and at time te, the diamond tool moves out of the workpiece. By setting y 'k y 'k 1 yo and z 'k z 'k 1 zo , the position and time at the entry point with respect to the (k+1)th
cr
ip t
cutting cycle can be determined from:
pL
a b2 2
(7)
(8)
M
an
us
pL yo 2 2 zo c 1 0.5 1 arcsin 0.5 to 2 f f
d
where is the forward feeding ratio defining the ratio between the pitch pL and the a 2 b 2 along the cutting direction. It is commonly much less
than 1, namely
.
Ac ce p
te
vibration amplitude
At point tm, corresponding to the maximal depth of cut (DoC), the requirement
z 'k ,m (c h) should be satisfied, leading to the following relationships:
y ' a2 b2 1 2 k ,m 2 1 arcsin 1 tm f 2 f
ch h 1 c c
(9)
(10)
14
Page 14 of 36
where the subscripts k and m denote the kth ellipse and the time tm, respectively; h is the nominal DoC, 1 is the cutting ratio defining the relationship between the
ip t
nominal DoC and the vibration amplitude along the cutting direction.
cr
By calculating the difference between the zv-axis values of the to-be-machined surface
us
and the cutting point at time tm, the maximal DoC is obtained as:
2
(11)
M
an
hc, max h c z k 1 ( yk ,m ) =c 1 1 2
te
expressed as:
d
By omitting the second order small term, 2 , in Eq. (7), the maximal DoC can be
Ac ce p
hc,max c 2 2 1 2
(12)
At time te, when the diamond tool moves out of the workpiece, the following relationship can be obtained by satisfying the requirement z 'k 1,e (c h) :
2 2 2 y' k 1,e pL a b 1 2 1 arcsin 1 te f 2 f
(13)
15
Page 15 of 36
Thus, the DC can be written as:
2
(14)
ip t
DC (te to ) f
arcsin 1 2 arcsin 0.5
n Rd 30 f 2
(15)
an
HSR
us
cr
and HSR is given by [14]:
M
The instantaneous DoC is described by the piecewise function:
(16)
Ac ce p
te
d
z y t z y t , t t tm h(t ) k k 1 k 1 k 1 o h c zk 1 yk 1 t , tm t te
With consideration of the velocity changes along the y’- and z’-axis directions, the instantaneous cutting direction relative to the workpiece can be written as [14]:
60 fc sin(2 ft ) (t ) arctan 60 f a 2 b 2 cos(2 ft ) nR d
(17)
and the effective rake and clearance angles relative to the workpiece expressed by [14]:
16
Page 16 of 36
(t ) 0 (t )
(18)
(t ) 0 (t )
(19)
values are two distinctly important
us
Remark: The newly defined and
cr
ip t
where 0 and 0 were the nominal rake face and clearance angles, respectively.
parameters directly determining the maximum DoC and the parameters DC and HSR
an
in cutting as shown by Eqns. (11), (13) and (14).
M
In vibration-assisted turning, the increase of the rotational distance Rd would lead to an increase of . It would further lead to an increase of the maximal DoC and HSR
te
d
deriving from the relationships shown by Eqns. (11) and (14), highly deteriorating,
Ac ce p
thereby, the performances in cutting of brittle materials [14, 16, 22].
In vibration-assisted milling, as reported in [23, 24], the ratio cos nt would 30
periodically change between 0 and 1 and, accordingly, result in a periodic changes of
between 0 to max . It is suggested by Eqns. (10), (13) and (14) that the effects of
the vibrations on material removal would also periodically vary between invalid and normal phases.
With the RSV-assisted diamond cutting system, the two parameters, and , appear to have no relationship to the cutting position, suggesting that a consistent 17
Page 17 of 36
material removal operation can always be achieved, even when processing large-scale
ip t
samples.
cr
3. Experimental setup
Experiments were performed on an ultra-precision lathe (Moore Nanotech 350FG,
us
USA) shown in Fig. 1(a). The CSV made of aluminum alloy 6061 was driven by three
an
piezoelectric stack actuators (P-880.51, Polytec PI, Inc., Germany) with three power amplifiers (PI E617.001). A Power PMAC control board (Delta Tau Data Systems,
M
Inc., USA) was used for signal communication and control of the vibrator. The amplitudes of the command signals were set to 0 V, 4 V, and 3 V at a frequency of 2
d
kHz for the piezo-actuators in the CSV along the xv-, yv- and zv-aixs directions,
te
respectively. By using a set of capacitive displacement sensors (Elite, Lion Precision,
Ac ce p
USA) in an off-line arrangement, the displacements of the end-effector along each of the three directions were captured and illustrated in Fig. 3(a), while the spatial ellipses formed by the three-axial vibrations are given in Fig. 3(b). As shown in Fig. 3(a), the amplitudes of the vibrations along the three directions were 0.5 μm, 4.8 μm and 2.4 μm, respectively. Since there was no command signal given for the x-axis motion, the
harmonic vibrations were induced by the dynamic coupling effects which would be detailed in future work.
18
Page 18 of 36
(a)
1
1 0
0 -0.5 -1 2 1
-2
0
y / μm
2.5
3
3.5 Time / s
4
4.5
5 x 10
-1
ip t
-1.5
-1
-3 2
(b)
0.5
-2
0 0.2 -0.2 x / μm
cr
Displacement / μm
2
a
1.5
z y x
z / μm
3
-3
us
Fig. 3. Tool vibrations: (a) vibrations in the time-domain and (b) the synthesized spatial ellipse.
an
A natural single crystal diamond tool (Contour Fine Tooling Inc., UK) with a round edge of radius of 0.104 mm and 0o rake face angle was used. To measure the cutting
M
force in the process, a three directional dynamometer (9255b, Kistler Group, Germany) was installed on the slide with the workpiece on it. Micro-grooving experiments on
te
d
monocrystalline silicon 〈001〉 were conducted using diamond cutting both with and without RSV assistance. During grooving, the sample was obliquely mounted on the
Ac ce p
slide with a preset inclination angle relative to the end-face of the spindle. Therefore, during one revolution of the diamond tool, it cut in and out of the workpiece with gradually varying DoC. To investigate the cutting performance with larger depths, side-feeding towards the direction with a higher slope was adopted using a feedrate of 0.1 mm/rev along the x-axis of the machine tool. The rotational distance of the diamond tool and the spindle speed were about 1.25 mm and 2 rpm, respectively. After cutting, the surfaces were cleaned with ultrasonic assistance in alcohol. An optical microscope (BX60, Olympus Corporation, Japan) was used to capture photographs of the machined surfaces. In addition, the Nexview 3-D Optical Surface
19
Page 19 of 36
Profiler (Zygo Corporation, USA) was employed to capture the 3-D topographies of the corresponding surfaces.
ip t
With the above-stated machining parameters, the theoretically obtained transient
cr
DoCs with respect to the nominal DoCs of 0.2 μm, 0.5 μm and 0.8 μm are illustrated
us
with respect to time in one cutting cycle in Fig. 4. For a small nominal DoC, the transient DoC shows an approximately linear relationship with respect to time in the
an
two cutting stages. With an increase of the nominal DoC, the nonlinearity of the transient DoC becomes apparent, showing an exponential dependence on time. The
M
HSR has no relationship with the nominal DoC, and it is about 0.01 in this case.
-4
d
Ac ce p
m m / uct of ht p e D
x 10
h=0.8 m
te
2
1
0 0
0.2
h=0.5 m h=0.2 m 0.4
0.6 Time / s
0.8
1
1.2 -4 x 10
Fig. 4. Evolution of estimated transient DoC in one cycle.
20
Page 20 of 36
4. Experimental results and discussion 4.1 Characteristics of the machined surface
ip t
Without RSV assistance, a micro-groove was firstly fabricated using the same spindle
cr
speed and rotational distance as employed in the cutting with RSV assistance to have a comparison of the machining performance, resulting in the optical microscopic
us
image shown in Fig. 5(a). A short distance after the entrance of the tool, a large
an
number of cracks is formed on the bottom of the micro-groove as characterized by the dark spots in Fig. 5(a). By means of the Zygo optical surface profiler, the surface
M
micro-topography of the micro-groove at the entrance position was further obtained as shown in Fig. 5(b). The cross-sectional profile along the cutting direction was also
d
extracted and shown in Fig. 5(c). It can be seen that the critical DoC at which
te
ductile-brittle transition occurs is about 58 nm without RSV assistance. This critical
Ac ce p
DoC is much smaller than the commonly reported values (about 100 nm). This is attributed to the small radius and zero rake face angle of the diamond tool adopted in the present work [1, 35]. From the micro- topography shown in Fig. 5(b), the generated cracks are relatively small in size at the initial stage. With further increase of the nominal DoC, particles with relatively large volume are being intermittently removed, leaving randomly distributed micro-pits on the machined surface. From the profile shown in Fig. 5(c), the depth of the pit is even much larger than the DoC, e.g., cutting with a 200 nm DoC induced a pit depth larger than 250 nm.
21
Page 21 of 36
ip t cr us an M
te
d
Fig. 5. Characteristics of the surface topography obtained without RSV assistance: (a) optical microscopic image, (b) projected surface micro-topography captured by the optical surface profiler and (c) extracted cross-sectional profile.
Ac ce p
The images at the initial entrance locations and the location with the maximal DoC for micro-grooves generated with RSV assistance, as captured by the optical microscope, are illustrated in Fig. 6(a) and Fig. 6(b), respectively. As shown in Fig. 6(a), the surface of each groove at the entrance location shows a bright part of a much larger length, indicating ductile mode cutting at this location. As shown in Fig. 6(b), although the machined surfaces with the maximal DoC in the two micro-grooves are full with cracks, the density of the breakages of the surfaces and the borders of the two micro-grooves are much slighter than those generated in cutting without RSV assistance (even at places with much smaller nominal DoC). To have a quantitative
22
Page 22 of 36
analysis of the generated surfaces, regions A and B, marked in Fig. 6a and Fig. 6b, were further measured by the optical surface profiler, resulting in the projected 2-D micro-topographies shown in Fig. 6(c) and Fig. 6(e), and the cross-sectional profiles
ip t
shown in Fig. 6(d), and Fig. 6(f). From the surface shown in Fig. 6(c), region A, close
cr
to the brittle-ductile transition point, is seen to be very smooth with no cracks, and the
us
profile in Fig. 6(d) further suggests that the critical DoC reached a value of about 744 nm, which was about 12.8 times of that obtained in conventional diamond cutting
an
without RSV assistance.
M
As shown in Fig. 6(e), the bottom of the generated micro-groove with the maximal DoC of about 2.4 μm featured a hybrid status of micro-cracks and a small volume of
te
d
micro-pits in zone B. The profile in Fig. 6(f) suggests that a relatively smooth curve with small fluctuations was achieved, which was probably induced by micro-cracks
Ac ce p
and micro-pits generated in cutting. Although brittle cutting with a DoC of about 2.4 μm dominated the process in RSV assisted diamond cutting, the resulting density of
micro-pits was much lower than that generated with a much smaller DoC (200 nm) in cutting without RSV assistance as shown in Fig. 5. This phenomenon is reasonable due to the fact that cracks generated in the cutting zone were partially removed in successive cutting passes in RSV-assisted cutting [14].
By removing the best-fitted curved surface via the analysis system of the Zygo software Mx, the surface micro-topographies at the two regions A and B are illustrated
23
Page 23 of 36
in Fig. 7(a) and Fig. 7(b), respectively. The regional roughness of the surface in region A, featuring almost only the vibration marks was about Sa = 4.3 nm, while that in region B was about Sa = 66.2 nm, attributed to the micro-cracks and micro-pits
ip t
formed on the machined surface after cutting. The results suggest that diamond
cr
cutting with RSV assistance is also very promising for rough machining of brittle
us
materials with large DoC and feedrates while resulting in acceptable surface
Ac ce p
te
d
M
an
roughness and micro-defects.
Fig. 6. Characteristics of surface topography obtained with RSV assistance: (a) and (b) optical microscopic images of the surface at the entrance and middle positions in the micro-grooves, (c) projected micro-topography, (d) cross-sectional profile with a DoC of about 744 nm captured by optical surface profiler, (e) projected micro-topography, and (f) cross-sectional profile with a DoC of about 2.403 μm captured by optical surface profiler.
24
Page 24 of 36
(a)
cr
ip t
(b)
us
Fig. 7. Micro-topographies of the surfaces generated with RSV assistance after removing the best-fitted curved micro-groove structure with DoC of (a) 744 nm and (b) 2.403 μm.
an
4.2 Characteristics of the cutting forces in RSV-assisted diamond cutting
M
Cutting force components along the three directions, namely the x-, y- and z-axis of the machine tool system shown in Fig. 1(a) were collected using the dynamometer in
d
the diamond cutting processes both with and without RSV assistance. The obtained
te
cutting forces with RSV assistance are illustrated in Fig. 8(a), while an enlarged view
Ac ce p
of the forces is shown in Fig. 8(b). As shown in Fig. 8(a), the amplitude of the cutting force components increases with the increase of the nominal DoC, and vice versa. Although the workpiece, together with the dynamometer did not move in the cutting process, the periodic interaction between the diamond tool and the workpiece generated forced vibrations of the workpiece, resulting in impact forces which were strongly coupled with the original cutting force components along all the three directions as shown in Fig. 8(a) and Fig. 8(b). Furthermore, with the cutting force in one vibration cycle of the RSV, the periodic variation of the DoC as shown in Fig. 4(a) also induced multi-frequency vibrations of the system. From the forces shown in Fig.
25
Page 25 of 36
8(b), it can be seen that there are about three fluctuation peaks in one vibration cycle for the cutting force along the y-axis direction, and two fluctuation peaks in one
ip t
vibration cycle along both the x- and z-axis directions.
cr
By employing a Chebyshev low-pass filter with a cut-off frequency of 1 kHz, the
us
cutting forces in the process with RSV-assistance were extracted and shown in Fig. 8(c). In general, the cutting forces are directly related to the nominal DoC with
an
imposition of small bursts which are induced by the intermit formation of micro-cracks and micro-chippings in the brittle removal mode of silicon. The
M
maximal cutting forces along the y- and z-axis were about 0.06 N and 0.015 N, respectively. Meanwhile, the three directional cutting forces obtained in cutting
te
d
without RSV assistance are also illustrated in Fig. 8(d) using the same filtering method as mentioned above. As shown in Fig. 8(d), the cutting forces along the y- and
Ac ce p
z-axis directions are approximately symmetric with respect to cutting time, and an
imposition of much larger bursts was also observed, attributing to the chipping in brittle mode removal. The maximal cutting forces along the y- and z-axis are about 0.3
N and 0.025 N, respectively. On the other hand, the force bursts along each of the direction were much larger than those obtained in the RSV-assisted diamond cutting system. For example, the maximal force bursts along the y-axis direction were about 0.012 N and 0.036 N for the processes with and without RSV assistance, respectively. This suggested that much stronger cracking and chipping were taking place in cutting without RSV assistance. This could also be demonstrated from the obtained
26
Page 26 of 36
micro-topographies of the machined surfaces.
(a)
-0.8 0
2
4
Time / s
6
8
0.012 N
Fz Fy Fx
-0.06 4
Time / s
6
8
ip t 5.0005
0.1 0 -0.1
-0.3
-0.4 0
10
5.001 5.0015 Time / s
5.002
5.0025
(d)
-0.2
M
Cutting force / N
-0.02
2
-0.4
(c)
0
-0.08 0
0
-0.8 5
10
0.02
-0.04
0.4
cr
-0.4
Fy Fz Fx
us
0
(b)
One cycle
an
0.4
0.8
Cutting force / N
Fy Fz Fx
Cutting force / N
Cutting force / N
0.8
0.036 N
2
4
Fz Fy Fx 6 Time / s
8
10
12
Ac ce p
te
d
Fig. 8. Characteristics of the three directional cutting force components: (a) original forces in the process with RSV assistance, (b) enlarged view of the original cutting forces, (c) the filtered force components after removing the high frequency components, and (d) the original forces obtained without RSV assistance.
5. Conclusions
The concept of rotary spatial vibration (RSV) method was introduced in the present study for practically facilitating the removal of brittle materials in diamond cutting. The superposition of the rotary motion and of 3D non-resonant vibrations of the diamond tool offers the cutting system the unique capability to overcome some inherent defects and limitations in conventional vibration-assisted cutting. Taking monocrystalline silicon for a case study, circular micro-grooves with varying depths of cut (DoC) were machined. The main conclusions can be drawn as follows:
27
Page 27 of 36
(i) Two key parameters, namely the forward feeding ratio ratio
,
and the vertical cutting
were defined. They closely relate the machine tool and the spatial
vibration system’s parameter. Accordingly, closed-form descriptions of some of
ip t
the critical parameters and the evolution of the DoC during the process were
cr
obtained to give a better understandings of the cutting process and to guide
us
parameter selection.
an
(ii) Experiments on the generation of circular micro-grooves with varying DoC were conducted both with and without RSV assistance. The critical DoC was about
M
745 nm for the RSV-assisted cutting, which was about 12.8 times that obtained without RSV assistance. Surface roughness of Sa = 4.3 nm and Sa = 66.2 nm was
te
d
achieved with nominal DoCs of 744 nm and 2.403 μm in RSV-assisted diamond
Ac ce p
cutting, respectively.
(iii) The cutting forces in the process with RSV assistance mainly featured nominal DoC dependent trends with the superposition of high frequency inertia forces as well as transient DoC-induced force variations. Due to the much smaller maximal DoC, the trend in cutting with RSV assistance obtained by using low-pass filtering was much smaller than that obtained in cutting without RSV assistance. Furthermore, the smoother features with much smaller force bursts suggested a less brittle way of material removal in RSV-assisted diamond cutting.
28
Page 28 of 36
(iv) Compared to vibration-assisted turning, the constant rotational distance in the RSV-assisted cutting system facilitates consistent cutting parameters for
ip t
processing arbitrarily large areas, including cutting speed, horizontal speed ratio
cr
and duty cycle which significantly dominate cutting performance. On the other
us
hand, benefiting from the resulting complex spatial vibratory motions, effective vibration assistance in material removal can be always guaranteed in
an
RSV-assisted cutting when compared with vibration-assisted milling.
M
Although the feasibility of using the rotary vibration in diamond cutting of brittle materials was demonstrated, the following aspects are required to optimally process
te
d
intricate structures on brittle materials: i) to determine the optimal vibration plane with respect to a given material and the desired surface shape, which requires the
Ac ce p
proper selection of the three directional vibrations; ii) to synthesize motions of the vibration system and of the machine tool to have a coordinated operation for ultra-precision generation of the intricately shaped surfaces.
Acknowledgment The work described in this paper was supported by the Research Committee of The Hong Kong Polytechnic University (RTJZ).
29
Page 29 of 36
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ip t
Processing Technology, 225 (2015) 439-450.
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us
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cr
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an
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M
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d
profile and surface grinding, Precision Engineering, 39 (2015) 67-78.
te
[5] H. Zhu, C. Huang, J. Wang, Q. Li, C. Che, Experimental study on abrasive
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F.
Fang,
L.
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Ultra-precision
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glass,
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CIRP
ip t
crystal
Annals-Manufacturing Technology, 60 (2011) 527-530.
cr
[11] S. To, H. Wang, E. Jelenković, Enhancement of the machinability of silicon by
hydrogen ion implantation for ultra-precision micro-cutting, International Journal
us
of Machine Tools and Manufacture, 74 (2013) 50-55.
an
[12] D. Ravindra, M.K. Ghantasala, J. Patten, Ductile mode material removal and high-pressure phase transformation in silicon during micro-laser assisted
M
machining, Precision engineering, 36 (2012) 364-367.
[13] H. Mohammadi, D. Ravindra, S.K. Kode, J.A. Patten, Experimental work on
d
micro laser-assisted diamond turning of silicon (111), Journal of Manufacturing
te
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Figure captions:
cr
photography of the system, and (b) photography of the CSV.
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Fig. 1. System configuration of the RSV assisted diamond cutting system, (a)
us
Fig. 2 Schematic of (a) the rotary tool motion and (b) the relative tool loci in the
an
orthogonal cutting planes.
Fig. 3. The used tool vibration in cutting, (a) the vibrations in the time-domain and (b)
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the synthesized spatial ellipse.
d
Fig. 4. Evolution of estimated transient DoC in one cycle.
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Fig. 5. Characteristics of surface topography obtained without assistance of the RSV,
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(a) the optical microscopic image, (b) the projected surface micro-topography captured by the optical surface profiler and (c) the extracted cross-sectional profile.
Fig. 6. Characteristics of surface topography obtained with assistance of the RSV, (a) and (b) optical micro-scopic images of the surface at the entrance and middle positions in the micro-grooves, (c) the projected micro-topography and (d) the cross-sectional profile with DoC of about 744 nm captured by optical surface profiler, (e) the projected micro-topography and (d) the cross-sectional profile with DoC of about 2.403 μm captured by optical surface profiler. 35
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Fig. 7. Micro-topographies of the surfaces generated with assistance of the RSV after removing the best-fitted curved micro-groove structure with DoC of (a) 744
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nm and (b) 2.403 μm.
Fig. 8. Characteristics of the three directional cutting forces, (a) original forces in the
cr
process with RSV assistance, (b) enlarged view of the original cutting forces,
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(c) the extracted tendency component of the force by removing the high frequency component, and (d) the original forces obtained without RSV
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te
d
M
an
assistance.
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