Filament Winding: Mandrel Kinematics, Winding Angle & Burst Pressure Design

Filament winding produces the highest fibre volume fraction of any composite manufacturing process — and the highest structural efficiency for cylindrical and spherical pressure vessels. CNG (compressed natural gas) cylinders for auto-rickshaws and buses (Type IV CFRP over HDPE liner) are produced by filament winding at Gujarat Filaments, Worthington Industries India, and Shriram Cylinders. GFRP pipes for oil & gas (Fibre Reinforced Plastic pipes — FRP pipes) produced by Amiblu and National Fibre Glass are filament wound. Understanding geodesic winding, netting theory, and burst pressure design is essential.

• Explain the machine kinematics: mandrel rotation, carriage traverse, and winding angle control.
• Calculate winding angle α for given mandrel radius and traverse speed parameters.
• Apply netting analysis (membrane theory) to calculate burst pressure of a cylindrical vessel.
• Distinguish hoop winding (90°), helical winding (15–75°), and geodesic domes.
• Identify ASTM D2105 (axial tensile), ASTM D2290 (hoop tensile — split disk), and IS 12709 standards.

3.1 Machine Kinematics — Winding Angle Control

The winding angle α (measured from the cylinder axis) is controlled by the ratio of carriage traverse speed to mandrel surface speed:

$$\tan \alpha = \frac{v_{traverse}}{v_{surface}} = \frac{v_c}{\pi D_m N}$$

Where: v_c = carriage traverse speed (mm/s), D_m = mandrel diameter (mm), N = mandrel rotation speed (rev/s).

3.2 Netting Analysis — Burst Pressure (Membrane Theory)

For a thin-walled closed-ended cylindrical pressure vessel (internal radius R, wall thickness t):

Hoop (circumferential) stress:

$$\sigma_\theta = \frac{P \cdot R}{t}$$

Axial stress:

$$\sigma_a = \frac{P \cdot R}{2t}$$

For a filament wound cylinder with winding angle α, the fibre stress components:

$$\sigma_\theta^{fibre} = \sigma_f \sin^2 \alpha, \quad \sigma_a^{fibre} = \sigma_f \cos^2 \alpha$$

For axial:hoop stress ratio = 1:2, the optimum winding angle α satisfies:

$$\tan^2 \alpha = \frac{\sigma_\theta}{\sigma_a} = 2 \quad \Rightarrow \alpha = \arctan(\sqrt{2}) = \textbf{54.7°}$$

Burst pressure from netting analysis:

$$P_{burst} = \frac{2 \sigma_f V_f t}{R}$$

3.3 Type IV CNG Cylinder Structure

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Problem: A GFRP filament wound pipe has R = 100 mm, wall t = 8 mm, winding angle ±55°, V_f = 0.65, E-glass fibre strength σ_f = 3450 MPa. Calculate burst pressure from netting analysis.

$$P_{burst} = \frac{2 \sigma_f V_f t}{R} \times \sin^2\alpha$$ $$= \frac{2 \times 3450 \times 0.65 \times 0.008}{0.1} \times \sin^2(55°)$$ $$= \frac{35.88}{0.1} \times (0.819)^2 = 358.8 \times 0.671 = \textbf{240.7 \text{ MPa}}$$

Converting to practical pressure: For a 200 mm diameter pipe (R = 100 mm): P_burst ≈ 241 MPa — far exceeding the 0.1 MPa (10 bar) working pressure of a water distribution pipe. The design safety factor = 241/0.1 = 2410 → highly conservative; indicates that wall thickness of 8 mm for GFRP water pipe is primarily driven by installation stiffness, not burst pressure.

Worthington Industries India (Pune, JV) manufactures Type IV CFRP CNG cylinders for auto-rickshaws and CNG buses under IS 15995. Each cylinder undergoes hydrostatic burst test (proof pressure = 2× working pressure = 400 bar) and fatigue cycling (11,250 cycles at 200 bar per IS 15995).

Amiblu Hobas (formerly Flowtite/Hobas, GRP Pipes India, Vadodara) manufactures filament wound GFRP/polyester pipes (DN 300 to DN 3000) for irrigation and water treatment infrastructure. Pipe stiffness class (SN2500 to SN16000) per ISO 10639 is the primary design criterion for buried pipe applications.

• Winding angle α: Angle from cylinder axis; controlled by traverse/surface speed ratio.
• Optimal angle ±54.7°: Netting theory optimum for closed-end pressure vessels under internal pressure.
• Netting analysis: Fibre-only membrane theory for burst pressure — matrix contributes nothing.
• Hoop stress: σ_θ = PR/t — twice the axial stress in a closed-end cylinder.
• Type IV cylinder: HDPE liner + CFRP filament wound overwrap — lightest CNG storage solution.
• IS 15995: Indian standard for composite CNG cylinder design and testing.

1. ASTM D2105 — Axial tensile properties of reinforced thermosetting plastic pipe
2. ASTM D2290 — Split disk tensile (hoop strength) of plastic pipe
3. IS 15995 — Fully wrapped carbon fibre composite CNG cylinders
4. ISO 11439 — High pressure cylinders for on-board storage of natural gas
5. ISO 10639 — Glass-reinforced thermosetting plastics (GRP) pipes — stiffness testing

1. A mandrel of diameter 300 mm rotates at 2 rev/s. Carriage traverse speed = 18.85 mm/s. Calculate the winding angle α.
2. Why is the optimal winding angle for a closed-end pressure vessel ±54.7° and not 90°?
3. Explain the function of each layer in a Type IV CNG cylinder and why HDPE is chosen for the liner.

Q1. Optimal winding angle for a closed-end pressure vessel is: C) ±54.7° (Netting theory) Q2. Hoop stress in a thin-walled cylinder: A) σ_θ = PR/t Q3. Type IV CNG cylinder uses which liner material? B) HDPE Q4. ASTM D2290 (split disk test) measures: B) Hoop tensile strength of filament wound pipe Q5. Which Indian standard governs CFRP CNG cylinders? C) IS 15995