Numerical Simulation of Boiler Serpentine Tube Elbow Die-Bending Forming Process

Literature Overview

This 2017 paper from Shanghai Boiler Works Co., Ltd., published in Energy Research and Information, presents a numerical simulation study of the die-bending forming process for serpentine tube elbows used in large power plant boiler economizers, superheaters, and reheaters. The authors modeled the structural changes, dimensional variations, and residual stress evolution during the die-bending process and validated the numerical model against experimental data. The study provides quantitative insights into how bending angle, deformation rate, and rolling wheel position affect roundness, wall thickness variation, plastic strain, and residual stress distribution.

Serpentine Tube Application Context

Serpentine tubes are extensively used in large power plant boilers as heat transfer elements in economizers, superheaters, and reheaters. These components operate under high-temperature and high-pressure conditions and are subject to cyclic thermal loading that makes them susceptible to low-cycle fatigue and creep damage. The elbows connecting the straight tube sections experience significant plastic deformation during manufacturing, and the resulting residual stress state directly affects the component's fatigue life and long-term reliability. Understanding the forming-induced residual stress distribution is therefore critical for predicting in-service performance.

Numerical Simulation Methodology and Validation

The authors developed a finite element model of the die-bending process that captured the key kinematics of the forming operation, including the rolling wheel deformation mechanism, contact interactions between tooling and tube, and material plasticity behavior. The model was validated against experimental measurements of dimensional accuracy and residual stress, providing confidence in the simulation predictions.

The validation approach is important because numerical models for metal forming are only as good as their underlying material models and boundary condition assumptions. By comparing simulation results with experimental data, the authors demonstrated that the model could reliably predict the key process outcomes: roundness variation, wall thickness change, plastic strain distribution, and residual stress levels.

Key Simulation Results

The simulation results reveal several important process behaviors:

1. Roundness variation: The roundness (ovality) of the elbow increases with bending angle, reaches a peak near 45 degrees, and then decreases at larger angles. This non-monotonic behavior is attributed to the complex interaction between the rolling wheel contact pressure distribution and the progressive geometric change of the tube during bending.
2. Wall thickness variation: The maximum wall thickness change is linearly proportional to the elbow deformation rate. Higher deformation rates (sharper bends relative to tube diameter) produce greater wall thickness variation, which is consistent with the fundamental mechanics of pipe bending where the inner arc experiences compression and the outer arc experiences tension.
3. Plastic strain and residual stress trends: Both plastic strain and residual stress levels decrease overall as the deformation rate decreases. This indicates that gentler bending geometries produce lower forming-induced damage, which has direct implications for fatigue life prediction.
4. Residual stress distribution: The residual stress after bending is more pronounced on the inner surface of the side subjected to rolling wheel compression, while the outer surface exhibits more significant plastic deformation. This asymmetric stress distribution is critical for understanding the subsequent stress state during service.

Engineering Practice Implications

For boiler designers and manufacturing engineers, these simulation results provide actionable guidance for optimizing the serpentine tube elbow forming process. The finding that roundness peaks at approximately 45 degrees of bending suggests that quality control inspections should pay particular attention to elbows with bend angles in this range, as they are most likely to exhibit dimensional deviations. The linear relationship between wall thickness variation and deformation rate implies that the minimum bend radius specification should be set based on the acceptable wall thickness tolerance, which can be directly calculated from the deformation rate.

The residual stress findings have direct implications for post-forming stress relief procedures. The concentration of residual stress on the inner surface of the rolling wheel compression side suggests that stress relief treatments should be designed to effectively reduce compressive residual stresses at this location. For components operating under cyclic thermal loading, the residual stress state interacts with thermal stresses to create a complex multiaxial stress state that can significantly affect fatigue life.

Study Insights

This paper demonstrates the value of numerical simulation as a tool for understanding and optimizing metal forming processes in power plant boiler manufacturing. The integration of simulation with experimental validation provides a rigorous basis for process development that reduces the need for costly physical trials. The specific findings regarding roundness behavior, wall thickness variation, and residual stress distribution provide quantitative data that can be directly incorporated into manufacturing specifications and quality control procedures. For engineers transitioning from empirical process development to simulation-based optimization, this paper provides a clear example of how numerical methods can be applied to practical manufacturing problems in the power generation industry.