6.6
Inverse structural modification on the FTV5
The advantage of inverse SM method over the direct method is that the tool holder geometry can be optimised by solving a single equation. This involves building a single partially constructed numerical model and is thus computation- ally less expensive than the direct method. It will now be shown that, despite the additional complexities of machine data, the inverse SM method may be used to optimise tool holder geometry.
In section 6.3.2 it was shown that the tool holder geometry may be optimised in terms of the stability lobe location, by applying the inverse SM method in a single direction. Since the amplitude of the dominant mode in the y-direction is larger than that of the x-direction, it was used for optimisation purposes, as this mode will have the lowest stability limit. In practice, consideration must be given to the values of µx and µy, as they may change the dominance of these modes
when the oriented FRF is calculated.
It was shown earlier that the undamped direct method was capable of accurately predicting the natural frequency of the modified structure. For this reason, it is unnecessary to include damping when using the inverse method.
6.6.1
Methodology
The data from the modified holder on the FTV5 demonstrates that the modi- fied holder produces a dominant mode at 936 Hz. Therefore using the y-direction experimental model HAas described in section (6.5.1) and the undamped numer-
ical model B(d2) given in Eq. (6.19), both evaluated at ωseek = 2π(936) rad/s,
the inverse SM method was applied using Eq. (6.7). Again this resulted in a polynomial of degree 36 with complex coefficients, since d2 is real, the real and imaginary parts were set to zero and solved using MATLAB’s vpasolve. From the 36 solutions, the negative results and the results out of the possible range of d2 were removed, leaving a single acceptable solution of 0.0336 m, within 1.2% of the expected value of 0.034 m.
GEOMETRY
6.6.2
Discussion
It has been shown that, despite the added complexities of machine data, the in- verse SM method, can be used to optimise the tool holder geometry. Despite the fact that, the location of the stability lobes depends on the resonant frequencies of the oriented FRF, because of the inherent properties of any FRF, the inverse method may be successfully applied in a single direction.
Whilst the direct SM method has the advantage over receptance coupling, that no additional measurements (such as contact stiffness and damping) must be taken; it was shown in section 6.5.2 that damping must still be included in the modi- fication matrix. Moreover, optimising the tool holder geometry using the direct method, still involves the construction of several numerical models. However, the inverse method may be used, without the inclusion of damping, to optimise the holder geometry by solving a single equation, a feature that is not present in the receptance coupling method.
6.7
Summary
The purpose of this chapter was to apply the higher rank SM method to the problem of chatter avoidance in high speed milling operations. The first impor- tant contribution from this investigation was that the inverse SM method may be applied in either the x- or y-direction, despite the stability of a milling operation being dependent on a linear combination of them both. This is an important finding as it simplifies the inverse method, making a solution more likely. Both the direct and inverse SM methods were then applied to experimental data from a spindle rig. The direct method can be successfully used to model how changes in the tool holder geometry affect the tool tip dynamics, and thus the stability of the milling operation. In terms of optimisation, the inverse method has greater potential, as a single equation can be solved to predict a tool holder diameter that will result in stability lobes at a particular spindle speed. When applying the di- rect method to data from the FTV5 milling machine, a viscous damping model was included in the modification matrix, to improve the amplitude prediction.
6.7. SUMMARY Importantly, unlike receptance coupling, no further measurements were needed. The inverse method was applied to data from the FTV5; however in this case, it is unnecessary to include the damping model, as it has little or no effect on the natural frequency. The results of this investigation are important for two reasons, firstly, it provides an efficient method of optimising the tool holder geometry for a given milling operation, which has obvious benefits over the receptance coupling method. And secondly, it provides a new passive chatter avoidance method, that is much simpler than anything that has been presented in previous research.
Chapter 7
Design and Testing of a Tuneable
Tool Holder
The previous chapter demonstrated how structural modification (SM) theory may be used to model and optimise the geometry of a standard HSKA63 tapered tool holder. Consequently, an optimal tooling structure may be selected in order to maximise the mass removal rate of a milling operation. However, the method shown still relies on the user having a large selection of tool holders, with a range of geometers, from which to choose.
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7.1
Introduction
Production rates in high value manufacturing are severely limited by the self- excited vibration known as chatter, and research efforts have thus far concen- trated on using the cutting tool to avoid the onset of such vibrations. Using the method outlined in Chapter 6, it possible to optimise the dynamics of a machine by selecting a tool holder with optimal geometry; however, this involves a signifi-
cant financial investment. Similar to the idea of the variable pitch and helix angle tools [30], a range of tool holders, with variable geometries must be purchased, so that any operation can be optimised.
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. This chapter will, firstly, describe the design process for the new tool holder, from design specification to finalisation and manufacturing. Subsequently, the finished prototype will be tested tested in terms of its suitability for machining trials, and its ability to tune the dynamics of a spindle.