1 Introduction

Energy prices have risen in recent decades, making the purchase of energy a crucial input resource and cost factor for companies [1, 2]. In addition, energy supply and consumption generate greenhouse gas emissions that cause and intensify the climate crisis [1]. For this reason, some greenhouse gas emissions are regulated, e.g., in the EU emission trading system, where the cap, i.e. the EU’s annual emissions ceiling, is reduced by 2.2% per year. This increases the pressure on companies to reduce emissions [3]. In addition, consumers are increasingly demanding more sustainable products [4]. Therefore, more and more companies are taking action to increase their energy efficiency to remain competitive [5]. One possible approach to this is the use of energy-efficient manufacturing technologies. In general, there are three categories of manufacturing processes, which are shown in Fig. 1:

  • In subtractive manufacturing processes, the geometry of an object is created by removing defined volumes. Examples of subtractive processes are turning and milling.

  • In formative manufacturing processes, the volume of the object remains constant but is transformed from one initial shape into another shape. Examples of formative manufacturing processes are forging and casting.

  • In additive manufacturing processes, a defined shape is created from scratch by joining material together [6].

Fig. 1.
figure 1

Categories of manufacturing processes [7]

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Each manufacturing technology has different advantages and disadvantages regarding its energy demand and resource consumption, depending on the specific application and the manufactured part. For example, additive manufacturing is claimed to be highly resource-efficient during manufacturing of the part. In addition, the parts are claimed to result in higher energy efficiency during their use due to the possibility of lightweight design [8]. Additive manufacturing thus offers companies the potential to enable energy- and resource-efficient manufacturing [9]. However, this potential is individual for each part and each application. Therefore, it must always be decided individually whether a part is manufactured with additive manufacturing or with another manufacturing process. For this decision-making process, in addition to technical requirements, energy considerations should also be taken into account. But how can the energy demand that arises during additive manufacturing of a part be predicted individually without actually manufacturing the part? To address this issue, this paper aims to develop a procedure for developing a customized energy prediction model for an arbitrary AM machine. Afterwards, this methodology is applied and validated on a high-speed laser directed energy deposition (HS DED-LB) system.

2 State of the Art

2.1 High-Speed Laser Directed Energy Deposition as an Additive Manufacturing Process

2.1.1 Additive Manufacturing

The general term of additive manufacturing (AM) comprises technologies that generate objects based on a geometric representation through the successive application of material. The material is usually added in layers and each new layer is bonded to the previous one, e.g. by fusing using a heat source [10]. Since the first commercial additive manufacturing system in 1987, various process principles have been developed [7, 11]. According to DIN EN ISO 17296, seven categories of additive manufacturing processes can be distinguished:

  • Vat Photopolymerization

  • Sheet Lamination

  • Material Extrusion

  • Material Jetting

  • Binder Jetting

  • Powder Bed Fusion

  • Direct Energy Deposition

Hereby, a comparable new and emerging process is directed energy deposition (DED). This process uses focused thermal energy to melt and thus fuse materials as they are deposited [12]. As a thermal source for this, a laser, electron beam, or plasma arc is used, which creates a melt pool, typically 0.25 to 1 mm in diameter and 0.1 to 0.5 mm deep, on the part to be manufactured, into which material, as powder or wire, is continuously fed. Thus, the material is melted in the melt pool [12,13,14]. The nozzle for the material is located together with the output of the thermal source in the deposition head [14]. The deposition head and the part are continuously moved relative to each other [15]. Thus, the melt pool migrates along the desired contour, the scan path, and solidifies together with the deposited material as the thermal source moves along. This progressively creates a new layer. Depending on the AM machine, either the build platform and thus also the part move, the deposition head moves, or both move. After the layer is completed, the build platform and the application head move the thickness of one layer away from each other, to keep the distance between the deposition head and the build surface constant [14].

The manufacturing principle of DED leads to the following advantages compared to other AM processes which offers great potential for industrial applications.

  • Larger material deposition rates lead to shorter process times [16],

  • DED has larger build areas compared to other AM processes, which allows the manufacturing of larger parts [17],

  • Multiple materials can be used within a build process, creating in-situ generated composites and heterogeneous parts [11, 14],

  • DED can be used to remanufacture defective parts or components such as turbine blades [14],

  • DED can be used to apply thin layers of corrosion-resistant and wear-resistant materials onto parts to improve their performance and durability [14].

Based on the last advantage, the surface coating with DED, the HS DED-LB found its origin.

2.1.2 High-Speed Laser Directed Energy Deposition

The process of HS DED-LB differs from other DED processes mainly by the powder focus which has been shifted upwards and is about one centimeter above the build surface, as shown in Fig. 2 [18, 19]. Thus, the powder is melted above the melt pool by the laser beam and is therefore applied in a liquid state [20, 21]. The melting of the material by the laser is much faster than the melting of the material in the melt pool. Therefore, with HS DED-LB, significantly faster feed rates of up to 200 m/min can be achieved and the processing time is five to ten times shorter compared to other DED processes [21, 22]. Since the laser mainly melts the powder, the melt pool on the part’s surface is smaller, resulting in a lower specific heat input [19].

The material is stored as powder in a container on the powder feeder. Inside the container is a stirrer to avoid agglomeration of the powder. Through an opening at the bottom of the container, the powder falls onto the conveyor disk. The conveyor disc rotates at a defined speed and transports the powder to the inert gas stream, the carrier gas flow, which carries the powder to the nozzle [23]. The nozzle shapes the powder-gas flow into a cone and its tip is the powder focus. The powder focus is ideally at the same point as the focus of the laser beam [21]. The laser beam is generated in a separate subsystem, the laser generator, and guided through the laser optics to the deposition head. To protect the laser optics from contamination from smoke and powder buildup, another inert gas flow, the shielding gas flow, is fed through the inner center of the nozzle. Both inert gas flows also create an inert gas atmosphere at the process point and thus avoid oxidation of the material [23].

Powder that has not been applied is removed from the build chamber by a suction system. The suction system is connected through a connection at the bottom of the AM machine [24].

Fig. 2.
figure 2

Principle of HS DED-LB process

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The laser optic cannot be moved at high speeds due to its fragility. Therefore, for HS DED-LB systems, the build platform is moved. For this, three linear motors are connected to the building platform via a tripod system. This allows the build platform to be moved in the three Cartesian dimensions [19]. To manufacture a part, the individual subsystems are used simultaneously. Therefore, HS DED-LB is a single-stage process.

2.2 Current Discussion of the Environmental Impact of DED

AM is claimed to have great potential to save resources and is therefore often referred as a sustainable manufacturing technology. However, in the literature, the environmental impact of AM is widely discussed. Through lightweight design, the consolidation of components, and functional integration, a reduction of the environmental impact during the use of additive manufactured parts can be achieved, e.g. through weight reduction [8]. This also leads to high material efficiency, since only the material necessary for the final geometry is required, including a comparatively small addition for post-processing [25, 26]. Therefore, on the one hand, there is less environmental impact from the extraction and processing of the raw material [27] and, on the other hand, less technical scrap and waste are produced [25, 28].

The material efficiency is strongly dependent on the AM process. In powder bed-based processes, for example, only less than 30% of the used metal powder contributes to the part geometry. The remaining 70% must be removed at the end of the process [29]. This is similar to HS DED-LB, where only around 27% of the conveyed powder is deposited [19]. Some of the powder can be reused for reprocessing after a sieving process [30]. However, the reuse is limited due to the decreasing powder quality, which influences the part quality [31]. Moreover, the energy demand is individual for each AM process and each manufactured part [32]. However, the energy demand to manufacture a part with AM is usually higher than manufacturing using formative or subtractive processes [33, 34]. Therefore, from an ecological point of view, AM is only advantageous for individual parts or small batches, since the environmental impact of specific process tools is omitted here [35]. Besides, the specific energy demand (SEC) does not adapt to different process parameter settings.

To take full advantages of AM, eco-design for AM must be considered. This can potentially reduce material consumption during manufacturing as well as energy consumption during use. However, scan paths based on the geometry of the part affect the energy demand. In addition, suitable process parameters must be defined. To compare the energy demand of different parts and process designs, the effects of different scan paths and process parameters must also be considered, without actually manufacturing the part. Thus, an energy prediction model is needed that allows the prediction and comparison of the energy demand during the design stage.

For this, first, it is important to investigate the energy and resource requirements and thus the environmental impact of AM in detail. The energy demand of different AM processes was analyzed for example by Baumers et al, Fredrikson, Kellens et al. and Faludi et al. [36,37,38,39]. Regarding DED, several studies have been performed, which can be divided into the following categories.

In the first category, the environmental impact of the DED process or the environmental impact caused during manufacturing of a specific part with DED is determined. A common method used for this purpose is life cycle assessment (LCA) [40]. Liu et al. [25] and Jiang et al. [41] compare the additive manufacturing of a gear with the combined subtractive and formative manufacturing within the framework of an LCA. An analysis of the ECO-indicator 99 based on the LCA of DED was carried out by Le Bourhis et al. [26, 42] Kerbrat et al. [43], and Serres et al. [44]. Xiong et al. [45] and Morrow et al. [28] also compared the environmental impact of the AM process with subtractive processes. The results of these studies are part-specific and can therefore hardly be transferred to other parts or adapted to other DED processes.

In the second category, a basis for comparison is provided by determining the SEC. Wipperman et al. compare DED processes with powder bed fusion and subtractive processes. The study concludes that the SEC of DED is lower than that of powder bed fusion processes [46]. Huang et al. compared DED with subtractive and formative processes and found that DED has the highest SEC [47]. Jackson et al. calculated the SEC which arises during the process chain of manufacturing a part with DED based on literature [48]. The SECs calculated in the presented approaches give a first indication of the energy demand during manufacturing with DED. However, the transferability to other parts is limited here, since these values are individual for the process under consideration and the manufacturing process of the part.

The third category thus includes reusable and customizable energy calculation models. Watson and Taminger created a calculation model that can be used to determine whether additive or subtractive manufacturing is more energy efficient for manufacturing a metal part [49]. Within the model, the energy requirements for material and powder production, DED, post-processing, and transportation are considered. However, the model is based on average values which do not reflect the influence of different process parameter settings. In addition, this does not allow an analysis of the composition of the energy demand. Wegener developed a comprehensive model to calculate the energy and resource requirements of DED. Within the energy model, the energy demand of the individual process steps is calculated and the individual power consumption of the individual subsystems is already taken into account [50]. However, the model can only be used to predict energy demand to a limited extent. In addition, it is not shown how the power consumption can be determined as a function of the selected process parameters.

Methodologies to develop energy prediction models already exist for unspecified manufacturing processes. Dietmair and Verl developed a generic method for modeling the energy demand of machines and plants based on a statistical discrete event formulation. The procedure is exemplified by a milling process [51]. Schmidt et al. developed a methodology for predicting energy demand that can be applied to any manufacturing process and system. The approach aims to achieve a prediction quality of 80% with as little measurement effort as possible. For this purpose, the processes and systems are classified in terms of their complexity with the aid of a decision tree. Based on this, instructions are given for the creation of parametric or empirically based energy prediction models [5]. However, the model is also based on the SEC and can therefore only reflect the various setting of process parameters to a very limited extent.

2.3 Requirements

The studies listed in the previous chapter lack in particular a sufficient level of detail; both the effects of different process parameter settings and different process steps, and subsystems are usually not or only insufficiently considered. As a result, sufficient forecast accuracy for previously unregarded parts or sets of process parameters is not achieved. To achieve this and additionally enable in-depth analysis of the system to identify optimization potentials, the knowledge of when, how much, and which subsystem consumes power is necessary. Based on this, the following requirements for a methodology to develop an individual energy prediction model for an AM process arise:

  • The model resulting from the methodology must have a very high forecast quality. The modeled energy demand must therefore not deviate from the actual energy demand by more than 5%.

  • The resulting model allows a detailed analysis of the composition of the energy demand within the different process steps and subsystems.

  • Within the model developed in the methodology, the influence of the process parameter setting on the energy demand is included.

  • The methodology can be used with no or little prior knowledge.

  • The model enables the reduction of the experimental effort compared to other prediction models while maintaining the prediction accuracy.

3 Approach for Creating an Energy Prediction Model

To create a model to predict the energy demand for additive manufacturing systems, especially for DED, four steps are necessary. First, the structure of the whole system must be captured. Then, the process and its individual process steps have to be analyzed. Subsequently, the process parameters and their effect on power consumption are investigated by experiments. Based on these results, the model is then developed, validated based on real parts, and, if necessary, further improved.

3.1 Capturing the Structure

The aim of capturing the structure is to obtain basic knowledge of the investigated system and to establish the technical requirements for the following steps. First, all energy-related subsystems of the investigated system are identified and then classified. On the one hand, there are systems whose power consumption remains constant during the entire process and is not changed by process parameters or other possible settings. These can be grouped as peripherical subsystems. On the other hand, there are subsystems whose power consumption changes during the process or depends on process parameters or other settings. For these subsystems, the power consumption must be analyzed individually and later a specified model must be created.

Based on this analysis, energy measurement sensors have to be implemented. Hereby, one energy measurement sensor must measure the power of the entire system. Furthermore, for each subsystem whose power consumption was found to be variable, additional energy measurement sensors must be implemented. Depending on availability and possibility, an energy measurement sensor can be omitted for one of these subsystems. The power consumption of this subsystem can be calculated based on the power consumption of the entire system by subtracting the power consumption of the other subsystems. The sampling rate of the sensors must be matched to the process speed and variability of the machine and the process.

After the initial examination of the subsystems, the adjustable process parameters are identified. These are then structured by assigning them to the subsystems whose settings they change. The identified structure is shown in Fig. 3.

Now, the basic knowledge of the investigated system has been obtained and the energy measurement system provides the opportunity to analyze energy demand.

Fig. 3.
figure 3

Exemplary structuring of an investigated system

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3.2 Process Analysis

In the next step, the process analysis, the build cycle is examined regarding its individual process steps and the behavior during power consumption of the individual subsystems. For this purpose, in initial experiments, first parts are manufactured and the power consumption is measured. For this purpose, typical or frequently manufactured parts and their corresponding process parameters are selected. The choice of parts, however, is not crucial and can be chosen almost freely. The power data is then examined in two steps.

Firstly, different process steps are defined. If they are not known before, they must be detected during those experiments. Usually, the different process steps can be clearly distinguished by the power consumption of the subsystems. Similar patterns occur for all of the investigated parts. Some subsystems are only active during the actual manufacturing process, others only during preceding or subsequent process steps. For example, many systems require a warm-up before the start and a cool-down after finishing the actual manufacturing process. This knowledge about the different process steps may also exist before those initial experiments.

Subsequently, the behavior of the individual subsystems during the individual process steps is investigated. Here it is examined when power is consumed by the subsystems and how the power consumption behaves. The following characteristics should be identified:

  • When or at which process step which subsystem becomes active from standby or off?

  • How does the power consumption of the subsystems behave within each process step?

  • How does the power consumption behave during start-up, running, and shutdown?

For example, the power consumption of a subsystem can be constant, fluctuate randomly, or follow certain rules. If the power consumption is constant, the subsystem is either on standby or is currently at its set level and consumes power almost constantly, such as the peripherical subsystems and subsystem 4 in Fig. 4. Random fluctuations mostly occur during constant operation, e.g. subsystem 3, and periodic fluctuations by repetitive switching on and off, e.g. subsystem 1 and subsystem 2 in Fig. 4.

Fig. 4.
figure 4

Example of subdividing a manufacturing process into process steps based on power consumption curves

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3.3 Analysis of the Process Parameters

The analysis of the process parameters is conducted in two steps. First, in full factorial design of experiments (DOE), those process parameters are identified, which significantly affect the power consumption of the respective subsystem and if there are interaction effects between the process parameters. Subsequently, in a second step, those process parameters, which were identified as relevant for the power consumption for the subsystem, are analyzed more closely.

During the capturing of the structure of the investigated system, the adjustable process parameters and their respective subsystem are identified. Now, for each subsystem, a full factorial DOE is developed. Here, the principles of random order, repetition for statistical significance, and blocking must be considered. Each test must be performed at least three times. If the results vary greatly, increasing the number of trials may be necessary. Also, if there are many adjustable process parameters for a subsystem, the number of experiments required for a full factorial DOE can become very large. For such cases, a partial factorial DOE may also be appropriate. While performing the experiments, the power consumption is measured, and the collected data are evaluated. Statistical values such as the p-value can then be used to determine, which process parameters affect the power consumption, and thus the energy demand of the subsystems. In addition, interaction effects between process parameters are also identified, as shown in Fig. 5a. Verification of the influence must be carried out for all previously identified process steps. For example, power is often consumed by a subsystem during standby, but the quantity is usually independent of process parameters. In the further steps of creating the model, only the significant process parameters are considered.

Fig. 5.
figure 5

Examples for evaluating the trials, a) for identifying relevant process parameters and their relation, b) for evaluating the changing power consumption with an increasing setting of the process parameter, c) for identifying the behavior during the process

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The relevant process parameters are analyzed in more detail in the second step. For this purpose, in further experiments, only the investigated process parameter is varied from the minimum setting to the maximum setting in several steps, while all other process parameters are kept constant. Here, the trials are also performed at least three times in random order and grouped into blocks. Based on these trials, it is investigated how the power consumption behaves with increasing process parameter settings. For example, the averaged power consumption can increase, with a gradual increase in the process parameter, either approximately linearly or over proportionally, as shown in Fig. 5b. Each measured power curve is analyzed in detail. The individual phases of standby, start-up, constant operation, and shutdown, as well as other possible phases, are evaluated separately, as shown in Fig. 5c.

3.4 Creating the Model

The procedure for creating the model for energy prediction follows a structured approach, which is shown in Fig. 6.

In general, the total energy demand of a system Etotal is composed of the energy demand of its subsystems Ei. Therefore Eq. 1 applies.

$$ \begin{array}{*{20}c} {E_{total} = \mathop \sum \limits_{i = 1}^{I} E_{i} } \\ \end{array} $$
(1)

In the previous steps, the power consumption of each subsystem and its corresponding process parameters was analyzed in detail. These findings are now being transferred for model creation. To develop a model that can predict energy demand as accurately as possible and, at the same time, analyze the composition of the energy demand of the entire system, a separate model is created for each subsystem.

During process analysis, the process was divided into several process steps within which the power consumptions of the individual subsystems are structurally similar. Thus, the energy demand of subsystem Ei is the sum of its energy demands during each process step Ei,ps, as shown in Eq. 2.

$$ \begin{array}{*{20}c} {E_{i} = \mathop \sum \limits_{ps = 1}^{PS} E_{i,ps} } \\ \end{array} $$
(2)

Within each of these process steps, the pattern of the power curve is analyzed for each subsystem. Here, the pattern of the power curve can either be almost constant, fluctuate regularly or irregularly, or increase or decrease. Depending on the pattern, the further procedure is chosen. If a fluctuation occurs that is time-dependent or influenced by other process parameters, i.e., a regular fluctuation, or if the power curve increases or decreases once, for those subsystems several models need to be developed for each process step. For this, the process step is subdivided into several individual sections s, for which the power consumption Pi,ps,s is individually modeled. The models are then summarized to represent the entire process step, as shown in Eq. 3 and Eq. 4.

$$ \begin{array}{*{20}c} {E_{i,ps} = \mathop \sum \limits_{s = 1}^{S} E_{i,ps,s} } \\ \end{array} $$
(3)
$$ \begin{array}{*{20}c} {E_{i,ps,s} = P_{i,ps,s} \cdot t_{ps,s} } \\ \end{array} $$
(4)
Fig. 6.
figure 6

Overview of the approach to create a model for energy prediction.

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The individual sections are treated hereafter as the energy demand of the process steps. Therefore, for this case in the following, Pi,ps,s is to be read and treated as Pi,ps. In the end, the energy demands of the sections Ei,ps,s are summarized to the energy demand of the process steps Ei and then to the total energy demand Etotal.

To determine Pi,ps,s, the procedure is the same as described below for power consumptions with a regular fluctuating or a constant pattern, instead of the process steps, however, the individual sections within the process steps are now examined.

The energy demand of a subsystem during a process step Ei,ps can then be calculated based on Eq. 5. The power consumption of a subsystem within a process step or section Pi,ps is approximated with the mean power consumption for each process step or section.

$$ \begin{array}{*{20}c} {E_{i,ps} = P_{i,ps} \cdot t_{ps} } \\ \end{array} $$
(5)

In the simplest case, the power consumption does not depend on any process parameter. Here Eq. 6 applies, as the power consumption of the subsystem can be approximated as constant.

$$ \begin{array}{*{20}c} {P_{i,ps} = constant} \\ \end{array} $$
(6)

If only one process parameter exists, the energy demand of the subsystem is determined by the power consumption depending on the setting of the process parameter Pi,ps,pp, as shown in Eq. 7.

$$ \begin{array}{*{20}c} {E_{i,ps,pp} = E_{i,ps} = P_{i,ps,pp} \cdot t_{ps} } \\ \end{array} $$
(7)

If the process parameter is cardinally scaled, the power consumption as a function of the set process parameter Pi,ps,pp equals the power consumption of the entire subsystem Pi,ps. However, if the process parameter is only nominally or ordinally scalable, a case distinction has to be carried out. For this purpose, a sufficient number of different settings of the process parameter is defined for each process step or section of a process step. The averaged power consumption is then assigned for each process parameter setting. This case distinction, also shown in Eq. 8, makes it possible to approximate the power consumption for different process parameter settings.

$$ \begin{array}{*{20}c} {P_{i,ps} = \left\{ {\begin{array}{*{20}c} {P_{i,ps,pp,case\, 1} = constant, if\, case\, 1} \\ \ldots \\ {P_{i,ps,pp,case\, C} = constant, if \,case\, C} \\ \end{array} } \right.} \\ \end{array} $$
(8)

Similarly, if several process parameters influence the energy demand of a subsystem, it is necessary to examine whether they are scaled nominally, ordinally, or cardinally. If all process parameters are cardinally scaled, the power consumption of the subsystem Pi,ps for a considered process step or section in a process step can be approximated by Eq. 9. Each subsystem has a basic power consumption Pbasic, which is not changed by the process parameter settings. Additionally, each process parameter causes a power consumption Pi,ps,pp,n based on its setting.

$$ \begin{array}{*{20}c} {P_{i,ps} = P_{i,ps,basic} + \mathop \sum \limits_{n = 1}^{N} P_{i,ps,pp,n} } \\ \end{array} $$
(9)

If not all process parameters are cardinally scaled, i.e. at least one process parameter is ordinally or nominally scaled, it is necessary to check whether interaction effects exist between the process parameters. These were determined in the previous analysis of the process parameters. If interaction effects exist, a separate model for power prediction for each assumed case needs to be developed, as shown in Eq. 10. Combinations of possible cases may also be necessary for several nominally or ordinally scaled process parameters. Depending on the case of the nominally and ordinally scaled process parameters, a corresponding model of the cardinally scaled process parameters is now selected to predict the power consumption of the subsystem during the considered process step. The individual models for each case are structured in the same way as Eq. 9.

$$ \begin{array}{*{20}c} {P_{i,ps} = \left\{ {\begin{array}{*{20}c} {P_{i,ps,pp,case\, 1} = P_{i,ps,basic} + \mathop \sum \limits_{n = 1}^{N} P_{i,ps,pp,n} , if\, case\, 1} \\ \ldots \\ {P_{i,ps,pp,case\, C} = P_{i,ps,basic} + \mathop \sum \limits_{n = 1}^{N} P_{i,ps,pp,n} , if\, case\, C} \\ \end{array} } \right.} \\ \end{array} $$
(10)

If no interaction effects exist, separate models are developed for each process parameter and summed up, which follows the structure of Eq. 9. Pi,ps,pp,n is determined for ordinal and nominal scalable process parameters within a case distinction, as shown in Eq. 8, and can be assumed to be constant. The constant power consumptions of ordinally or nominally scaled process parameters were previously quantified in the process parameter analysis experiments and can thus be applied.

Now, for all cardinally scalable process parameters Pi,ps,pp, further considerations are necessary. For this purpose, the development of the mean power consumption with an increasing process parameter setting is now investigated. First, it is checked whether there is a threshold value of the process parameter setting at which the development of the power consumption changes. For example, there may be a minimum setting below which the power consumption remains constant despite a higher process parameter setting and only increases gradually with an increasing setting above the threshold value. In parallel, there can also be an upper threshold at which the power consumption does not increase any further. When one or more such thresholds occur, case distinction must be performed. A separate model is created for each case, as shown in Eq. 11.

$$ \begin{array}{*{20}c} {P_{i,ps} = \left\{ {\begin{array}{*{20}c} {P_{i,ps,pp} = P_{i,ps,pp, case\, 1} , if \,S_{p,ps,pp,set} < lower\, threshold\, value} \\ {P_{i,ps,pp} = P_{i,ps,pp,case\, 2} , if\, P_{p,ps,pp,set} > upper\, threshold\, value} \\ {P_{i,ps,pp} = P_{i,ps,pp,n} , else} \\ \end{array} } \right.} \\ \end{array} $$
(11)

For the individual power consumptions of the subsystems during the process step or section depending on the setting of the process parameters, several types of cases can be distinguished by how the power consumption changes with increasing process parameter setting.The power consumption can be constant and thus independent of the process parameter in certain process steps, as shown in Eq. 12. This is often the case below lower threshold values or above upper threshold values.

$$ \begin{array}{*{20}c} {P_{i,ps,pp} = constant} \\ \end{array} $$
(12)

In most cases, however, the power consumption increases with an elevation of the process parameter setting. This can be linear or disproportionate. To obtain a regression for a linear slope, the slope of the function can be calculated by using the difference between the maximum power consumption and the minimum power consumption. The minimum power consumption also serves as the y-axis intercept. The x-axis intercept is then calculated by the proportion of the selected process parameter setting to the maximum process parameter setting, which is shown in Eq. 13.

$$ \begin{array}{*{20}c} {P_{i,ps,pp} = \left( {P_{i,ps,pp,max} - P_{i,ps,pp,min} } \right) \cdot \frac{{S_{i,ps,pp,set} }}{{S_{i,ps,pp,set,max} }} + P_{i,ps,pp,min} } \\ \end{array} $$
(13)

If there is no linear relationship, a function of any degree can be derived using the gauss elimination. For this, however, additional points must be integrated, whose values need to be determined within experiments. Equation 14 shows an example of the second-degree function resulting from the Gauss elimination.

$$ \begin{aligned} P_{{i,ps,pp}} = & \left( {2P_{{i,ps,pp,max}} - 4P_{{i,ps,pp,50\% }} + 2P_{{i,ps,pp,min}} } \right) \cdot \left( {\frac{{S_{{i,ps,pp,set}} }}{{S_{{i,ps,pp,set,max}} }}} \right)^{2} \\ + & \;~\left( { - P_{{i,ps,pp,max}} + 4P_{{i,ps,pp,50\% }} - 3P_{{i,ps,pp,min}} } \right) \cdot \left( {\frac{{S_{{i,ps,pp,set}} }}{{S_{{i,ps,pp,set,max}} }}} \right) + P_{{i,ps,pp,min}} \\ \end{aligned} $$
(14)

The model is then validated using reference parts. This allows the identification of potential deficits in the model. If necessary, the model can then be improved by increasing the level of detail, e.g. by implementing additional caste distinctions or sections within a process step.

4 Example of an Application Using HS DED-LB

4.1 Capturing the Structure

For the investigated HS-DED system, a Ponticon pE3D1, four independent subsystems can be distinguished, which have adjustable process parameters and tend to have a variable power consumption during the process. Other systems, such as the system control, can be grouped as peripheral subsystems.

The distinguished subsystems, which are also shown in Fig. 7, are:

  • As laser generator, a Laserline LDF 8000–6 diode laser is used. Both adjustable process parameters, the set laser power and the laser spot diameter can be varied continuously between 504 W and 8400 W and 0.5 mm and 1.8 mm.

  • The stirrer speed and the conveyor disc speed of powder feeder Twin-150-ARN216-OP by Oerlikon Metco can also be varied continuously up to 3300 rpm and between 0.2 and 10.0 rpm.

  • For the suction system Dustomat 4–24 W3 eco + dry extractor by ESTA only the extracted volume can be adjusted. The extracted volume can be varied between 770 m3/h and 2540 m3/h in steps of 50 m3/h.

  • The trajectory system consists of three dynamic linear motors which move the build platform. Here, any scan path can be traveled at a continuously adjustable speed of up to 200 m/min.

In addition to power measurement sensors for the entire system, separate power measurement sensors were implemented for the laser generator, the powder feeder, and the suction system. The energy demand of the subsystems, which is assumed to be constant, and the trajectory system can then be calculated. As power measurement sensors, four current transformers and a corresponding EtherCAT Terminal from Beckhoff are used, which measure the consumed power at a frequency of 1 kHz, i.e. the consumed power per millisecond.

Fig. 7.
figure 7

Structure of the investigated HS DED-LB system

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4.2 Process Analysis

Based on the initial experiments, a typical process workflow could be identified and the process was divided into three process steps [24]:

  • Pre-step: At the beginning of the build cycle, a homogeneous powder gas flow is generated. For this, the two inert gas flows, the carrier gas flow, and the shielding gas flow, are first switched on. After a few seconds, the powder feeder is switched on and the powder is transported to the application head. After a few seconds, the powder cone has built up homogeneously. The trajectory system and the laser generator are on standby, and the suction operates constantly.

  • In-step: The in-step is the actual additive manufacturing process. Thus, the part is additively manufactured. For this, the build platform moves along the scan path at a defined speed. Depending on the scan path, extra paths are necessary for decelerating and reaccelerating the build platform. In such cases, the laser is not continuously melting the powder. Therefore, the laser only switches on at defined points and melts the powder to apply the material at the desired locations. The powder feeder and the suction system constantly run during this process step.

  • Post-step: When the manufacturing process is finished, the laser and the powder feeder turn back into standby, and the inert gas flows stop. Depending on the setting, the build platform stops moving or can move at a slow speed to a previously defined position for better part removal. The post-step takes usually only a few seconds until the powder-gas cone has completely dissolved, and the build chamber can be entered.

For all subsystems, the power consumption varies only during their operation. In standby mode, experimental observations show that the power consumption remains constant and thus independent of any process parameters.

4.3 Analysis of the Process Parameters

For three of the investigated subsystems, there are two process parameters each. Accordingly, their influences on the power consumption of the subsystem and the interactions between parameters were investigated in full-factorial DOE. Additional experiments were then carried out for the relevant process parameters. The results presented here are based on research by Ehmsen et al. [24].

It was observed that the power consumption of the laser generator depends only on the set laser power and does not show any observable correlation to the selected laser spot diameter. Accordingly, only the laser power was investigated in further experiments. Here, it was determined that the power consumption increases approximately linearly with an increasing laser power setting. However, at which moment the laser is switched on and for how long depends on the part geometry and the resulting scan path.

In contrast, the power consumption of the powder feeder was dependent on both the stirrer speed and the conveyor disc speed. However, no interaction of the process parameters was observed. Both process parameters were then increased stepwise and independently of each other. For both, starting from a base power consumption, a linear increase with rising rotational speeds could be observed.

Since for the trajectory system the process parameter of the scan path is only nominally scaled, two cases were defined for the DOE: A circular scan path and a square scan path. Both the speed and the scan path affect the power consumption of the trajectory system, there are even interaction effects. For both cases of the scan path, the speed has now been increased successively. Furthermore, it was determined that for rather circular scan paths, the power consumption increases overproportionally. In contrast, for rather linear scan paths, the power consumption increases approximately linearly. However, for process safety reasons, for linear scan paths only a maximum speed of 100 m/min, i.e. 50%, could be set.

In the case of the suction system, only the power consumption with increasing extraction volume was investigated. Here, a lower threshold value was detected. Below an extraction rate of 36%, the power consumption is constant and corresponds to the standby level. Above an extraction rate of 36%, the power consumption increases overproportionally.

Thus, all process parameters except for the laser spot diameter must be considered in the model.

4.4 Creating the Model

To create the customized model to predict the energy demand of the HS DED-LB system, for each subsystem the procedure described in Sect. 3.4 was carried out.

The peripheral subsystem is constant throughout the entire process. Therefore, to calculate its energy demand, constant power is assumed, which was quantified previously in the experiments, and integrated over the entire process time.

The laser is on standby during the pre-step and the post-step and has constant power consumption here, which is independent of any process parameters. However, the power consumption during the in-step varies depending on the scan path. Thus, the process step is subdivided into further sections. There are sections in which the laser is in mode “ready to fire” and has a power consumption slightly above the standby level. The level is independent of the set laser power. In the sub-process steps, where the laser is on during scanning, the power consumption depends on the set laser power. A linear model was created here to predict the power consumption.

The powder feeder is only on standby during the post-step. Here, too, the power consumption was modeled by a constant. During the pre-step and the in-step, the powder feeder operates continuously. To capture the influence of both process parameters, independent linear models were developed for both, which were summarized with a constant base power input.

The suction system operates during the entire build cycle. Here, a case distinction between different extraction rates is necessary. Below an extraction rate of 36%, the power consumption is at the same level as during standby. Above an extraction rate of more than 36%, power consumption increases overproportionally with rising extraction rates. This increase can be approximated with a quadratic function obtained by the Gaussian elimination.

For the trajectory system, a case distinction was made for two different scan path patterns, a rather rotationally symmetric scan path, and a rather linear scan path. For both cases, a separate model was developed that predicts the power consumption as a function of the selected trajectory speed. Based on the results of the previous experiments, a linear model was developed for the case of the rather linear scan path. For the rather rotationally symmetric scan path, a third-degree function with the Gaussian elimination was received. During the pre-step and optionally also during the post-step, the trajectory system is not in motion and thus on stand-by. Therefore, it can be considered independent of any process parameters in these process steps.

Based on the modeled power consumption for each process step or sub-process step, the energy demand of each subsystem and thus the total energy demand of the HS DED-LB system can be determined. It may be necessary to model the build cycle time and the duration of the individual process steps as well. The exact models and their equations are presented in Ehmsen et al. [52].

4.5 Exemplary Application and Validation

To validate the accuracy of the model, a reference part was manufactured. The dimensions of the part and the corresponding process parameters are listed in Table 1. During manufacturing the part the power consumption was measured for each millisecond. The resulting power curve is illustrated in Fig. 8. Based on the power consumption, the energy demand which arises during the process was calculated and compared with the energy demand predicted by the model. As shown in Fig. 9, the predicted energy demand is only 2% lower than the measured energy demand.

Table 1. Process parameters of the reference part for validation
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Fig. 8.
figure 8

Power curve of the manufacturing of the reference part

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Fig. 9.
figure 9

Comparison of measured energy demand with modeled energy demand.

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5 Conclusion

The research objective of the paper was to develop a methodology to create a customized model to predict the energy demand for an arbitrary AM system.

The model resulting from the methodology met the requirements to be detailed enough to identify potentials to reduce the energy demand and at the same time be able to model different process parameter settings. Due to the detailed description of the procedure and the specification of calculation formula, the methodology can be applied even with little or no prior knowledge of the investigated AM system and process. With a comparatively small amount of experiments, enough knowledge about the investigated AM system can be built up and at the same time, necessary data for the model creation can be collected. The functionality of the methodology was applied to the HS DED-LB process as an example, where a reference part was manufactured. The resulting model showed a very high prediction accuracy and deviate only 2% from the measured energy demand. This high quality was achieved through the following key findings:

  • To obtain a detailed model, the process must be analyzed in depth and individual process steps and the individual influence of process parameters must be included.

  • For each subsystem, the build cycle must be divided into individual process steps or sections in as much detail as necessary and as roughly as possible, to reduce complexity.

  • For cardinally scaled process parameters, the development of the power consumption can be approximated by regression, whose function can be obtained based on a small number of process points.

  • Nominal and ordinal scaled process parameters have to be approximated using a case distinction of averaged constant power consumption.

The results therefore indicate that the methodology is a powerful tool to develop a customized model and thus, predict the energy demand for different AM processes. In the future, the model will be applied to other AM processes such as powder bed fusion. Furthermore, it will be important to investigate whether this methodology can also be used for formative or subtractive processes.