## 3 Materials and Methods
### Linear Axis Testbed, and Data Collection and Analysis  
The experiment to generate the vibration data was conducted on the linear axis testbed at the McMaster Manufacturing Research Institute (MMRI). The testbed was designed to replicate the operation of a horizontal linear axis in a CNC machine, without the noise and dynamic effects of other subsystems. As illustrated in Figure 4, LR3 was used as the monitored component. The operation of the testbed was pre-defined to a specific motion cycle consisting of a velocity of 105 mm/s and stroke displacement of 700 mm in the forward and reverse directions. The experiment consisted of inducing a right horizontal misalignment on LR3 past the halfway point of the stroke, and the fault creation procedure followed a similar approach to the research work presented by [38]. As reported by [34], regardless of the type of misalignment present in the linear axis, pre-mature failure may still occur due to the excessive forces introduced by the fault. Due to the floater design of LR3, it is most susceptible to horizontal deviations when assembling it compared to vertical ones. Furthermore, the floater aspect of the guide rail requires the use of a \"reference\" rail (LRR) and gauge to properly align it, as described in [35]. Therefore, the horizontal misalignment fault was selected to be studied. To induce this misalignment on LR3, the bolts that attached the linear guide rail to the testbed were loosened. Then, the linear guide rail was pushed to the right, until a misalignment of 0.5 mm on the backend was achieved. Before retightening the bolts, a dial indicator mounted on a separate carrier block on LRR was used to measure the misalignment relative to LRR. Due to the horizontal nature of the misalignment, there were certain sections that had a lower misalignment measurement when getting further from the backend; these sections and their respective measurements are detailed and shown in Figure 5. Lastly, the experiment concluded by repairing the induced misalignment and evaluating the repair data through the segmentation technique, to analyze any changes the fault may have caused on the system. Figure 4: Linear axis testbed component breakdown. Figure 3: Research methodology framework. The collected data consist of vibration data from the external accelerometers mounted on the linear guide rail, LR3, and the carrier block, B6. The operational data was gathered from the motor's built-in encoder. The generated datasets consisted of one hour of operation after an initial warm-up, equivalent to 125 cycles of vibration data and 60 cycles of operational data. Table 2 summarizes the data acquisition and sensor characteristics. After data acquisition was concluded, each signal was subjected to pre-processing before segmentation. The pre-processing includes three main steps. Firstly, each signal is separated based on the direction of the stroke either being forward or reverse. Then, the transient portions of the signal are removed by using the average acceleration and \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Data Acquisition Equipment** & **Category** & \
\begin{tabular}{c} **Sampling** \\ **Frequency (Hz)** \\ \end{tabular} & **Sensitivity (mV/g)** &
\begin{tabular}{c} **Measurement** \\ **Range (g)** \\ \end{tabular} \\ \hline NI-CDAQ 9234 & & & & \\ Data acquisition (DAQ) card & Data acquisition & - & - & - \\ (Testforce Systems Inc., Pickering, ON, Canada) & Data acquisition & - & - & - \\ \hline PCB Piezotronics 356A25 & & & & X = 24.62 & \\ Tri-Axial Accelerometer & Sensor & 5000 & Y = 24.88 & \(\pm\)100 \\ (Dalimar Instruments, Vaudreuil-Dorion, QC, Canada) & & & Z = 24.69 & \\ \hline Kistler 8702B50 & & & & \\ Mono-Axial Accelerometer & Sensor & 5000 & 98.9 & \(\pm\)500 \\ (Kistler Instrument Corp., Mississauga, ON, Canada) & & & & \\ \hline Optical Absolute Internal Motor & & & & \\ Encoder & Sensor & 333 & & \(\pm\)120 \\ (Bosch Rexroth Canada Corp., Welland, ON, Canada) & & & & \\ \hline \hline \end{tabular}
\end{table}