Investigation of cutting force oscillations when high productivity milling

The article analyzes cutting force oscillations of highproductivity milling. Based on end-milling experiments using a milling machine tool, characteristics of spatial oscillations of cutting forces were identified. The data analysis using software and oscillation theory methods showed that at high spindle rotation frequencies under certain milling conditions, interaction of the cutting edges and the workpiece is not uniform which deteriorates the machined surface. As the spindle rotation frequency increases due to resonances in the tool and spindle and mutual oscillations of the workpiece and the tool, the cutting force spectrum varies. Some extra harmonic components appear. They index the failure of interaction of the cutting edges and the workpiece.


Introduction
Milling as a technological process is characterized by discontinuous force impacts of the mill on the workpiece [1,2]. It causes regular cutting force oscillations P(t) with a gear mesh frequency of fz=n1•z/60=z•f1 where n1 is the angular speed of mill rotation (rpm); z is the number of mill teeth; f1 is the rotational frequency (Hz). These regular interferences cause forced oscillations of the mill, spindle, tool and workpiece. Mill and workpiece oscillations influence the cutting force. During the high-productivity milling process, resonances and spatial oscillations of the mechanical structure and machine unit occur. They influence the dynamic characteristics of the machine and milling quality [2]. Cutting vibrations also decrease the machine tool resistance. One more negative vibration effect is milling performance degradation due to limited cutting modes.
A set of researches deal with cutting forces during the milling process [3][4][5][6][7][8]. Their authors develop mathematical models for end milling process simulation. Models describing deformation in cutting found wide application [1,8,9,11]. Along with design and geometry parameters of cutting tools, they take into account material properties. For example, some researchers suggest using cutting force ratios [1,8,11]. Orthogonal cutting experiments are carried out to determine their values.
Most researches deal with monolithic end mills made from hard material or high-speed steel [4][5][6][7]. A smaller number of works deal with end mills with inserts [8] due to a simpler description of design and geometry parameters of monolithic tools. The fact that the tool body and inserts are made from different materials with different mechanical properties influences the dynamics of cutting. It makes the mathematical process model more complex.
Despite the type of mills, the adequacy of developed mathematical models can be tested. It should be taken into account that in the aircraft industry, high-productivity milling is characterizing by a large volume of chip and is performed with values ае, which can be equal to the cutting diameter of the tool Dc [7,8]. Most researchers prefer milling with a small radial cutting depth ае [9,10] due to better chip formation control and capacitive constraints, particularly power and a spindle torque. Thus, experimental studies approving the milling process under conditions which are most closely approximate the real manufacturing ones are relevant.

Material and method
The experiments were carried out using DMG HSC 75V Linear Milling Machine Center. The machine has a high-speed spindle with a maximum rotation speed of N=28000 rpm. Cutting forces were measured with Kistler 9253B23 which can measure three special force components Fx, Fy, Fz ( Fig.1). Technical data of the dynamometer platform are presented in Table 1. Deformable aluminum alloy 1933T2 consisting of Al-89%, Zn-7%, Mg-2%, Cu-1%, Zn-0.15% was used for machining. The samples were 400х300х50 mm in size.
A R790-025HA06S2-16L mill with R790-160408PH-NL Н13А inserts was used for milling ( Fig. 2).   To specify cutting data, modal analysis of the tooling set-up was carried out [1,11,12]. Its results and stability lobes are presented in Figure 3. Based on the modal analysis results, the following cutting data were specified: Vc -cutting speed, ap -axial cutting depth, ae -radial cutting depth, fz -feed per tooth, n1 -spindle rotation frequency. All these data as well as typical cutting force frequencies and amplitudes on harmonics of rotational Af1 and gear mesh Afz frequencies are presented in Table  2.  Figure 4 shows the oscillograms of three milling force projections Fx, Fy, Fz along feed axis X for measurements 2 and 6. Figure 5 shows milling force oscillation spectra for the same measurements. During the ideal milling process when cutting edges are loaded evenly, the spectral component at a gear mesh frequency fz exceeds significantly the amplitudes of the other harmonics (see the spectrum in Figure 3 for measurement 2). However, the data of 16 measurements processed in DynoWare developed by Kistler (Fig.4) are opposite. Only for measurements 1 and 2, the amplitudes of spectral components at a gear mesh frequency fz exceed the amplitude of spectral peaks at rotational frequency f1. In other measurements, the spectral component of the rotational frequency was fundamental (e.g., see Fig. 5 and 6 of the force spectrum for measurement 6).
The spectral analysis data for milling forces can be explained from a resonance perspective. In most experiments, natural frequencies of the dynamometer table are close to rotational and gear mesh frequencies of force excitation. Along with its weight, its piezoelectric sensitive elements form a spatial oscillation system which distorts a signal occurring when milling. Therefore, near-resonant oscillations of the Kistler dynamometer platform were calibrated. Figure 6 shows changes in the amplitudes of the first harmonic of rotational and gear mesh frequencies under varying milling conditions.  These conclusions are supported by the diagrams of milling force oscillation orbits in X and Y (Fig. 7,8). For example, for measurement 2 (Fig. 5) when gear mesh frequency oscillations are fundamental, the orbit corresponds to two closed paths. The orbit of milling forces was determined by processing experimental data using LabView and filtering highfrequency harmonics. The orbit of measurement 2 illustrates an ideal milling process when both cutting edges are loaded evenly and work along the chipping area. For measurement 6 ( Fig. 8) when rotational frequency oscillations prevail, the orbit of milling forces per 1 sec measurement corresponds to one closed path. The cutting edges work unevenly.
As the spindle rotation frequency increases due to resonances of the technological system, the normal conditions of cutting using two edges get disturbed [13][14][15][16]. According to the experimental measurements, the frequency of the first mill oscillations was 6820 Hz. Therefore, excitation oscillations with rotational and gear mesh frequencies within the range of 200 Hz to 900 Hz do not influence mill oscillations. Hence, the main factors disturbing the normal milling conditions are resonances of the technological system at high angular spindle rotation speeds.