elevated temperatures in the grinding zone which can cause thermal damage to the workpiece and accelerated wheel wear. Grinding fluid helps to reduce these ...
Proceedings of the ASME 2014 International Manufacturing Science and Engineering Conference MSEC2014 June 9-13, 2014, Detroit, Michigan, USA
MSEC2014-3971
PREDICTIVE FORCE MODELING IN MQL (MINIMUM QUANTITY LUBRICATION) GRINDING Yamin Shao, Steven Y. Liang Georgia Institute of Technology George W. Woodruff School of Mechanical Engineering Precision Machining Research Center (PMRC) Atlanta, GA, USA KEYWORDS Grinding force modeling, Minimum quantity lubrication, Single grit interaction, Wheel topography
elevated temperatures in the grinding zone which can cause thermal damage to the workpiece and accelerated wheel wear. Grinding fluid helps to reduce these undesirable thermal effects by providing lubrication to reduce the amount of energy generated and through direct cooling of the workpiece by convection [2]. However, economic and environmental drawbacks have been noticed for conventional flood cooling. Researchers have been seeking for alternative cooling methods such as MQL. MQL refers to the use of grinding fluids of only a minute amount, typically of a flow rate of 50 to 500 ml/hour. This is about three to four orders of magnitude lower than the amount commonly used in flood cooling condition, where, for example, up to 10 liters of fluid can be dispensed per minute [3]. The lubricant medium is usually mixed with pressured air for delivery to the grinding zone. Although the concept of MQL has been brought about 2 decades ago, MQL grinding is still a relatively new research area and has only been studied by a few researchers [4-8]. Most current researches on MQL grinding are empirical analyses which lack physical understanding of the process. In this paper, an analytical approach is established to calculate the grinding force under MQL grinding conditions. The single grit interaction is first investigated. From an analytical point of view, the grinding forces are generated by single grit contacts. In this sense, the cutting processes such as turning or milling and grinding are comparable and intrinsically the same phenomena. The single grit force model is adapted from previous works [9,10]. Next, the single grit interaction is extrapolated to all grits on the grinding wheel surface by topography modeling. To address the influence of MQL, the friction coefficient is calculated based on the boundary lubrication model [11]. For validation, the predicted grinding forces are compared with experimental data in the grinding of
ABSTRACT Using grinding fluid is the most common strategy to generate cooling and lubrication during the grinding process. However, economic and environmental drawbacks have been noticed for conventional flood cooling. MQL, which is to apply minimum amount of lubricant directly into the contact zone, is an alternative to deal with those concerns. In order to advance the MQL technique into practical manufacturing situations, understanding of the process and evaluation of the performance is necessary. This paper presents the predictive modeling of MQL grinding force through considerations of boundary lubrication condition, single grit interaction, wheel topography, material properties, and dynamic effects. The friction coefficient was first calculated based on boundary lubrication theory. Subsequently, the single grit interaction is studied considering both chip formation and ploughing mechanisms. Then the undeformed chip thickness distribution and dynamic grit density has been calculated for extrapolating the single grit interaction to the whole wheel. Finally, the predicted tangential and normal forces were presented and compared to surface grinding experiment data. INTRODUCTION Grinding is an important finishing process for components requiring high dimensional accuracy and surface integrity. It is one of the major manufacturing processes in industry which accounts for 20% to 25% of the total expenditures on machining operations [1]. Grinding process requires an extremely high energy input per unit volume of material removal and the majority of this energy is converted to heat. This leads to
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AISI 1045 steel with 36A120-KVBE wheel under MQL conditions.
n0
z
PROPOSED GRINDING FORCE MODELING Friction coefficient in MQL grinding based on boundary lubrication theory A prominent effect of the applied air-oil mixture in MQL is lubrication which changes the friction coefficient in the single grit contact. In MQL grinding, due to the limited amount of lubricant, the lubricant film is not fully established. Therefore, the boundary lubrication theory is a more proper description of the MQL condition instead of hydrodynamic lubrication. In boundary lubrication, part of the load is carried by the metallic contacts between asperities on both surfaces and the other part is carried by adsorbed lubricant film contact. The friction coefficient in boundary lubrication can be calculated [11]:
C1as3 C2C3 as tb as3 as3
C2
3
a t s
3
b
as3
(1)
W
pm Q
where
Q
0
A0
Contact area (mm2)
W
Normal load (N)
pm
Yield pressure of metallic contact area (MPa)
A0 z 2 20 From calculation From calculation Material property
Single grit interaction model It is found by many researchers [12,13] that the single grit interaction is dominated by high negative rake angle and high strain rate. In addition, since the size of the grit is very small and there is a possibility for wear flat, the cutting edge radius must be addressed in modeling the shape of the grits. In this study, the grit shape is assumed to be conical with a rounded tip. Due to the large ratio of tool radius to the cutting depth of single grit, the ploughing effect is significant [14]. A critical cutting thickness [10] has been defined as a critical value below, which the workpiece material is deformed by the ploughing mechanism, and above, which is deformed by chip formation. Assuming that the single grit cutting process is orthogonal by treating the created chip as a series of elements with infinitesimal width, the individual grit grinding can be simplified as a 2-D material removal process involving chip formation and ploughing, as shown in Figure 1.
where the approach of two surfaces as is estimated from the cubic function: as3 3C2 tb as2 3C2 tb2 as C2 tb3
Total asperity number Linear distribution density of asperities per unit length (mm-1)
(2)
Rn0 D 2 2 6 H max
The physical meanings and representative values of the parameters above are given in Table 1. TABLE 1 – PHYSICAL MEANINGS AND REPRESENTATIVE VALUES OF THE PARAMETERS
Parameter tb C1 C2
C3
H max
Physical meaning Adsorbed lubricant film thickness ( m) Coefficient for shearing strength at metallic contact area Coefficient for mean contact pressure at adsorbed lubricant film contact area Coefficient for shearing strength at adsorbed lubricant film contact area Distribution height of asperities ( m)
Representative value 0.2
FIGURE 1 - SINGLE GRIT INTERACTION ILLUSTRATION
From calibration
Notice that all the rake angles here have negative values. The critical rake angle cr corresponds to the critical undeformed chip thickness tcr . When undeformed chip thickness t is larger than tcr , the material removal mechanism is chip formation. When t reaches tnom , the rake angle will be equal to the nominal rake angle which is calculated from the grit cone angle. This micro-cutting mechanism can be represented by applying the Merchant model to each of the infinitesimal elements. The incremental chip formation force can be expressed as:
0.5
0.5 10
R
Radius of asperity tip ( m)
20
D
Inclination of distribution function
1.5
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b cos( ) dFtg ,chip sin cos( ) dt1 b sin( ) dF dt1 ng , chip sin cos( )
The workpiece material below critical undeformed chip thickness is plastically deformed in front of the grit without chip formation. This phenomenon is referred to as the ploughing effect. Shaw [15] adapted a Brinell indentation hardness test to describe this mechanism since the behavior of material beneath a Brinell ball resembles the material deformation below a grit with a rounded tip. The Brinell hardness number, HB, is defined as the ratio of the load to the curved area of indentation: [16]
(3)
where is the workpiece material flow stress, b is the local cutting width, is friction angle, is local rake angle, is local shear angle. The local shear angle and local rake angle are related by cutting ratio rc .
rc
sin( ) cos( )
HB
(4)
In the grinding process, the plastically deformed zone by the singe grit rotates in the direction of movement. Therefore, the ploughing force can be calculated from the indentation force acting in the direction of half of the critical rake angle with respect to the normal direction. Additionally, a friction force between the grit and the workpiece is generated due to the relative movement. The tangential and normal ploughing forces per grit can thus be estimated by considering the indentation effect and the friction reaction as:
(5)
The local width is expressed as:
b 2r cos t tnom b 2 r cos nom tan( )
when t tnom when t tnom
(6)
cr cos cr Ftg , ploughing Fp sin 2 2 F Fp cos cr sin cr ng , ploughing 2 2
By integration of the incremental tangential and normal forces per unit width in the two dimensional simplified configuration, the chip formation force of each grit is calculated. The total tangential and normal force can thus be expressed as: When t tnom , s cos( ) 2r 2 cos2 d Ftg ,chip sin cos( ) cr s sin( ) 2 2 F ng ,chip sin cos( ) 2r cos d cr
(10)
The total single grit forces are the summation of chip formation forces and ploughing forces in tangential and normal direction. Wheel topography model The single grit interaction is extrapolated to all grits on the grinding wheel surface by topography modeling. Due to the randomness of grit distribution on the wheel surface, grits will have different engagement depth in the grinding process. The spectrum of undeformed chip thickness generated can be described by a Rayleigh probability density function [16].
(7)
When t tnom , nom cos( ) 2r 2 cos2 d Ftg ,chip sin cos( ) cr nom sin( ) 2 2 Fng ,chip sin cos( ) 2r cos d cr t tnom cos( nom ) t 2 r cos nom tan( ) dt1 sin cos( nom ) tnom t tnom sin( nom ) t 2 r cos nom tan( ) dt1 sin cos( nom ) tnom
(9)
Dt
where Fp is the indentation force.
From geometrical relationship, dt1 r cos d
Fp
t / 2 e t f (t ) 0
2
/2 2
t0
(11)
t0
The expected value and variance is expressed as: (8)
E ( h ) / 2 sd (h ) 0.429
(12)
The parameter , that completely defines this p.d.f., was calculated as a function of the grinding wheel microstructure (grain shape, static grit density), dynamic effects (local grain
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1045 steel with a width of 9.5mm. The grinding wheel used for the experiments was Norton 38A120-KVBE aluminum oxide friable wheels. The wheel was dressed by Norton single point diamond dresser with 16 of dressing depth. Kistler 9257b dynamometer and compatible data acquisition system were used to record the grinding forces. The experiment setup is shown in Figure 3.
deflection and wheel-workpiece contact deflection), and grinding conditions (wheel depth of cut, wheel and workpiece tangential velocity).
aVw 1 t2 1 cr 2Vs lcCd tan( ) 2
(13)
where a is wheel depth of cut, Vs is wheel speed, Vw is workpiece speed, lc is the real contact length due to wheelworkpiece contact deformation, and Cd is the dynamic grit density. The calculation details can be found in [16]. The variables lc and Cd depend on the dynamic effects governed by the force developed between the wheel and the workpiece, which at the same time is determined by the undeformed chip thickness. This cross relationship results in a complicated mathematical problem. The iterative approach is employed to calculate the undeformed chip thickness distribution and single grit force at the same time. The overall algorithm for the force modeling is shown in Figure 2. FIGURE 3 - EXPERIMENT SETUP
The process parameters used to calibrate and validate the model are shown in Table 2. Figure 4 shows the simulated and the experimental forces for the calibration as well as the validation data for a different set of experiments. The prediction error is within 20%. TABLE 2 - MQL GRINDING EXPERIMENT CONDITIONS
Test No. Wheel speed (m/s) Feed rate (m/min) Depth of cut ( m)
FIGURE 2 - OVERALL ALGORITHM OF FORCE MODELING
MODEL VALIDATION A series of surface grinding experiments are conducted to validate the predicting models. Before conducting the grinding tests, the wheel surface topography was measured and characterized. There are several methods for measuring wheel surface statically such as profilometry methods, scratch methods, and microscopic methods [1]. In this project, Zygo white light interferometer was used to measure the 3D profile of a small area on the wheel surface. Due to the optical property of grit material, results of direct measurement are not desirable. The wheel surface profile was inversely measured by imprinting onto a polished lead plate. A series of experiments were performed on the Bridgeport GX480 Vertical Milling Center. The CNC milling center was used instead of the grinding machine for the following reasons: 1) simple set up of the measurement equipment, 2) precise control of spindle rotational speed up to 10000RPM, and 3) a positional accuracy of 0.0001in. The MQL system is manufactured by UNIST, Inc. with the lubrication medium of vegetable oil and flow rate of 396ml/hr. The workpiece is AISI
Calibration 1
2
Validation 3 4
31.92
31.92
15.96
31.92
2.03
2.03
2.03
4.06
15.24
7.62
7.62
15.24
FIGURE 4 - COMPARISON BETWEEN PREDICTION AND EXPERIMENT DATA
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CONCLUSIONS In this study, an analytical model to predict the forces under MQL grinding conditions is developed and validated. The physical understanding of the grinding process including force formation and wheel structure as well as the lubrication effect of MQL were built during the modeling process. The model is comprised of boundary lubrication model, single grit force analysis and wheel topography model. The effect of boundary lubrication on friction coefficient in the grinding zone was addressed first. Subsequently, the interaction between the workpiece and an individual single grit is studied considering both chip formation and ploughing mechanisms. For wheel topography modeling, a probabilistic expression of the undeformed chip thickness distribution with the calculation of dynamic grit density has been developed for extrapolating the single grit interaction to the whole wheel. In this analysis, convoluted relationships between several intermediate parameters take place in that the friction coefficient in boundary lubrication is governed by the force developed between the wheel and the workpiece and the contact geometry. Further, the undeformed chip thickness distribution and dynamic grit density is indirectly influenced by the single grit force. In the meanwhile, the single grit force is determined by the undeformed chip thickness and friction coefficient. The iterative procedure used during the simulation process was shown to be stable at various conditions. Surface grinding of AISI 1045 workpiece with aluminum oxide wheel under various process parameter combinations were pursued, and the predicted grinding forces were compared to experimental measurements and reasonable agreements in the context of magnitudes and trends were found.
grinding,” Proceedings of the International Seminar on Improving Machine Tool Performance, 2, pp. 643-654. [5] Silva, L.R., Bianchi, E.C., Catai, R.E., Fusse, R.Y., and Franca, T.V., 2005. “Study on the behavior of the minimum quantity lubricant - MQL technique under different lubricating and cooling conditions when grinding ABNT 4340 steel,” Journal of the Brazalian Society on Mechanical Sciences and Engineering, 27(2), pp. 192-199. [6] Tawakoli, T., Hadad, M.J., Sadeghi, M.H., Daneshi, A., Stockert, S., and Rasifard, A., 2009. “An experimental investigation of the effects of workpiece and grinding parameters on minimum quantity lubrication - MQL grinding,” International Journal of Machine Tools and Manufacture, 49(12-13), pp. 924-932. [7] Shen, B., and Shih, A.J., 2009. “Minimum quantity lubricatino (MQL) grinding using vitrified CBN wheels,” Transactions of the North American Manufacturing Research Institution of SME, 37, pp. 129-136. [8] Barczak, L.M., Batako, A.D.L., and Morgan, M.N., 2010. “A study of plane surface grinding under minimum quantity lubrication (MQL) conditions,” International Journal of Machine Tools and Manufacture, 50(11), pp. 977-985. [9] Park, H.W., and Liang, S.Y., 2008. “Force modeling of micro-grinding incorporating crystallographic effects,” International Journal of Machine Tools and Manufacture, 48(15), pp. 1658-1667.
FUTURE WORK Suggested future studies include the investigation on the influences of different MQL parameters such as lubricant flow rate, air pressure, and nozzle distance on the tribology behaviors. Furthermore, the thermal and surface integrity aspects of MQL influence on grinding could also be of future research interest.
[10] Son, S.M., Lim, H.S., and Ahn, J.H., 2005. “Effects of the friction coefficient on the mininum cutting thickness in micro cutting,” International Journal of Machine Tools and Manufacture, 45(4-5), pp. 529-535. [11] Kato, S., Marui, E., and Hashimoto, M., 1998. “Fundamental study on normal load dependency of friction characteristics in boundary lubrication,” Tribology Transactions, 41(3), pp. 341-349.
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[15] Shaw, M., 1996. “Principles of Abrasive Processing.” Oxford University Press, UK.
[16] Hecker, R.L., Liang, S.Y., Wu, X.J., Xia, P., and Guo, W.J., 2007. “Grinding force and power modeling based on chip thickness analysis,” International Journal of Advanced Manufacturing Technology, 33(5-6), pp. 449459.
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