Theoretical Analysis of Steel Pipe Roll Drawing

Literature Overview

This paper by Jiang Zhengyi, Liu Xianghua, Xie Chunrong, Wang Guodong, and Zhang Qiang from Northeastern University, published in Steel Pipe in 1996, presents a rigorous theoretical analysis of the roll drawing process for steel pipes. The authors derive analytical expressions for the roll drawing force and roll die pressure using mechanics of materials principles, including the mean value theorem of integration and horizontal force equilibrium conditions. The analytical solutions are validated against experimental data, demonstrating good agreement. This work provides a fundamental reference for the calculation and optimization of roll drawing parameters in steel pipe manufacturing.

Roll Drawing Process Characteristics

Roll drawing is a cold forming process used to reduce the diameter and/or wall thickness of steel pipes while maintaining dimensional accuracy and surface quality. Unlike conventional rolling, which uses multiple rolls to deform the pipe, roll drawing employs a set of rolls arranged in a specific configuration to simultaneously reduce the pipe diameter and control the wall thickness.

The key characteristic of roll drawing that distinguishes it from other pipe forming processes is the simultaneous application of radial compression and axial tension. The rolls exert radial pressure to reduce the pipe diameter, while the forward pulling force creates axial tension that drives the deformation. The balance between these two force components determines the process stability and the quality of the final product.

Analytical Derivation of Roll Drawing Force

The authors derive the roll drawing force by considering the force equilibrium of a differential element of the pipe within the roll gap. The key assumptions include:

• The pipe deforms uniformly along the contact arc.
• The friction coefficient between the roll and pipe surface is constant.
• The material follows a power-law hardening model: σ = Kεⁿ.
• The deformation is plane strain in the circumferential direction.

The resulting analytical expression for the roll drawing force is:

F_draw = π × D_mean × t × σ_flow × μ / (1 - μ × tan(α/2))

where:

• D_mean is the mean diameter of the pipe within the roll gap
• t is the wall thickness
• σ_flow is the flow stress at the deformation strain
• μ is the coefficient of friction
• α is the roll gap angle

This expression shows that the drawing force increases with mean diameter, wall thickness, flow stress, and friction coefficient, and decreases with the roll gap angle. The denominator term accounts for the self-locking tendency of the rolls, which becomes more significant at smaller gap angles.

Roll Die Pressure Analysis

The roll die pressure is determined using the mean value theorem of integration combined with the horizontal force equilibrium condition. The authors consider the pressure distribution along the contact arc between the roll and the pipe surface. The pressure is not uniform but varies from a maximum at the entry of the roll gap to a minimum at the exit, following a distribution that can be approximated as:

p(x) = p_max × exp(-μ × x / (R × sin(α)))

where x is the distance along the contact arc, R is the roll radius, and p_max is the maximum pressure at the entry point.

The mean roll die pressure is obtained by integrating this distribution over the contact arc and dividing by the contact length:

p_mean = p_max × (1 - exp(-μ × L_contact / (R × sin(α)))) / (μ × L_contact / (R × sin(α)))

where L_contact is the total contact arc length.

Validation Against Experimental Data

The authors validate their analytical solutions against experimental data obtained from roll drawing tests on carbon steel pipes. The comparison shows that the analytical predictions agree with experimental measurements within 10–15% for most parameter combinations. The largest deviations occur at high reduction ratios (above 6%) and at low rolling speeds (below 10 m/min), where thermal softening effects and strain rate sensitivity become more significant.

Engineering Significance

The analytical framework presented in this paper has direct practical applications in roll drawing process design. Engineers can use the derived expressions to:

• Predict the required motor power for a given reduction ratio and pipe size.
• Optimize the roll gap angle to minimize drawing force while maintaining process stability.
• Estimate the roll die pressure to select appropriate roll materials and surface treatments.
• Determine the maximum feasible reduction ratio before wall thinning or buckling occurs.

The paper also highlights the importance of friction control in roll drawing. The use of appropriate lubricants (typically graphite-based or synthetic emulsions) can reduce the friction coefficient from 0.2–0.3 to 0.1–0.15, resulting in a 15–25% reduction in drawing force and improved surface quality of the drawn pipe.

Reflections and Implications

The theoretical rigor of this paper is commendable, and the analytical expressions remain useful tools for preliminary process design. However, modern roll drawing practice increasingly relies on finite element analysis (FEA) for detailed process simulation, which can capture the non-linearities and three-dimensional effects that analytical methods necessarily simplify. Nevertheless, the analytical approach provides valuable physical insight into the dominant parameters and their interactions, which is essential for developing intuition in process optimization. Engineers should use the analytical framework as a starting point for FEA model development and as a quick-check tool during production trials.