Commenced in January 2007
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Paper Count: 2

Search results for: Stability lobes

2 Chatter Stability Characterization of Full-Immersion End-Milling Using a Generalized Modified Map of the Full-Discretization Method, Part 1: Validation of Results and Study of Stability Lobes by Numerical Simulation

Authors: Chigbogu G. Ozoegwu, Sam N. Omenyi

Abstract:

The objective in this work is to generate and discuss the stability results of fully-immersed end-milling process with parameters; tool mass m=0.0431kg,tool natural frequency ωn = 5700 rads^-1, damping factor ξ=0.002 and workpiece cutting coefficient C=3.5x10^7 Nm^-7/4. Different no of teeth is considered for the end-milling. Both 1-DOF and 2-DOF chatter models of the system are generated on the basis of non-linear force law. Chatter stability analysis is carried out using a modified form (generalized for both 1-DOF and 2-DOF models) of recently developed method called Full-discretization. The full-immersion three tooth end-milling together with higher toothed end-milling processes has secondary Hopf bifurcation lobes (SHBL’s) that exhibit one turning (minimum) point each. Each of such SHBL is demarcated by its minimum point into two portions; (i) the Lower Spindle Speed Portion (LSSP) in which bifurcations occur in the right half portion of the unit circle centred at the origin of the complex plane and (ii) the Higher Spindle Speed Portion (HSSP) in which bifurcations occur in the left half portion of the unit circle. Comments are made regarding why bifurcation lobes should generally get bigger and more visible with increase in spindle speed and why flip bifurcation lobes (FBL’s) could be invisible in the low-speed stability chart but visible in the high-speed stability chart of the fully-immersed three-tooth miller.

Keywords: chatter, flip bifurcation, modified full-discretization map stability lobe, secondary Hopf bifurcation

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1 Milling Chatter Prevention by Adaptive Spindle Speed Tuning

Authors: Nan-Chyuan Tsai, Din-Chang Chen, Rong-Mao Lee, Bai-Lu Wang

Abstract:

This paper presents how the real-time chatter prevention can be realized by feedback of acoustic cutting signal, and the efficacy of the proposed adaptive spindle speed tuning algorithm is verified by intensive experimental simulations. A pair of microphones, perpendicular to each other, is used to acquire the acoustic cutting signal resulting from milling chatter. A real-time feedback control loop is constructed for spindle speed compensation so that the milling process can be ensured to be within the stability zone of stability lobe diagram. Acoustic Chatter Signal Index (ACSI) and Spindle Speed Compensation Strategy (SSCS) are proposed to quantify the acoustic signal and actively tune the spindle speed respectively. By converting the acoustic feedback signal into ACSI, an appropriate Spindle Speed Compensation Rate (SSCR) can be determined by SSCS based on real-time chatter level or ACSI. Accordingly, the compensation command, referred to as Added-On Voltage (AOV), is applied to increase/decrease the spindle motor speed. By inspection on the precision and quality of the workpiece surface after milling, the efficacy of the real-time chatter prevention strategy via acoustic signal feedback is further assured.

Keywords: Chatter compensation, Stability lobes, Non-invasivemeasurement

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