3.1. Experimental Results
In order to simulate the tool wear according to Usui et al. [22
], it is necessary to determine the thermomechanical tool load in the form of sliding velocity, temperature and the normal stresses at the cutting wedge. The normal stress is especially challenging for a comparison with the simulation due to the fact that the experimentally determined normal stresses are based on methods which do not represent the cutting process sufficiently accurately, for example by using split tools or stress–optical materials. As a result, the friction between material and tool has been influenced in particular. Bergmann therefore developed a method to determine the stresses at the cutting wedge based on the measured incremental process forces and contact lengths [23
]. In order to consider all the materials, the normal stresses are shown for a cutting edge rounding of Sα
= 30 μm. Especially, the application of larger cutting edge roundings leads to the formation of the built up edges in planing of Al7075T6. Therefore, the calculation of the stresses is incorrect.
For the wear simulation, the influence of the cutting edge rounding on the normal stresses has to be determined. Hereof, Bergmann reveals that the normal stresses at the cutting edge rounding as well as on the rake face are slightly influenced in comparison to the tangential stresses [23
]. However, it is well known that different wear rates result by machining various materials. Thus, knowledge the influence of the material properties on the normal stresses is necessary for the wear simulation for different materials. With this knowledge, the simulation can be compared with the resulting loads on the cutting wedge and can thus be used for the wear simulation for different materials.
It is well known that the stresses on the rake face are influenced by the process forces as well as the contact length cl [24
]. Therefore, in addition to the strength of the material, the change of the contact length cl on the rake face has to be considered. Thus, for the normal stress on the rake face, a relationship between the resulting maximum normal stresses at the rake face and a so-called “stress factor B” could be determined (Figure 4
). The stress factor B is the quotient of the heat penetration coefficient b and the tensile strength Rm. The heat penetration coefficient b can be used to describe the heat flux density [25
]. For materials with low heat penetration coefficients b, the tendency for thermal softening is reduced [24
]. An increase in the tensile strength of the material tends to lead to an increased mechanical load on the cutting wedge. As presented in Figure 4
, it can be seen that with decreasing stress factor B, the normal stresses on the rake face increases. This can be explained by the fact that with a decreasing heat penetration coefficient and an increasing tensile strength the chip formation is characterized by shear chip formation, as it is the case in machining Ti6Al4V.
This leads to a significant reduction of the contact length at the rake face. The result is an exponential increase of the normal stresses due to process forces, which appear on a significantly reduced surface. This effect occurs mainly in the case of hardened materials. Figure 4
illustrates this effect in the case of the heat-treated material AISI 1045. As a result, the normal stress increases as the material strength increases. The lowest normal stresses exhibit the aluminum alloys. Here, beside the lowest material strengths, in machining aluminum, the largest contact lengths occur [26
]. Consequently, the normal stresses for the aluminum alloys decrease significantly in comparison with the ferrous metals. Altogether, it can be stated that by means of the stress factor B, the normal stresses for ferrous and non-ferrous metals at the rake face can be modelled and thus these findings can be used for the validation of the simulation. This knowledge is particularly necessary to prove the validity of the wear simulation for different materials.
3.2. Simulation Results
With the knowledge of the normal stresses, the validation of the simulation can be done more precisely in comparison by a validation based on process forces. This can be explained by the fact that the stresses, in comparison to the process forces, represents more exactly the load on the wedge. For a systematic design of cutting edge roundings, however, the temporal wear-related change of the microgeometry is of particular interest. A suitable way of predicting the continuous loss of material along the contact zone is the coupling of chip formation simulations and wear rate models [22
]. The latter describe the functional relationship between the loss of material per unit of time and the local thermo-mechanical loads (see Figure 5
). The overall objective of the following simulative investigations is therefore the verification of the application suitability of FE-based chip formation simulations for the prediction of continuous tool wear of different rounded cutting edges.
Based on the wear rate models investigated in the current state of knowledge, primarily the normal stresses, temperatures and relative velocities acting in the contact zone are analyzed in the following. The characteristic load collective in the contact zone is illustrated as an example in Figure 6
for an idealized unworn tool with a symmetrical cutting edge rounding of Sα
= 50 μm.
In accordance with the findings from the literature, the normal stress has a distinct maximum in the area of the cutting edge rounding. In this case, a linear decrease in the normal stress can be observed in the area of the rake and the flank face. The distribution of the simulated normal stress corresponds qualitatively to those proposed by Usui et al. [16
] and those measured by Zorev and Uteschew [27
] using rounded cutting edges.
The normal stress distribution in the region of the cutting edge is primarily affected by the presence of a so-called stagnation zone, which is characterized by low material flow rates. At the material separation point on the cutting edge rounding, the relative sliding speed is equal to zero. Starting from the separation point in the direction of the free surface, the relative velocity increases rapidly. This results in high velocity gradients. In the area of the global maximum on the flank face, the relative sliding velocity assumes values which approximately correspond to the applied cutting speed. On the rake face, the relative sliding velocity continuously increases up to the separation point of the chip on the rake face. However, due to the deflection of the material in the primary shear zone and the friction processes in the tool-chip interface, overall lower relative sliding velocities result than on the flank face.
The temperature profile shown is the result of the thermal energy converted during the machining in the primary shear zone, which is transmitted to the tool by conduction due to the temperature gradient between tool and chip, or the workpiece. Furthermore, the tool is subject to additional thermal loads as a result of friction processes in the contact zone. In this case, the converted thermal energy per unit time due to friction can be calculated from the product of the friction force and the relative speed. Following this connection, local temperature maxima result, in particular in the areas of high relative sliding speed, on the rake face and flank face. In contrast, the lowest temperatures are in the area of the cutting edge rounding. These fundamental relationships were recorded in different degrees of severity for all of the materials investigated.
In order to validate the simulated maximum normal stresses, a comparison of simulated values with the experimental data calculated by Bergmann is shown in Figure 7
Here, the maximum normal stress is described by means of a power function depending on the stress factor B. The stress factor B results from the quotient of the heat penetration coefficient b and the tensile strength Rm.
Based on the results, a mean deviation of 17 % can be observed with regard to the magnitude of the maximum normal stress. The material-specific deviations can be traced back to uncertainties regarding the choice of the material model of the workpiece. However, over the entirety of the examined materials, a high degree of consistency of the derived power functions can be determined. Based on the results it can be stated that the influence of the material properties on the maximum normal stresses in the contact zone is approximated with sufficient accuracy.
The influence of different material properties on the stress distribution in the contact zone between tool and chip is shown in Figure 8
It can be seen that the normal stress curves differ significantly with respect to their distribution and magnitude along the rake face. This can be explained by differences regarding the contact length. It can be stated that the contact length during machining of TiAl6V4 is significantly lower compared to Al7075T6 and AISI1045. This is primarily caused by the segmented chip formation in the simulation, which was induced by implementing the Cockroft and Latham fracture criteria [28
] into the simulation model. Significant differences were also observed with regard to the normal stress in the area of the cutting edge rounding. In the case of the TiAl6V4 alloy, the induced force components were concentrated in the area of the cutting edge. This results in significantly increased normal stresses when the normal forces were applied to the contact surface.
Due to the cyclic shearing of the chip segments, the normal stress distribution during the machining of the TiAl6V4 alloy had a temporally periodic character. Figure 9
shows the stress distributions during the different phases of segmented chip formation. The beginning of the compression phase was characterized by a continuous increase in the contact length with a simultaneous decrease in the normal stress. As the compression progresses, shear stress was induced along the primary shear zone caused by local material failure. During the shearing off of the chip segment, the contact length decreased significantly, which resulted in increased normal stresses in the area of the cutting edge rounding. Due to the complexity of the segmented chip formation with respect to the thermomechanical load and the resulting tool wear, such processes were not considered further in the subsequent simulative analyses of the wear behavior.
In addition to the material properties, the characteristics of the normal stresses were influenced by the shape of the cutting edge rounding, illustrated in Figure 10
for machining of AISI4140. Here it was evident that the increase in the cutting edge rounding did not significantly influence the amount of maximum normal stress. By increasing Sα
from 30 to 100 µm, the maximum normal stress was decreased by only 16%. However, the increase in the cutting edge rounding lead to a significant widening of the range of maximum normal stresses in the area of the cutting edge rounding.
In addition to the size of the cutting edge rounding, the load on the cutting wedge is essentially determined by the tilting of the rounding to the rake face or flank face. Figure 11
therefore compares different asymmetrical cutting edges with regard to their effect on the output values required for the wear calculation according to Usui.
In the case of a cutting edge rounding with K = 0.5, the maximum temperature shifts in the direction of the flank face. This can be attributed to the significantly increased relative sliding speeds as well as the higher contact length in the area of the flank face. In addition, the range of maximum normal stresses is much more pronounced on the flank face. Due to the higher normal stress components in the feed direction, it can be expected that the cutting wedge will be subjected to less bending stress than with K = 2. Consequently, a reduction in the tendency of the cutting edge to break out can be assumed. Regarding the distribution of the relative sliding velocity along the contact zone, it becomes clear that the stagnation zone for K = 2 is clearly extended further in the direction of the rake face. This results in significantly lower temperatures in the area of the cutting edge rounding and the adjacent rake face. Only minor differences can be observed with regard to the relative sliding velocity on the rake face at the point of the chip detachment.
To visualize the local thermomechanical load spectrum as a function of the cutting edge microgeometry, so-called load maps were developed (see Figure 12
These provide information about the load at any point along the contact zone and serve as input variables for the calculation of the local wear rate according to Usui’s wear equation. The load maps were calculated based on 10 support points using the Delauney triangulation algorithm. Three points each form a triangle in which a linear interpolation of the respective output quantity takes place. For the calculation of the flank wear the local loads in the area of the flank face are used, which are exemplarily shown in Figure 12
for an unworn tool.
Since the normal stress at the flank face is homogenously distributed and approximately identical for the investigated cutting edge geometries, the relative sliding velocity and the temperatures are focused in Figure 12
. The results indicate that the calculated temperatures have a high correlation with the relative sliding velocities. This can be attributed to the already described effect of the increasing frictional heat development at high relative sliding velocities. Furthermore, it becomes clear that the temperatures increase significantly with the increase of Sα
, especially for cutting edges with K < 1. The further validation of the simulated sliding velocity as well as the tool temperature in comparison to experimental results considering the adapted simulation model is presented in detail in the works of Breidenstein et al. [29
] and Denkena et al. [30
] For an accurate prediction of the resulting wear, a parameterization of the wear rate model has to be carried out for every workpiece/tool combination. Since these investigations are an absolute comparison of the wear behavior of different cutting edge microgeometries with the same workpiece/tool combination, this can be neglected. Therefore the constants were adopted from the work of Binder et al. [31