The Tightening and Untightening Modeling and Simulation of Bolted Joints
Bibliographic record
Abstract
Although bolted joints may appear simple and are easy to manipulate, they are challenging to model and analyze due to their complex structural patterns and statically indeterminate nature. Ensuring the structural integrity of these joints requires maintaining proper bolt preload and clamping force, which is crucial for preventing failures such as overload, excessive bearing stress, fatigue, and stripping caused by seizing or galling. Achieving the necessary clamping force involves carefully controlling the input tightening torque, which is divided into the pitch torque and the friction torques at the bolt or nut bearing surfaces and in the engaged threads. The resulting clamping force is critical for generating the required force within the bolt. However, the achieved bolt force depends on several factors, such as friction at the joint’s contact surfaces, grip length, and the relative rotation between the bolt and nut during tightening. Friction at the contact surfaces, particularly beneath the bolt head or nut and between the threads, consumes a significant portion of the applied tightening torque—approximately 90%. This paper explores the three existing bolt internal pitch, bearing, and thread friction torques that are generated by the external applied torque in a bolted joint, as well as their contributions and variations throughout a loading cycle composed of three phases: tightening, settling, and untightening. An analytical model is developed to determine these torque components, and its results are compared with those obtained from finite element (FE) modeling and experimental testing from previous studies. Finally, this study examines the torque–tension relationship during bolt tightening, offering insights into the required accuracy of bolt and clamped member stiffness. The bolt samples used in this study include M12 × 1.75 and M36 × 4 hex bolts.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".