Analysis of milling cutter working part displacements during milling of steel

* Dr hab. inż. Paweł Twardowski (pawel.twardowski@put.poznan.pl), prof. dr hab. inż. Adam Hamrol (adam.hamrol@put.poznan.pl), mgr inż. Natalia Znojkiewicz (natalia.w.znojkiewicz@doctorate.put.poz-nan.pl), dr inż. Szymon Wojciechowski (szymon.wojciechowski@put.poznan. pl) – Politechnika Poznańska Badania miały na celu analizę przemieszczeń części roboczej fezu kulistego w trakcie obróbki zahartowanej stali z różnymi wartościami wysunięcia narzędzia z oprawki. Pomiary przeprowadzono dla przemieszczeń narzędzia w dwóch kierunkach: normalnym oraz posuwowym. Zmierzono siły i drgania oraz parametry chropowatości obrobionej powierzchni. SŁOWA KLUCZOWE: frezowanie, dynamika, chropowatość powierzchni

Displacements and mechanical vibrations of milling cutters during machining are phenomena that should be minimized because they have an adverse effect on process stability, accuracy of workpiece, machined surface quality, tool durability and technical condition of the machine tool. The variability of the geometrical parameters of the surface texture is of great importance for the cutting process dynamics -the variation of the area of cut as a function of the milling cutter rotation angle. This has a direct effect on the phenomena that are inseparably associated with the milling process, such as vibrations, forces and displacements. This in turn affects the roughness of the surface [1]. Knowledge of these issues allows for an in-depth evaluation of the milling process and -as a result -the selection of appropriate machining parameters to achieve the desired technological effects.
The magnitude of displacements depends on many factors, and the most important are the total cutting force and its components. Under the influence of forces, the cutter deforms elastically and creates a shape error [3]. Knowledge of the components of total cutting force [2] and stiffness of the system allows estimating the amount of deflection and displacement of the working part of the cutter, and thus also the roughness of the machined surface [4,5]. Therefore, the work focuses on the description of these phenomena and the relationship between the studied quantities. In addition, causal relationships regarding mutual relations are presented.

Scope and methodology of research
The research was aimed at analyzing displacements of the working part of a ball end mill during the machining of hardened steel at different values of the tool's overhang. Measurements were made for tool displacements in two directions: normal and feed. The forces and vibrations were measured, and after milling, the roughness parameters of the machined surface were examined.
The machined material was X155CrVMo12-1 steel (56HRC). The tests were carried out on a vertical milling machine Avia FND-32F. The process of upward milling was carried out. The material was mounted in an APX 125 mm machine vice. The ER32 holder was used to attach the tools.
Ball end mills of the same diameter and working part geometry were used, but with different overhangs ( fig. 1, table).

TABLE. Basic dimensions of the used cutters
The same milling parameters were adopted in all tests: rotational speed n = 1400 rpm, effective diameter def = 8.83 mm, effective speed vce = 39 m/min, feed per tooth fz = 0.03 mm/tooth, axial infeed ap 0.3 mm, radial infeed ae = 0.3 mm, the thickness of the machined layer hex = 0.22 mm, and only the tool overhang L was variable. Nine tests were carried out -three tests for each L value.
The effective cutting diameter and the uncut chip thickness are shown in fig. 2. The workpiece is mounted in such a way that its surface is at an angle of 45 °to the tool axis.
The displacement measuring path of the tool consisted of two Micro-Epsilon optoNCDT ILD1700-10 LL sensors, measuring displacements in the feed direction and perpendicular to the feed direction ( fig. 3). Sensors with a measuring range of 10 mm were used, which allowed measuring to an accuracy of 0.5 μm.
Vibration accelerations and components of total cutting force were measured in three directions using standard measuring paths, using piezoelectric sensors.
A Hommel stylus profiler was used to measure the roughness of the machined surface. This measurement was made on a distance of LT = 4.8 mm, and was repeated five times for each milling pass. The waveforms show that changes in time displacements for the feed direction are pulsating. This is particularly visible in fig. 6, which shows the duration of one cutter rotation and describes the individual teeth. Similar relations were observed for the second direction -feed normal YfN. The pulsating character of the changes is also confirmed by vibration patterns, for example shown in fig. 7.
The used ball end mill had two teeth, i.e. the angle of the lateral pitch is Ψz = 180°. After taking into account the depth of cut, it is easy to determine the tool angle, which in this case is Ψ = 1.2°.
This means that most of the time, the teeth do not work. Since one turn of the cutter lasts t = 0.0428 s, the working time of two teeth for one revolution is t = 0.00028 s, which is 0.67% of the time of one revolution. The components of total cutting force have the same type of course. In the case of vibration acceleration, forcing, i.e. entering the tooth into the workpiece and leaving it, is very short and 99.33% of the time needed for one rotation is dominated by free vibrations.   This can be referred to the entire process -i.e. for surface milling in the Lf cutting path, free vibrations dominate and only forced vibration is temporary.
This mechanism determines the impulse nature of displacements of the working part of the cutter, which is clearly visible on the spectral characteristics ( fig. 8), where two frequencies prevail. The first one is the basic frequency, derived from the rotational speed n = 1400 rpm (basic frequency f0 = n / 60 = 23.33 Hz). The second one, with the  dominant amplitude, is the frequency of the milling process, i.e. the tool rotational frequency multiplied by the number of teeth z (z • f0 = 46.44 Hz). The following bands are the harmonics of these two frequencies.
The spectral characteristics in the case of forces ( fig. 9) and vibrations are slightly different. Harmonics are the dominant frequencies from the point of view of the amplitude values. This does not mean, however, that the pulsating character of dynamic enforcements has changed, which adversely affects the tool life and the machined surface roughness.
In order to present phase diagrams of displacements for the investigated cases, all signals were subjected to digital filtration -in this way, high-frequency components disrupting the course of displacements were eliminated. A low-pass filter with setting fd = 200 Hz was used to obtain waveforms only from the milling process. In the first place, the displacements during the idle movement of the machine tool were analyzed -the results are shown in fig. 10.
The greatest displacement values were achieved by the milling cutter with L3 = 95 mm and for the feed direction it was Xf = 27 μm, and for the normal direction of feed YfN = 29 μm. Similar conclusions can be drawn from the displacement analysis during milling ( fig. 11). It is confirmed that the more rigid the tool, the smaller deflection of the milling cutter and displacement and -as a result -smaller shape errors and roughness parameters ( fig. 12). Differences in the roughness parameters are very large between the milling cutter running at L1 = 32 mm and the milling cutter with L3 = 95 mm -for the Rmax parameter, the differences in the roughness parameters are up to seven times.  However, the removal of the milling cutter does not significantly change the value of the tested force amplitudes ( fig. 13), but has a significant effect on the level of vibrations in the examined directions ( fig. 14).

Conclusions
Changing the rigidity of ball end mills by changing the tool overhang has a significant impact on the displacement of the working part of the cutter. This affects directly to the values of vibration amplitudes, and thus the roughness parameters of the machined surface. This, in turn, does not affect the amplitude values of the forces. The deep pockets should be machined with the largest diameter cutters to ensure the highest rigidity of the tool.