A New Collision Model for Analysing the Vibro-Impact of Spur Gears

Abstract

A model of a central centric collision of two fictive rolling disks, with radii equal to the radii of pitch diameters of coupled gears, is used to describe the vibro-impact dynamics of spur gears. Total deformations vary during the operation of spur gears with involute profile, particularly as a result of variable number of pairs of teeth in contact. These variations, as well as tooth profile misalignments or damages, lead to the backlash, the appearance of internal dynamic forces, and impact. Particular values of tooth profile parameters and transmission ratio create the conditions for a vibro-impact vibration regime. The vibro-impact gear dynamics is characterized by vibro-impact vibrations in the contact between the pinion tooth and the wheel tooth during a short period of time after the collision. New formulas for the calculation of the time periods between two tooth collisions, as well as between two successive tooth collision impacts, are devised. Also, a set of equations for the calculation of the disturbance angular velocity of the pinion called the transmission error is developed; the transmission error has a role of an excitation for vibro-impact vibrations in the gear tooth contact.

Numerical modeling and dynamic characteristics study of coupling vibration of multistage face gearsplanetary transmission

“…Dong and Hu (2018) established the bend-torsion coupling dynamics load-sharing model of the helicopter face gear split torque transmission system by using the concentrated quality standards, to analyze the dynamic load-sharing characteristics, which provided a theoretical basis and data support for its dynamic performance optimization design (Dong and Hu, 2018). Atanasovska and Hedrih (2018) used a model of a central centric collision of two fictive rolling disks, with radii equal to the radii of pitch diameters of coupled gears, in order to describe the vibroimpact dynamics of spur gears. A set of transmission error equations for the calculation of the disturbance angular velocity of the pinion was developed; the transmission error had a role of excitation of vibro-impact vibrations in the gear tooth contact (Atanasovska and Hedrih, 2018).…”

“…Atanasovska and Hedrih (2018) used a model of a central centric collision of two fictive rolling disks, with radii equal to the radii of pitch diameters of coupled gears, in order to describe the vibroimpact dynamics of spur gears. A set of transmission error equations for the calculation of the disturbance angular velocity of the pinion was developed; the transmission error had a role of excitation of vibro-impact vibrations in the gear tooth contact (Atanasovska and Hedrih, 2018). L. N. proposed a dynamic model of an N-stage powersplit planetary gear set.…”