## 2 SSADT Analysis of Motorized Spindle
### SSADT Stress Analysis  
The structure of the motorized spindle is shown in Figure 2. In order to obtain an effective SSADT scheme of the motorized spindle, it is necessary to analyze the stress of the motorized spindle when it works. The data of 520 reliability tests of motorized spindles from a machining center over 3 months (June-August 2016) are summarized, as shown in Table 1.  
Figure 1: SSADT profile with multiple stresses. Figure 2: Structure of motorized spindle. 1. Roller bearing; 2. flange; 3. stator; 4. rotor; 5. cooling line; 6. lubrication line; 7. hydraulic cylinder; 8. encoder; 9. disc spring; 10 and 11. broach system. The fault information of the spindle system in Table 1 is marked in the form of a fault tree, the event label is shown in Table 2, and the fault tree of the established spindle system is shown in Figure 3.  
According to the law of large numbers of Bernoulli [33], if the probability of the bottom event is replaced by the frequency of the bottom event, the frequency of each bottom event in the spindle system is shown in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Fault Location** & **Fault Phenomenon** & **Fault Cause** &
\begin{tabular}{c} **Number of** \\ **Times** \\ \end{tabular} & **Percentage** \\ \hline \multirow{3}{*}{Bearing} & Spindle swing big, spindle abnormal noise, workpiece with tool marks, locked, not tight tool, the cutting tool will not stick & Bearing fatigue and damage & 27 & 67.5\% \\ \cline{1-1}  & & The cutting tool dropping & Loose and poor preload & 3 & 7.5\% \\ \cline{1-1}  & & sequence error, abnormal bus connection & Servo amplifier failure & 3 & 7.5\% \\ \cline{1-1}  & & Large speed deviation, servo system alarm & Motor damage & 2 & 5\% \\ \cline{1-1}  & & Brake circuit failure & Brake resistor burned & 2 & 5\% \\ \cline{1-1}  & & The spindle cannot hold the cutting tool & Claw damage & 1 & 2.5\% \\ \cline{1-1}  & & Abnormal noise of motorized spindle & Cone wear & 1 & 2.5\% \\ \cline{1-1}  & & Spindle overheat alarm & Water in cooling system & 1 & 2.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Failure of motorized spindle system in field reliability test. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Event** & **Code** & **Event** & **Code** \\ \hline Abnormal noise of motorized spindle & F101 & Wear of inner cone of spindle & E305 \\ The spindle cannot hold the cutting tool normally & F102 & Fault of servo amplifier & E306 \\ Fatigue damage of bearing & E301 & Burn out of brake resistor & E307 \\ Failure of cooling system & E302 & Looseness of positioning block & E308 \\ Abnormal of the motor & E303 & The preload of positioning block is not enough & E309 \\ Claws broken & E304 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Result event label of top event TOP. Figure 3: FTA of spindle system. The potential improvement potential (IP) method is used to calculate the importance of the bottom event [34], and the calculation formula is shown in Equation (1):  
\[H^{\text{IP}}(R|T)=h[1_{R},p(T)]-h[p(T)] \tag{1}\]  
where \(p_{R}(T)\) is the reliability of bottom event \(R\)(\(R\) = 1, 2,..., \(N\)), \(h[p(T)]\) is the reliability of the system, and \(h[1_{R},p(T)]\) is the conditional probability of the system working normally when the bottom event \(H\) is working normally. The importance of each event is shown in Table 4.  
As the bottom event \(R\) occurs, there is a difference in downtime maintenance time. Therefore, the average downtime \(\overline{t_{R}}\) is taken (\(R=1,2,\ldots 9\)). The relative downtime coefficient \(k_{T}\) is defined:  
\[k_{T}=\frac{\overline{t_{R}}}{\max\limits_{1\leq R\leq 9}(\overline{t_{R}})} \tag{2}\]  
where \(\max\limits_{1\leq R\leq 9}(\overline{t_{R}})\) is the longest downtime in the bottom event. In this field reliability test, the average downtime of E304 (claws broken) is the longest, which is 115 min.