The thickness of an oil film lubricant can contribute to less gear tooth wear and surface failure. The purpose of this research is to use artificial neural network (ANN) computational modelling to correlate spur gear data from acoustic emissions, lubricant temperature, and specific film thickness (
Predicting the performance of a gear system is a serious function, as it is a crucial component in machinery. Danger to human life and potentially large-scale economic consequences can result from failures that cannot be predicted. Periodic inspection is essential in gear teeth or bearings, so that crack propagation or the other damage can be identified beforehand. Typical failures in gears are generally associated to bending, fatigue, contact fatigue, wear, and scuffing, all of which can be monitored by testing vibration and acoustic signals, temperature, torque, and lubrication film thickness. This can be carried out through continuous or online monitoring. Damage to gear teeth alters the parameters originating in the gear shaft. Damage also affects the oil film thickness and the type of wear that occurs [
The consequences of lost production and decreased reliability due to unplanned shutdown have a serious impact; thus machine performance monitoring is increasingly important in industry. The first step to monitor any deterioration is to establish a monitoring programme which can guide maintenance decisions. A number of monitoring methods for machinery with rotating components are available, including monitoring the lubrication, vibration, and acoustic emissions [
Emerging technologies, such as artificial intelligence (AI) techniques and complex computational analysis, have led to the advancement in machine condition monitoring. Artificial intelligence has several advantages as compared to the traditional mathematical modelling and statistical analysis. This includes dispensing of the necessity for detailed system behavior knowledge which can be replaced by relatively simple computational methods [
The prediction for the condition of moving components in machines can be assessed by measuring the lubricating oil film thickness. This has been a typical approach applied by numerous researchers in the past. An adequate lubrication regime is essential to prevent or reduce surface wear on gear teeth. The ability to predict and rectify wear-related damage will improve the performance of gear transmission systems. The established methods have to include monitoring the performance that can detect changes in vibration, sound, wear, and lubricant behavior [
In the past, research has been carried out to correlate acoustic emission with specific lubricant film thickness in spur gears. The method used to establish the relationship involved spraying liquid nitrogen onto a rotating gear wheel. This lowered its operating temperature and changed the response of the lubricant under a range of load and speed conditions [
The decision to apply ANN modelling in this research was based on its suitability and potential existence in wide range of applications to recognize specific patterns that can lead to the detection, classification, and diagnosis of changes in performance [
ANN training and testing of condition monitoring system.
Acoustic emission signals are outside human hearing and occur on the surface or from within materials when elastic waves at 20 kHz–1 MHz are released [
The test rig used in these experiments was a standard back-to-back gearbox with oil bath lubrication as illustrated in Figure
Test gears specifications.
Number of teeth, pinion : gear | 49 : 65 |
Base diameter, pinion : gear (mm) | 138.13 : 183.24 |
Pitch diameter, pinion : gear (mm) | 147.00 : 195.00 |
Tip diameter, pinion : gear (mm) | 153.00 : 201.00 |
Contact ratio | 1.33 |
Module (mm) | 3.00 |
Addendum modification coefficient | 0 |
Surface roughness, Ra (mm) | 2.00 |
Face width (mm) | 30.00 |
Pressure angle (°) | 2.00 |
Modulus of elasticity (GPa) | 228.00 |
Lubricant properties.
Viscosity | |
40°C (cSt) | 680.0 |
100°C (cSt) | 39.2 |
Density at 15.6°C (kg/L) | 0.91 |
Viscosity index | 90.0 |
Pour point (°C) | −9.0 |
Flash point (°C) | 285.0 |
Pressure viscosity coefficient, |
2.2 × 10−8 |
Back-to-back test gearbox arrangement [
The setup includes a model WD wideband AE sensor capable of picking up relatively flat responses in the range 100 kHz–1 MHz with the operating temperature range of −65 to 177°C (Physical Acoustic Corp.). The AE signals from the rotating test pinion were transmitted to a commercial data acquisition system by silver contact slip rings (Figure
AE sensor and thermocouple location on test pinion gear [
The gearbox test rig was set to continuously record AE RMS signals which were captured by software interfaced with an analogue-to-digital converter (ADC). The torque loading parameters were 60, 120, and 250 Nm and the gearbox was run at 700 and 1450 rpm. The selected speed represented approximately one complete revolution of the pinion at 700 rpm. Using the accumulated squared ADC values, the RMS could then be calculated. An antialiasing filter was used before signal sampling at the ADC. The AE waveform sampling rate was 10 MHz and the digital filtering range was 100–1200 kHz. The temperature sampling rate was set at 1 Hz and the accuracy was 70.1% on a 1°C resolution [
The selection of lubrication system for the test rig was based on gear tangential speed. Methods of lubrication that are generally used in gears are three primary methods.
They are grease lubrication (0 to 6 m/s tangential gear speed), splash lubrication (4 to 15 m/s tangential gear speed), and forced oil circulation lubrication (above 12 m/s tangential gear speed). The splash or oil bath lubrication system was selected for the purpose of this research programmer since the tangential speed during the test mostly ranges from 5.39 m/s to 12.20 m/s.
Oil lubrication prevents the gear teeth from coming into direct contact and reduces friction, vibration, heat buildup, and corrosion. The predicted fatigue life of the gears can be understood by the lambda (
The film thickness is indicative of the lubrication regime between two rough surfaces. The film is affected by high pressure contact and sliding, which causes heat generation and changes in physical properties. Typical operating conditions cause the lubricant to become thin, reducing protection against rubbing at the surfaces and resulting in lubricant failure. The characteristics of the lubricant are therefore crucial to maintain the minimum film thickness under specific operating conditions and this would require a sufficiently large
Three different lubrication regimes can be distinguished depending on the lubricant film thickness which are hydrodynamic lubrication (HL), elastohydrodynamic lubrication (EHL), and boundary lubrication (BL). Mixed lubrication is an intermediate regime between elastohydrodynamic and boundary lubrication. Full hydrodynamic lubrication would normally occur at
The Stribeck curve and specific film thickness (
Modelled on thinking mechanisms that have been mapped in the human brain, an ANN architecture consists of input and output layers, several neuron layers, and one or more hidden layers. Information flows through different layers from the input to the output and each layer is connected by neurons to adjacent layers. The layered network matrix connections will assign numerical values based on the connective arcs and the weight they are given, which can be adjusted during the training phase.
In this study, oil temperature and acoustic emission signals are the inputs and the specific film thickness (
When designing a neural network there are a number of different parameters that must be decided. Some of these parameters are the number of training iterations, the number of layers, the learning rate, the number of neurons per layer, and the transfer functions, and so forth.
The ANN parameter is generally performed by a developer through a trial-and-error procedure [
Multilayer FFNN modelling can be used in fault detection and diagnosis in rotating machinery. The neural networks are trained using a back-propagation algorithm to estimate lubrication film thickness [
Tan-sigmoid (nonlinear outputs between −1 and +1), Log-sigmoid (nonlinear outputs between 0 and +1), and transfer function linear outputs (between −1 and +1) can be used in hidden and output layers. Different transfer functions are explained in Figure
ANN structure and transfer function types of feed-forward back-propagation.
One of the earliest training algorithms was developed by Levenberg and Marquardt (LM). It is commonly used in conjunction with feed-forward neural networks. It can resolve a number of problems in nonlinear multilayered networks [
This is a semirecursive neural network which identifies patterns from a sequence of values by the back-propagation through time learning algorithm. First proposed by Jeffrey Elman in 1990, it is a recurrent neural network that enables sequential learning and recognition of patterns in series of values or events which unfolded over time and can be predicted. In Figure
ANN structure and transfer function types of Elman network.
The Elman ANN uses the Log-sigmoid and Purelin transfer functions in its hidden layer and output layers, respectively, providing approximation to any function. The Levenberg-Marquardt (LM) training algorithm also improves performance compared to other network training methods.
Training (Tr) in a neural network is the most intense and important computation that takes place. When the training is complete, rapid identification of any unknown input samples in the network is possible. A relationship between input data can be established, even if arising from spurious signals.
During training, the node weighting is continually adjusted to get as close to the real value associated with all available inputs. This involves extensive amounts of information and is a very important process to improve the functionality of the network. However, once an overfitting is identified the analytical processing is halted.
Overfitting takes place when the model is performing well during training; then it starts to decline when tested with unseen data. Cross-validation which estimates the performance of a predictive model can overcome overfitting. Training and validation require two distinct data sets. The mean squared error (MSE) of the validation data first decreases when overfitting takes place, reaches a minimum, and then increases. However, the training data MSE continues to decrease. It is assumed that when the validation data set MSE increases, the regression algorithm is overfitting the training data and training is stopped [
The supervised training method was used in this study. The network has an input layer (2 neurons), a hidden layer (5 neurons), and an output layer (1 neuron). The number of neurons in the hidden layer is assumed to be the number of inputs multiplied by two, plus one (number of inputs × 2 + 1) [
In this research, performance of a network is evaluated by statistical error analyses which identify the most suitable model. Three types of error analysis were used to evaluate and compare the models.
An error is the difference between the predicted and actual value. The MSE finds the average of the squares of the predicted errors, which corresponds to the risk factor the network represented, because of quadratic or square error loss. The cause of the difference is due to either the random approach or the fact that certain information has not been processed during the prediction, which would have produced a more accurate estimate. If
The MAPE is a method which can measure the accuracy of constructing fitted time series values and estimating the trend. Accuracy is measured in percentage error using the following equation:
The absolute value is summed for each fitted or predicted point in time, divided by the number of fitted points (
The MAE is a quantity comparing the closeness of predicted and actual values given by the following equation:
In this study, the data was taken from previous research to investigate and understand the influence of specific film thickness (
In this study of the lubrication regimes, the data was divided into 6 categories; each category represents one load and speed condition. The first load and speed condition is (S1L1), with the speed at 700 rpm (S1) and torque loading conditions 60 N m (L1). The data for temperature, acoustic emission, and specific film thickness comprise 1000 sets each and the same for (S1L2), (S1L3), (S2L1), 18 (S2L2), and (S2L3). This study has a total of 6 load and speed conditions for 2 speed and 3 torque loading conditions.
The simulation of the network was done using SIMULINK of MATLAB and then tested by the test data set. The data set is comprised of 20% for each input and output, variables for tow speed and three load conditions (2 × 3). Classification program was designed and used to classify the prediction output to hydrodynamic lubrication (HL), elastohydrodynamic lubrication (EHL), and boundary lubrication (BL) based on the specific film thickness magnitude.
The input data for ANN are temperature and RMS of the acoustic emission signal. The output data is the specific film thickness. This data was divided into two sets which are training and testing. From all the data 80% was used for training and 20% for testing.
Neural network toolboxes in MATLAB use many types of training algorithms and training functions. Feed-forward back-propagation networks with the Levenberg-Marquardt training algorithm and Elman back-propagation with the Levenberg-Marquardt training algorithm were used in this study to improve oil film regime predicting accuracy. The number of neurons was determined to be (number of inputs × 2 + 1) neurons [
Since the study included two speeds and three load conditions, by using two networks (12 load and speed conditions), a lot of information from each condition was obtained. For that reason, only the best and the poorest performances from the six conditions in each network are discussed.
Table
Statistical error value in training and testing.
Network | MSE | MAE | MAPE | |||
---|---|---|---|---|---|---|
Training | Testing | Training | Testing | Training | Testing | |
Elman | 3.4684 × 10−4 | 6.5959 × 10−4 | 7.2 × 10−3 | 2.31 × 10−2 | 2.388 × 10−1 | 4.58 × 10−1 |
FFBP | 1.3524 × 10−5 | 5.848 × 10−4 | 2.6 × 10−3 | 2.18 × 10−2 | 1.617 × 10−1 | 4.548 × 10−1 |
The advantage of FFNN is that it is easy to construct. During the development of FFNN, after all the parameters (such as input layer, hidden layer, and output layer) are confirmed, the weights and biases of the network are saved as one model.
Table
FFBP performance.
FFBP network | MSE | MAE | MAPE |
---|---|---|---|
S1L1 | 2.6965 × 10−4 | 1.3 × 10−3 | 3.127 × 10−2 |
S1L2 | 1.0253 × 10−4 | 7.05 × 10−3 | 1.784 × 10−1 |
S1L3 | 1.3524 × 10−5 | 2.6 × 10−3 | 1.617 × 10−1 |
S2L1 | 9.4002 × 10−5 | 6.6 × 10−3 | 2.359 × 10−1 |
S2L2 | 7.1003 × 10−4 | 1.01 × 10−2 | 8.836 × 10−1 |
S2L3 | 1.1 × 10−3 | 1.5 × 10−2 | 9.447 × 10−1 |
Figure
FFBP network training output and the target.
On the other hand, the network delivered for (S2L3) was not fully satisfactory with the MSE equal to 6.1 × 10−3, which was made clear when testing this network with unseen data. As shown in Figure
FFBP network testing output and the target.
The MSE error is plotted against a number of epochs of training for S1L3 and S2L3. Figure
Validation performance for FFBP network: (a) S1L3 and (b) S2L3.
The FFBPP network is trained and regression performed on its targets and outputs. Regression testing can be used for testing the correctness of a module and for tracking the quality of its output. Figure
Feed-forward network regression performed on its targets and outputs.
The EN was selected in this paper for a modelling process because of its ability to learn temporal patterns and store information for future reference.
The Elman network for load and speed conditions (S1L1) gave a great performance, as can be seen from Table
Elman network performance.
Elman network | MSE | MAE | MAPE |
---|---|---|---|
S1L1 | 9.7594 × 10−4 | 1.5 × 10−3 | 3.47 × 10−2 |
S1L2 | 3.4684 × 10−4 | 7.2 × 10−3 | 2.388 × 10−1 |
S1L3 | 2.1 × 10−3 | 2.73 × 10−2 | 1.0187 |
S2L1 | 1.16 × 10−2 | 6.78 × 10−2 | 2.012 |
S2L2 | 3.5 × 10−3 | 1.08 × 10−2 | 4.599 × 10−1 |
S2L3 | 2.1 × 10−3 | 1.91 × 10−2 | 3.5312 |
Elman network training output and the target.
Meanwhile, the network performance provided a less accurate prediction for S2L1, since the value of the error measurement is higher than the other load and speed conditions (as shown in Table
Elman network testing output and the target.
Figure
Validation performance for Elman network: (a) S1L1 and (b) S2L1.
The result above indicates that the networks performed very well during training and validation processes for load and speed conditions (S1L1) and less for the other load and speed conditions, especially for (S2L1).
This work is important in confirming the optimal network that can be used for predicting the oil film thickness. For that purpose, a comparison between FFBP and Elman networks is done in order to select the most suitable network for the modelling process. The network which produces the lowest validation error during training is selected as the optimum network.
Table
Best validation performance for FFBP and Elman networks during training.
Load and speed condition | FFBP network | Elman network | ||
---|---|---|---|---|
Best validation | Iteration number | Best validation | Iteration number | |
S1L1 | 6.2725 × 10−5 | 247 | 6.4130 × 10−5 | 459 |
S1L2 | 1.9810 × 10−5 | 993 | 6.9132 × 10−5 | 351 |
S1L3 | 1.5007 × 10−5 | 1000 | 2.5177 × 10−3 | 420 |
S2L1 | 8.6352 × 10−5 | 1000 | 8.9168 × 10−3 | 208 |
S2L2 | 4.6211 × 10−4 | 131 | 2.6495 × 10−3 | 883 |
S2L3 | 4.5334 × 10−3 | 369 | 5.1342 × 10−3 | 438 |
Figure
Compression between Elman and FFBP network testing error. (a) S1L1, (b) S1L2, (c) S1L3, (d) S2L1, (e) S2L2, and (f) S2L3.
From this figure it can be seen that the FFBP network testing error was smaller than the Elman testing error. This means that the predicted output from the FFBP network is more accurate than Elman and is almost the same as the target.
Classification program is designed and used to classify the oil film regime in gear, the program used with estimated data. When the two networks were tested with input data sets and targeted outputs, the networks yielded a predicted output. This output was used in the program. In this way, the result, as shown in Table
Networks classification success results.
Load and speed condition | FFBP network | Elman network | ||
---|---|---|---|---|
Training classification | Testing classification | Training classification | Testing classification | |
S1L1 | 100% | 100% | 100% | 100% |
S1L2 | 100% | 100% | 100% | 100% |
S1L3 | 100% | 100% | 100% | 99.5% |
S2L1 | 100% | 100% | 100% | 99.2% |
S2L2 | 100% | 99.7% | 100% | 99.5% |
S2L3 | 100% | 99.7% | 100% | 99.6% |
At the end, the two networks can be utilized in industry fields for condition monitoring of oil regime in gear, since the oil film thickness problems could be identified and alarmed through a comparison between actual and estimated thickness. The appropriate messages are generated if the estimated levels of any input variables differ significantly from the nominal level over a period of time.
The use of ANN in rotating machine condition monitoring based on acoustic emission signal is very rare. Therefore we cannot do any comparison between this work and other researchers’ works, because most of researchers used vibration data as input and output of ANN. Sreepradha et al. [
An ANN techniques approach was proposed to improve the accuracy of oil film thickness prediction for spur gear. The results showed that FFBP and Elman models were effective and this suggested technique attained 100% success in prediction and classification at high speed during training. The FFBP is better than Elman during testing and gives very good result in prediction and classification. The present study concludes that FFBP is better than EN, with better performance, prediction, classification, and less error. The architecture and topology of the network through specific systems can be used for online monitoring of oil film thickness and to predict any causes of failure of spur gear operation.
The authors declare that there is no conflict of interests regarding the publication of this paper.