Abstract: This study was developed the Finite Element Model (FEM) and Response Surface Method (RSM) to investigate the effect of milling parameters on frictions when milling Hastelloy C-22HS. This study gain better understanding of the friction distribution in metal cutting process. The RSM was used to minimize the number of simulation. The contour plot from RSM shows the relationship between input variables including the cutting speed, feed rate and axial depth and responses including the friction coefficient, friction angle, friction stress and friction force. Feed rate, axial depth and cutting speed play major role to generate high friction coefficient, friction angle, friction stress and friction force. When all the variables at highest value the friction stress become larger, on the other hand reduce the feed rate and increase other variable, it cause high friction coefficient, angle and force. The combination of numerical analysis and statistical method are very useful to analysis the distribution of friction in milling. It is suitable to use middle value of cutting speed, feed rate and axial depth when milling same type of materials.
INTRODUCTION
Milling is typically used to produce parts that are not axially symmetric and have many features such as holes, slots, pockets and even three dimensional surface contours. Parts that are fabricated completely through milling often include components that are used in limited quantities, perhaps for prototypes, such as custom designed fasteners or brackets. The milling process requires a milling machine, workpiece, fixture and cutter. The workpiece is a piece of pre-shaped material that is secured to the fixture, which itself is attached to a platform inside the milling machine. The cutter is a cutting tool with sharp edge that is also secured in the milling machine and rotates at high speed. By feeding the workpiece into the rotating cutter, material is cut away from this workpiece in the form of small chips to create the desired shape. The direct experimental approach to study machining process is expensive and time consuming, especially when a wide range of parameters is included: tool geometry, materials, cutting conditions, etc. The alternative approaches are mathematical simulations where numerical methods are applied. The finite element methods are most frequently used (Mackerle, 2003). The goal of finite element studies are to derive a computational model predicting the deformations, stresses and strains in the workpiece, as well as the loads on tool working under specific cutting parameters (Mackerle, 2003). Ueda and Manabe (1993) used a numerical approach and simulated the chip formation in the cutting process. Lovell et al. (1998) introduced an explicit dynamic FEM method to simulate orthogonal cutting with sharp edge but a restricted contact cutting tool. Friction conditions at the chip-tool interface in early FEM models of metal cutting have been largely ignored (Klamecki, 1973; Tay et al., 1974). Carroll and Strenkowski (1988) assumed to be constant with a coefficient of friction based on Coulomb’s law at the entire chip-tool interface. Shih et al. (1990) introduced a model that consists of the sticking region for which the friction force is constant and the sliding region for which friction force varies linearly according to Coulomb’s law. Usui and Shirakashi (1982) performed rigid-plastic FE simulations of steady state orthogonal cutting process. The mechanistic approach has been widely used for the force predictions and also been extended to predict associated machine component deflections and form errors (Kline et al., 1982, 1983; Sutherland and DeVor, 1986; Budak and Altintas, 1994, 1995). Another alternative is to use mechanics of cutting approach to determine the milling force coefficients as used by Armarego and Whitifeld (1985). In this approach, an oblique cutting force model together with an orthogonal cutting database is used to predict milling force coefficients (Budak et al., 1996). This approach was applied to the cases of complex milling cutter geometries and multi-axis milling operations (Altintas and Lee, 1996; Altintas and Engin, 2001; Ozturk and Budak, 2005). Interfacial friction on tool rake face is not continuous and is a function of the normal and frictional stress distributions. The normal stress is greatest at tool tip and gradually decreases to zero at point where the chip separates from the rake face (Zorev, 1963). As shown in Fig. 1, shape of the secondary plastic zone in the sticking region can be assumed triangular according to Tay et al. (1974). On the rake face point N is located at interface between the sticking and sliding regions. Line MN is an II slip-line that is assumed to be straight. Oxley (1989) was proposed similar approach proposed to analyze the hydrostatic stresses along MN.
| Fig. 1: | Simplified deformation zones in orthogonal cutting |
The researchers developed an analytical model to predict the cutting forces, average temperatures and stresses in the primary and secondary deformation zones by using:
| • | Flow stress of the work material as a function of strain and velocity-modified temperature which couples strain rate to temperature |
| • | Thermal properties of the work material |
| • | Tool geometry |
| • | Cutting conditions |
On the contrary, friction model becomes strategically important when other variables are considered, such as shear angle, normal pressure and thermal effects even if either normal pressure or temperature were found with accuracy using shear model too. In fact, the success and reliability of numerical models are heavily dependent upon work material flow stress, friction parameters between the tool and work material interfaces, the fracture criterion and the thermal parameters (Childs, 2006). Tay et al. (1974) were proposed an experimentally determined the slip-line field of secondary deformation zone, which is used to determine the shearing stress kint in the sticking region and coefficient of friction μ in the sliding region. The objective of this study is to develop the frictions parameters using statistical and FEM method. The models will be indicated the relationship between milling variables (cutting speed, federate and axial depth) with frictions parameters (friction coefficient, friction angle, friction stress and friction force).
MATERIALS AND METHODS
This study was conducted at Advanced Machining laboratory, Department of Mechanical Engineering, Universiti Tenaga Nasional. The duration of the project is July 2007 to June 2009.
Finite Element Model
The finite element model is composed of a deformable workpiece and a rigid
tool. The tool penetrates through the workpiece at a constant speed and feed
rate. The model assumes plane-strain condition since generally depth of cut
is much greater than feed rate. Thirdwave AdvantEdge was used with six-noded
quadratic triangular elements to developed the finite element model. AdvantEdge
is an automated program and it is suitable to input process parameters to develop
a two-dimensional simulation of orthogonal cutting operation. The workpiece
material of HASTELLOY C-22HS and cutting inserts of coated carbide grade with
a TiAIN (PVD-KC520M) were used in this study. The geometry parameters of the
tool were controlled accordingly to International Organization for Standardization
(ISO) SPHX1205ZCFRGN1W as shown in Fig. 2. The nose radius
of the inserts is 90°, clearance angle 11° and positive rake angle.
Every one pass (80 mm), the simulation stopped. The spindle speed can be determined
from Eq. 1:
| (1) |
AdvantEdge was used an analytical formulation for material modeling. In a typical machining event, the primary and secondary shear zones very high strain rates are achieved, while the remainder of the workpiece deforms at moderate or low strain rates.
| Fig. 2: | KC520M insert |
In order to account for this, Thirdwave AdvantEdge incorporates a stepwise variation of the rate sensitivity exponent which is expressed as either Eq. 2:
| (2) |
where,
The von Mises stress (σf) can be rewrite as Eq. 3:
| (3) |
where, T is the current temperature, σ0 is the initial yield
stress at reference temperature T0,
In the present study, it is assumed that the tool is not plastifying. Hence, it is considered as rigid. Heat can be transferred to the tool only from the workpiece. The separation of nodes, thus forming the chip from the workpiece during a cutting simulation is achieved by continuous remeshing. Therefore, during metal cutting the workpiece material is allowed to flow around the cutting tool edge and when the elements in this vicinity become distorted and lose accuracy, Thirdwave AdvantEdge alleviates element distortion by updating the finite element mesh periodically by refining large elements, remeshing distorted elements and coarsening small elements. The initial position of the workpiece and cutting tool with selected mesh is shown in Fig. 3. The initial coolant temperature is selected as the room temperature. Since, flood coolant is selected heat flux due to coolant is applied to all exposed and noncontacting surfaces on tool and workpiece, except the bottom face of the workpiece and the faces on the tool where constant temperature is applied.
| Fig. 3: | Initial position of the workpiece and cutting tool with selected |
Response Surface Method
The RSM is a combination of experimental and regression analysis and statistical
inferences. The concept of a response surface involves a dependent variable
(y) called the response variable and several independent variables x1,
x2, . . .,xk (Schey, 2000; Montgomery, 2001). If all of
these variables are assumed to be measurable, the response variable can be expressed
as Eq. 4.
| (4) |
where, (x1 = lnV), feed (x2 = lnf), axial depth (x3 = lnax) that optimize response. The observed response (y) as a function of the speed, feed rate and axial depth can be written as Eq. 5 (Schey, 2000; Montgomery, 2001):
| (5) |
where, y is the response, C, m, n and p are constants.
Equation 5 can also be written in Eq. 6:
| (6) |
where, x0 = 1(dummy variables), x1= cutting speed, x2 = Feed rate and x3 = Axial depth β0 = C and β1, β2 and β3, are the model parameters.
Whilst the properties of the materials were not coincident except for tensile strength, some materials machined by a tool with a chamfer have been found to result in microstructure change because of temperature effect (Wu and Matsumoto, 1990; Matsumoto et al., 1986). Boothroyd (1975) and El Baradie (1993) were investigated the effect of speed, feed and depth of cut on steel and grey cast iron and then emphasized the use of RSM in developing a surface roughness prediction model.
Wu (1964) were proposed a prediction model by using Takushi method and RSM. By using the factors including the cutting speed, feed and depth of cut, Alauddin et al. (1998) were developed the surface roughness models and to determine the cutting conditions for 190 BHN steel and Inconel 718. The authors found that the variations of tool angles have important effects on surface roughness. In order to model and analyze the effect of each variable and minimize the cutting tests, surface roughness models utilizing response surface methodology and the experimental design were carried out in this investigation. Some key features of BBD include allow efficient estimation of first- and second-order terms, desirable design properties of orthogonal blocks, less expensive to run compared to CCD having the same number of factors, all the design points fall within the safe operation zones and all factors are never set to their extreme (low or high) levels, simultaneously.
| Table 1: | Level of independence variables |
| Table 2: | Simulation condition |
The suitable levels of the factors were used to deduce the design parameters as shown in Table 1 and 2 after run some preliminary run. In this study, 3 variables have been selected such as the cutting speed, feed rate and axial depth. For the radial depth, 3.5 mm was selected for every experiment.
RESULTS
The component of the resultant cutting force (R) resolved on the primary shear plane generates the shear force per unit area (k) adequate to cause the primary flow. The direction of friction angle (λ) of resultant cutting force to the normal of rake face is measurement of the average friction interaction (friction angle) between the chip and tool. The values of cutting force (Fc) and thrust force (Ft) are taken from the simulation results are shown in Table 3. Simulation results for experiment number 5 and 9 are shown in Fig. 4 and 5, respectively. A minimal description of chip formation is shown in Fig. 6. The friction angle (λ) and average friction coefficient (μav = tan λ), shear stress (k) and average friction stress (τ) between the chip and tool, relative to k, can be estimated with Fc and Ft the force per unit cutting edge engagement length (Childs, 2006). The average friction coefficient, shear stress and ratio of average friction stress to shear stress are expressed in Eq. 7-9, respectively:
| (7) |
| (8) |
| Table 3: | Simulations results |
| Fig. 4: | Force simulation result for experiment No. 5 |
| Fig. 5: | Force simulation result for experiment No. 9 |
| Fig. 6: | A minimal description of chip formation |
| (9) |
where, φ is the shear angle, α is the rake angle, ac is the uncut chip thickness and lOB is the contact length between the cutting tool and chip. In the simplest case, deformation takes place by intense shearing in a plane, the shear plane, inclined by shear angle (φ). The chip thus formed has a thickness (ha). The shear angle determines the cutting ratio, rc (Childs, 2006), which can be expressed as Eq. 10.
| (10) |
where, ha is the chip thickness.
In milling, Eq. 11 can be used to estimated h and assume ha will equal to feed rate (Budak, 2005).
| (11) |
where, c is the feed rate and θ is the angular position. The angular position can be defined as Eq. 12 (Abou-El-Hossein et al., 2007).
| (12) |
where, Ω is the angular speed (rad sec-1) or Ω = 2πm/60 , n is the spindle speed in rpm and t is the time. The value of rc gives valuable clues regarding the efficiency of the process.
From the geometry of the process, the shear angle is defined as Eq. 13 (Budak, 2005):
| (13) |
In deformation processes one of the contacting materials (the workpiece) deforms and doing so slides against the harder surface (cutting tool). A frictional stress, τ is again generated, but this time there is a limit to μ, because the material will choose a deformation pattern that minimizes the energy of deformation (Boothroyd, 1975).
| Fig. 7: | Sticking friction |
If friction is high, interface shear stress τ will reach, in the limit, the shear flow stress τs of the workpiece material. At this point, the workpiece refuses to slide on the tool surface; instead, it deforms by shearing inside the body. In general, it is more accurate to say that the coefficient of friction becomes meaningless when τi = τf, since there is no relative sliding at the interface. This is described as sticking friction as shown in Fig. 7, even though the workpiece does not actually stick to the workpiece. From the point of view of forces acting on the tool, the resultant force Fr may be regarded as being composed of the normal force Fn acting perpendicular to the tool face and the friction force F acting along the face. Their magnitude may be calculated from simulation forces and the rake angle (Boothroyd, 1975):
| (14) |
DISCUSSION
The calculated friction coefficient, friction angle, friction stress and friction force using Eq. 4-6 and 11 are shown in Table 4. After run the 15 simulation, the average friction coefficient, friction angle, friction stress and friction force values used to find the parameters appearing in the postulated first order model Eq. 14. To do the calculation of these parameters, the method of least squares is used with the aid of Minitab. The first order linear equation of friction parameters are expressed as Eq. 15-18:
| (15) |
| (16) |
| (17) |
| (18) |
| Table 4: | The calculated friction coefficient, friction angle, friction stress and friction force |
| Table 5: | Analysis of Variance (ANOVA) for friction coefficient |
| Table 6: | Analysis of Variance for friction angle |
| Table 7: | Analysis of Variance for friction stress |
From these linear equations, one can easily notice that the response y1, y2, y3 and y4 (Friction coefficient, Friction angle, Friction stress, Friction force) is affected significantly by the feed rate followed by axial depth of cut and then by cutting speed. Generally, the increase in feed rate, axial depth and cutting speed causes the friction stress to become larger. On the other hand, the decrease in feed rate and increase in cutting speed and axial depth causes friction coefficient, friction angle and friction force increase gradually. The adequacy of the first-order model is verified using the Analysis of Variance (ANOVA). At a level of confidence of 95%, the model is checked for its adequacy. Analysis of variance for friction coefficient, friction angle, frictional stress and friction force are given in Table 5-8, respectively. It can be observed from Tables 5 to 8 that p-values of 0.367, 0.666, 0.282 and 0.206 (>0.05) are not significant with the lack-of fit and F-statistic are 2.07, 0.81, 2.91 and 4.23. This implies that the model could fit and it is adequate (Abou-El-Hossein et al., 2007; Kadirgama et al., 2008). The prediction error for cutting (tangential) force is drastically lower than feed force when fully sliding or fully sticking conditions are assumed in friction modeling (Filice et al., 2007).
| Table 8: | Analysis of Variance for friction force |
| Fig. 8: | (a) Friction coefficient, (b) friction angle, (c) friction stress and (d) frictional force contours in the cutting speed-feed rate plane for axial depth 2 mm |
It is a well known phenomenon that the apparent friction coefficient increases with increases of rake angle. Simulations using the proposed model are conducted for AISI 1050 steel with coated carbide tool for different rake angles at cutting speed and feed rate of 300 m min-1 and 0.1 mm rev-1, respectively (Ozlu et al., 2007; Budak and Ozlu, 2008).
The developed linear model Eq. 15-18 were used to plot contours of the friction coefficient, friction angle, friction stress, friction force at different axial depth of cut, respectively. Figure 8a-d show the friction coefficient, friction angle, friction stress, friction force contours at cutting speed-feed rate plane for axial depth 2 mm. It is clearly seen that the increase of cutting speed, feed rate and axial depth causes the friction stress increase dramatically. Meanwhile, the friction coefficient, angle and force increases with decreases of feed rate and increases of cutting speed and axial depth. Kadirgama et al. (2009) indicated that the feed rate was the most dominant cutting condition on the cutting force, followed by the axial depth, radial depth of cut and then by the cutting speed. The cutting force increases with increasing the feed rate, depths of cut but decreases with increasing cutting speed.
CONCLUSION
The milling parameters cutting speed, feed rate and axial depth play the major role to produce the high fiction force, coefficient, angle and stress. High friction generates heat. From the first order model, the responses (friction coefficient, friction angle, friction stress and friction force) are affected significantly by feed rate followed by axial depth of cut and then cutting speed. The increases of friction stress increasing of feed rate, axial depth and cutting speed. On the other hand, friction coefficient, friction angle and friction force increases gradually with decreases in feed rate and increases of cutting speed and axial depth. The combination of numerical analysis and statistical method are very useful to analysis the distribution of friction in milling. It is suitable to use moderate value of cutting speed, feed rate and axial depth when milling same type of materials. When use very low feed rate, it cause higher friction coefficient, friction angle and force.
ACKNOWLEDGMENT
The authors would like to express their deep gratitude to Universiti Tenaga Nasional (UNITEN for provided the laboratory facilities and financial support by Malaysian Government through MOSTI under Project No. 03-99-03-0011-EA 0041.