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A new methodology for the optimization of bolt tightening sequences for ring type joints
Ibai Coria, Mikel Abasolo, Imanol Olaskoaga, Arkaitz Etxezarreta, Josu Aguirrebeitia
TL;DR
Uniform bolt load distribution matters for leak-free service, but bolt loads vary during tightening. This work validates EICM for RTJs and develops TAM; it reports highly satisfactory TAM loads and identifies the need for tests on other RTJ geometries.
Problem
Achieving uniform bolt load distribution is critical to leak-free service, while tightening changes the loads in previously tightened bolts.
Source: §1 · p. 1, §4.1 · p. 8Method
The work validates EICM for Ring Type Joints and develops the Tetraparametric Assembly Method, evaluating it against a complete EICM sequence.
Source: §6.3 · p. 16, §7 · p. 20Results
TAM achieved an average load of 198 kN with a standard deviation of 5.1 kN, and its validity is supported by comparison with a complete EICM sequence.
Source: §6.3 · pp. 16, 18Takeaways & Limitations
The reported results support TAM for the RTJ joint studied, while broader validity requires testing other RTJ geometries.
Source: §6.3 · pp. 16, 19Further tests are necessary to prove TAM's validity in other RTJ geometries.
Source: §6.3 · p. 19
Abstract
from arXiv · showhide
Achieving uniform bolt load distribution is critical to obtain leak-free service in pressure vessel gasketed joints used in offshore pipelines. This is a difficult task due to bolt load variations during the assembly process. In this sense, the Elastic Interaction Coefficients Method has been developed in previous works to define tightening sequences that provide the target load at the end of the sequence in one or two passes. The method is very costly because a complete sequence must be simulated and the load of every bolt must be measured after each tightening operation. The present work validates this method for Ring Type Joints and further develops a numerically and experimentally validated new methodology that provides highly satisfactory results with a significantly lower cost.
1. Introduction
Uniform bolt loading is important for leak-free service, but tightening one fastener changes loads in previously tightened bolts, with effects that depend on difficult-to-predict joint and assembly parameters. This work studies sequence optimization for Ring Type Joints, validates EICM for them, and introduces the lower-cost Tetraparametric Assembly Method.
1. Introduction
- Bolt tightening changes loads in previously tightened fasteners, and the resulting variation depends on multiple difficult-to-predict parameters.These include joint geometry and material, load magnitude, bolt spacing, and assembly pattern.Source: §1 · p. 1
- Standards describe indicative, generalist sequences and recommend that assemblers develop sequences suited to their products and working conditions.Uniform gasket stress supports leak-free service of the joint.Source: §1 · pp. 1–2
- Research has sought single- or two-pass sequence optimization, with EICM identified as the most popular method in the specialized literature.The method aims to provide a uniform load distribution at the end of assembly.Source: §1 · p. 2
- The study examines tightening-sequence optimization for metallic-gasketed Ring Type Joints used in high-pressure applications.The gasket is confined in a groove and has two sealing surfaces; its sealing pressure increases with service pressure.Source: §1 · p. 2
- The authors study EICM validity for RTJs and introduce TAM as a significantly lower-cost methodology for RTJ sequence optimization.The work describes the FE model and test bench used for its analyses.Source: §1 · pp. 2–3
2. Joint under study and operational variables
The study uses a 24-inch NPS Class 150 RTJ with SCHD 40 flanges and an R76 octagonal metallic ring gasket. It varies tightening load, assembly pattern, and flange–gasket friction in its analyses.
2. Joint under study and operational variables
- The work studies a Ring Type Joint comprising two 24-inch NPS Class 150 RTJ SCHD 40 flanges and an R76 metallic ring gasket with octagonal profile.The flange material is ASTM A105 steel.Source: §2 · p. 3
- Analyses use tightening loads of 200 kN and 300 kN, approximately 40% and 70% of bolt yield stress, across two assembly patterns.The patterns are illustrated in Fig. 2.Source: §2 · pp. 3–4, Figure 2 · p. 4
3. FE model and test bench
A finite-element model and a test bench support the sequence-optimization analyses and validation. Their final bolt-load results are similar, with average relative errors of 6% and 3.5% in two analyses.
3. FE model and test bench
- The FE model and test bench are used in parallel to optimize sequences and validate the model and results.The model was built in Ansys Workbench; the test bench uses a hydraulic torque wrench.Source: §3 · p. 4
3.1. FE model
- The FE model uses symmetry to represent one flange and half the gasket, with bolt–flange and flange–gasket contacts and bolt pretension sections.Components were meshed with eight-node bricks and ten-node tetrahedrons.Source: §3.1 · p. 4
3.2. Test bench
- Because torque–load measurements have large scatter, the test bench measures bolt loads directly using i-bolt ultrasonic technology.The bench comprises two pipes welded to the bolted flanges, tightened with a hydraulic torque wrench.Source: §3.2 · p. 5
3.3. Validation of the FE model
- FE and experimental final bolt loads were similar, with average relative errors using absolute differences of 6% and 3.5% in the first and second analyses, supporting high-accuracy measurement of bolt load variations.The authors suggest measurement error and short-term relaxation may contribute to the small errors.Source: §3.3 · p. 6
4. Elastic Interaction Coefficients Method (EICM)
The EICM uses matrix [A] to calculate bolt tightening loads for a target uniform final distribution, but obtaining [A] requires simulating the full sequence. The section describes this calculation and notes that nonlinear joint response may require iterative recalculation, before introducing TAM.
4. Elastic Interaction Coefficients Method (EICM)
- The EICM calculates each bolt's tightening load to achieve a target uniform final load distribution in a single pass.The method relates initial and final bolt-load vectors through matrix [A].Source: §4 · p. 7
4.1. Background
- For n bolts, [A] relates initial and final loads, and its inverse gives the initial loads needed for a target final distribution.The loads are represented as vectors, with each bolt numbered in tightening order.Source: §4.1 · p. 8
4.2. Calculation algorithm of matrix [A]
- Calculating [A] requires simulating the full tightening sequence and measuring every bolt's load after each operation; [Sh] stores loads across that sequence.The method derives the interaction coefficients from the stored sequence loads.Source: §4.1 · p. 8, §4.2 · p. 9, §4.3 · p. 10
4.3. Discussion on the method
- The relation assumes linear behavior, but nonlinear gasket materials, changing contact, or large deflections can require iterative calculation of [A], increasing the work.The iterative calculation is intended to suit [A] to the working loads.Source: §4.3 · p. 10
- Analysis of the EICM results led to TAM, a new optimization methodology based on the EICM.The methodology is introduced here for explanation afterward.Source: §4 · p. 7, §4.3 · p. 10
study
FE simulations using EICM-derived initial loads produced near-uniform final distributions for two target loads. The results support EICM for the studied RTJ without iterative calculation of [A].
study
- The FE validation applied EICM-derived initial loads for a 350 kN target with pattern 1 and a 200 kN target with pattern 2.The simulations compared the initial EICM loads with the resulting final loads.Source: study · p. 10
- The EICM gave very satisfactory results for the studied joint without iterative calculation of [A], despite the joint's nonlinear behavior.The validation used FE simulations.Source: study · p. 11
- 347 kN and 200 kN average final loads, with standard deviations of 4.7 kN and 0.4 kN, respectively, accompanied targets of 350 kN (pattern 1) and 200 kN (pattern 2).The paper describes both final distributions as completely uniform.Source: study · p. 10, Figure 7 · p. 11
6. New methodology: Tetraparametric Assembly Method (TAM)
This section presents the Tetraparametric Assembly Method (TAM), which estimates the interaction matrix with two load steps to optimize bolt tightening sequences, and reports accurate final bolt loads in test-bench experiments on the studied Ring Type Joint. Its validation is limited to that geometry and depends on conditions including excessive initial loads and coefficient-calculation accuracy.
6.1. Study of the elements of matrix [A]
- For a given joint, α, β, γ, and δ are practically invariant to load and friction (δ is negligible); tightening patterns change their predictable positions, so [A] can be obtained from one simulation.The coefficients were almost identical for the two load magnitudes and similar across the tested patterns and friction coefficients.Source: §6.1 · pp. 11–12
6.2. Development of the Tetraparametric Assembly Method (TAM)
- For the studied joint, tightening a bolt affects only nearby bolts; more flexible RTJ geometries may need more coefficients, and their validation remains future work.The procedure can be generalized to those more flexible cases.Source: §6.2 · p. 13
- TAM calculates [A] in two load steps: tighten several bolts, then others to create the required load cases and measure the first bolts’ load variations.The first-step load magnitude is not important, though a level similar to the target final load is recommended.Source: §6.2 · pp. 14–15
6.3. Results and discussion
- Initial-load predictions from TAM and EICM had relative errors below 2% for every value, validating TAM.The coefficient values calculated with TAM were also described as very similar to those obtained by simulating the complete sequence with EICM.Source: §6.3 · p. 16
- Different friction coefficients produced about 5% discrepancy in matrix coefficients, but the study found friction had no significant effect on the initial-load results.The initial-load predictions from TAM and EICM remained highly coincident across the reported values.Source: §6.3 · p. 16
- For a 200 kN target, pattern 1 achieved a 207 kN average load with 6.6 kN standard deviation; torque-wrench loads differed slightly from specified values.The authors attribute part of the error to the discrepancy between applied tightening loads and the Fig. 11 values.Source: §6.3 · p. 18, Figure 11 · p. 18
- In the optimization experiment with a 200 kN target load, the star-circular pattern produced an average load of 198 kN (standard deviation 5.1 kN), a highly satisfactory result.Source: §6.3 · pp. 18–19, Figure 12 · p. 19
- Further tests are needed to establish validity for other Ring Type Joint geometries, and excessive initial bolt loads were not considered.If excessive initial loads risk bolt yielding, tightening should use two passes; TAM can calculate the first-pass matrix, while adapting it for the second pass remains under study.Source: §6.3 · p. 19
- Although large bolt loads can locally yield the gasket, this was verified not to materially affect elastic interaction, supporting the elastic-material assumption used for cost efficiency.The two-step analysis used elastic material properties to obtain the TAM coefficients.Source: §6.3 · p. 19
- The experimental results confirm that assuming elastic material in the two-step analysis does not compromise TAM accuracy, but the analysis should be performed experimentally rather than with FEA for greater accuracy.The passage also recommends experimental analysis to obtain accurate α, β, γ, and δ values.Source: §6.3 · pp. 16, 19
7. Conclusions and further research
The Elastic Interaction Coefficients Method (EICM) is costly, while analysis of Ring Type Joints (RTJs) led to a lower-cost method with satisfactory test-bench results. The authors also identify extensions and validation needed to establish its broader application.
7. Conclusions and further research
- EICM is costly because it requires a complete tightening-sequence simulation and repeated measurements, with iterative matrix updates for joints with nonlinear behavior.Each previously loaded bolt must be measured after each tightening operation; iterative updates add cost.Source: §7 · p. 20
- The RTJ matrix composition was almost invariant across load magnitude, friction coefficient, and tightening pattern, motivating the joint-specific Tetraparametric Assembly Method (TAM).The authors describe the matrix as almost invariable regardless of these operational conditions.Source: §7 · p. 20
- TAM used two load steps and few measurements, achieved satisfactory test-bench results for the joint studied, and cost much less than EICM.The method calculates tightening loads with fewer load measurements than EICM.Source: §7 · p. 20
- Further work includes generalizing TAM to two-pass sequences and validating its application range across RTJ nominal sizes, classes, and schedules.The authors report promising tests at different nominal pipe sizes and schedules, while further validation is needed to establish the range.Source: §7 · p. 20
- The authors propose exploring an RTJ matrix library for assembly standardization and adapting the methodology to other bolted joints, including spiral-wound gasketed joints.The spiral-wound gasket is described as more flexible than the flange, so the methodology may need adaptation to represent joint behavior during tightening.Source: §7 · pp. 20–21