Keywords

1 Introduction

Thermally-induced displacements have been known for a long time as a relevant cause of the reduced machining accuracy of machine tools. In the course of the last decades, thermal problems have been extensively investigated in the research. As a result, measurement methods and simulation methods are now available for recording temperature gradients and the resulting displacements in the entire machine structure [1]. With the help of these methods, it was possible to develop a large number of correction and compensation solutions to minimize thermally induced displacements [2].

However, these solutions differ greatly in their approaches and have been explored in research under different conditions, for example on different machine tools or with different working conditions. This makes direct comparability difficult in terms of effort and benefit in the application, since a possible advantage by applying a method on one machine tool can become obsolete on another tool [3]. Moreover, due to production-related different boundary conditions and requirements of each manufacturer as well as different development statuses of the methods from research, it is difficult to estimate the advantages and disadvantages of one method compared to other alternatives for a potential user interested in applying such a solution.

Due to the increasing research in this field, more literature focusses on the comparison of different compensation or correction methods [3, 4]. However, the methods in these works are considered and compared from the perspective of their technical functioning. A comparative consideration of the economic effects in terms of resource consumption as well as implications for manufacturing are lacking in the literature.

For this reason, an evaluation metric has been developed in the course of the research project Collaborative Research Centre Transregio 96 (CRC/TR96), which allows a statement about the estimated effort and benefit of correction and compensation solutions developed in this research project from an economical process-oriented as well as technical point of view with respect to application-specific use cases. This metric is the baseline for a software-based application that offers a potential industrial user the possibility of a user-specific evaluation by comparing the different solutions based on personal preferences, suggesting suitable solution methods which meet the user’s requirements. The approach presented in this paper to make a comparative evaluation based on economical as well as technical aspects from a process perspective and the development of a software-based evaluation tool is, best to the authors knowledge, new to research.

In the following, the development of this recommender tool and the underlying evaluation metric are presented.

2 Methodology

In order to be able to evaluate the solutions developed in the project holistically concerning technological as well as economic aspects, an evaluation metric was developed that should assess these aspects on a case-by-case basis, meaning that the gathered criteria are to be assessed based on an application scenario, taking into account machine tool configuration possibilities, operational boundaries and technological use cases. The overall assessment of the solution methods will thereby, be application-specific. The evaluation metric is depicted in Fig. 1.

Fig. 1.
figure 1

Evaluation metric.

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In order to derive the assessment criteria needed, two approaches were pursued.

To evaluate the effort involved, expert interviews were conducted with the researchers responsible for the respective solutions [5]. To be able to comprehensibly map the required resources and risks during implementation and application, the implementation process of the solution was modeled from the interviews using the semi-formal modeling language Business Process Model and Notation (BPMN), and the required resources were directly applied to the respective work steps. On the one hand, it was possible to derive properties for the solutions from the evaluation of the interviews according to which the various processes can be uniformly classified, which enables comparability. On the other hand, quantifiable criteria could be identified for which an estimation of the expected amount of effort was made by the experts interviewed [5]. The identified criteria are demonstrated in Table 1.

Table 1. Quantifiable criteria and properties of correction and compensation methods following [5].
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To prove the effectiveness of the developed methods, a test workpiece developed within the CRC/TR 96 is used to quantify thermal defects [6]. For this purpose, load regimes were defined that represent the technological use cases of single-unit production and series production. For all solutions, the load regimes are run on different machine tools, each with and without implementation of the method, and an improvement of the thermal error at the tool center point is demonstrated by test measurements on the test workpiece.

Since both of the aforementioned aspects of cost-effectiveness and technology are to be part of the evaluation basis for comparing the solutions with each other, a suitable analysis method must be found as the basis for evaluation. The evaluation of the identified efforts and benefits for each solution, however, bears some challenges. First, the identified criteria are of both, qualitative and quantitative nature. Second, a user-specific assessment must be made possible that considers the user’s preferences and initial operational situation. For this purpose, the collected effort must be differentiated to enable the user to compare the criteria with each other. For these reasons, the use of a multi-criteria decision analysis (MCDA) method will be used since it enables a display of evaluation results in ranking order, incorporates the user’s preferences into the analysis, and allows for a sensitivity analysis of the criteria used [7,8,9]. Available MCDA methods were analyzed regarding their feasibility. The analysis resulted in the use of the Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE I) as a basis for the implementation of the evaluation metric.

The documentation of the technological and economic aspects as well as the implementation of the evaluation metric serve as a basis for the development of the web-based decision support tool. This is explained in the following.

3 Development of a Documentation and Evaluation System

To document the developed compensation and correction solutions and their assessments and to implement an application-specific effort-benefit assessment from them, a web-based software solution was developed. In this documentation and assistance system, the various solutions are both uniformly documented and analyzed, and evaluated on a case-by-case basis.

The documentation is based on the identified criteria and is uniform for all solutions. In addition to the criteria and the mapping of the implementation process as BPMN, a detailed description of the individual process steps and the resources required in each case is presented. This makes the collection of the effort comprehensible and transparent for the user. Furthermore, the measurements carried out to prove the effectiveness of the solutions are documented in detail so that the user receives an overview of the test set-up, the test protocol, and an evaluation of the measurement results. This documentation can be accessed independently from the evaluation process and therefore, serves as an information and overview function of the solutions developed in the project.

Regarding the recommendation function of the system, the quantifiable criteria as explained in Table 1 are being used as a baseline for the evaluation. As already mentioned, the interpretation of efforts can vary between users. For example, a high amount of material costs needed for the implementation of a solution can be an exclusion criterion for one user, whereas another user, due to staff shortages, would prefer a solution that requires few engineering hours and does not place so much emphasis on the use of materials. In order to be able to take these personal preferences into account, the MCDA method used for the calculation of the ranking provides for a weighting of the criteria. Since it is difficult for users to determine individual weightings, the Simple Multi-Attribute Rating Technique (SMART) method for weighting the criteria was implemented as an auxiliary tool. With this technique, 100 points are assigned to the most important attribute in the eyes of the user of the system. All other attributes are assigned points in the range between 0 and 100 depending on their relative importance concerning this criterion (e.g. 50 = half as important, 100 = equally important). The sum of all points is then used to determine the percentage of each characteristic, which ultimately represents its weighting. Figure 2 exemplarily shows the implementation of criteria weighting for material and immaterial resource requirements. Depending on the weighting of the criteria, the calculated ranking of the solutions changes accordingly.

Fig. 2.
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Excerpt of weighting options for quantitative criteria based on the SMART method.

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The identified properties as shown in Table 1 are implemented as filtering criteria. This allows the user to further limit the selection of solutions and adapt more to his individual situation, for example by only displaying solutions in the result ranking that do not require permanent intervention in the machine structure and hall air conditioning during operation time.

The MCDA method underlying the calculation uses a calculation of input and output flows for each alternative based on the defined weights of the criteria to determine the ranking. The output flow describes how strongly the procedure dominates all others, i.e. how strongly the procedure fulfills the criteria weighting compared to the other procedures and is the better the larger the value.

The input flow describes the opposite, i.e. how strongly the procedure is dominated by all others and is better the smaller it is. The input flow thus indicates how unsuitable the procedure is in relation to the criteria weighting compared to the other procedures. According to this logic, an alternative is preferred over another if its output flow is greater and its input flow is smaller, its output flow is greater and its input flow is equal, or its output flow is equal and its input flow is smaller than that of the others. This means that the favored alternative is characterized by more strengths and at the same time fewer weaknesses. The result of this difference is expressed in net flow. The best net flow indicates the most suitable solution. The resulting ranking accordingly shows the user which solutions correspond most to the weighting of the criteria, i.e. his preferences. In the software tool, the calculated flows are displayed as a bar chart for traceability as shown in Fig. 3, where the alternative methods are arranged in descending order from left to right according to their ability to fit the user’s preferences. By changing the weightings (see Fig. 2), the user can independently perform a sensitivity analysis to see to what extent the ranking would change or remain the same if the weightings were shifted.

Fig. 3.
figure 3

Display of the calculated ranking order based on input and output flows

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The user can then view the documentation of the corresponding solutions to get a detailed overview of the implementation steps and general properties, as well as the determined resource input and functional measurements carried out.

4 Discussion

It has to be emphasized that the effort of the solutions surveyed in the interviews with the experts is only an abstract survey, as the solutions are basic research and have not yet reached a final stage. The mapping of the effort, as well as the measurements, is thus not static and can change as the development of the solution progresses. Accordingly, the system can only be seen as a representation of an intermediate state and must be continuously adapted. A further step could be an extended development of the evaluation metric, in which improvement potentials of the solutions can be taken into account and assumed when a higher research state is reached, which could lead to a reduction of the effort and thus improve the evaluation of the solutions. Compensation and correction methods could, therefore, be classified according to the Technology Readiness Level.

Furthermore, it must be noted that the documentation of the measurements carried out is currently not included in the evaluation, as a direct comparison of the measurement results cannot be carried out. This is because, within the CRC/TR 96, different machine tools are being used as demonstrator machines for the test measurements. A direct comparison of measurements can, therefore, not be carried out since the baseline situation of the tests is not the same. The documentation of the measurements allows an interested user to get a rough orientation of the effectiveness of the process and a detailed description and test data.

In the current state, only solutions from the CRC/TR 96 research project are documented in the system. To evaluate the applicability of the documentation method and the evaluation metrics, further solutions from the research could be integrated into the system in a further step. Moreover, the evaluation of solutions is based on abstract estimations of effort and properties of the methods. However, no concrete problems from industrial practice can be queried in the recommender system; the solutions are not yet developed far enough for this.

5 Conclusion

The development of methods that correct the thermal error on machine tools is a current field of research that produces diverse possibilities for correcting the thermal error. These procedures are very different in character and method.

On the one hand, the development of the system presented in this thesis enables the structured and uniform documentation of the solution methods developed in the CRC/TR 96.

Thus, the state of research is recorded and the many different solutions, which vary in character, are clearly presented. This can also serve as a link to structured documentation for further procedures developed outside the underlying research project, which can facilitate the overview for researchers. Furthermore, starting points for future research fields can be revealed by showing development potentials in the system.

On the other hand, the recommendation system is a step toward facilitating the transfer of the developed methods to industry.

Future research steps should focus on integrating other solutions outside the CRC/TR 96 into the system and depicting concrete use cases from the industry to test the system for transferability and suitability and develop it further based on this.