1 Introduction

Integrating Finite Element (FE) simulations with actual temperature measurements using Ansys Mechanical software is a sophisticated technique that enhances the accuracy of simulation outcomes and validates the model validation process [1].

FE simulations are computer-generated mathematical models that predict the performance of complex engineering systems under various circumstances. Ansys Mechanical is a robust software tool that empowers engineers to simulate various physical phenomena and structures [2].

However, the precision of even the most advanced simulation models relies on the input data that generates them. This is the state where actual temperature measurements become critical. By gathering information on the actual temperature of a system or structure during its operation, engineers can compare it with the simulated outcomes and make necessary adjustments to the model [3].

This approach is precious for complex systems with multiple variables that can affect the results. By merging real-world data with computer simulations, engineers can understand how a system will perform under different conditions and make informed decisions about improving its design [4].

2 Experimental

2.1 Carrying out the Temperature Measurements

When evaluating a system, it is necessary first to determine its essential components, interfaces, and locations where temperature measurements are needed. This process involves considering factors like how temperature changes may affect the system’s performance and the importance of its components and interfaces. Once measuring points have been identified, temperature readings can be taken and analyzed to gain insights into the system’s behavior and performance. This information can optimize the system’s performance, detect potential issues, and improve its reliability and safety.

To measure temperatures in specific areas, appropriate sensors must be chosen. Depending on the application’s requirements, sensors like thermocouples, thermistors, infrared cameras, or other temperature sensors may be used. We selected four thermocouples for our experiments and placed them on a 50 × 50 × 3 mm aluminum sample, as illustrated in Fig. 1. These thermocouples were positioned at the most critical points: the center bottom and top sides of the substrate (T1 and T2), the last point of contact between the plasma and substrate (T3), and the first point of contact between the plasma and substrate (T4) (Fig. 2).

Fig. 1
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Setup of the temperature measurements

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Fig. 2
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Extract from the results of the experimental temperature measurements at constant current (100 A) and increasing travel speed (50, 100, 150, and 200 mm/s)

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The aluminum platform and the sample were traversed in a meander-shaped grid with a traverse length of 100 mm and a path offset of 5 mm. Table 1 shows the currents and travel speeds used.

TABLE 1 The plasma parameters used for the simulation and experimental implementation
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INO GmbH in Attnang-Puchheim, Austria, utilized the InoCoat3 Plasma Jet as the plasma source (Fig. 3).

Fig. 3
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Experimental setup during the plasma measurements with the shroud atmospheric pressure plasma

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2.2 Integration of the Measurement Data into the Simulation

Simulating power flux density involves converting temperature results while accounting for critical parameters such as the current and voltage of the plasma source, the distance between the plasma source and substrate, and the efficiency of the plasma system.

In Finite Element (FE) modeling for simulating real-world events, it is essential to incorporate measurement data into the models to achieve accurate results. This process may entail modifications such as additional measurement points, defining boundary conditions based on measured temperatures, or other adjustments to ensure the simulation aligns with the actual physical conditions (Table 2).

TABLE 2 Material data used in the FE simulation
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The structural analysis begins with a 3D model of the structure or an imported one into Ansys Mechanical. The model includes components that interact with each other. The thermal properties of a material include thermal conductivity, specific heat, and density, which are essential for calculating heat transfer. The thickness of the material also plays an important role. Therefore, the dimensions of the materials used and simulated must match exactly otherwise the measurement results cannot be compared. During mesh generation, the model is divided into meshes (element size of 1 mm), and boundary conditions determine the system’s behavior in different circumstances. Ansys Mechanical uses the finite element method to solve heat transfer equations accurately. After the simulation, results are analyzed to extract meaningful information. Validation and iteration verify the accuracy of results, refine the model, and optimize the design [2, 5].

3 Results and Discussion

3.1 Comparison of Simulation and Measurements

During the validation and iteration stage of a simulation, it is essential to verify the accuracy of the results. This verification is done by comparing the results with the available experimental data to ensure that the simulation can be relied upon for informed decision-making. A thorough examination of the simulation results and comparison with experimental data helps to identify any discrepancies or gaps in the model. If any issues are found, the simulation model can be refined and improved through iterations. This process is invaluable for optimizing the design and addressing any problems that may have arisen during the simulation. Continuous validation and iteration can enhance the accuracy of the results, making the simulation a reliable tool for decision-making.

Analyzing a match efficiently requires a careful comparison of simulated and measured temperatures. Visual aids like diagrams, comparison plots, or thermal images can be helpful in this process, as well as quantitative assessments that identify potential causes and account for any deviations. However, it is essential to approach these comparisons cautiously to ensure accuracy in identifying and resolving discrepancies. When comparing temperatures, it is crucial to consider all relevant variables, such as humidity, gas flows, and intensity. Additionally, quantitative comparisons are necessary for detecting deviations and potential causes. Considering these factors, a thorough and reliable analysis can be obtained.

The deviations between the measured and simulated temperatures are analyzed to determine their underlying causes. This analysis involves determining whether the errors are due to model inaccuracies, measurement errors, or other factors influencing them. Improving accuracy may require iterating the model or measurement configuration. The results of this analysis are shown in Fig. 4.

Fig. 4
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Comparison of the simulation step: a First simulation results still deviate very firmly from the actual measured values; b after some optimization steps in the area of power flux, the simulation could be adapted very well to the actual measured values

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Once the simulation process is complete, it is essential to carefully analyze the results to extract meaningful information (Fig. 5). This process may include parameters such as the maximum temperature, distribution of temperature changes over time, heat flow patterns, and other relevant data. The images in Fig. 5 were taken from the video created by the software.

Fig. 5
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Results of the temperature simulations. Two parameters were compared (100 A and 150 A at 100 mm/s). The results from above are shown on the left, and the results from the cross-section on the right: a after half a pass, and b after one and a half passes

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3.2 Validation and Optimization

In engineering, finite element (FE) models are widely used for critical analyses, such as predicting the thermal performance of various designs. To ensure that such models are reliable and accurate, conducting a comprehensive validation process that compares simulation results with actual measurement results is essential. This validation process also helps identify discrepancies between the two sets of results and, if necessary, refine the model’s boundary conditions to improve its validity.

Once the FE model has been validated, it can simulate various scenarios that help identify optimal design changes for enhancing thermal performance. By subjecting the model to different simulations, engineers can predict the effects of potential design changes, which makes it easier to determine the most viable options. This process is particularly useful in optimizing designs for energy-efficient buildings.

By validating simulated results, a high degree of accuracy can be achieved in matching measured temperatures. This precision allows for a quick determination of plasma parameters and an optimization of the testing procedure. With a minimal deviation from actual measurements, the focus can be shifted towards more intricate simulations, offering a deeper comprehension of the processes at hand [2].

Figure 6 compares measured and simulated results, displaying current levels of other experiments conducted at the same travel speed. The results indicate that the temperature reaches its highest point when the amperage is high and the travel speed is low. Conversely, a substantial reduction in temperature is observed when the amperage is lowered, and the travel speed is increased, as expected. These trends are valuable for predicting outcomes at both lower and higher currents.

Fig. 6
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Comparison of the simulated and measured temperature values with the same travel speed according to the current

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In order to accurately identify any discrepancies, we conducted a thorough analysis of the temperature readings obtained from both recording and simulation methods. We aimed to compare the results obtained under similar conditions but at different speeds. To this end, we used various tools and techniques to measure the temperature at various points and locations. Our findings, as illustrated in Fig. 7, indicate that a higher travel speed is associated with a significant reduction in temperature. This information can help us better understand the impact of speed on temperature and guide future research on this topic.

Fig. 7
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Comparison of the simulated and measured temperature values at the same current according to the travel speed

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As previously discussed, Ansys Mechanical simulation heavily relies on the power flux parameter, encompassing a range of factors, including current, voltage, plasma-substrate distance, plasma efficiency, and plasma area. Throughout the simulation study, we have identified some significant trends in the power flux, illustrated in Fig. 8. For instance, the power flux value increases with higher travel speeds. However, it is worth noting that the software assumes an optimal and uniform movement, which does not necessarily reflect real-world complexities like friction, air resistance, and environmental heating. Therefore, it is crucial to adjust the power flux accordingly. The power flux value reaches its maximum at higher speeds but decreases at lower currents. At lower currents, the impact of temperature on the environment is significantly less than at higher currents, which can help make more precise predictions about plasma pre-treatments and coatings.

Fig. 8
figure 8

Comparison of the power flux values from the simulation results according to the travel speed

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4 Conclusion

Incorporating precise actual temperature measurements into finite element (FE) simulations is vital for understanding a system’s thermal behavior and ensuring accurate predictive models. With FE simulations, we can replicate complex physical phenomena and anticipate a system’s behavior under different conditions. By integrating actual temperature measurements, we can enhance the accuracy of FE simulations, identifying potential design flaws and optimizing product performance. This technique is especially crucial in industries where effective thermal management is essential, such as aerospace, automotive, and electronics. Accurate thermal simulations can help reduce development costs, shorten time-to-market, and improve product reliability. Thus, integrating actual temperature measurements in FE simulations is essential in develo** and optimizing products and processes.