# Experimental investigation of the influence of friction, surface roughness and material hardness on the external load factor in threaded joints

## TL;DR

This study experimentally examines how friction, surface roughness, and material hardness affect the load distribution in bolted joints, aiming to optimize joint reliability.

## Contribution

A second-order regression model is developed to quantify the influence of friction, surface roughness, and hardness on the external load factor in threaded joints.

## Key findings

- Material hardness has the strongest influence on the external load factor, with χ decreasing as hardness increases.
- Surface roughness has a nonlinear effect on the external load factor.
- Optimal joint performance is achieved with μ = 0.1809, Ra = 3.5181 μm, and HB = 216.859, yielding a composite desirability of 0.9996.

## Abstract

Threaded joints, particularly bolted joints, are critical components in the design and fabrication of mechanical systems due to their high strength and ease of disassembly. Their widespread application spans across structural engineering, transportation, bridge construction, and industrial machinery. The external load factor (χ), which characterizes the load-sharing behavior between the bolt and the clamped components, plays a vital role in assessing joint performance and reliability. This study presents an experimental investigation into the effects of friction coefficient, surface roughness, and material hardness of the clamped plates on the external load factor in threaded joints. A second-order regression model is developed using the Box–Wilson design method to quantitatively describe the influence of these parameters. The results reveal that all three factors significantly affect χ, with material hardness showing the strongest influence, χ decreases as hardness increases. Surface roughness exhibits a nonlinear effect, while the friction coefficient also has a notable impact. An optimization was carried out to identify the parameter combination that meets the target external load factor of χ = 0.2501. The optimal conditions include a friction coefficient μ = 0.1809, surface roughness Ra = 3.5181 μm, and material hardness of HB = 216.859. The resulting composite desirability of 0.9996 confirms the model’s predictive accuracy and the high reliability of the joint under the specified conditions. These findings allow better design of reliable bolted joints in engineering applications.