Fundamental investigation on the time-variance of process stability

The workpiece material for the force measurement, the tool wear as well as the dynamic investigations was the Aluminium Alloy EN AW-7075. In order to compare different cutting tool materials with different wear rates, HSS and carbide end mills were tested (Table 1). The cantilever length was l = 25 mm, resulting in an aspect ratio of 3.125. With this ratio, significant differences in the stability limit could be shown over the tool life.

The intention of the described investigation was to quantify tool life dependent variances with respect to the dynamic critical process stability and to evaluate correlations with the process forces and tool wear. The dynamic properties of the tool were determined by means of experimental modal analysis and can be assumed to be constant over the operation period. Considering the modelled dynamics stability diagrams were calculated applying a geometric physically-based milling simulation. Two process configurations were selected, comprising high and low process stability predictions, which were used to perform the force measurements and dynamic tests. Iteratively, a defined material volume was machined after which process force and flank wear measurements as well as dynamically critical machining test were conducted (Fig. 1).

The dynamically critical milling test was realized by programming a tool path with a linear increase of the radial depth of cut a_e, whereby the stability limit is exceeded and dynamic instabilities start to occur.

The axial depth of cut was a_p = 3.5 mm. A linearly increasing radial infeed of a_{e, min} = 0 mm up to a_{e, max} = 8 mm was used (Table 2). At the beginning of the iteration loops, a small amount of material was removed, since it was known from previous preliminary investigations that a large variance of the stability limit can occur in this range. For this purpose, a material removal of 35,000 mm³ was taken in the first 4 iteration loops and 70,000 mm³ thereafter. The termination criterion was defined as a stationary state in the stability limit.

The experiments were carried out on a Röders Tec RFM 1000 3-axis machine tool. After each tool wear iteration, the cutting forces were measured on the 9257B dynamometer from Kistler. Small and thus light specimen dimensions were used to not influence the natural frequencies of the dynamometer negatively with respect to the high tooth pass frequencies. The cutting forces were measured stationary in all 3 spatial directions and converted into the cutting force and the cutting normal force for further consideration (Fig. 2).

The acoustic measuring device Tascam DR-40 was used for in-process measurements. This data was used to determine the stability level and to compare the results with those of the optical analysis.

To determine dynamically critical operating points, the underlying modal parameters of a machining system must be determined. For this purpose, the frequency response function (FRF) of the tool was determined using experimental modal analysis (Fig. 3). The system was excited using an impact hammer of the type 8206-002 by Brüel and Kjær, and the response was measured by an ultra-lightweight acceleration sensor (PCB Model 352C23).

The modal input parameters mass, stiffness and damping, which are necessary for the stability calculation, are then fitted using iterative optimization (Table 3).

The geometric physically-based process simulation [11] was applied with specifically calibrated models of cutting force and dynamics and typical process parameter values for the investigated application (Fig. 4). Based on the stability diagram, spindle speeds between n_min = 16,950 min⁻¹ and n_max = 27,600 min⁻¹ were selected, which comprise high and low process stability predictions. The selection of the operating points results in cutting speeds between v_c,min ≈ 426 m/min and v_c,max ≈ 693 m/min. The HSS and solid carbide tools were experimentally applied in dynamically critical milling processes with regard to the structure- and spindle speed-specific stability limit.

The machined workpiece surfaces were analyzed due to characteristic properties like chatter. In addition the acoustic emission during the experiment was evaluated in spectral analyses. Based on these measurements tool- and operation time-specific stability limits could be identified (Fig. 5). The spindle speed at f_n = 460 Hz and tooth engagement frequency f_t = 920 Hz are marked. When chatter marks start to occur, the amplitude increases in the frequency range of the first natural frequency of the tool. Based on the maximum width of cut a_e,max and the ratio of t_stab to t_tot, the critical width of cut a_e,crit can be determined by the spectrogram. Here t_stab represents the process time up to the dynamically critical process point and t_tot the overall process time. By multiplying the ratio of these two values by a_e,max, a_e,crit can be calculated due to the linearly increasing axial infeed.

Figure 6 shows the width of the flank wear and stability limit of the HSS tool over the tool life. The initial stability limit at a_e,crit = 3.85 mm is followed by a decrease to a value of a_e,crit = 2.4 mm after V_r = 70,000 mm³. The stability limit exhibits an increased variance in this range. With further tool life, the limit increases above the initial stability limit to a_e,crit = 5.7 mm. Regarding the wear mark width VB at the circumferential cutting edge, an initial gradual increase can be observed. This converges in the further process at a value of V_m = 45 µm. A correlation between the progressions of wear mark widths and the stability limits is not evident.

The width of the flank wear represents the mean value of 2 tools used, each with 3 defined measuring points starting from the corner of the cutting edge (Fig. 7). In one of the tools used, a breakout of the cutting edge corner also occurred at the end of the tool life. The results of the stability test were therefore not considered in the last wear condition in order to exclude interactions on the process stability.

The process forces F_c and F_c,N are shown over the tool life in (Fig. 8). The forces were evaluated at the same angle of rotation. The values shown are the averaged maximum values from several tooth engagements around the force maximum. The cutting force F_c increases from 229 to 264 N; an increase of 15%. The cutting normal force F_C,N increases from 29 to 108 N is thus almost five times higher. Despite the increased deflection force, the stability limit of the process increases. Interdependencies between the process force, the width of flank wear and the stability limit therefore require more complex analytical approaches. The development of the flank wear and the cutting normal force are very similar. The stability limit is different. The high variances at the beginning of the tool life can neither be explained by the process force nor by the wear of the main cutting edge. A measurement of the microstructure, such as the cutting edge radius, could provide further information here.

In Fig. 9, the wear mark widths and stability limits of the carbide cutting tools are presented. The tool wear investigations were carried out under dynamically stable operating conditions. The examination of process stability was conducted at a dynamically critical operating point with n = 16,950 min⁻¹. Analogous to the HSS tools, an initial drop in the stability limit a_e,krit can also be observed at V_r = 70,000 mm³. However, this value rises again, but unlike the HSS tools, does not exceed the value of the initially measured stability limit. In general, the stability level is lower compared to HSS, which might be explained by the lower inherent damping of the carbide compared to HSS. The increased wear resistance of the cemented carbide is evident in the wear mark width over the tool life. This initially increases continuously and then assumes an almost constant value at VM = 12 μm. The progression of the width of the flank wear also does not provide direct conclusions to be drawn about process stability. Compared to the HSS tools, the wear mark width is more homogeneously distributed over the circumferential cutting edge and no major breakouts were observed. The cutting volume was set to be smaller compared to the HSS tools, as stationary cutting conditions were achieved faster.

Similarly, in Fig. 10 the force components F_c and F_c,N over the tool life are depicted. In both force components, an initial increase is recognizable. Subsequently, both components settle at a nearly constant value. Compared to the results of the cutting normal force of the HSS tools, the values only slightly increase over the tool life. This can also be seen from the results of the wear mark width.