Surface Roughness and Thermo-mechanical Force Modeling for Grinding Operations
with Regular and Circumferentially Grooved Wheels
D. Aslan and E. Budak
Manufacturing Research Laboratory
Sabanci University, Istanbul, Turkey
Abstract
A thermo-mechanical model is developed to predict forces in grinding with circumferentially
grooved and regular (non-grooved) wheels. Grinding wheel grit geometric properties needed
in the modeling are determined individually through optical measurements where surface
topography of the wheel and kinematic trajectories of each grain are obtained to determine the
uncut chip thickness per grit and predict final surface profile of the workpiece. Contact length
between the abrasive wheel and workpiece is identified by the thermocouple measurement
method. In this approach, a few calibration tests with a regular wheel are performed to obtain
sliding friction coefficient as a function of grinding speed for a particular wheel-workpiece
pair. Once the wheel topography and sliding friction coefficient are identified it is possible to
predict cutting forces and surface roughness by the presented material and kinematic models.
Theoretical results are compared with experimental data in terms of surface roughness and
force predictions, where good agreement is observed.
Keywords: Grinding, Surface roughness; Thermo-mechanical force model; Sticking and
sliding contact; Grooved wheels.
1. Introduction
In abrasive machining, tool consists of randomly oriented, positioned and shaped grits which
act as cutting edges and remove material from the workpiece individually to produce final
workpiece surface. Considering the stochastic nature of the abrasive wheel topography and
high number of process variables, chances of achieving optimum conditions in a repeatable
manner by only experience are quite low. Therefore, modeling of the process is crucial in
order to design a successful process. Process models for abrasive machining vary in a large
scale. The distribution and shape of the abrasive grits strongly influence the forces and surface
finish. Tönshoff et al. (1992) stated that the kinematics of the process is characterized by a
series of statistically irregular and separate engagements. They presented both chip thickness
and force models and compared different approaches. Brinksmeier et al. (2006) claimed that
grinding process is the sum of the interactions between the abrasive grains and workpiece
material. Abrasive wheel topography is generally investigated as a first step for both surface
1
roughness and force analysis in the literature; the wheel structure is modeled by using some
simplifications such as average distance between and average uniform height of abrasive
grains (Brinksmeier et al. 2006). Lal and Shaw (1975) formulated the undeformed chip
thickness for surface grinding in term of the abrasive grit radius and discussed the importance
of the transverse curvature of the grit. Some parameters such as wheel topography related
ones and material properties were often represented by empirical constants as presented by
Malkin and Guo (2007). Empirical surface roughness models have had more success in the
industry since they do not require abrasive wheel topography identification and extensive
knowledge about the chip formation mechanism and process kinematics, Hecker and Liang
(2003). However; lack of accuracy and need for excessive experimental effort are drawbacks
of these models.
There are semi-analytical surface roughness models in the literature as well (Tönshoff et al.
1992). They need experimental calibration of some parameters required in semi-analytic
formulations. Once these parameters are determined correctly, it is claimed that roughness can
be calculated by these equations. The approach in the literature for semi-analytical models
consists of two categories, statistical and kinematic approaches. Gong et al. (2002) stated that
the statistical studies focus on distribution function of the grit protrusion heights whereas
kinematic analyses investigate the kinematic interaction between the grains and the
workpiece. Hecker and Liang (2003) used a probabilistic undeformed chip thickness model
and expressed the ground surface finish as a function of the wheel structure considering the
grooves left on the surface by ideal conic grains. Agarwal and Rao (2010) defined chip
thickness as a random variable by using probability density function and established a simple
relationship between the surface roughness and the undeformed chip thickness. In one of the
representative works for kinematic analysis; Zhou and Xi (2002) considered the random
distribution of the grain protrusion heights and constructed a kinematic method which scans
the grains from the highest in a descending order to predict the workpiece profile. Liu et. al
(2013), on the other hand, investigated three different grain shapes (sphere, truncated cone and
cone) and developed a kinematic model based simulation program to predict the workpiece
surface roughness. They also presented a single-point diamond dressing model having both
ductile cutting and brittle fracture components. Apart from these studies, Gong et al. (2002),
used a numerical analysis utilizing a virtual grinding wheel by using Monte Carlo method to
simulate the process generating three-dimensional surface predictions. Mohamed et. al (2013)
examined circumferentially grooved wheels and showed groove effect on workpiece surface
topography by performing creep-feed grinding experiments. They showed that the grinding
efficiency can be improved considerably by lowering the forces with circumferentially
grooved wheels.
Once the abrasive wheel topography and grain properties are determined, force prediction
becomes possible through chip thickness analysis. Models often need experimental calibration
of cutting or ploughing force coefficients in semi-analytical formulations as well (Malkin and
Guo, 2007). Durgumahanti et al. (2010) assumed variable friction coefficient focusing mainly
on the ploughing force. They established force equations for ploughing and cutting phases
which need experimental calibration. Single grit tests were performed in order to understand
2
the ploughing mechanism where the measured values are used to calculate the total process
forces. Chang and Wang (2002) focused more on stochastic nature of the abrasive wheel and
tried to establish a force model as a function of the grit distribution on the wheel.
Identification of the grit density function is challenging, requiring correct assumptions for grit
locations. Hecker et al. (2003) followed a deterministic way in analyzing the wheel
topography and then generalized the measured data through the entire wheel surface.
Afterwards they examined the force per grit and identified the experimental constants. Rausch
et al. (2012) focused on diamond grits by modeling their geometric and distributive nature.
Regular hexahedron or octahedron shaped grits are investigated and the model is capable of
calculating engagement status for each grain on the tool and thus the total process forces.
Koshy et al. (2003) developed a methodology to place abrasive grains on a wheel with a
specific spatial pattern and examined these wheels’ performance.
There is a need for a model that requires less calibration experiments and do not require
additional measurements for different wheel geometries and process conditions. In addition,
secondary shear zone is usually ignored for abrasive machining processes in the literature;
however it should be investigated in order to increase the accuracy of the process models. In
this study, wheel topography and geometrical properties of abrasive grains (i.e. rake and
oblique angle, edge radius) are identified for an abrasive wheel. Workpiece surface profile is
obtained through kinematic analysis of abrasive grains’ trajectories. A novel thermomechanical model in the primary shear zone with sticking and sliding contact zones on the
rake face of the abrasive grit were established to predict forces in abrasive machining by
assuming abrasive grits behave similar to a micro milling tool tooth. This approach reduces
amount of experimentation needed for modeling, and represents the process physics in a more
accurate way. Majority of the semi-analytical force models presented in the literature require
calibration of certain coefficients for each cutting velocity and a particular wheel-work
material pair. By utilizing thermo-mechanical analyses and Johnson-Cook material model, a
few calibration tests for an abrasive type-workpiece pair are sufficient to predict process
forces for different cases involving the same workpiece-abrasive material however with
different arrangements and process parameters. Presented material and cutting force models
for grinding are believed to provide a significant improvement over previous studies which
neglected the secondary shear zone effects and needed excessive amount of calibration tests.
In this work, dual-zone analysis involving sticking and sliding regions in the secondary shear
zone is applied to grinding processes for the first time which improves the accuracy of force
predictions. Both force and surface roughness models presented for circumferentially grooved
wheels are a step ahead from the previously developed mechanistic models in the literature by
Yueming et al. (2013) and Rausch et al. (2012). It is believed that the micro milling analogy
and modeling of abrasive grits' kinematic trajectories will also be useful in expanding these
models to thermal and stability analyses of abrasive processes.
3
Nomenclature
a
b
agrit
bgrit
feed
feedr
h
Vc
ϴ
M
S
lc
lc-area
lcr
lp
D
R
bwheel
C
Warea
Tgrains
Ag
α
αn
r
hcuz
dgx
hmax
hθ
Ftc
Fnc
Frc
Ftp
Fnp
Frp
Ftc-g
Fnc-g
Frc-g
Ff
Fs
MRR
Øs
Øns
β
βn
i
ηc
τ
Δ
γ
γ'
γ0'
T
Tr
Tm
Tw
qw
µa
µ
Vchip-grit
N
P0
Msf
Mgr
Axial depth of cut (mm)
Radial depth of cut (mm)
Axial depth of cut per grit (mm)
Radial depth of cut per grit (mm)
Workpiece velocity (mm/s)
Workpiece velocity per revolution (mm/rev)
Instantaneous uncut chip thickness (mm)
Cutting velocity (m/s)
Grit position angle (degrees)
Grit number
Structure number of the grinding wheel
Length of cutting zone between wheel and workpiece (mm)
Area of cutting zone between wheel and workpiece (mm2)
Length of contact at rake face of abrasive grit (mm)
Length of sticking contact at rake face of abrasive grit (mm)
Diameter of the grinding wheel (mm)
Radius of the grinding wheel (mm)
Width of the grinding wheel (mm)
Grain number per mm2
Area of grinding wheel surface (mm2)
Total number of grains on the grinding wheel
Active grain number
Grain rake angle (degrees)
Normal rake angle (degrees)
Grain edge radius (µm)
Grain penetration depth (µm)
Maximum grain diameter (µm)
Maximum chip thickness (mm)
Instant chip thickness (mm)
Force in tangential direction (N)
Force in normal direction (N)
Force in radial direction (N)
Ploughing force in tangential direction (N)
Ploughing force in normal direction (N)
Ploughing force in radial direction (N)
Force per grain in tangential direction (N)
Force per grain in normal direction (N)
Force per grain in radial direction (N)
Frictional force (N)
Shear force (N)
Material removal rate (mm3/s)
Shear angle (degrees)
Normal shear angle (degrees)
Friction angle (degrees)
Normal friction angle (degrees)
Oblique angle (degrees)
Chip flow angle (degrees)
Shear stress (MPa)
Average distance between abrasive grits (µm)
Shear strain
Shear strain rate
Reference shear strain rate
Absolute temperature (°C)
Reference temperature (°C)
Melting Temperature (°C)
Absolute temperature of the workpiece (°C)
Heat transferred into the workpiece material through contact length
Apparent friction coefficient
Sliding friction coefficient
Volume of the chip removed from work material by a single grain (mm3)
Normal force acting on the rake face (N)
Normal stress on the rake face at the grit tip (N)
Moment at the grit tip due to normal shear force acting on the shear plane (Nm)
Moment at the grit tip due to the normal pressure on the rake face (Nm)
4
2. Identification of Abrasive Wheel Topography and Surface Roughness Calculation
It is essential to identify the abrasive wheel topography and geometrical properties of grains
in order to model kinematics and mechanics of the grinding process. Agarwal and Rao (2010)
indicated that there are numerous methodologies which involve scanning of the wheel surface
to determine grain properties. In this study, a camera system with a special lens is utilized to
measure the abrasive grain number per mm2, “C”, on the abrasive wheel. Then, a special areal
confocal 3D measurement system is used to determine the geometric properties of the grains
such as rake and oblique angles, edge radius and their distribution. Single point diamond
dressing tool’s tip is also scanned to identify the groove geometry of the circumferentially
grooved wheel. Investigation of oblique angle by optical measurements is introduced in this
study as an extension to 2D abrasive grain analysis reported in the literature by Hecker and
Liang (2003). In Figure 1, it can be seen how C parameter is obtained for a silicon carbide
wheel.
a)
b)
c)
Figure 1: (a) C parameter identification (b) & (c) Samples for scanned grains
A 100 nm sensitive dial indicator was used to align the abrasive wheel on X and Y axes of the
measurement device. Measurements are done on both type of wheels (Alumina and SiC), but
presented results here are for SiC. Mean values for the rake angle is -17o, oblique angle is 18o
and the edge radius is 0.5µm with standard deviations of 4.5o, 7o, 0.2µm, respectively. These
values are obtained by scanning a hundred of abrasive grains on each wheel from various
locations in both radial and circumferential directions. Since a Gaussian distribution with
mean and standard deviation is used to randomly assign the angle and geometrical values to
each abrasive grain when simulating the wheel topography, stochastic nature of the wheel is
represented. Single point diamond dresser is also scanned and the tip profile is obtained. This
is crucial since the dresser tip determines the groove geometry and the profile on the grooved
abrasive wheel. Dresser tool's tip radius is identified as 93µm.
Parameters identified in this section highly depend on the wheel type and dressing conditions.
Therefore, one may obtain different geometric properties with different dressing
arrangements. In this work, it is assumed that abrasive grits will have the same distribution
properties with same dressing procedure as agreed in the literature (Malkin and Guo, 2007).
Without this assumption, entire dressing process should be modeled by considering all of the
random parameters which has not achieved yet. Considering the fact that dresser and wheel
material, grain size and hardness do not change, keeping the dressing parameters constant
5
should give a similar distribution for the specified geometrical properties (i.e. rake and
oblique angle).
Average abrasive grit height and width for SiC 80 wheel are 64 µm and 52 µm, respectively.
Standard deviation for the height is 11 µm and for the width 8 µm (Table 1). Dressing
parameters that are used for regular and circumferentially grooved wheels can be seen in
Table 2. Abrasive wheel topography can be simulated as a whole, however; simulating a
small portion of a flat surface or one groove is more time efficient and sufficient to perform
roughness analysis since it is assumed that entire surface share the same topographical
characteristics.
Abrasive grit
Mean
Standard Deviation
Height
64 µm
11 µm
Width
52 µm
8 µm
Rake Angle
-17o
4.5o
Oblique Angle
18o
7o
Edge Radius
0.5µm
0.2µm
Table 1: Geometrical properties of abrasive grits
a)
b)
gaussian distribution of grit rake angles
gaussian distribution of grit oblique angles
0.09
0.08
0.06
c)
d)
probability density
probability density
0.05
0.07
0.06
0.05
0.04
0.03
0.02
0.04
0.03
0.02
0.01
0.01
0
-40
-35
-30
-25
-20
-15
-10
-5
0
0
-10
5
0
10
20
30
40
50
grit oblique angle (degrees)
grit rake angle (degrees)
Figure 2: (a) Grit geometric properties(b) Sample Rake angle identification (c) Rake angle distribution (d) Oblique angle
distribution
6
By moving cursors in the correct locations and checking their X, Y and Z coordinates (see
Figure 2-b), any geometrical property of the abrasive grain can be measured. If two cursors
are not enough, it can be switched up to five cursors, it is required especially for
determination of the region that a single grain occupies by placing them around the abrasive
grain visually. Oblique angle can be determined by placing two cursors to both edges of the
grit tip. Height is taken from ground (bond) material to the grit tip and width is measured both
in X and Y directions. In reality, a single grit might have more than one active cutting edge
and not necessarily with same angles. In order to consider that effect; a distribution for
distance between grits is used to assign locations to the abrasive grains in wheel topography
simulation (Section 2.1). Average distance between abrasive grits (Δ) and standard deviation
are identified and the distance value can be lower than the width of a grain in some cases
during the wheel topography simulation. That means two abrasive grains might intersect
which will create a single combined grain with multiple cutting edges with different rake and
oblique angles. Combined abrasive grains are evaluated for both surface roughness and force
analyses.
2.1. Uncut Chip Thickness Calculation
Due to stochastic nature of the abrasive tool and in-process vibrations, complete prediction of
the final workpiece surface topography is a sophisticated problem. Consequently, the
assumptions presented by Warnecke and Zitt (1998) are used in this work as well. They are;
- Grinding wheel vibration is neglected.
- The material of the workpiece in contact with the abrasive grits is cut off, in other words,
removed as chips without any failure.
Average interval between abrasive grits is measured by optical measurements and compared
with Zhou and Xi's (2002) Equation (1).
  137.9  M 1.4

(1)
32  S
Δ value is the average distance between abrasive grits and required for simulation of the
wheel topography, however; it does not consider whether these grits are active or not. In this
study, simple peak count method is used to detect active grits in the specified region as
presented in Figure 4 where Y axis represents the height of the grit and X is the position.
As Jiang et al. (2008) claimed there should be a cut-off height to determine these active grits.
Cut-off height is identified as 69 µm by volume density and Jiang’s height analysis on wheel
surface. Peak count analysis is used to detect the highest points in the scanned area by the
commercial software µsurf® of the measurement system. Confocal microscopy which is an
optical imaging technique used to increase optical resolution and contrast of a micrography by
using point illumination and eliminates the out of focus light. It is used to detect the peaks as
illustrated in Figure 3. The interaction between grain and workpiece material can be divided
into three types as mentioned before; rubbing, ploughing and cutting. These phases are related
with the grain penetration depth and diameter. Critical condition of ploughing and cutting can
7
be checked from ℎ𝑐𝑢𝑧 < 𝜉𝑝𝑙𝑜𝑤 𝑑𝑔𝑥 and ℎ𝑐𝑢𝑧 > 𝜉𝑐𝑢𝑡 𝑑𝑔𝑥 where hcuz is the grain penetration
depth and dgx is the maximum grain diameter. Grain will be in sliding stage when the first
inequality holds and in cutting stage if the other. In between, it will be in plowing stage where
corresponding forces are identified by linear regression analysis. ξplow and ξcut are identified as
0.015 and 0.025 for SiC wheels. In this study, grains are not assumed as sphere; therefore
dgxis taken as the width of the abrasive grain. In Figure 3-a, dashed area represents the bond
material and hcuz,max is the maximum penetration depth of a grain and hcu,max is the maximum
penetration depth from all over the grains. By using the ℎ𝑐𝑢𝑧,𝑚𝑎𝑥 = ℎ𝑐𝑢,𝑚𝑎𝑥 − (𝑑𝑚𝑎𝑥 −
𝑦) equation presented by Jiang and Ge (2008) and Jiang and Ge (2013), cut-off distance can
be identified to determine number of active abrasive grains per 1 mm2.
a)
b)
Figure 3: (a)The grain distribution within the abrasive wheel [16] (b) Active abrasive grit identification by height analysis
Red sections observed in Figure 3-b, reflect more light indicating that these regions are higher
than rest of the material around them. By zooming in and out, optimal position is found for a
lens in Z direction and all the peaks are counted by considering the cut-off weight which
determines whether these grits are active or not. C parameter identification should be
performed by taking samples from many points. Considering the random distribution of the
abrasive grains, observation of a single 1x1 mm2 will not be enough to determine the C. In
this study, fifteen 1x1 mm2 regions are scanned for each abrasive wheel and a unique C is
identified for each of them. Although C does not vary in a large range for the different regions
of the same wheel, an average of these fifteen values is taken for more accurate analysis.
After that step, whole surface map is extracted as X, Y and Z coordinates and stored in arrays.
In Figure 4, it can be seen that there are 5 grits in 0.94 mm2 region which are higher than the
cut-off height. This also agrees with the camera system measurement presented in Figure 1.
Other grits below the cut-off value are assumed to be inactive in the sense of chip formation
during the operation. They contribute majorly to the rubbing and ploughing components of
the process forces and included in the force model.
8
Z ( µm )
100.00
90.00
80.00
70.00
60.00
50.00
40.00
30.00
20.00
10.00
0.00
Grit Height Histogram
X ( µm )
Figure 4: Peak count of abrasive grit heights
After all these measurements, abrasive wheel topographies for regular and circumferentially
grooved wheels are simulated via MATLAB®.
In order to simulate a single grain, 8 values are selected from the constructed Gaussian
distributions which are, rake angle, oblique angle, edge radius, width, height and X, Y, Z
coordinates. Grit size is the size of individual abrasive grains in the wheel and can be obtained
from the wheel specification charts. However; in order to perform more accurate analysis, it is
identified by the presented measurement and wheel simulation techniques. These 8
parameters are randomly selected from the distributions and same procedure is repeated for
each abrasive grain. For example, if there are fifty thousand abrasive grains on a wheel, same
procedure should be repeated fifty thousand times since each abrasive grain requires 8
parameters which are given above. Therefore random nature of the abrasive wheel topography
can be represented in the simulated surface as well (Figure 5). The procedure can be
summarized as follows. First the trajectory of an abrasive grit is calculated and its intersection
with the work material is obtained. Volume of the grit that lies inside of the grit penetration
depth is subtracted from the work material. The same procedure is followed for each grain by
considering its trochoidal movement along the surface. Neglecting the third deformation zone
for surface roughness analysis is not a major drawback for grinding since the feed rate is
usually small enough for upcoming grains to remove the material that is stick on the
workpiece surface. In turning or milling operations, feed per revolution-tooth is high
compared to grinding operations and third deformation zone becomes crucial for surface
roughness analysis. However, for force, energy and temperature analysis, third deformation
zone and ploughing forces should be considered as done in this work.
9
a)
b)
2.2
0.5
2
0.4
1.8
z (mm)
height (mm)
0.6
0.3
0.2
1.6
1.4
1.2
0.1
1
0
1
0.8
0.5
1
1
0.4
0.8
0.5
0.3
0.6
0.2
0.4
radial direction (m m )
0
0.1
0.2
0
circum ferential direction (m m )
y (mm)
0
0
0.2
0.4
0.6
0.8
x (mm)
Figure 5: (a) Abrasive wheel & (b) Single groove topography (SiC 80 tool)
Average distance between the abrasive grits is calculated as 40 µm from equation 1 which
does not consider whether a grain is active or not. Distance between active grits that are above
the cut-off height is obtained as 173 µm from the surface topography measurements.
Calculation of a single abrasive grit’s trajectory is presented as follows:
x  feedr  t  ( R  height grit )  sin( )
(2)
z  ( R  height grit )  (1  cos( ))
If there is an abrasive grain with multiple cutting edges (intersected grains), trajectories are
calculated separately for both of them and corresponding work materials (chips) are removed
accordingly.
a)
b)
Figure 6-(a) Trajectory and penetration depth of a single grit (b) Grit trajectory and chip thickness variation
Abrasive grit on the same radial line (in perpendicular to the circumferential (Y) direction)
over the wheel is considered as a “set” and an ID number is assigned to each set. Each set has
a circumferential distance in-between (dseti) which was assigned by normal distribution of
measured grit distances (Figure 6).
x(setID#)  feedr  t  ( R  height grit )  sin( )
y(setID#)  ( R  height grit )  (1  cos(  (setID# 1)  delay ))
10
(3)
Uncut chip thickness per grit can be calculated by neglecting the trochoidal movement of the
abrasive wheelas follows, Jiang and Ge (2008):
h  2  dseti  (
feed r
a
)  ( )0.5
Vc
D
(4)
Equation 4 uses a simplification by ignoring the trochoidal movement of the grits. Martellotti
(1945) indicated that it can be neglected for the low𝑓𝑒𝑒𝑑𝑟 /𝐷 ratio cases where diameter of
the cutter tool is substantially larger than the feed per revolution as in grinding operations;
however, for more accurate analysis, trochoidal movement is also considered. Uncut chip
thickness differs for each abrasive grain since its geometric properties are assigned from
normal distribution of measured parameters. Geometric properties of the grits are stored in an
array; uncut chip thickness and grit penetration depth calculation are done accordingly.
Maximum and instant uncut chip thickness can be calculated without neglecting the
trochoidal movement as follows:
hmax  ( xex1  xex 2 ) 2  ( yex1  yex 2 ) 2  ( zex1  zex 2 ) 2
h  ( xkm  xij ) 2  ( ykm  yij ) 2  ( zkm  zij ) 2
(5)
Coordinate values of exit 1 and 2 points are illustrated in Figure 6 and obtained through
kinematic trajectories and real contact length identification. Uncut chip thickness is calculated
for each active abrasive grain since they have different geometrical properties that are
assigned from the Gaussian distributions as explained earlier. It was shown in the literature
that the real contact length is substantially larger than the geometric contact length (Pombo
and Sanchez, 2012). Pombo and Sanchez (2012) claimed that the increased area of contact is
mainly due to deflection of the wheel and grits under the action of the normal force. In this
work, the real contact length between abrasive wheel and work material is identified via
temperature measurements.
Volume of the material removed from the workpiece by a single grit is calculated by
kinematic analysis as well. Surface area of the chip in X-Z plane is calculated and multiplied
by bgrit to obtain total volume.
xex
Vchip  grit  (  f ( xkm , zkm )  f ( xij , zij ))  bgrit
(6)
xst
f ( xkm , zkm )  (( feed r  t  ( R  height grit  agrit )  sin( ), ( R  height grit  agrit )  (1  cos( ))) (7)
f ( xij , zij )  ( feed r  t  ( R  height grit )  sin( ), ( R  height grit )  (1  cos( )))
(8)
4. Thermo-mechanical Force Model
Primary aim of the presented model is on the mechanics of primary and secondary shear
zones; therefore ploughing forces from the third deformation zone are determined via linear
regression analysis and subtracted from the corresponding grinding forces in this section.
They are considered separately and added to the grinding forces as a final step to predict total
process forces. The primary shear zone model that was developed by Molinari and Dudzinski
11
(1992) and Dudzinski and Molinari (1997) and dual-zone model presented by Ozlu, Molinari
and Budak (2010) are used in this study with some modifications. They are;
-
Instead of a defined cutter tool (turning insert or an end mill), there are hundreds of
randomly oriented and shaped abrasive particles. Theory and formulation are repeated
for each of them which are active and located in the contact zone between wheel and
workpiece. That means that the shear angle is found iteratively for each of them by
using the minimum energy principle, and then the primary and secondary shear zone
analysis are performed.
-
Force directions are different for each abrasive particle considering its unique rake and
oblique angles as well as height, width and the uncut chip thickness. The forces for
each grain are oriented in a global scale to obtain total grinding forces accurately.
-
Especially for the grooved wheels, grains on the flat regions and groove walls are
investigated in 3D which means moment at the grain tip due to normal shear force on
the shear plane and normal pressure on the rake face should be evaluated according to
the oblique cutting theory.
-
Due to the process geometry, axial depth of cut parameter at Ozlu et al.’s (2010)
formulation is replaced with width of cut per abrasive grain. There are other
modifications on the formulations as well.
-
Rather than one rake face contact length with sticking and sliding components as in
the case in a cutting operation, there are as many as the number of active abrasive
grains for an abrasive process. In computations, they should be stored in an array to
calculate the corresponding forces. Some recursive algorithms are developed to
overcome this issue.
-
Main contribution of this study is to develop a methodology to handle the abrasive
particles as conventional cutter teeth, and apply the previously developed JohnsonCook material deformation based process model (Ozlu et al., 2010) with some
modifications by considering the dual-zone theory on grain rake face as well.
Considering the remarkable advantages of using the Johnson-Cook material and dualzone contact model, ability to use them on abrasive machining is believed to be a
significant contribution to the literature.
Molinari and Dudzinski (1992) assumed that the primary shear zone has a constant thickness,
and no plastic deformation occurs before and after the primary shear zone up to the sticking
region on the rake face. Johnson-Cook material model is used to represent the workpiece
material behavior, (Ozlu et al., 2010).
m
n 
 .  


v
1
   

   

A B
  1  ln  .   1  T 
3 
 3   
  0  

 
(9)
In Equation 9, γ, γ' and γ0' are shear strain, shear strain rate and reference shear strain rate
respectively. A, B, n, m and v are material constants. The actual temperature divided by its
12
critical temperature which is defined as the reduced temperature is defined by Equation 10. T
is the absolute temperature, Tr is the reference temperature and Tm is the melting temperature
of the material. Absolute temperature, Tr is obtained by conservation of energy which means
adiabatic conditions apply when high cutting speeds are used (Moufki et al., 2004).
T
(T  Tr )
(Tm  Tr )
(10)
Shear stress of the material entering to the primary shear zone is denoted by τ0 and
considering the inertia effects; τ1, the shear stress at the exit of the shear plane, is not the same
as τ0. τ0 can be calculated by assuming a uniform pressure distribution along the shear plane,
(Ozlu et al., 2010). Shear stress at the exit of the shear zone can be calculated via Equation 11
considering the equations of motion for a steady state solution, (Ozlu et al., 2010).
 1   (V sin n cos i) 2  1   0
(11)
By assuming adiabatic conditions, following expression can be obtained;
T  Tw 

  2 2 2
 Vc sin    0 
c 
2

(12)
Tw is the absolute temperature of the workpiece, c and β are the heat capacity and fraction of
the work converted into heat, respectively. For grinding operations β is often considered as
0.95-0.97, (Malkin and Guo, 2007). Considering the compatibility condition (Ozlu et al.,
2010);
.
d  d  dt d  dt




dy dt dy dt dy Vc sin 
(13)
where;
T  Tw
at y  0
 0
at y  0
   1  tan(   ) 
1
tan 
(14)
at y  h
Equation 13 can be iteratively calculated to get the τ0 with the boundary conditions introduced
above. In this study, a classical Runge-Kutta method is utilized for that purpose. When τ0 is
obtained, τ1 can be obtained from Equation 11 which will also be used in rake face contact
analysis and give the corresponding temperature value in Johnson-Cook formulation.
4.1 Dual-Zone Contact Model for Grinding Process
Ozlu, Molinari and Budak (2010) presented the dual zone contact model for orthogonal
cutting where forces in the secondary deformation zone, i.e. on the rake face, are calculated by
using the predicted sticking and sliding contact lengths between the chip and tool. In this
study, process forces are calculated by both sticking-sliding contact analysis and assumption
13
of an average friction coefficient on the rake face of the grit in order to compare their
performances. Chip formation mechanism for abrasive machining is usually considered to be
orthogonal (Malkin and Guo, 2007); however, it has been noted that consideration of the
obliquity improves the accuracy of the thermo-mechanical model (Moufki et al., 2004).
Oblique angle distribution of the grits is obtained as presented in Section 2 and a random
oblique angle from that distribution is assigned to each grain for simulations.
As the second law of thermodynamics indicates, for a closed system with fixed entropy, the
total energy is minimized at equilibrium. A physical situation that increases the shear energy
required in the secondary zone would also increase the total shear energy. Therefore, the
principle of the minimum energy requires the stress arrangement to occur in such a way that
the total energy for generation of the chip during a material removal process is minimized.
This principle has been commonly used (Yiang et al., 2012) for prediction of shear angle in
cutting since Merchant (1945), and it is applied in this study as well.
Workpiece material that leaves the shear plane is exerted with a high normal pressure on the
rake contact which yields sticking starting from the abrasive grit tip. As the material continues
to move on the rake face, the normal pressure decreases and the contact condition turns into
sliding (Ozlu et al., 2010);. This phenomenon can be observed by scanning the abrasive grits
under a microscope after an operation. Material stuck on the abrasive grit’s tip towards the
rake face is visible; however, it is not straightforward to verify the predicted sticking and
sliding contact lengths considering the stochastic nature of the process. According to the
plastic flow criteria, the shear stress cannot exceed the flow stress (τ1) of the workpiece
material on the rake face. Therefore, stress conditions for sticking and sliding regions can be
defined as follows:
  1
x  lp
  P
lp  x  lcr
(15)
where lcr and lp are total and sticking contact lengths respectively, x is the distance on the rake
face from the grit tip. In oblique cutting, the third direction and the chip flow angle should
also be taken into account for the dual-zone analysis (Ozlu et al., 2010). Pressure and shear
stress distribution is selected parallel to the chip flow direction. P(x) is the normal pressure
distribution as illustrated in Figure 7, P0is the normal stress on the rake face at the grit tip and
ζ is the distribution exponent.
14
Figure 7: Chip flow and the pressure distribution on the grit rake face
Normal force (N) acting on the rake face can be calculated from P0 as follows (Ozlu et al.,
2010):

agrit lcr cosc

x
N   P0 1   wc dx  P0
  1 cos i
 lcr 
0
lcr
(16)
The normal force can also be defined in terms of the shear force on the shear plane as (Ozlu et
al., 2010):
N  Fs cos ' s
cos  n
cos(n   n  an )
(17)
where the shear force is;
Fs   1 As   1
agrit h
(18)
sin n cos i
By equating equation 13 and 14, P0 can be written as:
P0   1
cos s cos  n
h
lcr sin n cosc cos(n   n  an )
(19)
where ηs is the shear flow angle, ηc is the chip flow angle, αn is the normal rake angle and βn is
the normal friction angle. Normal friction angle can be calculated as 𝛽𝑛 = 𝑡𝑎𝑛𝜆𝑎 𝑐𝑜𝑠𝜂𝑐 where
µa is the apparent friction coefficient and identified from 𝜆𝑎 = 𝑡𝑎𝑛−1 µ𝑎 .
4.2 Sticking and Sliding Contact Length Identification
Contact length identification from normal stress distribution on the rake face was studied
before by equating the tangential stress to the shear yield stress of the workpiece material at
the end of the sticking zone (Ozlu et al., 2010). Once the pressure distribution is identified,
sticking contact length on the grit rake face can be calculated as follows (Ozlu et al., 2010):
15

l p  lcr  lcr ( 1 ) 
P0 
1
(20)
Moment due to normal shear force (Msf) acting on the shear plane at the abrasive grit tip can
be calculated by Equation 21 using the assumption of uniformly distributed normal stress on
the shear plane. Also, moment at the grit (Mgr) tip due to the normal pressure on the rake face
is presented in Equation 22. Equating these two moments to each other lead us to the total
contact length between chip and abrasive grit.
M sf   1
agrit h coss tan(n   n   n )


x
  xP0 1   cosc agrit dx
 lcr 
0
lcr
M gr
(21)
sin 2 n cos i
2
(22)
By plugging Equation 16 into 19 Mgr can be extended and the total contact length can be
calculated from the moment equilibrium as follows:
lcr 
h sin(n   n   n )
2 sin n cos  n cosc
(23)
Shear and chip flow angles can be calculated as proposed earlier by Merchant (1945) and Ozlu
et al., (2010). It has been noted that it is reasonable to assume that the shear force and shear
velocity directions are equal. Experiments show that the chip ratio and chip flow angle are
independent of both the width of cut and the chip thickness. Armarego and Brown (1969)
derived the following expression:
tan(sn   n ) 
cos  n tan i
tan c  sin  n tan i
(24)
Øns is the normal shear, βn is the normal friction and αn is the normal rake angle. The
following expression for the chip flow angle ηc is obtained as (Armarego and Brown 1969):
A sin c  B cosc  C sin c cosc  D cos 2 c  E
(25)
where;
A  r cos  n  cos i tan 
B  tan  sin  n sin i
C  r sin  n tan 
(26)
D  r tan  tan i
E  sin i cos  n
Equation 22 is solved numerically for each operation by Newton-Raphson Method.
Measurement of the cut chip thickness is a difficult task in abrasive machining since chip
thicknesses per grains are in a micron scale.
16
r cos a
)
1  r sin a
s  tan 1 (
(27)
Chip ratio r, which is required for the equations listed above, is calculated from Equation 27.
4.3 Friction Coefficients and Forces
Two friction coefficients can be used to define the contact on the rake face: apparent (µa) and
sliding (µs) friction coefficients Ozlu et al., (2010). Ratio between the total friction and normal
forces acting on the rake face is the apparent friction coefficient (µ𝑎 = 𝐹𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛 ⁄𝑁) where
total friction force on the rake face can be identified from contact lengths (Ozlu et al., 2010).
The normal force on the rake face was represented by Equation 13 and the relationship
between the apparent and sliding friction coefficient is (Ozlu et al., 2010):

    1  
1 
a 
1   1   1   
  P0    
P0 


(28)

If one of the friction coefficients is known, the other can be calculated using Equation 28.
Sliding friction coefficient equation is obtained for an abrasive type-workpiece material pair
from calibration tests. Sliding friction coefficient can be detected by this equation and used in
the contact length and force calculations.
Once the friction coefficients and corresponding contact lengths are identified, shear angle is
calculated by (Ø) minimization of the cutting energy as described earlier. A simulation code
which uses the proposed thermo-mechanical model scans a given range of shear angles and
the one that gives the minimum cutting power is selected. Grinding forces per abrasive grit in
three directions (normal, tangential and radial, respectively) are obtained by the identified
angles and the shear stresses as follows (Ozlu et al., 2010):
Fnc  g   1bgrit h
Ftc  g   1bgrit h
Frc  g   1bgrit h
cos(  n  an )  tan s tan c sin  n
sin n cos 2 (n   n  an )  tan 2 c sin 2  n
sin(  n  an )
sin n cos 2 (n   n  an )  tan 2 c sin 2  n cos s
cos(  n  an ) tan s  tan c sin  n
sin n cos 2 (n   n  an )  tan 2 c sin 2  n
(29)
(30)
(31)
As presented in Section 3, abrasive grits may have different uncut chip thickness based on
their locations and geometric properties. Hence, forces are calculated for each abrasive grain
and integrated over number of active grits to obtain the total grinding forces. Ploughing forces
are identified through linear regression analysis and can be added to the grinding forces to
obtain total process forces (Aslan and Budak, 2014).
17
Ag
Fnc 
F
Ag
nc  g ( i )
i 1
, Ftc 
F
tc  g ( i )
i 1
Ag
, Frc 
F
r  g (i )
(32)
i 1
Radial direction is usually ignored in the literature for surface grinding operations, however; it
is vital for circumferentially grooved wheels due to the 3D geometry of grooves and abrasive
grits on its walls. In Figure 8-a, between A and C points, grit and workpiece are in contact,
however; there is no cutting action. At the very first stage of the interaction between abrasive
grit and the workpiece, plastic deformation occurs, temperature of the workpiece increases
and normal stress exceeds the yield stress of the material. After a certain point, the abrasive
grit starts to penetrate into the material and starts to displace it, which is responsible for the
ploughing forces. Finally, shearing action starts and the chip is removed from the workpiece
(Durgumahanti et al., 2010).
a)
b)
Figure 8-(a) Shear and Deformation Zones (b) Engagement section and division into sections
As it is illustrated in Figure 8-b (Durgumahanti et al., 2010), grit-workpiece engagement
section is divided into sections in order to investigate the local angles such as side edge
cutting, effective rake and oblique angles. Afterwards, they are used to calculate forces at that
particular section and projected into normal, tangential and radial directions in order to obtain
total process forces for that grain. Figure 8-b is an exaggeration in order to illustrate the
methodology properly; section heights should be small enough to be precise in force
calculations. It has been noted that by using this local sectioning and projection analysis, more
accurate results are obtained for process forces.
In the case of non-grooved wheels, process forces can be predicted by equations and the
methodology presented until now. However, for the circumferentially grooved wheels,
grooves and grits on the groove walls should be carefully investigated in order to predict the
forces. Grooved wheels can improve grinding efficiency by lowering the energy required to
displace a unit volume of material from the workpiece. Since grooves introduce a helix angle
to the abrasive wheel similar to a milling tool, it can be referred as transformation from
orthogonal to oblique cutting which is more desirable in the sense of efficiency and lower
forces (Moufki et al. 2004). They also cause an increase in workpiece surface roughness
compared to a regular (non-grooved) wheel. Their performance on workpiece surface profile
is also investigated in this study.
18
Figure 9-Groove profile and directions for sectioning analysis
As it can be seen from Figure 9 (1 groove included), grooves are investigated by sectioning
them similar to the grit edge radius analysis. Normal, tangential and radial directions are
determined for each element and uncut chip thickness per section is calculated. i, k and j lines
are normal, tangential and radial directions, respectively. Sectioning is arranged such that each
element has only one abrasive grain. Once the uncut chip thickness per grain is calculated for
a grain on the groove wall, by using local direction and angles, forces are calculated by the
presented model and projected into the global X, Y and Z axes.
5. Simulation and Experiment Results
5.1 Measured and Predicted Forces
Experiments have been conducted with different process parameters in order to validate the
presented models. AISI 1050 steel and 150*25*20 “SiC 80 J 5 V” grinding wheel are used as
workpiece and tool respectively. Single point diamond dresser with 2 carat grade is used for
dressing the regular and circumferentially grooved wheels. Four different axial depth of cuts
at 0.03, 0.05, 0.1 and 0.15 mm and four feed values at 0.075, 0.11, 0.15 and 0.18 mm per
revolution with 5 different cutting velocities were used in the experiments. Forces are
measured for each operation by utilizing a Kistler 3 axis dynamometer located under the work
material. Finally, surface roughness and texture of the final workpiece are measured using
special areal confocal 3D measurement system.
Figure 10-(a)Experimental setup (b)Dressing operation
Wheel Type / Conditions
Regular (A)
Feed (mm/rev)
Depth (mm)
Groove Width (mm)
Overlap Ratio
Helix Angle
0.04
0.05
NA
11
NA
19
Groove 1 (B)
2
0.1
1.1
11
0.24
Groove 2 (C)
4
0.1
1.1
11
0.6
Groove 3 (D)
5
0.1
1.1
Table 2-Dressing conditions
11
0.72
No coolant is used in the experiments in order to avoid miscalculations when measuring
process temperatures for real contact length. Experimental setup can be seen in Figure 10.
Dressing conditions for regular and circumferentially grooved wheels are presented in Table
2. In order to obtain the real contact length between the abrasive wheel and workpiece,
temperature at the cutting zone is measured by embedding a K type thermocouple into the
workpiece as illustrated in Figure 11. Power (P), total heat transferred into the workpiece
material through contact length (qw) and total width of cut (b) is known, real contact length
can be obtained as follows:
P
(33)
qw 
lreal  b
Therefore, active grit number is obtained more accurately which improves both surface
roughness and force predictions. Similar to the sliding friction coefficient analysis (Section
4.3), a function dependent on cutting speed and feed rate for abrasive type and workpiece
material is identified for real contact length parameter as well. This function is obtained by
same experiments for sliding friction investigation; hence no additional calibration
experiments are necessary. Thermocouple with a 0.8 mm diameter is embedded into the
workpiece with epoxy in a 1 mm diameter blind hole opened by EDM drilling. The hole
should be blind because when the grinding wheel reaches the thermocouple, thermocouple
smears with the workpiece which ensures full contact between them [8]. Once the contact
length function is obtained for an abrasive wheel and work material pair, real contact length
can be calculated for different arrangements and process parameters (Figure 12).
Figure 11-(a)Thermocouple fixation diagram (b)Exposed thermocouple junction after an operation
20
contact length (mm)
7
6
a)
0.18 mm/rev - geometrical
0.18 mm/rev - thermocouple
5
4
3
2
1
0
0.02
0.04
0.06
0.08
0.1
0.12
axial depth of cut (mm)
0.14
0.16
0.18
0.2
0.14
0.16
0.18
0.2
0.14
0.16
0.18
0.2
7
contact length (mm)
b)
0.15 mm/rev - geometrical
0.15 mm/rev - thermocouple
6
5
4
3
2
1
0
0.02
0.04
0.06
0.08
0.1
0.12
axial depth of cut (mm)
contact length (mm)
7
6
c)
0.11 mm/rev - geometrical
0.11 mm/rev - thermocouple
5
4
3
2
1
0
0.02
0.04
0.06
0.08
0.1
0.12
axial depth of cut (mm)
Figure 12-Comparison of contact lengths identified by geometrical formulation and thermocouple measurement
Linear regression analysis was used to determine ploughing forces and corresponding
coefficients (Aslan and Budak, 2013). Ploughing forces were obtained as 13.8, 20, 30 and
39,6 N for 0.03, 0.05, 0.1 and 0.15 mm axial depth of cuts (Figure 13). Identification of
ploughing force coefficients and real contact lengths were performed by using regular wheel
and used for grooved ones as well.
21
550
500
450
400
Fn(N)
350
a=0.03 mm
a=0.05 mm
linear
a=0.1 mm
a=0.15 mm
300
y = 1.3e+003*x + 20
250
200
150
100
50
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
feed rate (mm/rev)
Figure 13: Ploughing force identification for the regular wheel (illustrated for 0.05 mm axial depth)
B, C and D wheels that were produced by a single point diamond dresser are illustrated in
Figure 14.They are identified per grit as: 0.009, 0.012, 0.017 and 0.023 N for 0.01, 0.02, 0.03
and 0.06 mm axial depth of cuts as well.
a)
b)
c)
Figure 14-(a)B (b)C (d)D type wheels
Sliding friction coefficient as a function of cutting speed is obtained through calibration
experiments (Equation 25) which are conducted at cutting speeds of 7.8 m/s, 12.5 m/s, 15.7
m/s, 19.6 m/s, 24.7 m/s and 31.4 m/s and at feed rates of 0.075 mm/rev, 0.11mm/rev, 0.15
mm/rev and 0.18 mm/rev. The Johnson-Cook parameters for AISI 1050 steel are obtained
from (Ozlu et al., 2010) are given in Table 3.
A(MPa)
B(MPa)
n
m
v
880
500
0.234
0.0134
1
Table 3-Johnson-Cook Parameters for AISI 1050 Steel [22]
22
0.8
sliding friction coefficient
quadratic
µ
0.6
0.4
0.2
0
5
10
15
20
25
30
Vc (mm/s)
Figure 15-Sliding friction coefficient for AISI 1050 steel and SiC abrasive material
35
The variation of the sliding friction coefficient with the cutting speed is represented by the
following function (Figure 15):
  0.0009Vc2  0.0566Vc  0.1671
(32)
Ozlu et al. (2009) showed that for the ceramic (AB30) tool, which includes Al2O3-TiC, the
sliding friction coefficient increases with the cutting speed contrary to the decreasing trend
observed for carbide tools. Considering that most of the modern ceramic materials include
alumina (Al2O3) or silicon carbide (SiC), (Eom et al., 2013), it can be concluded that the
relation between sliding friction and cutting speed observed in this study agrees with Ozlu et
al. (2009).
Thermo-mechanical force model’s solution procedure was applied to each abrasive grain
which means sticking and sliding contact lengths are identified for every one of them.
Material that is stuck on the rake face close to the grit tip can be observed; however, it is
almost impossible to identify sticking and sliding contact lengths precisely since
determination of the transition point from sticking to sliding is not that very clear with the
confocal 3D measurement system (Figure 17). Therefore, dual zone (sticking + sliding), full
sliding and full sticking cases are considered and it has been noted that the dual zone model
provides the best predictions. Sticking and sliding lengths are calculated by equation 17 and
20 and presented in Figure 16 for the conditions given in Table 4.
Test #
Vc(m/s)
feedr
a
1
2
3
4
5
6
7
8
9
10
11
12
12.5
0.11
0.03
12.5
0.15
0.03
12.5
0.18
0.03
12.5
0.11
0.1
12.5
0.15
0.1
12.5
0.18
0.1
19.6
0.11
0.03
19.6
0.15
0.03
19.6
0.18
0.03
19.6
0.11
0.1
19.6
0.15
0.1
19.6
0.18
0.1
Test #
13
14
15
16
17
18
19
20
21
22
23
24
Vc(m/s)
feedr
a
12.5
0.11
0.03
12.5
0.11
0.05
12.5
0.11
0.1
12.5
0.11
0.15
15.7
0.11
0.03
15.7
0.11
0.05
15.7
0.11
0.1
15.7
0.11
0.15
19.6
0.11
0.03
19.6
0.11
0.05
19.6
0.11
0.1
19.6
0.11
0.15
Table 4-Selected experiments to present dual zone model results
23
0.08
lcr
lp
mm
0.06
0.04
0.02
0
0
5
10
15
20
25
Test #
Figure 16-Total and sticking contact lengths on the rake face of the grit
Figure 17: (a) Stuck material on scanned grains (b) Regions where stuck material is observed
In order to show the necessity and accuracy of the dual zone contact model presented in this
paper; fully sliding, fully sticking and dual zone approaches are compared with the
experimental forces. The comparisons for two different cutting speeds can be seen in Figure
18.
Vc=7.85 m/s
600
a)
Fn(N)
500
400
Experiment
Sticking+Sliding
Fully Sliding
Fully Sticking
300
200
100
0.06
0.08
0.1
0.12
0.14
feed rate (mm/rev)
24
0.16
0.18
0.2
Vc=19.63 m/s
350
b)
Experiment
Sticking+Sliding
Fully Sliding
Fully Sticking
300
Fn(N)
250
200
150
100
50
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
feed rate (mm/rev)
Figure 18: Comparison of experimental and predicted results for (a) 7.85(m/s) - (b) 19.63(m/s) cases (a = 0.1 mm)
250
a)
Exp-Regular
Exp-Groove1
Exp-Groove3
Sim-Regular
Sim-Groove1
Sim-Groove3
Fn(N)
200
150
100
50
0
0
0.02
0.04
0.06
0.08
0.1
0.12
axial depth of cut (mm)
0.14
0.16
0.18
0.2
0.08
0.1
0.12
axial depth of cut (mm)
0.14
0.16
0.18
0.2
40
b)
Exp-Regular
Exp-Groove1
Exp-Groove3
Sim-Regular
Sim-Groove1
Sim-Groove3
35
30
Fr(N)
25
20
15
10
5
0
0
0.02
0.04
0.06
Figure 19- (a) Comparison of wheel types (0.11 mm/rev feed) - (b) Radial forces (0.11 mm/rev feed)
25
As it can be seen in Figure 18-a-b, grinding force predictions obtained by the proposed dual
zone model are well correlated with the experimental results. Thus, it is obvious from these
results that neglecting either sticking or sliding contact lead to significant errors. It was
expected that the fully sliding condition would give lower forces than the dual zone case and
the opposite results are observed for the simulation results. It is believed that the reason for
that is the increase in the contact length between chip and abrasive grit for the fully sliding
condition. The dual zone model provides the best prediction capability, therefore even without
contact length verification by optical measurements, it can be said that dual zone theory can
be applied to abrasive machining processes.
On the other hand, since the presented model works in an abrasive grit scale, by correct
calculation of uncut chip thickness (h) and local angles (rake, oblique, chip flow, shear angle
etc.), it can be used for various wheel geometries. Figure 19-(a) illustrates results for regular,
groove 1 and groove 3 type wheels. Process forces can be reduced up to 45% by increasing
the number of grooves on the wheel. Contact length between the wheel and work material
increases with the grooves which enables more grains (increased active grain number) to
remove chips from the workpiece with less chip thicknesses. Introducing the radial direction
with the circumferential grooves and increasing the obliquity of the process contributes to
lower grinding forces. It is observed that increasing the groove number is more important than
increasing the helix angle of the grooves for obtaining lower forces. Specific energy was
reduced 50% with B wheel which is a measure of the amount of energy required to displace a
unit volume material (Tönshoff et al. (1992). In addition, the circumferentially grooved wheel
does not accelerate the wheel wear process as discussed and validated by Mohamed et al.
(2013). Experiments are repeated with same conditions without dressing the wheel and the
increase in force and consumed power were measured after each operation. Rate of increase in
grinding force is very close to each other for regular and circumferentially grooved wheels as
illustrated in Figure 20. Workpiece surface roughness often decreases with wheel wear since
the abrasive grains become duller and workpiece material fills the cavities on wheel surface.
These effects make grinding process close to polishing and wheel polish the workpiece
surface rather than removing chips.
Wear behavior of regular and grooved wheels
140
Regular Wheel
Groove 1
Groove3
120
Fn(N)
100
80
60
40
20
0
1
2
3
4
5
6
# of repetition
7
8
9
Figure 20: Wear behavior of wheels for a=0.03 mm &feedr = 0.11 mm/rev
26
10
11
Radial forces for each wheel are presented in Figure 19-(b). It is believed that the assumptions
made in the wheel surface topography and grit property identification steps as well as
neglecting the single point diamond dresser wear are the main reasons behind the
discrepancies between the measured and simulated forces. At each groove formation
operation, brand new diamond dresser was used; however, as the dresser tool moves along the
wheel surface, dresser tip becomes duller. Tip radius of the fresh dresser was measured as 93
µm while after the formation of grooves 1, 2 and 3 it was found as 152, 134 and 116 µm
respectively. That means the groove ground radius increases towards the end.
5.2 Measured and Predicted Surface Roughness
The proposed model is applied to simulate the final surface profile of the workpiece and the
results are compared with the experimental data. Surface roughness in perpendicular to feed
direction is considered since it enables us to observe grit scratches and groove prints on the
surface. Grooved wheels cause an increase in surface roughness compared to a regular wheel
as expected. Groove marks on the workpiece surface can be observed by 3D confocal
microscope which is the main actors for rougher surface results (Figure 21). Although surface
finish is one of the most important reasons for using abrasive machining, grinding and SAM
(Super Abrasive Machining) operations can be used for difficult-to-cut materials such as
nickel and titanium alloys. Grinding is considered a cost effective alternative for roughing
operations as abrasive machining technology and super abrasive machining techniques
develop. Hence, grooved wheels can be used for roughing operations; lower forces are vital to
prevent thermal damages on work material as Mohamed et al. (2013) and Aslan and Budak
(2014) indicated.
Figure 21-Groove marks on final workpiece surface for Wheel b ( feed = 0.11 mm/rev & a = 0.1 )
Surface profile (peaks and inverted valleys) for a specified sample length is simulated and
arithmetic average value of the departure from the center line (Ra) is obtained. Simulation and
experiments results are not presented for wheel C (groove 2) since values are considerably
close to the regular wheel (+- 0.074 µm – average).
Surface roughness increases with the groove number on the wheel (Figure 22). Hence it can
be said that there is a trade-off between lower process forces (lower energy) and surface
quality. Both of them can be predicted by the presented model and optimum wheel type,
groove geometry and process parameters can be determined for a desired outcome.
27
0.9
Exp-Regular
Exp-Groove1
Exp-Groove2
Sim-Regular
Sim-Groove1
Sim-Groove2
0.8
0.7
Ra (µm)
0.6
0.5
0.4
0.3
0.2
0.1
0.08
0.1
0.12
0.14
feed rate (mm/rev)
0.16
0.18
0.2
Figure 22-Ra for abrasive wheel types (a = 0.1 mm)
As Tönshoff et al. (1992) and Malkin and Guo (2007) stated; in order to avoid burn and
metallurgical damage on workpiece surface, process temperature should be low enough. It can
be achieved by circumferentially grooved wheels at the cost of increased surface roughness of
the workpiece. In this paper, roughness values are quite high for a regular grinding operation
and reason for that is the usage of SiC 80 M which has a medium-fine grit size. By using finevery fine grit sizes, surface roughness can be decreased but material removal rate should be
lower as well. Measured and simulated surface profiles are presented in Figure 23 for a
regular and groove 1 type wheels, respectively.
Ra(µm) for regular wheel - feed = 0.11 mm/rev, a = 0.1 mm
56
a)
measurement
simulation
55.5
55
µm
54.5
54
53.5
53
52.5
0
200
400
600
800
µm
28
1000
1200
1400
1600
Ra(µm) for Groove 1 (A) wheel - feed = 0.11 mm/rev, a = 0.1 mm
63
measurement
simulation
b)
62.5
62
µm
61.5
61
60.5
60
59.5
59
0
200
400
600
800
1000
1200
1400
1600
µm
Figure 23-Measured and simulated surface profiles for regular and A type wheels
Simulated and scanned surface textures agree with 18-20% error. It is believed that the
differences between measured and simulated surface profiles are due to the assumptions made
in surface roughness model. Neglecting the grinding wheel vibration should be the main actor
for these discrepancies.
6. Conclusion
A novel grinding model with thermo-mechanical material deformation at the primary shear
zone and dual zone contact on the rake face of the abrasive grit is presented in this paper. A
method to simulate abrasive wheel topography and predict uncut chip thickness per grit is
utilized to support the presented cutting model and obtain the final workpiece surface profile.
Abrasive particles are considered individually and detailed investigation of the chip formation
and chip-abrasive particle interaction on the rake face are done. Since the material behavior of
the workpiece and the interaction between the chip and abrasive particle are considered,
accurate force prediction for abrasive machining processes can be done. The contact length
between the grinding wheel and workpiece is identified by embedding a K type thermocouple
into the workpiece and measuring the process temperature. It has been noted that the real
contact length is substantially larger than the ideal contact length (geometric), therefore with
this method number of active abrasive grains can be calculated more accurately. Once the
active grit number is obtained, each grain is evaluated separately and the primary and
secondary shear zone analyses are performed. The presented cutting model is believed to
provide a significant improvement with respect to previous semi-analytical cutting models for
abrasive machining. Once the wheel topography and friction coefficient equation is
determined for a certain abrasive type-workpiece material pair, it is possible to predict
grinding forces for different conditions. It should be noted that the model calibration needs a
few number of tests compared to the mechanistic or semi-analytical models and does not
require additional tests for different wheel geometries or process conditions. Finally, surface
profile of the workpiece is obtained for both regular and circumferentially grooved wheels by
considering abrasive grits on the flat and groove wall surfaces. All the predictions are found
to be in good agreement with experimental results.
29
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