Finite Element Simulation of Steel Tube Drawing Through Chinese-Style Dies

Literature Overview

The paper by Han Baoyun, Jin Ming, and Zhong Qianxia (2000), published in Steel Pipe, Vol. 29, No. 5, pp. 42-46, presents a comprehensive computer finite element simulation study of the steel tube drawing process through Chinese-style dies. Conducted at the Central Iron and Steel Research Institute (now part of the China Iron and Steel Research Institute Group), this research involved 72 simulation runs under various process parameters to develop mathematical models for the major process variables and to analyze the stress and deformation distribution characteristics during the drawing operation.

Process Description and Chinese-Style Die Configuration

The cold drawing of steel tubes through Chinese-style dies is a specialized forming process that differs from conventional drawing through conical or plane dies. The Chinese-style die typically features a specific entry and exit geometry that provides controlled material flow and reduced drawing forces. The process involves pulling a heated or cold steel tube through a die that reduces its outer diameter and/or increases its inner diameter, depending on the presence and position of a mandrel.

The key process parameters investigated in the simulation include:

The 72 simulation runs were designed using a factorial or orthogonal experimental design approach, systematically varying the key parameters to capture their individual and interactive effects on the process outcomes.

Stress and Deformation Analysis

The finite element simulation provides detailed information on the stress and strain state within the tube material during drawing:

1. Equivalent stress distribution: The maximum equivalent stress typically occurs in the die entry region, where the material undergoes the most severe deformation. The stress state is triaxial, with radial compressive stress from the die wall, axial tensile stress from the drawing force, and circumferential (hoop) stress that depends on the presence of a mandrel.
2. Strain distribution: The strain is concentrated in the deformation zone, with the maximum strain occurring at the die exit. The strain distribution through the wall thickness is non-uniform, with higher strain at the outer surface and lower strain at the inner surface (or mandrel contact surface).
3. Material flow: The material flow pattern is influenced by the die geometry and friction conditions. In the absence of a mandrel (free drawing), the material flows inward from both the outer and inner surfaces, resulting in uniform wall thinning. With a mandrel (constrained drawing), the inner surface is constrained, and the material flow is primarily from the outer surface, resulting in more uniform wall thickness.
4. Drawing force prediction: The simulation-derived mathematical models allow for the prediction of drawing force as a function of the process parameters. The force is primarily governed by the deformation resistance of the material, the friction at the die and mandrel interfaces, and the geometry of the die.

Mathematical Models and Process Optimization

The 72 simulations yielded mathematical models for the major process variables, which can be expressed in the form:

• Drawing force: F = f(ε, α, β, μ, D_0, t_0, material properties)
• Wall thickness variation: Δt = f(ε, α, β, μ, t_0, D_0)
• Surface quality index: Q = f(α, β, μ, material surface condition)
• Dimensional accuracy: ΔD = f(ε, α, β, springback, material properties)

These models are valuable for process optimization and for predicting the effects of parameter changes without requiring physical trials. The optimization objective is typically to minimize the drawing force while maintaining acceptable wall thickness uniformity, surface quality, and dimensional accuracy.

Engineering Practice and Quality Control

For engineers involved in steel tube drawing, the simulation results provide several practical guidelines:

• Die design: The entry angle should be kept within the range of 3-7 degrees to balance drawing force and surface quality. Excessively large entry angles increase the drawing force and may cause surface cracking, while excessively small angles reduce the productivity.
• Friction control: The friction coefficient has a significant impact on the drawing force and surface quality. Appropriate lubrication is essential, with the lubricant selected based on the material grade, reduction ratio, and desired surface finish. The lubricant should maintain a stable film thickness throughout the drawing process.
• Reduction ratio limits: The maximum reduction ratio per pass is limited by the material's formability and the risk of defects such as cracking, wrinkling, or excessive thinning. For carbon steel tubes, a reduction ratio of 20-30 percent per pass is typically acceptable, while higher-strength alloys require lower reductions.
• Dimensional control: The simulation predicts the dimensional changes during drawing, including the effects of elastic springback. The die geometry should be designed to compensate for the expected springback, ensuring that the final dimensions fall within the required tolerances.
• Defect prevention: Common defects in tube drawing include transverse cracking, longitudinal cracking, surface roughness, and dimensional non-uniformity. The simulation results help identify the parameter combinations that minimize the risk of each defect type, enabling proactive quality control.

Study Insights and Reflections

This paper represents an early application of finite element simulation to steel tube forming processes, conducted at a time when computational resources were limited and simulation techniques were still maturing. The systematic approach of performing 72 simulation runs to develop mathematical models is methodologically sound and provides a foundation for process optimization. The study highlights the importance of understanding the stress and deformation states within the material, which cannot be directly measured in production but can be inferred from the simulation results. For modern practitioners, this work serves as a historical reference and a demonstration of the value of simulation in process development. The mathematical models derived from the simulations can be incorporated into process control systems to enable real-time monitoring and adjustment of the drawing parameters, improving yield and reducing waste. The study also underscores the need for a deep understanding of the material behavior, die geometry, and friction conditions, all of which interact in complex ways to determine the final product quality.