Induction-Heated, Unrestricted-Rotation Rectangular-Slot Hot End for FFF

Abstract

This work presents a fused-filament fabrication (FFF) hot end that combines an unrestricted-rotation C-axis with a rectangular-slot nozzle and an induction-heated melt sleeve. The architecture replaces the popular resistive cartridge and heater block design with an external coil that induces eddy-current heating in a thin-walled sleeve, threaded to the heat break and nozzle, reducing thermal mass and eliminating wired sensors across the rotating interface. A contactless infrared thermometer targets the nozzle tip; the temperature is regulated by frequency-modulating the inverter around resonance, yielding stable control. The hot end incorporates an LPBF-manufactured nozzle, which transitions from a circular inlet to a rectangular outlet to deposit broad, low-profile strands at constant layer height while preserving lateral resolution. The concept is validated on a desktop Cartesian platform retrofitted to coordinate yaw with XY motion. A twin-printer testbed compares the proposed hot end against a stock cartridge-heated system under matched materials and environments. With PLA, the induction-heated, rotating hot end enables printing at 170 °C with defect-free flow and delivers substantial reductions in job time (22–49%) and energy per part (9–39%). These results indicate that the proposed approach is a viable route to higher-throughput, lower-specific-energy material extrusion.

1. Introduction

Fused-filament fabrication (FFF) is the dominant material extrusion (MEX) desktop modality. It employs a heated nozzle to melt and extrude unfilled or composite thermoplastic filaments to form continuous strands according to programmed toolpaths [1]. As of 2024, FFF represents approximately 45–50% of desktop-printer unit sales [2]. Yet, despite its growing role in prototyping and short-run production [3,4], protracted manufacturing times and high specific energy prevent it from being a cost-effective solution [5,6,7]. In fact, a modest 100 cm³ part in polylactic acid (PLA) can require up to 2.4 kWh of energy [8]. The situation worsens when processing higher-temperature polymers [9,10]. Therefore, to compete in medium and large batches, faster and lower energy printing is critical [5,11].

To optimize consumption, statistical, physics-guided or hybrid models have been proposed to relate geometry and printing parameters to energy use [12,13,14,15,16]. All of them show that printing speed and layer height are the primary drivers of energy demand, with temperature being a distant third [17,18]. Therefore, three sorts of strategies arise to minimize consumption, but all of them impose quality penalties: (i) increasing the layer height, which degrades surface finish and interlayer strength [15,17], (ii) raising the feed rate, which promotes shear-induced defects such as “shark-skin” [19] and (iii) boosting volumetric flow by adopting larger-diameter circular nozzles (at the expense of lateral resolution and corner fidelity) and often driving conventional cartridge heaters beyond their practical thermal delivery capacity [20,21].

An alternative route to higher productivity is to widen the extruded road while maintaining a constant layer height. This strategy preserves the nominal vertical resolution and staircase pitch in the z-direction yet increases the in-plane deposition rate and reduces build time by covering more area per pass. A rotating rectangular slot in the nozzle can deposit anything from a knife-thin trace to a broad “ribbon”, since the projection of the slot in the build plane changes with the yaw angle. First sketched in industrial patents, yaw was coordinated on the fly to print wide tracks for infill and narrow ones for detail [22]. Subsequent experimental studies have tightened the yaw mechanics and control loops [23,24], quantified how orientation dictates strand geometry and accuracy [25,26] and extended the idea to multi-axis platforms with rotation-aware tool paths [27].

Even if the longer edge of the slot stays tangential to the tool path (no width modulation), a rectangular nozzle can still dispense strands several times wider than the typical $0.4\mathrm{m}\mathrm{m}$ circular counterpart. Yet, two practical obstacles appear. On the one hand, sustained rotation twists the filament, the wiring and the cooling lines. This hampers smooth re-orientation around closed contours or sharp corners, degrading surface finish and dimensional fidelity [27]. On the other hand, the higher volumetric flow overwhelms conventional cartridge heaters [28], while thermal inertia lengthens the warm-up times [29], inflates idle power draw [30] and harms the response to flow transients [31].

Induction heating offers a viable alternative to the thermal limitations by delivering contactless, volumetric heat with low thermal inertia, thereby improving the thermal response while reducing parasitic losses. Prototype studies have achieved millisecond-scale temperature transients and more homogeneous melt zones by optimizing coil geometry, incorporating high-frequency in situ sensing, and implementing closed-loop power control [32,33,34]. In addition, the only inductive hot end currently on the market, to our knowledge, for MEX reports substantially lower thermal inertia and a reduced moving mass, compared with conventional resistive designs [35]. However, to the best of our knowledge, there is currently no hot end design that simultaneously combines unrestricted C-axis rotation, a rectangular-slot nozzle for wide strands and a low-inertia induction-heated melt zone with closed-loop temperature control. In addition, the consequences of such an architecture for printing time and energy use have not yet been systematically evaluated relative to conventional cartridge-heated hot ends.

The larger cross-section of rectangular-slot strands increases the thermal load and demands a fast, well-controlled heat input to maintain a homogeneous melt at higher volumetric flow rates; in conventional cartridge-heated blocks, especially when mounted on a rotating head, this leads to heavy, thermally inert assemblies that are difficult to wire and limit both throughput and the practicality of unrestricted C-axis rotation. Induction heating is particularly attractive in this context because it concentrates heat generation in a thin metallic sleeve with low thermal inertia, enabling a rapid thermal response and efficient power delivery while keeping the inductor and power electronics stationary. The combination of a rectangular-slot nozzle with an induction-heated sleeve is therefore synergistic: the former exploits wider strands to reduce the toolpath length, while the latter provides the responsive, lightweight heating required to sustain such deposition in a rotating architecture.

Here, both techniques are integrated into a single structure: a rectangular nozzle is fitted to a continuously rotating C-axis with unlimited yaw control, and a non-contact induction heater is designed with closed-loop infrared thermometry. Working in concert, broad, low-profile strands are placed at a constant layer height, mitigating the need for multi-pass perimeter deposition. At the same time, warm-up delays and standby energy losses are reduced significantly. The concept is validated on a desktop Cartesian FFF printer retrofitted with a prototype of the new Unrestricted-Rotation Hot End (URHE), which is benchmarked against an unmodified machine. Test parts are manufactured with PLA. Comparative performance is quantified by the percentage reduction in manufacturing time and the percentage of plug-level energy savings per part.

2. Unrestricted-Rotation Hot End: Design and Optimization

2.1. Hot End System Architecture

The basic architecture of the URHE (Figure 1) integrates four subsystems: (i) an unrestricted-rotation C-axis for continuous yaw alignment of a rectangular nozzle, (ii) an induction-heated melt sleeve driven by an inverter, (iii) contactless infrared temperature sensing and control, and (iv) annular, quasi-isotropic part cooling.

2.1.1. Hot-End Stack and Rotation (C-Axis)

As in common commercial designs (Figure 2a), the hot end stack features a nozzle, a thin-walled thermal barrier or heat break, a finned heat-sink and a guidance polytetrafluoroethylene (PTFE) tube.

It differs, however, in the heating system. The resistance heater cartridge embedded in an aluminum block has been substituted by a non-rotating external coil which induces eddy currents in a hollow rotating component or sleeve (Figure 2b), into which both the nozzle and the heat break are threaded.

Heat is generated in situ by Joule heating uniformly along the sleeve. Through conduction, the filament melts within the central channel, establishing a symmetric liquefaction zone and allowing more homogeneous fusion of the material. The arrangement preserves nozzle interchangeability, eliminates all the wires in the rotating interface and reduces the overall thermal mass.

The interchangeable nozzle was designed with an upper 3.00 mm cylindrical inlet that morphs into a 1.20 × 0.40 mm rectangular outlet (Figure 3a,b). The 0.40 mm minor dimension was preserved so that the effective lateral resolution matches that of a conventional $Ø0.40\mathrm{m}\mathrm{m}$ nozzle. To promote stable flow and reduce pressure drop, the circular-to-rectangular transition was modeled as a smooth, curvature-continuous profile, generated by a lofted cut between intermediate cross-sections (Figure 3b). Because this geometry is difficult to reproduce reliably at this scale with conventional machining, the nozzle was manufactured by laser powder bed fusion (LPBF) in maraging steel M300 and then threaded for interchangeability (Figure 3b). Upstream, a Ti-6Al-4V heat break is co-bored and chamfer-matched to the nozzle to form a continuous flow channel, minimizing ledges at the cold–hot interface.

The finned heat-sink serves as the structural hub of the C-axis transmission, acting as the bearing journal and torque carrier for the rotating subassembly. The set is supported by a single-row deep-groove ball bearing (Figure 1), which promotes concentric rotation about the filament axis with low runout during sustained yaw. Upstream of the bearing, a GT2 timing pulley is assembled on the C-axis shaft and driven by a NEMA-8 stepper (Nanotec Electronic GmbH & Co. KG, Kapellenstr, Bavaria, Germany.) via a belt (Figure 1). It provides the required reduction while it isolates the motor mass and vibration from the rotating hot end components. Finally, the heat-sink is cooled by a fan placed on the stationary portion of the extruder head.

2.1.2. Induction Heating Assembly

For inductive heating, the sleeve acts as the core of a solenoid. The concentric, external winding placed around it is excited by a sinusoidal current which produces a magnetic field of the same frequency. As a result, eddy currents are induced on the core’s outer surface, with a penetration or skin depth $\delta$ (Equation (1)) that decays exponentially in radial direction and depends on the current frequency ($f$) and on the electric conductivity ($\sigma$) and magnetic permeability ($\mu$) of the material.

$$\delta ={\displaystyle \frac{1}{\sqrt{\pi f\sigma \mu }}}$$

(1)

A suitable combination of excitation frequency, geometry and sleeve material sets the eddy-current path resistance and produces Joule heating in the hot end. Because induction is confined to a thin surface layer, we adopt a cylindrical heater sleeve with a wall thickness of a few δ at the operating frequency to maximize efficiency, minimize thermal mass, and maintain uniform azimuthal coupling. The sleeve simultaneously serves as the mechanical interface for the threaded nozzle and heat break that encloses the melt channel that acts as a liquefaction chamber; accordingly, the electromagnetic design employs an axisymmetric, concentric induction coil to establish a uniform circumferential field with strong coupling.

An effective sleeve must concentrate magnetic flux (high permeability with shallow skin depth), enable strong eddy-current heating at tens of kilohertz (appropriate resistivity), conduct heat to the melt channel (adequate thermal conductivity) and remain ferromagnetic across the operating window (Curie point well above extrusion setpoints); taken together, these requirements make AISI 420 martensitic stainless steel (1.4021 (X20Cr13)) a balanced choice. Ferromagnetic, with a moderate electric resistivity (55 μΩ·cm) [36], a thermal conductivity of $24.9\mathrm{W}·{\mathrm{m}}^{-1}·{\mathrm{K}}^{-1}$ [36] and a Curie point above 600 °C [37], provides a convenient electric resistance in the eddy current path, an adequate heat diffusion and stable magnetic performance at typical temperatures of PLA extrusion (170–230 °C) [38].

To size the induction sub-system, we estimated the required thermal power under a deliberately conservative assumption. Because the thermophysical properties of the selected PLA were not precisely known, we adopted worst-case values corresponding to fully crystalline PLA (100% crystallinity) from Pyda et al. [39] and a density of $1.290\mathrm{g}·\mathrm{c}{\mathrm{m}}^{-3}$ [40]. For a representative deposition condition (0.2 mm layer height, and $50 \mathrm{m}\mathrm{m}·{\mathrm{s}}^{-1}$ print speed) assuming the rectangular slot design (1.2 mm strand width), the theoretical heat input to raise the polymer from 20 °C to 220 °C is 6.2 W. An iterative mechanical design fixed the heater as a cylindrical induction sleeve (external diameter: $Ø8\mathrm{m}\mathrm{m}$, internal thread (through hole): $M6$; axial length: 20.5 mm). For this geometry, parasitic losses by conduction, convection and radiation were estimated at 5.6 W. Accordingly, the total estimated power requirement is $11.8\mathrm{W}$.

Additionally, we performed thermal simulations using ANSYS Electronics (2022) to corroborate the analytical estimates. Because the electromagnetic skin depth is small, the induced Joule heating was modeled as an equivalent surface heat flux, rather than a volumetric source. In the simulation, the thermal properties of the materials used (previously mentioned) were considered, along with an ambient temperature of 25 °C and the simulation of a 2.2 cfm fan flow. Radiation is neglected as a second-order effect for the temperature range considered. The mesh consisted of more than 1.5 million elements (tetrahedral), with a maximum element size of $1\mathrm{m}\mathrm{m}$ and a minimum of 0.05 mm. A k–ε RNG turbulence model was used.

Figure 4 presents the simulated temperature field for the same operating conditions used in the theoretical calculations.

The simulation predicts a maximum nozzle temperature of 228.6 °C  (Figure 5), which is in good agreement with the 220 °C target (relative error 3.9%). Deviation likely arises from modeling simplifications in the theoretical estimate, like idealized geometry, temperature-independent properties, and approximate boundary/contact conditions. Based on these results, we specified a design margin and sized the induction subsystem to deliver up to 15 W, providing adequate headroom over the 11.8 W estimate.

Power to be transferred by magnetic coupling was analyzed with finite-element electromagnetics (FEMM 4.2 and ANSYS Electronics 2022). To size the inductor, we designed a 13-turn solenoid wound with Litz wire ($170\times Ø0.08 \mathrm{m}\mathrm{m}$), mean diameter $15 \mathrm{m}\mathrm{m}$ and axial length 20 mm, arranged to couple uniformly with the sleeve along the melt zone. The coil is wound around a flanged PEEK bushing, whose section has an inner diameter of 14 mm, so the radial distance to the outer surface of the sleeve is 3 mm.

The operating frequencies (>66 kHz) are high enough for efficient eddy-current heating, yet low enough to simplify the resonant driver and limit electromagnetic interference. With the core installed, the measured coil inductance is $L_1=2.23 \mathrm{\mu }\mathrm{H}$ at 70 kHz. A 24 V dc half-bridge inverter drives a series-LC tank formed by the coil, an external inductor $L_2=10 \mathrm{\mu }\mathrm{H}$, and a capacitor $C=470 \mathrm{n}\mathrm{F}$, setting the resonance near 66 kHz. The inverter operates slightly above resonance to achieve soft switching and to limit the peak tank current.

At 75 kHz (well above resonance), the current is 3.5 A RMS, which FEMM predicts corresponds to 3.8 W of sleeve heating (Figure 5). A frequency-control loop tunes the inverter: lowering the drive frequency toward resonance increases the series-LC current and thus, the delivered power. To prevent excessive hot end temperatures near resonance, the maximum heating power is software-limited to 15 W, reached at 68.5 kHz.

An electronic prototype and a simplified hot end (without the rotary assembly) were built to validate the inductive heating design. The inverter used two IRF540 MOSFETs driven by an IR2111 gate driver. At 75 kHz, the system delivered a quasi-sinusoidal 3.5 A RMS current to the heater winding. The measured inverter input power was 5.4 W, in reasonable agreement with the theoretical prediction (Figure 5) after accounting for semiconductor conduction losses and winding resistance.

2.1.3. Contactless Infrared Thermometry and Frequency-Modulated Control

Reliable temperature feedback is essential for stable extrusion, but the unrestricted rotation of the head rules out wired junction sensors (thermocouples/thermistors). Slip rings were considered and rejected because rotating leads and junction are susceptible to electromagnetic interference from the induction field, parasitic heating, and wear.

The adopted solution is a contactless infrared radiation (IR) thermometer MLX90614-DCI (Melexis, Ieper, Belgium) placed on the stationary case at a shallow angle so that its field of view intersects the nozzle tip (Figure 6). This sensor operates from 3.3 V over an I²C/SMBus digital link, reporting object and ambient temperatures. Narrow field of view optics (5°) and an internal chopper provide adequate immunity to the local electromagnetic environment. A two-point calibration (170 °C and 220 °C) against a contact reference established an effective emissivity $\epsilon =0.80$ for the nozzle. After calibration, residual error during static operation was within ±2–3 °C.

Because inductive power is a strong function of inverter frequency, temperature control is implemented using this parameter. For the initial warm-up, the inverter operates near resonance, 68.5–69.7 kHz, providing a large amount of power for rapid transients. Upon reaching the setpoint, the corresponding frequency is stored as $f_{\mathrm{m}}$. Then, closed-loop adjustments control the frequency above $f_{\mathrm{m}}$ with proportional steps to maintain error below $\pm 2°\mathrm{C}$. Low-temperature variations ($\left|\Delta T\right|>5°\mathrm{C}$) trigger a safeguarded fallback (fixed high-power frequency), while overshoot momentarily inhibits drive to prevent runaway. The loop updates every second, filtering the IR signal with a moving average to suppress jitter.

2.1.4. Azimuthally Uniform Layer Cooling

In conventional FFF heads, one or two blowers emit lateral jets toward the nozzle tip. As these jets come from a fixed azimuth, cooling and therefore solidification of the strands depend on its alignment with the air flow. This asymmetry is amplified when using a freely rotating head and a non-circular outlet, because their relative orientation changes continuously.

To avoid cooling directionality effects, the design incorporates an annular layer-cooling shroud (Figure 1). It delivers uniform airflow from the azimuth independently of the yaw angle. The shroud is fixed to the non-rotating portion of the head, surrounds the nozzle and incorporates evenly spaced radial outlets, aiming at the strand just below. A circumferential plenum is internally tapered to compensate pressure drops along the manifold, so that all ports discharge at nearly the same velocity and flow rate. The duct was dimensioned for fabrication by FFF and evaluated via steady-state computational fluid dynamics (SolidWorks Flow Simulation 2022). The inlet condition was set to $80\%$ of a 24 V dc blower nominal flow (5.36 cfm). Simulations (Figure 6b) show matching exit speeds across all ports, which indicate uniform cooling regardless of nozzle yaw. Nevertheless, in the present work, the predicted outlet velocities and flow distribution are obtained from CFD and are not yet supported by dedicated quantitative measurements.

To obtain a rapid, physically intuitive picture of the airflow pattern, a shallow tray of still water was placed directly beneath the stationary nozzle while the blower operated at its nominal printing speed. The water surface acted as a simple flow visualizer: the jets emerging from the annular shroud produced an approximately axisymmetric disturbance on the surface, indicating a nearly uniform circular distribution of cooling air (Figure 6c).

2.2. Synchronized C-Axis Toolpath Control

Generating toolpaths for a continuously rotating, non-circular nozzle introduces new challenges. Control adaptations are experimentally validated with Creality HP PLA filament (Shenzhen Creality 3D Technology Co., Ltd., Shenzhen, China), with a $1.75 \mathrm{m}\mathrm{m}$ nominal diameter.

The first trials updated the nozzle yaw at discrete reference points (segmented “orient” commands), causing intermittent in-place rotations and leading to local over-extrusion and surface artifacts (Figure 7a). To eliminate long gaps in rotations, yaw was incorporated directly into G1 linear moves that drive X–Y motion. In this synchronized scheme, to obtain smooth evolution in orientation throughout the deposition, the C-axis angle ($\theta$) is updated continuously along the arc length ($s$) of each segment. As rotational and translational components are kinematically linked, abrupt yaw changes can perturb the feed rate. Consequently, the incremental yaw was limited to tenths of a degree per planner step, allowing the rotational component to remain negligible with respect to the commanded tool speed.

A further refinement introduced the lead distance ($L_{Lead}$): instead of executing a yaw change exactly at a vertex, the nozzle begins reorientation slightly in advance, interpolating between incoming and outgoing segment angles (Figure 7b). When the space between vertices is shorter than $L_{Lead}$, explicit pre-rotation is skipped, and the yaw is blended with the concurrent X–Y move. This avoids static rotations over a single point and preserves near-constant head velocity on finely segmented or curved paths.

Empirically, the synchronized + lead strategy reduced discontinuities and over-deposition on the strand, with smoother surfaces. Nevertheless, sharp corners and intricate details require adequate $L_{Lead}$ values to prevent residual artifacts, achieving a noticeable quality improvement (Figure 8).

2.3. Practical Considerations

This section summarizes the prototype adjustments and implementation details that improved performance and reliability.

2.3.1. Stable IR Reading

Because the IR sensor is fixed while the nozzle/sleeve rotates, the temperature trace shows periodic oscillations as high as ±6 °C in early builds that vanish when the rotation stops; this is evidence of a systematic, not random, error. True circumferential gradients are unlikely, given inductive-heating symmetry; instead, changing surface is normal within the sensor’s field of view modulate emissivity, producing a cyclic bias. To mitigate this effect, we implemented three modifications: (i) rounding the nozzle outlet edges to prevent glints; (ii) applying a uniform matte-black circumferential coating at the measurement zone and (iii) low-pass filtering the signal ($1\mathrm{H}\mathrm{z}$, five-sample moving average). These measures reduced uncertainty to below ±2 °C and provided stable feedback during the continuous rotation.

2.3.2. Runout and Concentricity

Localized wall defects—lateral offsets between consecutive layers at specific azimuths—were observed in early trials. XY positioning errors can produce similar artifacts; however, inspection of the G-code and motion logs ruled out software or kinematic causes. The most probable mechanism was non-coaxiality between the heat-sink shaft and the nozzle orifice. Measurement of nozzle tip runout with a 0.01 mm resolution dial indicator yielded a total indicated runout of 0.46 mm (orbital radius of 0.23 mm), comparable to the 0.40 mm slot height and therefore sufficient to generate visible offsets. Such a level of runout would be unacceptable in a production system and should be viewed as a limitation of this prototype, rather than as an inherent restriction of the URHE concept. Future iterations will require a stiffer and more accurate rotary assembly, together with tighter control of the nozzle and sleeve geometry, to reduce radial error to the level typically expected from conventional hot ends. Nonetheless, after mechanical correction, confirmation prints were executed, which retained faint misalignments, indicating a residual concentricity error.

A secondary contributor was identified in the outlet geometry: the LPBF-fabricated, nominally rectangular orifice exhibited slight distortion (Figure 3b), consistent with sensitivity to powder size and local sintering conditions, introducing an additional angle-dependent displacement component. To mitigate this, the post-processor records the yaw at the first visit to each XY coordinate and enforces the same yaw on subsequent layers; applied to outer perimeters, this eliminated residual offsets and restored surface fidelity in the validation prints.

2.3.3. Extrusion Temperature

The initial screening showed that the induction-heated hot end delivers stable, defect-free extrusion at the lower bound of temperatures that are commonly reported for PLA in FFF (170 °C) [38], and below typical manufacturer recommendations. Because 170 °C lies above PLA’s typical melting range (150–160 °C) [41], this relatively low setpoint is mainly attributed to an improvement in thermal geometry with closer-to-the-target heat production. Accordingly, 170 °C was adopted as the process standard for all subsequent experiments with the URHE.

3. Materials and Methods

3.1. Materials

Two Cartesian 3D printers (Creality Ender-3, Shenzhen Creality 3D Technology Co, Ltd., Shenzhen, China) were selected for the comparison (Figure 9a). One serves as the reference, using a conventional cartridge-heated hot end with a circular 0.40 mm nozzle (CREALITY hot end). The other supports the proposed induction-heated URHE (Figure 9b) with a 1.20 mm × 0.40 mm rectangular slot. The unmodified printer runs on the original firmware (Marlin), while the modified one runs Duet firmware. The modified printer integrates a Duet 3 6HC, which allows for control of the rotary axis (C-Axis). Aside from the hot end assembly and C-axis hardware, both platforms remain indistinguishable.

Both printers are installed side-by-side to withstand the same ambient temperature, relative humidity and any other environmental condition (Figure 9a). They are also leveled using the same protocol: Z-offsets are adjusted to a common feeler-gauge standard. Additionally, the PLA filament is drawn from the same lot and conditioned identically. In the trials, the same jobs are launched simultaneously for both benchmarks. This twin design isolates the effect of the hot end architecture while holding the slicing, the motion constraints, the environment and the material constant, thereby supporting the consistency of the comparative analysis of time and energy measurements to produce the same parts with different architectures.

3.2. Methods

3.2.1. Time and Energy Comparative Test

Four different geometries are selected to cover a wide range of complexity: three hollow pieces with different shapes and a Moai statuette containing infill (Figure 10).

In every case, the same STL file is duplicated, so the two versions of a given part are dimensionally identical. Process parameters that could bias the total manufacturing time were kept identical: the layer height was fixed at 0.20 mm for the simpler shells and 0.15 mm for the more intricate models, and all hollow parts shared the same wall thickness (1.2 mm).

However, certain parameters of the process are necessarily different. The URHE operates at 170 °C (see Section 2.3.3), while the conventional one requires 210 °C to achieve adequate flow and bonding. Printing speeds could also differ between machines. However, in this case, any of these differences consistently works against the URHE, since its deposition speed is intentionally limited in certain scenarios to ensure process stability. Perimeter speeds are kept identical, ensuring that geometric fidelity and surface finish remain comparable. To avoid any speed-induced bias, the URHE infill was intentionally limited to 25–35 $\mathrm{m}\mathrm{m}·{\mathrm{s}}^{-1}$ (versus 40–60 $\mathrm{m}\mathrm{m}·{\mathrm{s}}^{-1}$ in the reference setup), so differences, where present, are confined to infill speeds. Therefore, no speed-related advantage is introduced that might artificially shorten the manufacturing times of the URHE.

Table 1. Printing configurations for comparison tests.

Geometry	Hot End	Layer Height [mm]	Nozzle Shape	Nozzle Size [mm]	Printing Speed [mm∙s−1]		Temperature [°C]
					Perimeters	Infill	Hot End	Bed
Cylindrical cup	CREALITY	0.2	Circular	0.4	50	50	210	60
	URHE	0.2	Rectangular	1.20 × 0.40	50	25	170	60
Regular vase	CREALITY	0.2	Circular	0.4	50	40	210	60
	URHE	0.2	Rectangular	1.20 × 0.40	50	30	170	60
Twisted vase	CREALITY	0.15	Circular	0.4	60	40	210	60
	URHE	0.15	Rectangular	1.20 × 0.40	60	30	170	60
Moai	CREALITY	0.15	Circular	0.4	60	60	210	60
	URHE	0.15	Rectangular	1.20 × 0.40	60	35	170	60

summarizes the main configuration of the parameters for each part and each printer, highlighting the critical settings.

To track the energy usage of each printer, a consumer-grade Ankrs plug-in power meter [42] records, among other parameters, total energy consumption (kWh) and peak current draw. Operating time is registered with a digital chronometer. For each trial, a single video simultaneously records the kinematic behavior of both printers, the real-time and cumulative energy readings of each power meter, and the total elapsed time from the onset of the job until each machine completes it (Video S1).

3.2.2. Steady-State Hot-End Power Measurement

Hot-end hold power $P_{Hold}$ is measured under static conditions (no filament motion), with the heat-sink fan ON and heat bed OFF. For both heads, setpoints $T_{Set}=170,180,190,200,210,220 °\mathrm{C}$ are commanded. After the temperature first enters $T_{Set}$, the system is allowed to stabilize for $\ge 1 \mathrm{m}\mathrm{i}\mathrm{n}$. Afterwards, $P_{Hold}$ is computed as the mean of a 60 s measurement.

3.2.3. Thermal Transients

Thermal transient tests were defined for both heating and cooling operations. Time-to-setpoint, $t_T$, is defined as the lapse between the moment the order is issued and the moment a given temperature, $T$, is first reached and maintained for more than 1 s. Cool-down time $t_{50}$ is defined as the interval from $T_{set}$ to $50\hspace{0.17em}\mathrm{℃}$, measured at the shroud sensor location with part-cooling off. For this test, the inductive head operates near resonance (68.5–69.7 kHz). Temperature and power are logged at 1 Hz.

3.2.4. Sustained Flow Rate

Maximum sustainable volumetric flow is determined using a straight toolpath $50\hspace{0.17em}\mathrm{m}\mathrm{m}$ in length with a fixed layer height of 0.2 mm. Tests start at $Q=10\hspace{0.17em}{\mathrm{m}\mathrm{m}}^3·{\mathrm{s}}^{-1}$ and increase in $\Delta Q=0.5 \mathrm{m}{\mathrm{m}}^3·{\mathrm{s}}^{-1}$ steps. Acceptance requires no visible gaps, and no feeder “clicks” or missed steps for each $Q$.

4. Results and Discussion

4.1. Manufacturing Time and Energy Comparative Test

Figure 11 presents the eight benchmark parts used for manufacturing time and energy comparison. The observable print quality was comparable within each pair, with surface finish and dimensional integrity preserved across both systems. The most noticeable difference is a visible seam artifact on the parts printed with the URHE (Figure 11b,d). This was anticipated, as the wider strand produced by the rectangular nozzle exaggerates the start–stop overlap, and no dedicated seam-hiding strategy was implemented in this prototype.

In contrast, the peripheral definition was slightly better in the URHE prints for parts with radial symmetry (e.g., the cylindrical cup and regular vase). The URHE-printed twisted vase, however, (Figure 11f) showed a lower surface fidelity than its conventional counterpart (Figure 11e), exhibiting a shallow, rotation-locked waviness along the helical ridges. This texture is consistent with the slot’s directional strand geometry, combined with residual nozzle–axis runout, finite-step yaw interpolation and the characteristics of the torsional geometry.

The results for build time and cumulative energy consumption are summarized in

Table 2. Results of the comparison tests.

Geometry	Extruder Head	Manuf. Time [min]	Time Reduction *	Energy Consumption [Wh]	Energy Savings *	Volume [cm3]	Energy Reduction Per PLA Deposited
Cylindrical cup	CREALITY	47	49%	82	39%	7.3	41%
	URHE	24		50		7.5
Regular vase	CREALITY	88	39%	151	27%	19.7	25.7%
	URHE	54		110		19.3
Twisted vase	CREALITY	271	35%	468	18%	48.7	14.3%
	URHE	175		386		46.9
Moai	CREALITY	54	22%	99	9%	7.3	18.6%
	URHE	42		90		8.1

* Reductions and savings are relative to CREALITY (baseline).

.

Results of manufacturing times show that the URHE achieves a significant reduction. This outcome aligns with expectations and is primarily attributed to the decrease in the number of passes required to deposit the outer shell, thanks to the wider strand extruded by the rectangular nozzle.

The reduction is especially pronounced in parts that do not require infill, reaching a maximum of 49% in the case of the cylindrical cup. Even in the more complex Moai model, which includes internal infill, the build time was reduced by 22%. These time savings translate directly into lower cumulative energy consumption, with reductions ranging from 9% (Moai) to 39% (cylindrical cup).

Overall, the comparative tests demonstrate that the proposed design delivers a substantial reduction in build time and appreciable energy savings, although the magnitude of these benefits varies depending on part geometry and toolpath structure. As expected, the reduction time is much greater in parts that have extensive perimeters and reduced or no infill. After all, the number of passes required to print the perimeters of the parts is reduced by one third, whereas the number of infill passes remains unchanged. While the exact contribution of each subsystem (geometry, heating method, thermal mass) remains coupled in the current design, the results suggest that revisiting URHE can yield gains that are not achievable through isolated parameter tuning. The variation in savings across parts also reinforces the need for geometry-aware optimization, in which nozzle shape, orientation, and thermal response are co-designed for specific toolpath patterns.

To illustrate differences in the overall geometric quality, the vase specimens have been digitized using a handheld laser scanner (FreeScan Combo, SHINING 3D, Hangzhou, China), and the resultant point-clouds are compared with Geomagic Studio 2013 (3D Systems, Rock Hill, SC, USA). Results are presented in Figure 12, where the color-mapped deviation field between the URHE part and the nominal CAD surface (right) shows that, apart from the layer-seam region, where a slightly thicker ridge is visible, the deviation map shows no systematic bulging, flattening or twisting. The average positive deviation is 66 μm, while the negative one is −228 μm, with a standard deviation of 167 μm. These results do not reveal a significant difference between both specimens, even when no specific dimensional calibration has been performed.

Additionally, an illustrative analysis of surface quality differences has been conducted over the vase surface. A small patch has been acquired from each specimen with a ConoScan 4000 conoscopic holography system (Optimet Metrology, Jerusalem, Israel). Then, each digitized surface patch was first fitted with a linear interpolation model in MATLAB R2025b (The MathWorks Inc., Natick, MA, USA), which allows for obtaining the Z coordinate for any X–Y combination within the digitized area. From this model, a Z matrix was generated on a regular X–Y grid and exported in the SPIP format. The resulting point cloud was then loaded into SPIP (Image Metrology A/S, Hørsholm, Denmark), where it was filtered using both an S-filter (to remove high-frequency/short-wavelength noise) and an L-filter (to remove low-frequency/long-wavelength curvature).

Following the common recommendations, the L-filter cutoff was set to 1 mm, approximately five times the wavelength of the coarsest texture of interest (≈0.220 mm), while the S-filter cutoff was set to 0.025 mm, a value greater than three times the capture resolution (0.012 mm), but still low enough to avoid excessive smoothing. After filtering, the areal surface parameters were computed using the processed dataset. Figure 13 shows a comparison between both patches.

The areal roughness parameters for the URHE and reference hot ends are of the same order of magnitude and fall within the range expected for MEX parts printed with a 0.20 mm layer height. The URHE patch shows a slightly higher roughness ($Sa=22.5\mathrm{\mu }\mathrm{m}$, $Sq=27.8\mathrm{\mu }\mathrm{m}$) than the CREALITY patch ($Sa=18.3\mathrm{\mu }\mathrm{m}$, $Sq=22.2\mathrm{\mu }\mathrm{m}$), together with a larger total height $Sz$ (261 µm vs. 189 µm). These differences indicate a moderately rougher surface for the URHE specimen, but in both cases, the overall values are consistent with the expected staircase- and bead-related topography. The skewness and kurtosis ($Ssk\approx -0.13$, $Sku\approx 3.1$ for URHE; $Ssk\approx 0.28$, $Sku\approx 2.6$ for CREALITY) are close to Gaussian in both cases, suggesting a similar texture character with only a slight tendency of the URHE surface toward deeper valleys.

4.2. Steady-State Hot End Power Measurement

Focusing specifically on the power drawn by the hot end in steady state ($P_{Hold}$) confirms that the inductive design delivers a clear energy advantage over the cartridge-heated head throughout the 170–220 °C  window. As Figure 14 shows, the URHE requires only 8.5 W at 170 °C and 12.1 W at 220 °C, whereas the conventional assembly draws 16.1 W and 21 W, respectively. Differences vs. theoretical expectations arise from geometric/thermal boundary simplifications and component losses.

Considering that the URHE employs a reference of 170 °C to provide the best dimensional fidelity and surface finish, while the resistive cartridge requires 210 °C, inductive solution cuts hot end energy consumption by approximately 58% (8.5 W vs. 20.1 W). Nevertheless, the hot end represents just one contributor to the total power draw; motion, bed heating and electronics also consume significant energy.

4.3. Thermal Transients

Thermal transients consume a non-negligible share of a desktop FFF build cycle. On the reference Creality Ender 3 with a resistive cartridge, the nozzle requires an average of $t_{170}=81.3 \mathrm{s}$ to reach 170 °C. The URHE, on the other hand, requires $t_{170}=28.2 \mathrm{s}$. The URHE’s more effective inductive heat delivery cuts warm-up time to about one third of the time required by the resistive cartridge. This reflects the higher heating efficiency of the induction system. Considering that the reference printer demands a 210 °C setpoint to achieve comparable printing consistency, it must be noted that it requires $t_{210}=135.3 \mathrm{s}$, which is $\approx 4.8\times$ longer than the URHE’s warm-up to its corresponding operating setpoint (170 °C).

The cool-down time to 50 °C likewise improves from $t_{50}=120.7 \mathrm{s}$ to $t_{50}=74.4 \mathrm{s}$, consistent with the lower thermal mass of the inductive assembly. For clarity, these non-productive transients are not included in the headline part-level time/energy comparisons in Section 4.1. Nevertheless, they further enhance the process’ productivity by shortening pre- and post-print dwell, thereby improving effective machine throughput.

The lower thermal mass of the URHE reduces thermal inertia [29]. This characteristic, combined with the generation of heat directly in the sleeve, produces faster transients—cutting warm-up and cool-down times by more than half—and thereby slashes the non-productive dwell that brackets every build.

4.4. Sustained Flow Rate

The URHE sustains $Q_{max}=30\hspace{0.17em}{\mathrm{m}\mathrm{m}}^3·{\mathrm{s}}^{-1}$ without observable under-extrusion, filament grinding, or dimensional slumping. Under identical conditions, the reference CREALITY hot end on the baseline printer reaches a practical $Q_{max}$ of $11.5\hspace{0.17em}{\mathrm{m}\mathrm{m}}^3·{\mathrm{s}}^{-1}$, beyond which insufficient melt delivery and intermittent feeder slip produce strand thinning. Crucially, this throughput headroom is not exploited to set the print speeds used in Section 4.1. The $Q_{max}$ comparison is reported here to document scalability and the robustness of melt delivery at elevated flow rates. These $Q_{max}$ values are consistent with Go et al.’s module-level analysis of FFF [28], which identifies conduction heat transfer into the filament core at the heater/nozzle as a primary rate limit; increasing the available heat flux at the hot end (and reducing losses) raises the steady-state volumetric flow ceiling.

Two design features were critical to this performance: the proposed design extends the heater length to 20.5 mm (the equivalent length of the original hot end is 11.5 mm), and the inductive heating deposits energy directly into the AISI 420 sleeve surrounding the filament path, significantly reducing the radial heat-transfer distance.

Conventional guidance favors short melt zones to preserve control during extrusion/retraction, even though longer liquefiers are often linked to higher throughput [21]. In contrast, the URHE shows no loss of start/stop precision and no increase in stringing at high flow. These results indicate that a longer, internally heated melt zone can sustain high volumetric rates without sacrificing quality, challenging the usual hot end heuristics [21]. With the heat source coaxial to the polymer path, the induction sleeve flattens the axial temperature profile and confines thermal inertia largely to the molten polymer, so residence time can be increased without slowing retraction response. Practically, the melt-zone length becomes a tunable parameter for throughput, not a fixed limit from control concerns. A longer channel also reduces the shear rate at a given flow, which may curb thermal/mechanical degradation and expand the window for viscosity-sensitive materials.

More broadly, the data indicate that heating topology—not only power—sets the trade-off between deposition rate and extrusion accuracy. When thermal uniformity and low thermal mass are preserved, extending the melt zone need not compromise deposition control, avoiding the usual escalation to heavier heaters and stiffer motion hardware [28].

4.5. Runout

As previously outlined, any eccentricity or angular misalignment—arising from the tolerances of the nozzle–hot end interface or from an imperfect non-circular outlet—displaces the extrudate from the ideal path that is assumed to lie on the rotational axis. When the head revisits the same XY location at a different yaw angle, this lateral offset accumulates as shifts in the interlayer contours, being perceived as banding and edge waviness. In the present prototype, mitigation by software (enforcing identical yaw at “analogous” XY coordinates across layers) is proposed as a compromise solution, which suppresses visible effects. However, it is true that it does not address the main cause of the problem and that more sophisticated printers should consider accuracy in the design and the manufacturing.

From the experimental tests of this study, minimizing the runout of the nozzle tip could be achieved by tightening the datum scheme and thread stack-up at the sleeve–nozzle–heat-break interface, improving outlet fidelity for LPBF nozzles via post-processing (micro-reaming/lapping) or providing an adjustable concentricity set. A complementary path would be in situ calibration: printing a short diagnostic ring to estimate the eccentricity vector and applying a slicer-level offset map. Implementing these measures would render software workarounds unnecessary and keep printed dimensions closer to nominal while preserving unrestricted rotation.

4.6. Temperature Measurement

Rotation-locked oscillations in the IR signal point to a geometric origin associated with the faceted nozzle tip. To suppress this effect, future designs should replace the local hexagonal flats in the line of sight with a narrow cylindrical band, concentric with the rotation axis, optionally combined with a short baffle to reduce specular glints. The controlled temperature is measured on the nozzle body, rather than directly at the melt exit, so a finite axial gradient between the measurement location and the outlet is expected. In conventional cartridge-heated hot ends, the sensor is typically embedded in the heater block, farther from the nozzle orifice, so the corresponding axial gradient is expected to be even larger than in the present URHE configuration.

In the present prototype, with a single miniature IR sensor integrated in the stationary shroud, operation remained stable over more than 150 h of continuous printing. Nonetheless, single-channel sensing is inherently vulnerable to drift or dropouts. For safety, we also recommend adding redundancy via a secondary independent IR channel, elevating the system from fail-silent to fail-safe without compromising unrestricted C-axis rotation.

4.7. Limitations of This Work

This first assessment of the URHE is subject to several limitations. All experiments were carried out with a single polymer (PLA) on one desktop Cartesian printer, so the quantitative time and energy savings reported here cannot be directly generalized to other materials or machine architectures. In addition, the prototype implementation exhibited prototype-level nozzle runout that had to be mitigated by software compensation; this is not acceptable for a production system and should be regarded as a limitation of the current hardware, rather than of the URHE concept itself.

A further limitation of the present study is that part quality has not yet been assessed in terms of mechanical performance or detailed microstructure. The benchmark geometries were chosen as process demonstrators for time and energy comparisons and are not suitable for standardized mechanical testing, and no cross-sectional analysis of internal porosity or interlayer bonding was performed.

Future work will address these points by testing additional materials and printer platforms and by adopting a mechanically refined rotating assembly with production-grade runout. This will include mechanical testing of appropriately designed specimens to quantify part performance. In addition, if this research is extended to metal/polymer extrusion (MEX/M), microstructural investigations of internal porosity and interlayer bonding will be required to verify that the wider URHE strand does not compromise the structural integrity.

5. Conclusions

The proposed hot end (URHE) replaces the heater block with an induction-heated sleeve, creating a low-inertia, internally heated melt zone; together with tip-aimed IR thermometry and axially uniform cooling, it enables unrestricted C-axis rotation. Employing a PBF-fabricated, interchangeable rectangular-slot nozzle permits wide, low-aspect-ratio strands at a constant layer height, maintaining lateral resolution.

We benchmark the proposed system against a commercial FFF printer by fabricating identical parts and logging build time and energy consumption. Across four representative geometries, the URHE shortens the manufacturing time by up to 49% and reduces plug-level energy up to 39%, relative to a conventional cartridge-heated reference. These part-level savings are underpinned by lower steady hold-power (8.5–12.1 W for 170–220 °C versus 16.1–21.0 W) and substantially faster thermal transients (warm-up and cool-down times reduced by 65.3% and 38.4%, respectively), which further improve effective throughput.

Additionally, the URHE sustained a maximum volumetric flow of 30 mm³ · s⁻¹ without under-extrusion or slumping, versus a practical 11.5 mm³ · s⁻¹ for the baseline platform. This achievement is related to the use of induction heating in a low thermal inertia design, keeping the melt uniform and responsive to retraction and extrusion cycles.

For most parts, the quality was comparable to the reference; the most visible defect was a seam accentuated by the wider rectangular strand. Nevertheless, the surface quality of the twisted vase was clearly worse, showing shallow, rotation-locked waviness on the helical ridges. This effect is plausibly caused by a combination of directional strand geometry, small nozzle–axis runout, finite yaw discretization and the torsional toolpath.

This first assessment is limited to PLA on a single desktop Cartesian printer and a prototype URHE with non-production runout mitigated by software compensation, so the quantitative results should not yet be generalized to other materials or machine architectures. However, the results indicate that the URHE provides a direct path to faster, lower-energy FFF. However, since geometric accuracy is sensitive to runout and outlet fidelity, future work will target mitigation via tighter tolerances and improved outlet finishing. In addition, future efforts will incorporate the development of an advanced toolpath-generation software that is capable of optimizing both perimeter toolpaths and, especially, infill toolpaths. This enhancement is particularly relevant given that, in the present study, these toolpaths were kept fixed. The planned optimization will help to reduce manufacturing time and, consequently, energy consumption, increasing process efficiency without compromising the mechanical properties of the part.

Moreover, beyond PLA and desktop duty cycles, the same heating topology and kinematic freedom are transferable to higher-temperature engineering polymers where cartridge heating is constrained by thermal mass and response. The same architecture merits evaluation in MEX/M, where pairing wide-strand deposition with continuous yaw control may enable step-change gains in the throughput and surface uniformity. Future work will therefore include mechanical testing and microstructural analysis of URHE-printed polymer and metal-filled parts to verify that the wider ribbon does not introduce harmful inner voids and can be exploited for structurally improved infill strategies.