How bolt looseness can be detected by acceleration
Bolts are an essential component of many structures, big and small. They are lost-cost, easy to install, strong, and replaceable. Bolts are everywhere from phones to cars, to industrial machines. Given enough time and energy, bolts in almost any mechanical structure can and will eventually come loose. Loose bolts can lead to bad load distribution while the surrounding bolts loosen faster leading to the system breaking down. A big source of loosening is vibration, and the more violently a system shakes, the more likely it is for its bolts to become loose. For example, Wind turbines often have their bolts checked for torque every 1-5 years, and in some cases, these bolts can come loose, and a blade can detach from the rotor hub. Situations like that, where bolts put in challenging situations that are difficult and expensive to monitor by a technician, are why bolt looseness monitoring can be so important.
Figure 1: Downed wind turbine blade caused by loose bolts connecting the blade to the rotor hub.
What is Bolt Looseness?
In its simplest form, a bolt helps keep two structures together. Although it can be difficult to imagine, a bolt is a spring which, when torqued, is stretched, sandwiching two components together. This stretching is caused by the bolt threading into a nut or a tapped hole, while the head of the bolt stays a fixed distance away. A bolt that is not tight enough can result in the bolted surfaces sliding apart, rotating, or even disconnecting. This initial stretch of the bolt corresponds to a tension force, which is often referred to as preload, which applies an equal and opposite clamping force, holding the bolted components together. When a bolted system is designed, the necessary clamping force to keep the structure working is determined, and the right number of bolts is chosen. That clamping load by each bolt is achieved by tightening the bolts to a specific torque, which is calculated using equation 1. The maximum torque a bolt can achieve is based on its material, size, pitch, and more. Bolt looseness occurs when a bolt is not torqued as tightly as specified leading to lower preload than designed. Looseness can occur from either bad installation, damage, or from vibrations slowly untwisting the bolt over time.
How is bolt looseness measured?
There are many ways to check if a bolt is loose, either manually or using sensors.
- Manual bolt testing:
- Use a torque wrench to tighten bolt to the specified torque
- Visual inspection
- Using a torque stripe
- Using specialized nuts
- Handheld ultrasonic tester
- Remote sensors:
- RT-bolt
- InterBolt
- Remote ultrasonic testers
Bolt looseness can only be indirectly measured in most practical applications. The only direct way to measure the clamping force applied by the bolt is to use a through-hole load cell between the bolt head and the clamping surface. Since[SL1] in most applications, a load cell can’t be placed under a bolt head to measure preload, due to its high cost or a lack of space, other measurements are required.
When measuring torque, the following equation 1 can be used to convert torque to preload force:
Where:
Using torque is generally a reliable way to measure the preload on a bolt, but it has to be noted that the nut factor is often variable due to differences in bolt lubrication, surface coating, roughness and more. The other [SL2] most common method for measuring preload is to measure the strain of the bolt as a measure of its elongation. In a healthy bolt, the more tension applied to it, the more it strains. The force acting on the bolt can be summarized with the following equations:
Summarizing to:
Where:
Since the variables in equation 5 needed to measure bolt force, are easily measurable, and consistent from one bolt to another, many products exist to measure the change in length of a bolt.
- Ultrasonic detectors work by attaching to the head of a bolt, pinging an ultrasonic wave through the body of the bolt and measuring the time it takes for the signal to come back to the head of the bolt. The change in time for the wave to rebound is directly proportional to the change in length of the bolt.
- Gauge pin depth sensors work by drilling a small hole into the bolt and then putting a free-to-move pin in the hole, then a sensor mounted to the top of the bolt measures the change in height of the pin sticking out from the hole. The drilled hole changes length at the same rate as the rest of the bolt, and the pin helps make that change in length easy for a sensor to read.
How is Acceleration Related to Preload
The systems most vulnerable to loosening bolts are often ones which undergo strong vibrations and variable loads. Those vibrations and loads cause the bolts to slip and move over time. Since the purpose of a bolt is generally to secure two structures together, these vibrations and loads apply a force to the bolted joint, and if the bolt is loose, the joint will not be rigid, and those very forces will be transferred from one structure to the other differently than with a properly torqued bolt. Force transferred from one object to another leads to acceleration, and by measuring the change in the acceleration signal of a either structure changes in the state of the bolts can be discovered.
Testing
We performed a demonstration of monitoring bolt looseness on one of our belt-driven test rigs to show how effective different analysis methods can be at finding bolt looseness in a real-world system.
The test rig has two big motors, one that drives the system, in this case at 1500 RPM, while producing 15 kilowatts of power, while the other acts as a generator, applying a load to the system. The driving motor is the subject of the test, and it is bolted down to the test-rig frame using four 5/8-11 bolts. These bolts are normally torqued down to 106 ft*lbs. to ensure a good connection between the motor and the frame. During testing, two of the bolts were loosened (circled in red), one at a time, while the machine was operating to see if any difference could by picked up by an accelerometer placed in two different locations. The goal of the testing was to see how much looseness is detectable, and where can it be detected from.
Figure 3: Locations of loosened bolts circled in red: bolt 4 on the left, bolt 1 on the right
Test Conditions:
To ensure stability in the testing, the belt was run for 30 minutes before recording, to ensure the system reached steady state. The steps below were taken with the accelerometer measuring 2-2-minute recordings at each step at 4000 Hz. The recordings were repeated for two accelerometer locations, one, with the sensor magnetically mounted to the motor’s electrical panel, and the other magnetically mounted to the frame.
- Torque all 4 bolts to 106 ft*lbs
- Loosen bolt #1 to 53 ft*lbs
- Fully loosen bolt #1 to 0 ft*lbs
- Loosen bolt #4 to 53 ft*lbs, retorque bolt #1 to 106 ft*lbs
- Fully loosen bolt #4 to 0 ft*lbs
- Retorque all 4 bolts to 106 ft*lbs
Figure 4: enDAQ mounted to motor frame
Figure 5: enDAQ mounted to test rig frame
What Acceleration Signals can be used to Measure Preload
Raw Signal:
Looking at the raw acceleration captured by the accelerometer on its own can’t really tell you much, most of the time. In this case, Figure 3 shows the raw acceleration measured by the enDAQ when all the bolts on the motor are fully torqued, while Figure 4 shows a similar acceleration signal, but with bolt 1 on the motor fully loosened.
Figure 6: Raw acceleration signal from enDAQ mounted to the test rig frame while all 4 bolts are fully torqued
Figure 7: Raw Acceleration signal from enDAQ mounted to the test rig frame with bolt 1 fully loosened
Figure 8: 1 Second zoomed in acceleration plot recorded with bolt 1 being fully loose
Looking at the raw data shows that there isn’t a clear difference that can be easily seen between the two signals. Overall, the amplitudes look similar, and there don’t seem to be any major events that clearly show the loose bolt in Figure 4. As a result, the data needs to be processed to get as much information as possible about the system. Some analysis methods are simpler than others, but each method has its own strengths and weaknesses, so I’ll demonstrate a few different techniques such as a simple time domain analysis, FFT, random Forest model, and an LSTM model. For a simple time domain analysis, if you look just at the mean, standard deviation, max value or RMS of the acceleration signals, not much changes from one test to another as seen below in Table 1
Table 1: Comparison of vibration values across each recording, compared to the first recording
Table 2: Comparison of vibration values measured with enDAQ mounted on the motor
Based on the results from table 2, there is a correlation between dropping RMS values and loosening bolts. If we now look at the Z axis results as shown in table 3: as the bolts are loosened, the RMS acceleration generally drops. The drop in RMS is not very consistent, meaning longer data samples, beyond two minutes, may need to be taken to get a good understanding of the system’s changing dynamics.
Table 3: Z-axis acceleration properties with enDAQ mounted to the motor
Looking just at individual acceleration metrics can be very helpful to get an idea of what happening in a system, but one or two metrics will never be able to get you the specificity and accuracy needed to determine which bolt is loose since there are many factors that can affect the rms vibration, or any other metric measured by an accelerometer.
Signal Processing:
Since bolted connections act as springs, the overall systems can be modeled by a spring-mass-damper system. By changing the tightness of a bolt, the overall system response at different frequencies will change, either in magnitude, or by moving peaks from one frequency to another. Depending on the system and the looseness of bolts, this difference can either be nearly imperceptible or easy to see. The best ways to look at the frequency content of the bolt change are either through Fast Fourier Transform (FFT) or through Power Spectral Density (PSD), which both break down the acceleration time series data into the frequency domain.
One easy trick to qualitatively check to see if there is any change in a signal in the frequency domain Is to take the FFT of two recordings and then subtract the two FFTs. The resulting FFT diference lets you know if any major peaks have move or changed in frequency. The problem with just looking at frequency data on its own is that often times the it is difficult to know what to look for in the FFT. This can be improved in a system where the natural frequencies, and material properties of the system are well know. In this case since this is a complex system, it is dificult to pick out the correct frequencies ahead of time.
Figure 9: FFTs of various vibration signals with the enDAQ mounted to the Motor. Baseline recordings compared(left); baseline compared to half loose bolt 1 (middle); baseline compared fully loose bolt 1 (right)
Machine Learning:
Machine Learning (ML) can be a very powerful tool that can combine many different methods and metrics for analyzing the loose bolt signals. Generally speaking, when it comes to making a machine learning dataset, a few parameters are necessary:
- Labeled data
- Data must be accurately labeled meaning that all the outputs you want the ML algorithm to give must be accurately measured and defined. In this case, the torque on the bolts must be accurately measured
- Broad data
- The training dataset must have as many of the possible conditions assume that the system could see
- Large datasets
- Training data must be large to help detect features while reducing randomness
Machine Learning can be most effective when a system’s environmental and setup conditions are well understood, but the correlation of one fault to another outcome in vibration is unknown. In the first case we will use a random forest machine learning algorithm to detect bolt looseness. If you want to learn more about the specifics how a random forest algorithm works, here is a link to a great blog post through IBM: https://www.ibm.com/think/topics/random-forest
When running a random forest algorithm, the features of importance need to be defined. Essentially you need to tell the program what features it should look for such as rms, kurtosis, max acceleration, and many more. Generally, you want to include as many metrics as reasonable, and then the algorithm will weigh their value in terms of helping to sort data. Feature importance is determined in a random forest model by tracking how often a given feature helps in making a correct decision. The random forest algorithm functions as a collection of decision trees where the value of each feature helps determine the state of the bolts. For example, Figure 6 show the differing weighting for each parameter used. There is a noticeable difference in weight of different parameters, depending on where the sensor is located. One of the parameters that varied the most in importance is Skew, which is very correlated with the accelerometer on the frame, and much less correlated with the accelerometer on the motor itself.
Figure 10: Feature weight for the random forest machine learning algorithm. Plot for enDAQ mounted to the frame (left). Plot for enDAQ mounted to the motor (right).
In order to run this ML algorithm, we need to establish what the training data will be, and what the testing data will be as well as what variables we will be looking at. If you use the same data for training as for testing, the results will likely look good, but it will be difficult to check if the algorithm is actually accurate. For my testing, I tested two different locations for the enDAQ, and made sure to get at least 2 2-minute recordings for each condition. If I use the same data for both training and testing, there are 12 samples for each accelerometer position, and the confusion matrices can be seen below:
Figure 11: Confusion matrix showing the result of a random forest ML algorithm while using the full dataset as both the training and the testing. Each count corresponds to a 2-minute recording. On the left, the matrix shows the recordings when the accelerometer is mounted to the rig’s frame. On the right, the matrix shows the results with the accelerometer mounted to the motor
The confusion matrices show a perfect correlation between what it predicts compared to what the system’s actual state. This implies that it made a nearly perfect model. Since it is training on the same dataset it tests on, it already knows the answers to the test, and gets the answers correct. To have a more accurate representation of the accuracy of the algorithm, the training dataset needs to be separated from the testing data. In this case that is done by splitting up the data into small sections, training on 80%, and then testing on the other 20%. This results in a slightly less accurate confusion matrix which shows that the ML algorithm isn’t perfect. One thing to note from both figures is that the results from the enDAQ on the motor appear to be more accurate, which is reasonable since there the accelerometer is much more coupled to the loose bolts, and closer in location. The mean accuracy of the Random Forest algorithm on data from the frame is 0.694, meaning that it is correct nearly 70% of the time, and it has an accuracy of 0.722 on the data from the enDAQ mounted to the motor. Interestingly, the algorithm is better at detecting if the bolt is fully loose, rather than partially loose, which makes sense since that state is the most distict.
Figure 12: Random Forest model confusion matrix with each 2-minute recording split into 200 sections and then analyzed using 5-fold cross validation
LSTM Model
LSTM stands for Long Short-Term Memory. LSTM models are generally used when looking exclusively at time-series data. The data we’re getting from our accelerometer comes directly in the time-domain, making LSTM a good choice. The great thing about LSTM models is that they can work very efficiently with raw data, and require less insight about a system to work well, and many of the parameters that are used to fine tune the system can be generated just by analyzing the results of the model, and without needing a fundamental understanding of the system. The drawbacks of an LSTM model are they generally need more data to become accurate, and since the model determines what patterns it should be looking for, it takes longer to analyze the data, even when compared to a random forest algorithm.
Since the dataset I’ve obtained for this experiment has a limited number of recordings, we will use 5-fold cross validation to check the LSTM model results[HD1] . Additionally, LSTM models can take a long time to train due to how many operations are needed to make a good model, so only a random 10% of the data taken from each recording is used and just the X-axis. Unlike the random forest algorithm that is given which parameters to look at, LSTM essentially starts as a blank canvas and needs to figure everything out from scratch. When developing an LSTM algorithm, there are a few different “knobs” that can be adjusted to give different results, often trading accuracy for time. The model below uses 80 epochs, a batch size of 64, and the number of units is 50.
With the accelerometer mounted to the motor, we can see that the LSTM algorithm works quite well with an accuracy of 95.92%. The model predicts when one bolt is fully loose the best, and slightly less accurate at determining the state of a half-loose bolt as seen in Figure 10 below.
Figure 13: Confusion matrix showing the accuracy of the LSTM model on the test portion of the dataset, where the enDAQ is mounted to the rig’s frame, with its ROC curve on the right
On the other hand, when the LSTM model is trained while mounted to the motor, as seen in Figure 11, the results are good (80.00% accuracy), but not as good as while on the frame.
Figure 14: LSTM model confusion matrix showing the results of testing when the enDAQ is mounted to the motor, with its ROC curve on the right
Conclusions:
Depending on your knowledge of a bolted system, the looseness of those bolts can be determined using different methods. If you know the system’s natural frequency, you can use frequency analysis to catch any changes which will show a change in the stiffness of the connection caused by loose bolts. If you know nothing about the system, there are various machine learning approaches that can be used. LSTM can work very well and accurately given enough training data but can be very time-consuming. Random forest on the other hand requires a little intuition about the system, and what parameters to look for, but can be fast and controllable.
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