# Hybrid Edge-Cloud-Based Smart System for Chatter Suppression in Train Wheel Repair
## 3 Smart Chatter Suppression in Wheel Reprofiling
### Continuous Spindle Speed Variation (CSSV)  
Some authors [25; 26; 27; 28; 31] have proposed the distortion of the regenerative effect by CSSV around a nominal speed. CSSV creates a time dependency in the delay that can improve stability. The effectiveness of this technique has been demonstrated in several studies in the literature [32; 33; 34].  
This technique is based on the introduction of a perturbation in the spindle speed command. There are different methods for varying the spindle speed, including sinusoidal [35; 36; 37; 38], triangular [39], rectangular [31], random [40], or continuous linear perturbation [41]. The sinusoidal signal has emerged as the most efficient technique compared to random, rectangular, or triangular shapes. Therefore, the sinusoidal spindle speed variation (SSSV) was selected. This consisted of a simple harmonic variation applied on the spindle speed around the nominal speed value.  
When the machining process takes place at low spindle speeds (A & B zones in Figure 5), small variations in the spindle speed bring about relatively large variations in the delay between successive waves. Therefore, low spindle speed amplitude variations can increase the stability in these zones without any relevant side effects. In these areas, the application of CSSV supposes a small increase  
Figure 7: (**a**) Time signal of the test and vibration spectrum at different spindle speeds: (**b**) 60 m/min; (**c**) 50 m/min; (**d**) 40 m/min.  
in the surface roughness and does not jeopardize the life of the main drive if the correct variation is applied [42]. Out of these zones, CSSV is not effective because the variation requirements are not physically reachable [10]. The selection of the amplitude and frequency for sinusoidal CSSV is already an open issue. [PERSON] et al. [37] proposed simple formulae to define the parameters of the variation. These formulae are only approximate and do not consider the effect of process damping, which was dominant in the present case. Nevertheless, some facts related to CSSV are well-known, such as the fact that the variation of the amplitude has a bigger effect than the frequency variation [36; 43].  
The portal lathe chattering problem in this work was placed in Zone A, which made the application of CSSV appropriate. In the case, the amplitude and frequency were selected experimentally, introducing the minimum possible variation in terms of amplitude and frequency. A soft variation based on a frequency of 0.5 Hz and an amplitude variation of 5% of the original speed were enough to stabilize all the cutting tests shown in Table 1.  
Figure 8 shows the variation of the vibration spectra in a cutting test of 15 mm depth of cut, 60 m/min cutting speed, and 1.3 mm/rev feed rate with and without CSSV.  
It can be concluded that CSSV technique for chatter suppression worked effectively in the present case study and, in addition, it did not alter productivity. However, sinusoidal variation of the rotating speed may lead to slipping between the wheels and the rollers due to the continuous acceleration/deceleration. On the other hand, the application of CSSV in stable conditions can reduce tool life [44], but its application in unstable condition drastically increases the tool life [45]. Therefore, this solution should be considered as a secondary option to be used only when the presence of chatter is confirmed.