Fundamental study on countermeasures against subharmonic vibration of order 1/2 in automatic transmissions for cars

In automatic transmissions for cars, a damper is installed in the lock-up clutch to absorb torsional vibrations caused by combustion in the engine. Although a damper with low stiffness reduces the torsional vibration, low-stiffness springs are difficult to use because of space limitations. To address this problem, dampers have been designed using a piecewise-linear spring having three different stages of stiffness. However, a nonlinear subharmonic vibration of order 1/2 occurs because of the nonlinearity of the piecewise-linear spring in the damper. In this study, we experimentally and analytically examined a countermeasure against the subharmonic vibration by increasing the stages of the piecewise-linear spring using the one-degree-of-freedom system model. We found that the gap between the switching points of the piecewise-linear spring was the key to vibration reduction. The experimental results agreed with results of the numerical analyses.

Effect of Stiffness Ratio of Piecewise-Linear Spring on the Occurrence of Subharmonic Nonlinear Vibration in Automatic Transmission Powertrain

In the torque converter, a damper with a piecewise-linear spring is used to reduce the forced vibration, and the subharmonic vibration occurs when the spring restoring torque characteristics approach the switching point. This research analyzed the effect of stiffness ratio between the neighboring piecewise-linear springs on the occurrence of the subharmonic nonlinear vibration in automatic transmission powertrain. The powertrain is modeled with multi degree-of-freedom nonlinear system as an actual vehicle. The result shows higher value of the stiffness ratio between the neighboring springs creates larger value of the subharmonic vibration.

FEM Modeling of Vibro-Impact Response of Metal Plates Excited by a High-Power Ultrasonic Transducer

When thin metal plates are excited by a high-power ultrasonic transducer, superharmonic and high-order subharmonic vibration phenomena of the plates are observed in our experiments. However, the nonlinear mechanism in the system is still not fully understood. In this paper, a finite element model is established based on the experimental conditions and numerical simulations are performed to explore the generation mechanism of the nonlinear vibration. By comparing the waveforms and frequency spectra of the vibration velocity of the plate to these of the contact force between the ultrasonic horn tip and the plates, it can be found that waveform distortion of the contact force is the main reason for generating the superharmonic vibration, while the intermittent contact-impact between the horn tip and the plate is the reason for subharmonic vibration in the plate. The FEM simulation results can explain reasonably the observed experimental phenomena, which are useful to help to improve the effects of the nonlinear phenomena occurred in ultrasonic processing.