Theoretical Calculation and Analysis of Tension Coefficient in Tension Reduction of Seamless Steel Tubes

Literature Overview

The paper by Li Jinshuo and Lv Qinggong, published in the journal Steel Pipe in 2015, presents a theoretical analysis of the tension coefficient in the tension reduction process of seamless steel tubes. The authors derive the plastic deformation equations for tension reduction and propose indicators for longitudinal, radial, and circumferential deformation. The study quantitatively analyzes the influence of the tension coefficient on deformation characteristics and determines the critical tension coefficient as a function of the diameter-to-wall-thickness ratio. The findings are validated through production application examples, demonstrating the practical utility of the theoretical framework.

Plastic Deformation Equations and Deformation Indicators

The tension reduction process involves the simultaneous application of axial tension and radial compression through mandrels, resulting in a complex triaxial stress state within the tube wall. The authors derive the plastic deformation equations based on the Levy-Mises flow rule and the associated flow law, considering the equilibrium of forces in the axial, radial, and circumferential directions. The deformation indicators are defined as the ratios of the respective deformation components to the original dimensions, enabling quantitative comparison of the deformation behavior in different directions.

Critical Tension Coefficient Analysis

The study identifies the critical tension coefficient as the value at which the deformation mode transitions from predominantly diameter reduction to predominantly wall thickness reduction. The critical tension coefficient is shown to depend solely on the diameter-to-wall-thickness ratio (D/t) of the tube. As the D/t ratio increases, the critical tension coefficient also increases, reflecting the greater resistance to diameter reduction in thinner-walled tubes. The theoretical range of the critical tension coefficient is determined to be between 0.35 and 0.50, with the upper bound of 0.50 being a hard limit regardless of the D/t ratio.

The practical implication of this finding is significant for production planning. By knowing the D/t ratio of the input tube, the tension coefficient can be selected to achieve the desired combination of diameter reduction and wall thickness reduction. Exceeding the critical tension coefficient leads to excessive wall thinning, which may violate product specifications and reduce the service life of the tube. Conversely, operating below the critical tension coefficient may result in insufficient diameter reduction, requiring additional processing steps.

Production Application and Engineering Implications

The authors validate the theoretical findings through production application examples, demonstrating that selecting the tension coefficient based on the D/t ratio is both practical and effective. The production examples show that the predicted deformation behavior matches the actual measured dimensions within acceptable tolerances, confirming the accuracy of the theoretical model. The tension coefficient selection provides a straightforward method for process optimization, reducing the need for trial-and-error adjustments in the production line.

From a quality control perspective, the tension coefficient analysis enables the prediction of dimensional deviations and the identification of potential defects such as excessive wall thinning, ovality, and surface cracking. The critical tension coefficient serves as a process control limit, and exceeding this limit should trigger an alarm or automatic adjustment of the tension setting. The D/t ratio should be monitored at the start of each production batch, and the tension coefficient should be adjusted accordingly to maintain consistent product quality.

The theoretical framework developed in this study can be extended to include the effects of material properties, temperature, and strain rate on the deformation behavior. The plastic deformation equations can be modified to account for work hardening, temperature-dependent yield stress, and viscoplastic effects, providing a more comprehensive model for advanced tension reduction processes. The integration of this model with process simulation software would enable virtual process optimization and digital twin implementation for seamless tube production lines.

The research by Li and Lv provides a clear and practical theoretical basis for the selection of tension coefficient in seamless tube production. The direct relationship between the critical tension coefficient and the D/t ratio simplifies the process design and control, reducing the reliance on empirical adjustments. Engineers involved in seamless tube manufacturing should adopt this framework as a reference for process optimization and quality assurance, ensuring that the tension reduction process is operated within the optimal deformation regime for consistent product quality.