Dynamic modeling of drill bit vibrations.

Abstract

Transverse vibrations of drill bits are modeled and experimentally validated. The model is based on Euler-Bernoulli beam theory. The equations of motion are transformed to a rotating fluted frame, and discretized conveniently using finite element techniques and st and ard beam elements. A computer program developed is capable of eigenanalysis as well as time response. The finite element solutions are validated by comparing them to known analytical results from the literature. Finite element solutions are also compared to laser holographic experiments. Fairly good agreement is observed. Initially a lumped parameter model is validated through drilling experiments using slender drills. Then, laser holographic interferometry methods are used to record the model shapes and modal frequencies of two st and ard drills under stimulated boundary conditions. The model developed is employed for parametric sensitivity studies. The effect of various parameters of drill transverse frequencies is investigated. These parameters are the cross sectional properties, the flute helix angle, the thrust force generated during drilling, and the rotational speed of the drill bit. From these studies it is found that, small changes in the cross sectional geometry will not improve the fundamental bending frequencies of drill bit. On the other h and it is found that increasing the helix angle increases the fundamental bending frequency. However, after approximately 1.5 rotations of the helix angle, the increase in the fundamental bending frequency is negligible. Thrust force, which is a function of feedrate, lowers the fundamental bending frequency, and buckling takes place at high thrust forces. Sensitivity studies have shown that long slender drills may buckle under the thrust forces generated at feeds appropriate for st and ard short drills. The cutting speed, measured at the drill periphery, is a function of drill diameter and rotational speed. Thus smaller diameter drills can be operated at higher rotational speeds. However this may lead to instability due to rotating unbalance in thin slender drills. The model developed can predict the change in bending frequencies with respect to drill geometric and operating parameters. It may be used for drill design, process design, process control. It may also be employed for vibration control in drilling. (Abstract shortened with permission of author.)