“…In the stationary case, the trajectory of the geometrical center of B (1) is deflected mainly in direction n (1) c (normal direction of the active tooth flank). This is a result of the eccentrically acting contact force between the teeth.…”
Section: Resultsmentioning
confidence: 99%
“…To derive differential equations which describe the behaviour, first a Hamilton functional H is set up which takes into account all participating components. During the shifting process, the gear input shaft, the clutch disc and the gear stick together, thus they are one rigid body B (1) (mass m 1 , inertia J 1 ). This component has a rotational DoFφ (1) e z and all translational DoFs u (1) .…”
Section: Modellingmentioning
confidence: 99%
“…Thus, for this body, the kinetic energy T G , the stored energy in the bearing U B and the dissipation δW B Diss contribute to H. Gear flanks on B (1) and B (2) have no penetration. This condition results in a nonholonomic constraint 0 = n (1) c · v rel as a simple but adequate gear model [4], where the Lagrange multiplier is the contact normal force. Friction effects in the gears and the influence of the flank stiffness are neglected.…”
Section: Modellingmentioning
confidence: 99%
“…They have been studied in models of simple structure like 1-DoFoscillators as well as in more complex ones like automotive disc brakes [1]. Low-frequency vibrations often arise because of the Stribeck effect, whereas the reason for higher frequency vibrations usually is a mode-coupling flutter instability.…”
Eek noise in a gearbox of a vehicle drivetrain is a phenomenon, which can arise while shifting between gears and which is not accepted by customers. Beneath audible squeaking, it can cause damage of mechanical components. There is a wide range of possible reasons for the occurrence of this effect, which strongly depends on properties of the considered gearbox (physical parameters, geometry, operation, ...). From the mathematical point of view, the occurrence can be predicted using linear stability analysis of the stationary behaviour of a physically motivated gearbox model. The components of a gearbox are clutch discs being in contact, gears and elastically supported shafts. In this contribution, a rigid multibody model of the device [4] is extended by the elastic modelling of the motor's side disc (rotating Kirchhoff plate). The aim of the overall system is to analyze the shifting process. The analysis reveals that beneath instability mechanisms which are known from systems with rigid bodies, new instabilities occur incorporating of out-of-plane vibrations of the plate. In a reasonable parameter region, the first two unsymmetrical modes of the lamella have the main contribution to the instability.
“…In the stationary case, the trajectory of the geometrical center of B (1) is deflected mainly in direction n (1) c (normal direction of the active tooth flank). This is a result of the eccentrically acting contact force between the teeth.…”
Section: Resultsmentioning
confidence: 99%
“…To derive differential equations which describe the behaviour, first a Hamilton functional H is set up which takes into account all participating components. During the shifting process, the gear input shaft, the clutch disc and the gear stick together, thus they are one rigid body B (1) (mass m 1 , inertia J 1 ). This component has a rotational DoFφ (1) e z and all translational DoFs u (1) .…”
Section: Modellingmentioning
confidence: 99%
“…Thus, for this body, the kinetic energy T G , the stored energy in the bearing U B and the dissipation δW B Diss contribute to H. Gear flanks on B (1) and B (2) have no penetration. This condition results in a nonholonomic constraint 0 = n (1) c · v rel as a simple but adequate gear model [4], where the Lagrange multiplier is the contact normal force. Friction effects in the gears and the influence of the flank stiffness are neglected.…”
Section: Modellingmentioning
confidence: 99%
“…They have been studied in models of simple structure like 1-DoFoscillators as well as in more complex ones like automotive disc brakes [1]. Low-frequency vibrations often arise because of the Stribeck effect, whereas the reason for higher frequency vibrations usually is a mode-coupling flutter instability.…”
Eek noise in a gearbox of a vehicle drivetrain is a phenomenon, which can arise while shifting between gears and which is not accepted by customers. Beneath audible squeaking, it can cause damage of mechanical components. There is a wide range of possible reasons for the occurrence of this effect, which strongly depends on properties of the considered gearbox (physical parameters, geometry, operation, ...). From the mathematical point of view, the occurrence can be predicted using linear stability analysis of the stationary behaviour of a physically motivated gearbox model. The components of a gearbox are clutch discs being in contact, gears and elastically supported shafts. In this contribution, a rigid multibody model of the device [4] is extended by the elastic modelling of the motor's side disc (rotating Kirchhoff plate). The aim of the overall system is to analyze the shifting process. The analysis reveals that beneath instability mechanisms which are known from systems with rigid bodies, new instabilities occur incorporating of out-of-plane vibrations of the plate. In a reasonable parameter region, the first two unsymmetrical modes of the lamella have the main contribution to the instability.
“…The annoying noise can cause customers to doubt the quality of their automobiles. Friction-induced vibration has been generally accepted as the main reason for brake squeal [1][2][3][4]. Another consequence of friction-induced disc vibration is data losses of a computer hard disc drive because of its undesirable vibration.…”
The transverse vibration of an elastic disc, excited by a preloaded mass-damper-spring slider dragged around on the disc surface at a constant rotating speed and undergoing in-plane stick-slip oscillation due to friction, is studied. As the vertical vibration of the slider grows at certain conditions, it can separate from the disc and then reattach to the disc. Numerical simulation results show that separation and reattachment between the slider and the disc could occur in a low speed range well below the critical disc speed in the context of a rotating load. Rich nonlinear dynamic behaviour is discovered. Time-frequency analysis reveals the time-varying properties of this system and the contributions of separation and in-plane stick-slip vibration to the system frequencies. One major finding is that ignoring separation, as is usually done, often leads to very different dynamic behaviour and possibly misleading results.
The phenomenon brake squeal has been an ongoing topic for decades, both in the automotive industry and in science. Although there is agreement on the excitation mechanism of brake squeal, namely self‐excitation due to frictional forces between the disk and the pad, in the subject of squeal it is very complex to discover all relevant effects and to take them into account. Several of these problems are related to nonlinearities, for example, in the contact between pad and disk or drum or in the behavior of the brake pad material. One of these nonlinear effects, which has been almost completely neglected so far, is that the brake can engage, mainly due to the bushing and joint elements within the brake, different equilibrium positions. This in fact has serious influence on the noise behavior as shown in experimental studies. For example, it is observed in experiments that, despite identical operating parameters, squeal sometimes occurs and sometimes not. In initial experimental studies, this could be related to the engaged equilibrium position. Following these experimental studies, the present paper introduces a minimal model by extending the well‐known minimal model by Hoffmann et al. by corresponding elements and nonlinearities allowing the system to engage different equilibrium positions. As will be presented, the stability behavior strongly depends on the engaged equilibrium position. Therefore, the minimal model represents the key experimentally observed issues. Additionally, a limit cycle behavior can also be observed.
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