Linear Axis Guide Rail Misalignment Detection and Localization Using a Novel Signal Segmentation Analysis Technique

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The developed technique was applied in an industrial-level linear axis testbed, and its potential application is in an actual CNC machine’s linear axis subsystem.

Abstract

Maintenance of the linear axis and its components such as the linear guide can be significantly costly due to the difficult nature of the repair procedure and the downtime the machine exhibits while being repaired. This is a decision that must be made carefully and with proper justification. Therefore, it is crucial that the condition-based monitoring (CBM) system in the machine can detect and localize faults in the linear axis. The presented paper proposes a novel vibration signal segmentation analysis technique that detects and localizes misalignment in the linear guide rail, which is considered a leading root-cause failure fault. The results demonstrated that the usability of time domain features such as RMS was doubled by applying segmentation analysis. Also, evaluating both stroke directions aided in the localization of the misalignment. Overall, the practical value of the proposed technique is to function as both a localization and repair verification tool when performing linear axis maintenance.

1. Introduction

Maintenance is a crucial and necessary activity in the industrial sector to ensure the nominal operation of computer numerical control (CNC) production machines, their systems, and components. When timely and accurate maintenance is conducted, an increase in the competitive edge of an industry due to higher uptime, productivity, and lower unscheduled downtime can be observed. However, conducting maintenance in a system must be properly managed, since it can quickly become very costly. In the survey conducted by [1], it was estimated that the total cost of annual maintenance on average is USD 220 billion. In the report by [2], the goal of maintenance is to use its personnel more efficiently to reduce costs. Nevertheless, maintenance work may fall into three categories including unnecessary, unproductive, and counterproductive work. Where unnecessary work refers to routine equipment checks and equipment maintenance that was never needed. Unproductive work is related to activities such as data entry and retrieval, work-order reporting, and other types of paperwork that reduce the time an expert can spend working on the damaged machine. Lastly, counterproductive work is a maintenance activity that reduces the equipment’s reliability, such as incorrect assembly, incorrect tightening, misalignment among other errors. According to [2], 70% of equipment failures can be traced back to improper initial installation or major preventative maintenance. Maintenance becomes more difficult due to the complex nature of the CNC machine. Therefore, separating the CNC into its crucial subsystems simplifies the maintenance required. The linear axis is one of the CNC’s most crucial subsystems. Its capability for precise and robust positioning dictates the quality of the manufactured part. The operational and maintenance costs of the linear axis can be significant if no action is taken when faults start to develop. Furthermore, if faults are undetected or untreated in a timely manner, they can lead to part quality issues and complete system breakdown. To put it into perspective, the complete failure in the components of the linear axis, such as the linear guide rail, will warrant the need for immediate action, where a full replacement repair job must take place. This can be very costly due to the immense downtime needed to replace the damaged component and realign the axis. For instance, as reported by [3], the maintenance of linear axis components can cost over USD 10,000 per hour. As an example, it was reported that a production line lost an estimated USD 200,000 per day due to improper maintenance. Moreover, as discussed by a recent report by [4], an hour of unplanned downtime due to failure of machines and their components can cost the automotive sector USD 2 million. With the continuously increasing competition in the manufacturing industry, maintenance for CNCs and their components must be conducted smarter and with more precision.

This goal has become more of a reality with the introduction of condition-based monitoring (CBM). CBM utilizes data collected from external sensors and the machine’s operation to determine its health condition and that of its components. Through signal processing of the collected data, a CBM system can detect machine faults (diagnosis) and calculate the remaining useful life (RUL) (prognosis). Finally, the CBM system outputs a condition report that can be used to schedule maintenance activities without affecting the critical operational uptime of the machine. The detailed framework of a CBM system is illustrated in Figure 1.

As previously mentioned, the complexity of the CNC machines and the noisy nature of the industrial environment makes the application of a holistic CBM system difficult, thus separating into its critical subsystems is crucial. In the literature, CBM and its application has a wide variety of research papers and reviews available in this field alone, some recently published review papers are referenced for the reader [5,6,7,8,9,10].

Furthermore, in recent years there have been new emerging technologies in CBM research. For instance, the application of machine learning models in CBM has grabbed the interest of multiple researchers. The comprehensive review by [9] provided a discussion on the application of machine learning models in diagnostic methods. In the research work by [11], the applicability of Shapley Additive explanation (SHAP) machine learning algorithm to identify critical features for fault detection and classification in rotating machinery was investigated. The algorithm demonstrated that, when applied alongside diagnosis models such as Support Vector Machines (SVM) and k-Nearest Neighbour (kNN), prediction accuracies above 98.5% are achieved. Similarly, the work by [12] showcased the application of an artificial neural network (ANN) and Gaussian process regression model to diagnose the transfer robot’s multi-component health condition and system performance. Another interesting application of machine learning is in the work by [13], where a Generative Adversarial Network (GAN) coupled with a cycle consistency loss function was applied to generate synthetic bearing fault data to substitute its experimental counterpart. Lastly, another emerging area of CBM research is estimation theory, more specifically the application of Kalman filters. For example, the work by [14] proposed the application of an intelligent digital twin coupled with machine learning to identify bearing crack size. They employed the use of a Kalman Filter (KF) in the signal estimation section of their methodology. Similarly, the work by [15] applied an extended KF (EKF) to estimate the bearing end-of-life time. Moreover, ref. [16] conducted a comparative study between the EKF and Unscented KF (UKF) to detect faults in permanent magnet synchronous generators (PMSG). Lastly, the recent published work by [17] merged both a deep belief machine learning network and a minimum UKF to develop a diagnostic model for early bearing fault diagnosis. Their proposed model, when tested on two datasets, achieved accuracy prediction rates above 98% and 99%, respectively, at different operational parameters. Moreover, their model performed significantly higher than other proposed methods, especially at the 300 rpm range. All in all, these various works demonstrate how CBM is a research area filled with new opportunities and emerging technologies.

For the presented paper, the focus of the literature review was aimed towards the segmentation of data and misalignment fault detection for linear axis. Detection of faults in a CBM system falls under the diagnosis section. This is a research area filled with multiple opportunities to advance knowledge in the CBM field. However, to reach a proper diagnosis of the system’s health state, the collected data must undergo signal processing and analysis.

Therefore, to address the challenges of maintenance, a novel vibration signal segmentation technique was developed to detect and localize a horizontal misalignment on the linear guide rail. The paper was structured into five sections. Section 1 offers a concise introduction about the cost of maintenance in industry and research in CBM. Section 2 provides a comprehensive literature review in the application of signal segmentation in CBM systems and discusses how misalignment impacts the linear axis system and why it should be detected promptly. In Section 3, the research methodology and proposed signal segmentation technique are presented. Section 4 discusses the results from the conducted studies. Finally, Section 5 summarizes the conclusion and future work for the presented technique.

2. Related Work

Segmentation techniques proposed in the literature are a well-established signal processing method that are mainly focused on improving the signal’s quality or detecting operational change points in the signal for a more efficient and focused analysis. This can be observed, for instance, in the presented research work by [18]. An automatic time series segmentation technique was proposed to identify and characterize machine tool operational states. Their technique divided the power factor curve to identify the machine’s constant (stand-by, operational readiness) and non-constant (acceleration, deceleration, machining, and set-up) operational segments. It was concluded that with their proposed segmentation, signal preparation in an industrial environment can be conducted for possible automatic device number recognition and load disaggregation at a machine perspective. Furthermore, through signal segmentation, operational state-based and self adaptive CBM is possible. Finally, detecting constant and non-constant operational states through their proposed segmentation method can be utilized to determine value and non-value-added operational times for a more efficient use of the machine. Similarly, the research work presented by [19] proposed a vibration signal segmentation technique for condition monitoring of wind turbine gearboxes. The segmentation technique segments the non-stationary signal to match specific speed profiles to the component. An improvement on signal features for fault diagnosis was observed when applying their proposed segmentation technique. Moreover, their technique aimed at removing redundant information that is contained within the non-stationary portion of the evaluated vibration signal. It was concluded that their approach yielded a 97% classification accuracy. Furthermore, their proposed methodology was able to accurately segment the signal to match a component rotation. However, their technique was dependent on an external sensor to synchronize the signal for accurate segmentation. Another example of signal segmentation application was presented by [20]. In their work, the use of signal segmentation to increase the accuracy of a convolutional neural network (CNN) in identifying gear faults was showcased. Since, it was identified that neural networks are tested against the same datasets as validation. However, in practice, faults may develop somewhere else, which may lead to erroneous health assessments. The proposed segmentation technique divided the signal based on the corresponding gear teeth interval. The method demonstrated its performance-enhancing capability for the CNN to detect artificially infused faults accurately. However, they identified, as a future step, the need to test it in actual machining environments. More recently, ref. [21] proposed a ballscrew health monitoring method by evaluating its health through inertial sensor data. In their method, signal segmentation was applied as a pre-processing step to separate the signal based on its steady and transient states. It was concluded that their presented method was capable of detecting faults in the ballscrew system and quantify backlash error. Similarly, ref. [22] proposed a novel acoustic emission signal segmentation framework for bearing fault analysis. The framework utilized signal segmentation as a pre-processing method with the main objective of accurately extracting REB fault impact characteristics, with the aim of maximizing detection rate. Likewise, in the work presented by [23], a signal segmentation procedure was utilized for the analysis of seismic signals. In their work, their method isolated events from the collected seismic signal and evaluated them individually. Finally, ref. [24] applied a signal segmentation technique that primarily divided the signal into sections so they can be assigned to specific machine operational states including idle, machining, and anomalies. Their segmentation utilized an RMS windowing function to detect change points in the signal. Their study concluded by demonstrating the robustness behind their segmentation technique when used under varying parameter conditions. In summary, the segmentation techniques discussed in the literature review are applied to improve the quality of the evaluated signal, such as detection and/or removal of transient and steady state portions, and process change point detection to differentiate between operational states. Comparatively, there is a lack of signal segmentation methods that are applied for localizing faults in a CNC linear axis.

The crucial nature of the linear axis in the operation of the CNC machine is well established. In the recent comprehensive review by [25], a detailed discussion of the components found in the linear axis and the different efforts in advancing CBM in this area was provided. The review concluded by stating that application of CBM in the linear axis is a growing field of research. The importance of the linear axis is further highlighted in the legacy work by [26], where a comprehensive review of the control and design was explored to build an understanding on the linear axis. However, like any other subsystem in a CNC machine, the linear axis is not exempt from deterioration and developing failure faults (FFs) throughout its operational lifecycle. As stated by [27], when the components of a linear axis begin to wear, it may cause operational errors in positioning, straightness, and angular motions. Most recently, the research works in this field have focused in detecting localized wear, such as spalling, in the different components of the axis including the leadscrew, linear guide rail, and carrier block [21,28,29,30,31,32,33]. Despite these efforts, from a maintenance perspective, if localized damage has already developed in the linear axis component, it warrants the need to immediately be replaced. Therefore, it is crucial to take a step back and understand as to how the damage developed in the first place. From an industrial perspective, the root-cause of why localized damage occurs in the raceway and rolling components can be traced back to lack of lubrication, excessive loads, and dirty environment, but most importantly misalignment. According to the report by [34], misalignment represents one of the leading causes of premature wear in the components of the linear axis. When misalignment is present in the system, regardless of the type, it will result in uneven loading on the rolling elements and raceways. These uneven loads typically will lead to wear in the form of pitting. As discussed in [35], there are two types of misalignments that need to be addressed when installation of the linear axis is being done, as illustrated in Figure 2.

First, vertical misalignment refers to the offset relative to the base the linear axis component sits on. Secondly, the horizontal misalignment refers to the right or left offset relative to a reference linear guide. Both offsets must be below the tolerances suggested by the manufacturer to ensure no accelerated wear affects the system. Research on the effect and detection of misalignment in the linear axis has not received enough attention compared to other critical subsystems and components, as stated by [36]. Recent efforts in misalignment analysis and detection are outlined in

Table 1. Summary of linear axis component FF diagnosis studies.

Authors	Component Analyzed	Misalignment FF Creation Process	Detection Method
[36,37]	Leadscrew	Right and left misalignment (0.5 mm, 1 mm) was introduced at the second support block of the leadscrew.	Ref. [36] Applied various combinations of machine learning models including convolutional neural network (CNN), autoencoder (AE), temporal convolutional network (TCN), and long short-term memory (LSTM). Ref. [37] Applied fast Fourier transform (FFT) alongside statistical feature analysis on the collected current data.
[27]	Linear guide rail	Vertical misalignment was introduced by removing bolts and applying a specialized pushing mechanism underneath the guide rail to cause maximum deformation (max 91 µm).	Implemented an inertial measurement unit (IMU) on the linear axis to calculate the geometric error motions.
[38]	Linear guide rail	Horizontal misalignment was introduced on the evaluated linear guide rail by loosening the end bolts and placing feeler gauges ranging from 20 µm to 200 µm.	Applied a micro-electromechanical system (MEMS) sensor to collect vibration data and analyzed the signals in the time and frequency domains.
[39]	Leadscrew	Applied a series of misalignments on the leadscrew’s end bearing (0.002″–0.007″) and ball nut (0.007″).	Collected vibration data and applied an unsupervised self-organizing map (SOM) alongside the minimum quantization error (MQE) index to detect the distance from the baseline dataset.

.

Nevertheless, all these different works focused in analyzing the full stroke data in a holistic manner without considering detecting the location of the misalignment within the stroke. Furthermore, the reviewed literature works concluded their experiments once the misalignment was detected. However, there is no mention as to how the repair of the misalignment varies from their baseline dataset. Given that the linear axis travels a specified distance throughout its operation, detecting where a misalignment could be present in the stroke can be beneficial in its maintenance, since, with a location, the need to troubleshoot may decrease. Finally, localizing the misalignment in the axis stroke can aid in making well-informed maintenance decisions, and determine if the machine requires immediate repair based on the fault’s severity.

Gaps and Contribution

The diagnosis of faults for CNC linear axis components is a research domain filled with multiple opportunities to advance the CBM field. The research article was motivated by the following identified gaps:

• Previous signal segmentation analysis methods were used to improve signal quality and detect operational state changes. However, its application to detect and localize faults such as misalignments is not well explored.
• Misalignment detection studies focused on analyzing the full stroke data and detecting if a misalignment was present. Regardless, these studies did not locate where the misalignment was present in the stroke by analyzing both stroke directions.
• Health monitoring studies in linear axis components, especially the ones reviewed for misalignment, lacked a discussion of how a repair state varies from the baseline state.

The main contribution from the research work is to provide a CBM tool that applies signal segmentation in vibration monitoring to localize a misalignment and evaluate its effect on the linear axis in both stroke directions. Additionally, to address the identified gaps and demonstrate the capability of the proposed segmentation technique, a right horizontal misalignment was introduced to the linear guide rail and two studies were conducted from it. The studies consisted of applying the segmentation technique and analyzing the vibration signals from both stroke directions (forward and reverse) independently. Ultimately, to build an understanding of how the misalignment changes the vibration signal based on the stroke’s direction:

• Study A consisted of applying the segmentation technique and analyzing the vibration data from the stroke’s forward motion.
• Study B was conducted to comparatively analyze the collected vibration data after applying the segmentation technique for the reverse motion stroke.

Lastly, both studies were further enhanced by conducting an analysis on the repair state condition of the linear guide rail after the misalignment. The analysis at the repair state primarily focused on understanding through segmentation if there were any changes to the system.

3. Materials and Methods

The research methodology, as illustrated in Figure 3, was designed to test the localization capability of the proposed signal segmentation technique. The purpose of the proposed technique is to localize a misalignment fault on the linear guide rail based on the vibration signature the linear axis stroke generates in both directions.

First, a right horizontal misalignment fault was introduced on the linear guide rail component at the halfway mark of the stroke. Then, vibration data were collected and processed through the segmentation technique. The segmented data were analyzed to localize the area of the misalignment, assess its severity, and provide a repair decision to the user. The details of the linear axis testbed and data acquisition equipment used in the presented article are outlined in Section 3.1. Finally, a detailed description and flowchart of the signal segmentation technique are outlined in Section 3.2.

3.1. 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.

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. Data acquisition and sensor key characteristics.

Data Acquisition Equipment	Category	Sampling Frequency (Hz)	Sensitivity (mV/g)	Measurement Range (g)
NI-CDAQ 9234 Data acquisition (DAQ) card (Testforce Systems Inc., Pickering, ON, Canada)	Data acquisition	-	-	-
PCB Piezotronics 356A25 Tri-Axial Accelerometer (Dalimar Instruments, Vaudreuil-Dorion, QC, Canada)	Sensor	5000	X = 24.62	±100
			Y = 24.88
			Z = 24.69
Kistler 8702B50 Mono-Axial Accelerometer (Kistler Instrument Corp., Mississauga, ON, Canada)	Sensor	5000	98.9	±500
Optical Absolute Internal Motor Encoder (Bosch Rexroth Canada Corp., Welland, ON, Canada)	Sensor	333		±120

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 deceleration times calculated from the internal encoder data. Finally, a bandpass filter is applied to remove electrical noise (60 Hz and its harmonics) from each of the collected vibration signals for better data quality.

3.2. Signal Segmentation Technique

As discussed in the literature review, signal segmentation is an important data analytics process used to improve the quality of the evaluated signal and detect operational state changes. Nonetheless, insights about the signal may be missed when evaluated holistically. For the presented study, a novel signal segmentation technique was applied to divide the collected vibration signal into smaller segments and evaluate them individually to detect areas of major change from the baseline. Upon detecting the anomalous segment, a further comparative analysis is conducted to determine its location, severity of the damage, and provide a repair decision. A flowchart of the proposed technique is illustrated in Figure 6.

This technique was developed to localize a misalignment fault from the collected vibration signal of the monitored linear guide rail component of the testbed. Then, conduct a deeper analysis to determine the severity and impact on the system. The proposed technique segments the vibration signal by dividing it in half until it reaches a pre-determined number of segments, as shown in (1).

$$n_s=2^n$$

(1)

where $n_s$ is the total number of segments and $n$ is the user defined number of iterations. For instance, if the user selects n = 2 number of iterations, the system will divide the signal into 4 segments. Each of these segments are evaluated as individual signals. First, a time domain analysis where statistical features such as RMS, standard deviation, Peak-to-Peak, and kurtosis are calculated. For the next step, the evaluated features are compared against their baseline state to determine their percentage error. If the segment’s percentage error is between 10–20%, the segment will be deemed as suspect and delineated yellow in the analysis. Any segment above 20% error will be deemed a faulty segment and depicted red in the analysis. Finally, to determine the location of the anomaly, the technique divides the total stroke distance travelled by the number of segments to determine the position and compares the anomalous segments by evaluating both stroke directions.

4. Results and Discussion

Upon completion of the misalignment fault experiment, the collected vibration datasets of the baseline and faulty states were first analyzed at the full stroke length. As illustrated in Figure 7, it can be observed that typical time domain features used in vibration analysis such as RMS (a) and standard deviation (b) have a percentage error of less than 10% when comparing both health states.

At first glance, this small difference shown from the results may mislead its interpretation by believing that the misalignment had no effect on the vibration signal. Therefore, the signal segmentation was applied to both datasets, and the same features were evaluated to identify how they changed. To conclude the studies, the segmentation technique was applied to the repair state dataset to determine how the features improved when compared to the faulty state and if they changed when compared to the baseline.

4.1. Study A: Forward Stroke Analysis through Segmentation Technique

Study A consisted in applying the segmentation technique to the three health state datasets and evaluating the change in their features for the forward stroke motion. Figure 8 illustrates the RMS feature that when the segmentation technique is applied to the baseline dataset, limits at 10% (green line) and 20% (red line) above the feature’s magnitude were placed to visualize suspect and faulty segments, respectively. The number of divisions used was $n$ = 3, thus generating $n_s$ = 8 segments as per Equation (1). This was selected since the misalignment was introduced past the halfway mark of the stroke, approximately 350 mm from the starting position, and the position where the misalignment was above 0.25 mm was approximately 570 mm from the starting position, as shown in Figure 5.

As previously shown in Figure 7, the difference of the evaluated features (RMS and standard deviation) is below 10%, and can lead to the system being operated at a misaligned state. Comparatively, other features, such as kurtosis and peak-to-peak, demonstrated a percentage error of approximately 20% when compared to the baseline state at the full stroke analysis, as depicted in Figure 9.

This result leads to a deeper investigation of the former features. When the segmentation technique is applied to the faulty dataset of vibration signals and the same features are calculated, a change can rapidly be observed. As illustrated in Figure 10, the signal’s RMS exceeds the 10% limit at the half stroke analysis. Upon further segmentation, at the quarter stroke, it can be observed that the last quarter segment exceeds the 20% limit focusing the analysis in that area. When segmenting once more at the eighth-stroke level, the signal’s RMS in the last section of the stroke has a percentage error of 42%. Comparatively, the standard deviation of the vibration signal also exhibits similar results to that of the RMS feature. These results are significant, since they demonstrated that, by utilizing the segmentation technique, the usability of the RMS and standard deviation features increased by going from a 6% error at the full stroke level to a 42% error when compared to the baseline state.

Finally, the analysis is taken a step further by relating each evaluated segment to the position of the linear axis. As per the methodology described in Section 3.1, the full stroke is equivalent to a travelled distance of 700 mm. Therefore, when segmenting the vibration signal, each segment consists of an equivalent travelled distance based on the number of segments.

Table 3. Segment level analysis characteristics.

Segment Level	Segment Level Characteristics
Quarter Stroke Segment	Segment #	1		2		3		4
	Distance Travelled (mm)	0–175		175–350		350–525		525–700
Eighth Stroke Segment	Segment #	1	2	3	4	5	6	7	8
	Distance Travelled (mm)	0–87.5	87.5–175	175–262.5	265.5–350	350–437.5	437.5–525	525–612.5	612.5–700

#: Refers to the segment number being evaluated.

outlines each segment and their respective distance travelled.

As previously stated, the misalignment was introduced at the back end of the testbed, as shown in Figure 5, approximately at the 350 mm mark. Due to the nature of the misalignment introduced, the measured deviation progressively increased up to 0.5 mm at the end of the stroke. Through the segmentation technique, the results demonstrated that, as the linear axis moved in the forward direction, the vibration exceeded the proposed limits at the last 175 mm (4th quarter stroke) of the stroke where the misalignment ranged between 0.25–0.5 mm.

The other evaluated statistical features, such as peak-to-peak and kurtosis, demonstrated approximately a 20% error at the full stroke analysis when compared to the baseline dataset. However, when the segmentation technique was applied, as shown in Figure 11, the following results occurred:

• The peak-to-peak demonstrated a remarkable result when the segmentation technique was applied. Since the healthy segments all stayed below the 10% limit (green line), only the segments where the introduced misalignment was above 0.25 mm consistently showed a 20% error.
• Kurtosis also showed an interesting result as the signal was further segmented. As the segment levels increased, the segment where the misalignment is present goes from a 20% error at the half stroke to approximately 10% at the quarter stroke level and ultimately to no difference when compared to other healthy segments. This phenomenon is due to the nature of the feature, since it analyzes the distribution of a signal, and as the signal is further segmented, the closer to a normal distribution each segment becomes.

Study A was concluded by applying the segmentation technique and evaluating the repair state dataset. When looking at the full stroke analysis the results of the repair state for the evaluated features are similar to the baseline state. However, the RMS and standard deviation features showed an interesting result when the segmentation technique is applied on the dataset. It was observed that at the quarter and eighth level segment analysis, each of their last segments where the misalignment was more pronounced, the features exhibited a percentage error of 11% and 15%, respectively, as illustrated in Figure 12.

This information is useful, since it can be utilized to update thresholds at different segment levels to avoid false alarms. Additionally, the results also demonstrated that even after a repair the system exhibited a slight change to its baseline operation, and should be further investigated. The other statistical features used in the analysis showed a decrease from the faulty state, and were once again stabilized within the limits of the baseline state, as illustrated in Figure 13.

4.2. Study B: Reverse Stroke Analysis through Segmentation Technique

Study B focused on evaluating the reverse stroke at the three different health states by applying the proposed signal segmentation technique. The vibration signal was segmented into 8 segments and used the 10% and 20% limits. When evaluating the RMS and standard deviation features in the reverse stroke direction, similar to the forward direction study, their percentage error is less than 5%, as depicted in Figure 7, while the other features, peak-to-peak and kurtosis, both exhibited percentage errors above the 20% limit, as demonstrated in Figure 14.

Similar to study A, both RMS and the standard deviation features were further evaluated under the applied signal segmentation technique. The results for both features, also illustrated in Figure 15, were as follows:

• Both features in the half stroke analysis showed an increase in the first segment. However, unlike the results from study A, the feature magnitudes do not exceed the 10% limit. Nevertheless, when segmented at the quarter stroke level, immediately a major shift of the percentage error can be observed from 7% at the half stroke level to 26%.
• When the signal is segmented once more to the eighth stroke level, the feature’s magnitude increases once again reaching a percentage error of 46% when compared to the baseline state. Despite this major shift, another change can also be observed in the eighth segment that exceeds the 10% limit, deeming it a suspect area.

To localize the area of the misalignment, the evaluated segments like in study A were also related to the position of the linear axis. In contrast to the previous study, the segments that showed a major shift to the features are the initial segments rather than the last. Since the system starts at a misaligned state this shift on the features is higher at the beginning. This demonstrates how the reverse stroke is a mirror image to the forward stroke signal. Additionally, it can be observed that the misalignment had the most effect on the vibration signal in the first quarter stroke segment, which equates to the first 175 mm of travel in the reverse direction. However, when the signal is segmented once more to the eighth stroke level, the first segment that relates to the initial 87.5 mm of travel had the highest change to the vibration signal.

Similar to the forward stroke study, the kurtosis and peak-to-peak features had above 20% error when compared to the baseline at the full stroke level analysis. However, when subjected to the proposed segmentation technique, also demonstrated in Figure 16, the following results occur:

• The peak-to-peak feature consistently shows an above 20% error in the first segment at the half, quarter, and eighth stroke levels where the misalignment was most acute. In comparison, all other segments stay below the 10% error limit. Thus, demonstrating peak-to-peak is a useful feature when looking at the misalignment fault.
• Kurtosis showed quite a difference at the different segment levels. Firstly, at the half stroke level, the first segment where the misalignment was introduced showed approximately 30% error when compared to its baseline counterpart. However, the second segment exceeded the 10% limit as well, showing that the system underwent a change in the other half of the stroke. When segmented once more to the quarter level, the last segment exceeded the 20% limit while the first decreased to 16%. Finally, when segmented once more to the eighth stroke level, all segments decreased to baseline state values similar to study A, except the last two segments which exceeded the 10% established limit.

Study B was also concluded by evaluating the repair state condition of the linear axis. At the full stroke level analysis, all the evaluated features have a percentage error below 10% when compared to the baseline state. Furthermore, when the signal segmentation technique is applied, the segments for the RMS and standard deviation features all stabilize and are found to be within the 10% error limit. Moreover, the suspect segment, shown in the faulty dataset analysis in Figure 15, showed a magnitude decrease and fell below the 10% limit at the same segment level analysis after the repair, as Figure 17 illustrates.

However, when applying the segmentation technique to evaluate the kurtosis feature, it can be observed that at the half stroke level, as shown in Figure 18, the second half segment exhibits a kurtosis value with a 14% error when compared to the baseline state, exceeding the imposed 10% limit. When the signal is further segmented to the quarter stroke level, the last quarter segment exceeds the 20% limit, prompting the system to label that segment as faulty. This demonstrates the power of the segmentation technique, since it indicates other anomalous segments that should be also checked. Lastly, it can also be observed that the error of the feature, especially in the newly identified suspect segments, is much higher compared to the baseline state at the same segments.

5. Conclusions and Future Work

5.1. Conclusions

Failures in the critical subsystems of CNC machines are bound to happen during their operational lifetime, thus making maintenance a necessary activity to ensure nominal operation. The linear axis being one of these critical subsystems when it fails can lead to significant downtime and maintenance costs, especially when the failure cannot be easily detected or localized, and troubleshooting must be done to determine the root cause. Misalignment is one of these root-cause FFs that over time will lead to the complete failure of the linear axis if not promptly addressed. From the reviewed literature, there are a lack of studies that focus on utilizing signal segmentation processing techniques to localize misalignment. Additionally, the studies conducted on misalignment analyzed the full stroke to detect the fault, but did not focus on localizing the area where it was present. Finally, there are limited comparative studies that investigate what occurs after a repair is conducted on a faulty system and how it differentiates from the originally established baseline. Therefore, the presented paper aimed at filling these gaps by introducing and applying a novel vibration signal segmentation technique to localize a misalignment based on the change of evaluated time domain features. The three major conclusions from the performed studies include the following:

• The usability of RMS and standard deviation features was increased by applying the segmentation technique. Since at a full stroke analysis these features exhibited less than 10% error when compared to the baseline state. However, when the segmentation technique is applied the features’ percentage error increased above 20% at the quarter segment level, and above 40% at the eighth segment level.
• The presented technique localized the area where the misalignment was introduced by relating the distance traveled to the segment number. Furthermore, the localization was further confirmed when comparing both forward and reverse strokes due to their anomalous segments being identified on opposite sides.
• The repair state analysis demonstrated a 15% error of the RMS and standard deviation features in the forward direction where the misalignment was introduced, when compared to the baseline condition. However, these changes can only be observed when the signal is segmented to the quarter and eighth segment levels. Comparatively, the reverse direction showed that both of these features stabilized within the baseline limits. This is important, since segmentation can be utilized as a verification tool after a repair and to update operational thresholds based on segmented analysis to avoid false alarms.

5.2. Future Work

Although the proposed signal segmentation technique accomplished its objective of locating the portion of the linear axis stroke where the misalignment fault was introduced, there are still some limitations that can be used to generate new research opportunities. These have been identified as follows:

• The technique was applied to a single type of misalignment. Given that a vertical misalignment may occur in the assembly of the linear axis, a future direction is to apply the technique and evaluate the fault’s effect on the linear axis. Furthermore, the work can be extended by inducing both misalignment types at the same time and evaluating the vibration signal through the segmentation technique.
• The analysis was focused on time domain statistical features to evaluate if the segmentation technique can enhance their usability when the system is operating under a faulty condition. Future exploration should be conducted that apply machine learning methods or feature reduction methods such as principal component analysis on the segmented portions of the signal to build models and diagnose faults.
• The technique was applied in a controlled testbed environment with a single known induced fault. However, in industry CNC machines, it may exhibit various faults at a time. Therefore, a future direction should include applying the segmentation technique to industry data and evaluate anomalous segments to localize the possible fault and diagnose what fault it is.
• For the presented studies, percentage error limits at 10% and 20% were hard set for the analysis to identify the changes on the features. This may be considered as a limitation since it constrains the system’s operation. Future research work should be focused on utilizing the segmented signal and repair data condition to establish dynamic operational threshold limits to decrease the possibility of false alarms.