Experimental investigation and reliability-based optimization of the nut factor in bolted joints considering friction coefficient, surface roughness and material hardness

The nut factor is a critical parameter that defines the relationship between tightening torque and axial preload in bolted joints. Accurate estimation of this coefficient is essential to ensure joint integrity and reliability. This study presents a controlled experimental investigation to evaluate the effects of three key assembly parameters including friction coefficient (μ), surface roughness (Ra), and material hardness (HB) on the nut factor (K). A second-order regression model was developed based on experimental data to describe the nonlinear relationship between these variables. Furthermore, a Reliability-Based Design Optimization (RBDO) approach was employed, integrating Monte Carlo simulation and Genetic Algorithm, to determine the optimal combination of μ, Ra, and HB that minimizes the expected nut factor while ensuring that the probability of remaining within the safe range [0.2, 0.3] exceeds 99.9%. The results demonstrate that the RBDO approach yields a more robust and reliable tightening configuration compared to conventional optimization methods. Sensitivity analysis was also conducted to quantify the relative influence of each input variable on the reliability of the nut factor. The proposed methodology demonstrates the potential applicability of probabilistic optimization approaches for improving torque control and reliability performance of bolted assemblies under uncertainty.