Stress and stiffness analysis of a 7-teeth pinion/rack jacking system of an Offshore jack-up rig

Abstract In offshore mobile jack-up rig, platforms are generally supported by movable jacking system in which strength of rack and pinion are very crucial in determining the design life of the superstructure. In this study, a series of finite element (FE) models has been developed and analysed for a 7-teeth pinion with rack to investigate the strength, stiffness and fatigue life of the jacking system before its practical application in an offshore rig. Since rack/pinion contact patterns change with the rotation of the shaft, FE models are developed for each 10-degree rotations starting from 0 to 50 degree where elasto-plastic properties of both rack and pinion are considered in the FE analyses. A geometric analysis is also performed to determine shape and contact position between the rack and pinion at different angle of rotation. Finite element analyses are conducted for worst possible load cases of the jacking system including self-weight of the platform, wind load, hydrodynamics force as per American Bureau of Shipping (ABS) guideline. The stress distribution of the pinion shows that maximum stress occurs at the root of the tooth, mainly due to bending effect resulting from external torque. The FE analysis reveals that maximum von mises stress of pinion and rack are found to be 1105 MPa and 688 MPa, respectively which are very close to the corresponding strength of the materials. The FE results are validated with the established Lewis formula and American Gear Manufacturers Association (AGMA) guideline. Considering the design life of the offshore platform, fatigue performance of the pinion is investigated for different operational loading of the platform. A separate 3D FE model has been developed to check the stiffness of the gear box that actually presents the serviceability of shaft beam and pinion teeth. In the stiffness analysis, the maximum deflection of the beam and individual tooth are found to be 1.2 mm and 2.1 mm, respectively. The outcome of this study is expected to contribute in designing future rack/pinion system for offshore jack-up rigs and similar other structures.