Quantitative Analysis of Tolerance-Induced Static and Couple Unbalance in Steam Turbine Rotors

Abstract Rotor-system unbalance is a critical factor affecting the vibration performance and operational reliability of steam turbines and is strongly influenced by geometric and assembly tolerances introduced during manufacturing and installation. In blade–rotor systems, tolerance-induced deviations propagate through complex geometric relationships, leading to mass eccentricity and angular misalignment, and ultimately resulting in static and couple unbalance. However, a unified quantitative description linking typical geometric tolerances to rotor unbalance remains limited. In this study, a quantitative tolerance–unbalance transmission framework is developed to investigate the effects of blade and shaft tolerances on rotor unbalance. Based on coordinate transformation, the unbalance contributions of individual blades are mapped into the rotor reference frame, enabling explicit evaluation of static and couple unbalance. The framework is combined with parametric modeling and Monte Carlo simulation to capture stochastic variations in blade mass properties and assembly deviations. Sensitivity and interaction analyses are performed to identify dominant tolerance parameters and coupling mechanisms. The results demonstrate that static and couple unbalance are governed by fundamentally different mechanisms. Static unbalance is primarily controlled by blade-related geometric deviations associated with mass eccentricity, whereas couple unbalance is dominated by assembly clearance tolerance that induces blade tilt and angular misalignment, with significant nonlinear coupling effects among selected tolerances. These findings provide practical guidance for tolerance allocation and vibration-oriented design of turbomachinery rotors.