Surface roughness and thermo-mechanical force modeling for grinding operations with regular and circumferentially grooved wheels

Journal of Materials Processing Technology 223 (2015) 75–90

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Surface roughness and thermo-mechanical force modeling for grinding operations with regular and circumferentially grooved wheels D. Aslan, E. Budak ∗ Manufacturing Research Laboratory, Sabanci University, Istanbul, Turkey

a r t i c l e

i n f o

Article history: Received 7 January 2015 Accepted 18 March 2015 Available online 26 March 2015 Keywords: Grinding Surface roughness Thermo-mechanical force model Sticking and sliding contact Grooved wheels

a b s t r a c t A thermo-mechanical model is developed to predict forces in grinding with circumferentially grooved and regular (non-grooved) wheels. The geometric properties of the grinding wheel grits needed in the modeling are determined individually through optical measurements where the surface topography of the wheel and kinematic trajectories of each grain are obtained to determine the uncut chip thickness per grit and predict the final surface profile of the workpiece. The contact length between the abrasive wheel and the workpiece is identified with 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 has been found that 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. © 2015 Elsevier B.V. All rights reserved.

1. Introduction In abrasive machining, tool consists of randomly oriented, positioned and shaped grits which act as cutting edges and individually remove material from the workpiece to produce the final workpiece surface. Considering the stochastic nature of the abrasive wheel topography and high number of process variables, the 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 greatly. The distribution and shape of the abrasive grits strongly influence the forces and surface finish. Tönshoff and Peters (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 and Aurich (2006) claimed that the grinding process is the sum of the interactions between the abrasive grains and workpiece material. In literature, abrasive wheel topography is generally investigated as a first step for both surface roughness and force analysis; the wheel structure is modeled by using some simplifications such as

∗ Corresponding author. Tel.: +90 216 483 9519; fax: +90 216 483 9559. E-mail address: [email protected] (E. Budak). http://dx.doi.org/10.1016/j.jmatprotec.2015.03.023 0924-0136/© 2015 Elsevier B.V. All rights reserved.

average distance between and average uniform height of abrasive grains (Brinksmeier and Aurich, 2006). Lal and Shaw (1975) formulated the undeformed chip thickness for surface grinding in terms of the abrasive grit radius and discussed the importance of the transverse curvature of the grit. Some parameters such as those related to wheel topography 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, the drawbacks of these models are that they result in a lack of accuracy and cause an excessive need for experimentation. There is also literature concerning semi-analytical surface roughness models (Tönshoff and Peters, 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 studies analyze and 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

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Nomenclature a b agrit bgrit feed feedr h Vc  M S lc lc-area lcr lp D R bwheel C Warea Tgrains Ag ˛ ˛n r hcuz dgx hmax h Ftc Fnc Frc Ftp Fnp Frp Ftc-g Fnc-g Frc-g Ff Fs MRR Øs Øns ˇ ˇn i c    ’  0’ T Tr Tm Tw qw a

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 (␮m) grain penetration depth (␮m) maximum grain diameter (␮m) 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 (␮m) 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 Vchip-grit volume of the chip removed from work material by a single grain (mm3 ) N normal force acting on the rake face (N) P0 normal stress on the rake face at the grit tip (N) moment at the grit tip due to normal shear force Msf acting on the shear plane (Nm) Mgr moment at the grit tip due to the normal pressure on the rake face (Nm)

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 a 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. Yueming 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 the Monte Carlo method to simulate the process generating three-dimensional surface predictions. Mohamed et al. (2013) examined circumferentially grooved wheels and showed the 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 that there was 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 the ploughing mechanism where the measured values are used to calculate the total process forces. Chang and Wang (2008) focused more on the 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 process by 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 and Iwasaki (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 experimentation and no additional measurements for different wheel geometries and process conditions. In literature, secondary shear zone is usually ignored for abrasive machining processes;

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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 thermo-mechanical 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 the amount of experimentation needed for modeling, and represents the process physics in a more accurate way. The majority of the semi-analytical force models present in 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. The 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 in comparison to 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.

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 Fig. 1, it can be seen how C parameter is obtained for a silicon carbide wheel. 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 −17◦ , oblique angle is 18◦ and the edge radius is 0.5 ␮m with standard deviations of 4.5◦ , 7◦ , 0.2 ␮m, 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

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Table 1 Geometrical properties of abrasive grits. Abrasive grit

Mean

Standard deviation

Height Width Rake angle Oblique angle Edge radius

64 ␮m 52 ␮m −17◦ 18◦ 0.5 ␮m

11 ␮m 8 ␮m 4.5◦ 7◦ 0.2 ␮m

profile on the grooved abrasive wheel. Dresser tool’s tip radius is identified as 93 ␮m. 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, the entire dressing process should be modeled by considering all of the random parameters which have not been achieved yet. Considering the fact that dresser and wheel material, grain size and hardness do not change, keeping the dressing parameters constant 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 ␮m and 52 ␮m, respectively. Standard deviation for the height is 11 ␮m and for the width 8 ␮m (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. By moving cursors in the correct locations and checking their X, Y and Z coordinates (see Fig. 2b), 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 () and standard deviation are identified and in some cases the distance value can be lower than the width of a grain during the wheel topography simulation. That means two abrasive grains might intersect creating 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.

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Fig. 1. (a) C parameter identification, (b) and (c) samples for scanned grains.

Table 2 Dressing conditions. Wheel type/conditions

Feed (mm/rev)

Depth (mm)

Groove width (mm)

Overlap ratio

Helix angle

Regular (A) Groove 1 (B) Groove 2 (C) Groove 3 (D)

0.04 2 4 5

0.05 0.1 0.1 0.1

NA 1.1 1.1 1.1

11 11 11 11

NA 0.24 0.6 0.72

Average interval between abrasive grits is measured by optical measurements and compared with Zhou and Xi’s (2002) Eq. (1).

  = 137.9 × M

−1.4

 32 − S

(1)

 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 Fig. 4 where Y axis represents the height of the grit and X is the position. As Jiang et al. ( 2013) claimed there should be a cut-off height to determine these active grits. Cut-off height is identified as 69 ␮m by volume density and Jiang’s height analysis on wheel surface. Peak count analysis is used to detect the highest points in the scanned

Fig. 2. (a) Grit geometric properties, (b) sample rake angle identification, (c) rake angle distribution and (d) oblique angle distribution.

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Fig. 3. (a)The grain distribution within the abrasive wheel (Liang et al., 2012). (b) Active abrasive grit identification by height analysis.

area by the commercial software ␮surf® 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 Fig. 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 be checked from hcuz < plow dgx and hcuz > plow 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. plow and cut are identified as 0.015 and 0.025 for SiC wheels. In this study, grains are not assumed as sphere; therefore dgx is taken as the width of the abrasive grain. In Fig. 3a, 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 et al. (2013), cut-off distance can be identified to determine number of active abrasive grains per 1 mm2 . Red sections observed in Fig. 3b, 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 1 mm × 1 mm will not be enough to determine the C. In this study, fifteen 1 mm × 1 mm 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 Fig. 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 Fig. 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. 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 the same procedure is repeated for each abrasive grain. For example, if there are fifty thousand abrasive grains on a wheel, the same procedure should be repeated fifty thousand times since each abrasive grain requires 8 parameters which are given above. Therefore the random nature of the abrasive wheel topography can be represented in the simulated surface as well (Fig. 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 stuck 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. Average distance between the abrasive grits is calculated as 40 ␮m from Eq. (1) which does not consider whether a grain is active or not. Distance between active grits that are above the

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Fig. 4. Peak count of abrasive grit heights..

cut-off height is obtained as 173 ␮m from the surface topography measurements. Calculation of a single abrasive grit’s trajectory is presented as follows: x = feedr × t + (R + heightgrit ) × sin()

(2)

z = (R + heightgrit ) × (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. 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 (Fig. 6). x(setID#) = feedr × t + (R + heightgrit ) × sin() y(setID#) = (R + heightgrit ) × (1 − cos( − (setID# − 1) × delay ))

(3)

Uncut chip thickness per grit can be calculated by neglecting the trochoidal movement of the abrasive wheel as follows, Jiang and Ge (2008): h = 2 × dseti ×

 feed   a 0.5 r Vc

×

(4)

D

Eq. (4) uses a simplification by ignoring the trochoidal movement of the grits. Martellotti (1945) indicated that it can be neglected for the low 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

a)

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 − xex2 )2 + (yex1 − yex2 )2 + (zex1 − zex2 )2 (5)

(xkm − xij )2 + (ykm − yij )2 + (zkm − zij )2

h =

Coordinate values of exit 1 and 2 points are illustrated in Fig. 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 ) = ((feedr × t + (R + heightgrit − agrit ) × sin(), (R + heightgrit − agrit ) × (1 − cos()))

b) 0.6

2.2

0.5

2

0.4

1.8

0.3

1.6

z (mm)

height (mm)



0.2

1.4 1.2

0.1

1

0 1 1 0.8

0.5

0.6 0.4

radial direction (m m )

0

0.8 0.5 0.4 0.3 0.2 0.1

0.2 0

circum ferential direction (m m )

y (mm)

Fig. 5. (a) Abrasive wheel and (b) single groove topography (SiC 80 tool).

0

0

0.2

0.4

0.6

x (mm)

0.8

1

(7)

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81

Fig. 6. (a) Trajectory and penetration depth of a single grit and (b) grit trajectory and chip thickness variation.

f (xij , zij ) = (feedr × t + (R + heightgrit ) × sin(), (R + heightgrit ) × (1 − cos()))

(8)

3. Thermo-mechanical force model The 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 (1992) and Dudzinski and Molinari (1997) and dual-zone model presented by Ozlu et al. (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 Johnson-Cook 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 dual-zone 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).





1  = √ A+B √ 3 3

n 

1 + ln

 ˙ m  ˙ 0

v

[1 − (T¯ ) ]

(9)

In Eq. (9), ␥, ␥ and ␥0 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 critical temperature which is defined as the reduced temperature is defined by Eq. (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  0 and considering the inertia effects;  1 , the shear stress at the exit of the shear plane, is not the same as  0 .  0 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 Eq. (11) considering the equations of motion for a steady state solution (Ozlu et al., 2010). 2

1 = (V sin n cos i) 1 + 0

(11)

By assuming adiabatic conditions, following expression can be obtained: T = Tw +

ˇ

c



Vc2 sin2 

2 + 0  2



(12)

Tw is the absolute temperature of the workpiece, c and ˇ are the heat capacity and fraction of the work converted into heat, respectively. For grinding operations ˇ is often considered as 0.95–0.97

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(Malkin and Guo, 2007). Considering the compatibility condition (Ozlu et al., 2010): d ˙ d dt d/dt = = = dy dt dy Vc sin  dt/dy

(13)

where: T = Tw

at y = 0

 =0

at y = 0

1  = 1 = tan( − ˛) + tan 

at y = h

(14)

Eq. (13) can be iteratively calculated to get the  0 with the boundary conditions introduced above. In this study, a classical Runge–Kutta method is utilized for that purpose. When  0 is obtained,  1 can be obtained from Eq. (11) which will also be used in rake face contact analysis and give the corresponding temperature value in Johnson-Cook formulation. 3.1. Dual-zone contact model for grinding process Ozlu et al. (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 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 (Liang 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 toward 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 ( 1 ) of the workpiece material on the rake face. Therefore, stress conditions for sticking and sliding regions can be defined as follows:  = 1  = P

x ≤ lp 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

Fig. 7. Chip flow and the pressure distribution on the grit rake face.

direction. P(x) is the normal pressure distribution as illustrated in Fig. 7, P0 is the normal stress on the rake face at the grit tip and is the distribution exponent. Normal force (N) acting on the rake face can be calculated from P0 as follows (Ozlu et al., 2010):



lcr

N=



x lcr

P0 1 − 0



wc dx = P0

agrit lcr cos c + 1 cos i

(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 ˇn cos(n + ˇn − an )

(17)

where the shear force is: Fs = 1 As = 1

agrit h sin n cos i

(18)

By equating Eqs. (13) and (14), P0 can be written as: P0 = 1

h cos s cos ˇn lcr sin n cos c cos(n + ˇn − an )

(19)

where s is the shear flow angle, c is the chip flow angle, ˛n is the normal rake angle and ˇn is the normal friction angle. Normal friction angle can be calculated as ˇn = tan a cosc where a is the apparent friction coefficient and identified from a = tan−1 a . 3.2. 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): lp = lcr − lcr

  1/ς 1 P0 

(20)

Moment due to normal shear force (Msf ) acting on the shear plane at the abrasive grit tip can be calculated by Eq. (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 Eq. (22). Equating these two

D. Aslan, E. Budak / Journal of Materials Processing Technology 223 (2015) 75–90

moments to each other lead us to the total contact length between chip and abrasive grit. Msf = 1



agrit h cos s tan(n + ˇn − ˛n ) 2 sin2 n cos i lcr

Mgr =



xP0 1 − 0

x lcr

(21)

ς

cos c agrit dx

(22)

By plugging Eq. (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 + ˇn − ˛n ) 2 sin n cos ˇn cos c

cos ˛n tan i tan c − sin ˛n tan i

(24)

(25)

A = r cos ˛n + cos i tan ˇ B = tan ˇ sin ˛n sin i (26)

C = r sin ˛n tan ˇ D = r tan ˇ tan i E = sin i cos ˛n

Eq. (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. s = tan−1

 r cos a  1 − r sin a

(27)

Chip ratio r, which is required for the equations listed above, is calculated from Equation 27. 3.3. Friction coefficients and forces Two friction coefficients can be used to define the contact on the rake face: apparent (a ) and sliding (s ) friction coefficients Ozlu et al. (2010). The ratio between the total friction and normal forces acting on the rake face is the apparent friction coefficient 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 Eq. (13) and the relationship between the apparent and sliding friction coefficient is (Ozlu et al., 2010): 1 P0



1+ς



1−

  1/ς  1 P0 

cos(ˇn − an ) + tan s tan c sin ˇn

Ftc−g = 1 bgrit h sin n



cos2 (n + ˇn − an ) + tan2 c sin2 ˇn

(29)

(28)

If one of the friction coefficients is known, the other can be calculated using Eq. (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.



sin(ˇn − an ) cos2 (n + ˇn − an ) + tan2 c sin2 ˇn cos s (30)

Frc−g = 1 bgrit h

cos(ˇn − an ) tan s − tan c sin ˇn sin n



cos2 (n + ˇn − an ) + tan2 c sin2 ˇn

(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).





Ag

Fnc =



Ag

Fnc−g(i) , Ftc = i=1

where:

a =

Fnc−g = 1 bgrit h

(23)

Øns is the normal shear, ˇn is the normal friction and ˛n is the normal rake angle. The following expression for the chip flow angle c is obtained as (Armarego and Brown, 1969): A sin c − B cos c − C sin c cos c + D cos2 c = E

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):

sin n

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 + ˇn ) =

83

Ag

Ftc−g(i) , Frc = i=1

Fr−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 Fig. 8a, 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). As it is illustrated in Fig. 7b (Durgumahanti et al., 2010), gritworkpiece 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. Fig. 7b 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 to as transformation from orthogonal to oblique cutting which is more desirable in terms 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 (Fig. 9).

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D. Aslan, E. Budak / Journal of Materials Processing Technology 223 (2015) 75–90

Fig. 8. (a) Shear and deformation zones and (b) engagement section and division into sections.

Fig. 9. G roove profile and directions for sectioning analysis.

As it can be seen from Fig. 8 (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. 4. Simulation and experiment results 4.1. 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. 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 Fig. 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, the temperature at the cutting zone is measured by embedding a K type thermocouple into the workpiece as illustrated in Fig. 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: qw =

P lreal × b

(33)

Therefore, active grit number is obtained more accurately which improves both surface roughness and force predictions. Similar to the sliding friction coefficient analysis (Section 3.3), 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 performing the 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 (Eom et al., 2013). 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 (Fig. 12).

Fig. 10. (a) Experimental setup and (b) dressing operation.

D. Aslan, E. Budak / Journal of Materials Processing Technology 223 (2015) 75–90

85

Fig. 11. (a) Thermocouple fixation diagram and (b) exposed thermocouple junction after an operation.

Linear regression analysis was used to determine ploughing forces and corresponding coefficients (Aslan and Budak, 2014). 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 (Fig. 13). They are identified per grit as: 0.009, 0.012, 0.017 and 0.023 N for 0.03, 0.05, 0.1 and 0.15 mm axial depth of cuts as well. Identification of ploughing

force coefficients and real contact lengths were performed by using regular wheel and used for grooved ones. B, C and D wheels that were produced by a single point diamond dresser are illustrated in Fig. 14. Sliding friction coefficient as a function of cutting speed is obtained through calibration experiments (Eq. 25) which

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

contact length (mm)

7 6

b)

0.15 mm/rev - geometrical 0.15 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)

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)

Fig. 12. Comparison of contact lengths identified by geometrical formulation and thermocouple measurement.

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D. Aslan, E. Budak / Journal of Materials Processing Technology 223 (2015) 75–90 550 500

a=0.03 mm a=0.05 mm linear a=0.1 mm a=0.15 mm

450 400

Fn(N)

350 300

y = 1.3e+003*x + 20

250 200 150 100 50 0.06

0.08

0.1

0.12 0.14 feed rate (mm/rev)

0.16

0.18

0.2

Fig. 13. Ploughing force identification for the regular wheel (illustrated for 0.05 mm axial depth).

Fig. 14. (a) B, (b), C and (c) D type wheels.

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, 0.11 mm/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.

Table 3 Johnson-Cook parameters for AISI 1050 steel (Moufki et al., 2004). A (MPa)

B (MPa)

n

m

v

880

500

0.234

0.0134

1

0.8

µ

0.6

sliding friction coefficient quadratic

0.4 0.2 0 5

10

15

20

25

30

Vc (mm/s) Fig. 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 (Fig. 15):  = −0.0009Vc2 + 0.0566Vc − 0.1671

(32)

Ozlu et al. (2009) showed that for the ceramic (AB30) tool, which includes Al2 O3 -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 (Al2 O3 ) 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 (Fig. 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 Eqs. (17) and (20) and presented in Fig. 16 for the conditions given in Table 4. 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.

D. Aslan, E. Budak / Journal of Materials Processing Technology 223 (2015) 75–90

87

Table 4 Selected experiments to present dual zone model results. Test #

1

2

3

4

5

6

7

8

9

10

11

12

Vc (m/s) feedr a

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

Vc=7.85 m/s

0.08

600

l l

0.06

a) Experiment Sticking+Sliding Fully Sliding Fully Sticking

mm

500

Fn(N)

0.04 0.02

400

300 0

0

5

10

Test #

15

20

25

200

Fig. 16. Total and sticking contact lengths on the rake face of the grit. 100 0.06

0.08

0.1

0.12 0.14 feed rate (mm/rev)

0.16

0.18

0.2

0.16

0.18

0.2

Vc=19.63 m/s

350

b)

300 250 Fn(N)

The comparisons for two different cutting speeds can be seen in Fig. 18. As it can be seen in Fig. 18a and 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 yet opposite results are observed for the simulation results. It is believed that the reason for this 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. Fig. 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

Experiment Sticking+Sliding Fully Sliding Fully Sticking

200 150 100 50 0.06

0.08

0.1

0.12 0.14 feed rate (mm/rev)

Fig. 18. Comparison of experimental and predicted results for (a) 7.85 (m/s) – (b) 19.63 (m/s) cases (a = 0.1 mm).

reduced 50% with B wheel which is a measure of the amount of energy required to displace a unit volume material (Tönshoff and Peters, 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. The rate of increase in grinding force are very close to each other for regular and circumferentially grooved wheels as illustrated in Fig. 20. Workpiece surface roughness often decreases with wheel wear since the

Fig. 17. (a) Stuck material on scanned grains and (b) regions where stuck material is observed..

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D. Aslan, E. Budak / Journal of Materials Processing Technology 223 (2015) 75–90 0.9

a)

Exp-Regular Exp-Groove1 Exp-Groove3 Sim-Regular Sim-Groove1 Sim-Groove3

Fn(N)

200 150

Exp-Regular Exp-Groove1 Exp-Groove2 Sim-Regular Sim-Groove1 Sim-Groove2

0.8 0.7 Ra (µm)

250

100

0.6 0.5 0.4 0.3

50

0.2

0 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

axial depth of cut (mm) 40 35

Exp-Regular Exp-Groove1 Exp-Groove3 Sim-Regular Sim-Groove1 Sim-Groove3

Fr(N)

25

15 10 5 0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

axial depth of cut (mm) Fig. 19. (a) Comparison of wheel types (0.11 mm/rev feed) – (b) radial forces (0.11 mm/rev feed).

Wear behavior of regular and grooved wheels 140 Regular Wheel Groove 1 Groove3

120 100 Fn(N)

0.1

0.12 0.14 feed rate (mm/rev)

0.16

0.18

0.2

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 ␮m while after the formation of grooves 1, 2 and 3 it was found as 152, 134 and 116 ␮m respectively. That means the groove ground radius increases toward the end.

20

80 60 40 20 0

0.08

Fig. 22. Ra for abrasive wheel types (a = 0.1 mm).

b)

30

0 0

0.1

1

2

3

4

5 6 # of repetition

7

8

9

10

11

Fig. 20. Wear behavior of wheels for a = 0.03 mm and feedr = 0.11 mm/rev.

abrasive grains become duller and workpiece material fills the cavities on wheel surface. These effects make the grinding process close to polishing as the wheel polishes the workpiece surface rather than removing chips. Radial forces for each wheel are presented in Fig. 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

4.2. 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 (Fig. 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 difficultto-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 the work material as Mohamed et al. (2013) and Aslan and Budak (2014) indicated. 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 ␮m – average). Surface roughness increases with the groove number on the wheel (Fig. 22). Hence it can be said that there is a trade-off between

Fig. 21. Groove marks on final workpiece surface for Wheel b (feed = 0.11 mm/rev and a = 0.1).

D. Aslan, E. Budak / Journal of Materials Processing Technology 223 (2015) 75–90 Ra(µm) for regular wheel - feed = 0.11 mm/rev, a = 0.1 mm

56

a)

55.5

measurement simulation

55 µm

54.5 54 53.5 53 52.5

0

200

400

600

800 µm

1000

1200

1400

1600

Ra(µm) for Groove 1 (A) wheel - feed = 0.11 mm/rev, a = 0.1 mm

63

b)

62.5

measurement simulation

62 µm

61.5 61

89

ideal contact length (geometric), therefore with this method, the 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, the 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.

60.5 60

References

59.5 59

0

200

400

600

800 µm

1000

1200

1400

1600

Fig. 23. Measured and simulated surface profiles for regular and A type wheels.

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. As Tönshoff and Peters (1992) and Malkin and Guo (2007) stated; in order to avoid burning and metallurgical damage on workpiece surface, process temperature should be low enough. This 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 the reason for that is the usage of SiC 80 M which has a medium-fine grit size. By using fine-very 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 Fig. 23 for a regular and groove 1 type wheels, respectively. 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. 5. 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 realized. 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

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