The stability of the output speed of a hydraulic system has a great influence on the working performance of hydraulic equipment. It changes with the system working conditions. The increase in leakage caused by the wear of the hydraulic kinematic pair and the slip of the motor lead to the instability of the output speed. Although the hydraulic system can satisfy the output requirements of the active control scheme with ex ante decision making or the passive feedback control strategy with ex post compensation, it also causes an increase in system complexity and manufacturing cost. The speed stiffness as a basic characteristic of the output of the hydraulic system has not been sufficiently investigated and evaluated. In this paper, the IFMDH (inverter-fed, motor-driven hydraulic) system is taken as the object, and the coupling relationship of each link of the system is revealed by mathematical modelling. The reliability of the model is verified under a wide range of speed and load variations in combination with experiments. By redefining the speed stiffness quantification method, the effects of load conditions, motor stiffness, and speed ratio at the output end on the speed stability of the system are discussed in conjunction with the system coupling mechanism model. The conclusions show that the motor stiffness and the addition of a speed reducer have a significant effect on the system speed stiffness, where changing the output speed ratio has a significant effect on the speed stiffness. The conclusions of the study provide technical support for the rapid design, selection, and system optimisation of hydraulic systems in common scenarios.

Purpose—The flexspline of a harmonic drive constitutes a thin-walled structure with discontinuous gear rim and cylinder configuration, where cyclic stresses induce stress concentration, followed by crack initiation, propagation, and ultimately fatigue failure. This paper reviews advancements in understanding its mechanical properties and fatigue failure mechanisms, aiming to establish a foundation for enhancing operational longevity and guiding future research. Design/Methodology/Approach—The study integrates meshing theory, tooth shape parameters, cylinder stress influencers, and assembly/meshing stress considerations. Theoretical analysis, finite element simulations, and experimental methods are employed to examine stress patterns and fatigue dynamics. Structural parameters and tooth profiles are systematically analyzed for their impact on stress distribution and fatigue life. Findings—Flexspline fatigue failure arises from tooth root stress concentration and cylinder bending stress accumulation. The double-circular-arc tooth profile boosts load capacity by 35% relative to the involute profile, yet demands high-precision machining to preserve meshing performance. Increasing cylinder length mitigates stress concentration but reduces torsional stiffness, while optimized root fillet radii can lower the stress concentration coefficient by 28%. Assembly interference and meshing contact stress accelerate crack initiation, as validated by transient dynamics simulations. Surface strengthening processes (e.g., shot peening) enhance fatigue life by up to 66% through residual compressive stress regulation. Originality/Value—This paper synthesizes multi-scale research on flexspline design, structural optimization, and fatigue mechanisms, proposing novel approaches such as “manufacturability-oriented optimization” and digital twin-driven monitoring. By linking dynamic loads, material properties, and geometric parameters, it bridges theoretical gaps and provides actionable insights for high-precision harmonic drives in robotics and aerospace, advancing reliability in precision transmission systems.