Dynamic Load and Strain Analysis for the Optimization of Micro End Mills
E. Uhlmann' (2), K. Schauer ' 'Institute for Machine Tools and Factory Management, Berlin University of Technology, Berlin, Germany
Abstract Micro-milling with cemented carbide micro end mills is characterized by high frequency tool loads and infeeds smaller than 100 pm. In this paper, measurements of technological characteristics during the micromilling process are presented. The results are used to carry out a load analysis of current micro end mills. Interpreting this analysis, an innovative tool design of micro end mills is developed using the parameter technology in a FEM strain simulation. The new tool design presented here has been successfully verified by micro-milling the tool steel PM X19OCrVMo 20 with a hardness of up to 62 HRC.
Keywords: Milling, Micromachining, Tool Design
1 INTRODUCTION Micro-cutting using cemented carbide end mills has the potential necessary for the economic manufacture of complex steel microcomponent geometries [1,2]. However, various aspects make it difficult for this technology to find wide acceptance: low process reliability due to frequent tool failure, the short tool life of today's micro end mills, and the entailed high costs. The manufacturing process most frequently applied for micro end mills of cemented carbide is grinding [3-51. The smallest micro end mills available on the market are 50 pm in diameter. The manufacture of tools with diameters significantly below 50 pm is currently being tested in research institutions. Such institutions have
Figure 1: Conventional and optimized micro end mills
succeeded in using different technologies to manufacture tools with diameters from 45 pm to 10 pm . Concentricity faults and diameter deviations of micro end mills are caused by grinding and located in the tolerance range o f f 5 pm . These errors are considerably larger than the theoretical feed per tooth 4. The differences of strain on tool cutting edges within a rotation are partly a result of these errors. The objective of the research presented in this paper was to develop micro end mills of high stability, which could facilitate the process-reliably manufacture of micro cavities in tool steel with aspect ratios higher than 2 : l . The results achieved are based on the weak points as identified in current conventional micro end mills using FEM strain analysis (Figure 1 a, b). The necessary boundary conditions were determined through technological investigations. Evaluating the weak points identified, an innovative parametric tool design was developed for micro end mills using the method of FEM si m u I at i o n and ve rifi ed by ex pe ri mental testi n g .
2 EXPERIMENTAL SETUP The process forces and tool deflections that occur under real processing conditions must be determined for an analysis of dynamic load and strain. The extremely small machining zone affected by micro cutting with end mills of the smallest diameter, and the high dynamics of the process, make an accurate measurement of the very small characteristics of the process quite difficult. The tests were carried out on a Gamma 303 High Performance five axes machine tool by Wissner, Gottingen, Germany, a machine tool with a gantry structure and three, 350-mm long translating axes. Each axis achieves a positioning accuracy of less than 1.5 pm. The machine tool is equipped with two spindles, overlapping a range from 5,000 - 150 000 rpm. The axes 1 can be accelerated at a rate of 15 m/s . The process forces were shown to have considerable influence on the process reliability of micro end mills [4, 5, 61. For the measurement of process forces a type 9265A dynamometer by Kistler, Winterthur, Switzerland, was used with a resolution that allows the determination of
cutting forces up to 0.1 N. The device has an eigenfrequency fe of 5.5 kHz, allowing high-quality measurement results with implementations of up to a critical frequency of 2 kHz. In tests with two-edged end mills this means that measurements at spindle speeds n of up to 60,000 rpm can be realized.
Table 1: Processing conditions for micromilling of steel.
Table 1 shows published processing conditions for micro- milling of steel [4, 51. From these processing conditions it can be derived, that up to a tool diameter D of 0.2 mm, the majority of the spectrum of technological investigations can be performed using the spindle speeds n as mentioned above.
work piece material: micro end mill (D x I ) : cutting speed v,: 40 m/min
PM X19OCrVMo 20, 52 HRC 0.5 mm x 1.5 mm
feed per tooth 6: 1 IJm
Figure 2: Dynamic analysis of micromilling
Laser vibrometers are suitable measuring instruments for the experimental determination of highly dynamic processes . With a laser vibrometer it is possible to measure the vibration speed v of an object over time. From the velocity signal it is then possible to calculate technological process characteristics such as the tool deflection 6 For the tests presented in this paper a type OFV-353 laser vibrometer by Polytec, Waldbronn, Germany was used with a measure-point diameter of 10 pm and a resolution significantly less than 1 pm, up to a maximum frequency of 10 kHz.
3 For the determination of realistic tool loads technological investigations have been carried out. All test tools were coated with TiAlN according to Byrne et al. . Rough milling conditions were selected such as full section cut and a depth of cut of 20 % of the tool diameter D. The method of process analysis is exemplified by Figure 2. The displacements s of micro end mills during engagement can be calculated by integrating the vibration speed v measured with the laser vibrometer. Figure 2b contrasts sections of the calculated displacements s at tool penetration for two rotations. A rise in amplitudes with respect to the idle signal (i) is apparent. The differences in amplitude between the phases of tool penetration show the extent of tool deflection 6 Through fast Fourier transformation of the measurement signals during idle operation (i), the first eigenfrequencies fe, of the micro end mills can also be determined. Moreover, a difference can be established between the two amplitudes of one rotation of the tool. The causes of this are irregular wear on the two cutting edges, or a difference between the rotational axis and the barycentre axis of the cross-section of the tool as a consequence of inaccuracies during tool manufacturing. As shown in Figure 2c, the area of continuous machining (iii) is used as the basis for determining the maximum process forces. Here, too, the two amplitudes differ within one rotation. Figure 3 contrasts the measurement results for different micro end mills and compares these qualitatively.
DYNAMIC LOAD AND STRAIN ANALYSIS
Figure 3: Investigation results of micromilling
The processing conditions were the same for all experiments. The width of cut a, was identical with the tool diameter D. The spindle speed n was scaled in order to realise the constant cutting speed v,. An increase of the spindle speed n leads to excitations of the micro end mills of frequencies fn which are close to the measured eigenfrequencies fe,. The excitation frequency fn is the product of the spindle speed n and the number of cutting edges z. It can be stated that a critical excitation may take place as the spindle speed n increases, especially for higher cutting speeds v, and minimal tool diameters D. Furthermore, high tool loads result from the increasing influence of the cutting edge roundness rp if ever smaller tool diameters D are used [ lo] . If the results from the technological investigations are used as boundary conditions in an FEM strain simulation, the cause of frequent tool failure at the change from the flute length to the taper can be shown (Figure 1 b). The stability of the micro end mill is quite low because of the extension of the helical flutes to the location with the highest load. A further effect is that scratches in the micro topography which are ground into the complex tool surfaces have the effect of inducing a crack formation, especially since cemented carbide is very brittle and tends to fail in terms of linear elastics [ I l l . Thus, these micro end mills cannot compensate spontaneous load peaks during machining, which can occur, e.g., when the infeeds are changed.
and tapering, the influence of the axial angle of the flute pA on the tool stability is eliminated, in contrast to conventional micro end mills. The minor diameter d is decisive for the stability of the micro end mill. Its minimum value is defined by the optimal micro geometry of the cutting edges for the work material, and by the depth of the helical flute. The geometry of the helical flute is determined by the chip space, which depends on the rake angle x the feed per tooth f; and the depth of cut ap. Theoretically, the optimal value of a minor diameter d is achieved when its enlargement results in an unstable taper (Figure 5) and thus in a rise in tool deflection d Using parameter technology in the FEM strain simulation makes systematic tool optimization possible. Through simulation studies all parametrically established geometrical properties of the given tool model can be varied and optimized in reciprocal dependency.
4 PARAMETRIC TOOL DESIGN In evaluating the tests above, an approach to the tool design was developed that does justice to the load and the application. This approach is illustrated in Figure 4.
Figure 5: FEM-study of minor diameter d.
The FEM-simulation of the optimized tool design, exemplarily shown in Figure I d , provides a significant advantage compared to conventional micro end mills. Through the tangential change, strain peaks contingent to the tool's geometry can be eliminated in the neck area. Furthermore the minimum circular cross-section is shifted nearer to the tool tip. The maximum equivalent stress at this position is significantly lower, in keeping in line with the bending moment, than that of a conventional micro end mill of the same length.
Figure 4: Parametric tool design for micro end mills
The main objective is to reduce the maximum length of the cutting part a to the depths of cut ap, thereby taking into account a safety margin for wear. The connection of the cutting part with the effective tool length / for the application has the radius r. This radius r is tangent to both the minor diameter d and the taper at the neck from the shaft to the cutting part. From this the radius r is determined by geometry. The tapering of the tool realized on the basis of these calculations prevents contact with the work piece, thus reducing additional strain through friction forces. The tool diameter D of the micro end mill is set depending on the application. The axial angle of the flute pA allows for a soft penetration into the work piece . Its minimum value results from the demands of tool manufacturing technology. For instance, for a micro end mill manufactured by grinding, with a tool diameter of D = 0.5 mm and an effective tool length of / = 2.5 mm, a minimum axial angle of the flute of pA = 15 O can be realized. By reducing the cutting part to the tool tip
5 In order to verify the parametric tool design, micro end mills were manufactured with D . / = 0.5 mm . 2.5 mm (Figure I c ) and D . I = 0.1 mm . 1 mm (Figure 6). For the tools with diameter D of 0.5 mm, the minor diameter d was also varied in accordance with theoretical considerations. All test tools were coated with TiAIN.
EXPERl M ENTAL VERl FI CATION
Figure 6: Micro end mill with D = 0.1 mm.
Figure 7 illustrates the results of the tests of total machined length W. A series of experiments with micro end mills of conventional geometry and an effective tool length / of 1.5 mm were used as a reference. For these experiments processing conditions for finishing were
selected, such as e.g. a depth of cut ap and a width of cut ap of 0.05 mm respectively. A mean roughness depth Rz of 5 pm was defined as a criterion of tool life and the tests ended after tool breakage or when the machined surface clearly deteriorated. One result that could be shown was a reduced risk of tool breakage because of the optimized parametric tool design. Another was a process- reliable increase in tool life of almost 30 %. It also became clear that enlarging the minor diameter d does not necessarily contribute to an increase in the stability of the micro end mill and thus to an improvement in the machining result. The deterioration of the machined surface is a result of the low stability of the tool with the higher minor diameter d, as could already be shown in the FEM-study of the minor diameter d.
Figure 7: Total machined lengths for various tool designs (*: broken tools /total number of test tools).
Going beyond the test of total machined length W, the hardness of the work material PM X19OCrVMo 20 was increased step-by-step. Then reference structures were milled on it. The processing conditions were identical with those of the tests of the total machined length W. It was milled in a full and a local section. With the micro end mill d = 0.4 mm, it was possible to achieve an aspect ratio of the flute of 5 : l at a hardness of 62 HRC (Figure 8). Further, it was possible to generate nearly burr-free thin walled bars in various shapes.
Figure 8: Micro cavities in PM X19OCrVMo 20 (62 HRC).
6 CONCLUSION Micro cutting using cemented carbide end mills is a highly dynamic machining process. The tool loads resulting from this process must be taken into consideration in the design of such tools. In this paper a weak-point analysis showed that the design of today's micro end mills is not appropriate for the type of load they have to withstand. As a result of this analysis, a parametric tool design was developed for micro end mills with which the previous machining limits of this technology could be extended. The tool design is characterized by a reduction of the length of
the cutting part to realistic processing conditions as well as by a tangential change from the cutting part to the taper. A further characteristic is the tapered shape of the tool avoiding any contact with the work piece outside of the machining zone. The innovative tool design was verified successfully by machining the tool steel PM X19OCrVMo 20. With this a process-reliable increase in endurance of up to 30 % and an aspect ratio of 5.1 could be achieved for a hardness of 62 HRC. With these machining results it could be shown that the limits of micro cutting with cemented carbide end mills have not been reached by conventional tool concepts. In fact, it is possible to tap new potential, especially for application areas such as mould and die production for mass manufacturing of micro components for consumer products, or for the direct production of micromechanical steel components.
7 This work is supported by the "Federal Ministry of Econom...