Development of Automatic Chatter Suppression System in Parallel Milling by Real-Time Spindle Speed Control with Observer-Based Chatter Monitoring

Abstract

To maximize the potential for high material removal rates in simultaneous processes such as parallel milling, developing strategies for successful chatter suppression/avoidance is an important concern for manufacturers. In this study, the effectiveness of the spindle speed difference method (SDM) for chatter suppression is discussed in a parallel end-milling process where a flexible workpiece is machined by two tools rotating in opposite direction. The process model is developed, considering that the dynamic variation due to the regenerative effect occurs on a plane perpendicular to the tool axis direction. Through the process simulations and the experiments, this study provides informative discussion for comprehending the process behavior. Additionally, a real-time active chatter suppression system with adaptive SDM, where the spindle speed difference is sequentially optimized during the process according to the tracked chatter frequency, is developed by integrating a chatter monitoring system based on sensorless cutting force estimation with sliding discrete Fourier transform. The results show that the developed real-time adaptive system of spindle speed suppresses chatter vibrations more effectively than non-adaptive SDM system; hence, the integrated system can contribute self-optimizing machining systems oriented to Industry 4.0.

Appendix

Equation (10) can be rearranged as follows:

$$\begin{aligned} & \left\{ {\begin{array}{*{20}c} {F_{z}^{w} } \\ {F_{y}^{w} } \\ \end{array} } \right\} + \frac{1}{2}a_{p} K_{tc} \left[ {DM_{\Delta } } \right]\left[ {TF} \right]\left\{ {\begin{array}{*{20}c} {F_{z}^{w} } \\ {F_{y}^{w} } \\ \end{array} } \right\} = \frac{1}{2}a_{p} K_{tc} \left\{ {\left[ {A_{0} } \right] - e^{{ - i\varepsilon^{t1} }} \left[ {DM_{\Delta } } \right]} \right\}\left[ {TF} \right]\left\{ {\begin{array}{*{20}c} {F_{z}^{w} } \\ {F_{y}^{w} } \\ \end{array} } \right\} + \frac{1}{2}a_{p} K_{tc} \left[ {DM_{\Delta } } \right]\left[ {TF} \right]\left\{ {\begin{array}{*{20}c} {F_{z}^{w} } \\ {F_{y}^{w} } \\ \end{array} } \right\} \\ & \quad \to \left\{ {\left[ I \right] + \frac{1}{2}a_{p} K_{tc} \left( {\left[ {DM_{\Delta } } \right] - \left[ {A_{0} } \right]} \right)\left[ {TF} \right]} \right\}\left\{ {\begin{array}{*{20}c} {F_{z}^{w} } \\ {F_{y}^{w} } \\ \end{array} } \right\} = \frac{1}{2}a_{p} K_{tc} \left( {1 - e^{{ - i\varepsilon_{1} }} } \right)\left[ {DM_{\Delta } } \right]\left[ {TF} \right]\left\{ {\begin{array}{*{20}c} {F_{z}^{w} } \\ {F_{y}^{w} } \\ \end{array} } \right\} \\ & \quad \to \left\{ {\left[ I \right] + \frac{1}{2}a_{p} K_{tc} \left( {\left[ {DM_{\Delta } } \right] - \left[ {A_{0} } \right]} \right)\left[ {TF} \right]} \right\}\left\{ {\begin{array}{*{20}c} {F_{z}^{w} } \\ {F_{y}^{w} } \\ \end{array} } \right\} = \lambda \left[ {DM_{\Delta } } \right]\left[ {TF} \right]\left\{ {\begin{array}{*{20}c} {F_{z}^{w} } \\ {F_{y}^{w} } \\ \end{array} } \right\} \\ \end{aligned}$$

(17)

By solving the general eigenvalue problem of Eq. (17) and obtaining the eigenvalues, the critical axial depth of cut, a_p(lim) can be derived similarly as in the conventional milling process, as follows:

$$a_{{p\left( {\lim } \right)}} = \frac{{\lambda_{R} }}{{K_{tc} }}\left\{ {1 + \left( {\frac{{\lambda_{I} }}{{\lambda_{R} }}} \right)^{2} } \right\}$$

(18)

The axial depth of cut term is included in the left-hand side of Eq. (17). Therefore, the eigenvalues were searched such that the initially set value of the axial depth of cut was equal to the value calculated using Eq. (18) while updating the initial value.