The first fractal model for the loading–unloading process between two cylindrical surfaces with friction is presented. The nonlinear relation between the real contact area and the contact load in different deformation stages are deduced for a load–unload cycle. The impacts of parameters in the model are discussed. The numerical results show that for a given dimensionless contact load, the dimensionless real contact area of the loading–unloading process of cylindrical contact surface with friction, as well as the differences of the dimensionless real contact area between the loading and unloading processes, increase with the increase of the loading interference and fractal dimension, decrease of the profile scaling parameter and curvature radius, or the substitution of external contact for internal contact.

The all-electric subsea gate valve actuator is one of the critical components of the all-electric subsea production control system. To bridge the gap of the low-power holding mechanism in the all-electric subsea gate valve actuator of the subsea production system, minimize the power consumption and cable number for control and improve the open-position keeping performance of all-electric subsea gate valve actuator, this paper proposed a novel low-power holding mechanism for the all-electric subsea gate valve actuator which can be applied to all-electric subsea gate valve actuators with various valve sizes and process pressure ratings. The proposed low-power holding mechanism uses an electromagnet as a driving element, combines the spiral transmission and the cam-like transmission, and only requires a holding force of approximately 2–7% of the maximum load of the closing spring to keep the valve open. The proposed low-power holding mechanism converts the axial force of the closing spring into the circumferential force, which substantially reduces the output force required for the driving element of the low-power holding mechanism and the number of the actuator’s control cables. Analytic models are created for the lockable maximum load of the closing spring and the permissible stroke of the locking tab with regard to the design variables. The parameter effects and the corresponding sensitivities are discussed by numerical analysis. The design parameters and the lockable maximum load of the closing spring of the low-power holding mechanism are obtained.