Axial vibration generators improve oilwell drilling efficiency by reducing drillstringwellbore friction. However, tool vibration can cause unwanted vibrations of the drillstring, and thus premature failure of components. The only effective way to benefit from the positive consequences of these tools is to develop vibration models to predict the vibration pattern of the drillstring for any mode of interest, and implement suppression tools, such as a shock sub to isolate the imposed vibration from the rest of the drillstring.

Transverse vibration, which is coupled to axial vibration, is the main cause of premature failure of drillstrings. Nonlinear coupled axial-transverse vibration of a drillstring with a downhole vibration generator and shock sub is investigated. Analytical elastodynamic and finite element models are developed.

The Newtonian approach and the "Bypassing PDEs" method were implemented in developing the analytical models and the ABAQUS Explicit solver package® was used to develop finite element method (FEM) models. The bottom-hole assembly was assumed as a multi-span bottom-hole assembly (BHA) and realistic boundary conditions were assumed. The lateral comparison functions for a multi-span BHA and axial comparison functions for a system of hybrid continuous (step-beam drillstring) and discrete elements (springs and dampers of the shock sub and the equivalent top boundary condition) were developed analytically. The effects of mud damping, spatially varying axial force along the drillstring, bit-rock interaction and lateral contacts were included. Nonlinearities due to strain energy, geometry, axial stiffening and Hertzian contact forces were also captured in the models.

The simulation results were used to extract modal characteristics and analyze the downhole vibration trends of a drill string with a shock sub and vibrating tool installed on the BHA. Multi-mode analysis in the expanded Galerkin's method with accurate comparison functions enabled a multi-point contact analysis, multi mode modal dynamic analysis, and prediction of more realistic critical rotary speeds. A simulated shock sub effectively isolated the vibrating tool from the drillstring, while amplifying the tool force at the bit. Analytical and FEM models showed excellent agreement. The models in their current form can be used to guide the design of drillstrings and to predict drilling parameters such as speed and weight-on-bit (WOB) that will result in acceptable vibration levels.