Публикации

D. Pogorelov, O. Dmitrochenko, G. Mikheev, R. Gandikota. Flexible multibody approaches for dynamical simulation of beam structures in drilling.

Proc. of the ASME 2014 10th Int. Conf. on Multibody Systems, Nonlinear Dynamics, and Control, MSNDC2014, August 17-20, 2014, Buffalo, New York, USA. DETC2014-35113.

Abstract.

Many engineering dynamic problems can be simulated as beam structures. For example, such models are applied in well drilling. Dynamic simulation allows optimizing shape of well bore and operation parameters of the drilling. Calculation speed of simulation of dynamics of a drill string depends on size of matrices of the model and on efficiency of numerical methods.

Two approaches for simulation of dynamics of drill strings are suggested in the paper.

In the first approach, the drill string is presented as a set of uniform beams connected via force elements. Flexibility of the beams is simulated using the modal approach. Thus, each beam has at least twelve degrees of freedom: six coordinates define position and orientation of a local frame and six modes are used for modeling flexibility. For simulation of the drilling processes, implicit Park method with computing Jacobians of stiff forces is used. Parallel computations are implemented for increasing the solver efficiency. Analysis of vibration, rock cutting, buckling and post-buckling behaviour and other processes of the drilling can be successfully modeled using the approach. But it has some disadvantages.

Firstly, number of degrees of freedom could be decreased if a single nonlinear finite element model were used instead of the model including great number of beams. Secondly, simulation of real rotation of the drill string using the modal approach is related to costly calculation of Jacobians. The expressions for the modal coordinate derivatives of the stiff forces are variable since each mode is calculated in the local frame of the beam and rotates together with the frame.

The second approach is dynamic simulation of the drill string using nonlinear finite element model. The proposed beam finite element use Cartesian coordinates of its nodes and node rotation angles around axis of Cartesian coordinate system as generalized coordinates. The nonlinear finite element is developed based on so called method of. Rotation angles in the nodes can be arbitrary large.

Equations of motion of beam structure are derived in the paper. The number of degrees of freedom is decreased by factor two as compared with the modal approach. In addition, the expressions of Jacobians are much simpler in this case.

Thereby, calculation speed under simulation of dynamics of long drill strings is considerably increased.

The features of creating the models and numerical methods as well as results obtained by applying both approaches are discussed in the paper.

 
 
 

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