# Hybrid Edge-Cloud-Based Smart System for Chatter Suppression in Train Wheel Repair
## 2 Description and Diagnosis: Engineering Knowledge for Smart Data Collection
### Cutting Tests  
Cutting tests in different diameter wheelsets (33\", 36\", and 38\") were performed while varying the depth of cut until the stability limit was found. The material was a standard wheelset steel approved by the Association of American Railroads (AAR). A temporary set up of the sensors based on external shielded cables permitted a fast change of the position, being the type of sensor used suitable for an industrial environment. Finally, vibrations were successfully recorded by means of a triaxial piezoelectric accelerometer (IMI 604B31) placed in the left turret and a uniaxial (IMI 627A01) accelerometer in the left upper roller (see Figure 2). Sound pressure was also measured with a microphone (MG MK250). All the signals were processed in a vibration analyzer.  
Figure 1: General view of the portal lathe.  
Figure 2: Sensor location during the cutting tests and frequency response function (FRF) determination. The left turret accelerometer was integrated into the hybrid edge–cloud-based smart system.  
In these tests, the presence of the self-excited vibrations popularly known as chatter was detected and related to the marks in the wheel surface. A summary of the tests is shown below in Table 1. The green ticks stand for the stable tests, whereas the red crosses represent the unstable ones (chatter tests). Four different wheelsets were studied. The depth of cut (mm in radius) was increased until the stability limit was reached at different cutting speeds.  
The recorded chatter cases featured a high vibration amplitude (see Figure 3a), which turned out to be very harmful for the machine and the machined wheelset, resulting in scrapped parts due to severe surface marks (see Figure 3b). Vibration amplitudes up to 16 mm/s rms in the left turret and up to 40 mm/s rms in the upper roller were measured. The chatter frequency lay between 60-62 Hz at every unstable test. Both accelerometers showed similar vibration patterns and were more robust at detecting chatter than the microphone. Therefore, only one accelerometer, the left turret triaxial accelerometer, was selected to be included in the smart system. Additionally, based on the vibration levels of the left turret accelerometer, different machining stability conditions were defined in this phase.  
The measured distance between chatter marks in the wheel was around 13 mm, which in a 900 mm diameter wheel and at a rotating speed of 18 rpm approximately matched the measured chatter frequency (62 Hz).  
The lobe number \(k\) or the number of waves per revolution was calculated through Equation (1):  
\[k=\frac{f_{c}}{f_{N}}=\frac{60f_{c}}{ZN}=\frac{60\text{-}62}{18}=206.7, \tag{1}\]  
where: _fc_: chatter frequency (Hz), _Z_: number of inserts, _N_: spindle speed (rpm).  
Therefore, the part was marked with around 207 marks in the peripheral surface of the machined train wheel, with an approximate distance of 13 mm.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Cutting Speed/V\({}_{\text{c}}\) (m/min)**} \\ \hline  & \multicolumn{3}{c}{**Wheelset 33”**} & \multicolumn{3}{c}{**Wheelset 36”**} & \multicolumn{3}{c}{**Wheelset 38”**} \\ \hline \(\mathbf{a_{p}}\) (mm) & 40 & 50 & 60 & 54 & 60 & 66 & 40 & 50 & 60 \\ \hline
7.5 & & & & & & & & \\
11 & & & & & & & & \\
15 & & & & & & & & \\
18 & & & & & & & & \\
21 & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Cutting test results.  
Figure 3: Machining of 36” wheelset (Vc = 66 m/min; \(\mathbf{a_{p}}\) = 15 mm): (**a**) Vibration spectrum from the left turret accelerometer (_X_ axis). (**b**) Corresponding chatter marks.