# A Study on Improving the Machining Performance of Scrolls
## 3 Chatter Suppression  
After the rough machining processes, most of the workpiece materials are removed and the stiffness of the scrolls is significantly diminished. The overall stiffness of the milling machine will be also reduced if the spindle speed and the feed rate are raised to increase the machining efficiency. These conditions are prone to eventually induce the occurrence of chatter. Therefore, it is worth considering the issues of chatter suppression while confronting such conditions during the machining of thin-wall workpieces for the manufacture of scrolls, as mentioned above. In end-milling processes, [PERSON] [26] proposed the vibration model to be a system with two degrees of freedom. The vibration amplitude simulated from this system corresponds to the regenerative waviness and can be used to compute the chip thickness. The phase shift occurring between two tool paths affects the chip thickness, decreases the machining quality, and varies the force on the cutting edge. Applying a varying force to a machining process system eventually induces the occurrence of chatter. Therefore, to stabilize the machining processes, it is necessary to keep the chip thickness consistent and avoid the occurrence of phase shifts. The relationship between vibration frequency and tooth frequency is shown by the following equation [27]:  
\[\frac{h}{h_{z}}=N+\frac{\varepsilon}{2\pi} \tag{4}\]  
where \(h\) is the vibration frequency, \(h_{z}\) is the tooth frequency, \(N\) is the number of complete waveforms between adjacent teeth, and \(\varepsilon\) is the phase shift angle between two corrugations. When chatter occurs, the vibration frequency \(h\) shown in Equation (4) is also called the chatter frequency. As mentioned above, the phase shifts between the cutting ripples occurring in the milling processes, except for phase angles equal to \(0^{\circ}\) and \(180^{\circ}\), vary the chip thickness and are prone to induce the occurrence of chatter. It can also be observed from Equation (4) that the ratio between vibration frequency and tooth frequency is not an integer when chatter occurs. As shown in Figure 2, the relationships between the spindle speed and the depth of the cut, which are named the stability lobes, can be obtained from the transfer function of the vibration system mentioned above. The results shown in Figure 2 can also be obtained by subjecting the cutter to a percussion test. In the milling process, the machining parameters may be located in the upper region of the stability lobes (for example, the red diamond indicated in Figure 2), and this also means that cutting instability occurs. To prevent the occurrence of chatter, two methods can be used: one is to reduce the axial cutting depth and the other is to change the spindle speed. For example, as shown in Figure 2, the red diamond can be moved to the locations of the green dots or blue squares, which are stable regions. As the axial cutting depth cannot be directly changed during the machining process, we changed the real-time spindle speed to suppress the occurrence of chatter. Differently from the detecting methods used by [PERSON] et al. [28]--i.e., with vibration sensors embedded in the spindle--we utilized a microphone to capture the audio signals and detect the tooth frequency. A general-purpose microphone was sufficient for the experiments since the monitored chatter frequency was around 2300 Hz. In addition, a line-directional microphone was chosen to minimize the effects of environmental noise. The fast Fourier transformation (FFT) was used to convert the audio frequencies from the time domain to the frequency domain promptly. The results were used to observe the distribution and intensity of the tooth frequency. We also used the amplitude to determine the magnitude of the tooth frequency when chatter occurred and calculated the multiple factor, which is denoted \(K\) and defined as the ratio between the tooth frequency and the vibration frequency detected by the microphone.