Coupled interaction of dynamic responses of tool and workpiece in thin wall milling

https://doi.org/10.1016/j.jmatprotec.2013.03.018Get rights and content

Highlights

  • Coupled dynamic response between thin wall workpiece & tool is studied in machining.

  • Two types of geometries – straight cantilever and ring type casing are considered.

  • Tooth frequency harmonics are modulated at machine tool & workpiece frequencies.

  • For straight wall tool bending and workpiece modes noticed at all depths of cut.

  • Ring type casing shows participation of tool torsional mode instead of bending mode.

Abstract

Chatter free thin wall machining requires knowledge of the dynamics of a machine-tool system and workpiece either for designing damping solutions or for modelling impact dynamics. Previous studies on thin wall milling mostly focussed on stability studies. However studies on the interaction between the tool and workpiece responses in thin wall machining are scarce in the literature. In this work, the coupled dynamic response of tool and workpiece is presented both for an open (thin wall straight cantilever) and for closed (thin wall ring type casing) geometry structures. Experiments were carried out for different tool overhangs and depths of cut and the machining vibration signal was analysed in time–frequency domain to study the interaction, i.e. coupling, of tool–workpiece dynamic response at various cutting tooth engagement/idle times. The findings from this study highlight the importance of tool's frequency, particularly torsional and first bending modes, in impact dynamics of thin wall milling. Moreover, the differences in dynamic response interaction between a cutting tool and thin wall plate and a cylinder are identified. While the analysis of the open geometry structure showed the presence of tool and workpiece responses for any depth of cut, results on closed geometry structure exhibited a complete dominance of tool mode at higher depths of cut. These findings are of critical importance in understanding the impact dynamics in thin wall milling and also of effectiveness of passive damping solutions.

Introduction

Thin wall integrally stiffened structures are common in aerospace industries due to the advantages they offer, such as low specific weight and lesser design and fabrication time, while fulfilling the required part functionality. With thin wall machining of complex geometry parts, the need for expensive, time-intensive multiple-part manufacturing including laborious setups on different machines and the riveting is eliminated significantly. One example of thin wall machining of an integrally stiffened structure is a Boeing avionics rack which had 44 parts riveted previously and was converted to a 6-piece assembly with a reduction in manufacturing time from 1028 h to 38.6 h and also a cost reduction of 73% (Koelsch, 2001). The inherent low stiffness of thin wall geometries can introduce machining challenges, related to static deflections of the workpiece and chatter. Characterisation and control of static deflections and chatter are crucial to achieving dimensional accuracy of the machined component and maintaining optimum consumable and machine-tool life.

Tobias and Fishwick (1958) proposed initial chatter stability theory with the concept of dynamically varying chip thickness (regenerative chatter) in orthogonal cutting. Tlusty and Polacek (1963) proposed oriented transfer function in the direction of resultant cutting force for dynamic forces and displacements. Both these theories yield inaccurate results for oblique cutting where the cutting edge is inclined with respect to the direction of cutting. Moreover this theory was developed based on linear stability assumption, which ignores factors such as tool jumping the cut, process damping, and nonlinear cutting constant due to varying cutting force direction. Sridhar et al. (1968) made a comprehensive model of milling dynamics and proposed time-varying directional dynamic milling coefficients and then used numerical procedures for evaluating stability limits. Minis and Yanushevsky (1993) applied stability concepts of periodic systems for evaluating the stability of milling model proposed by Sridhar et al. (1968). Budak and Altintas (1998) developed analytical formulation in frequency domain for predicting milling stability considering both endmill and workpiece as multi-DOF systems and this model is being widely used due to its faster computation time as compared to previous time domain simulations and also due to its ability to predict chatter frequency. The stability algorithm essentially takes the cutting coefficients and transfer functions in X & Y directions for endmill and workpiece at different nodes along axial depth and formulates the problem as an eigenvalue equation and performs stability analysis to find out stable spindle speeds and corresponding axial or radial depth of cuts. Subsequent studies on thin wall machining researched into finite element prediction of deflection of thin wall, tool and workpiece systems with similar dynamic response, process planning strategies, error compensation strategies and numerical prediction of workpiece response. Kersting and Biermann (2012) while using time domain simulation for simulating the milling process proposed an alternate approach of modelling workpiece dynamics in the form of multiple decoupled oscillators thereby increasing speed of workpiece displacement calculations as compared to traditional finite element approach of modelling the workpiece. Using this methodology they presented 3D stability lobes with height of workpiece as the third dimension, to consider for varying dynamics of thin wall during machining. Altintas and Weck (2004) gave an in-depth review including the mathematical formulation of chatter stability in various metal cutting processes: turning, boring, drilling, milling and grinding. They have also reviewed the passive and active strategies for mitigating the chatter. Recently Quintana and Ciurana (2011) also presented a review of chatter research and related publications and reported the research by categorising them into online and offline strategies for chatter mitigation and also passive and active chatter damping.

The knowledge of the dynamic response interaction of tool and workpiece complements the analytical models for predicting stable machining parameters in high speed machining, particularly in peripheral milling where cutting is intermittent. It also helps in evaluating the effectiveness of damping of milling vibrations through the study of frequency spectrum. It is this latter part that is of interest in this work. Davies and Balachandran (2000) studied the vibrations measured on a thin wall plate using various tools such as time series, power spectra, phase portraits, etc. They reported that the tooth cutting frequency and its harmonics are noticed in the power spectrum and that these harmonic peaks are modulated over a wide frequency band where a workpiece mode exists. The prominent appearance of tooth engagement frequency with increasing radial depth of cut was highlighted using auto bi-spectra. However, they did not make any mention about tool's natural frequency in the acquired vibration spectrum. Also while the time series and phase portrait plots show the tool workpiece interaction and workpiece free vibration, no study was reported on the actual toolworkpiece interaction during and after the cut. This offers an insight into the evolution of tool and workpiece frequencies as the thin wall is being machined and also the extent to which each of this dominates the spectrum. Homberg et al. (2013) presented coupling of process and structure models to predict the stable and unstable machining conditions in end milling of solid block and thin walls. They modelled the machine-tool as multibody systems and workpiece as thermo-elastic body and evaluated the process as stable or unstable using the frequency spectrum plots of cutting force and chip thickness variation. However as their focus was on finding stability of the process they did not analyse the reason for amplification of selected harmonics in the frequency spectrum which is needed to study coupled interaction.

The above-mentioned research deals with milling of only thin walls probably due to the importance of improving productivity in machining thin wall ribs and walls in aerospace structures such as integrally stiffened fuselage panels and bulk heads. However, thin wall casings and rings such as in jet engine casings also present machining challenges due to chatter. And the dynamic characteristics of a thin wall casing are different from that of straight thin wall owing to the inherent stiffness it offers and also due to symmetry of the structure. Lai and Chang (1995) studied the stability characteristics while turning a thin wall cylindrical workpiece clamped by a three-jaw chuck. They reported that the vibration properties such as stiffness coefficient and vibration direction angle of beam and shell modes change with the relative position of the cutting tool to the chucking jaw. However no work was reported on the dynamic interaction of tool and workpiece. One of the significant conclusions from both Davies and Balachandran (2000) and Lai and Chang (1995) is that the vibration characteristics of workpiece changes with the position of the cutting tool along a toolpath. So these studies indicate participation of different workpiece modes at different positions of machining. Bera et al. (2010) reported the effect of cutter and workpiece flexibilities on static error during machining of thin wall tubular geometries through mechanistic modelling of forces and prediction of error using numerical analysis. But dynamic interaction of tool and thin wall tube is not covered. Little research on the dynamics of thin casing machining and the interaction of tool and workpiece is reported.

With the above findings, present work was focussed on understanding of the following two aspects, which were hitherto not reported but useful in modelling the impact dynamics which can be used in simulating passive and active damping solutions.

  • Importance of tool's frequency in the coupled dynamic interaction of tool and workpiece in thin wall machining

  • Variation in the coupled interaction for closed geometry structures such as ring type casings with respect to open geometry structures which were researched in the literature

The interaction of the tool and workpiece is studied when successive teeth are engaged in cutting and during the idle period. The work has been directed to understand (via time–frequency domain) of the acceleration signals how the resultant coupled dynamic response varies at the different levels of cutting forces (as a result of cutting teeth engagement/disengagement). Two workpiece geometries were considered:

  • Milling of a simple thin wall straight cantilever (an open geometry) – This has been conducted to study the tool–workpiece interaction for a plate type structure; the results of which will be compared with that presented in Davies and Balachandran (2000).

  • Milling of a thin wall ring type casing (a closed geometry) – This has been conducted to understand how the difference in dynamic nature of a thin wall plate and cylinder affects the vibration coupling between the tool and workpiece.

All the experiments were conducted in stable (chatter-free) machining zone. That is, the coupled interaction between tool and workpiece is studied in forced vibration situation due to excitation of tool. This consideration looks reasonable mainly due to the facts: (a) most of the aerospace casings are made of superalloys for which the cutting speeds are low and hence chances for machine-tool system induced chatter are low where process damping is significant, (2) the circular casings are inherently stiff due to their closed geometry making workpiece induced chatter relatively difficult phenomenon to appear as compared to thin straight wall (open geometry). The methodology of evaluation of tool–workpiece coupling or interaction is schematically shown in Fig. 1 and essentially contains the following steps:

  • Step 1:

    Determine the dynamic response (frequency response function) of tool and workpiece using impact hammer testing; this gives information regarding the natural frequencies of the tool and workpiece and their relative flexibilities.

  • Step 2:

    Acquire the vibration signal and cutting force synchronously during the machining of a thin wall component.

  • Step 3:

    Analyse the vibration signal for one tool rotation and make sections corresponding to various force levels (exerted during tooth's engagement) which enables the understanding of how the coupling varies with contact pressure between the tool and workpiece.

  • Step 4:

    Evaluate the frequency content of the signal in each section through fast Fourier transform (FFT); this shows the evolution of each frequency component as the cutting engages and disengages the workpiece.

Steps 3 and 4 can be combined using short time Fourier transform (STFT) analysis which basically does the same process of sectioning data and finding FFT for each section data. However, STFT is more useful when the modes are distinct and far apart so that energy is not spread across many frequencies, in which case it will be difficult to draw quantified conclusions from the contours of the STFT plot; hence in this work, STFT is used in cases where few modes exist (straight thin wall) and a waterfall plot of FFTs (3D FFTs) at various sections in more complex situations (thin wall cylinder).

Section snippets

Experimental setup

In order to identify the coupling interaction between the thin wall structures and tool/machine tool system sets of experiments have been organised on two main categories of workpiece geometries: thin wall open structure (straight cantilever) closed structure (ring type casing). The reason for choosing these categories is to understand the preponderance of torsional and bending modes of tool on the open (e.g. cantilever type) and closed (e.g. ring type) structures.

Results and discussion

In this section, the results of the dynamic response coupling of the tool and workpiece and interpreted through frequency and time-frequency domain analysis of the machining signals will be presented for both open (e.g. cantilever plate) and closed (e.g. ring type casing) part geometries. Attention is paid on the variation of frequency components with time of cutting tooth engagement into the workpiece.

Conclusions

The interaction of the tool and workpiece dynamic responses in thin wall machining is experimentally demonstrated through two case studies – machining of open (straight cantilever) and closed (ring type casing) geometry workpiece structures. Analysis in frequency domain (FFT) and time-frequency domain (STFT & 3D FFTs) was carried out on the acceleration signals acquired during machining. An FFT shows the different modes that are participating in the machining vibration thereby offering insight

Acknowledgements

The authors would like to thank EPSRC and Rolls-Royce for providing the funding under Dorothy Hodgkin Postgraduate Award scholarship through grant number EP/P505917/1 to undertake this research. They would like to thank Mr Peter Winton of Rolls Royce and Dr Mark Raffles of Rolls Royce UTC at University of Nottingham for their support through discussions and reviews. Special thanks also go to Stuart Branston and Mark Daine of University of Nottingham for supporting all the experimental

References (13)

There are more references available in the full text version of this article.

Cited by (68)

  • Towards high milling accuracy of turbine blades: A review

    2022, Mechanical Systems and Signal Processing
View all citing articles on Scopus
View full text