Modeling of wave propagation in drill strings using acoustic transfer matrix method
In order to understand critical vibrations of a drill bit such as stick-slip and bit-bounce and their wave propagation characteristics through a drillstring system, it is critical to model the torsional, longitudinal, and flexural waves. The objective is to model these waves propagating through the drillstring in a computationally efficient way. Here, a modeling method based on an acoustic transfer matrix between two sets of wave variables at the ends of a cylindrical pipe is proposed. For a drillstring system with multiple pipe sections, the total acoustic transfer matrix is calculated by multiplying all individual matrices of which each is obtained for an individual pipe section. Since drillstring systems are typically extremely long, conventional numerical analysis methods such as FEM require a large number of meshes, which makes it difficult to analyze these drillstring systems. On the contrary, the analytical acoustic transfer matrix method requires significantly low computational costs. For the validation, experimental and numerical data are obtained from a laboratory measurement and by using a commercial FEM package, ANSYS, respectively. They are compared to the modeling results obtained by using the proposed method. It is shown that the modeling results are well matched with the experimental and numerical results.
Effects of rotation on the dynamics of a circular cylindrical shell with application to tire vibration
Abstract For the purpose of understanding the effects of rotation on wave propagation within a tire’s treadband, the vibration of an inflated, circular cylindrical shell, rotating about a fixed axis has been considered here. The equations of motion of the rotating shell are formulated in a fixed reference frame (i.e., Eulerian co-ordinates). By assuming wave-like solutions for the free vibration case, the natural frequencies and corresponding wave-like basis functions can then be obtained. A natural frequency selection procedure is introduced that can be used to associate each of the basis functions with a single natural frequency. The basis functions are then superimposed to represent the forced response of the system when driven by a point harmonic force at a fixed location in the reference frame. By using the procedure described here, the coefficients of the basis functions can be obtained directly by solving an uncoupled ordinary differential equation. Finally, the resulting forced responses are presented in both the spatial and wave number domains, and the wave number spectrum of the rotating shell is compared with that of a stationary shell. Based on the results presented here, it is suggested that at typical rotational speeds it may be possible to use a stationary tire analysis to predict the characteristics of a rotating tire after performing a simple kinematic compensation.
STRUCTURE-BORNE SOUND ON A SMOOTH TYRE
Abstract The vibration behaviour of tyres is the link between noise-generating mechanisms and radiated tyre noise. Although the problem has often been discussed, this paper goes more deeply into several aspects of the vibration of unloaded smooth tyres. Measurements on a stationary tyre are compared with a two-dimensional model, called the circular ring model. The characteristics discussed in this text are phase velocity and damping of waves along the circumference. The point admittance, measured in the radial direction, is compared with results which are calculated using the theoretical model. The influence of the area on which the force operates is analysed with respect to the admittance. It will be shown that the ‘local stiffness’ is of importance for noise-generating mechanisms such as roughness excitation and friction.