Distortion Simulation and Control in Large Diameter Tube Sheet Surfacing

Literature Overview

The paper by Du Jintao, Pan Xiujuan, Wang Ziwei, and Zhang Jianxiao, published in the Petrochemical Equipment journal (2016, Vol. 45, Issue 6, pp. 61-64), addresses the critical engineering challenge of distortion control during strip electrode surfacing of large diameter bowl-shaped tube sheets. The research was conducted at Lanzhou Lanchi Heavy Equipment Co., Ltd. and the Gansu Provincial Key Laboratory of Pressure Vessel Special Material Welding. The work combines finite element analysis (FEA) with practical process development to achieve acceptable flatness after surfacing, which is essential for the proper sealing and assembly of pressure vessel heads.

Engineering Background

Large diameter bowl-shaped tube sheets are critical components in synthesis reactors and other high-pressure equipment used in the petrochemical industry. These tube sheets are characterized by their large diameter (typically 2000–5000 mm) and relatively thin wall thickness (relative thickness ratio of 2–5%), which makes them particularly susceptible to welding distortion. The surfacing operation, typically performed using strip electrode submerged arc welding (SAW), introduces significant heat input that causes thermal expansion and subsequent contraction, resulting in characteristic "shallow basin" distortion patterns.

The distortion problem is particularly severe because:

• The large diameter creates a high aspect ratio, amplifying the effects of differential thermal expansion
• The bowl shape introduces geometric nonlinearity, causing complex stress and strain distributions
• The relative thinness of the tube sheet reduces its stiffness and resistance to distortion
• The surfacing layer itself adds material to one side, creating an asymmetric thermal and mechanical load
• The flatness requirements for proper gasket sealing are stringent (typically 3–5 mm for large diameter tube sheets)

Finite Element Analysis

Model Development

The authors developed a three-dimensional finite element model of a specific synthesis reactor tube sheet to simulate the distortion during strip electrode surfacing. The model incorporated:

The thermal analysis employed a coupled thermo-mechanical approach, where the temperature field was calculated first using a moving heat source model, and the resulting thermal stresses were then used to compute the mechanical response and distortion. The material properties were defined as temperature-dependent, including elastic modulus, thermal expansion coefficient, yield strength, and thermal conductivity.

Simulation Results

The FEA simulation predicted the distortion distribution across the tube sheet surface:

The distortion pattern is characteristic of "shallow basin" deformation, where the center of the tube sheet deflects upward (toward the surfacing layer) by the maximum amount, and the deflection decreases monotonically toward the edge. This pattern is consistent with the thermal expansion of the surfacing layer and the associated bending moment distribution.

Distortion Control Strategy

Based on the simulation results, the authors proposed and implemented a distortion control strategy based on pre-forming the tube sheet with a convex surface before surfacing. The approach is analogous to the "springback" concept used in sheet metal forming, where the initial geometry is deliberately over-formed to compensate for the expected deformation during welding.

Implementation Details

Process Sequence

1. Pre-forming: The tube sheet is hydraulically formed to introduce a 30 mm convex surface at the center, with the profile following the predicted distortion curve.
2. Surfacing: Strip electrode SAW surfacing is performed in a center-outward spiral pattern, with interpass temperature control to minimize residual stress.
3. Measurement: The flatness of the surfacing layer is measured using a coordinate measuring machine or laser profiler.
4. Flattening: Any remaining distortion is corrected using a hydraulic press, applying uniform pressure across the surfacing surface.
5. Final inspection: The final flatness is verified to ensure compliance with the drawing specification (≤ 5 mm).

Practical Results

The implementation of the distortion control strategy yielded the following results:

• The pre-formed convex surface effectively compensated for the majority of the predicted distortion
• The post-surfacing flatness (before flattening) was reduced to 10–15 mm, compared to the predicted 30 mm without pre-forming
• After hydraulic press flattening, the final flatness was controlled to within 5 mm, meeting the drawing specification
• The surfacing layer quality was maintained, with no cracks, lack of fusion, or other defects observed
• The process was successfully replicated on multiple tube sheets, demonstrating its reproducibility and reliability

Engineering Practice Integration

The approach described in this paper has significant implications for the manufacture of large diameter tube sheets and similar components in the pressure vessel and pipe industry. The combination of FEA-based distortion prediction with pre-forming compensation represents a systematic, engineering-driven approach to distortion control that can be adapted to other large-diameter surfacing applications.

Key Process Considerations

1. FEA model accuracy: The reliability of the distortion prediction depends on the accuracy of the FEA model, including material property data, boundary conditions, and welding heat source characterization. Validation against experimental data is essential.
2. Pre-forming tolerance: The pre-formed convex surface must be controlled within tight tolerances to ensure effective distortion compensation. Hydraulic forming or spinning processes are typically used for this step.
3. Surfacing sequence: The center-outward spiral pattern is critical for minimizing residual stress accumulation and ensuring uniform distortion. Alternative patterns (such as concentric rings) should be evaluated for specific applications.
4. Post-flattening control: The hydraulic press flattening operation must be carefully controlled to avoid excessive plastic deformation or cracking of the surfacing layer. The flattening pressure and rate should be optimized based on the surfacing layer thickness and material properties.

Key Questions and Reflections

The study demonstrates the effectiveness of the pre-forming compensation strategy for controlling distortion in large diameter tube sheet surfacing. However, several questions remain for further investigation. First, the approach relies on accurate FEA predictions, which may not always be available or reliable for complex geometries and material combinations. Second, the pre-forming step adds complexity and cost to the manufacturing process, and its economic justification depends on the value of the component and the severity of the distortion problem. Third, the approach is specific to the bowl-shaped tube sheet geometry and may not be directly applicable to other geometries without significant modification.

The study also raises broader questions about the role of simulation in welding process development. The successful combination of FEA-based prediction with practical process implementation demonstrates the value of simulation as a tool for process optimization and distortion control. However, the reliance on simulation also highlights the need for accurate material property data, validated constitutive models, and experienced engineers to interpret and apply the simulation results.

Study Insights and Implications

This research represents a practical, engineering-driven approach to solving a real-world manufacturing challenge. The key insight is that distortion control in large diameter tube sheet surfacing can be achieved through a combination of FEA-based prediction, pre-forming compensation, and post-flattening correction. The approach is systematic, reproducible, and adaptable to similar applications in the pressure vessel and pipe industry. For engineers involved in the manufacture of large diameter tube sheets, synthesis reactor heads, and similar components, this study provides a valuable framework for distortion control that can be implemented with existing equipment and processes. The successful control of final flatness to within 5 mm, meeting the drawing specification, demonstrates the practical viability of the approach and its potential for industrial application.