Transient multimode heat transfer of an industrial automated tape laying process under rapidly changing conditions

Bernhard Rameder; Hubert Gattringer; Andreas Müller; Ronald Naderer

cs.ROAug 26, 2026

Transient multimode heat transfer of an industrial automated tape laying process under rapidly changing conditions

Authors: Bernhard Rameder, Hubert Gattringer, Andreas Müller, Ronald Naderer

Organizations: Institute of Robotics, Johannes Kepler University Linz, Altenberger Straße 69, 4040 Linz, Austria

Abstract

This work presents a transient heat-transfer model of an industrial automated tape laying (ATL) process designed to overcome the limitations of conventional thermal models in composite manufacturing. The model solves the heat-conduction equation with coupled advection, conduction, convection, and radiation. A key innovation is the implementation of an analytical view factor approach that accounts for finite emitter and tape widths, thereby correcting systematic overestimations of radiative heat flux inherent in 1.5D simplifications. Furthermore, a local convection assessment incorporates mixed convection effects characterized by the Richardson number, ensuring accuracy across a wide range of process speeds. The ATL system is represented by two interacting subsystems: the moving tape substrate and the infrared heat sources. The tape is discretized using a two-node model that resolves the physical phase shift between the heated and monitored surfaces. Numerical stability under high dynamics is ensured by a monolithic solution strategy using a high-order implicit integration scheme. Model predictions were validated on an industrial ATL line, demonstrating an overall deviation of only 1.08% (NRMSE) under rapid velocity and current modulations. This framework provides a high-fidelity, physics-based foundation for thermal state estimation, supporting consistent in-situ consolidation and improved part quality.

Figures & tables

Aspect	Existing ATL Models	Present Model (Novelty)	Advancement / Advantage
Segmented IR Emitter Model	Spatially averaged heat source neglecting non-uniform transient filament dynamics.	Discretized segment-specific emitter power evaluation capturing inrush current dynamics.	Allows precise mapping and resolving of local transient temperature profiles, which directly affects radiation heat exchange.
Finite-Geometry View Factor	Infinite parallel-plate and cylinder assumption or computationally expensive numerical integration.	Analytical view factor formulation specifically tailored for finite geometries.	Eliminates boundary errors and reduces computation time while maintaining high accuracy.
Two-Node Tape Model	Single isothermal node across the tape thickness (bulk temperature approximation).	Computationally efficient two-node thermal laminate model resolving surface-specific temperatures.	Predicts rapid, asymmetric surface-specific temperature gradients of the UD tape with high precision.
Local & Mixed Convection Assessment	Averaged convection coefficients only for forced convection.	Local evaluation and consideration of mixed convection (natural + forced).	Improves local accuracy (nip- and measurement point) and captures heat loss changes even during start-stop cycles.
Monolithic Coupling	Staggered, uncoupled, or sequentially time-lagged solvers for individual heat-transfer modes.	Monolithic solution strategy using a high-order Radau IIA integration scheme.	Eliminates time lags by solving coupled equations simultaneously. Ensures robustness under rapidly changing conditions.

Table 1: Comparison and advancements of the present model against existing ATL process models.

Figure 1: ATL prototype design. (1) Infrared heaters. (2) Temperature sensor. (3) Consolidation roller. (4) Active contact flange (ACF). (5) Tape cutter. (6) Tape feed. (7) Tape guide roller. (8) Tape storage spool.

Figure 2: Heating and consolidation area of the ATL system. (1) Mold. (2) Consolidation roller. (3) Nip point. (4) Tape guide plates. (5) Infrared heaters. (6) Return springs. (7) Tape. (8) Temperature sensors. (9) Domain start. (10) Blade.

Figure 3: Green boxes: Governing heat transfer equations. Blue boxes: Interconnecting coupling heat transport phenomena. Gray boxes: Overall system and numerical solver.

Figure 4: Process model scheme with two infrared heaters. (1) UD tape. (2) Nip point. (3) Tape guide plates (radiation shield). (4) Infrared heater perpendicular to tape. (5) Infrared heater parallel to tape. (6) Convection area inside radiation cavity. (7) Convection area surroundings.

Figure 5: Tape architecture and heat transfer mechanisms.

Figure 6: Heraeus Noblelight Duo Gold infrared heater. (1) Gold reflector. (2) Contact/Mounting wire. (3) Filament coil. (4) Guiding/Distance plates. (5) Quartz glass envelope.

Figure 7: Infrared heater geometry considering a single tube. Discretized in

N_{h}

segments with index

k

. (1) Gold reflector. (2) Contact/Mounting wire. (3) Filament coil. (4) Guiding/Distance plates. (5) Quartz glass envelope. (6) Filament wire in detailed view.

Figure 8: Surface assignment for outer radiation cavity. (3.k, 7.k) Segment

k

of the simplified rectangular heater surface for emitter 1 or 2, respectively. (9) Surrounding surfaces. (10.i) UD tape surface of segment

i

. (

\eta_{1},\eta_{2}

) Blockage factors accounting for geometrical obstruction due to tape guide plates.

Figure 9: Left: Surface assignment for radiation within heater. (1,5) Filament coil surfaces. (2,6) Internal quartz glass surfaces. (3,7) External quartz glass surfaces. (4,8) Internal gold reflector surfaces. [(,…) indicates surface index of second heater] Right: Rectangular emitter simplification.

Figure 10: Geometry basement for view factor calculation of cylindrical surfaces. (1) Concentric cylinders of infinite length. (2) Infinitely long cylinder to interior of a concentric semi-cylinder. (3) Infinitely long semi-cylinder to itself with presence of a concentric, coaxial cylinder. (4) Infinitely long parallel cylinders of same diameter with distance

s

. (

d_{q,e}=2r_{q,e}

d_{r}=2r_{r}

)

Figure 11: Geometry basement for view factor calculation of rectangle to rectangle in a parallel plane.

r

represents a segment of the rectangular simplification of the double-tube geometry shown in Fig. 8 and

t

a segment of the tape.

Figure 12: Geometry basement for view factor calculation of rectangle to rectangle in a perpendicular plane.

r

represents a segment of the rectangular simplification of the double-tube geometry shown in Fig. 8 and

t

a segment of the tape.

Figure 13: Experimental setup with plane test object as mold. (1) Handling robot. (2) Test mold. (3) Automated tape laying system (ATL).

Figure 14: Supply current measurement

i_{e}

during test trajectory.

Figure 15: Tape velocity

v_{T}

during test trajectory.

Figure 16: Temperature simulation at measuring point (MP) and nip point (NP) on both sides of tape during test trajectory.

Figure 17: Simulated

\overline{T}_{m,s}

and measured

T_{m,s,meas}

temperature at measuring point on tape side facing the surroundings during test trajectory.

Figure 18: Absolute and relative error between simulated and measured temperature at specific measuring point.

Figure 19: Spatio-temporal temperature distribution along the tape domain with highlighted profiles $T_{m,s}$ at measuring point (MP) and nip point (NP), including experimental measurement data $T_{m,s,meas}$ at the MP for validation.

Metric	Value	Unit
$max(e_{abs})$	13.52	$\mathrm{\SIUnitSymbolCelsius}$
$max(e_{rel})$	4.19	$\mathrm{\%}$
$RMSE$	4.02	$\mathrm{\SIUnitSymbolCelsius}$
$NRMSE$	1.08	$\mathrm{\%}$

Table 2: Error evaluation compared to measured temperature on tape at surface facing the surroundings.

Figure 20: Filament temperature simulation $T_{f,k}$ and its derivative $\dot{T}_{f,k}$ at each segment $k$ .

Figure 21: Quartz glass temperature simulation $T_{q,k}$ and its derivative $\dot{T}_{q,k}$ at each segment $k$ . MP = Monitoring Point.

Figure 22: Spatial distribution of the line-source power and heat transfer rates along the axial position $z$ of the infrared heater at different time steps according to Eq. 20 . The first subplot displays the sum of all terms, which is the net linear heat rate $q_{f,net}^{\prime}$ .

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