Thermoforming Process Physics: Plug-Assist & Draw Ratio Optimization

Thermoforming is the primary process used to manufacture thin-walled plastic packaging (cups, trays, lids) and large structural parts (refrigerator liners, vehicle interior panels). Because thermoforming stretches a flat sheet over or into a mould, wall thickness variations are highly dependent on the part's draw ratio. Designing tooling and process parameters, such as vacuum/pressure triggers and plug-assist geometry, is a core skill for packaging engineers at Indian firms like Supreme Industries and packaging converters to minimize raw material usage and prevent thin-corner defects.

• Compare vacuum forming, pressure forming, and plug-assist thermoforming in terms of wall thickness distribution.
• Calculate sheet draw ratio and estimate final part wall thickness.
• Explain the role of sheet temperature uniformity and the polymer processing window (above $T_g$, below $T_m$).
• Identify key thermoforming defects (webbing, chilling, sheet scorching) and their corrective actions.
• Reference international thermoforming standards and guidelines.

3.1 Thermoforming Process Variants

• Vacuum Forming: Sheet is heated, clamped over a mould, and atmospheric vacuum draws it against the tool. High wall thickness at the entry edges; thin at the bottom corners (for female moulds).
• Pressure Forming: Uses compressed air (up to 0.6 MPa) in addition to vacuum. Provides sharper detail and faster cycles.
• Plug-Assist Thermoforming: A mechanical plug pushes the heated sheet into the cavity before vacuum/pressure is applied. This pre-stretches the material, distributing thickness more uniformly to the bottom corners.

3.2 Draw Ratio & Thickness Estimations

The average wall thickness of the thermoformed part ($t_f$) relates to the initial sheet thickness ($t_s$) and the draw ratio ($DR$):

$$\text{Draw Ratio (DR)} = \frac{A_{part}}{A_{sheet}} = \frac{\text{Surface Area of Molded Part}}{\text{Projected Area of Sheet}}$$ $$t_f \approx \frac{t_s}{DR}$$

For a simple rectangular box of length $L$, width $W$, and depth $H$:

$$DR = \frac{L \cdot W + 2H(L + W)}{L \cdot W} = 1 + 2 H \left( \frac{1}{L} + \frac{1}{W} \right)$$

3.3 Sheet Heating and Sintering Mechanics

Thermosheaking polymers are heated using infrared heaters. The sheet must reach a uniform temperature within its rubbery elastic zone: range $T_g < T < T_m$ for semi-crystalline polymers (e.g., PP) and $T_g < T < T_g + 80^\circ$C for amorphous polymers (e.g., PS, ABS). High temperature gradient through-thickness leads to uneven stretching and wrinkling.

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Problem: A rectangular yogurt tub of dimensions $L = 10.0$ cm, $W = 8.0$ cm, and depth $H = 6.0$ cm is thermoformed from a HIPS sheet of thickness $t_s = 1.20$ mm. Calculate:

1. The draw ratio ($DR$) of the part.
2. The estimated average wall thickness ($t_f$) of the finished tub.

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Solution:

1. Calculate the draw ratio $DR$:

$$DR = 1 + 2 H \left( \frac{1}{L} + \frac{1}{W} \right)$$ $$DR = 1 + 2 \times 6.0 \times \left( \frac{1}{10.0} + \frac{1}{8.0} \right) = 1 + 12.0 \times (0.10 + 0.125)$$ $$DR = 1 + 12.0 \times 0.225 = 1 + 2.70 = \textbf{3.70}$$

1. Estimate average wall thickness $t_f$:

$$t_f = \frac{t_s}{DR} = \frac{1.20 \text{ mm}}{3.70} = \textbf{0.324 mm}$$

Interpretation: Due to the area expansion (3.70× area increase), the wall thickness drops from 1.20 mm to an average of 0.324 mm. If plug-assist is not used, the bottom corners will thin to $< 0.10$ mm, causing structural collapse. Tool designers must use a heated syntactic foam plug-assist to distribute material to the base.

Supreme Industries operates packaging plants in India, thermoforming millions of dairy cups and disposable trays daily from PP and polystyrene sheets. They utilize inline extrusion-thermoforming lines where the sheet is formed while still hot from extrusion, saving energy and minimizing cooling shrinkage.

Indian toolrooms design plug-assist shapes using specialized engineering resins (like syntactic polyurethane foam) to prevent sticking and localized chilling of the sheet during pre-stretching.

• Draw Ratio: The ratio of the final part surface area to the original sheet projected area; indicates degree of thinning.
• Plug-Assist: A tool used to pre-stretch a heated polymer sheet into a cavity prior to vacuum/pressure forming.
• HIPS: High Impact Polystyrene; standard material for thermoformed cups due to its wide processing window.
• Webbing: A molding defect forming triangular folds/wrinkles at the corners of a thermoformed part.
• PIAT: (Not applicable, rotomoulding parameter).

1. ISO 294-3 — Injection moulding of test specimens of thermoplastic materials (relevant to sheet extrusion)
2. ASTM D638 — Tensile testing (used to verify oriented sheet properties)
3. SPI Sheet Thermoforming Industry Guidelines and Tolerances

1. Sketch the wall thickness profiles for a female cup mould formed via: (a) straight vacuum forming, and (b) plug-assist vacuum forming. Label the thinnest regions.
2. Explain why semi-crystalline polymers (like Polypropylene) are more difficult to thermoform than amorphous polymers (like HIPS). Reference melting peak sharpness and sag.
3. Calculate the draw ratio of a hemispherical bowl of radius $R = 15$ cm thermoformed from a flat circular sheet.

Q1. Which thermoforming technique is preferred to achieve a uniform wall thickness in deep-draw female cavities?

• B) Plug-assist thermoforming

Q2. The draw ratio ($DR$) of a thermoformed part is defined as the ratio of:

• C) Part surface area to initial sheet projected area

Q3. What is the primary material choice for manufacturing disposable yogurt cups via high-speed thermoforming?

• A) HIPS (High Impact Polystyrene)

Q4. A sheet thermoforming defect characterized by triangular folds at the corners is called:

• B) Webbing

Q5. To thermoform a polymer sheet successfully, the heating temperature must be kept:

• C) Above the glass transition temperature ($T_g$) but below the melting temperature ($T_m$)