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

AI summary

Overview

Research area: Robotics and composite manufacturing process modeling — specifically thermal modeling of an automated tape laying (ATL) process for thermoplastic composites, combining heat transfer physics with numerical simulation.

Technical level: Advanced. The paper formulates coupled partial differential equations for conduction, advection, convection and radiation, uses dimensionless flow analysis (Reynolds, Prandtl, Grashof, Rayleigh and Richardson numbers), and applies an implicit 2-stage Radau IIA integration scheme.

Scope in one sentence: The paper develops and experimentally validates a transient, multimode heat-transfer model that predicts the through-thickness and surface-specific temperature of a moving unidirectional tape heated by infrared emitters under rapidly changing velocity and current conditions.

What This Paper Is About

In the automated tape laying process, a unidirectional tape is heated by infrared emitters and pressed onto a mold at the nip point, and the material must be at the correct bonding temperature at that exact spot. Because the nip point is too confined to measure temperature directly, sensors must sit at a distance — on the opposite side of the tape — so an accurate physics-based model is needed to infer the actual nip point temperature from measured inputs. This paper builds such a model for an industrial ATL platform, capturing all four heat transfer modes plus the electrical-thermal dynamics of the infrared heaters, and validates it against measurements on a real system under fast velocity and current modulations.

Key Contributions

1. Segmented transient infrared emitter model. Instead of treating the heater coil as one averaged homogeneous block, each tube is discretized along its axial direction into N_h segments, capturing the rapid localized heating during the inrush current phase. Because tungsten has a positive temperature coefficient, hotter segments generate more energy until an equilibrium between heat dissipation and energy input is reached.

2. Analytical view factor formulation for finite geometries. The model accounts for the finite width of both the emitter and the tape, correcting the systematic overestimation of radiative heat flux inherent in 1.5D simplifications that assume infinite widths. This captures edge energy losses and gives a deterministic, noise-free irradiance distribution at a fraction of the cost of optical ray tracing.

3. Two-node thermal laminate tape model. The tape is discretized into two layers through its thickness, resolving the physical phase shift between the heated (cavity-facing) surface and the monitored (surroundings-facing) surface. This goes beyond a single lumped isothermal node, which would miss the temperature gradient produced by strongly asymmetric one-sided radiative heating.

4. Local mixed convection and monolithic coupling. Convection is assessed locally through boundary layer development with a transition to mixed convection characterized by the Richardson number, rather than using a single constant forced-convection coefficient. All coupled equations are solved simultaneously with a high-order implicit Radau IIA scheme, eliminating time lags and maintaining numerical stability under extreme parameter fluctuations.

Main Findings

• Validated accuracy of 1.08% NRMSE: The model was validated on a self-developed industrial ATL line by comparing the simulated temperature profile with the measured value at the defined measuring spot, showing an overall deviation of only 1.08% (NRMSE) under rapid velocity and current modulations.

• Through-thickness gradients reach 6 K: Evaluations show a maximum through-thickness temperature difference of ΔT_m,max = 6 K between the measuring-side and nip-side surfaces of the tape.

• Lumped model error can reach ~2%: Relative to the corresponding mean temperature level of 334 K, the error from a pure lumped capacitance treatment is approximately 2% in the specific evaluated case, but the paper states this value can increase depending on prevailing process conditions.

• The tape qualifies as thermally thin, yet one-sided heating breaks the uniform-temperature assumption: The Biot number evaluates to Bi ≈ 0.021 using a conservatively assumed maximum convection coefficient of h_m,max = 50 W m⁻² K⁻¹, falling well below the standard threshold of 0.1 — but the severe one-sided radiative heat input violates the assumption of a completely uniform temperature field, motivating the two-node extension.

• Mixed convection regime confirmed: Evaluating the Richardson number with expected maximum parameters gives Ri ≈ 6.23, identifying the flow regime as combined natural and forced convection rather than purely forced convection.

• Laminar flow confirmed across the operating range: The Reynolds number reaches Re ≈ 658, below the 5 × 10⁵ threshold, and the Rayleigh number reaches Ra ≈ 2.19 × 10⁶, below the 10⁹ threshold, keeping both forced and natural boundary layers laminar.

• Large efficiency gain over ray-tracing/FEM frameworks: Compared with the referenced laser-based ray-tracing/FEM framework of Xu et al. (which required 20 minutes of single-run simulation time for a physical horizon of only a few seconds, and which is bounded to constant velocity regimes and static power settings), the presented formulation requires just 5.8 minutes for an extended process horizon of over 40 seconds.

• Modeled material and geometry: The tape is a unidirectional carbon-fiber-reinforced HDPE tape with fiber volume fraction φ_cf = 0.33, using the Voigt rule-of-mixtures model for the longitudinal conductivity direction and a self-consistent formula for the transverse direction (the latter shown to agree well for moderate fiber contents, φ_cf ≤ 0.5).

• Not reported: The truncated paper content does not report the validation plot values, the specific experimental velocity or current profiles, the number of segments N_x or N_h used in the reported simulations, the tape thickness, or the absolute temperature errors at individual operating points. These would appear in the validation section and supplementary material referenced but not included here.

Methodology in Plain English

The researchers set up the problem on a fixed spatial grid (an Eulerian frame) through which the tape moves, rather than following the tape itself. The process zone runs from where the tape leaves the feeding section to the nip point where it is tacked onto the mold.

For the tape, they start from the transient heat-conduction equation and add an advection term to represent the moving material. Because the tape is thin, the problem is collapsed to one dimension along the direction of motion, and the heat entering and leaving the surfaces is folded into an effective volumetric source. Recognizing that one side of the tape faces the hot infrared emitters while the other faces cooler ambient surroundings, they split the material thickness into two layers coupled by through-thickness conduction, which lets them compute separate temperatures for the cavity-facing and surroundings-facing surfaces and then recover the mean temperature and the surface difference.

For convection, they compute local heat transfer coefficients from boundary layer theory: a Sakiadis correlation for forced convection over a vertically moving thin plate in still air, the Churchill-Chu correlation for natural convection from a vertical plate, and a combined Nusselt number (with exponent n ≈ 3) that blends the two. Whether forced or natural convection dominates is decided by the Richardson number.

For the heat source, they model a Heraeus Noblelight Duo Gold double-tube heater: two quartz-glass tubes each containing a coiled tungsten filament in a noble-gas fill (assumed neon). Each tube is divided into segments along its axis so that the fast inrush current dynamics are captured. Local energy balances are written for the filament control volumes and for the quartz glass envelope, accounting for electrical power dissipation, neon conduction, radiation and convection losses.

Radiation exchange among the tape, heater tubes, guide plates, and housing is handled by a gray-body radiosity/view-factor enclosure model that supplies the net radiative flux to each surface patch. The guiding sheet metal parts are included as radiation shields that reduce the transferred radiant heat — conduction to them is neglected because of the short flyby duration and the constructed gap between the materials. The tape is assumed to move fully vertically to simplify the convection coefficient calculations.

Finally, instead of solving each subsystem in a staggered, time-lagged sequence, all the coupled equations are solved at once using an implicit 2-stage Radau IIA scheme, so current temperatures are used simultaneously to evaluate every heat transfer phenomenon.

Why This Matters

This work sits at the intersection of high-fidelity physics and industrial practicality. Existing ATL thermal models typically rely on constant heat transfer coefficients, spatially averaged heat sources, and infinite-width radiation assumptions, or else they depend on computationally expensive ray tracing that is restricted to constant velocity and static power. The presented framework removes those restrictions while keeping simulation times tractable, which matters because real ATL machines operate in start-stop cycles with rapidly modulated speeds and heater currents.

Real-world applications:

• Aerospace composite structures: The paper notes the aerospace sector seeks high-performance composite parts; a 1% reduction in an aircraft's operating empty weight is cited as translating into roughly a 1% reduction in fuel consumption.
• Automotive lightweighting: A 10% mass reduction is cited as improving fuel economy by 6% to 8%, making accurate thermal control of composite layup directly relevant to vehicle efficiency.
• Defense and other high-performance sectors: The paper names defense alongside aerospace and automotive as industries increasingly seeking these parts to lower overall mass.
• In-situ consolidation of thermoplastic composites: The model provides a physics-based foundation for thermal state estimation, supporting consistent in-situ consolidation and improved part quality at the nip point.

Industry relevance: The authors state that replacing traditional steel with continuous fiber-reinforced polymer composites can enable weight reduction of up to 70%, which is the driving incentive behind processes like ATL. The key industrial constraint is that material-dependent bonding temperatures and pressures must be respected at the nip point, and since that point cannot be measured directly due to space constraints, model-based estimation is the practical route. A validated model with 1.08% NRMSE under rapid modulation is directly usable for process monitoring and control on industrial ATL lines.

Future Directions

• Extension toward computation-time-critical optimization cycles: The authors explicitly note that the two-node through-thickness approach offers advantages for future optimization cycles where computation time is critical, provided the tape is considered thermally thin.
• Broader parameter studies: The paper argues that the efficiency gain over ray-tracing methods is crucial for "conducting extensive parameter studies within a reasonable timeframe," implying such studies as a natural next step.
• Closing the remaining physics gaps: The model assumes the tape moves fully vertically and neglects conduction to the guide plates, even though the real tape has a feed angle and turns around the compaction roller close before the nip point — these simplifications are candidates for refinement.
• Open question on the limits of the mean-temperature treatment: The lumped-capacitance error is only about 2% in the evaluated case but the paper states it "can increase depending on the prevailing process conditions," leaving the boundary conditions under which the simplification breaks down as an open question. The later sections of the paper (validation results, discussion and the Section 5 summary) are not included in the available content, so any further directions stated there are not reported here.

Target Audience

This paper is aimed at researchers and engineers working on thermal modeling and process control for composite manufacturing, particularly those involved with automated tape laying and in-situ consolidation of thermoplastic composites. It is also relevant to robotics researchers interested in model-based estimation for manufacturing equipment, to control engineers who need accurate transient predictions under fast-changing inputs, and to simulation specialists evaluating the trade-off between high-fidelity ray tracing and analytical view-factor approaches. Readers will need a working background in heat transfer and numerical integration to follow the governing equations, though the motivation and the validation result in the introduction are accessible to a broader engineering audience.

Authors’ 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.