EXPERIMENTAL VALIDATION OF CUMULATIVE SURFACE LOCATION ERROR FOR TURNING PROCESSES

The aim of this study is to create a mechanical model which is suitable to investigate the surface quality in turning processes, based on the Cumulative Surface Location Error (CSLE), which describes the series of the consecutive Surface Location Errors (SLE) in roughing operations. In the established model, the investigated CSLE depends on the currently and the previously resulted SLE by means of the variation of the width of cut. The phenomenon of the system can be described as an implicit discrete map. The stationary Surface Location Error and its bifurcations were analysed and flip-type bifurcation was observed for CSLE. Experimental verification of the theoretical results was carried out

Cumulative Surface Location Error for Milling Processes Based on Tool-tip Frequency Response Function

AbstractIn milling processes, the desired machined surface cannot be perfectly achieved even in case of chatter-free machining due to the thermally induced errors, the trajectory following errors and the most significant one: the cutting force induced vibration errors. In case of vibration, the error is represented by the so-called Surface Location Error (SLE), which is the distance between the machined and the required surface position. In case of roughing operations, these errors can have a significant impact on the surface position due to the interaction between the subsequent SLEs. The machined surface depends on the previously resulted SLE through the variation of the radial immersion. In this paper, the series of the consecutive SLEs are investigated in a multi-degree-of-freedom model. The dynamical behaviour of the milling tool is described by frequency response functions. The variation of the SLE values is governed by a discrete map, which may lead to an unpredictable final surface position. The parameter range where this unpredictable final SLE occurs is presented together with the traditional stability chart representing the chatter-free domains of cutting parameters. With the proposed methods, the traditional stability chart can be improved, from which chatter-free and CSLE-stable technological parameters can be selected

In-Process Monitoring of Changing Dynamics of a Thin-Walled Component During Milling Operation by Ball Shooter Excitation

During the milling of thin-walled workpieces, the natural frequencies might change radically due to the material removal. To avoid resonant spindle speeds and chatter vibration, a precise knowledge of the instantaneous modal parameters is necessary. Many different numerical methods exist to predict the changes; however, small unmodelled effects can lead to unreliable results. The natural frequencies could be measured by human experts based on modal analysis for an often interrupted process; however, this method is not acceptable during production. We propose an online measurement method with an automatic ball shooter device which can excite a wide frequency range of the flexible workpiece. The method is presented for the case of blade profile machining. The change of the natural frequencies is predicted based on analytical models and finite element simulations. The measurement response for the impulse excitation of the ball shooter device is compared to the results of impulse modal tests performed with a micro hammer. It is shown that the ball shooter is capable of determining even the slight variation of the natural frequencies during the machining process and of distinguishing the slight change caused by different clamping methods. An improved FE model is proposed to include the contact stiffness of the fixture

EXPERIMENTAL VALIDATION OF CUMULATIVE SURFACE LOCATION ERROR FOR TURNING PROCESSES

The aim of this study is to create a mechanical model which is suitable to investigate the surface quality in turning processes, based on the Cumulative Surface Location Error (CSLE), which describes the series of the consecutive Surface Location Errors (SLE) in roughing operations. In the established model, the investigated CSLE depends on the currently and the previously resulted SLE by means of the variation of the width of cut. The phenomenon of the system can be described as an implicit discrete map. The stationary Surface Location Error and its bifurcations were analysed and flip-type bifurcation was observed for CSLE. Experimental verification of the theoretical results was carried out

Stochastic semidiscretization method: Second moment stability analysis of linear stochastic periodic dynamical systems with delays

In this paper, an efficient numerical approach is presented, which allows the analysis of the moment dynamics, stability, and stationary behavior of linear periodic stochastic delay differential equations. The method leads to a high dimensional stochastic mapping with periodic statistical properties, from which the periodic first and second moment mappings are derived. The application of the method is demonstrated first through the analysis of the stochastic delay Mathieu equation. Then a practical case study, where the effect of spindle speed variation on the stability and the resulting surface quality of turning operations is investigated

Stochastic semi-discretization for linear stochastic delay differential equations

An efficient numerical method is presented to analyze the moment stability and stationary behavior of linear stochastic delay differential equations. The method is based on a special kind of discretization technique with respect to the past effects. The resulting approximate system is a high dimensional linear discrete stochastic mapping. The convergence properties of the method is demonstrated with the help of the stochastic Hayes equation and the stochastic delayed oscillator

Stochastic modeling of the cutting force in turning processes

The main goal of this study is to introduce a stochastic extension of the already existing cutting force models. It is shown through orthogonal cutting force measurements how stochastic processes based on Gaussian white noise can be used to describe the cutting force in material removal processes. Based on these measurements, stochastic processes were fitted on the variation of the cutting force signals for different cutting parameters, such as cutting velocity, chip thickness, and rake angle. It is also shown that the variance of the measured force signal is usually around 4–9% of the average value, which is orders of magnitudes larger than the noise originating from the measurement system. Furthermore, the force signals have Gaussian distribution; therefore, the cutting force model can be extended by means of a multiplicative noise component

Chatter formation during milling due to stochastic noise-induced resonance

In this paper, the stochastic dynamical model of a single-degree-of-freedom milling operation is formulated, where a Gaussian white noise process models the high-frequency variation in the cutting force. With the help of this stochastic model, it is shown, that large-amplitude stable vibrations can occur near the critical machining parameters, due to stochastic noise-induced resonance. During the analysis, the second moment stability and stationary first and second moment behavior of the periodic stochastic delay differential equation (SDDE) describing the milling operation are investigated. The behavior of these quantities are then compared to the evolution of the so-called “chatter peak” in the Fourier-spectrum of the vibrations, that is used to experimentally determine the presence of chatter, in the stable machining parameter domain. Furthermore, it is discussed, how the statistical properties of the resonant vibrations can be used to predict the stability boundary and the formulation of chatter, while the machining parameters are kept in the safe region. The theoretical calculations are supported by experiments performed on a single-degree-of-freedom system