insight - Scientific Computing - # Bolted Joint Optimization

Optimizing Gasket Stress Distribution in Bolted Joints Under External Loads Using a Numerical Finite Element Method

Q: Could the reliance on linear interpolation within the algorithm be a limiting factor in accurately capturing the complex non-linear behavior of certain gasket materials under high loads?

Yes, the reliance on linear interpolation within the algorithm could be a limiting factor, especially when dealing with highly non-linear gasket materials under high loads. Here's why: Gasket Material Behavior: Many gasket materials exhibit significant non-linearity in their stress-strain behavior, particularly at high compressive loads. This non-linearity arises from factors like material plasticity, creep, and damage. Contact Mechanics: The contact interface between the gasket and the flange faces is also a source of non-linearity. As the load increases, the contact area changes, and frictional effects become more pronounced. Linear Interpolation Limitations: Linear interpolation assumes a straight-line relationship between variables. When applied to highly non-linear systems, it can lead to significant inaccuracies, especially over large load increments. Potential Refinements: Non-Linear Interpolation: Instead of linear interpolation, explore the use of non-linear interpolation techniques like polynomial interpolation or spline interpolation. These methods can better approximate the non-linear relationships between bolt load and gasket stress. Piecewise Linearization: Divide the load range into smaller segments and use linear interpolation within each segment. This piecewise linearization approach can improve accuracy but increases the computational cost. Iterative Solution with Smaller Increments: Reduce the step size used in the iterative algorithm. Smaller load increments can minimize the errors introduced by linear interpolation. Direct Non-Linear Solution: For highly non-linear cases, consider using a non-linear FEA solver that can directly handle the non-linear material behavior and contact mechanics. This approach provides the highest accuracy but is computationally more expensive. The choice of refinement depends on the degree of non-linearity exhibited by the gasket material, the desired accuracy level, and the available computational resources.

Q: If achieving perfectly uniform gasket stress is not always feasible or necessary, how can this methodology be refined to determine the most efficient bolt load distribution for a desired level of sealing performance?

You are correct that achieving perfectly uniform gasket stress might not always be feasible or strictly necessary. This methodology can be refined to target a desired sealing performance level, which is often a more practical objective. Here's how: Define Sealing Performance Metric: Instead of aiming for uniform gasket stress, establish a specific sealing performance metric as the target. This could be: Minimum Gasket Stress: Define a minimum allowable gasket stress across the entire gasket surface to ensure sufficient sealing pressure. Leakage Rate: Set a maximum permissible leakage rate for the bolted joint under operating conditions. Gasket Stress Variation: Allow a certain degree of variation in gasket stress, as long as it remains within acceptable limits for sealing performance. Modify the Algorithm's Objective Function: The current algorithm aims for a target gasket stress value. Modify this objective function to reflect the chosen sealing performance metric. For example: Minimize Leakage Rate: The algorithm iteratively adjusts bolt loads to minimize the predicted leakage rate based on a leakage model. Constraint Optimization: Set constraints on the minimum gasket stress or gasket stress variation, and the algorithm finds the bolt load distribution that satisfies these constraints. Incorporate Safety Factors: Introduce safety factors into the target sealing performance metric to account for uncertainties in operating conditions, material properties, and the accuracy of the model. Experimental Validation: Validate the refined methodology through experimental testing. Measure the actual sealing performance (e.g., leakage rate) under different bolt load distributions and compare it to the model predictions. By shifting the focus from perfect uniformity to a desired sealing performance level, this methodology becomes more flexible and applicable to a wider range of bolted joint designs and operating conditions.

Core Concepts

A non-uniform bolt load distribution can compensate for external loads in bolted joints, ensuring a uniform gasket stress distribution and preventing leakage failures.

Abstract

Bibliographic Information:

Coria, I., Martín, I., Bouzid, A., Heras, I., & Abasolo, M. (2018). Efficient assembly of bolted joints under external loads using numerical FEM. International Journal of Mechanical Sciences, 142-143, 575–582. https://doi.org/10.1016/j.ijmecsci.2018.05.022

Research Objective:

This paper presents a novel methodology to determine the optimal non-uniform bolt load distribution in bolted flange joints subjected to external axial and bending loads, aiming to achieve a uniform gasket stress distribution and prevent leakage.

Methodology:

The researchers developed a superelement-based Finite Element (FE) model in Ansys® Mechanical APDL to simulate the behavior of a bolted flange joint under external loads. An iterative algorithm, programmed via APDL scripts, calculates the non-uniform bolt load distribution required to achieve a uniform gasket stress distribution, taking into account the target gasket stress value obtained from an ideal assembly simulation without external loads.

Key Findings:

The proposed methodology successfully determined the specific non-uniform bolt load distribution needed to compensate for external loads and achieve a uniform gasket stress distribution. The iterative process, validated against experimental data, demonstrated rapid convergence (within 3 minutes) and high accuracy (1.9% average error compared to conventional FE models).

Main Conclusions:

The study highlights the effectiveness of using a non-uniform bolt load distribution to mitigate the adverse effects of external loads on bolted joints. This approach offers a practical solution for assemblers to ensure the safe and reliable performance of bolted joints in real-world applications, potentially increasing admissible maximum axial and bending loads.

Significance:

This research provides a valuable tool for optimizing the assembly process of bolted joints subjected to external loads, contributing to improved sealing performance, reduced risk of leakage failures, and enhanced safety in various industrial applications, particularly in the oil and gas sector.

Limitations and Future Research:

The study focuses on a specific type of bolted joint and gasket material. Further research could explore the applicability of the methodology to different joint configurations, gasket types, and loading conditions. Investigating the influence of various optimization criteria on the final bolt load distribution and gasket stress uniformity could further enhance the methodology's practicality.

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Stats

Target gasket stress value: 36.4 MPa (±3%).
The iterative process converged in 21 iterations.
The entire iterative process took only 3 minutes.
The average error compared to conventional FE models was only 1.9%.

Quotes

Key Insights Distilled From

Efficient assembly of bolted joints using numerical FEM

by Ibai Coria, ... at arxiv.org 11-06-2024

https://arxiv.org/pdf/2411.02903.pdf

Efficient assembly of bolted joints using numerical FEM

Deeper Inquiries

How could this methodology be adapted for use in real-time monitoring and adjustment of bolt loads during operation, particularly in dynamic loading scenarios?

Adapting this methodology for real-time monitoring and adjustment in dynamic loading scenarios presents a significant engineering challenge. Here's a breakdown of the complexities and potential approaches:
Challenges:

Sensor Integration:  Real-time monitoring necessitates integrating sensors (e.g., strain gauges, ultrasonic sensors) into the bolted joint to measure bolt loads or gasket contact pressure. This integration must be robust and reliable in potentially harsh operating environments.
Dynamic Load Characterization: Dynamic loading scenarios involve fluctuating loads, making it crucial to accurately characterize the load history and frequency content. This information is essential for predicting the bolted joint's response.
Computational Speed: The iterative FEM-based algorithm needs to be significantly accelerated to provide timely adjustments. This might involve model reduction techniques, high-performance computing, or developing computationally less demanding predictive models.
Control System: A sophisticated control system is required to process sensor data, execute the modified algorithm, and command actuators (e.g., hydraulic bolt tensioners) to adjust bolt loads dynamically.
Potential Approaches:

Hybrid Modeling: Combine the FEM-based model with a faster-solving model (e.g., reduced-order model, machine learning model) that captures the essential dynamics of the bolted joint. The FEM model could be used for offline calibration and validation of the faster model.
Adaptive Control Strategies: Implement adaptive control algorithms that continuously adjust bolt loads based on real-time sensor feedback. These algorithms can adapt to changing load conditions and system uncertainties.
Digital Twin Technology: Develop a digital twin of the bolted joint, which is a virtual representation that mirrors the physical asset. The digital twin can be used to simulate different operating scenarios and optimize bolt load adjustments in real-time.

Overall, achieving real-time monitoring and adjustment for dynamic loading requires a multidisciplinary approach involving sensor technology, control systems, advanced modeling techniques, and high-performance computing.

Could the reliance on linear interpolation within the algorithm be a limiting factor in accurately capturing the complex non-linear behavior of certain gasket materials under high loads?

Yes, the reliance on linear interpolation within the algorithm could be a limiting factor, especially when dealing with highly non-linear gasket materials under high loads.
Here's why:

Gasket Material Behavior: Many gasket materials exhibit significant non-linearity in their stress-strain behavior, particularly at high compressive loads. This non-linearity arises from factors like material plasticity, creep, and damage.
Contact Mechanics: The contact interface between the gasket and the flange faces is also a source of non-linearity. As the load increases, the contact area changes, and frictional effects become more pronounced.
Linear Interpolation Limitations: Linear interpolation assumes a straight-line relationship between variables. When applied to highly non-linear systems, it can lead to significant inaccuracies, especially over large load increments.
Potential Refinements:

Non-Linear Interpolation: Instead of linear interpolation, explore the use of non-linear interpolation techniques like polynomial interpolation or spline interpolation. These methods can better approximate the non-linear relationships between bolt load and gasket stress.
Piecewise Linearization: Divide the load range into smaller segments and use linear interpolation within each segment. This piecewise linearization approach can improve accuracy but increases the computational cost.
Iterative Solution with Smaller Increments: Reduce the step size used in the iterative algorithm. Smaller load increments can minimize the errors introduced by linear interpolation.
Direct Non-Linear Solution: For highly non-linear cases, consider using a non-linear FEA solver that can directly handle the non-linear material behavior and contact mechanics. This approach provides the highest accuracy but is computationally more expensive.

The choice of refinement depends on the degree of non-linearity exhibited by the gasket material, the desired accuracy level, and the available computational resources.

If achieving perfectly uniform gasket stress is not always feasible or necessary, how can this methodology be refined to determine the most efficient bolt load distribution for a desired level of sealing performance?

You are correct that achieving perfectly uniform gasket stress might not always be feasible or strictly necessary. This methodology can be refined to target a desired sealing performance level, which is often a more practical objective. Here's how:

Define Sealing Performance Metric: Instead of aiming for uniform gasket stress, establish a specific sealing performance metric as the target. This could be:

Minimum Gasket Stress: Define a minimum allowable gasket stress across the entire gasket surface to ensure sufficient sealing pressure.
Leakage Rate: Set a maximum permissible leakage rate for the bolted joint under operating conditions.
Gasket Stress Variation: Allow a certain degree of variation in gasket stress, as long as it remains within acceptable limits for sealing performance.

Modify the Algorithm's Objective Function:  The current algorithm aims for a target gasket stress value. Modify this objective function to reflect the chosen sealing performance metric. For example:

Minimize Leakage Rate: The algorithm iteratively adjusts bolt loads to minimize the predicted leakage rate based on a leakage model.
Constraint Optimization: Set constraints on the minimum gasket stress or gasket stress variation, and the algorithm finds the bolt load distribution that satisfies these constraints.

Incorporate Safety Factors: Introduce safety factors into the target sealing performance metric to account for uncertainties in operating conditions, material properties, and the accuracy of the model.

Experimental Validation:  Validate the refined methodology through experimental testing. Measure the actual sealing performance (e.g., leakage rate) under different bolt load distributions and compare it to the model predictions.

By shifting the focus from perfect uniformity to a desired sealing performance level, this methodology becomes more flexible and applicable to a wider range of bolted joint designs and operating conditions.