Torsional vibrations of gear systems with single and dual mass flywheels: modelling and analyses

Nowadays, the expectation of comfort and performance from vehicles is at an increasing level. One of the critical factors in vehicles which affects comfort and performance is vibration and noise levels of the vehicle. Developments aiming to reduce vibration and noise in vehicles lead to increased ride comfort and extended life of mechanical components. Power transmission makes the most substantial contribution to vehicle vibration and noise in automobiles. Gear systems are crucial components in transmission of power and motion. Noise due to gear systems is divided into two main types which are named gear whine and gear rattle. Gear whine is caused by friction at the surfaces of the contacting teeth of a gear pair. Gear rattle, which causes significantly more noise than gear whine, occurs due to the backlash between contacting gears which is needed for proper assembly and lubrication of the gear pair. Teeth of the gear pair find the ability to move back and forth in the backlash and collide each other causing noise and vibration. One of the major causes for gear rattle is the oscillating torque provided to the transmission by the internal combustion engine. The oscillating torque of the internal combustion engine, which is due to its design and nature, causes the contacting gears to move back and forth with respect to each other and leads to gear rattle. Gear rattle is observed especially in cases where a counter-torque is not present on the gear pair, which causes increased levels of vibration and noise and thus, reduced ride comfort and transmission component life. A traditional flywheel is placed between the crankshaft and the transmission in order to reduce vibrations and noise due to the internal combustion engine. The traditional flywheel reduces the vibration transfer from the crankshaft to the transmission, though only by a small amount. In today's standards of comfort and performance, more efficient methods are needed to reduce vibrations in vehicles. The dual mass flywheel, which is modelled and analyzed in this thesis, offers a more efficient method to reduce noise and vibration in vehicles. When the dual mass flywheel is placed between the crankshaft and the transmission, torque oscillations from the internal combustion engine, which causes gear rattle, are reduced. As a result of reductions of torque oscillations, ride comfort, the life of transmission components and transmission efficiency are increased. The dual mass flywheel can be thought of as two traditional flywheels, which is also referred to as single mass flywheels within this thesis, connected with a torsional spring between them. This design is similar to the design of a typical vibration isolator. The connecting torsional spring is selected so that vibrations above a certain frequency are reduced. The main purpose of this thesis is to demonstrate the effect of the dual mass flywheel on reduction of vibration of gear systems. In this context, various gear system models are examined in order to explain gear dynamics. Firstly, the dual mass flywheel is integrated into a linear gear system model and its efficiency is investigated. Subsequently, a nonlinear gear system model is built to account for the collisions due to backlash between the gears and the efficiency of the dual mass flywheel is investigated in comparison with the efficiency of the single mass flywheel. The first chapter of this thesis explains the vibration and noise problems observed in gear systems. Then, a comprehensive literature survey is given and previous work on the subject is examined in detail. At this point, the gear system models in the literature are grouped and research on each group is investigated. Therefore, previous work on the subject is considered to help and guide this thesis and possible future work. Lastly, the work done in this thesis is briefly explained and the problems which are aimed to be solved are defined. The second chapter explains the necessary theory to understand the subjects related to vibration and noise of gear systems and dynamics of gear systems. The definition and the mathematical representation of transmission error is given. Additionally, the mathematical procedure to calculate the contact stiffness in gear pair models is presented. Backlash in gear pairs which is necessary for the gear pair to operate without being locked up but also causes gear rattle is explained. Lastly, the working principle of the dual mass flywheel is explained. The third chapter introduces a linear gear system model to examine the efficiency of the dual mass flywheel on gear systems based on linear analyses. The efficiency of the dual mass flywheel is examined for its various configurations. Lastly, vibration transmissibility graphs are presented for comparisons of aforementioned configurations. The fourth chapter introduces a nonlinear gear system model in order to demonstrate the advantages of the dual mass flywheel on a more realistic and accurate model. Firstly, existing nonlinear models are revisited and simulated. Secondly, the dual mass flywheel model is integrated into the gear system model including backlash, and its efficiency is examined and compared to the efficiency of the single mass flywheel in the same model. For the purpose of comparison, transmissibility functions for a nonlinear system are defined. First of the transmissibility functions is defined as the ratio of the amplitude of the output signal to the amplitude of the input signal for at the excitation frequency. Second of the transmissibility function is defined as the ratio of the RMS value of the output signal to the RMS value of the oscillatory part of input (excitation) signal. Finally, the gear rotor system with dual mass flywheel is modeled in the Adams program and it is aimed to form a basis for more complex models for future work. In this thesis, it is found that if dual mass flywheel is added to the geared systems, vibration isolation is achieved substantially compared to single mass flywheel integrated system. Also, it is shown that there will be considerable reductions in impact induced noise and vibration levels. The final chapter gives a comparison of the results obtained from the linear and nonlinear models. Suggestions for future work is also given.