Active vibration control of planetary gears by pole placement

Abstract

This numerical study focuses on the assignment of poles to a planetary gear train to avoid resonance, which can cause the failure of the system. The control strategy is output feedback, which involves feeding back the displacement and velocity to achieve active stiffness and damping respectively. The reverse process was considered. This occurs when the predicted control gains were assigned by the actuators, which were placed on the translational directions of either the carrier or the sun gear bearing mounted on the shaft. In addition, the closed-loop poles were assigned in the case whereby the actuators were positioned in the translational directions of either the carrier or the sun gear. The active control was considered using both the fixed and rotating frames of reference at a carrier speed of 100 rpm. Numerical examples are presented using both reference frames with the sensors and actuators collocated. The results show that the poles of the modes with lower frequencies, which are predominantly translational modes, can be shifted while the poles of the higher modes, which are predominantly rotational remain unchanged.

Research Progress on the Dynamic Characteristics of Planetary Gear Transmission in a Non-Inertial System

“…The effects of the installation position and damping fluid on the damping characteristics of gear shafting were studied. In 2019, Olanipekun et al [105] Figure 13. The planetary gear-rotor transmission system [98].…”

“…The effects of the installation position and damping fluid on the damping characteristics of gear shafting were studied. In 2019, Olanipekun et al [105] applied the pole placement theory to the planetary gear system to avoid resonance. The control strategy was to provide feedback on the displacement and speed response of the system output.…”

Pole Assignment for Active Vibration Control of Linear Vibrating Systems through Linear Matrix Inequalities

“…The assignment of the dynamic response of vibrating mechanical systems, such as structures, mechanisms, or multibody systems, is often performed by properly assigning the poles of the controlled systems. Both active feedback control [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and passive approaches (i.e., parameter modifications, see e.g., [19][20][21]) or are exploited to accomplish this important task. Indeed, the system poles, which are often denoted as the eigenvalues, define the system stability as well as the properties of the transient response such as the damping ratio, the rise time, and the settling time.…”

“…A ground-breaking advancement in the field of pole placement in active vibration control is the receptance method proposed by Ram and Mottershead in [1] that uses only the measured receptances of the system, in lieu of a first-order model. Such a formulation has been later exploited and extended by other researchers, for example to damp friction-induced vibrations [2], in robust pole placement [3], to control of flexible multibody systems [4], or to avoid resonances in planetary gear trains [5].…”

Active vibration control of gearbox housing using inertial mass actuators

“…They achieved 7 dB of reduction in gear angular vibrations at the tooth meshing frequencies. Olanipekun et al [5] presented a numerical study that focuses on planetary gear vibration control by pole placement method using output feedback. Their active control method considered using both the fixed and rotating frames of reference by assigning a pole to both the beam and the Sun gear, which resulted in better vibration control than assigning poles to only one of the two.…”