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.
Modeling Tire Treadband Vibration
A static tyre was driven radially at a point on its tread band and measurements of the resulting radial tread band vibration were made around the treadband circumference by using a laser Doppler velocimeter. By performing a circumferential wave number decomposition of the measured space-frequency data, the wave propagation characteristics were visualized, In an attempt to understand these experimental results in detail, the tyre treadband was modelled as a ring-like, circular cylindrical shell with air pressure acting on its interior surface. The model makes allowance for general boundary conditions at the lateral edges of the ring, and the sidewall of the tyre is modeled as a distribution of springs and dampers. Both analytical and finite element methods were applied to obtain the vibration response. These solutions were compared with both the experimental result and the response of the infinite length plate driven by point excitation. This shell model was found to explain the propagation characteristics of the waveguide modes that are visible in the experimental results. In particular, the low frequency, flexural wave characteristics associated with finite curvature and which result in efficient radiation of sound were well reproduced. Fast in-plane waves that are potentially significant sound radiators at high frequencies were also well reproduced by this model; the excitation of these modes results from wave coupling within the curved shell. (A) For the covering abstract see ITRD E113232.