Model-Based Estimation of Clamp Force in Bolted-Joint Tightening

Sammanfattning

Bolted joints are widely used in mechanical assemblies, and their reliability dependsstrongly on the clamp force generated during tightening. Direct measurement ofclamp force in industrial applications is often impractical. Conventional torquebasedtightening methods estimate clamp force by assuming a constant coefficientof friction (CoF). However, the accuracy of this assumption is influenced by surfaceconditions, lubrication, tightening speed, and other factors. Therefore, accurateclamp force estimation remains a challenging problem. Previous Extended KalmanFilter (EKF) and Unscented Kalman Filter (UKF)-based approaches achieved estimationerrors of approximately 3–5%, but were found to be sensitive to initial stateassumptions. In addition, the coupling between clamp force and CoF can producesimilar torque outputs for different state values, resulting in non-unique estimates.This thesis focuses on developing system formulations for tightening in the elasticregion. The main states considered are clamp force and CoF, which are strongly coupledthrough the torque expression. To analyze the resulting non-uniqueness in stateestimation, both local and global observability perspectives are considered. Multipleobserver-based estimation approaches are then evaluated, including an LMI-basedLuenberger observer using an LPV formulation, an output-inverted EKF, and aRao-Blackwellized Particle Filter (RBPF). The EKF and RBPF formulations reducethe dimensionality of the directly estimated state space.The results indicate that the system is theoretically observable from the local observabilityanalysis, but the near-marginal values of the observability matrix suggestlimitations in state estimation. The output-trajectory-based observability studyfurther shows trajectory-dependent regions of practical unobservability, making itdifficult to generalize a single unobservable region across different tightenings. TheLMI-based Luenberger observer was highly sensitive to initial-state errors and reliedstrongly on the motion model, whereas the output-inverted EKF was mainlylimited by derivative-induced noise amplification in the measurement model. TheRBPF provided improved estimations by maintaining multiple hypotheses, but itsperformance depended strongly on both initialization and the nonlinearity of theoutput trajectory. Overall, the study shows that reliable reconstruction of clampforce and CoF is fundamentally constrained by weak observability, low effective CoFcontribution to the measured output, and model mismatch under nonlinear tighteningconditions.