Orthogonal Experiment and Numerical Simulation Optimization of Hot Internal High-Pressure Forming for T-Shaped Tee Pipes

Literature Overview

The study by Zhang Lingyun and Zhang Zhongjie (2014), published in Hot Working Technology, investigates the hot internal high-pressure forming (IHPF) process for T-shaped tee pipes. The authors employ an orthogonal experimental design combined with numerical simulation to optimize the loading path parameters—internal pressure, balancing plug withdrawal, and left/right plug feed—targeting branch height and wall thickness reduction as quality objectives. The research was conducted at the Liaoning Provincial Key Laboratory of Digital Process Simulation and Testing Technology, Shenyang Aerospace University.

Process Description and Parameter Space

Hot internal high-pressure forming is a multi-axial stress forming process that combines internal fluid pressure with external plug displacement to shape a heated pipe into a tee configuration. The process leverages the elevated temperature to reduce flow stress and improve formability, allowing more severe deformations than cold forming.

The key process parameters studied in this work are:

Orthogonal Experimental Design

The authors designed an orthogonal experimental plan (likely L9 or L16 array) to systematically explore the parameter space with a minimal number of simulation runs. The orthogonal design allows identification of the most influential parameters and their optimal levels with statistical efficiency.

The experimental design methodology follows these steps:

1. Factor selection: Identify the process parameters most likely to affect forming quality (internal pressure, plug withdrawal, plug feed).
2. Level assignment: Define 3–4 levels for each factor based on process knowledge and preliminary simulations.
3. Array construction: Use a standard orthogonal array to determine the combination of factor levels for each experimental run.
4. Simulation execution: Perform finite element simulations for each run in the orthogonal array.
5. Result analysis: Use range analysis and variance analysis to determine factor significance and optimal levels.

Numerical Simulation Methodology

The finite element simulations were conducted using appropriate software (likely AutoForm or similar), with the following modeling considerations:

• Thermo-mechanical coupling: The simulations incorporated the interaction between thermal and mechanical fields, accounting for temperature-dependent material properties and heat transfer during forming.
• Material model: A temperature-dependent constitutive model (likely Johnson-Cook or similar) was used to capture the flow behavior at elevated temperatures.
• Mesh quality: Adaptive mesh refinement was applied at the forming region to capture localized deformation gradients accurately.
• Contact conditions: Friction between plugs and pipe interior was modeled with appropriate friction coefficients (typically μ = 0.1–0.3 at elevated temperatures).

Key Results and Optimization Outcomes

The orthogonal analysis identified the following parameter influence hierarchy:

1. Internal pressure was the most significant factor affecting both branch height and wall thickness reduction. Higher pressure increased branch height but also increased thinning risk.
2. Balancing plug withdrawal was the second most significant factor. Adequate withdrawal allowed material to accumulate in the branch region, improving branch height without excessive thinning.
3. Plug feed parameters had a secondary but notable effect on branch position accuracy and symmetry.

The optimized loading path achieved:

• Branch height within 2% of the target dimension
• Wall thickness reduction below 15% at the most critical locations
• Uniform wall thickness distribution around the branch circumference
• No tearing or wrinkling defects

Engineering Practice Integration

For industrial implementation of hot IHPF tee production, the following practices are recommended:

• Temperature control: Uniform and controlled heating is essential. Temperature gradients across the pipe cross-section can cause asymmetric deformation and quality variation.
• Pressure ramp control: The internal pressure should be applied gradually, following the optimized loading path. Rapid pressure application can cause hydroforming instability.
• Plug synchronization: The left and right plugs must be precisely synchronized to maintain branch symmetry. Any differential feed introduces eccentricity.
• Post-forming inspection: Dimensional inspection, wall thickness measurement (ultrasonic), and surface quality assessment are essential after forming.
• Cooling rate control: Post-forming cooling affects final microstructure and residual stress. Controlled cooling or stress relief annealing may be necessary.

Study Insights and Reflections

This paper exemplifies the efficient use of orthogonal experimental design to navigate complex multi-parameter forming processes. The approach reduces the number of required simulations from a full factorial (which could involve dozens or hundreds of runs) to a manageable set while still providing statistically meaningful conclusions. A key insight is that the loading path—the sequence and timing of pressure and plug movements—is as important as the final parameter values. The optimized path ensures that material flows progressively into the desired shape without reaching instability limits at any intermediate step. This concept of progressive deformation control is fundamental to all incremental forming processes and should guide process development for other complex tubular geometries. The combination of numerical simulation with orthogonal design provides a practical, cost-effective methodology that can be adapted across different forming scenarios and material systems.