Journal of Manufacturing Processes 50 (2020) 520–527
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Journal of Manufacturing Processes
journal homepage: www.elsevier.com/locate/manpro
Mechanism study on ultrasonic vibration assisted face grinding of Hard and
brittle materials
T
Xiaofeng Zhanga, Lin Yanga, Yan Wangb,*, Bin Lina, Yinghuai Dongb, Chang Shib
a
b
Key Laboratory of Advanced Ceramics and Machining Technology, Ministry of Education, Tianjin University, China
Tianjin University of Science and Technology, Tianjin, China
ARTICLE INFO
ABSTRACT
Keywords:
UAFG
Surface generating
Grinding force modeling
Surface
Morphology
Vibration
Amplitude
Ultrasonic vibration assisted face grinding (UAFG) has excellent performance in hard and brittle materials
processing. In order to reveal the surface generating mechanism and improve the machining quality, this study
was dealing with investigation on ultrasonic energy distribution and surface generating characteristics. Based on
the modeling of grinding force, surface generation and material removal volume, the grinding mechanism of
UAFG is analyzed and presented in detail. The surface generating process is described by grain trajectory interference and overlap, and the grinding force model is established based on fracture mechanics of brittle materials. According to the mathematical modeling, an innovation for surface adjustment and grinding force calculation in UAFG is proposed. Depend on the theoretical study, the combined effect of ultrasonic vibration and
processing parameters on grinding force and surface micro structure in UAFG is reported. The surface characteristics can be designed and simulated by process parameter optimization; high performance surface can be
achieved due to the theoretical calculation. The correctness of the theoretical derivation is verified by numerical
calculation and comparative experiments. This investigation can be used as a basic principle for machining
surface improvement and processing technology modification in UAFG.
1. Introduction
Engineering ceramics, optical glasses, semiconductor and other hard
and brittle materials are difficult to machine due to their high stiffness
and low thermal expansion coefficient, which are widely applied in
high technology fields such as aerospace, national defense and electronics [1]. Therefore, Ultrasonic machining is particularly important
for nonconductive and brittle materials processing [2]. Xiao put forward an innovation for the cutting force modeling of ultrasonic vibration assisted side grinding of ceramic [3]. Jiang presented ultrasonic
vibration assisted grinding (UAG) is one of the impactful machining
methods for processing hard and brittle materials [4].Sun introduced
that ultrasonic energy intervention can reduce cutting force, improve
material removal rate and machining quality [5]. Ali showed that the
grinding force and surface roughness are significantly lower after ultrasonic treatment [6]. Agarwal developed a novel surface roughness
analysis model based on the randomness of grinding process [7]. Uhimann reported that no thermal burns and physical and chemical
changes were found in the workpiece in UAG [8]. Moreover, Wang
pointed out that lower scallop height on workpiece surface and smaller
grinding force can be obtained in UAG due to the system matching
⁎
mechanism [9]. Wang pointed out the surface machining quality and
the grinding force can be modified by ultrasonic vibration parameters
selection [10]. For functional surface processing, Wang obtained surface roughness reduction and better surface integrity [11]. Ding designed surface microstructure and surface morphology by regulating
the grain trajectory [12]. Gong found that UAG has less tool wear than
common grinding under the same conditions [13]. Most importantly,
Rabiei showed that UAG features high machining performance and long
cutting tool life, which can return high economic efficiency [14].
Current research has focused on process parameter optimization
during machining experiments regarding ultrasonic machining, but
theoretical studies on material removal mechanism and surface generation in UAFG are less reported. The purpose of this investigation is to
clarify the surface generation mechanism in UAFG and indicate the
grinding force variation affected by ultrasonic vibration parameters.
The experimental device is illustrated in detail and the results analysis
is carefully executed in this study. Theoretical calculation followed by
mathematical modeling is implemented and shows good correlation
with the experimental data, the effects of ultrasonic vibration on
common face grinding for brittle material are comprehensive investigated. According to the study, the surface morphology can be
Corresponding author at: No. 1038 Dagu Nanlu, Hexi District, Tianjin, P.R. China.
E-mail addresses: xijiyu82@163.com (X. Zhang), satansdestiny@163.com (Y. Wang).
https://doi.org/10.1016/j.jmapro.2020.01.003
Received 11 September 2019; Received in revised form 26 November 2019; Accepted 3 January 2020
1526-6125/ © 2020 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
Journal of Manufacturing Processes 50 (2020) 520–527
X. Zhang, et al.
Fig. 1. The motion model of ultrasonic vibration assisted face grinding.
predicated and regulated by the theoretical deduction. The surface
microstructure can be improved due to the grinding force control.
2. Model development
As shown in Fig. 1, three kinds of grain motions (grinding tool
feeding motion, ultrasonic vibration and grinding tool rotation) were
simultaneously appeared in the UAFG process.
The following assumptions were carried out for the object of research [15]:
(1) The grains are evenly distributed on the surface of the grinding
tool;
(2) Ultrasonic vibration maintains a stable state during the grinding
processing;
(3) The grains are rigid spheres of the same size, and their shapes
remain unchanged during the grinding process;
(4) The grains will not detach from the grinding tool during the
grinding processing.
Fig. 3. The indentation process of abrasive grain.
2.2. Surface generating mechanism modeling
As Fig. 3 shows, the grinding wheel continuously knocks on the
surface as a result of ultrasonic vibration effects. Cracks are generated
when the diamond grains are pressed into the surface of the workpiece.
The crack size can be obtained by simplifying the grains into Vickers
indenter [16]:
Transverse crack length:
2.1. Single grain trajectory modeling
Cl = 1•
The single abrasive grain trajectory model can be obtained according to kinematics analysis of UAG:
x = R cos( t ) + vw t
z = A cos(2 ft +
0)
3
4
(4)
Transverse crack depth:
(1)
Ch =
(2)
y = R sin( t )
Pm
KIc
2•
Pm
Hv
1
2
(5)
Where Cl istransverse crack length, Ch is transverse crack depth, HV is
material hardness, KIc is plane strain fracture toughness, ζ1 and ζ2are
proportionality coefficients, Pmis single grain contact force.
Fig.4 shows the transverse cracks interference which is generated by
the same diamond grain in adjacent vibration periods. The relations
between ultrasonic frequency, transverse cracks length and rotation
speed in critical state can be illustrated as following equations:
(3)
Where ω is grinding wheel angular velocity, vw is feed rate, f is ultrasonic frequency, R is grinding wheel radius, t is time, 0 is vibration
initial phase, A is vibration amplitude. The single grain trajectory can
be painted as Fig. 2 shown.
Fig. 2. Grain trajectory in two rotation periods of grinding wheel.
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Fig. 4. Critical state of single grain trajectory self-overlapping in Y direction.
Fig. 6. Grain trajectory self-overlapping in both X, Y direction.
Fig. 5. Critical state of adjacent trajectory self-overlapping in X direction.
T=
2Cl
R
1
T=
f
(6)
Fig. 7. Effective contact time of abrasive particles in a single ultrasonic vibration cycle.
(7)
between diamond grain and the surface of the workpiece, the effective
contact time Δt is explained in Fig.7, following equation can be obtained:
Fig.5 shows the transverse cracks interference which is generated by
the same diamond grain in adjacent rotation periods. The relations
between rotation speed, transverse cracks length and feed rate can be
illustrated as following equations:
2
2Cl
=
vw
t = 2(t1
2R
2 vw
1
cos
f
1
1
A
(10)
Where t1 and t2are the time in different phase, δ is grain pressed depth.
According to the Hertz contact theory proposed by Timoshenko and
Goodier [17], maximum contact force of single grain Pm can be expressed as:
(8)
Substitute (6) and (7) into (8),the critical relationship between ultrasonic vibration frequency and grinding parameters can be found:
f=
t2) =
(9)
Pm =
In Eq. (9), the ultrasonic vibration frequency has a critical state for
cracks interference. The grinding force, MMR and surface generation
accuracy can be adjusted due to the ultrasonic parameters control. The
surface generation process can be described in following figure:
As Fig.6 shows, the ground surface is generated by cracks interference both in X, Y direction, the surface generation accuracy is
decided by interference degree, and the surface microstructure can be
predicted and designed due to the grain trajectory planning.
8
E
9 1 v2
2
d
3
1
2
(11)
Where E is Young's modulus of the workpiece material, v is Poisson's
ratio of the workpiece, d is the diameter of the grain. Single grain
movement is consisting by the grinding wheel feed and the rotation, but
in actual machining process, the machine tool feeding speed much
smaller than the spindle rotation speed. For simplicity, this study assumes that the trajectory of single grain is only determined by the
spindle rotation, the single grain trajectory can be defined as:
L = t• •r
2.3. Grinding force modeling
(12)
Where r is the distance from abrasive grain center to the grinding wheel
center.
As a result of the average distribution of diamond abrasive grains on
the end surface of the grinding wheel, different diamond grains have
different radius relative to the center of the grinding wheel.
As Fig.8 shows, the abrasive grain trajectory on the1/2 radius of
grinding wheel is selected to substitute all diamond grains trajectory on
the whole end surface. The single grain trajectory can be expressed as:
The grinding force is greatly influenced by processing parameters
and it has a significant relationship to the ground surface quality.
Although the feeding directional grinding force contributes to the material removal rate, the normal grinding force is the mainly factor for
the cracks formation and growth. The machined surface is generated by
the cracks interweaved when grains are pressed into the workpiece
surface. Therefore, normal grinding force is studied in this investigation.
Within each vibration period, there is an effective contact time
L = t•
522
R
2
(13)
Journal of Manufacturing Processes 50 (2020) 520–527
X. Zhang, et al.
Fig. 10. Electroplating diamond grinding tool.
Fig. 8. Grain distribution on the end surface of the grinding wheel.
Table 1
Si3N4 property parameters and grinding parameters.
Parameters
Mark
Value
Fracture toughness
Vickers hardness
Elasticity modulus
Poisson's ratio
Crack ratio
Diamond grain diameter
KIc
Hv
E
5Mpa·m1/2
18GPa
320GPa
0.25
0.24
100μm
d
Fig. 11. The end face of grinding tool (a) Test 1 (b) Test 3 (c) Test 5 (d) Test 13.
Table 3
Experimental parameters.
Fig. 9. The experiment setting.
Table 2
Experimental conditions.
Types
Contents
Machining Center
Ultrasonic generator
Abrasive tools
CNC-650
YC-UGSL11A
Electroplating diamond grinding
tool
150
Grain number through the dynamic grinding
area in unit time
Tool diameter
Dynamometer
Vibration frequency
Diamond grain diameter
Spindle
speed(r/
min)
Feed
rate
(mm/
min)
Vibration
frequency
(Hz)
Vibration
amplitude
(μm)
Grinding
depth(mm)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1500
2000
2500
3000
3500
2500
2500
2500
2500
2500
2500
2500
2500
2500
2500
120
120
120
120
120
180
240
300
120
120
120
120
120
120
120
26500
26500
26500
26500
26500
26500
26500
26500
26500
26500
26500
26500
26500
26500
26500
3
3
3
3
3
3
3
3
3
3
3
5
5
5
5
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.01
0.03
0.04
0.01
0.02
0.03
0.04
(15)
Ww = Nds•2Cl Ch•L• t•f
Macroscopic material removal volume in unit time can be obtained:
3.5mm
YDC-III09
26500 Hz
100μm
Wh = vw•2R•
(16)
P
Where p is grinding depth. If let Wh = Ww and simultaneous Eqs. (4),
(5),(11),(13),(15) and (16), the following equation can be obtained:
Simultaneous Eqs. (4),(5) and (13), single grain material removal
volume can be obtained:
Ww = 2Cl Ch•L
Serial
number
=
(14)
Assume the grain number through the dynamic grinding area in unit
time is Nds, whole microscopic material removal volume in unit time
can be obtained:
Nds• 1
2
2
8
15
•
vw•
•
8
15
3
1
4
2
p•K Ic •Hv •
8
9
(
1
)d
2
E
v2
5
8
• cos
1
1
8
15
A
(17)
If substitute (17) into (11), the following equation can be obtained:
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Fig. 12. Surface morphology measured by the White Light Interferometer (a) Test 1 (b) Test 3 (c) Test 5 (d) Test 13.
3
8
15
Pm =
2
8
E
d
9 1 v2
Nds• 1 2
2
8
15
•
3
1
v w• p•KIc4 •Hv2 •
•
8
9
(
)d
2
E
1
v2
5
8
• cos 1 1
1
2
F=
1
Nds cos 1 1
8
15
A
A
2
8
E
d
9 1 v2
Nds• 1 2
2
8
15
Pm dt
Pm t
(19)
(
)d
2
E
1
v2
• cos 1 1
8
15
A
3. Experimental validation
The Si3N4 ceramic is employed in the experimental validation. Si3N4
property parameters are shown in Table 1.
The inner diameter and outer diameter of the workpiece are 40 mm
and 55 mm respectively. The experiment setting can be seen in following Fig. 9.
Grinding experiments are presented by a CNC-650 Machining
Center assisted with YC-UGSL11A ultrasonic generator. The grinding
force in vertical direction is measured by YDC-III09Dynamometer. The
experimental conditions are shown in Table 2.
The grinding tool and its end surface topography are illustrated in
Figs. 10 and 11.
The lower spindle speed and grinding depth is used in the experiments to avoid tool damage. The detail of experimental parameters
setting is listed in Table 3.
(20)
Where F is the grinding force. If simultaneous Eq.s (19) and (20), the
following equation can be obtained:
F = Pm Nds f t
8
9
5
8
Eq. (22) shows that grinding force is related to many parameters
including ultrasonic frequency and amplitude, the changing trend of
grinding force can be obtained by the mathematic formula and the
surface generation can be improved due to the grinding force control.
The impulse can also be expressed by the grinding force in single
vibration cycle:
F
I=
Nds f
1
v w• p•K Ic4 •Hv2 •
1
2
(22)
Due to the conservation law of impulse, the impulse of single grain
in a single vibration cycle can be obtained:
I=
3
•
•
(18)
cycle
3
8
15
(21)
If substitute (10) and (18) into (21), the grinding force can be obtained:
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Journal of Manufacturing Processes 50 (2020) 520–527
X. Zhang, et al.
Fig. 13. Surface morphology measured by the SEM (a) Tests 1, 3 and 5 (b) Tests 3 and 13.
Fig. 14. Surface roughness measured by the profilometer.
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Journal of Manufacturing Processes 50 (2020) 520–527
X. Zhang, et al.
contributes to the improvement of surface roughness.
4.2. Grinding force analysis
The grinding process can be divided into five stages:
1.The grinding tool has not entered the machining surface;
2.The grinding tool has not completely entered the machining surface;
3.The grinding tool has completely entered the machining surface;
4.The grinding tool has not completely left the machining surface;
5.The grinding tool has completely left the machining surface.
The five stages can be seen in Fig. 15. The grinding force measured
by the dynamometer in the grinding process is shown in Fig. 16. Obviously, the grinding force is zero in stages 1 and 5. Stages 2 and 4 are
the time periods when grinding force rapidly increasing and decreasing.
In comparison, the grinding force is relatively stable when the grinding
tool has completely entered the machining surface (stage 3). According
to Eq. (22), F (the grinding force) is proportional to Nds (the grain
number through the dynamic grinding area in unit time), and Nds is
basically constant in stage 3. However, Nds increases and decreases in
stages2 and 4 respectively.
For accuracy and simplicity, the average value of the grinding force
in stage 3 is used as the experimental data for the following analysis.
The comparison between experimental data and theoretical calculation
results is shown in Fig. 17.
According to Fig. 17, both high spindle speed and high vibration
amplitude can effectively reduce the grinding force. Nevertheless, the
grinding force increases as feed rate or grinding depth increases. It is
interesting to find that the theoretical calculation shows good correlation with the experimental data. The results show the feasibility and
effectiveness of the mathematical model to predict the grinding force in
UAFG. The slight deviation between experimental data and theoretical
calculation results may be caused by the uneven distribution of the
grains on the surface of the grinding tool, the different sizes and shapes
of the grains, the detachment of the grains from the grinding tool or the
unstable condition of ultrasonic vibration during the grinding process.
Fig. 15. The five stages in the grinding process.
Fig. 16. The change of grinding force during the grinding process (a) (b) (c).
4. Results and discussions
4.1. Surface morphology analysis
The machined surface morphology is obtained by a Contour GT-K
White Light Interferometer and a Phenom XL Scanning Electron
Microscope (SEM).
Fig. 12(a)(b)(c) and Fig. 13(a)(b)(c) show the machined surface
morphology at different spindle speeds (1500 r/min, 2500 r/min and
3500 r/min). It is interesting to note that the machined surface is
smoother and the distance between grooves is smaller (97.2 μm, 52 μm
and 33.3 μm) as the spindle speed increases. The results indicated that
the grain trajectory is more compact and the material is removed more
evenly at a higher spindle speed, which can generate higher quality
surface.
Fig. 12(b)(d) and Fig. 13(b)(d) show the machined surface morphology at different vibration amplitudes (3 μm and 5 μm). It is found
that the height difference between the wave peaks and troughs on the
surface is effectively reduced as the vibration amplitude increases, but
some pits are formed at the same time. It is reasonable to infer that the
material removal rate is improved and the surface wave peak is easier
to be removed due to the increase of ultrasonic energy. However, excessive ultrasonic energy causes material breakage easily, which resulted some pits are formed. The surface roughness is measured by a
NANOVEA ST400 Profilometer and the results are shown in Fig. 14.
The results presented in Fig. 14(a) shown that the surface roughness
is effectively reduced as the spindle speed increases. According to
Fig. 14(b), it can be inferred that the enhancement of ultrasonic energy
5. Conclusions
1. The mathematical model of grinding force is derived from the
grain trajectory interference and overlap and the fracture mechanics of
brittle materials.
2. The contrast experimental results showed the feasibility and effectiveness of the mathematical model to predict the grinding force in
UAFG.
3. With the increase of grinding depth and feed speed, the material
removal rate and grinding force increased. The grinding force could be
effectively reduced by increasing spindle speed and vibration amplitude. Meanwhile, high quality surface could be generated by increasing
the spindle speed and vibration amplitude appropriately. Furthermore,
some pits are formed on the machining surface by excessive vibration
amplitude, which reduced the surface quality.
4. The grinding force is significantly reduced due to the ultrasonic
vibration energy interference. The surface roughness can be further
regulated by ultrasonic vibration parameters modification.
Declaration of Competing Interest
The authors declared that they have no conflicts of interest to this
work.
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Journal of Manufacturing Processes 50 (2020) 520–527
X. Zhang, et al.
Fig. 17. The comparison between experimental data and theoretical calculation when some parameters changing: (a) spindle speed; (b) feed rate; (c) grinding depth
and vibration amplitude.
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The authors wish to thank the Tianjin natural science foundation
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