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Continuous Learning Support Vector Machine to Estimate Stability Lobe Diagrams in Milling Continuous Learning Support Vector Machine to Estimate Stability Lobe Diagrams in Milling Jens Friedrich*, Henning Hartmann, Alexander Verl, and Armin Lechler * Corresponding author: Tel.: (+49711) 685 82416; Fax: (+49711) 685 72416; Email: jens.friedrich@isw.unistuttgart.de 1Department University or Company City, State, Zip Code, Country Institute for Control Engineering of Machine Tools and Manufacturing Units, University of Stuttgart, D70174 Stuttgart, Germany 3Department University or Company City, State, Zip Code, Country ABSTRACT The productivity of milling processes is limited by the occurrence of chatter vibrations. The correlation of the maximum stable cutting depth and the spindle speed can be shown in a stability lobe diagram (SLD). Today it is a great effort to estimate the SLD. Lot´s of experiments are necessary to measure the SLD or derive a detailed mathematical model to calculate the SLD. Moreover not only cutting depth, but also the cutting width should be taken into account. This paper presents an approach to learn the multidimensional stability lobe diagram (MSLD) during the production based on continuously measured signals using a support vector machine. The support vector machine is extended to make it capable for continuous learning and timevariant systems. The process conditions are classified as stable or unstable. The learned MSLDs are very similar to the analytically calculated MSLDs. Changes over time in the system dynamics can also be learned by the proposed algorithm. 1. INTRODUCTION Increasing the productivity and performance is one of the most important objectives in todays’ machining industries. One of the limiting factors of productivity is chatter. The chatter vibrations can cause bad surface quality or even damage the work piece, the tool, or the machine tool itself. The appearance of chatter vibrations depends on the spindle speed, the machine dynamics, the tool, the material and the depth of cut [1]. To reach maximum productivity the width and depth of cut should be chosen close to the stability limit. Thus it is necessary to provide the information about the stability limit for each toolmaterialcombination to the machine user. Regenerative chatter is the main problem limiting the productivity of turning and milling processes. Due to the flexible structure of the machine tool, the interaction between the surface left by the last tooth and the current tooth of the cutting tool leads to selfexcited vibrations. Thus this effect can be described as a timedelay system, which time delay is given by the rotation speed of the spindle [2]. Since the late 1950s there have been several studies investigating the effect of regenerative chatter [3] [4]. As the chatter is a feedback with time delay the spindle speed, causing the delay, and the depth of cut, causing the excitation, are the main parameters influencing the stability of the system. All pairs of spindle speed and depth of cut can be classified as stable or unstable. This can be graphically represented in a stability lobe diagram (SLD) where the border between stable and unstable conditions is drawn [5]. There exist several ways to generate the SLDs. Experimentally they can be extracted by doing cuts for each spindle speed with increasing depth of cut. Based on the measured results for each spindle speed the maximum stable depth of cut can be estimated [6]. A similar approach is to cut with constant depth of cut but increasing spindle speed. By analyzing the vibration signal for each depth of cut the stable spindle speeds can be located [7]. Based on a mathematic model of the milling process the SLDs can also be simulated or calculated. For example Zatrain [8] analyzed the results in time and frequency domain. The semidiscretization method [9] is another possibility to analyze the stability of time delayed systems. Based on the SLD, the spindle speed with the maximum depth of cut can be selected. Budak [10] showed, that the critical depth of cut depends on the width of cut. The SLDs are changing for different widths of cut. To reach maximum material removal rate the SLD has to be extended to find optimal pairs of width and depth of cut [10]. Thus the two dimensional SLDs are only suitable to select the optimal depth of cut for one width of cut. The main drawback of the methods to estimate the SLD mentioned above is, that there are several measurements necessary to extract the SLD itself or to get the mathematical model that can be used to calculate the SLD analytically.
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Transcript  Continuous Learning Support Vector Machine to Estimate Stability Lobe Diagrams in Milling Continuous Learning Support Vector Machine to Estimate Stability Lobe Diagrams in Milling Jens Friedrich*, Henning Hartmann, Alexander Verl, and Armin Lechler * Corresponding author: Tel.: (+49711) 685 82416; Fax: (+49711) 685 72416; Email: jens.friedrich@isw.unistuttgart.de 1Department University or Company City, State, Zip Code, Country Institute for Control Engineering of Machine Tools and Manufacturing Units, University of Stuttgart, D70174 Stuttgart, Germany 3Department University or Company City, State, Zip Code, Country ABSTRACT The productivity of milling processes is limited by the occurrence of chatter vibrations. The correlation of the maximum stable cutting depth and the spindle speed can be shown in a stability lobe diagram (SLD). Today it is a great effort to estimate the SLD. Lot´s of experiments are necessary to measure the SLD or derive a detailed mathematical model to calculate the SLD. Moreover not only cutting depth, but also the cutting width should be taken into account. This paper presents an approach to learn the multidimensional stability lobe diagram (MSLD) during the production based on continuously measured signals using a support vector machine. The support vector machine is extended to make it capable for continuous learning and timevariant systems. The process conditions are classified as stable or unstable. The learned MSLDs are very similar to the analytically calculated MSLDs. Changes over time in the system dynamics can also be learned by the proposed algorithm. 1. INTRODUCTION Increasing the productivity and performance is one of the most important objectives in todays’ machining industries. One of the limiting factors of productivity is chatter. The chatter vibrations can cause bad surface quality or even damage the work piece, the tool, or the machine tool itself. The appearance of chatter vibrations depends on the spindle speed, the machine dynamics, the tool, the material and the depth of cut [1]. To reach maximum productivity the width and depth of cut should be chosen close to the stability limit. Thus it is necessary to provide the information about the stability limit for each toolmaterialcombination to the machine user. Regenerative chatter is the main problem limiting the productivity of turning and milling processes. Due to the flexible structure of the machine tool, the interaction between the surface left by the last tooth and the current tooth of the cutting tool leads to selfexcited vibrations. Thus this effect can be described as a timedelay system, which time delay is given by the rotation speed of the spindle [2]. Since the late 1950s there have been several studies investigating the effect of regenerative chatter [3] [4]. As the chatter is a feedback with time delay the spindle speed, causing the delay, and the depth of cut, causing the excitation, are the main parameters influencing the stability of the system. All pairs of spindle speed and depth of cut can be classified as stable or unstable. This can be graphically represented in a stability lobe diagram (SLD) where the border between stable and unstable conditions is drawn [5]. There exist several ways to generate the SLDs. Experimentally they can be extracted by doing cuts for each spindle speed with increasing depth of cut. Based on the measured results for each spindle speed the maximum stable depth of cut can be estimated [6]. A similar approach is to cut with constant depth of cut but increasing spindle speed. By analyzing the vibration signal for each depth of cut the stable spindle speeds can be located [7]. Based on a mathematic model of the milling process the SLDs can also be simulated or calculated. For example Zatrain [8] analyzed the results in time and frequency domain. The semidiscretization method [9] is another possibility to analyze the stability of time delayed systems. Based on the SLD, the spindle speed with the maximum depth of cut can be selected. Budak [10] showed, that the critical depth of cut depends on the width of cut. The SLDs are changing for different widths of cut. To reach maximum material removal rate the SLD has to be extended to find optimal pairs of width and depth of cut [10]. Thus the two dimensional SLDs are only suitable to select the optimal depth of cut for one width of cut. The main drawback of the methods to estimate the SLD mentioned above is, that there are several measurements necessary to extract the SLD itself or to get the mathematical model that can be used to calculate the SLD analytically. 