A Novel Induction Heater for Sintering Metal Compacts with a Hybrid Material Extrusion Device

Abstract

The traditional sintering of metallic components shaped via Material Extrusion Additive Manufacturing (MEAM) is a time-consuming process that involves sophisticated energy-intensive heating systems. This work describes a novel induction heater capable of efficiently tailoring temperature profiles to densify MEAM powder compacts. In situ sintering within the same device is achieved indirectly by heating a graphite crucible, whereby the heater is based on an inverter with a half-bridge topology using the Zero-Voltage Switching (ZVS) technique. The system comprises a bank of capacitors that, in conjunction with a work coil, form a parallel-topology resonant circuit. This design allows the inverter to be used as a current amplifier, thereby increasing its efficiency to deliver an output power of up to 5 kW. The device operates at a 62.86 kHz resonant frequency, achieving a 2.01 mm penetration depth and a 1365.7 °C crucible temperature with only 1.313 kW of consumption, providing an increase in efficiency compared to other low-cost systems. Equipped with a feedback circuit, it offers five distinct control techniques that enable the self-tuning of the crucible temperature. The results indicate that the Cohen–Coon tuning method is more robust compared to the Ziegler–Nichols, damped, no overshoot, and mixed techniques. Sintering with this novel induction heater provides an alternative method for reducing the processing times for MEAM geometries, paving the way for increased efficiency and reduced energy consumption. Circuit diagrams, simulations, and experimental data on the temperature, time, and output voltage are provided in this article.

1. Introduction

The manufacturing industry is being transformed by the widespread implementation of additive manufacturing (AM), which has become one of the fastest growing fields in manufacturing due to the increase in processable materials [1], the allowed part complexity [2,3], and the enhanced micro- and macroscopic material properties [4]. One such method is material extrusion AM (MEAM), which is a novel and powerful method for producing metallic and ceramic bodies. This method employs material feedstocks that contain a high packing density of powder granules, enabling the fabrication of intricate shapes. With this approach, geometries are shaped, debinded, and sintered in a multistep process until the completion of the part, resulting in dense near-net-shaped functional products. Sintering is a critical step in MEAM and involves the application of heat, leading to the densification of the powder compacts. Through solid-state sintering, the granules coalesce, and necks are formed between neighboring particles. The necks progressively advance until the pores are eliminated, resulting in a solid body [5]. Mass transport diffusion is the driving mechanism for sintering, whereby material is transported between neighboring granules. This enables control of the final microstructure and the porosity of the product [6].

Conventionally, sintering is conducted in energy-intensive systems such as electric or flame furnaces [7]. More recently, other highly effective methods have been developed, such as microwave sintering [8,9], Spark Plasma Sintering (SPS), Field-Assisted Sintering (FAST) [10], and direct [11,12,13] and indirect [14,15] induction heating (IH). IH offers advantages compared to other methods, as it allows for direct heating of the target and reduces waste and heating times due to its high power densities and minimal thermal inertia. This approach is highly efficient, with efficiency values exceeding 90%, and has minimal standby equipment losses. It can reach high temperatures while minimizing the waste heat in the surrounding environment. The temperature profiles can be predefined using control techniques, and advanced features such as local heating can be achieved. The heating tool is contactless and highly selective in depth and along the surface of the workpiece. The process improves the quality, maximizes the productivity, and generates heat inside the part, and the temperature in the heating area’s surroundings is lower compared to the furnace or flame methods. Additionally, IH can be applied in various processing atmospheres such as air, protective gas, or vacuums. Unlike fossil fuel furnaces, IH does not cause local pollution in the surrounding space [16].

One well-known drawback of the technology lies in the time-consuming sintering process, which typically requires energy-intensive heating systems. Sintering is traditionally carried out after shaping the parts using expensive and bulky equipment, and few advancements have been made in terms of processing parts locally in situ without the use of sophisticated postprocessing equipment. In this work, a novel hybrid MEAM machine is integrated with an induction heater. The method involves shaping and debinding within the same volume and subsequently applying an indirect induction sintering treatment. Previous results [17] have demonstrated the capability of sintering MEAM metal parts using induction heating in a decoupled approach with an efficient concentration of energy, rendering dense bodies in only 6 min of soak time, as opposed to hours required by the traditional approach. Being able to sinter in situ significantly decreases the manufacturing time and costs.

This article presents a novel induction heater that can be coupled with a MEAM device to locally densify the metallic and ceramic powder compacts. The custom-developed highly efficient heater allows for the control of the temperature curves and the densification of the stainless steel 316L samples using a graphite crucible. One of the key challenges is the need for a compact, cost-effective, and user-friendly heating system capable of accurately controlling the temperature of the target material. A unique design that addresses the limitations of commercially available heaters and provides several distinct advantages is described in this work. The system consists of an inverter based on the Mazzilli Zero-Voltage Switching (ZVS) topology. It employs a parallel configuration that is modified in the switching stage of the MOSFETs to control the temperature by adjusting its duty cycle. The system also features a rectifier connected to a single-phase 220 V${}_{AC}$ power supply that can supply up to 5.7 kW of power. A user-friendly graphical interface allows for setting the desired temperature and time parameters. It also displays the electrical parameters, the temperatures of the entire system, and the water flow of the cooling system for monitoring purposes. The experimental results show that the circuit design can accurately monitor the temperature curve using different types of Proportional Integral Derivative (PID) controllers, demonstrating its effectiveness and reliability. The combination of material extrusion AM and local induction sintering is a novel hybrid additive manufacturing method, with a patent application filed by the Technical University of Berlin [18]. The method is illustrated in Figure 1.

2. Materials and Methods

2.1. Background

IH is used in a wide range of industrial applications such as annealing, bonding, brazing, hardening, melting, soldering, susceptor heating, and wire heating [19,20]. However, with technological advancements, IH has expanded its scope beyond the industrial sector, with increased use in domestic applications [21,22], as well as biomedical fields such as hyperthermia treatment and thermotherapy [23,24]. Typically, an induction heater comprises three main components, namely the power electronics, the control electronics, and the work coil. A schematic of this type of heater is provided in Figure 2.

2.1.1. Power Electronics

The AC Power Supply (ACPS) comprises an AC-DC converter and a DC-AC converter, with the latter being the most crucial component, as it provides medium- to high-frequency currents to the work coil [25]. The heat station is responsible for load matching to deliver the maximum available power from the ACPS to the workpiece. A capacitor bank is connected to the work coil to create a resonant or tank circuit (TC). Resonant inverters can be classified into full-bridge [26,27], half-bridge [28,29], or single-switch [30] topologies. Recently, multi-coil systems have been developed to enhance heat distribution, whereas dual-frequency generators can feed the work coil sequentially or simultaneously with different frequencies, thereby increasing the flexibility in penetration depths.

2.1.2. Control Electronics

Different approaches exist to regulate the power transfer from the ACPS to a work coil. Closed-loop control is recommended for accuracy, especially feedback from the thermal characteristics of the workpiece when heated. The most common methods include varying the rectifier DC link voltage, the duty cycle of the inverter’s semiconductors with different modulation techniques (e.g., square wave [31], asymmetrical control [32] or Pulse Density Modulation (PDM) [33]), the inverter’s operating frequency, or the Phase Shift Full-bridge (PSFB) control. The amount of this phase shift decides the amount of energy transferred, which makes this method highly effective, with minimized reactive current flow through free-wheeling diodes and without detuning the system from the resonant frequency of the work coil. Nowadays, digital signal processors (DSP) or field-programmable gate arrays (FPGA) are used for digital implementation due to their advantages in terms of the configurability and performance.

2.1.3. Work Coil

The work coil or induction coil is the most critical magnetic device in an IH system, which is modeled, designed, and optimized using analytical or finite element analysis. During work coil design, the most critical aspects to consider are the electrical-equivalent parameter extraction, the efficiency optimization, and the heat distribution optimization. These are classified into two types based on the direction of the induced magnetic flux lines: transversal and longitudinal. Its design must avoid the cancellation of magnetic fields and should consider that a higher flux density near the heating area induces a higher current in the workpiece. In some cases, the workpiece may require rotation to provide uniform exposure. Multiple-coil systems may have magnetic screens and flux concentrators to adjust the magnetic fields and adapt to different materials and positions. The overall system efficiency is defined as the ratio of the energy transferred to heat the workpiece and the electrical energy sourced from the power line. This depends on the power supply efficiency, the tuning of the IH circuit, the load matching, and the coupling distance.

2.2. Proposed System

The design of the IH system considered several aspects, in particular:

• The system is based on an inverter working as a resonant circuit.
• Among the resonant circuit topologies, the half-bridge is the most commonly used in applications up to 5 kW.
• The Zero-Voltage Switching (ZVS) technique is preferred due to its high efficiency in semiconductor switching.
• The work coil and capacitor bank are designed as a tank circuit, which can be arranged in a parallel topology to amplify the current.
• To achieve maximum efficiency, the tank circuit should operate at the resonant frequency, where the current flowing through the work coil is at its maximum.
• A higher current through the work coil induces a more potent magnetic field and determines the penetration depth on a workpiece.

Moreover, the guidelines of the design fulfill the following requirements:

• Demonstrating the IH working principle for a hybrid MEAM device;
• Interacting with cylindrical pieces from 38 mm to 60 mm in diameter;
• Heating a graphite susceptor up to 1200 °C;
• Providing real-time data to the user;
• Ensuring electrical safety.

The engineered IH system comprises four distinct subsystems, namely the power electronics, the digital control, the structure, and the Data Viewer & Parameters Setting (DV&PS), with the block diagram shown in Figure 3. The power electronics stage provides AC to the work coil at a specific frequency through the rectifier and inverter. The digital control part manages the system’s sensors, such as the water flow, the frequency, and the temperature, and implements a closed-loop control system. The structure houses the digital control and power electronics and provides mechanical adjustments to the sensors, work coil, and water cooling system for assembly. Lastly, the DV&PS module displays sensor data and allows tuning the experiment parameters, such as the desired temperature, the operation time, and the rectifier output voltage.

2.3. Design and Development

2.3.1. Power Electronics

Based on the system requirements, a 5 kW programmable rectifier with an interface for programming and monitoring electrical parameters was identified as necessary. The option of using two R4850G rectifiers in parallel was selected to achieve the required power. For this, additional hardware was required, a two-independent module diode was used.

Table 1. R4850G2 rectifier specifications fulfilling the selection criteria.

Operating Voltage	1-Phase, 85–300 V${}_{\mathit{AC}}$
$V_{OUT}$	42–58 V
$I_{OUT}$	0–60 A
Power	3000 W
Interface	CANBUS
Program Options	$V_{OUT},I_{OUT},V_{IN},I_{IN}$
Efficiency	up to 96%
Qty.	2-unit
Width, Height, Depth	105 mm, 40.8 mm, 281 mm
Mass	2 kg

provides the main parameters of the rectifier used in the system.

The circuit topology of the system is a half-bridge configuration that connects the inverter, the heat station, and the work coil in a single stage, with the schematic diagram provided in Figure 4. The parallel tank circuit operates at the resonant frequency and employs the Zero-Voltage Switching (ZVS) method. The design is based on the Mazzilli ZVS driver circuit [34], integrating a modified MOSFET gate driver to mitigate the parasitic oscillation and the ringing voltage and providing avalanche breakdown protection. Additionally, a gate driver power supply was implemented for temperature control.

The output voltage of the rectifier is denoted as V${}_{DC}$. The flyback diode, D${}_3$, eliminates voltage spikes across inductive loads when the supply current is suddenly interrupted. The inductors, L${}_1$ and L${}_2$, are used as chokes to prevent high-frequency oscillations from reaching the rectifier and to limit the current to acceptable levels. Placing the rectifier in series with L${}_1$ and L${}_2$ increases the efficiency by acting as a current source. The inverter oscillates when the digital control stage closes the switch SW${}_1$. One of the MOSFETs, such as Q${}_1$, saturates due to its gate driver, generating V${}_{AC}$ at the N end of the work coil with a peak voltage of $\pi ·$V${}_{DC}$. When this value drops to 0 V, Q${}_1$ is cut off by diode D${}_2$, which generates a gate voltage of 1.3 V. Immediately, Q${}_2$ saturates, generating a V${}_{AC}$ at the M end of the work coil with the same peak value as in the previous case. D${}_1$ is responsible for cutting off Q${}_2$ when V${}_{AC}$ drops to 0 V. The oscillation frequency is determined by the capacitance and inductance values of the capacitor bank and work coil.

Since energy flows between the work coil and the capacitor bank in the tank circuit, the capacitors must withstand high currents and temperatures. Polypropylene film capacitors are commonly used for high-frequency high-power applications such as IH. To avoid stressing the capacitors due to the high current, an array of 8 capacitors in parallel, each with a capacitance of 0.33 $\mathsf{\mu }$F, was used to obtain a total capacitance of 2.64 $\mathsf{\mu }$F capable of withstanding 2000 V${}_{DC}$. An air-cooling system consisting of two 120 mm × 120 mm × 12 mm fans operating at 2000 rpm when powered by 12 V was also implemented. The design of the MOSFET gate driver aimed to prevent parasitic oscillation on the gate and ringing on the drain caused by inductive loads. Figure 5 shows the use of R31 and C25 as the RC low-pass filter, while R37 is set to an appropriate value to enable a soft start and reduce the occurrence of parasitic oscillation. Additionally, R37 mitigated ringing. Including the Zener diode D11 allowed the MOSFET to saturate at 15 V, causing its internal R${}_{DS}$ resistance to decrease to 38 m$\Omega$ and avoiding a power loss. When M dropped to 0 V, R43 facilitated the discharge of D11, which initially dropped to the V${}_F$ value of D17 (1.3 V). The snubber circuit, comprising R51 and C38, safeguarded against an avalanche breakdown caused by the flyback effect when inductive loads were used. A similar response was noted in the MOSFET on the N side of the work coil.

This study used the LTSpice electronic circuit simulation software to assess the inverter’s performance and analyze the behavior of its associated tank circuit in the absence of a load. To achieve this, the schematic circuit shown in Figure 4, which represents the proposed design, was constructed within the simulation software environment, whereby one out of the six identical switching stages is depicted in Figure 6.

Upon feeding the inverter with the rectifier (represented by V1), the tank circuit exhibited an unstable voltage and current oscillation lasting approximately 6 ms before attaining stability, with the simulations provided in Figure 7. The results indicate that the current passing through the work coil attained 293.96 A${}_P$ or 207.86 A${}_{RMS}$, as depicted in Figure 8. In the unstable region, these anomalous behaviors can be attributed to resonance phenomena between the capacitor bank (C1) and the choke inductors (L1 and L2). The primary function of the choke inductors is to effectively filter the AC voltage and current from the supply voltage. However, these undesired effects can be mitigated by employing choke inductors’ values with a magnitude of at least ten times the work coil inductance. By doing so, minimal interference is ensured at the resonant frequency established by the tank circuit components’ values. Within the unstable region, the tank circuit’s voltage oscillated at a frequency of 44.29 kHz, while the work coil’s current fluctuated within the range of 39.06 to 45.66 kHz. Following the dissipation of these effects, the subsequent stable region demonstrated the voltage and current oscillating at a frequency of 49.36 kHz determined by the specific values of the capacitor bank and the work coil, reaching a current value of 138.30 A${}_P$ or 97.79 A${}_{RMS}$, achieving the desired system performance, as shown in Figure 9.

However, sustaining a current of 207.86 A for only 6 ms during each inverter startup and 97.79 A for most of the time is impractical for a single MOSFET. Consequently, up to six MOSFETs were arranged in parallel to reduce the current to a manageable range of 16.30 A and distribute the thermal load. Nevertheless, employing multiple MOSFETs in parallel and sharing the same gate driver may lead to a voltage surge at the common gate connection. To circumvent this, each parallel MOSFET must have its gate drive network positioned between the gate and the shared gate driver connection.

2.3.2. Digital Control

The digital control system was electrically isolated from the power electronics and included a controller, sensors, actuators, control algorithm, and communication interface with the rectifier stage and DV&PS, with the block diagram illustrated in Figure 10. The implemented algorithm incorporated safety measures to ensure the stable operation of the inverter, including stabilizing the output voltage of the rectification stage and maintaining a minimum flow rate of 9 mL/s in the work coil cooling stage. Prior to communicating with the GUI, the system verified that no contingencies occurred in the rectification stage. After receiving a start command, the controller was tuned for a maximum time of 25 s based on the work coil connected to the inverter. Once tuned, the PID controller was activated to regulate the temperature for the duration specified by the user, with the flowchart of the control algorithm provided in Figure 11 and the power electronics and digital control stages given in Figure 12.

2.3.3. Thermal Analysis

CENOS IH 3 simulation software [35] was used to analyze four simulation cases. The simulations were performed with two different geometries of graphite crucibles exposed to magnetic fields generated by four multi-turn helical work coils. The physical properties of graphite, including thermal conductivity (55 to 150 W/mK), heat capacity (690 to 1926 J/kgK), density (1720 kg/m${}^3$), electric conductivity (71,000 to 118,124 S/m), and magnetic permeability, were considered.

In Case 1, a tubular graphite crucible with the dimensions of a 38 mm outer diameter, a 28 mm internal diameter, and a 40 mm height was used along with a work coil with a 75 mm outer diameter, a 60 mm height, seven windings, and both geometric centers coinciding. The crucible was heated to a temperature between 1188 °C and 1222 °C in 200 s with a resonant frequency of 60 kHz. The work coil required a power of 2.13 kW from the rectifier to receive 1.88 kW of total power with a current density of 1.8 × 10${}^8$ A/m${}^2$.

In Case 2, the same graphite crucible as Case 1 was used, and a work coil with a 75 mm outer diameter, a 60 mm height, six windings, and both geometric centers coinciding was employed. The crucible reached a temperature between 1297 °C and 1341 °C in 200 s with a resonant frequency of 60 kHz. The work coil required a power of 2.75 kW from the rectifier to receive 2.50 kW total with a current density of 2.3 × 10${}^8$ A/m${}^2$.

In Case 3, a tubular graphite crucible with a 60 mm outer diameter, a 48 mm internal diameter, and a 42 mm height was used with a work coil with a 90 mm outer diameter, a 40 mm height, and four windings, with a distance of 10 mm from their geometric centers. The crucible reached a temperature between 1306 °C and 1609 °C in 200 s with a resonant frequency of 60 kHz. The work coil required a power of 7.00 kW from the rectifier to receive 6.30 kW total with a current density of 3.2 × 10${}^8$ A/m${}^2$.

In Case 4, the same graphite crucible as Case 3 was used with a work coil having a 90 mm outer diameter, a 40 mm height, and five windings, with a distance of 10 mm from their geometric centers. The crucible reached a temperature between 1173 and 1410 °C in 200 s with a resonant frequency of 60 kHz. The work coil required a power of 4.70 kW from the rectifier to receive 4.30 kW total with a current density of 2.4 × 10${}^8$ A/m${}^2$.

The results suggest that the crucible used in Cases 1 and 2 represented a lower energy load for the rectifier stage due to its smaller volume compared to the one used in Cases 3 and 4. However, the requirement of reaching 1200 °C was met in all conditions, as shown in Figure 13. Case 2 had the lowest energy consumption and a margin of 141 °C concerning the desired temperature, whereas Case 1 had the lowest margin of 22 °C. To increase the efficiency and prevent a voltage drop in the working portion due to the work coil leads’ length, the distance between them was reduced to 14 mm. Figure 14 and Figure 15 display the developed work coil based on Case 2 of the thermal analysis, and

Table 2. Comparison of the simulated and developed work coils’ dimensions.

	Simulated Work Coil	Developed Work Coil
Outer diameter	75 mm	76 mm
Height	60 mm	60 mm
# windings	6	6
Profile diameter	6 mm	6.4 mm
Profile thickness	0.8 mm	0.8 mm
Resonant freq.	60 kHz	62.86 kHz

summarizes the differences between the simulated and developed work coils.

3. Results and Discussion

3.1. Validation of the Simulation Data

The presented results are categorized into two subsections. The first subsection compares the waveforms obtained from the simulations and experimental data. In the second section, the focus shifts to demonstrating the outcomes derived from the thermal analysis in contrast to the temperature and power curves acquired from the system under equivalent conditions.

3.1.1. Waveforms

The experimental results displayed in Figure 16 reveal a significantly reduced voltage stabilization time of only 520 $\mathsf{\mu }$s while resonating at 62.86 kHz, as observed in Figure 17, compared to the simulated waveform of the tank circuit voltage, illustrated in Figure 7, showcasing a stabilization time of 6 ms upon system activation, with resonance occurring at 49.36 kHz once it is in the stable region as seen in Figure 9.

The stabilization time disparity can be attributed to the graphite crucible present in the inverter during the experimental tests. Furthermore, the discrepancy in the resonance frequency between the simulation and experimental results is attributed to the selected inductance value. The simulation employed an inductance of 4 $\mathsf{\mu }$H, whereas the current work coil’s inductance, determined experimentally, was found to be 2.43 $\mathsf{\mu }$H. It is worth noting that the theoretically calculated inductance for the work coil was 2.37 $\mathsf{\mu }$H, while the value obtained using an LCR meter was 5.2 $\mathsf{\mu }$H. This suggests that for low inductance values, the theoretical calculation provides a more accurate estimation.

Figure 16 presents the maximum voltage of the tank circuit within the unstable region, measuring 244 $V_P$. This value deviated from the simulated value of 200.24 $V_P$ depicted in Figure 8, primarily due to the voltage breakdown characteristic of the selected MOSFET model in the software, which had a limit of 200 $V_P$. The chosen model aligned with the system requirements since the maximum simulated voltage amounted to 172.10 $V_P$ within the stable region, as shown in Figure 9. This value was close to the experimental observation of 178 $V_P$ illustrated in Figure 17 resulting in a difference of 3.43% from the simulation.

Figure 18 presents the gate’s waveforms of the MOSFET arrays A and B, exhibiting an average voltage of 15 V. Further examination of the gate’s rising edge, framed in green, is depicted in Figure 19, while Figure 20 provides detailed insight into the falling edge, framed in purple.

On the rising edge with a duration of 1.074 µs, and to achieve an adequate trade-off between the overdamping effect and the suppression of the ringing phenomenon, an exploration of various gate resistor values was undertaken using simulation software. It was observed that increasing the resistance effectively mitigated the ringing effect; however, it simultaneously prolongs the rise time of the MOSFET’s gate, imposing limitations on its switching frequency. Considering the ringing effect, the MOSFET gate rising edge waveform revealed success in suppression, albeit over-damped.

Conversely, during the falling edge, which lasted approximately 158 ns, an aberration in the natural behavior of the waveform was observed, disrupting the initial formation of the tank circuit voltage within 180 ns. In high-current applications, these voltage transients during the MOSFET switch-off are often encountered, primarily caused by parasitic inductance within the MOSFET package. Methods to mitigate these switch-off transients include introducing a resistor in parallel to the gate resistor, along with a series diode, to slow down the MOSFET switch-off process, in addition to implementing an RC snubber between the drain and source. The last was considered to further reduce the ringing effect during the MOSFET switch-off, as depicted in Figure 5.

Consequently, this deviation resulted in a dissipation of energy that was not utilized for inducing a current in the graphite crucible but instead generated heat in the work coil. Nevertheless, the magnitude of this energy loss was relatively minor, considering that the voltage during the disturbance ranged from 4 V to 10 V, relative to a value of 178 $V_P$, occurring for a duration of 180 ns every 15.95 $\mathsf{\mu }$s, as depicted in Figure 21.

3.1.2. Thermal Tests

The acquired data from the conducted free-run tests were meticulously compared with the preceding thermal analysis simulation outcomes. Specifically, in Case 2, the thermal simulation indicated that the graphite crucible would attain a temperature of 1341 °C within 200 s, accompanied by a power consumption of 2.75 kW. Nevertheless, the experimental results revealed that the graphite crucible achieved temperatures ranging from 1286.3 to 1310.3 °C during the same time interval. This observed variation can be attributed to the progressive loss of graphite material resulting from oxidation within the ambient atmosphere. Notably, at 300 s, the highest temperature recorded was 1365.7 °C. At the same time, the power consumption stood at a mere 1.313 kW, approximately half the value estimated in the simulation, as shown in Figure 22. A ceramic crucible was employed to minimize the heat dissipation as an intermediate barrier between the work coil and the graphite crucible throughout the testing process.

3.2. Choosing the Controller Tuning Method

A series of tests was conducted to evaluate the effectiveness of the available tuning method alternatives with the purposed system. These tests focused on three fundamental parameters: the rate at which the desired temperature was achieved, the percentage of the overshoot, and the long-term stability of the attained temperature.

To select an initial desired temperature, it must be considered that the densification temperature of a material exhibits a dependency on its specific type. In the case of 316L stainless steel, a notable acceleration in densification is observed within the temperature range of 600 °C to 800 °C, while its rate gradually diminishes beyond 1350 °C. This temperature regime leads to a relative density reaching up to 0.99, a value grounded in theoretical considerations. Concurrently, grain shrinkage is influenced by the temperature, with the most pronounced contraction rates observed at 830 °C and 1150 °C. Furthermore, temperature intervals spanning 700 °C to 920 °C and 1000 °C to 1300 °C are characterized by elevated contraction rates. These observations align with the findings presented by [36]. Based on the interval of acceleration in densification and the initial contraction rate interval, a target temperature of 700 °C was determined for the experimental tests of the current subsection. Additionally, considering the interval exhibiting the highest contraction rate, a second designated target temperature of 1200 °C was established for which the analysis and discussion of the results in relation to these specific temperature conditions are provided in Section 3.3.

Figure 23 portrays the system’s response under the proposed tuning methods. Notably, the tuning process for the PID controller exhibited durations ranging from 24.4 to 29.6 s, during which the temperature attained values ranging from 583.6 to 602.1 °C. Some details, including the corresponding tuning process duration, achieved temperature, computed PID controller gain values, the time required to reach the desired temperature, and the maximum temperature attained, can be found in

Table 3. The tuned PID controller specifications.

	Ziegler–Nichols	Cohen–Coon	Damped Oscillation	No Overshoot	Mixed
Tuning time (s)	29.6	28.0	28.8	24.4	24.4
Tuning temp (°C)	593.7	602.1	583.6	600.5	586.6
Gains	$K_p$ 33.223 $K_i$ 1.250 $K_d$ 5.000	$K_p$ 3.928 $K_i$ 0.760 $K_d$ 6.883	$K_p$ 36.545 $K_i$ 0.056 $K_d$ 0.139	$K_p$ 33.105 $K_i$ 0.015 $K_d$ 6.621	$K_p$ 26.721 $K_i$ 0.520 $K_d$ 4.255
Time (700 °C) (s)	174.8	51.2	NA	NA	323.2
Max. temp. (°C)	712.0	715.5	641.3	674.4	703.7

.

Based on the results obtained from the self-tuning process, it is evident that the damped oscillation, no overshoot, and mixed methods, which averaged the gains from the four methods mentioned above, led to an overdamped response of the system, resulting in the attainment of the desired temperature within a time of 323.2 s in the mixed method. In contrast, the other two methods would require more than 400 s to achieve the target temperature. Notably, when employing the mixed method, it was observed that once the desired temperature was reached, the system exhibited stability, maintaining the temperature with a maximum fluctuation of 0.529%.

In the case of the Ziegler–Nichols method, the system response was critically damped, reaching the desired temperature within a time of 174.8 s. However, this method demonstrated fluctuations of 1.714% around the target temperature. On the other hand, the Cohen–Coon method yielded an underdamped response with an initial overshoot of 2.214%. Nevertheless, it achieved stability within a shorter duration of only 82 s, with fluctuations of merely 0.514%.

Given that a temperature of 715.5 °C does not adversely impact the sintering process but rather contributes positively to it, considering its alignment with the elevated contraction rates, the Cohen–Coon method was deemed suitable for implementation in the present study. It is critical to bear in mind that the derivative gain must be adjusted manually to reduce the overshoot. However, the proposed system must incorporate an autotune PID controller because the system was designed to hold different work coils, which implies variations in the controller gains based on the work coil employed. In this regard, an algorithm was developed to automatically adjust these parameters.

3.3. System Parameter Configuration to Follow a Temperature Profile

Upon the completion of the PID controller tuning, the subsequent step involved the implementation of the temperature control. Configuring the input span parameter was necessary to carry out this process. This parameter was determined by calculating the difference between the system’s expected maximum and minimum temperatures. Considering the experimental temperature profile employed in this study, which consisted of two distinct temperature levels with varying durations, the conducted tests aimed to analyze the system’s behavior in attaining and maintaining stability at these desired temperatures within their specified time frames. A crucial aspect to be determined was whether the controller needed to be retuned each time the target temperature changed and identifying the optimal value for the input span through a series of three experimental evaluations.

The experimental configuration encompassed three distinct cases. In Case A, a single controller tuning was conducted with a high input span of 955 °C. Similarly, Case B entailed a single tuning, akin to Case A, but with a low input span of 725 °C. Finally, Case C involved tuning the controller each time the desired temperature changed, employing an input span value equivalent to Case A.

As illustrated in Figure 24 and detailed in

Table 4. Quickness and efficacy in reaching and sustaining the temperature profile of 700 °C and 1200 °C for 100 s each.

	Case A	Case B	Case C
Input span	955 °C	725 °C	955 °C
Time to reach 700 °C	19.6 s	25.8 s	31.9 s
Duration 700 °C	19.6–119.6 s	25.8–125.8 s	31.9–131.9 s
Min. temp. 700 °C	702.6 °C	692.3 °C	702 °C
Max. temp. 700 °C	811.9 °C	726.7 °C	806.7 °C
Tuning time 700 °C	27.6 s	27.4 s	41 s
Standard deviation 700 °C	23.71 °C	4.39 °C	14.64 °C
Time to reach 1200 °C	224.2 s	254.2	239.5 s
Min. temp. 1200 °C	1195.3 °C	1193.7 °C	1190.3 °C
Max. temp. 1200 °C	1207.8 °C	1207.1 °C	1217.8 °C
Duration 1200 °C	224–324 s	255.4–355.4 s	239–339 s
Tuning time 1200 °C	NA	NA	30.7 s
Standard deviation 1200 °C	2.23 °C	2.77 °C	4.96 °C

, using a high input span value of 955 °C for temperature control demonstrated suboptimal efficacy in maintaining a temperature of 700 °C. These instances exhibited fluctuations ranging from 0.371% to 15.98%, with a standard deviation of 23.71 °C when employing a single tuning approach. Furthermore, when retuning the controller due to a target temperature change, fluctuations between 0.286% and 15.242% were observed, with a standard deviation of 14.64 °C. Conversely, adopting a low input span value of 725 °C combined with a single tuning strategy resulted in diminished fluctuations ranging from $-1.1\%$ to 3.814% and a standard deviation of 4.39 °C. Notably, the fluctuations were reduced in all cases when reaching the temperature of 1200 °C, as shown in Figure 25. Specifically, the standard deviations for Cases A and B were 2.23 °C and 2.77 °C, respectively, while for Case C, it amounted to 4.96 °C.

Considering the analysis outcomes, Case B demonstrates the lowest standard deviation, indicating greater consistency in achieving the target temperature of 700 °C. Although it requires longer than the other cases to reach 1200 °C, the standard deviation remains comparable to the lowest observed value. Consequently, to ensure a more reliable system response, the characteristics of Case B were chosen for implementation.

4. Conclusions

A novel induction heater that can be coupled to a MEAM device was developed in this work, revealing that heating of a graphite crucible can be achieved efficiently in very short operating cycles. The capacity to sinter MEAM metallic parts with this approach allows achieving very high production rates. The high concentrated power densities of the induction sintering process resulted in the technology being highly efficient. The disclosed device allows tailoring temperature curves using five distinct PID techniques, with the most optimal method being the Cohen–Coon technique. The following conclusions were drawn:

• The experimental results demonstrate that the system reduces error with an increased duration of maintaining the target temperature. Specifically, when the temperature was sustained at 700 °C for 100 s, the mean standard deviation measured was 4.39 °C. However, increasing the temperature duration to 200 s resulted in a significant decrease in the mean standard deviation to 1.32 °C.
• The power input remained constant at 1.313 kW throughout the experiments, regardless of the target temperature, which demonstrates the stability and reliability of the system under varying temperature conditions.
• The observed power discrepancy between the simulations and the measurements is attributed to the electromagnetic properties within the simulation software, whereby comparative tests were conducted using an alternative induction heater as a benchmark for evaluating the simulation results. To closely approximate the experimental conditions, the peak voltage magnitude was utilized as a parameter in the simulations, albeit as DC. This modification resulted in an increment in the temperature results and a reduction in the discrepancies compared to the AC, with an associated error margin of 2.31%. Given that the software employed in this study is used in the induction heating industry and is grounded in empirical data, the findings presented in this manuscript indicate that the designed equipment exhibits a superior efficiency level compared to the traditional counterparts.
• However, an observation is that graphite crucible oxidates when heated under ambient atmospheric conditions. After several tests with the same crucible, heating curves with shorter time intervals were exhibited to achieve the target temperatures. This phenomenon highlights the influence of oxidation on the heating process. It emphasizes the need to consider replacing the crucibles periodically to retain the experimental conditions or utilizing an air-free environment.
• The results demonstrate that the maximum voltage attained before stabilization closely approached the MOSFET breakdown voltage. Specifically, an observation of 244 V was made, indicating its proximity to 250 V. Future investigations will prioritize the reduction in the maximum voltage within the unstable region by incorporating a soft-starter stage or selecting an alternative MOSFET with a breakdown voltage of 300 V.
• An uneven heat distribution within the MOSFETs during system operation was also identified. The three rows of MOSFETs positioned farthest from the work coil maintained an average of 30 °C, while the fourth and fifth rows recorded 31 °C and 33.5 °C, respectively. In contrast, the closest row registered an average of 37 °C. The temperature discrepancy is attributed to the varying magnitude of the current flowing through each. The current system’s connection involves both work coil ends directly connected in front of the capacitor bank. Consequently, the distance from the work coil ends to each capacitor increases. Therefore, the shorter distance corresponds to a lower resistance, resulting in a higher current flow through both the MOSFETs and the capacitor nearest to the ends. Although these differences in current distribution are relatively minor, even slight variations in resistance can have a considerable impact, particularly when operating with high current magnitudes typical in induction heating applications. To address this, an alternative connection scheme is proposed wherein one work coil end is connected to the nearest capacitor while the other is connected to the furthest capacitor. This new arrangement would ensure a more balanced current distribution, resulting in a better thermal distribution.
• The analysis of the MOSFET gate’s rising edge waveform revealed success in suppressing the ringing effect, albeit with an overdamped response. This level of overdamping does not pose any significant issues for the frequency range the system was designed for, between 50 to 100 kHz. However, if there is a need to extend the operating frequency range to higher values, it would become necessary to reduce the gate resistor value accordingly. It is important to note that decreasing the resistor value leads to an increase in current flow. Therefore, recalculating the resistor power is essential to ensure the replacement resistor can handle the increased current load.
• The aberration during the gate’s falling edge persisted, although to a lesser extent. This indicates the ringing effect could not be effectively mitigated due to the low resistance value utilized in the snubber circuit. The perturbation suppression can be achieved by increasing the resistor value within the snubber circuit. Furthermore, introducing a capacitor between the gate and source terminals offers an alternative approach to extending the falling edge time to address this issue.
• Additionally, alternative graphite crucible and work coil dimensions will be explored to determine the system’s maximum operational capabilities. The utilization of alternative crucible materials, such as a platinum–iron alloy, will also be considered to assess their performance characteristics compared to previous results.

A hybrid machine combining local indirect induction sintering with AM is proposed, allowing the sintering of parts locally without the need for part transportation to inefficient energy-intensive heating systems. The reported improvements in heating rates exceed those obtained with traditional electric furnaces and underline a significant breakthrough in technology, reducing the processing times of metallic and ceramic processing.

5. Patents

The combination of material extrusion AM with local sintering is a novel hybrid additive manufacturing method with a patent application filed by the Technische Universität Berlin [18].