Product Surface Quality Control

Reference ID: MET-7E76 | Process Engineering Reference Sheets Calculation Guide

Introduction & Context

In process engineering, the surface quality of extruded products—such as pasta, rubber profiles, or thermoplastic polymers—is governed by the rheological behavior of the melt as it passes through the die land. Surface defects like sharkskin, melt fracture, or matte finishes are typically caused by excessive shear stress at the die wall or elastic memory effects within the material.

This calculation is essential for process optimization, allowing engineers to predict the onset of surface defects before production begins. By balancing the die geometry (length and height) with thermal control and flow rates, engineers can ensure the product remains within the stable processing window, minimizing waste and ensuring consistent surface finish.

Methodology & Formulas

The following methodology calculates the wall shear rate, shear stress, and elastic stability of the melt. The system assumes a slit die geometry where the flow is driven by a constant volumetric flow rate.

1. Shear Rate Calculation

The apparent wall shear rate is first determined based on the slit geometry. For non-Newtonian fluids, this is corrected using the power-law index n:

\[ \dot{\gamma}_{w} = \left( \frac{6 \cdot Q}{W \cdot H^{2}} \right) \cdot \left( \frac{2 \cdot n + 1}{3 \cdot n} \right) \]

2. Viscosity and Shear Stress

The viscosity η is adjusted for temperature using the Arrhenius relationship. The wall shear stress τ_w is then derived from the corrected shear rate:

\[ \eta(T) = m_{\text{ref}} \cdot \dot{\gamma}_{w}^{(n - 1)} \cdot \exp\left[ \frac{E_{a}}{R} \cdot \left( \frac{1}{T_{\text{wall}} + 273.15} - \frac{1}{T_{\text{ref}} + 273.15} \right) \right] \] \[ \tau_{w} = \eta \cdot \dot{\gamma}_{w} \]

3. Residence and Weissenberg Numbers

To account for elastic defects, we calculate the residence time t_res and the Weissenberg number Wi, which indicates the ratio of elastic forces to viscous forces:

\[ t_{\text{res}} = \frac{L}{V_{\text{avg}}} = \frac{L \cdot W \cdot H}{Q} \] \[ Wi = \dot{\gamma}_{w} \cdot \lambda \]

Operational Regimes and Criteria

Parameter	Condition	Engineering Implication
Wall Shear Stress	\(\tau_{w} > \tau_{\text{crit}}\)	High risk of gross melt fracture or sharkskin.
Weissenberg Number	\(Wi > 1\)	Elastic stress accumulation; potential for surface roughness.
Residence Time	\(t_{\text{res}} < \lambda\)	Insufficient time for stress relaxation; high risk of exit defects.
Die Geometry	\(5 < \frac{L}{H} < 80\)	Standard empirical range for stable extrusion land length.

To establish reliable baselines for extrudate surface quality, process engineers should follow these steps:

Use an online optical profilometer or laser scanning system to continuously monitor the extrudate surface during steady-state production.
Perform periodic sampling (e.g., every 30 minutes) and measure Ra and Rz values using a calibrated surface roughness tester on cooled, solidified extrudate samples.
Calculate process capability indices (Cp, Cpk) based on the upper specification limit for surface roughness, ensuring a minimum Cpk of 1.33 for stable production.
Document measurement conditions—line speed, melt temperature, and die temperature—as surface quality varies with processing parameters and must be correlated to operating conditions.
Record the measurement orientation (transverse vs. longitudinal to the extrusion direction) and the profilometer cutoff length to ensure repeatability across different shifts.

Monitoring surface quality degradation caused by die condition is critical for predictive maintenance. Look for the following signs:

A gradual increase in surface roughness (Ra) over production runs as the die land surface wears or micro-scratches develop on the die lips.
Appearance of die lines or continuous streaks parallel to the extrusion direction, caused by material deposits, degraded polymer buildup, or scratches on the die land.
Dimensional changes in the extrudate cross-section (thickness or width) caused by uneven wear or erosion of the die lips.
Increased frequency of sharkskin or melt fracture defects at previously stable operating conditions, indicating that the critical wall shear stress threshold has shifted due to die surface deterioration.
Visible surface haze or gloss variation resulting from changes in the die surface roughness transferring to the extrudate.

Melt temperature uniformity and material consistency directly impact the surface integrity of extruded products. Implement these controls:

Ensure consistent drying of hygroscopic materials (e.g., pasta semolina, engineering polymers) to prevent moisture-induced steam bubbles, surface roughness, or splay marks on the extrudate surface.
Maintain tight temperature control across all barrel zones and the die head; temperature variations alter melt viscosity and can shift the operating point into the melt fracture regime.
Install static mixers or use a gear pump between the screw and die to homogenize melt temperature distribution and dampen pressure pulsations that cause periodic surface defects.
Monitor melt pressure before the die entry; fluctuations in pressure often precede the onset of surface defects and can indicate feeding inconsistencies or temperature control issues.
Verify that the melt temperature remains safely below the material degradation limit (T_max) to prevent thermal decomposition, which generates volatiles and degrades surface finish.

Worked Example: Pasta Dough Extrusion Surface Quality

A rectangular slit die is used to extrude pasta dough. The die land length must be set to avoid sharkskin and melt fracture. The following inputs are given for the process:

Flow rate, \(Q = 500.0\; \text{mm}^3/\text{s}\)
Slit height, \(H = 2.0\; \text{mm}\)
Slit width, \(W = 50.0\; \text{mm}\)
Die land length, \(L = 20.0\; \text{mm}\)
Die wall temperature, \(T_{\text{wall}} = 60.0\; ^{\circ}\text{C}\)
Reference temperature, \(T_{\text{ref}} = 60.0\; ^{\circ}\text{C}\)
Power-law index, \(n = 0.5\)
Consistency index at \(T_{\text{ref}}\), \(m_{\text{ref}} = 20000.0\; \text{Pa}\cdot\text{s}^n\)
Activation energy, \(E_a = 80000.0\; \text{J/mol}\)
Universal gas constant, \(R = 8.314\; \text{J/(mol}\cdot\text{K)}\)
Relaxation time, \(\lambda = 0.5\; \text{s}\)
Critical shear stress, \(\tau_{\text{crit}} = 0.15\; \text{MPa}\)
Degradation temperature limit, \(T_{\text{max}} = 90.0\; ^{\circ}\text{C}\)

The L/H ratio is \(10.0\), which is within the empirical bounds (5–80) and the die temperature is below the degradation limit.

Step A – Compute wall shear rate

First calculate the apparent shear rate for a wide rectangular die:
\[ \dot{\gamma}_{\text{app}} = \frac{6 \cdot Q}{W \cdot H^{2}} = \frac{6 \cdot 500.0}{50.0 \cdot (2.0)^{2}} = 15.0\; \text{s}^{-1} \]
Correct for the power-law behaviour:
\[ \dot{\gamma}_w = \dot{\gamma}_{\text{app}} \cdot \frac{2n+1}{3n} = 15.0 \cdot \frac{2 \cdot 0.5+1}{3 \cdot 0.5} = 20.0\; \text{s}^{-1} \]
Step B – Compute viscosity and shear stress

Since \(T_{\text{wall}} = T_{\text{ref}}\), the Arrhenius shift factor is unity. The viscosity at the wall is:
\[ \eta = m_{\text{ref}} \cdot \dot{\gamma}_w^{\,n-1} = 20000.0 \cdot (20.0)^{0.5-1} = 4472.136\; \text{Pa}\cdot\text{s} \]
The wall shear stress is:
\[ \tau_w = \eta \cdot \dot{\gamma}_w = 4472.136 \cdot 20.0 = 89442.719\; \text{Pa} \]
Convert to MPa:
\[ \tau_w = 0.089\; \text{MPa} \]
Step C – Compare to critical shear stress

The critical shear stress for melt fracture is \(\tau_{\text{crit}} = 0.15\; \text{MPa}\). Since \(\tau_w = 0.089\; \text{MPa}\) is less than \(\tau_{\text{crit}}\), no melt fracture is predicted (fracture_risk = false).
Step D – Check residence time and Weissenberg number

Average velocity in the die:
\[ v_{\text{avg}} = \frac{Q}{W \cdot H} = \frac{500.0}{50.0 \cdot 2.0} = 5.0\; \text{mm/s} \]
Residence time in the die land:
\[ t_{\text{res}} = \frac{L}{v_{\text{avg}}} = \frac{20.0}{5.0} = 4.0\; \text{s} \]
Weissenberg number:
\[ Wi = \dot{\gamma}_w \cdot \lambda = 20.0 \cdot 0.5 = 10.0 \]
Since \(Wi = 10.0\) is much greater than 1.0, the elastic defect risk is true. This indicates high elastic stresses at the die exit, likely causing surface roughness even though the shear stress is below the fracture threshold.

Final Answer:

The calculated wall shear stress (0.089 MPa) is below the empirical critical limit (0.15 MPa), so no gross melt fracture is expected. However, the Weissenberg number (10.0) far exceeds unity, indicating a high risk of surface defects due to insufficient stress relaxation. The residence time (4.0 s) is longer than the relaxation time (0.5 s), but the very large elastic stress still leads to exit distortion.

Recommended actions:

Increase die wall temperature (e.g., to 70–80 °C, staying below 90 °C) to reduce viscosity and relaxation time.
Alternatively, increase land length to \(L = 40.0\; \text{mm}\) (L/H = 20) to allow more time for stress relaxation, though this raises pressure drop.

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle