4.1. Overview of Experimental Setup
The experimental data considered in this section were measured on the experimental setup shown in Figure 4
. This experimental setup is located in the Centre for Asset Integrity Management laboratory at the University of Pretoria and consists of three helical gearboxes, an electrical motor and an alternator which are highlighted in Figure 4
a. The electrical motor drives the system and the alternator dissipates the rotational energy from the system and can be used to induce time-varying speed and load conditions.
The vibration of the test gearbox is measured with a tri-axial accelerometer located on the back of the gearbox as shown in Figure 4
b. The axial channel of the tri-axial accelerometer is used for monitoring the condition of the helical test gearbox. The instantaneous rotational speed of the input shaft is measured with the optical probe and zebra-tape shaft encoder shown in Figure 4
b. The instantaneous operating conditions that were present during the experiments are shown in Figure 5
The gearbox contains helical gears, which mask the impulses generated by damaged gear teeth, and additionally the vibration signals are inherently impulsive. This impedes detecting damage in the gearbox.
The suitability of the SASE and the suitability of the proposed SMSE to detect localised damage are investigated in the next section.
4.2. Localised Gear Damage Investigation
Localised gear damage was induced by seeding a slot in one of the teeth of the gear as shown in Figure 6
a. This gearbox was operated under operating condition one in Figure 5
, until the damaged gear tooth had failed. The gear after the completion of the test is shown in Figure 6
The raw vibration signal is order tracked by using the tacho signal generated with the zebra tape shaft encoder and the optical probe to obtain an angle-domain representation of the signal . Two-hundred measurements spaced over the life of the gear are investigated in this section.
The SASE and the SMSE are calculated for the damaged gear, by using Equation (9
shaft rotation, and for the healthy pinion Equation (9
) was used with
shaft rotations, and presented in Figure 7
. Even though two-hundred measurements are considered in this section, only twenty signals, evenly spaced over the life of the gear, are shown in Figure 7
to ensure that the results are easy to interpret.
The SASE for the gear in Figure 7
a contains impulses scattered randomly over the rotation of the gear and gear damage that is located in the vicinity of 135 degrees. The aforementioned impulses are not related to the health of the gears and therefore impede the fault detection process. The only reason why it is possible to identify the gear damage at 135 degrees is because the measurements are aligned, which ensures that the position of the gear damage is the same between the different measurements. However, in applications where tacholess order tracking methods are used [37
], it is not easy to align the different measurements and therefore the gear damage may be perceived as part of the random noise.
The SMSE is calculated with Equation (10
) and presented in Figure 7
b. The SMSE performs significantly better than the SASE, because the gear damage can clearly be seen at approximately 135 degrees, while the impeding impulses seen in the SASE are completely attenuated. The superiority of the SMSE over the SASE is further emphasised by the results of the pinion seen in Figure 7
c,d; the impulses seen in SASE are not related to the condition of the pinion and make it difficult to determine its condition. In contrast, the SMSE of the pinion does not contain any evidence of damage and therefore provides the correct representation of the condition of both the gear and the pinion.
The metrics using the SASE in Equation (11
) and SMSE in Equation (12
) are presented in Figure 8
for the gear and the pinion.
The metrics obtained with the SASE and SMSE of the gear shown in Figure 8
a,b allow the degradation of the gear to be detected over time. The performance of the SASE indicator is attributed to the fact that the characteristics of the impulsive noise remained the same over measurement number, i.e.,
in Equation (5
) was constant. However, it is conceivable that the characteristics of the impulsive noise could change over measurement number and would therefore lead to confusing metrics that make the fault diagnosis process more difficult. The pinion was relatively constant for both methods, which is correct. In the next investigation, it is shown that the condition indicator of the SASE could change as other mechanical components degrades as well.
4.3. Distributed Gear Damage Investigation
In the second investigation, distributed gear damage was induced on the gear by leaving the gear in a corrosive environment for approximately 1.5 years, with the result shown in Figure 9
This gear was operated for approximately 8 days with the operating conditions shown in Figure 5
whereafter the experiment was stopped due to excessive vibration. Three-hundred-and-twenty (320) measurements were acquired during the test, with the condition of the gear after the test shown in Figure 10
The excessive vibration was caused by the failure of one gear tooth and the significant damage of two adjacent gear teeth. The pinion was again in a healthy condition for the duration of the test.
The same procedure is followed as Section 4.2
. Firstly, the vibration signals are order tracked, whereafter the SASE and SMSE are calculated for the gear and the pinion of the test gearbox. The SASE and SMSE of the gear and the pinion are presented in Figure 11
. Only twenty of the 320 measurements are presented in the figure to ensure that it is easy to interpret.
The SASE and SMSE of the gear and the pinion perform very similarly as seen in Figure 11
a,b. Much impulsive components can be seen over the rotation of the gear, e.g., between 45 and 90 degrees. This is attributed to the fact that distributed gear damage is present. At approximately the 150th measurement number, i.e., in the middle of the measurement number axis in Figure 11
a,b, an event can be seen at approximately 0 degrees. A very large spike occurs which indicates that a gear tooth became severely damaged or has failed. This component also becomes more broad over measurement number which is indicative that adjacent teeth are potentially damaged as well.
The benefits of using the SMSE over the SASE is highlighted when investigating the results of the pinion in Figure 11
c,d. The magnitude of the SASE of the pinion in Figure 11
c contains very impulsive information which increases over measurement number. This is attributed to the SASEs sensitivity to the gear damage components, i.e., the SASE is not robust to non-synchronous impulsive components. The implication of this is that the condition of the pinion can be interpreted as becoming worse over measurement number. The SMSE in Figure 11
b delivers completely different results; the first measurement contains some impulsive information which is attributed to wear in process of the gears, however, after this it can be seen that the SMSE of the pinion does not contain any impulsive information and is very uniform over measurement number. This means that the SMSE of the pinion is unaffected by the severely damaged gear and therefore provides a reliable representation of the condition of the pinion.
These results are corroborated when investigating the metrics over measurement number in Figure 12
The metrics of the gears, shown in Figure 12
a,b for the SASE and the SMSE respectively, are able to detect the wear-in that occurred at the first few measurements due to the potential improvement of the corrosive surface of the gear. At measurement number 148, an event, indicated by Event 1 in Figure 12
, occurred which resulted in a significant discontinuity in the metrics associated with the gear. When combining this information with the results in Figure 11
a,b, this discontinuity is attributed to the sudden failure of a gear tooth. At measurement number 280, another event, indicated by Event 2 in Figure 12
, occurred which is attributed to the failure of the adjacent teeth.
The SASE metric of the pinion in Figure 12
c has a very similar behaviour of the gear; it is influenced by the condition of the gear and therefore is dependent on the measurement number. Hence, the SASE is unreliable for performing condition monitoring on gearboxes. The SMSE metric of the pinion in Figure 12
d is unaffected by the changes in the condition of the gear and therefore remains relatively constant over measurement number. This correctly indicates that the pinion was healthy for the entire duration of the test and therefore the SMSE provides a more reliable estimate of the individual mechanical components under consideration. An example of the practical implication of diagnosing the condition of the gears incorrectly is that the maintenance department may order pinions and gears from the suppliers, while only gears are necessary. This can have significant financial implications when large gearboxes found in the power generation and mining industries are monitored.
The benefits of using the SMSE instead of the SASE are highlighted in Figure 13
where the condition indicators are presented over the rotational speed of the gearbox. The same presentation could not be performed for the localised gear damage experiment, since the gearbox was operating under the same time-varying operating conditions (i.e., OC: 1 in Figure 5
) for each measurement.
This representation in Figure 13
allows the condition of machines to be inferred under time-varying operating conditions [4
]. The four clusters on the rotational speed axis are attributed to the four operating conditions of the gearbox (i.e., see Figure 5
Since the SASE does not provide a reliable estimation of the condition of the gearbox, two distinct clusters are formed when investigating the pinion for a specific operating condition state. This indicates that as the condition of the gear deteriorates, the condition indicator of the pinion erroneously indicates that the pinion is deteriorating as well. In contrast, the SMSE makes it possible to distinguish between the damaged gear and the healthy pinion. The condition indicator in Figure 13
d is sensitive to operating conditions, however, when using the conditional representation in Figure 13
, i.e., presenting the condition indicators against the operating conditions, the condition indicator becomes much more robust to changes in the operating conditions of the machine. Hence, the SMSE is a very simple method improvement to the SASE for performing gearbox fault diagnosis under time-varying and non-Gaussian noise conditions.