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In percussive drilling of rock, use is made of high-amplitude short-duration force pulses generated through impacts of a hammer on a drill bit or a drill rod assembly. The mass of the hammer is crucial for the impact velocity and the impact frequency, while its length and variation of characteristic impedance control the duration and shape of the force pulses. High efficiency of conversion of kinetic impact energy to work results if the force pulses have suitable shapes and durations. Commonly, hammers of hydraulic rock drills are nearly uniform and generate nearly rectangular force pulses admitting high efficiencies. When space is constrained, short hammers are advantageous as they allow short rock drills. Here, therefore, shorter substitutes for uniform original hammers are sought. They should have the same mass as the original hammer, be shorter than the original hammer, and generate approximately the same impact force history as the original hammer. A method based on 1D theory is developed for realization of substitute hammers with axially periodic characteristic impedance. Impact force histories generated by such hammers agree well with that generated by a uniform original hammer in a 1D context, and also in a 3D context if 3D effects are small enough. Also, for bit-rock interaction conditions from soft to hard, the efficiencies obtained by use of substitute hammers agree well with that obtained by use of the original hammer.

Axial impact between two elastic rods with piecewise constant characteristic impedance is considered. The distribution of characteristic impedance of the impacted rod and the impact velocity are given. By use of a 1D recursive algorithm, the characteristic impedances of the impacting rod are determined as long as they are all positive so that a prescribed impact force is realized. A condition for positivity of the characteristic impedance is derived in terms of transmission coefficients for wave energy. At the time from which positivity of all characteristic impedances cannot be maintained, or earlier, the characteristic impedance of the impacting body is continued, e.g., at the level of the last positive characteristic impedance or at level zero corresponding to cutting off the impacting rod. Examples of prescribed exponentially decreasing and linearly increasing impact forces are presented for a uniform impacted rod with constant characteristic impedance. In these examples, there is good agreement between the prescribed impact force and the impact force obtained from 3D FE simulation with a piecewise linear diameter of the impacting body that approximates the piecewise constant diameter obtained by use of the 1D recursive algorithm.

The effect of pre-impact waves on the coefficient of restitution (COR) in longitudinal impact of a uniform elastic rod on a linear elastic or bilinear inelastic spring supported by a fix rigid wall is studied. The spring models may represent the quasi-static response of, e.g., a small elastic cylinder or the inelastic bit-rock interaction in percussive drilling. The rod is accelerated to its impact momentum either by a force of relatively short duration which generates significant pre-impact waves in the rod (pre-impact wave case) or by a force of long duration which does not generate such waves (reference case). Analytical and numerical results based on the 1D wave equation are presented in dimensionless form. It is shown that the work performed by the accelerating force is much larger in the pre-impact wave case than in the reference case, and that the COR generally depends on spring stiffness, elasticity parameter, initial rod-spring separation, and wave transit time. In the pre-impact wave case, the COR may be significantly larger or smaller than in the reference case. It may also be significantly larger or smaller than unity. A pre-impact wave mechanism leading to super rebounds with COR up to 1.4261 is described.

Because of variability of the force vs. penetration relationship (FPR) from one blow to another in percussive drilling, and difficulty to predict FPRs under such conditions, use is commonly made of simple FPR models, such as the bilinear one defined by its loading/unloading slopes. Here a biconvex model with an added parameter representing convexity is considered. One aim is to study the effect of convexity on maximal penetration, maximal force and efficiency. Another is to assess, with the biconvex FPR as an example, how well a bilinear FPR can be used to approximate one that is nonlinear. A simple percussive top-hammer drill model is considered, comprising a hammer, a drill rod and a bit with the same characteristic impedance. The maximal penetration is found to decrease and the maximal force to increase with increasing convexity. The efficiency has a maximum for a finite hammer length (incident wave duration), and the highest maximal efficiency is obtained for a linear FPR With increasing convexity, the maximal efficiency decreases and occurs for shorter hammers (incident waves). The bilinear approximation of a biconvex FPR accurately predicts the position of the maximum in efficiency, even for large convexity, but somewhat overestimates its height and width.

Abstract The problem of finding the optimal incident wave of given duration that maximizes the efficiency of conversion of wave energy into work in percussive drilling with detachable drill bit is considered. The drill rod is modelled as 1D linearly elastic and the drill bit as a rigid mass. The bit/rock interaction is described by a history-dependent force versus penetration relation with different constant slopes for primary loading and unloading/reloading. A functional expressing the dependence of the efficiency on the shape of an arbitrary incident wave of given duration is derived and maximized. For short incident waves, there is a weak influence of the bit mass on the optimal wave shape which is nearly rectangular. For longer incident waves, there is a strong influence of the bit mass on the optimal wave shape which significantly differs from rectangular. The efficiencies for optimal waves approach those for rectangular waves for short waves. For long waves they approach or assume values which are independent of wave duration but decrease with increasing bit mass. Relative to commonly-used rectangular waves significant increase in efficiency can be achieved through optimization of the wave shape if the wave is not too short. Optimal incident waves can be realized accurately, e.g., by piezoelectric means.

Methods for estimation of the complex modulus generally produce data from which discrete results can be obtained for a set of frequencies. As these results are normally afflicted by noise, they are not necessarily consistent with the principle of causality and requirements of thermodynamics. A method is established for noise-corrected estimation of the complex modulus, subject to the constraints of causality, positivity of dissipation rate and reality of relaxation function, given a finite set of angular frequencies and corresponding complex moduli obtained experimentally. Noise reduction is achieved by requiring that two self-adjoint matrices formed from the experimental data should be positive semidefinite. The method provides a rheological model that corresponds to a specific configuration of springs and dashpots. The poles of the complex modulus on the positive imaginary frequency axis are determined by a subset of parameters obtained as the common positive zeros of certain rational functions, while the remaining parameters are obtained from a least squares fit. If the set of experimental data is sufficiently large, the level of refinement of the rheological model is in accordance with the material behavior and the quality of the experimental data. The method was applied to an impact test with a Nylon bar specimen. In this case, data at the 29 lowest resonance frequencies resulted in a rheological model with 14 parameters. The method has added improvements to the identification of rheological models as follows: (1) Noise reduction is fully integrated. (2) A rheological model is provided with a number of elements in accordance with the complexity of the material behavior and the quality of the experimental data. (3) Parameters determining poles of the complex modulus are obtained without use of a least squares fit.

For a tube with doubly symmetric cross section and perforations by helical slots there is a coupling between extension and torsion. In this paper a one dimensional (1D) model structure for a tube with such a helical slot segment (HSS) is established, and parameters accounting for the coupling between extension and torsion are estimated from wave propagation experiments. In these experiments incident extensional waves were generated through axial impact by strikers of different lengths, causing reflected and transmitted waves of extensional and torsional type which were measured in terms of surface strains on either side of the HSS part of the tube. A statistical test on the experimental data shows that the output residuals (the difference between modeled and experimental output) cannot be explained by measurement noise alone. This is not surprising since the 1D model structure is based on some simplifying assumptions concerning the geometry of the HSS. Parameters for two different geometries of the HSS are estimated, and the models are assessed in terms of model fa, simulations and wave energy distribution. It turns out that for one case, where the geometrical assumptions are valid, the 1D model is adequate, while for another case, where the validity of the assumptions is questionable, it is not. It is concluded that the 1D model structure provides a simple and efficient description of the HSS if the geometrical assumptions are valid.

In a conductor carrying electric current, the Lorentz force gives rise to mechanical stresses. Here, we study a long elastic cylindrical conductor that moves axially with constant velocity through two electrode plates. The aims are to explore how the stresses in the conductor depend on the velocity in the stationary case of constant current and to assess the validity of the analytic method used. The diffusion equation for the magnetic flux density is solved by use of Fourier transform, and the current density is determined. The stresses, due to the Lorentz force, are found by use of an analytic method combining the solutions of a quasi-static radial problem of plane deformation and a dynamic axial problem of uniaxial stress. They are also determined through FE analysis. Radial field profiles between the plates indicate a velocity skin effect signifying that the current and the magnetic field are concentrated near the cylindrical surface up-stream and are more uniformly distributed downstream. The radial and hoop stresses are compressive, while the axial stress is tensile. The von Mises effective stress increases towards the symmetry axis, in the downstream direction, and with velocity. There are circumstances under which a large current can produce an effective stress in a copper conductor of the order of the yield stress without causing a significant temperature rise. The stresses obtained with the two methods agree well, even relatively near the electrode plates. The analytical method should be useful in similar cases as well as for the provision of test cases for more general simulation tools.

Simulations have been performed to evaluate the possibility of reproducing the fragmentation of a long-rod projectile impacted by a moving oblique plate. When the moving plate slides along the projectile, fractures due to shear loading may occur in the projectile. Therefore, a fracture model suggested by Xue–Wierzbicki was used for the projectile together with the Johnson–Cook strength model. This fracture model is based on an equivalent plastic strain of fracture which depends on a stress triaxiality and a deviatoric stress parameter. The results of the simulations were compared with experimental results of a preceding study in which the impact conditions were varied in such a way that the projectile fractured in some but not all tests. The comparisons show that the simulations reproduced the fractures in the projectile well. Also, the transition from a deformed non-fractured to a severely fractured projectile was captured. The benefit of including the deviatoric stress parameter and the mechanisms leading to fragmentation of the projectile are discussed.