In this work, the self-propelling ability of a truncated double-cone gravitational motor, rolling on straight V-shaped divergent or convergent rails, is theoretically and experimentally evaluated. Movies of the self-propelled double-cone made of A5052 aluminum alloy along rails made of the same aluminum alloy, were shot for various opening angles of the rails. Number of rotations and the travelling time of the double-cone, rolling on rails of constant length, but variable opening angles, were estimated through the slow-motion processing of the recorded movies. Previously proposed model, for this particular contact problem, was improved by including the effect of a small descending inclination angle of the rails. Based on such model, it became possible to explain the experimentally observed self-propelling ability of the double-cone, even on parallel and convergent rails. Experimental data gained on the average travelling speed of the double-cone can be used to achieve the proper design of such gravitational motor, which can be potentially used also as an electrical power generator.
Recently, wave-powered electrical generators, using double-cones moving on circular rails, have been proposed. Rotational motion of the generator’s hull, induced by waves, is changed into the rotational and translational movement of either a rigid magnetized double-cone, rolling on divergent-convergent circular rails, or a double-cone geared motor-generator, rolling on concentric circular rails. However, if such generator is not directly floating on the water waves of random direction, period and height, but it is placed inside of the hull of a ship, the movement of the double-cone is one-directional and dictated by the rolling period and amplitude of the ship’s hull. In such case, divergent-convergent straight rails resembling an O letter might be more efficient than the circular rails. In this work, the optimal design conditions of such a mechanism are examined. Concretely, the O-rails are fixed on the hull of a ship, which is excited to roll along its longitudinal axis, by using a pendulum. Movies of the double-cone moving on the O-rails were shot, and the total travelling time was determined through the slow motion processing of the movies, for various values of the inclination angle of the hull, and energies introduced into the system by the pendulum. Optimal geometry of the O-rails was decided in order to maximize the kinetic energy of translation of the double-cone. Apparent spring constants and damping ratio for the oscillatory movement of the double-cone were experimentally found and validated by a theoretical model. Experimentally observed optimal length of the pendulum arm, to maximize the total traveling time of the double-cone, was justified by a two degree of freedom vibration model of the test rig.
In this work the dynamic characteristics of a double-cone, self-propelled on a straight V-shape horizontal rail, are evaluated. Such simple mechanism can be regarded as a gravitational motor, which transforms the input potential energy into kinetic energy, of rotation and translation. Movies of the freely rolling double-cones, made of carbon steel and wood, against V-shape horizontal rails, made of aluminum alloy, were taken for various opening angles of the rails. Number of rotations, the variable rotation period, and the total traveling times of the double-cones were determined through the slow motion processing of taken movies. Several theoretical models were proposed and validated against the experimental results. One proved that the Hertzian contact point moves on the conical surface along a logarithmic spiral. Based on the proposed dynamical model, the traction force and the traction torque acting on the double-cone were identified. One proved that the traction force is always smaller than the translation friction force. However, the double-cone is able to self-propel on the rails if the traction torque exceeds the rolling friction torque. Results obtained in this work can be used to achieve the proper design of such gravitational motor.
In this paper, a mechanism consisted of a double-cone rolling on two divergent-convergent rails is proposed to be used in the construction of a wave-powered electrical generator. Such divergent-convergent rails, attached to a buoy, can be materialized by using either straight V-rails, or eccentric circular rails. Rotational movement of the buoy, induced by the waves, is transformed into the rotational and translational motion of a magnetized double-cone. In this way, a variable magnetic field is extended over several coils, connected in parallel. Power generation is obtained through the electromagnetic induction effect. Firstly, a geometrical model is proposed to determine the length and radii of contact between the double-cone and the circular rails. Variation of the number of rotations, theoretically obtained, versus the rails eccentricity is validated by tests, where a double-cone, made in S45C carbon steel, is rolling on circular rails, made of A5052 aluminum alloy. Then, a model to evaluate the pressure of contact, and the change of potential energy of the double cone, is advanced. Based on such model, variation of the maximal contact pressure versus the rails eccentricity is clarified, for various loading patterns, corresponding to waves of different heights.
A design method of a novel mechanism consisted of a double-cone and two circular rails eccentrically positioned, is proposed. On one hand, this mechanism can be regarded as a gravitational motor that transforms the potential energy into kinetic energy, of rotation and translation. On the other hand, it can be regarded as a mechanism, able to transform the kinetic energy of translation into kinetic energy of rotation. Several applications can be envisaged for this kind of mechanism, but it seems to be appropriate for electrical power generation from the energy of ocean and sea waves. Concretely, in this work, movies of a double-cone made in S45C carbon steel, rolling on straight and circular rails made of aluminum alloy and placed on a horizontal table, were shot. Number of rotations, the variable period of rotation, and the total travelling time were determined through the slow motion processing of the movies. A geometrical model to describe the particular kinematics of the double-cone, and a contact model for such particular Hertzian contact problem, were proposed and validated by experimental results. Such models produce the foundation of the suggested design method for the double-cone mechanism, based on which, the optimal design of the associated gravitational motor and generator can be achieved.