## 2 Preliminary Experiments
### Investigation of Tool Wear Patterns and Cutting Vibration Patterns  
In a stable machining process, when the number of cuts increases, the tool wear of a cutter increases with a repeatable pattern. Through empirical analysis, the correlation of tool wear and the number of cuts can be obtained and used to build the pattern. Subsequently, the pattern can be used to check whether the tool wear increases normally or not. If the tool wear increases following the pattern, it could be estimated based on the statistical model built with collected experimental data. In the preliminary experiments, the machining processes T03 and T04 were consecutively conducted, and the relationship between tool wear and its associated numbers of cuts was investigated. The tool wear was measured using a vision-based measurement system. Figures 5 and 6 respectively, show the correlation of tool wear and the numbers of cuts of T03 and T04. It is noted that the tool wear of a cutter have three developing stages: faster wear, normal wear, and critical wear. The fast wear stage usually happens when a new cutter has begun to be used, because the new cutter is sharper and wear occurs more easily. At the normal wear stage, the tool wears slowly and stably. After the normal wear stage, tool wear will increase again at a faster rate. When a cutter is close to its tool life, tool wear will increase rapidly and it will soon to be worn out. This is regarded as critical wear. When critical wear occurs, the cutter wears out quickly and could damage the work piece. Therefore, critical wear could be a significantly signal to monitor for cutter replacement. From the figures, it was found that the cutter had fast wear when it was new (for example, for the first 50 cuts for T03, and the first 60 cuts for T04), and then the wear increased slowly until the accumulated wear was close to the upper limit of the dimension tolerance of 0.1 mm. As we can see from Figure 5, the tool wear of T03 increased slowly and stably when the accumulated wear was within the range of 40 \(\upmu\)m to 77 \(\upmu\)m. This period was regarded as the normal wear stage. The total number of cuts made within this range were 425 (from cut 51 to cut 476). The tool wear that happened at this stage was very small (<1 \(\upmu\)m). After the 476 th cut, the tool wear increased rapidly at about 90 \(\upmu\)m for about 100 cuts. Since the required tolerances of the machining are \(\pm\)10 \(\upmu\)m for both the inner diameter and the outer diameter, it is easy to produce a No-Go (_i.e._, dimension accuracy not qualified) part when the accumulated wear of the cutter approaches 0.1 mm. Therefore, the cutter should be replaced at this  
Figure 5: Tool wear _vs._ number of cuts of T03. Figure 6: Tool wear _vs._ number of cuts of T04. time. According to the results, the tool life for T03 and T04 could be respectively defined as 450 cuts and 250 cuts. Different levels of tool wear will cause different cutting resistances, which will generate different cutting vibrations. In order to use cutting vibration as the index for tool wear monitoring, it is necessary to understand the characteristics of the change in the cutting vibration pattern caused by tool wear. Thus, while conducting the preliminary experiments for the relationship between tool wear and the number of cuts, the associated cutting vibration signals were also on-line measured by the accelerators. Figures 7 and 8 respectively, show the cutting vibration at different cuts of T03 and T03. It is noted that when the cutter showed light wear, the cutting vibration (<2 g) was quite stable (for cut 2 and 250 for T03; cut 2 and 100 for T04). As the tool wear increased, few significant vibrations (4 g) occurred (cut 200 for T03; cut 350 for T04). When the tool wear became greater, significant vibration occurred more frequently (this happened at cut 450 and 500 for T03 and cut 300 and 350 for T04). When comparing Figures 5 and 6 it can be concluded that the significant vibrations were mainly caused by the tool wear.