DOI: https://doi.org/10.21203/rs.3.rs-2715838/v1
This paper introduces a prediction model based on machine learning techniques for dimensional control in the manufacturing process of side flange bearing housings, according to the technical standard DIN 31693. The process is implemented in a journal-bearing manufacturing industry positioned among the three brands with the highest participation in the international market in 2023. The manufacturing process consists of rigid machining processes composed of a universal horizontal machining center and dimensional control composed of a coordinate measuring machine. After machining, the piece is measured, and its dimensional report is generated. Qualified professionals use deviations obtained from this report to support the decision-making. The method used is based on the holistic monitoring of the surface geometry of the machined piece. The approach used to compensate for dimensional deviations is based on monitoring and modeling the total deviation. In this context, the effects of all sources of systematic errors are compensated regardless of their origin. The heuristic is used for the steps that make up the decision-making process. The way to implement the predictive model in the production line is based on the interaction between human and machine experience. This paper proposes using the regression decision trees for defining the displacement parameters of the machining center axes from the dimensional results of housings obtained in the coordinate measuring machine. The model is validated if the mean absolute error is less than or equal to 0.003mm. A comparison between an assembled model is performed to verify the performance between different predictive models.
Journal bearings are one of several elements that form a constructive part of machines and equipment. They are components designed to support the load while in contact with the surface of the shaft [1]. Its operation is based on sliding between a shaft that rotates freely supported on a metal casing lodged in a housing called the shell. The shell ensures alignment during assembly, and that loads are evenly distributed. In addition, the housing protects the assembly from contaminants while retaining lubricant and houses monitoring equipment [2].
The responsibility linked to the machining processes and dimensional control of the journal bearings is highlighted, since the perfect functioning of complex systems, with close tolerances, depends on them, where the error can compromise the entire assembly performance, causing operational and safety risks and various costs. It is essential to highlight that bearings are responsible for 40% of failures in machines and equipment [3].
In this sense, a coordinate measuring machine is required to determine the size, form, and position of the journal bearings produced by the machining processes. A coordinate measuring machine provides ultra-precise measurement results and is widely used in precision manufacturing. The contact measurement approach, performed using a touch probe, is widely used in measurement processes in the industry due to its efficiency, adaptability, and accuracy [4].
The journal bearings’ dimensional reports, produced by a coordinate measuring machine, are commonly evaluated and interpreted by operators and programmers who work to adjust the machining process. This human interaction in analyzing and interpreting such reports can cause unpredictability in the manufacturing process. Besides that, the ability to control all the machining process variables has surpassed human limits, delegating to machines and intelligent systems a good part of the tasks that ensure precise manufacturing [5].
Despite the application of modern process control systems for manufacturing journal bearings by machining, finding pieces with surfaces outside the tolerance limits is not uncommon. Therefore, it is impossible to guarantee that the machining parts will have the same form and size. But it is necessary to ensure their surfaces are within tolerance limits [4].
During manufacturing, several factors can influence dimensional errors, such as physical and kinematic phenomena, the dynamic behavior of the machine structure, and the geometric or dimensional imperfection of the process components. Thus, journal-bearing manufacturers face a major challenge in dimensional control: mapping the relevant data to understand the correlations between variables throughout the process stages fully. One of the forms mentioned by Domínguez et al. [6] to achieve this goal is through proactive control of the process.
Considering the complex interrelationships between various factors that compose the journal-bearing housing manufacturing process, techniques based on machine learning have become essential tools due to their speed, robustness, and non-linear characteristics when working with data. These techniques sustain the intelligent utilization of manufacturing resources and the adaptive adjustment of manufacturing processes that support an organization called smart factories [5].
To overcome the difficulties mentioned earlier and guided by the relevance of the theme for the metalworking industry, this work proposes a new approach using machine learning techniques and data obtained from the coordinate measuring machine to develop, evaluate, and validate a prediction model for the dimensional control of side flange bearing housings, according to the technical standard DIN 31693 [7]. The proposed approach aims to automate the steps of analysis of dimensional reports and decision-making that result in corrections in the displacement of the axes of the machining center through adjustments in the CNC machining program.
This work directly contributes to improving the manufacturing processes of journal-bearing. Furthermore, the proposed prediction model produces reliable and repeatable results, reducing dimensional errors in the housings produced by machining processes. This will cause: (i) increased productivity due to less production downtime awaiting analysis and all activities involving the decision-making process; (ii) cost reduction with the generation of non-conforming housings and reduction of hours of rework.
The remainder of this paper is organized as follows: Section 2 provides a review of related works presented in the literature. Next, Section 3 presents the scope and purpose of the predictive model, where the manufacturing process and dimensional control of industrial journal bearings are detailed. Then, in Section 4, the applied methodology is demonstrated, describing each step for model development. Finally, Section 5 presents the conclusions that involve the results obtained with the development of the model, its limitations, and proposals for future work.
In the context of the machined parts control, several approaches were presented to simultaneously reduce dimensional error and verify the technical requirements with the preservation of a high-intensity machining process. Related results in the literature refer mainly:
Techniques and methodologies for monitoring the operating condition, fault detection, and diagnosis.
Process and product optimization.
Machining theory considers aspects of process kinematics, wear of tools, and physical phenomena.
Prediction of the quality of machined pieces.
Some research has presented a broader approach for applying machine learning to machining manufacturing [8–10]. These addressed the problem-solving process using machine learning, showing product quality and productivity applications. On the other hand, the work proposed in this paper differs from [8–10] because the approach and method used were defined to solve a specific problem in the metalworking industry, restricting the scope of the research to the subject of dimensional control of machined side flange bearing housings.
In [11], the focus was on process improvement based on product quality prediction in a continuous flow process chain. For each process, a classification and regression tree (CART) algorithm was trained to classify whether the corresponding product would be in or out of specification at the end of the process chain. The proposed work differs from this research due to the use of the CART algorithm for a regression problem as opposed to the one introduced by the author, who used it for a classification problem.
In [12], a manufacturing process optimization approach was demonstrated by applying a production trend prediction model. First, the developed solution collects data from the factory floor. Then, based on concrete manufacturing values, production trend classes, and results are defined as trend forecasts in each manufacturing situation. The proposed work differs from this research because the machine learning solution is applied for prediction in a flexible production cell where housings are manufactured, in different sizes and models, by specific production order.
In [6], it is proposed to develop prediction models integrated with a digital twin to improve the performance of a multistage-bearing production line. The prediction models could determine the ideal operating conditions and final bearing adjustment under different machining conditions through implementation. The selected model was the exponential regression compared to 12 other algorithms, such as decision trees, SVM, or other Gaussian process regressions (GPR). The proposed work differs from this research in the methodology used due to the holistic approach to evaluating the piece's geometry and the heuristics used in the definition and adjustment stages of the process.
Maik and Robert [13] developed a prediction model for production process control to avoid critical conditions in the milling process to guarantee product quality. Random forest, gradient boosting, and long short-term memory (LSTM) algorithms were tested, and the Neural Networks algorithm (LSTM) presented the lowest root-mean-square error (RMSE). The proposed work differs from this research because the machine learning technique is applied to monitoring the dimensions contained in the dimensional reports produced by a coordinate measuring machine instead of monitoring the amplitude of vibration.
Mateusz and Arkadiusz [14] discuss the influence of the machine tool's external and internal temperature variation on the phenomenon of thermal deformation in the high-precision machining of pieces with thin walls and complex geometries. The finite element method was used for numerical simulation. The proposed work differs from this research because an approach is used to compensate for dimensional deviations based on monitoring and modeling the total deviation regardless of the error sources and components.
In [15], an approach for compensating the dimensional deviation by adaptive tool path programming is proposed. A comparative experimental analysis for implementing of the method demonstrated that the adaptive-optimal algorithm presented the best accuracy result. However, it cannot be applied to the first 10 to 15 samples of the batch, for which the adaptive-predictive algorithm is indicated. The proposed work differs from this research because the sci-kit-learn library performs part of the necessary tasks to develop the predictive modeling project.
Based on the review, the search for ways and means of applying predictive models in machining processes can be seen from different perspectives. However, more studies are needed to investigate recent algorithm advances and approaches under development. In this scenario, this work focuses on validating the machine learning technique based on regression decision trees for dimensional control of side flange-bearing housings through a holistic approach to monitoring the surface geometry of the machined pieces, heuristics for the steps that make up decision-making and employing the open-source machine learning python module sci-kit-learn1.
Side flange bearing housings, standard line DIN 31693 [7], are manufactured in upper and lower halves to facilitate installation and maintenance. These housings are produced in nodular cast iron and have a flange for final assembly on the machine or equipment for which it is intended. The spherical accent ensures alignment during assembly, and that loads will be evenly distributed into the lower part of the housing. They have channels for sealing, threaded holes for monitoring the temperature, oil inlet and outlet, and oil level. The upper half of the housing has a sight glass, which allows the oil ring to be seen. The basic design can incorporate cooling tubes, an oil sump heater, horizontal, vertical, and axial vibration sensors, and earthing devices if necessary. The assembled side flange bearing is shown in Fig. 1(a). The upper and lower halves of the housing are shown in Fig. 1(b).
Milling, drilling, and tapping machining processes, composed of a universal horizontal machining center, a CNC machining program, and an operator, are used to manufacture bearing housings. In addition, each manufactured half is dimensionally controlled by a metrological process composed of a coordinate measuring machine, measurement program, and operator.
The machining process provides the piece which will be measured and controlled in the metrological process. The metrological process results in the report from which the dimensional deviations are obtained, referring to the critical dimensions subject to evaluation by qualified professionals. The review of qualified professionals results in adjustments in the CNC machining program for the displacement parameters of the machining center axes to compensate for all sources of systematic error.
It is desired that the proposed predictive model automates the analysis steps of the dimensional reports and the decision-making that results in corrections in the displacement of the machining center axes, through adjustments in the CNC machining program, in addition to automatically suggesting or adopting adjustment parameters to obtain suitable housings to their critical dimensions.
A methodology based on the cross-industry standard process for data mining (CRISP-DM) [16] was applied to develop the predictive model, a. Six fundamental steps, each with its particularities and functionalities, were followed. The first three steps seek to contextualize, collect and organize the data to be analyzed. They contain the definition of the problem, the definition of the raw data, and the pre-processing of the base. The last three steps aim to create the model based on the previous steps and put this model into practice. These are algorithm definition, model validation, and deployment. This set of predefined steps, ordered in a flow, aims to ensure the correct transcription of the project scope into a product capable of implementing improvements in an existing process. The implementation stage will not be addressed in this work.
Machining and dimensional control of journal-bearing housings require high-tech equipment. Still, it is observed that human interaction is used in decision-making, which causes unpredictability in processes, resulting in low productivity and increased costs. In this context, a predictive model based on machine learning techniques is essential to achieve predictability in processes and increase industrial competitiveness.
Based on the description of the manufacturing process and dimensional control (Section 3), the housing size corresponding to the shaft diameter ranges from 160 to 220mm, and the critical dimensions D1, D2, D3, and D4 were defined for the development of the predictive model.
The critical dimension D1 corresponds to the measure of the radius of the spherical where the shell is supported. The D2 dimension corresponds to the measurement from the spherical center to the housing divider. Dimension D3 corresponds to the distance from the center of the spherical to the flanged face. Dimension D4 corresponds to the distance from the center of the spherical to the face opposite the flanged face. The criterion for choosing these dimensions was based on the requirements of dimensional tolerances, and the complexity of the machining and assembly process. The critical dimensions D1, D2, D3, and D4 of the upper half are shown in Fig. 2, and the lower half in Fig. 3.
In order to detail the characteristics and requirements of the critical dimensions, an analysis of the technical information contained in the housing manufacturing documents, dimensional control reports, and their relationships with the analysis stage and process decision-making was carried out. Afterward, it was possible to identify and describe the data for use in the proposed model. The possible minor adjustment on the machining center axes is 0.001mm. Table 1 contains the critical dimensions and respective machining and geometry information.
| Dimension | Machining process | Measurement Tolerance (mm) | Geometric Tolerance | |
| Characteristic | Tolerance (mm) | |||
| D1 | Milling | 0,029 | Concentricity | 0,010 |
| Circular | ||||
| Interpolation | ||||
| D2 | Milling | 0,020 | Flatness | 0,050 |
| Linear | Perpendicularity | 0,050 | ||
| Interpolation | Symmetry | 0,050 | ||
| D3 | Milling | 0,040 | Perpendicularity | 0,050 |
| Linear | ||||
| Interpolation | Parallelism | 0,100 | ||
| D4 | Milling | 0,040 | Perpendicularity | 0,050 |
| Linear | ||||
| Interpolation | Parallelism | 0,100 | ||
The data of interest for the elaboration of the model were obtained in the dimensional reports, in the historical adjustments in the CNC machining program, in the ambient temperature record at the time of machining, and in the thermal equalization condition of the piece at the time of measurement. Two types of parameters are classified [17]:
Dependents variables: represents a quantity whose value depends on the independent variables. It is the output data of the model and the adjustments in the CNC machining program.
Independent variables: represents a quantity whose value significantly influences the dependent variables. It is the input data of the model.
As a premise for the cause-and-effect analysis (the definition of relevant variables), specialists' knowledge and experience were used to create a relationship matrix between the dependent and independent variables shown in Table 2. This matrix presents the dependent variables A1, A2, A3, and A4, which are the adjustments of the displacement parameters of the machining center axes of the respective critical dimensions D1, D2, D3, and D4, and the following independent variables:
Temperature: this is the measured value of the ambient temperature at the time of the final machining of the housings.
Climatized: refers to the condition in which the piece has its temperature equalized with the coordinate measuring machine before being measured.
Deviation: represents the difference between the measured value and the nominal measure of a critical dimension.
Out of tolerance (OOT): represents the value exceeding a critical dimension's measurement tolerance limits.
It is possible to verify that the independent variables temperature and climatized influence all the dependent variables (A1, A2, A3, and A4). In addition, the independent variable deviation of the critical dimensions, D1 and D2, have a relationship. This fact indicates that the definition of adjustment A1 depends on the measures of D1 and D2, and the same is applied to the definition of adjustment A2.
| Independent variables | Dependents variables | |||
|---|---|---|---|---|
| A1 | A2 | A3 | A4 | |
| Temperature | X | X | X | X |
| Climatized | X | X | X | X |
| Deviation (D1) | X | X | - | - |
| OOT (D1) | X | - | - | - |
| Deviation (D2) | X | X | - | - |
| OOT (D2) | - | X | - | - |
| Deviation (D3) | - | - | X | - |
| OOT (D3) | - | - | X | - |
| Deviation (D4) | - | - | - | X |
| OOT (D4) | - | - | - | X |
To obtain valuable and efficient data from raw data, it is essential to carry out a set of data preparation, organization, and structuring activities. This step is very important, as it determines the quality of the data that will be analyzed. It can even impact the predictive model generated.
The data (detailed in Section 4.2) were initially evaluated concerning its structure. First, it is verified that the data have a predefined pattern, a well-defined and rigid structure. It can be represented by a collection of rows and columns organized within tables. These characteristics define the database as structured [18]. Next, the database was analyzed for missing and irrelevant data, identifying and removing outliers, and resolving inconsistencies. Finally, the data were in appropriate and suitable formats for the analyses and tests. Therefore, no transformations were performed on the original data.
The definition of the algorithm considered the following conditions:
Non-linear relationships.
Ability to define decision boundaries.
Speed of execution.
Metrics and scoring.
Interpretability of the algorithm.
Domain knowledge.
The decision tree is a robust algorithm built on the basic human decision-making process based on some criteria or thresholds. Decision tree-based models are among those with the fastest response, in addition to visually presenting a set of “if-then” rules to improve the understanding and interpretation of results. This feature is fundamental because the model will be applied in a manufacturing environment with intense man-machine relationships. The problems and corresponding datasets, objects of decision-making, are domain specific. Therefore, choosing the algorithm is highly dependent on the experience of the team members involved.
A decision tree consists of a hierarchy of nodes connected by branches. The node, also known as the decision node, is the decision-making unit that evaluates, through a logical test, which will be the next descendant node. The leaf or terminal node associated with the result value is found at the last level of the hierarchy [19].
Instead of implementing our algorithm version, we used the Python Sci-kit-learn module to develop the predictive model. It implements many popular machine learning algorithms while maintaining an easy-to-use interface fully integrated into Python [20].
Sci-kit-learn uses an optimized version of the classification and regression tree (CART) algorithm. It is characterized by building binary trees, so each internal node has exactly two output conditions. CART builds binary trees using the feature and threshold that generate the most information gain at each node. An important feature of CART is its ability to generate regression trees. In regression trees, the leaves predict a real number rather than a class. In the case of regression, CART looks for splits that minimize the squared error of the prediction. The prediction in each leaf is based on the weighted average for the node [21].
The dataset used to train and validate the model was based on 62 pieces manufactured between May and December 2022. Sci-kit-Learn provides some functions to divide datasets into several subsets in different ways. The most straightforward function is train_test_split [21]. However, the k-fold cross-validation method was used to split the total dataset into 5 mutually exclusive subsets of the same size, and from there, a subset was used for testing. The remaining 4 were used for parameter estimation.
The assembled random forest algorithm was used to compare the performance of the proposed regression tree model. Random Forest uses many individual decision trees created by randomizing the split at each decision tree node. The random forest algorithm is very efficient for analyzing large multidimensional datasets. However, due to its random nature, it is not always intuitive and understandable for the user [19]. The mean absolute error (MAE) was defined as a metric for error analysis and subsequent evaluation of the model result.
The execution of the simulations was based on scaling as a method for incrementally improving the model's performance and the consequent definition of the independent variables that contribute to the improvement of its performance. The following parameters have been defined for scaling:
min_samples_split: minimum number of samples to split a node.
min_samples_leaf: minimum number of samples needed on a leaf.
kfold_split: number of subsets for testing and validation.
n_estimators: number of trees in the forest.
Tables 3 and 4 show the configuration of the selected parameters for the simulation.
| Condition | A | B | C | D | E | F | G | H | I | J | K | L | M | N |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| min_samples_split | 2 | 3 | 4 | 5 | 2 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 5 | 5 |
| min_samples_leaf | 2 | 2 | 2 | 2 | 3 | 4 | 5 | 3 | 4 | 3 | 4 | 5 | 4 | 5 |
| Kfold_split | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| Condition | A | B | C | D | E | F | G | H | I | J | K | L |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| n_estimators (D1) | 10 | 10 | 10 | 10 | 35 | 35 | 35 | 35 | 310 | 310 | 310 | 310 |
| n_estimators (D2) | 10 | 10 | 10 | 10 | 55 | 55 | 55 | 55 | 300 | 300 | 300 | 300 |
| n_estimators (D3) | 3 | 3 | 3 | 3 | 29 | 29 | 29 | 29 | 47 | 47 | 47 | 47 |
| n_estimators (D4) | 3 | 3 | 3 | 3 | 7 | 7 | 7 | 7 | 11 | 11 | 11 | 11 |
| min_samples_leaf | 2 | 3 | 4 | 5 | 2 | 3 | 4 | 5 | 2 | 3 | 4 | 5 |
| Kfold_split | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
The first simulation run was performed by setting the dependent variable and toggling the independent variable separately. Then, the best result was set for the next round. This systematic continued until all independent variables were evaluated individually in each simulation run. At the end of the process, a regression tree model and respective set of correlations of variables with the smallest MAE for each adjustment of the respective critical dimension were obtained. Tables 5 and 6 show the results with the lowest MAE after simulations.
| ADJUSTMENT | ALGORITHM | CONDITION | MAE (mm) |
|---|---|---|---|
| A1 | Regression Tree | E / H / J | 0,001495 |
| A2 | Regression Tree | E / H / J | 0,002042 |
| A3 | Regression Tree | E / H | 0,001456 |
| A4 | Regression Tree | D | 0,001121 |
| ADJUSTMENT | ALGORITHM | CONDITION | MAE (mm) |
|---|---|---|---|
| A1 | Random Forest | A | 0,001312 |
| A2 | Random Forest | C | 0,002011 |
| A3 | Random Forest | A | 0,001226 |
| A4 | Random Forest | E | 0,001186 |
After obtaining the results, through the simulation stage that culminated in defining the optimal variables and parameters for each predictive model related to each critical dimension adjustment, the graphic model of a regression tree was generated to improve the understanding and interpretation of the results by the operators. Figures 4, 5, 6, and 7 show the graphic model for each adjustment variable.
The results show that the machine learning technique based on regression decision trees demonstrated adequate performance in the dimensional control process of side flange bearing housings, according to DIN 31693. Furthermore, the models developed for the critical dimensions D1, D2, D3, and D4 resulted in adjustments A1, A2, A3, and A4, with a maximum MAE of 2.042µm, i.e., a value below the validation metric defined for the project which is MAE less than 3 µm.
The performance evaluation strategy between the regression tree algorithm and the random forest proved adequate for the comparative purpose. It was verified that both results fit within the project validation metric. The assembled random forest algorithm achieved slightly better results for critical dimensions D1, D2, and D3 and slightly worse for D4. The prediction results' ease of understanding and interpretation were defined as requirements for the machine-learning model implementation strategy. c
The independent variable deviation was defined as representative of all four trained models. The D1 model was complemented with the independent variables deviation (D2) and temperature. The interrelation between dimensions D1 and D2 confirms the cause-and-effect analysis carried out, using the knowledge and experience of qualified professionals as a basis for creating the relationship matrix between the dependent and independent variables (Section 4.2). The temperature variable considerably influences the spherical deformation, which justifies its selection by the model. The D2 model presented, in addition to the deviation (D2), the variables climatized and OOT (D2). The D3 model shows, in addition to the deviation (D3), the variable climatized. Therefore, acclimatizing the piece before measuring on the CMM is relevant for the critical dimensions D2 and D3. The D4 model comprised the deviation (D4) and OOT (D4) variables. Therefore, we can say that the model of D4 is exclusively geometric.
The graphical model demonstrated clarity in representing decisions and decision-making visually and explicitly. In addition, the definition of model development stages proved effective for the orderly execution of data selection, algorithm definition, and validation.
The experimental results indicate that the compensation strategy is based on a holistic approach, where the effects of all systematic error sources are compensated regardless of their origin and heuristics, for the steps that make up the decision-making process, in addition to manufacturing specificities for each proposed critical dimension, can be applied to the actual precision machining process.
The validation of the predictive model, based on a regression decision tree, for dimensional control of side flange bearing housings through a holistic and heuristic approach, using the open-source machine-learning python module sci-kit-learn, confirms the possibility of implementing the methodology on the production line and collaborates for future advances in the development of dedicated software for real-time control.
The holistic approach applied in the development of the model seeks comprehensiveness which can cause non-identification and possible coexistence with existing problems in the condition of the machine and the process. Heuristics are convenient for reducing the many different issues to facilitate problem-solving. However, it can lead to imperfect answers to difficult and complex questions. The regression tree is an easily interpretable model. However, it is extremely dependent on the training data. A small change can modify the entire tree.
Further improvements can be achieved by investigating an approach that improves the holistic method to identify the origins of possible systematic problems existing in the process and that the predictive model compensates. In addition, more studies are needed to examine the cognitive load weighting used mainly for predicting difficult and complex tasks to improve the performance of model predictions. Furthermore, approaches to guarantee the stability of the regression tree from the insertion of new data must be developed and evaluated.
Funding
The authors declare no funding.
Competing interests
The authors declare no competing interests.