A Study on Attenuating Gear Teeth Oscillations at Low Engine Speeds Using Nonlinear Vibration Absorbers

Abstract

Gear oscillations are one of the most common sources of Noise, Vibration and Harshness (NVH) issues manifested in automotive powertrains. These oscillations are generated mainly due to impacts of the meshing gear teeth over a broad frequency range. To mitigate NVH phenomena, automotive manufacturers traditionally couple linear tuned vibration absorbers to the driveline. Common palliatives used are clutch dampers and dual mass flywheels, which generally suppress vibrations effectively only over narrow frequency bands. Nonlinear Energy Sinks (NESs) are a class of vibration absorbers with essentially nonlinear characteristics that are designed for dissipating vibration energy over broad frequency ranges (due to the employed nonlinearity). The NES does not have a preferential natural frequency; this is rather characterized by the nonlinear stiffness. An NES functions on the principle of transferring energy between the primary system (e.g. driveline) and the absorber in two ways: (i) the NES induces a unidirectional transfer of the vibration energy excess from the primary system to the absorber and (ii) the NES induces a redistribution of the vibration energy excess in the modes of the primary structure, enhancing the energy dissipation capabilities of the primary structure. This paper presents a study on the use of NESs for reducing oscillations on gear pairs operating at low engine operating speeds. Numerical simulations were performed using a gear pair model equipped with an absorber with essentially cubic nonlinear stiffness, attached to the gear wheel. The stiffness and inertia properties of the absorber were varied with the objective of obtaining the parameter combination that induces significant attenuation of the oscillatory motion of the gear wheel. The occurring motion of the system using different sets of parameters is studied and presented.

A Nonlinear Energy Sink Design to Attenuate the Torsional Oscillations of Lightly Loaded Gear Pairs

“…The numerical model that is used in this paper has been presented in detail in Friskney et al [27]. For completeness, we reiterate some of the key aspects and findings from this previous work.…”

“…The equations of motion of the system shown in Figure 1 are given in Equations ( 1)-(3) below. The reader is referred to previous work [27] for a comprehensive description and detailed documentation of the model parameters. Note that the model parameters are informed by the experimental setup that is used in the current work, and therefore the interested reader is referred to [27] for the gear pair setup details.…”

“…The time-varying meshing stiffness is a function of the angular position of the pinion and the applied torque and it is denoted by 𝐾 𝑀 . The mesh displacement 𝑥 𝑡 is described by a piecewise linear function with backlash [27]. The damping coefficient in the pinion-gear contact is 𝐶 𝑀 , and the NES damping coefficient is denoted by 𝐶 𝑁 , whereas the NES nonlinear stiffness coefficient is 𝐾 𝑁 = 𝑘 3 , where an essentially cubic nonlinearity is assumed.…”

“…Closer observation of this NNM in the frequency range of interest (up to 200 Hz) in Figure 2b reveals the NES frequency coverage that motivates this experimental study to reduce gear speed fluctuations by the action of an NES The equations of motion of the system shown in Figure 1 are given in Equations ( 1)-( 3) below. The reader is referred to previous work [27] for a comprehensive description and detailed documentation of the model parameters. Note that the model parameters are informed by the experimental setup that is used in the current work, and therefore the interested reader is referred to [27] for the gear pair setup details.…”

“…A theoretical analysis involving a spur gear pair coupled with a rotary NES has been presented [26], showing that targeted energy transfer (TET) can be activated, introducing quasiperiodic motion. The effect of NES mounted on a spur gear pair that operates at low, harmonically varying operating loads (resembling rattling conditions of transmission unloaded gears) has been studied theoretically to demonstrate the performance of the NES in attenuating the gear's torsional oscillations [27]. In this paper, a rotational NES prototype utilising thin shims is experimentally tested.…”