Journal of Mechanical Science and Technology

, Volume 32, Issue 12, pp 5597–5613

# Dynamic analysis of a pulley-belt system with different pulley radii and support stiffness

• Minsung Kim
• Jintai Chung
Article

## Abstract

Herein we present a new model to describe a pulley-belt system with various ratios of spring constants supporting the two pulleys and various ratios of pulley radii. The main object of this paper is to analyze the effects of differences between the radii of the two pulleys and the two spring constants on the dynamic characteristics of the pulley-belt system. To this end, five equations of motion and eight boundary conditions are derived using Hamilton's principle, and the governing equations are discretized using Galerkin's method. The natural frequencies and the mode shapes corresponding to the various radius ratios of the two pulleys and ratios of the two spring constants are obtained, and the responses are calculated to verify the dynamic characteristics of the pulley-belt system. This study shows the exact cause of the coupling between the rigid-body motions and belt deflection motions, and the difference between natural frequency veering and crossing phenomena is analyzed by confirming the mode shapes near each phenomenon. In addition, we confirm the influences of the radius ratio of the two pulleys and the ratio of the two spring constants on the changes of the natural frequencies according to the moving velocity of the belt.

## Keywords

Rigid-body motion Pulley-belt system Natural frequency crossing Natural frequency veering Mode coupling

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