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Influence of grain wear on material removal behavior during grinding nickel-based superalloy with a single diamond grain
Author’s Accepted Manuscript Influence of grain wear on material removal behavior during grinding nickel-based superalloy with a single diamond grain Chenwei Dai, Wenfeng Ding, Jiuhua Xu, Yucan Fu, Tianyu Yu www.elsevier.com/locate/ijmactool
PII: DOI: Reference:
S0890-6955(16)30405-9 http://dx.doi.org/10.1016/j.ijmachtools.2016.12.001 MTM3213
To appear in: International Journal of Machine Tools and Manufacture Received date: 17 October 2016 Revised date: 1 December 2016 Accepted date: 2 December 2016 Cite this article as: Chenwei Dai, Wenfeng Ding, Jiuhua Xu, Yucan Fu and Tianyu Yu, Influence of grain wear on material removal behavior during grinding nickel-based superalloy with a single diamond grain, International Journal of Machine Tools and Manufacture, http://dx.doi.org/10.1016/j.ijmachtools.2016.12.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Influence of grain wear on material removal behavior during grinding nickel-based superalloy with a single diamond grain Chenwei Daia, Wenfeng Dinga*, Jiuhua Xua, Yucan Fua, Tianyu Yub
a
College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China
b
Department of Aerospace Engineering, Iowa State University, Ames, IA 50010, USA
Corresponding author. E-mail: [email protected] (W.F. Ding)
Abstract In order to explore the effect of grain wear on material removal behavior during grinding nickel-based superalloy Inconel 718, the grinding experiment with a single diamond grain was carried out. The variations of grain wear, grinding force and force ratio, and pile-up ratio were investigated under the conditions of undeformed chip thickness (UCT) ranging from 0.2 to 1 μm. The results show that a critical UCT value, such as 0.3 μm, could be determined according to the pile-up ratio and could also be used to quantify the material removal process. The wear behavior of a diamond grain shows four types, such as crescent depression on the rake face, abrasion on the flank face, grain micro-fracture, and grain macro-fracture. Furthermore, these classifications were determined by the dwell time of rubbing, ploughing and cutting at different UCT values applied. The grinding force ratio increased with increasing of the negative rake angle of a diamond grain. In the rubbing and ploughing stages, the material removal efficiency is proportional to the wear width on the rake face. However, in the cutting stage, the material removal efficiency is diminished in the absence process of crescent depression.
Keywords: Single diamond grain; Material removal; Grinding force; Wear; Pile-up.
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1 Introduction In the past decades, grinding with diamond and cubic boron nitride (CBN) superabrasive wheels have become popular to machine difficult-to-cut materials, i.e., nickel-based superalloy and titanium alloy [1, 2]. However, the wear behavior of abrasive tools can greatly affect the machined surface quality and integrity [3], the reason of which is that the different wear status of the abrasive tools could produce different material removal behavior during grinding. Generally, the classification of wear behavior in grinding includes the wear of abrasive tools and the wear of abrasive grains. In recent years, more attention has been paid to the research on wear behavior of abrasive tools from the macro perspective. For example, Shen et al. [4] and Herman et al. [5], respectively, investigated the wear behavior of diamond and CBN superabrasive wheels, in which the radial wear has been investigated as an evaluation parameter for the grinding performance. At the same time, Upadhyaya et al. [6] also discussed the effects of the wear of CBN wheels on the surface roughness during grinding. It is noted that, however, further studies are still necessary on the wear behavior of abrasive grains from the micro perspective since several micro-cutting events happen simultaneously on thousands of active cutting grains (Fig.1). Furthermore, with the significant development of grinding methods with a single diamond or CBN grain in the present days [7-9], great efforts have been made to further understand the material removal mechanism [10, 11]. Besides, more and more research work has also been carried out to investigate the grain wear behavior based on the single grain grinding method [12-14]. Particularly, Buhl et al. [13] and Wu et al. [14], respectively, reported that the rake angle and grain shape have great influence on the grinding force and wear resistance of abrasive grains. It should be noted that, the investigation on grain wear behavior is still lacking from the micro aspect perspective, especially the evolution of wear behavior under different process parameters, which would affect abrasive tool wear in the grinding process. It is also a well-known fact that, according to the previous publication about grinding mechanism [15], the maximum undeformed chip thickness (UCT for short in this article) greatly affects the grinding process in not only the grains grinding force, but also in the grinding temperature within the wheel-workpiece contact zone. Under such conditions, the grain wear behavior is highly dynamic and hard to predict in the grinding process. For these reasons, in order to improve the abrasive tool life and material removal efficiency, it is particularly important to investigate the effect of grain wear behavior on the material removal mechanism by controlling the UCT. In the present work, nickel-based superalloy Inconel 718, as a typical difficult-to-cut material, has been chosen as workpiece material during the grinding experiments with a single grain. In order to control the initial cutting edge condition more easily, the diamond grains with regular shape are utilized rather than CBN grains with irregular shape. Grinding force with a single grain has been measured. Pile-up ratio is also calculated to detect the material removal behavior. Meanwhile, in order to further investigate the variation of the grain wear behavior, grain morphologies and grinding force are analyzed under different values of UCT. Finally, the influence of grain wear behavior on material removal process has been discussed. Accordingly, in the future research work, the abrasive tool wear could be controlled to improve the material remove rate (MRR) based on the currently experimental and theoretical findings.
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Wheel
ap
vs Grain
vw Fig. 1
Workpiece
Schematic diagram of the grinding process with monolayer diamond or CBN abrasive wheels.
2 Experimental method and details The experimental set-up for the present single grain grinding operation is displayed in Fig. 2. Surface grinding tests were carried out on a high-speed surface grinder (PROFIMAT MT 408) with the capabilities of workpiece infeed speed ranging from 15 mm/min to 25 m/min, the maximum spindle power of 45 kW, the highest revolution of 8000 rpm. Besides, the coolant with pressure of 15 MPa and flowrate of 90 L/min was utilized; as such, the effect of grinding temperature on grain wear could be generally ignored due to the excellent cooling condition. The cub-octahedral diamond grains [9, 14] in 35/40 mesh size with regular shape were used for the purpose of controlling the cutting edge more easily. According to Ref. [14], the wear resistance of a diamond grain usually differs significantly when grinding with different crystal faces, where crystal face (100) shows a better performance than that at crystal face (111). In order to keep a constant grinding condition, the diamond grains were controlled at the particular crystal face (100) from the top view. Under such conditions, each diamond grain would have a better wear resistance to work for a longer time in single grain grinding. Besides, in each grinding test, only one cutting edge for each diamond grain perpendicular to the wheel speed direction was used. Therefore, the present single grain grinding operation is similar to the conventional cutting operation (such as milling) which uses a tool with fixed geometrical shape and angles. As a result, in the current work, it is generally reasonable to refer to the tool wear behavior in the micro-milling operations (such as, Ref. [16-19]) to discuss the grain wear behavior during grinding. Wheel Grain holder
LabVIEW
Ag-Cu-Ti alloy
vs Diamond grain
Data capture
Kistler 5018 charge amplifier
Kistler 9317C
Singles amplifier
Undeformed chip
AE sensor
Top view ap Workpiece Clamp Dynamometer Worktable vw
Fig. 2
Cutting edge vs Material flowing direction Crystal face Crystal face (111) (100)
Schematic diagram of the present single grain grinding operation.
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Wheel ds agmax vs
ap Workpiece vw
Fig. 3
Schematic diagram of wedge-shaped chips.
A single diamond grain was brazed with Ag-Cu-Ti alloy on a steel holder, which was mounted to a steel block with screws. The assembled components were then fixed in a V-shaped slot of the wheel substrate. The workpiece material was nickel-based superalloy Inconel 718. Prior to the single grain grinding tests, a precision surface grinding had been carried out using alumina wheels on the workpiece in order to obtain the required ground surface roughness, such as Ra 0.4 μm. In the trials, the single diamond grain was precisely preset by using an acoustic emission instrument (DITTEL AE6000). The grinding force was measured in different grain wear stages by the three components piezoelectric dynamometer (KISTLER 9317C) attached with a charge amplifier (KISTLER 5018). The radius of the cutting edge circle of single diamond grains applied has been measured using an atomic force microscope (AFM). The dimension of the radius was nearly 0.54 μm. For this reason, tests were conducted in grain wear-free status to better understand the material removal process. A parametric study has been first conducted under various UCT values, ranging from 0.16 to 1 μm. Then, in order to comprehensively investigate the grain wear behavior, the UCT values were set at three different levels, such as 0.2 μm, 0.5 μm and 1 μm. For generation of wedge-shaped chips as shown in Fig. 3, the required workpiece infeed speed could be calculated according to the following formula [15]:
agmax 2
vw vs
ap
(1)
ds
where λ is the spacing between active grains (taking λ=πds/2 here), agmax is the UCT, vw is the workpiece infeed speed, vs is the wheel speed, ap is the depth of cut and ds=390 mm is the wheel diameter. Table 1 lists the parameters applied in the present grinding tests with single diamond grains.
Table 1
Grinding process parameters Values
Process parameters
Grain wear-free
Undeformed chip thickness (UCT) agmax (μm)
Grain wear
0.16-1
0.2, 0.5, 1
Depth of cut ap (mm)
0.02
0.02
Wheel speed vs (m/s)
30, 50, 80
30
16.4-223.5
20.5, 51.3, 102.6
Workpiece infeed speed vw (mm/min) Grinding mode
Up grinding, water based coolant
During the grain wear experiment, for each group of grinding parameters, the grinding force has been first collected in every two passes (each pass length is 60 mm). From the ninth pass, reading of the grinding force was carried out for every three passes. During the whole grinding tests, after each force reading, the diamond grain morphology has been recorded with the 3D optical profiler (SENSOFAR S NEOX) by disassembling the grain holder from the wheel substrate. The grain wear morphology has been characterized quantitatively in each test. Since each grain size is different in different test, the specific material removal volume (SMRV) ΔV′ is used to evaluate the amount of material
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removed:
V ' V / b a p L
(2)
where V is the material removal volume, b is the groove width which is different for different grain, ap=0.02 mm is the depth of cut in the current experiment, and L is the length of the total grinding pass. The pile-up ratio, which is defined as the ratio of the total pile-up area to the total groove section area, is a sound method to quantify the material removal behavior [7]. As illustrated in Fig. 4, the pile-up areas are B1 and B2, and groove section area is characterized by A. Thus the pile-up ratio Rs could be expressed as:
Rs ( B1 B2 ) / A
(3)
In order to obtain the values of pile-up ratio, the cross-section profiles have been measured three times along the workpiece longitude direction by using 3D optical profiler for each test. Then, AutoCAD has been used to reconstruct the cross-section profiles and the average value of these three pile-up ratios has been calculated. Cutting out
Cutting in
A B1 Fig. 4
B2
3D morphology and cross-section profiles of a single grain grinding surface.
3 Results and discussion 3.1 Material removal characteristics in the case of grain wear-free In general, the grinding-workpiece contact could be separated into three stages: rubbing, ploughing and cutting [20-22]. In rubbing, only elastic deformation occurred, in which each grain slides on the material with small penetration into the workpiece. When the grain penetrates deeper into the workpiece, ploughing occurs in both elastic and plastic deformation form, where the scratch becomes more evident with ridges formed on both sides. As the grain further penetrates, the material is removed rapidly and chip formation takes place [15]. Since the pile-up ratio reflects the material removal ability, it is obtained at different UCT values under grain wear-free condition to identify different material removal stages, as shown in Fig. 5. Obviously, if the UCT value is smaller than 0.3 μm, the pile-up ratio increases gradually with increasing of UCT values. That is to say, more materials are left over the workpiece surface, which indicates that the ploughing stage dominates. Once the UCT value reaches 0.3 μm, the pile-up ratio drops rapidly. Then, it remains a constant as the UCT value is larger than 0.4 μm. In this case, the amount of left pile-up material has decreased for the reason that the workpiece material is mainly removed as chip formation rather than the pile-up around the scratch groove. Thus, a critical UCT value ag, critical, i.e., about 0.3 μm, can be identified for nickel-based superalloy Inconel 718, which can be expressed as:
ag ,critical 0.56re where re is the radius of cutting edge.
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(4)
0.30 vs=30m/s
0.28
vs=50m/s
Pile-up ratio Rs
0.26 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.0
0.2 0.4 0.6 0.8 1.0 Undeformed chip thickness agmax (μm) Fig. 5 Pile-up ratio versus UCT.
Specific grinding energy es (J/mm3)
35
Grinding force F (N)
30 25 20 15 vs=30m/s, Ft
10
vs=30m/s, Fn
5
vs=80m/s, Ft vs=80m/s, Fn
0 0.2
vs=30m/s vs=80m/s
500 400 300
es=110a-0.83 gmax
200 100 0 0.0
0.4 0.8 1.2 1.6 2.0 Undeformed chip thickness agmax (μm) (b) Specific grinding energy Size effect on grinding force and specific grinding energy.
0.4 0.6 0.8 1.0 1.2 Undeformed chip thickness agmax (μm) (a) Grinding force Fig. 6
600
Moreover, by comparing the measured grinding force at different values of UCT (Fig. 6(a)), it could be found that the grinding force varies in two different stages due to the different material deformation characteristics in grinding, which agrees well with the results of Hahn [23]. On one hand, when the UCT value is less than 0.3 μm, the grinding process is in rubbing and ploughing stages where the material is frictioned and pulled along the front and side faces of a grain. On the other hand, in the case of the UCT larger than 0.3 μm, chip formation takes place and the material removal increases rapidly. The definition of critical UCT value from the variations of pile-up ratio and grinding force can be interpreted from the specific grinding energy. In the current grinding tests, the undeformed chip is in a wedge shape, which can be approximated as a triangle. The specific grinding energy es is defined as the energy consumed to remove per unit volume of material, which can be expressed as:
es W / V ( Fl t s ) / (ag max ls b / 2) 2 Ft / (ag max b)
(5)
where W is the energy consumption to remove the material in a single grain-workpiece contact zone, V is the volume of undeformed chip material to be removed, ls=(apds)1/2 is the length of grain-workpiece contact zone and b=0.3 mm is the width of the undeformed chip. It is reported that, the specific grinding energy is consumed by means of primary and secondary rubbing energy, ploughing energy and chip formation energy [24]. Among them, the ploughing energy and chip formation energy are constant for the determinate material, which are determined by the material mechanical properties, such as dynamic yield shearing strength and workpiece hardness. However, the rubbing energy is inversely proportional to the UCT. According to Eq. (5), the variation of specific grinding energy with increasing UCT is plotted in Fig. 6 (b). Obviously, the specific grinding energy obeys the typical size effect rule in grinding. In case of a small UCT (<0.3 μm particularly),
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the specific grinding energy has larger values and decreases quickly with the increase of UCT, which indicates that it is mainly composed of the high rubbing energy and relatively low ploughing energy. However, as the UCT value gets larger, the specific grinding energy decreases at a slower rate, which shows the grinding process mainly consists of the cutting stage with small cutting energy. Based on the results shown in Fig. 6(b), the relationship between specific grinding energy and UCT could be calculated by Eq. (6):
es 110ag0.83 max
(6)
3.2. Classification of grain wear behavior in single grain grinding In general, during the single grain grinding of Inconel 718, the diamond grain wear behavior shows mainly four types: crescent depression on the rake face, abrasion on the flank face, grain micro-fracture, and grain macro-fracture, as schematically displayed in Fig. 7 and 8. The grain wear behavior obtained at different UCT values in the current investigation are tabulated in Table 2. It shows the wear evolution of diamond grains could be divided into two stages: (i) the initial wear stage, acting as the formation of crescent depression on the rake face and the abrasion wear on the flank face; (ii) the steady wear stage, in which the wear behavior on the rake and flank face is dramatically influenced by different UCT values. Crescent depresion
Abrasion
Cutting edge Flank face Rake face
Grain microfracture
Fig. 7 Abrasion
Grain macrofracture
Classifications of grain wear behavior. Grain macro-fracture
Grain micro-fracture New rake face
vs vs Cutting edge
Cutting edge
(b) agmax=0.5 μm, ΔV’=22.2 mm3/mm
(a) agmax=0.2 μm, ΔV’=5.44 mm3/mm Abrasion
Crescent depression
vs Cutting edge
(c) agmax=1 μm, ΔV’=2.88 mm3/mm
Fig. 8
Morphology of grain wear in the single grain grinding.
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Table 2 Grain wear behavior at given UCTs. Classification agmax=0.2 μm agmax=0.5 μm agmax=1 μm Crescent depression no yes yes Abrasion yes yes yes Grain micro-fracture yes yes no Grain macro-fracture yes yes no
According to the deduce of the critical UCT value in Section 3.1, the rubbing, ploughing and cutting stages at UCT of 0.2, 0.5 and 1 μm are schematically shown in Fig. 9. Obviously, the percentage of these three stages in the grain-workpiece contact zone is significantly different. When only the rubbing and ploughing stages take place in the grinding process, as shown in Fig. 9(a), the stress concentration on the cutting edge is so severe that abrasion and grain fracture appear, due to the attritious wear on the flank face and the spring-back effect from the elastic deformation of the ground surface material, respectively. However, no crescent depression occurs because chip formation of the material is rather difficult which is necessary in the rake face attritious wear. Seen from Fig. 9(b), when the dwell time of cutting stage is approximately the same as that of the rubbing and ploughing stages, the removed chips flow on the rake face, which increases the crescent depression caused by the frictional interaction with removed chips. When the cutting stage dominates, as displayed in Fig. 9(c), most of the load is shared by the rake face. Thus, the spring-back effect from ground surface in rubbing and ploughing stages is too weak to fracture the grains. Theoretically, according to the increasing of SMRV, the grain wear behavior could be interpreted in Fig. 10 based on the experimental results. Rubbing and ploughing
ag,critical
agmax
Accumulated material
(a) agmax=0.2 μm Cutting
Rubbing and ploughing Chip
agmax
ag,critical
(b) agmax=0.5 μm Chip
Cutting Rubbing and ploughing
agmax
ag,critical
(c) agmax=1 μm Fig. 9
Schematic diagram of the rubbing, ploughing and cutting stages. N e wc u t t i n g e d g ec i r c l e
Wear platform
crescent d epres sio n
Broken W ear pa ltform
R a k ef a c e wear
Rake face wear
vs
Flank face wear
C utt ing ed g e circle
vs
Flank face we ar
(a) agmax=0.2 μm (b) agmax=1 μm Fig. 10 Schematic diagram of wear behavior of diamond grain in the case of UCT of 0.2 and 1 μm.
3.3. Analysis of grain wear behavior from the viewpoint of grinding force Fig. 11 shows the relationship between grinding force and SMRV at three given levels of UCT in the present investigation. With the increase of SMRV, the normal grinding force Fn and tangential grinding force Ft tend to increase first and then keep stable. However, the growth rate of the grinding force is different at each level of UCT values. When the UCT is 0.2 or 0.5 μm, the grinding force rises up at a relatively higher growth rate in the initial wear stage. Moreover, the growth rate at the UCT of 0.2 μm is higher than that at 0.5 μm. This indicates stress concentration on the
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cutting edge is more prominent in the case of small UCT, which rapids the grain wear and the increase of grinding force. When the UCT further increases to 1 μm, the load mostly acts on the rake face. Thus, the grain wear around the cutting edge is not remarkable. Under such conditions, the grinding force increases slowly in the initial wear stage. However, when the SMRV reaches 6.8 mm3/mm, due to the appearance of crescent depression on the rake face, the grinding force grows quickly with a growth rate approximate to that in the case of UCT of 0.5 μm. 120
Grinding force F (N)
100 80 60 agmax=0.2μm, Ft agmax=0.2μm, Fn
40
agmax=0.5μm, Ft agmax=0.5μm, Fn
20
agmax=1.0μm, Ft agmax=1.0μm, Fn
0 0
5
10
15
20
25
30
Specific material removal volume V' (mm3/mm)
Fig. 11
Grinding force versus SMRV.
The changes of grinding force with increasing SMRV could be attributed to the grain wear behavior. When the UCT is 0.2 μm, seen from Fig. 12(a), since small chips are generated by removing material, more and more material accumulates on the rake face. Due to the stress concentration on the cutting edge, grain wear takes place quickly. As a result, the grinding force rises up at a large growth rate. Once the new rake face is formed, the amount of accumulated material keeps nearly a constant, which stabilizes the grinding force. Because of the continuous formation of new rake faces in the grain wear procedure, the grinding force fluctuates between 50 and 70 N. When the UCT is 0.5 μm, as displayed in Fig. 12(b), the crescent depression on the rake face keeps expanding in the early stage, which results in the increase of contact area between a grain and flowing chips. Thus, the grinding force gradually increases first and then remains stable until grain fracture appears around the cutting edge. When the UCT reaches at 1 μm, the crescent depression forms gradually in the initial wear stage, making the amount of flowing chip vary slightly, as demonstrated in Fig. 12(c). Therefore, the grinding force increases slowly. However, because the abrasion wear of a diamond grain on the flank face is getting serious, the load on the cutting edge is increased, which results in the suddenly expanded crescent depression. While the crescent depression disappears gradually with the increase of SMRV, the negative rake angle is enlarged. As a result, the grinding force increases. At last, once the crescent depression is completely transferred into the new sharp cutting edge, the grinding force remains stable.
Accumulated material
β1 Accumulated material
Accumulated material
β2
vs
vs
Accumulated material Grain microfracture
β3
β4 Grain macrofracture
vs
β1 ≈β2 ≈ β3 ≈ β4
vs
(a) agmax=0.2 μm
C h i p β1
C h i p β2
β23
Chip G r a i n m i c- r o fra ct ure
Chip vs
vs
β1 <β2 ≈ β3 ≈ β4
(b) agmax=0.5 μm
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vs
β4
G r a i n m a c- r o frc ture vs
Chip
β1
Chip
vs
Fig. 12
Chip
β2 vs
β1 ≈ β2 <β3 ≈ β4
Chip
β3
β4
vs
vs
(c) agmax=1 μm Schematic diagram of material removal behavior and the variation of the negative rake angle in grinding.
It could be found by further analysis of grinding force that, when the grinding force remains stable, the SMRV values are different at three levels of UCT. The critical values are 8.16, 14.4 and 21.84 mm3/mm at the UCT of 0.2, 0.5 and 1 μm, respectively. It is inferred that, by increasing the UCT value, more material would be removed when the grinding force becomes stable in the wear process. That is to say, the grain wear rate would be effectively reduced if the UCT is increased to twice the radius of cutting edge circle. 3.4 Relationship between grinding force ratio and negative rake angle in grain wear process Fig. 13 provides the relationship between grinding force ratio and the SMRV at different UCT values. Obviously, when the UCT is 0.2 μm, the grinding force ratio always fluctuates between 0.9 and 1.2. When it is 0.5 μm, the grinding force ratio first increases gradually, and then remains around 1.08 when the SMRV increases to 10 mm3/mm. When the UCT is 1 μm, the grinding force ratio first keeps a constant of 0.82 until the SMRV reaches at 10 mm3/mm, then gradually rise up to 1.12 with the SMRV increases to 20 mm3/mm, and finally they remain constants again at 1.12. It could be inferred from the grain wear behavior and the variation of grinding force ratio that, the gradually disappeared crescent depression on the rake face would result in the increase of actual negative rake angle, which is diagrammed in Fig. 12. In the case of UCT of 0.2 μm, since the workpiece material always presses the cutting edge, the rake and flank faces wear synchronously, as displayed in Fig. 10(a). Thus, little change in the negative rake angle (β1≈β2≈β3≈β4) makes the grinding force ratio a constant, as shown in Fig. 12(a). While in the case of UCT of 0.5 μm, seen from Fig. 12(b), the negative rake angle is enlarged (β1<β2) due to the expanding of crescent depression in the initial wear stage. When the grain fracture happens around the cutting edge, the rake and flank faces also wear synchronously, which causes the negative rake angle change slightly (β2≈β3≈β4). However, when the UCT is 1 μm, the generated crescent depression is insignificant in the beginning, so the negative rake angle doesn’t alter very much (β1≈β2), as displayed in Fig. 12(c). Once the crescent depression disappears gradually, the negative rake angle is increased (β2<β3). Finally, the negative rake angle remains a constant (β3≈β4) again as the new cutting edge is generated.
Grinding force ratio Fn/Ft
1.4 1.2 1.0 0.8 agmax=0.2μm agmax=0.5μm
0.6
agmax=1.0μm
0.4 0 5 10 15 20 25 30 Specific material removal volume V' (mm3/mm) Fig. 13 Grinding force ratio versus SMRV.
The specific grinding force Fp is defined as the force per unit area in the grain moving direction. The forces on the two sides of a grain are balanced out by each other. Only the forces on rake face are considered, as diagramed in Fig. 14.
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dFx
A
A
Y X
Cutting direction A-A dFx,n
β
dFfr,t
dFfr,n Fig. 14
dFx dFx,t
ag
dFfr
Grinding force model in single grain grinding.
In every cross-section X-X, the grinding force dFx perpendicularly loads on the rake face, which is calculated by :
dFx Fp dA cos
(7)
where β is the negative rake angle. The cell area in the grain-workpiece contact zone is:
dA ag dy cos
(8)
where ag is the actual cutting depth of the grain. Thus, Eq. (7) can be rewritten as:
dFx Fp ag dy
(9)
According to the grinding force model shown in Fig. 14, the force dFx could be decomposed into the force along and perpendicular to the cutting direction, which are written as:
dFx,t dFx cos
(10)
dFx,n dFx sin
(11)
The total friction force along the grain rake face dFfr makes the formed chip flowing out of the grain-workpiece contact zone, which is defined as:
dFfr dFx
(12)
where μ is the friction coefficient and the value is 0.23 [25]. As such, the friction force can also be decomposed into the force along and perpendicular to the cutting direction, which are expressed as follows:
dFfr ,t dFfr sin
(13)
dFfr ,n dFfr cos
(14)
Finally, by combining the component forces, the tangential and normal forces on the sampling unit of a single grain are calculated as:
dFtg dFx,t dFfr ,t (cos sin ) Fp ag dy
(15)
dFng dFx,n dFfr ,n (sin cos ) Fp ag dy
(16)
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Thus, considering that the actual load width of a single grain is a, the total grinding force on the whole grain is integrated as: a
Ftg 2a dFtg Fp aag (cos sin )
(17)
Fng dFng Fp aag (sin cos )
(18)
2 a 2 a 2
Commonly, the grinding force ratio ε is used to reflect whether a grain is blunt or not. From the given grinding force model in this article, it can be calculated as:
Fng / Ftg
sin cos tan cos sin 1 tan
(19)
which can be further rewritten as:
1
2 1 (1 tan )
(20)
According to Eq. (20), it is obvious that, with the increase of the negative rake angle β, the grinding force ratio ε is getting larger. In other words, a diamond grain is becoming blunt due to the grain wear behavior on the rake face. The calculated grinding force ratio in case of agmax=1 μm under the condition of negative rake angle ranging from 51.5° to 60.5° are provided in Fig. 15. Obviously, the calculated results match very well with the tested data in an error less than 5%. During the increasing of SMRV from 6.8 to 21.84 mm3/mm, the measured negative rake angles are 51.8°, 54°, 57°, 59° and 60.6°, while the corresponding calculated grinding force ratio are 0.8, 0.87, 0.97, 1.04 and 1.1, compared with tested values of 0.83, 0.9, 1.05, 1.05 and 1.16. 1.2
Grinding force ratio
Tested Calculated
1.1 1.0 0.9 0.8 0 5 10 15 20 25 30 Specific material removal volume V' (mm3/mm)
Fig. 15 Comparison of the tested and calculated grinding force ratio in the case of agmax=1 μm
3.5 Influence of grain wear behavior on material removal process In Section 3.1, the chip formation characteristics are discussed in the grain wear-free status. However, the material removal ability has decreased due to the attritious wear. In order to further investigate the influence of grain wear behavior on material removal process, the cross-section profiles of the scratch marks are obtained in different grain wear stages first; and then the pile-up ratio are discussed according to the increasing SMRV. The cross-section profiles in various single grain grinding conditions are shown in Fig. 16. Obviously, as expected, due to the blunt of a single grain, there is a clear tendency of large material pile-up manifested as pronounced higher and wider shoulders for all the UCT values, accompanied with a large groove width, thus constituting an extent of material rebuild rather than removal. Nevertheless, distinctly different material pile-up characteristics are produced at the given UCT values: a larger UCT value results in less amount of material pile-up in the sharp grain condition (Fig.
- 12 -
16(a), (c) and (e)); that is likely due to a longer period of cutting stage, rather than rubbing and ploughing stages at UCT values of 0.5 and 1 μm, to cut the material across the whole cross-section resulting in minor material rebuild. Furthermore, it is noticed from Fig. 16(b), (d) and (e) that, the shape of the scratch cross-section bottom changes from a line to an irregular curve or an arc due to the wear of cutting edge. The reason can be interpreted from two aspects: one is the grain fracture caused by the spring-back effect of material elastic deformation in the rubbing and ploughing stages, e.g. at the UCT values of 0.2 and 0.5 μm; the other is the abrasion at the two corners of the cutting edge due to stress concentration, e.g. at the UCT values of 0.5 and 1 μm. In addition, when a grain has been seriously worn, the pile-up area is bulk in case of a bigger value of UCT. That is because of the regenerated multi cutting edges caused by grain fracture at UCT of 0.2 μm, which facilities to cut the material more efficiently and results in narrow scratch shoulders. However, compared with multi cutting edges, the cutting efficiency in the case of abrasion at the two corners 16 12 8 4 0 -4 -8 -12 -16 -20 -24 300 400 500 Width Y (μm) (a) agmax=0.2 μm, ΔV’=2.72 mm3/mm
200
300 400 500 600 Width Y (μm) (b) agmax=0.2 μm, ΔV’=25.84 mm3/mm
600
30
30
20
20
Height Z (μm)
Height Z (μm)
100
10 0 -10
100
200
-10
-30
-30 200 300 400 500 Width Y (μm) (c) agmax=0.5 μm, ΔV’=2.8 mm3/mm
200
0
-20
100
100
10
-20
0
300 400 500 600 Width Y (μm) (d) agmax=0.5 μm, ΔV’=22.2 mm3/mm
600
20
20
15
15
10
10
Height Z (μm)
Height Z (μm)
16 12 8 4 0 -4 -8 -12 -16 -20 -24
Height Z (μm)
Height Z (μm)
of the initial cutting edge is low that the pile-up shoulders exhibits a little flat-wide.
5 0 -5 -10
5 0 -5
-10
-15
-15
-20
-20
-25 0
100
200 300 400 Width Y (μm)
500
-25
600
0
(e) agmax=1 μm, ΔV’=2.88 mm3/mm Fig. 16
100
200 300 400 500 Width Y (μm) (f) agmax=1 μm, ΔV’=29.52 mm3/mm
600
Influence of gain wear behavior on cross-section profiles.
The pile-up ratio at various increasing SMRVs are calculated, so as the measured widths of new rake face and
- 13 -
crescent depression. As shown in Fig. 17(a), when the grinding process mainly consists of rubbing and ploughing stages, the pile-up ratio varies nearly in the same tendency as the width of new rake face, and this trend results from the growing length of grain-workpiece contact zone on the rake face. Thus, bulk material rebuild and minor material removal occur. However, according to the decreased pile-up ratio, it is known that the regenerated multi cutting edges due to grain fracture at SMRV of 8 mm3/mm can improve the material removal ability. On the other hand, as shown in Fig. 17(b) and (c), the cutting stage dominates in grinding. The pile-up ratio is increased because of the increase of crescent depression on the rake face. It is noted that, the pile-up ratio increases rapidly when the width of the crescent depression is diminished (e.g. in the range of SMRV from 8 to 15 mm3/mm in case of UCT of 0.5 μm; from 14 to 22 mm3/mm in case of UCT of 1 μm). This is due to the increasing negative rake angle in the absence of crescent depression, as a result of lower MMR and enlarged grinding force ratio. Furthermore, when the pile-up ratio reaches about 0.33, the grain wear is expanded from rake face to the two corners of the cutting edge because of the enlarged scratch shoulders. At this time, the material removal behavior improves a bit due to the better material flowing ability around the corners. Besides, it could also be found that, before the material removal efficiency decreases obviously, the value of SMRV for high material removal efficiency (Rs<0.1) is increased with a bigger UCT (i.e. 5, 11, and 15 mm3/mm in case of 0.2, 0.5 and 1μm, respectively), which is attributed to a lower grain wear rate using relatively larger UCT as mentioned in
Pile-up ratio Rs
15 0.16 0.12
10
0.08 5 0.04 0.00
0.30
0
0 5 10 15 20 25 30 Specific material removal volume V' (mm3/mm) (a) agmax=0.2 μm 0.35
Pile-up ratio Rs
0.30
20 Rs
19
Wc
0.25
18
0.20
17
0.15
16
0.10
15
0.05
14
0.00
13
0 2 4 6 8 10 12 14 16 18 20 22 Specific material removal volume V' (mm3/mm) (b) agmax=0.5 μm 35
Rs Wc
30
0.25 0.20
25
0.15
20
0.10 15
0.05 0.00
10
0 5 10 15 20 25 30 Specific material removal volume V' (mm3/mm)
Width of the crescent depression Wc (μm)
Wr
0.20
0.35
Pile-up ratio Rs
20 Rs
Width of the new rake face Wr (μm)
0.24
Width of the crescent depression Wc (μm)
Section 3.3.
(c) agmax=1 μm Fig. 17 Relation between pile-up ratio and rake face wear.
4 Conclusions The influence of grain wear on material removal behavior has been discussed by the means of the single grain grinding operation on nickel-based superalloy Inconel 718. The key findings can be summarized as follows: (1) In the case of grain wear-free, a critical value of UCT about 0.3 μm is identified through the analysis of pile-up
- 14 -
ratio which is used for quantifying the material removal process. The grinding force and specific grinding energy in the single grain grinding greatly obey the size effect rule. (2) The grain wear behavior mainly shows as four types: crescent depression on the rake face, abrasion on the flank face, rain micro-fracture, and grain macro-fracture. The dwell time of rubbing, ploughing and cutting at different UCT values determines the grain wear types. (3) According to the constructed grinding force model, it is the increasing negative rake angle that enlarges the grinding force ratio, which lowers the material removal ability. (4) During the single grain grinding, the material removal efficiency is proportional to the wear width on the grain rake face in rubbing and ploughing stages. However, it is diminished in the absence of crescent depression in cutting stage. At the same time, the grain fracture and abrasion of cutting edge corners can improve the material removal to a certain extent. Acknowledgments The authors gratefully acknowledge the financial support for this work by the National Natural Science Foundation of China (No. 51235004 and No. 51375235), the Fundamental Research Funds for the Central Universities (No. NE2014103).
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[13] S. Buhl, C. Leinenbach, R. Spolenak, K. Wegener. Failure mechanisms and cutting characteristics of brazed single diamond grains. International Journal of Advanced Manufacturing Technology 66 (2013) 755-786. [14] H.Y. Wu, H. Huang, F. Jiang, X.P. Xu. Mechanical wear of different crystallographic orientations for single abrasive diamond scratching on Ta12W. International Journal of Refractory Metals and Hard Materials 54 (2016) 260-269. [15] S. Malkin, C. Guo. Grinding technology: theory and applications of machining with abrasives, 2nd edition. Industrial Press, New York, 2008. [16] X.W. Zhang, K.F. Ehmann, T.B. Yu, W.S. Wang. Cutting forces in micro-end-milling processes. International Journal of Machine Tools and Manufacture 107 (2016) 21-40. [17] E. Kuram, B. Ozcelik. Effects of tool paths and machining parameters on the performance in micro-milling of Ti6Al4V titanium with high-speed spindle attachment. International Journal of Advanced Manufacturing Technology 84 (2016) 691-703. [18] H.T. Liu, Y.Z. Sun, Y.Q. Geng, D.B. Shan. Experimental research of milling force and surface quality for TC4 titanium alloy of micro-milling. International Journal of Advanced Manufacturing Technology 79 (2015) 705-716. [19] Z.B. Zhan, N. He, L. Li, R. Shrestha, J.Y. Liu, S.L. Wang. Precision milling of tungsten carbide with micro PCD milling tool. International Journal of Advanced Manufacturing Technology 77 (2015) 2095-2103. [20] Y. Ohbuchi, T. Matsuo. Force and chip formation in single-grit orthogonal cutting with shaped CBN and diamond grains. CIRP Annals-Manufacturing Technology 40(1) (1991) 327-330. [21] T. Matsuo, S. Tayoura, E. Oshima, Y. Ohbuchi. Effect of grain shape on cutting force in superabrasive single grit tests. CIRP Annals-Manufacturing Technology 38(1) 1989 323-326. [22] E. Brinksmeier, A. Giwerzew. Chip formation mechanisms in grinding at low speeds. CIRP Annals-Manufacturing Technology 52(1) (2003) 253-258. [23] R.S. Hahn. On the mechanics of the grinding process under plunge cut conditions. Journal of Engineering for Industry 88(1) 1966 72-80. [24] S. Ghosh, A.B. Chattopadhyay, S. Paul. Modelling of specific energy requirement during high-efficiency deep grinding. International Journal of Machine Tools and Manufacture 48 (2008) 1242-1253. [25] W.B. Rowe. Principles of modern grinding technology. William Andrew publishing, Norwich, 2009.
Research Highlights
Material removal characteristics in the case of grain wear-free are provided. Classification of grain wear behavior in single grain grinding is analyzed. Grain wear behavior from the viewpoint of grinding force is discussed. Relationship between grinding force ratio and negative rake angle in grain wear process is confirmed. Influence of grain wear behavior on material removal process is discussed.
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Graphical abstract
Wheel Grain holder
LabVIEW
Ag-Cu-Ti alloy
vs Diamond grain
Data capture
Kistler 5018 charge amplifier
Kistler 9317C
Singles amplifier
Top view
Undeformed chip
ap Workpiece
AE sensor
Clamp Dynamometer Worktable vw
Fig. 2
Cutting edge vs Material flowing direction Crystal face Crystal face (111) (100)
Schematic diagram of the present single grain grinding operation.
- 17 -
PII: DOI: Reference:
S0890-6955(16)30405-9 http://dx.doi.org/10.1016/j.ijmachtools.2016.12.001 MTM3213
To appear in: International Journal of Machine Tools and Manufacture Received date: 17 October 2016 Revised date: 1 December 2016 Accepted date: 2 December 2016 Cite this article as: Chenwei Dai, Wenfeng Ding, Jiuhua Xu, Yucan Fu and Tianyu Yu, Influence of grain wear on material removal behavior during grinding nickel-based superalloy with a single diamond grain, International Journal of Machine Tools and Manufacture, http://dx.doi.org/10.1016/j.ijmachtools.2016.12.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Influence of grain wear on material removal behavior during grinding nickel-based superalloy with a single diamond grain Chenwei Daia, Wenfeng Dinga*, Jiuhua Xua, Yucan Fua, Tianyu Yub
a
College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China
b
Department of Aerospace Engineering, Iowa State University, Ames, IA 50010, USA
Corresponding author. E-mail: [email protected] (W.F. Ding)
Abstract In order to explore the effect of grain wear on material removal behavior during grinding nickel-based superalloy Inconel 718, the grinding experiment with a single diamond grain was carried out. The variations of grain wear, grinding force and force ratio, and pile-up ratio were investigated under the conditions of undeformed chip thickness (UCT) ranging from 0.2 to 1 μm. The results show that a critical UCT value, such as 0.3 μm, could be determined according to the pile-up ratio and could also be used to quantify the material removal process. The wear behavior of a diamond grain shows four types, such as crescent depression on the rake face, abrasion on the flank face, grain micro-fracture, and grain macro-fracture. Furthermore, these classifications were determined by the dwell time of rubbing, ploughing and cutting at different UCT values applied. The grinding force ratio increased with increasing of the negative rake angle of a diamond grain. In the rubbing and ploughing stages, the material removal efficiency is proportional to the wear width on the rake face. However, in the cutting stage, the material removal efficiency is diminished in the absence process of crescent depression.
Keywords: Single diamond grain; Material removal; Grinding force; Wear; Pile-up.
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1 Introduction In the past decades, grinding with diamond and cubic boron nitride (CBN) superabrasive wheels have become popular to machine difficult-to-cut materials, i.e., nickel-based superalloy and titanium alloy [1, 2]. However, the wear behavior of abrasive tools can greatly affect the machined surface quality and integrity [3], the reason of which is that the different wear status of the abrasive tools could produce different material removal behavior during grinding. Generally, the classification of wear behavior in grinding includes the wear of abrasive tools and the wear of abrasive grains. In recent years, more attention has been paid to the research on wear behavior of abrasive tools from the macro perspective. For example, Shen et al. [4] and Herman et al. [5], respectively, investigated the wear behavior of diamond and CBN superabrasive wheels, in which the radial wear has been investigated as an evaluation parameter for the grinding performance. At the same time, Upadhyaya et al. [6] also discussed the effects of the wear of CBN wheels on the surface roughness during grinding. It is noted that, however, further studies are still necessary on the wear behavior of abrasive grains from the micro perspective since several micro-cutting events happen simultaneously on thousands of active cutting grains (Fig.1). Furthermore, with the significant development of grinding methods with a single diamond or CBN grain in the present days [7-9], great efforts have been made to further understand the material removal mechanism [10, 11]. Besides, more and more research work has also been carried out to investigate the grain wear behavior based on the single grain grinding method [12-14]. Particularly, Buhl et al. [13] and Wu et al. [14], respectively, reported that the rake angle and grain shape have great influence on the grinding force and wear resistance of abrasive grains. It should be noted that, the investigation on grain wear behavior is still lacking from the micro aspect perspective, especially the evolution of wear behavior under different process parameters, which would affect abrasive tool wear in the grinding process. It is also a well-known fact that, according to the previous publication about grinding mechanism [15], the maximum undeformed chip thickness (UCT for short in this article) greatly affects the grinding process in not only the grains grinding force, but also in the grinding temperature within the wheel-workpiece contact zone. Under such conditions, the grain wear behavior is highly dynamic and hard to predict in the grinding process. For these reasons, in order to improve the abrasive tool life and material removal efficiency, it is particularly important to investigate the effect of grain wear behavior on the material removal mechanism by controlling the UCT. In the present work, nickel-based superalloy Inconel 718, as a typical difficult-to-cut material, has been chosen as workpiece material during the grinding experiments with a single grain. In order to control the initial cutting edge condition more easily, the diamond grains with regular shape are utilized rather than CBN grains with irregular shape. Grinding force with a single grain has been measured. Pile-up ratio is also calculated to detect the material removal behavior. Meanwhile, in order to further investigate the variation of the grain wear behavior, grain morphologies and grinding force are analyzed under different values of UCT. Finally, the influence of grain wear behavior on material removal process has been discussed. Accordingly, in the future research work, the abrasive tool wear could be controlled to improve the material remove rate (MRR) based on the currently experimental and theoretical findings.
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Wheel
ap
vs Grain
vw Fig. 1
Workpiece
Schematic diagram of the grinding process with monolayer diamond or CBN abrasive wheels.
2 Experimental method and details The experimental set-up for the present single grain grinding operation is displayed in Fig. 2. Surface grinding tests were carried out on a high-speed surface grinder (PROFIMAT MT 408) with the capabilities of workpiece infeed speed ranging from 15 mm/min to 25 m/min, the maximum spindle power of 45 kW, the highest revolution of 8000 rpm. Besides, the coolant with pressure of 15 MPa and flowrate of 90 L/min was utilized; as such, the effect of grinding temperature on grain wear could be generally ignored due to the excellent cooling condition. The cub-octahedral diamond grains [9, 14] in 35/40 mesh size with regular shape were used for the purpose of controlling the cutting edge more easily. According to Ref. [14], the wear resistance of a diamond grain usually differs significantly when grinding with different crystal faces, where crystal face (100) shows a better performance than that at crystal face (111). In order to keep a constant grinding condition, the diamond grains were controlled at the particular crystal face (100) from the top view. Under such conditions, each diamond grain would have a better wear resistance to work for a longer time in single grain grinding. Besides, in each grinding test, only one cutting edge for each diamond grain perpendicular to the wheel speed direction was used. Therefore, the present single grain grinding operation is similar to the conventional cutting operation (such as milling) which uses a tool with fixed geometrical shape and angles. As a result, in the current work, it is generally reasonable to refer to the tool wear behavior in the micro-milling operations (such as, Ref. [16-19]) to discuss the grain wear behavior during grinding. Wheel Grain holder
LabVIEW
Ag-Cu-Ti alloy
vs Diamond grain
Data capture
Kistler 5018 charge amplifier
Kistler 9317C
Singles amplifier
Undeformed chip
AE sensor
Top view ap Workpiece Clamp Dynamometer Worktable vw
Fig. 2
Cutting edge vs Material flowing direction Crystal face Crystal face (111) (100)
Schematic diagram of the present single grain grinding operation.
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Wheel ds agmax vs
ap Workpiece vw
Fig. 3
Schematic diagram of wedge-shaped chips.
A single diamond grain was brazed with Ag-Cu-Ti alloy on a steel holder, which was mounted to a steel block with screws. The assembled components were then fixed in a V-shaped slot of the wheel substrate. The workpiece material was nickel-based superalloy Inconel 718. Prior to the single grain grinding tests, a precision surface grinding had been carried out using alumina wheels on the workpiece in order to obtain the required ground surface roughness, such as Ra 0.4 μm. In the trials, the single diamond grain was precisely preset by using an acoustic emission instrument (DITTEL AE6000). The grinding force was measured in different grain wear stages by the three components piezoelectric dynamometer (KISTLER 9317C) attached with a charge amplifier (KISTLER 5018). The radius of the cutting edge circle of single diamond grains applied has been measured using an atomic force microscope (AFM). The dimension of the radius was nearly 0.54 μm. For this reason, tests were conducted in grain wear-free status to better understand the material removal process. A parametric study has been first conducted under various UCT values, ranging from 0.16 to 1 μm. Then, in order to comprehensively investigate the grain wear behavior, the UCT values were set at three different levels, such as 0.2 μm, 0.5 μm and 1 μm. For generation of wedge-shaped chips as shown in Fig. 3, the required workpiece infeed speed could be calculated according to the following formula [15]:
agmax 2
vw vs
ap
(1)
ds
where λ is the spacing between active grains (taking λ=πds/2 here), agmax is the UCT, vw is the workpiece infeed speed, vs is the wheel speed, ap is the depth of cut and ds=390 mm is the wheel diameter. Table 1 lists the parameters applied in the present grinding tests with single diamond grains.
Table 1
Grinding process parameters Values
Process parameters
Grain wear-free
Undeformed chip thickness (UCT) agmax (μm)
Grain wear
0.16-1
0.2, 0.5, 1
Depth of cut ap (mm)
0.02
0.02
Wheel speed vs (m/s)
30, 50, 80
30
16.4-223.5
20.5, 51.3, 102.6
Workpiece infeed speed vw (mm/min) Grinding mode
Up grinding, water based coolant
During the grain wear experiment, for each group of grinding parameters, the grinding force has been first collected in every two passes (each pass length is 60 mm). From the ninth pass, reading of the grinding force was carried out for every three passes. During the whole grinding tests, after each force reading, the diamond grain morphology has been recorded with the 3D optical profiler (SENSOFAR S NEOX) by disassembling the grain holder from the wheel substrate. The grain wear morphology has been characterized quantitatively in each test. Since each grain size is different in different test, the specific material removal volume (SMRV) ΔV′ is used to evaluate the amount of material
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removed:
V ' V / b a p L
(2)
where V is the material removal volume, b is the groove width which is different for different grain, ap=0.02 mm is the depth of cut in the current experiment, and L is the length of the total grinding pass. The pile-up ratio, which is defined as the ratio of the total pile-up area to the total groove section area, is a sound method to quantify the material removal behavior [7]. As illustrated in Fig. 4, the pile-up areas are B1 and B2, and groove section area is characterized by A. Thus the pile-up ratio Rs could be expressed as:
Rs ( B1 B2 ) / A
(3)
In order to obtain the values of pile-up ratio, the cross-section profiles have been measured three times along the workpiece longitude direction by using 3D optical profiler for each test. Then, AutoCAD has been used to reconstruct the cross-section profiles and the average value of these three pile-up ratios has been calculated. Cutting out
Cutting in
A B1 Fig. 4
B2
3D morphology and cross-section profiles of a single grain grinding surface.
3 Results and discussion 3.1 Material removal characteristics in the case of grain wear-free In general, the grinding-workpiece contact could be separated into three stages: rubbing, ploughing and cutting [20-22]. In rubbing, only elastic deformation occurred, in which each grain slides on the material with small penetration into the workpiece. When the grain penetrates deeper into the workpiece, ploughing occurs in both elastic and plastic deformation form, where the scratch becomes more evident with ridges formed on both sides. As the grain further penetrates, the material is removed rapidly and chip formation takes place [15]. Since the pile-up ratio reflects the material removal ability, it is obtained at different UCT values under grain wear-free condition to identify different material removal stages, as shown in Fig. 5. Obviously, if the UCT value is smaller than 0.3 μm, the pile-up ratio increases gradually with increasing of UCT values. That is to say, more materials are left over the workpiece surface, which indicates that the ploughing stage dominates. Once the UCT value reaches 0.3 μm, the pile-up ratio drops rapidly. Then, it remains a constant as the UCT value is larger than 0.4 μm. In this case, the amount of left pile-up material has decreased for the reason that the workpiece material is mainly removed as chip formation rather than the pile-up around the scratch groove. Thus, a critical UCT value ag, critical, i.e., about 0.3 μm, can be identified for nickel-based superalloy Inconel 718, which can be expressed as:
ag ,critical 0.56re where re is the radius of cutting edge.
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(4)
0.30 vs=30m/s
0.28
vs=50m/s
Pile-up ratio Rs
0.26 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.0
0.2 0.4 0.6 0.8 1.0 Undeformed chip thickness agmax (μm) Fig. 5 Pile-up ratio versus UCT.
Specific grinding energy es (J/mm3)
35
Grinding force F (N)
30 25 20 15 vs=30m/s, Ft
10
vs=30m/s, Fn
5
vs=80m/s, Ft vs=80m/s, Fn
0 0.2
vs=30m/s vs=80m/s
500 400 300
es=110a-0.83 gmax
200 100 0 0.0
0.4 0.8 1.2 1.6 2.0 Undeformed chip thickness agmax (μm) (b) Specific grinding energy Size effect on grinding force and specific grinding energy.
0.4 0.6 0.8 1.0 1.2 Undeformed chip thickness agmax (μm) (a) Grinding force Fig. 6
600
Moreover, by comparing the measured grinding force at different values of UCT (Fig. 6(a)), it could be found that the grinding force varies in two different stages due to the different material deformation characteristics in grinding, which agrees well with the results of Hahn [23]. On one hand, when the UCT value is less than 0.3 μm, the grinding process is in rubbing and ploughing stages where the material is frictioned and pulled along the front and side faces of a grain. On the other hand, in the case of the UCT larger than 0.3 μm, chip formation takes place and the material removal increases rapidly. The definition of critical UCT value from the variations of pile-up ratio and grinding force can be interpreted from the specific grinding energy. In the current grinding tests, the undeformed chip is in a wedge shape, which can be approximated as a triangle. The specific grinding energy es is defined as the energy consumed to remove per unit volume of material, which can be expressed as:
es W / V ( Fl t s ) / (ag max ls b / 2) 2 Ft / (ag max b)
(5)
where W is the energy consumption to remove the material in a single grain-workpiece contact zone, V is the volume of undeformed chip material to be removed, ls=(apds)1/2 is the length of grain-workpiece contact zone and b=0.3 mm is the width of the undeformed chip. It is reported that, the specific grinding energy is consumed by means of primary and secondary rubbing energy, ploughing energy and chip formation energy [24]. Among them, the ploughing energy and chip formation energy are constant for the determinate material, which are determined by the material mechanical properties, such as dynamic yield shearing strength and workpiece hardness. However, the rubbing energy is inversely proportional to the UCT. According to Eq. (5), the variation of specific grinding energy with increasing UCT is plotted in Fig. 6 (b). Obviously, the specific grinding energy obeys the typical size effect rule in grinding. In case of a small UCT (<0.3 μm particularly),
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the specific grinding energy has larger values and decreases quickly with the increase of UCT, which indicates that it is mainly composed of the high rubbing energy and relatively low ploughing energy. However, as the UCT value gets larger, the specific grinding energy decreases at a slower rate, which shows the grinding process mainly consists of the cutting stage with small cutting energy. Based on the results shown in Fig. 6(b), the relationship between specific grinding energy and UCT could be calculated by Eq. (6):
es 110ag0.83 max
(6)
3.2. Classification of grain wear behavior in single grain grinding In general, during the single grain grinding of Inconel 718, the diamond grain wear behavior shows mainly four types: crescent depression on the rake face, abrasion on the flank face, grain micro-fracture, and grain macro-fracture, as schematically displayed in Fig. 7 and 8. The grain wear behavior obtained at different UCT values in the current investigation are tabulated in Table 2. It shows the wear evolution of diamond grains could be divided into two stages: (i) the initial wear stage, acting as the formation of crescent depression on the rake face and the abrasion wear on the flank face; (ii) the steady wear stage, in which the wear behavior on the rake and flank face is dramatically influenced by different UCT values. Crescent depresion
Abrasion
Cutting edge Flank face Rake face
Grain microfracture
Fig. 7 Abrasion
Grain macrofracture
Classifications of grain wear behavior. Grain macro-fracture
Grain micro-fracture New rake face
vs vs Cutting edge
Cutting edge
(b) agmax=0.5 μm, ΔV’=22.2 mm3/mm
(a) agmax=0.2 μm, ΔV’=5.44 mm3/mm Abrasion
Crescent depression
vs Cutting edge
(c) agmax=1 μm, ΔV’=2.88 mm3/mm
Fig. 8
Morphology of grain wear in the single grain grinding.
-7-
Table 2 Grain wear behavior at given UCTs. Classification agmax=0.2 μm agmax=0.5 μm agmax=1 μm Crescent depression no yes yes Abrasion yes yes yes Grain micro-fracture yes yes no Grain macro-fracture yes yes no
According to the deduce of the critical UCT value in Section 3.1, the rubbing, ploughing and cutting stages at UCT of 0.2, 0.5 and 1 μm are schematically shown in Fig. 9. Obviously, the percentage of these three stages in the grain-workpiece contact zone is significantly different. When only the rubbing and ploughing stages take place in the grinding process, as shown in Fig. 9(a), the stress concentration on the cutting edge is so severe that abrasion and grain fracture appear, due to the attritious wear on the flank face and the spring-back effect from the elastic deformation of the ground surface material, respectively. However, no crescent depression occurs because chip formation of the material is rather difficult which is necessary in the rake face attritious wear. Seen from Fig. 9(b), when the dwell time of cutting stage is approximately the same as that of the rubbing and ploughing stages, the removed chips flow on the rake face, which increases the crescent depression caused by the frictional interaction with removed chips. When the cutting stage dominates, as displayed in Fig. 9(c), most of the load is shared by the rake face. Thus, the spring-back effect from ground surface in rubbing and ploughing stages is too weak to fracture the grains. Theoretically, according to the increasing of SMRV, the grain wear behavior could be interpreted in Fig. 10 based on the experimental results. Rubbing and ploughing
ag,critical
agmax
Accumulated material
(a) agmax=0.2 μm Cutting
Rubbing and ploughing Chip
agmax
ag,critical
(b) agmax=0.5 μm Chip
Cutting Rubbing and ploughing
agmax
ag,critical
(c) agmax=1 μm Fig. 9
Schematic diagram of the rubbing, ploughing and cutting stages. N e wc u t t i n g e d g ec i r c l e
Wear platform
crescent d epres sio n
Broken W ear pa ltform
R a k ef a c e wear
Rake face wear
vs
Flank face wear
C utt ing ed g e circle
vs
Flank face we ar
(a) agmax=0.2 μm (b) agmax=1 μm Fig. 10 Schematic diagram of wear behavior of diamond grain in the case of UCT of 0.2 and 1 μm.
3.3. Analysis of grain wear behavior from the viewpoint of grinding force Fig. 11 shows the relationship between grinding force and SMRV at three given levels of UCT in the present investigation. With the increase of SMRV, the normal grinding force Fn and tangential grinding force Ft tend to increase first and then keep stable. However, the growth rate of the grinding force is different at each level of UCT values. When the UCT is 0.2 or 0.5 μm, the grinding force rises up at a relatively higher growth rate in the initial wear stage. Moreover, the growth rate at the UCT of 0.2 μm is higher than that at 0.5 μm. This indicates stress concentration on the
-8-
cutting edge is more prominent in the case of small UCT, which rapids the grain wear and the increase of grinding force. When the UCT further increases to 1 μm, the load mostly acts on the rake face. Thus, the grain wear around the cutting edge is not remarkable. Under such conditions, the grinding force increases slowly in the initial wear stage. However, when the SMRV reaches 6.8 mm3/mm, due to the appearance of crescent depression on the rake face, the grinding force grows quickly with a growth rate approximate to that in the case of UCT of 0.5 μm. 120
Grinding force F (N)
100 80 60 agmax=0.2μm, Ft agmax=0.2μm, Fn
40
agmax=0.5μm, Ft agmax=0.5μm, Fn
20
agmax=1.0μm, Ft agmax=1.0μm, Fn
0 0
5
10
15
20
25
30
Specific material removal volume V' (mm3/mm)
Fig. 11
Grinding force versus SMRV.
The changes of grinding force with increasing SMRV could be attributed to the grain wear behavior. When the UCT is 0.2 μm, seen from Fig. 12(a), since small chips are generated by removing material, more and more material accumulates on the rake face. Due to the stress concentration on the cutting edge, grain wear takes place quickly. As a result, the grinding force rises up at a large growth rate. Once the new rake face is formed, the amount of accumulated material keeps nearly a constant, which stabilizes the grinding force. Because of the continuous formation of new rake faces in the grain wear procedure, the grinding force fluctuates between 50 and 70 N. When the UCT is 0.5 μm, as displayed in Fig. 12(b), the crescent depression on the rake face keeps expanding in the early stage, which results in the increase of contact area between a grain and flowing chips. Thus, the grinding force gradually increases first and then remains stable until grain fracture appears around the cutting edge. When the UCT reaches at 1 μm, the crescent depression forms gradually in the initial wear stage, making the amount of flowing chip vary slightly, as demonstrated in Fig. 12(c). Therefore, the grinding force increases slowly. However, because the abrasion wear of a diamond grain on the flank face is getting serious, the load on the cutting edge is increased, which results in the suddenly expanded crescent depression. While the crescent depression disappears gradually with the increase of SMRV, the negative rake angle is enlarged. As a result, the grinding force increases. At last, once the crescent depression is completely transferred into the new sharp cutting edge, the grinding force remains stable.
Accumulated material
β1 Accumulated material
Accumulated material
β2
vs
vs
Accumulated material Grain microfracture
β3
β4 Grain macrofracture
vs
β1 ≈β2 ≈ β3 ≈ β4
vs
(a) agmax=0.2 μm
C h i p β1
C h i p β2
β23
Chip G r a i n m i c- r o fra ct ure
Chip vs
vs
β1 <β2 ≈ β3 ≈ β4
(b) agmax=0.5 μm
-9-
vs
β4
G r a i n m a c- r o frc ture vs
Chip
β1
Chip
vs
Fig. 12
Chip
β2 vs
β1 ≈ β2 <β3 ≈ β4
Chip
β3
β4
vs
vs
(c) agmax=1 μm Schematic diagram of material removal behavior and the variation of the negative rake angle in grinding.
It could be found by further analysis of grinding force that, when the grinding force remains stable, the SMRV values are different at three levels of UCT. The critical values are 8.16, 14.4 and 21.84 mm3/mm at the UCT of 0.2, 0.5 and 1 μm, respectively. It is inferred that, by increasing the UCT value, more material would be removed when the grinding force becomes stable in the wear process. That is to say, the grain wear rate would be effectively reduced if the UCT is increased to twice the radius of cutting edge circle. 3.4 Relationship between grinding force ratio and negative rake angle in grain wear process Fig. 13 provides the relationship between grinding force ratio and the SMRV at different UCT values. Obviously, when the UCT is 0.2 μm, the grinding force ratio always fluctuates between 0.9 and 1.2. When it is 0.5 μm, the grinding force ratio first increases gradually, and then remains around 1.08 when the SMRV increases to 10 mm3/mm. When the UCT is 1 μm, the grinding force ratio first keeps a constant of 0.82 until the SMRV reaches at 10 mm3/mm, then gradually rise up to 1.12 with the SMRV increases to 20 mm3/mm, and finally they remain constants again at 1.12. It could be inferred from the grain wear behavior and the variation of grinding force ratio that, the gradually disappeared crescent depression on the rake face would result in the increase of actual negative rake angle, which is diagrammed in Fig. 12. In the case of UCT of 0.2 μm, since the workpiece material always presses the cutting edge, the rake and flank faces wear synchronously, as displayed in Fig. 10(a). Thus, little change in the negative rake angle (β1≈β2≈β3≈β4) makes the grinding force ratio a constant, as shown in Fig. 12(a). While in the case of UCT of 0.5 μm, seen from Fig. 12(b), the negative rake angle is enlarged (β1<β2) due to the expanding of crescent depression in the initial wear stage. When the grain fracture happens around the cutting edge, the rake and flank faces also wear synchronously, which causes the negative rake angle change slightly (β2≈β3≈β4). However, when the UCT is 1 μm, the generated crescent depression is insignificant in the beginning, so the negative rake angle doesn’t alter very much (β1≈β2), as displayed in Fig. 12(c). Once the crescent depression disappears gradually, the negative rake angle is increased (β2<β3). Finally, the negative rake angle remains a constant (β3≈β4) again as the new cutting edge is generated.
Grinding force ratio Fn/Ft
1.4 1.2 1.0 0.8 agmax=0.2μm agmax=0.5μm
0.6
agmax=1.0μm
0.4 0 5 10 15 20 25 30 Specific material removal volume V' (mm3/mm) Fig. 13 Grinding force ratio versus SMRV.
The specific grinding force Fp is defined as the force per unit area in the grain moving direction. The forces on the two sides of a grain are balanced out by each other. Only the forces on rake face are considered, as diagramed in Fig. 14.
- 10 -
dFx
A
A
Y X
Cutting direction A-A dFx,n
β
dFfr,t
dFfr,n Fig. 14
dFx dFx,t
ag
dFfr
Grinding force model in single grain grinding.
In every cross-section X-X, the grinding force dFx perpendicularly loads on the rake face, which is calculated by :
dFx Fp dA cos
(7)
where β is the negative rake angle. The cell area in the grain-workpiece contact zone is:
dA ag dy cos
(8)
where ag is the actual cutting depth of the grain. Thus, Eq. (7) can be rewritten as:
dFx Fp ag dy
(9)
According to the grinding force model shown in Fig. 14, the force dFx could be decomposed into the force along and perpendicular to the cutting direction, which are written as:
dFx,t dFx cos
(10)
dFx,n dFx sin
(11)
The total friction force along the grain rake face dFfr makes the formed chip flowing out of the grain-workpiece contact zone, which is defined as:
dFfr dFx
(12)
where μ is the friction coefficient and the value is 0.23 [25]. As such, the friction force can also be decomposed into the force along and perpendicular to the cutting direction, which are expressed as follows:
dFfr ,t dFfr sin
(13)
dFfr ,n dFfr cos
(14)
Finally, by combining the component forces, the tangential and normal forces on the sampling unit of a single grain are calculated as:
dFtg dFx,t dFfr ,t (cos sin ) Fp ag dy
(15)
dFng dFx,n dFfr ,n (sin cos ) Fp ag dy
(16)
- 11 -
Thus, considering that the actual load width of a single grain is a, the total grinding force on the whole grain is integrated as: a
Ftg 2a dFtg Fp aag (cos sin )
(17)
Fng dFng Fp aag (sin cos )
(18)
2 a 2 a 2
Commonly, the grinding force ratio ε is used to reflect whether a grain is blunt or not. From the given grinding force model in this article, it can be calculated as:
Fng / Ftg
sin cos tan cos sin 1 tan
(19)
which can be further rewritten as:
1
2 1 (1 tan )
(20)
According to Eq. (20), it is obvious that, with the increase of the negative rake angle β, the grinding force ratio ε is getting larger. In other words, a diamond grain is becoming blunt due to the grain wear behavior on the rake face. The calculated grinding force ratio in case of agmax=1 μm under the condition of negative rake angle ranging from 51.5° to 60.5° are provided in Fig. 15. Obviously, the calculated results match very well with the tested data in an error less than 5%. During the increasing of SMRV from 6.8 to 21.84 mm3/mm, the measured negative rake angles are 51.8°, 54°, 57°, 59° and 60.6°, while the corresponding calculated grinding force ratio are 0.8, 0.87, 0.97, 1.04 and 1.1, compared with tested values of 0.83, 0.9, 1.05, 1.05 and 1.16. 1.2
Grinding force ratio
Tested Calculated
1.1 1.0 0.9 0.8 0 5 10 15 20 25 30 Specific material removal volume V' (mm3/mm)
Fig. 15 Comparison of the tested and calculated grinding force ratio in the case of agmax=1 μm
3.5 Influence of grain wear behavior on material removal process In Section 3.1, the chip formation characteristics are discussed in the grain wear-free status. However, the material removal ability has decreased due to the attritious wear. In order to further investigate the influence of grain wear behavior on material removal process, the cross-section profiles of the scratch marks are obtained in different grain wear stages first; and then the pile-up ratio are discussed according to the increasing SMRV. The cross-section profiles in various single grain grinding conditions are shown in Fig. 16. Obviously, as expected, due to the blunt of a single grain, there is a clear tendency of large material pile-up manifested as pronounced higher and wider shoulders for all the UCT values, accompanied with a large groove width, thus constituting an extent of material rebuild rather than removal. Nevertheless, distinctly different material pile-up characteristics are produced at the given UCT values: a larger UCT value results in less amount of material pile-up in the sharp grain condition (Fig.
- 12 -
16(a), (c) and (e)); that is likely due to a longer period of cutting stage, rather than rubbing and ploughing stages at UCT values of 0.5 and 1 μm, to cut the material across the whole cross-section resulting in minor material rebuild. Furthermore, it is noticed from Fig. 16(b), (d) and (e) that, the shape of the scratch cross-section bottom changes from a line to an irregular curve or an arc due to the wear of cutting edge. The reason can be interpreted from two aspects: one is the grain fracture caused by the spring-back effect of material elastic deformation in the rubbing and ploughing stages, e.g. at the UCT values of 0.2 and 0.5 μm; the other is the abrasion at the two corners of the cutting edge due to stress concentration, e.g. at the UCT values of 0.5 and 1 μm. In addition, when a grain has been seriously worn, the pile-up area is bulk in case of a bigger value of UCT. That is because of the regenerated multi cutting edges caused by grain fracture at UCT of 0.2 μm, which facilities to cut the material more efficiently and results in narrow scratch shoulders. However, compared with multi cutting edges, the cutting efficiency in the case of abrasion at the two corners 16 12 8 4 0 -4 -8 -12 -16 -20 -24 300 400 500 Width Y (μm) (a) agmax=0.2 μm, ΔV’=2.72 mm3/mm
200
300 400 500 600 Width Y (μm) (b) agmax=0.2 μm, ΔV’=25.84 mm3/mm
600
30
30
20
20
Height Z (μm)
Height Z (μm)
100
10 0 -10
100
200
-10
-30
-30 200 300 400 500 Width Y (μm) (c) agmax=0.5 μm, ΔV’=2.8 mm3/mm
200
0
-20
100
100
10
-20
0
300 400 500 600 Width Y (μm) (d) agmax=0.5 μm, ΔV’=22.2 mm3/mm
600
20
20
15
15
10
10
Height Z (μm)
Height Z (μm)
16 12 8 4 0 -4 -8 -12 -16 -20 -24
Height Z (μm)
Height Z (μm)
of the initial cutting edge is low that the pile-up shoulders exhibits a little flat-wide.
5 0 -5 -10
5 0 -5
-10
-15
-15
-20
-20
-25 0
100
200 300 400 Width Y (μm)
500
-25
600
0
(e) agmax=1 μm, ΔV’=2.88 mm3/mm Fig. 16
100
200 300 400 500 Width Y (μm) (f) agmax=1 μm, ΔV’=29.52 mm3/mm
600
Influence of gain wear behavior on cross-section profiles.
The pile-up ratio at various increasing SMRVs are calculated, so as the measured widths of new rake face and
- 13 -
crescent depression. As shown in Fig. 17(a), when the grinding process mainly consists of rubbing and ploughing stages, the pile-up ratio varies nearly in the same tendency as the width of new rake face, and this trend results from the growing length of grain-workpiece contact zone on the rake face. Thus, bulk material rebuild and minor material removal occur. However, according to the decreased pile-up ratio, it is known that the regenerated multi cutting edges due to grain fracture at SMRV of 8 mm3/mm can improve the material removal ability. On the other hand, as shown in Fig. 17(b) and (c), the cutting stage dominates in grinding. The pile-up ratio is increased because of the increase of crescent depression on the rake face. It is noted that, the pile-up ratio increases rapidly when the width of the crescent depression is diminished (e.g. in the range of SMRV from 8 to 15 mm3/mm in case of UCT of 0.5 μm; from 14 to 22 mm3/mm in case of UCT of 1 μm). This is due to the increasing negative rake angle in the absence of crescent depression, as a result of lower MMR and enlarged grinding force ratio. Furthermore, when the pile-up ratio reaches about 0.33, the grain wear is expanded from rake face to the two corners of the cutting edge because of the enlarged scratch shoulders. At this time, the material removal behavior improves a bit due to the better material flowing ability around the corners. Besides, it could also be found that, before the material removal efficiency decreases obviously, the value of SMRV for high material removal efficiency (Rs<0.1) is increased with a bigger UCT (i.e. 5, 11, and 15 mm3/mm in case of 0.2, 0.5 and 1μm, respectively), which is attributed to a lower grain wear rate using relatively larger UCT as mentioned in
Pile-up ratio Rs
15 0.16 0.12
10
0.08 5 0.04 0.00
0.30
0
0 5 10 15 20 25 30 Specific material removal volume V' (mm3/mm) (a) agmax=0.2 μm 0.35
Pile-up ratio Rs
0.30
20 Rs
19
Wc
0.25
18
0.20
17
0.15
16
0.10
15
0.05
14
0.00
13
0 2 4 6 8 10 12 14 16 18 20 22 Specific material removal volume V' (mm3/mm) (b) agmax=0.5 μm 35
Rs Wc
30
0.25 0.20
25
0.15
20
0.10 15
0.05 0.00
10
0 5 10 15 20 25 30 Specific material removal volume V' (mm3/mm)
Width of the crescent depression Wc (μm)
Wr
0.20
0.35
Pile-up ratio Rs
20 Rs
Width of the new rake face Wr (μm)
0.24
Width of the crescent depression Wc (μm)
Section 3.3.
(c) agmax=1 μm Fig. 17 Relation between pile-up ratio and rake face wear.
4 Conclusions The influence of grain wear on material removal behavior has been discussed by the means of the single grain grinding operation on nickel-based superalloy Inconel 718. The key findings can be summarized as follows: (1) In the case of grain wear-free, a critical value of UCT about 0.3 μm is identified through the analysis of pile-up
- 14 -
ratio which is used for quantifying the material removal process. The grinding force and specific grinding energy in the single grain grinding greatly obey the size effect rule. (2) The grain wear behavior mainly shows as four types: crescent depression on the rake face, abrasion on the flank face, rain micro-fracture, and grain macro-fracture. The dwell time of rubbing, ploughing and cutting at different UCT values determines the grain wear types. (3) According to the constructed grinding force model, it is the increasing negative rake angle that enlarges the grinding force ratio, which lowers the material removal ability. (4) During the single grain grinding, the material removal efficiency is proportional to the wear width on the grain rake face in rubbing and ploughing stages. However, it is diminished in the absence of crescent depression in cutting stage. At the same time, the grain fracture and abrasion of cutting edge corners can improve the material removal to a certain extent. Acknowledgments The authors gratefully acknowledge the financial support for this work by the National Natural Science Foundation of China (No. 51235004 and No. 51375235), the Fundamental Research Funds for the Central Universities (No. NE2014103).
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Research Highlights
Material removal characteristics in the case of grain wear-free are provided. Classification of grain wear behavior in single grain grinding is analyzed. Grain wear behavior from the viewpoint of grinding force is discussed. Relationship between grinding force ratio and negative rake angle in grain wear process is confirmed. Influence of grain wear behavior on material removal process is discussed.
- 16 -
Graphical abstract
Wheel Grain holder
LabVIEW
Ag-Cu-Ti alloy
vs Diamond grain
Data capture
Kistler 5018 charge amplifier
Kistler 9317C
Singles amplifier
Top view
Undeformed chip
ap Workpiece
AE sensor
Clamp Dynamometer Worktable vw
Fig. 2
Cutting edge vs Material flowing direction Crystal face Crystal face (111) (100)
Schematic diagram of the present single grain grinding operation.
- 17 -