Principle of infrared temperature measurement for plastic laser welding: From radiation physics to process quality control Abstract

In plastic laser transmission welding, infrared temperature measurement serves as a non-contact process monitoring technique whose fundamental principle involves quantitative acquisition of attenuated thermal radiation signals at the weld interface. Based on principles of radiative heat transfer, this study systematically analyzes the relationship between measured temperatures and actual weld temperatures, elucidates the critical role of relative temperature values in quality control during mass production, and establishes a theoretical framework for process monitoring utilizing infrared radiation.

1. The essence of temperature measurement during welding: Is it the temperature of the weld joint?

In laser transmission welding, infrared temperature measurement represents a classic example of passive radiometric temperature measurement. Unlike active methods such as laser interferometric temperature measurement or actively excited thermal temperature measurement, passive temperature measurement does not emit any detection signals toward the target; it merely determines its temperature by detecting the infrared radiation emitted by the target due to thermal motion. The non-invasive nature and rapid response capability of this method make it ideal for online process monitoring, though its physical characteristics also contribute to the complexity of measurement results. In laser plastic transmission welding, the laser beam passes through the upper transparent material and is absorbed at the surface of the underlying absorptive material, where it is converted into thermal energy. The infrared thermometer measures not the traditional "surface temperature," but rather an apparent temperature derived from the interpretation of a composite radiation signal.

1.1 Physical Model: Three-layer Radiation System

The system can be modeled as a three-layer structure:

1. Upper light-transmitting material (temperature T_u, spectral emissivity ε_u(λ))

2. Welding interface (surface of the lower absorbent material; actual temperature T_i; spectral emissivity ε_i(λ))

3. Measuring Environment (Background Radiation)

According to Kirchhoff's law of radiation and Planck's law of black-body radiation, the spectral radiance Lλ reaching the detector at a specific wavelength λ can be expressed as:

Lλ = τu(λ)·εi(λ)·Lλ^bb(T_i) + εu(λ)·Lλ^bb(T_u) + ρu(λ)·Lλ^bb(T_env)

In the formula:

· tu(λ): The spectral transmittance of the upper material at wavelength λ

· εi(λ), εu(λ): Spectral emissivity of the interface and the upper material layer

· Lλ^bb(T): The spectral radiance of a black body at temperature T and wavelength λ (expressed as the Planck function).

· ρ(λ): Spectral reflectivity of the upper material

· Tenv: Ambient Temperature

Key findings: The first term (τ_u(λ) · ε_i(λ) · L_λ^bb(T_i)) contains temperature information of the welding interface but is attenuated; the second term represents the "background noise" radiated by the upper material itself.

1.2 The Physical Meaning of Measuring Temperature

An infrared thermometer measures the integrated radiation within the sensitive wavelength range [λ1, λ2].

E_measured = ∫_{λ1}^{λ2} R(λ)·L_λ dλ

In this formula, R(λ) represents the spectral response function of the detector.

The instrument substitutes EMeasured into the preset emissivity ε_set and solves the inverse Planck equation to obtain the apparent temperature TDisplayed:

E_measured = ∫_{λ1}^{λ2} R(λ)·ε_set·L_λ^bb(T_displayed) dλ

Key conclusion: T_displayed = T_i. It represents a composite characterization value combining the interface temperature attenuation signal, background radiation from the upper material layer, and environmental reflected radiation, and exhibits systematic deviation from the actual solder joint temperature.

2. The comparative relationship between relative temperature values and absolute temperature values

2.1 The Unavailability of Absolute Temperature

In the context of radiation transfer within the translucent medium of plastic welding, accurately determining T_i requires solving the complete radiative transfer equation and precisely knowing how all material optical constants (τ_u(λ), ε_i(λ), ε_u(λ), ρ_u(λ)) vary with temperature and wavelength. This is virtually impossible to achieve in practical applications.

2.2 Stability and Correlation of Relative Temperature

Although the absolute temperature T_displayed equals T_i, under fixed process conditions, the following relationship can be established:

ΔT_displayed / ΔT_i ≈ k (where k is a scaling coefficient, 0 <k <1)

The establishment of this relationship is based on the following assumptions:

1. The material exhibits stable optical properties (batch consistency).

2. Fixed geometric optical path (measured position and angle remain constant)

3. The temperature change of the upper material is much smaller than that of the interface (ΔT_u ≪ ΔT_i).

Engineering significance: The variation trend, peak magnitude, and curve shape of T_displayed exhibit strong correlations with changes in welding heat input. Under stable processing conditions, welding quality parameters (e.g., tensile strength, sealing performance) demonstrate empirical relationships with the characteristic values of T_displayed.

2.3 Quantitative Deviation Analysis

hypothesis ：

· The actual temperature of the interface is Ti = 250°C

· Upper material temperature Tu = 80°C

· The average transmittance of the upper material at the measurement wavelength is τavg = 0.6.

· The emissivity of the upper material is εu = 0.8

· Interface emissivity εi = 0.9

According to the principle of radiation superposition, under the approximation of a narrow band:

L_measured = τ_avg·ε_i·σ·T_i^4 + ε_u·σ·T_u^4

           = 0.6×0.9×5.67×10^-8×(523.15)^4 + 0.8×5.67×10^-8×(353.15)^4

           ≈ 0.54×431.5 + 0.8×88.6

           ≈ 232.9 + 70.9 = 303.8 W/m²

The apparent temperature T_displayed derived from this radiation intensity calculation is approximately 215°C, which is 35°C lower than the actual interface temperature but 135°C higher than that of the upper material layer.

3. Quality control in batch production: Key reference significance

3.1 Temperature Characterization of Process Capability Index Cpk

In statistical process control, welding temperature is considered a critical process parameter. Definition:

Cpk_T = min( (USL - μ_T) / 3σ_T,  (μ_T - LSL) / 3σ_T )

In the formula:

· USL, LSL: Upper and lower temperature control limits (determined based on welding quality)

· μ_T: The average value of T_displayed during mass production

· σ_T: The displayed standard deviation

Quality control logic: Even if the absolute value of T_displayed deviates, as long as its distribution remains stable within the empirically defined quality window [LSL, USL], the welding quality is consistently controlled.

3.2 Multi-parameter Monitoring of Temperature Curves

During mass production, it is essential to monitor not only peak temperatures but also extract multiple characteristic parameters from the temperature curve.

1. Heating rate slope: dT/dt_max, reflecting the heating rate

2. Peak Temperature: T_peak

3. Duration of high temperature: Δt> Tthreshold

4. Cooling Rate: dT/dt_cooling

5. Temperature curve integral: ∫T(t) dt, representing the total heat input

Establishing multivariate control charts (such as the Hotelling T² control chart) enables more sensitive detection of process anomalies.

3.3 Correlation Between Temperature Signals and Welding Defects

Statistical patterns observed in mass production:

4. Advanced temperature measurement technologies: From monochromatic to multispectral

4.1 Principle of Dual-Color (Colorimetric) Temperature Measurement

Measure the ratio of radiation intensity between two adjacent wavelength bands [λ1, λ1+Δλ] and [λ2, λ2+Δλ]:

R = (∫_{λ1}^{λ1+Δλ} L_λ dλ) / (∫_{λ2}^{λ2+Δλ} L_λ dλ)

According to the Wien approximation, when λT ≪ hc/k:

R ≈ (ε_λ1/ε_λ2)·(λ2/λ1)^5·exp[ hc/k·(1/λ2T - 1/λ1T) ]

By measuring R, temperature T can be directly calculated, theoretically independent of the absolute emissivity value. However, in translucent media, the effectiveness of this method depends on whether the transmittance ratio between the upper and lower layers across the two wavelength bands remains stable.

4.2 Active Differential Temperature Measurement Technology

Apply the known modulation thermal disturbance ΔQ and measure the temperature response ΔT_response:

ΔT_response/ΔQ = f (thermal properties of the material, interface contact state)

By analyzing the frequency response characteristics, the thermal resistance at the interface can be determined—a more direct quality indicator than absolute temperature.

5. Recommendations for Engineering Applications

5.1 Calibration Specifications for Temperature Measurement Systems

1. Calibration of material optical constants: For each batch of materials, measure their transmittance spectrum within the operating wavelength range.

2. Temperature-dependent calibration: Establish a correlation between T_displayed and actual welding quality (e.g., tensile strength).

3. Long-term stability validation: Regularly verify the drift of the temperature measurement system using a standard heat source.

5.2 Quality Control Strategies

if (T_peak ∈ [T_low, T_high] and

dT/dt_max ∈ [S_low, S_high] and

Δt_above_Tthreshold > t_min) then

The welding quality meets the required standards.

else

Trigger real-time adjustments (e.g., adjusting laser power) or alarms

end

5.3 Data Fusion and Intelligent Monitoring

Combine infrared temperature measurement data with:

1. Visual data: molten pool morphology, splashing conditions

2. Acoustic emission data: Stress waves during material curing

3. Process Parameters: Real-time values of laser power and welding speed

Establish an early defect prediction model using machine learning algorithms to intervene when temperature anomalies occur before defects form.

Conclusion

Infrared temperature measurement in plastic laser welding fundamentally involves quantitative monitoring of attenuated interface radiation signals. The measured value T_displayed does not represent the absolute temperature at the weld joint, but exhibits a stable correlation with both thermal input during welding and final product quality. In mass production, the stability, repeatability, and trend of this relative temperature value hold greater significance for quality control than its absolute value.

By gaining a deep understanding of radiation transfer physics, establishing scientific calibration methods, and extracting multidimensional characteristics from temperature curves, infrared thermometry can be upgraded from a simple "thermometer" into a comprehensive quality characterization system for welding processes. This not only enables defect detection but also allows adaptive adjustment of process parameters through real-time feedback control, providing the essential physical foundation and data support for achieving zero-defect manufacturing in plastic laser welding.

The future development direction lies in multi-physics field information fusion, integrating infrared temperature measurement with optical coherence tomography to achieve three-dimensional, real-time, quantitative characterization of welding interface morphology and properties, ultimately enabling predictive control of welding quality.