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This paper proposes an inertance calculation method of the ball-screw inerter when considering the nonlinear factors, which will be called as the nonlinear inertance. With the inerter increasingly used in vibration damping systems, the effects that caused by the nonlinear factors, especially by friction, have attracted a lot of attention. The inertance is deemed as the inherent property of the inerter. In most systems, an analysis with the application of the inertance of the ideal linear inerter (which will be called as the ideal linear inertance) may produce a considerable error, thus the consideration of nonlinear factors becomes increasingly significant when calculating the inertance. Based on the Frenet frame theory and Hertz contact theory, the relative sliding speed and sliding friction torque between balls and raceways of the ball-screw inerter have been deduced, thus obtaining the sliding friction efficiency of the balls, and then introducing the rolling friction efficiency of the balls, and finally obtaining the method of the nonlinear inertance calculation after friction consideration. Based on the jobs above, an experimental study on the inertance of ball-screw inerter was carried out. In addition, the ideal linear inertance, nonlinear inertance and experimental value were compared with each other. The results show that the nonlinear inertance is closer to the experimental value; it demonstrates the accuracy of the calculation method proposed in this paper. Besides, the influences of other parameters of the ball-screw mechanism on the inertance are also analyzed, including the nominal radius, lead, contact angle, ball radius and number of balls, the comparative results show that the lead and ball radius have a great influence on the inertance. These results provide a more accurate inertance calculation method for designing a ball-screw inerter and its application in engineering vibration damping systems, meanwhile the theory and approach about inerter will also be developed.

Research on nonlinear inertance calculation method of ball-screw inerter