Analysis of Wrinkling Mechanism in High-Pass Cold-Drawing of Steel Tubes

Literature Overview

The paper by Zhang Qichang and colleagues, published in the Journal of Tianjin University in 2005, addresses a persistent quality problem encountered in the multi-pass cold-drawing production of steel tubes: the formation of surface wrinkles, known as "douwen" or chattering marks. These wrinkles appear on the inner surface of the tube and are particularly problematic in high-pass drawing operations where the tube undergoes repeated deformation through successive dies. The authors propose a nonlinear dynamic model for the drawing process using a conical die and a short plug, and employ nonlinear dynamical systems theory to investigate the root cause of wrinkle generation. This work was supported by the Tianjin Natural Science Foundation (Grant No. 023615411).

Core Technical Viewpoints

The central thesis of the paper is that wrinkles in cold-drawn steel tubes are not caused by random process disturbances but are the result of a deterministic self-excited oscillation of the drawing plug, triggered by a Hopf bifurcation in the nonlinear dynamic system governing the drawing process. The authors identify the dry friction force at the inner surface of the tube as the fundamental cause of the plug's self-excited vibration. When the drawing speed reaches a critical threshold value, the plug begins to oscillate, and the amplitude of this oscillation is directly proportional to the length of the plug. In high-pass drawing, where the plug is necessarily longer to accommodate the accumulated material deformation, the oscillation amplitude becomes large enough to imprint visible wrinkles on the tube's inner surface.

Interpretation of Technical Points

The nonlinear dynamic model developed in this study treats the plug as a dynamically loaded component within the drawing system. The key insight is the identification of the Hopf bifurcation point as the critical condition under which the plug transitions from stable operation to self-excited oscillation. This is a fundamental concept from nonlinear dynamics: at the bifurcation point, a pair of complex conjugate eigenvalues of the system's Jacobian matrix crosses the imaginary axis, leading to the emergence of a stable limit cycle.

The authors further analyze how the process parameters of the drawing system influence the position of the Hopf bifurcation critical point. Specifically, the drawing speed is identified as the primary control variable: below the critical speed, the plug operates in a stable regime, but once the speed exceeds this threshold, the system enters an oscillatory state. The amplitude of the resulting limit cycle oscillation scales linearly with the plug length, which explains why high-pass drawing operations are far more susceptible to wrinkle defects than single-pass or low-pass operations.

Process Analysis and Engineering Countermeasures

The proposed solution in the paper is the use of a novel hollow plug design that allows supplemental lubricant to be delivered directly to the inner surface of the tube during drawing. This approach fundamentally addresses the root cause of the problem by modifying the friction condition at the plug-tube interface. By reducing the dry friction coefficient, the energy input mechanism for the self-excited oscillation is eliminated, and the Hopf bifurcation condition is never satisfied.

From an engineering practice perspective, this finding has significant implications for cold-drawing process optimization. Traditional approaches to wrinkle prevention have focused on reducing drawing speed, shortening plug length, or applying surface treatments to the tube blank. While these measures can shift the Hopf bifurcation critical point to a higher speed threshold, they do not address the underlying mechanism and are often constrained by production requirements. The hollow plug lubrication method offers a more systematic solution.

Study Insights and Implications

This paper is a valuable example of applying nonlinear dynamics theory to a practical manufacturing problem. The identification of Hopf bifurcation as the mechanism behind wrinkle formation provides a rigorous theoretical framework for process optimization. For engineers involved in cold-drawing operations, the key takeaway is that wrinkles should not be treated as random quality variations but as deterministic phenomena governed by well-defined dynamic instability conditions. Process control strategies should therefore focus on keeping the operating point safely below the bifurcation threshold, either by controlling drawing speed or by modifying the friction condition through improved lubrication.

The concept of self-excited vibration in drawing processes is also relevant to other tube forming operations, including cold-rolling, hydroforming, and tube bending, where similar friction-driven instabilities may occur. Engineers should be aware that any process involving sliding contact between tooling and workpiece under high pressure is potentially susceptible to Hopf bifurcation and should be evaluated for dynamic stability before full-scale production.