SubjectsPolymer CompositesLesson 01 · Filament Winding: Mandrel Kinematics, Winding Angle & Burst Pressure Design
Advanced MaterialsLesson 0119 PPE Syllabus Aligned

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

Filament winding process, geodesic trajectories, hoop vs helical winding angles, Netting Analysis for pressure vessel burst pressure, and mandrel extraction.

~35 min technical deep-dive·Standard Indian Curricula (CIPET / Anna Univ / ICT)

01 · Why This Matters in Industry & GATE XE-F

Applied directly across petrochemical refining, compounding plants, mold-flow simulations, and automotive part manufacturing (e.g., Reliance Industries, Supreme Petrochem, IOCL, CIPET testing protocols).

1

Molecular Mechanism: Master conformational physics, transition temperatures, and reaction kinetics.

2

Process & Quality: Predict viscosity behavior, solve molding defects, and apply ASTM/ISO testing standards.

02 · Technical Theory & Governing Equations

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

Woven carbon fiber fabric prepreg sheets - Visual reference for Filament Winding: Mandrel Kinematics, Winding Angle & Burst Pressure Design
Woven carbon fiber fabric prepreg sheets - Visual reference for Filament Winding: Mandrel Kinematics, Winding Angle & Burst Pressure Design

1. Why This Topic Matters

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.

2. Learning Objectives

  • 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. Core Theory

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⁡α=vtraversevsurface=vcπDmN\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).

Winding Patternα (°)Application
Hoop winding87–90°Maximise hoop strength — pressure vessels
Helical winding15–75°Combined axial + hoop loading
Polar winding5–15°Dome end closures, geodesic paths
Biaxial ±55°±54.7° (optimal)Internal pressure vessels — Netting theory optimum

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:

σθ=P⋅Rt\sigma_\theta = \frac{P \cdot R}{t}

Axial stress:

σa=P⋅R2t\sigma_a = \frac{P \cdot R}{2t}

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

σθfibre=σfsin⁡2α,σafibre=σfcos⁡2α\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⁡2α=σθσa=2⇒α=arctan⁡(2)=54.7°\tan^2 \alpha = \frac{\sigma_\theta}{\sigma_a} = 2 \quad \Rightarrow \alpha = \arctan(\sqrt{2}) = \textbf{54.7°}

Burst pressure from netting analysis:

Pburst=2σfVftRP_{burst} = \frac{2 \sigma_f V_f t}{R}

3.3 Type IV CNG Cylinder Structure

LayerMaterialFunction
LinerHDPE (6–8 mm)Gas-tight barrier — permeation resistance
Hoop overwrapCFRP ±90°Hoop burst pressure containment
Helical overwrapCFRP ±55°Axial loads, dome stress, impact
Protective layerGFRP or polyester veilUV, impact protection

4. Worked Example

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.

Pburst=2σfVftR×sin⁡2αP_{burst} = \frac{2 \sigma_f V_f t}{R} \times \sin^2\alpha =2×3450×0.65×0.0080.1×sin⁡2(55°)= \frac{2 \times 3450 \times 0.65 \times 0.008}{0.1} \times \sin^2(55°) =35.880.1×(0.819)2=358.8×0.671=240.7  MPa= \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.

5. Indian Industry Context

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.

6. Key Takeaways & Glossary

  • 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.

7. Standards Reference

  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

8. Practice Questions

  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.

9. Quiz

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

Filament Winding: Mandrel Kinematics, Winding Angle & Burst Pressure Design · Engineering Triad

Material Synthesis · Processing Hardware · Commercial Application

ASTM / ISO Aligned
1. MaterialResin / Chemistry

Standard Engineering Thermoplastic Resin

—[Monomer Backbone]ₙ— (Calibrated Molecular Weight & PDI)

Specific Gravity:1.05–1.42 g/cm³
Glass Transition (Tg):100–160 °C
Tensile Yield Strength:45–85 MPa
Melt Flow Index:5–25 g/10min
Morphology: Engineered Polymer Morphology (Amorphous / Semi-crystalline Matrix)
2. Machine & MouldShop Floor

Industrial Polymer Processing & Tooling System

Computer-Controlled Extrusion / Injection Moulding Hardware

Thermal Zones:180–280 °C (PID Controlled)
Injection / Melt Pressure:60–140 MPa
Cycle Time:15–45 seconds
Tooling Temperature:40–90 °C (Chiller Regulated)
Tooling: Hardened Tool Steel (H13/P20) Precision Cavity & Runner Layout
3. Real ProductApplication

Commercial Engineering Parts & Quality-Inspected Components

Automotive, Electrical, Medical & Packaging Applications

Standard:ASTM D3641 / ISO 294 / BIS Standard Compliance
Resin Grades: Reliance, SABIC, BASF, Covestro Standard Engineering Resins
Section 05 · Knowledge Check

Test Your Conceptual Understanding

In polymer science and processing thermodynamics, which factor most directly controls the critical transition temperature?

Select the correct option to verifyTake Complete Topic Assessment →
Summary Cheat Sheet & GATE Takeaways
  • Always evaluate molecular weight distribution (MWD) alongside zero-shear viscosity when calculating mold shear rates.
  • Differential Scanning Calorimetry (DSC) provides $T_g$, $T_c$, and $T_m$ to define optimal processing temperatures.
  • Comply with ASTM D638 / ISO 527 tensile specimen sizing to prevent premature necking artifacts.
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