Gear Rattle during a start-up transient in a driveline equipped with a tuneable torsional Vibration Damper with Magneto-Rheological Elastomers

The paper reports a numerical investigation on the dynamic behaviour of a vehicle driveline, equipped with a Torsional Vibration Damper (TVD) based on Magneto-Rheological Elastomeric (MRE) spring elements, during the start-up transient considering an abrupt manoeuvre of clutch engagement. The TVD device consists of a flywheel and a damper disk, with interposed some elastomeric samples which react for relative angular displacements of the two disks. The dynamical parameters of the TVD can be properly tuned by varying the magnetic field surrounding the MRE springs to mitigate the torsional oscillations of the flywheel, causes of many undesired inconveniences as critical speeds or vibro-acoustic issues. The present study promotes the use of the MRE torsional vibration damper to reduce the annoying vibroacoustic phenomenon of “gear rattle” arising in the unloaded gear pairs of the gear box, during and after the rapid clutch engagement transients in the vehicle start-up phase and is conducted on a simplified automotive driveline equipped with a dry clutch. The possibility of quickly tuning the mechanical properties of the MRE-TVD, makes this device particularly eligible for suppressing the above disturbance, adapting to the various operative conditions of the automotive driveline. Results of the analysis, by the help of a Gear Rattle Index (GRI), demonstrate the effectiveness of the proposed device in reducing the vibroacoustic phenomenon during the transient phases of the vehicle start-up, until the vehicles speed conditions are reached.

Dynamics of moving-object grasped by a hybrid hand

When a heavy object is cooperatively grasped to move by several fingers of the robot hybrid hand, the inertial properties and the mass distribution of the object must influence largely on the operation precision, grasping stability, and the safety of both the hybrid hand and the object. Hence, it is an important and significant issue to establish and analyze the dynamics model of the moving-object cooperatively grasped by the hybrid hand in order to ensure the safety and grasping stability of the hybrid hand and the object. However, this research has not been conducted. In this paper, a dynamics model of the moving-object grasped by the hybrid hand is established, and its dynamics is studied and analyzed. First, a three-dimensional model of a hybrid hand formed by a novel parallel manipulator and three fingers is designed for cooperatively grasping object. Second, the kinematic formulas for solving the Jacobian matrices, the Hessian matrices, the general velocity/acceleration of the moving platform, and four active limbs of the parallel manipulator are derived. Third, the composite Jacobian matrix and the composite Hessian matrix of the hybrid hand are derived, and the general velocity/acceleration of the moving-object grasped by the hybrid hand is derived. Fourth, dynamics model of the hybrid hand is established, the formulas for solving the dynamic actuation forces of the three fingers and the dynamic actuation forces/torque and constrained forces of the parallel manipulator are derived. Finally, the theoretical solutions of the dynamics model of the moving-object grasped by the hybrid hand are verified by its simulation mechanism.

Oscillation control of a pendulum structure using an inverted pendulum-type tuned mass damper

In reality, a pendulum structure can be used to model many real structures as a ropeway carrier, crane, balloon basket or ships in waves, etc, which often hung on moving points such as cables, wavefronts and balloons, etc. To the best knowledge of the author, however, there is no study to control oscillation of the pendulum structure excited by the hanging point. Therefore, this article deals with the oscillation control of the pendulum structure by using an inverted pendulum-type tuned mass damper, in which the system is subjected to the motion of the hanging point. In particular, the optimal parameters are determined in clear analytical solutions, making it easy for scientists to determine the optimal parameters to suppress the oscillation for the pendulum structure.

A vibration model of a rotor system with the sinusoidal waviness by using the non-Hertzian solution

The nonlinear contact forces and deformations between the balls and raceways can cause very complex vibration behaviours of rotor systems with the waviness in the support bearings. However, almost all previous works that used sinusoidal waviness took the Hertzian solution as the calculation method, which is not an accurate method based on Johnson’s formulation since the changes in the curvature at the sinusoidal contact surfaces. To overcome this issue, a new dynamic model of a rigid rotor system with the waviness in the support bearings is proposed. To provide a more accurate nonlinear contact force formulation for the sinusoidal waviness profile, the model used the Johnson’s extended Hertzian contact model to replace Hertzian contact model. This model can consider the time-varying curvature between the mating sinusoidal surfaces. The lubricating condition in the support bearing is also considered. A comparative study on the effects of Hertzian contact model, simplified Hertzian contact model, and Johnson's extended Hertzian contact model on the nonlinear vibrations of the rotor system is developed. The effects of the waviness amplitude and orders on the vibrations of the rotor system are discussed. The comparative simulations show that the proposed model can provide a more reasonable approach for predicting the vibrations of the rigid rotor system. Moreover, the simulations give that the nonlinear contact forces in the support bearings can greatly affect the system vibrations.

Stability and synchronous characteristics of a two exciters vibration system considering material motion

Nowadays, two exciters vibration system played an indispensable role in a majority of machinery and devices, such as vibratory feeder, vibrating screen, vibration conveyer, vibrating crusher, and so on. The stability of the system and the synchronous characteristics of two exciters are affected by material motion. However, those effects of material on two exciters vibration system were studied very little. Based on the special background, a mechanical model that two exciters vibration system considering material motion is proposed. Firstly, the system's dynamic equations are solved by using Lagrange principle and Newton's second law. Then, the motion stability of the system when material with different mass move on the vibrating body is analyzed by [Formula: see text] mapping and numerical simulation methods, and the motion forms of the material are also studied. Meanwhile, the frequency responses of the vibrating body are analyzed. Finally, the influence of material on the phase difference of the two exciters is revealed. It can be concluded that with the mass ratio of the material to the vibrating body increasing, the system's motion evolves from stable periodic motion to chaotic state, the synchronization ability of two exciters decline, and the unpredictability of abrupt change about the phase difference increases. Further, the uncertainties of both the abrupt change of phase difference and the collision location affect each other and eventually lead to the instability of the system.

Sliding mode control for overturning prevention and hardware-in-loop experiment of heavy-duty vehicles based on dynamical load transfer ratio prediction

Aiming at the rollover risk of heavy-duty vehicles, an adaptive rollover prediction and control algorithm based on identification of multiple road adhesion coefficients is proposed, and the control effect has been verified by hardware-in-the-loop experiments. Based on the establishment of a 3 DOFs (Degree of freedom) vehicle dynamic model, the roll angle of the vehicle dynamic model is estimated in real time by using Kalman filter algorithm. In order to ensure the real-time operation of anti-rollover control strategy for multi-body dynamic heavy vehicle model, a sliding mode variable structure controller for anti-rollover of vehicles is designed to determine the optimal yaw moment. Specially, the recognition algorithm of road surface type is integrated into the control rollover algorithm. When the control system with road recognition algorithm recognizes whether the vehicle is in danger of rollover, it can not only adjust the state of the vehicle, but also shorten the time to reach the stable area of the vehicle's lateral load transfer rate by about 2 s. In order to further improve its adaptability and control accuracy, a Hardware-in-loop test platform for three-axis heavy-duty vehicles is built to verify the proposed anti-rollover control strategy. The results prove that the proposed control strategy can accurately predict the rollover risk and control the rollover in time.

Optimization design for multiple dynamic vibration absorbers on damped structures using equivalent linearization method

The dynamic vibration absorber and tuned mass damper are widely used to suppress harmful vibration of the damped structures under external excitation. The multiple dynamic vibration absorbers have more benefit than the single dynamic vibration absorber. The multiple dynamic vibration absorbers are portability and easy to install because its size is significantly reduced compared to an individual damper. This paper proposes a design method to obtain optimal parameters of multiple dynamic vibration absorbers attached on damped primary structures by using the least squares estimation of equivalent linearization method. An explicit expression of damping ratio and tuning parameters of multiple dynamic vibration absorbers are determined for minimizing the maximum displacement of the primary structures based on the fixed-point theory. The new contribution is provided a reliable theoretical basis for optimizing parameters of the multiple dynamic vibration absorbers that are attached on the damped primary structures. The numerical results reveal the effectiveness of the proposed optimal parameters of multiple dynamic vibration absorbers in reduce vibration of damped primary structures. In the practical applications, this research results allow to divide a large dynamic vibration absorber into many equivalent small dynamic vibration absorbers, which are convenient for manufacturing and installing on the damped primary structures such as high buildings and cable-stayed bridges.

A regularization method for solving dynamic problems with singular configuration

In the simulation process for multi-body systems, the generated redundant constraints will result in ill-conditioned dynamic equations, which are not good for stable simulations when the system motion proceeds near a singular configuration. In order to overcome the singularity problems, the paper presents a regularization method with an explicit expression based on Gauss principle, which does not need to eliminate the constraint violation after each iteration step compared with the traditional methods. Then the effectiveness and stability are demonstrated through two numerical examples, a slider-crank mechanism and a planar four-bar linkage. Simulation results obtained with the proposed method are analyzed and compared with augmented Lagrangian formulation and the null space formulation in terms of constraints violation, drift mechanical energy and computational efficiency, which shows that the proposed method is suitable to perform efficient and stable dynamic simulations for multi-body systems with singular configurations.

Effect of structural parameters and service conditions on the tilt angle of double row angular contact ball bearing

In this paper, for double row angular contact ball bearing, a five-degrees-of-freedom bearing analysis model based on quasi-statics is proposed. This model is used to study the influence of structural parameters and service conditions on the tilt angle and limit tilt angle of the bearing. The results show that the radial clearance will increase the ultimate tilt angle. The coincidence degree between the roller and the inner raceway will reduce the ultimate tilt angle, but the coincidence degree between the roller and the outer raceway has the opposite effect. The increase in the external load of the bearing will increase the tilt angle. The moment load has the greatest effect on the tilt angle. The rotation speed of the bearing has no effect on the tilt angle. The coincidence degree between the roller and the raceway will reduce the tilt angle; furthermore, the influence of the coincidence degree between roller and different ring on the tilt angle is also different when different rings are fixed. The tilt angle will decrease with the increase of the initial contact angle, and this effect is more and more obvious. The fixation of different ring has no effect on this influence.

Vibration characteristics of the gear shaft-bearing system with compound defects under variable operating conditions

Due to the variable working conditions, there are compound defects in the gear shaft-bearing system easily, vibration signals are very complex, and the fault diagnosis of the system becomes more difficult. Thus, a 36 degrees of freedom (36-DOFs) dynamic model is established for discussing the vibration characteristics of the gear shaft-bearing system, the gear pair spalling defect is considered, there are localized defects on the inner raceway and outer raceway of the supporting bearing, the work conditions contain variable speed, variable load, speed fluctuation, and load fluctuation. The obtained vibration signal is processed by the short-time Fourier transform for the time–frequency distribution map. When the gear shaft-bearing system with compound defects operates under variable conditions, roller passing outer raceway frequency, roller passing inner raceway frequency, gearing meshing frequency, and the relative harmonic frequencies can also be found. The defect frequencies and frequency amplitude are increasing with the speed while the system makes the accelerated movement. While the load acting on the system increases, the defect frequencies remain unchanged, but the frequency amplitude becomes larger. If there are fluctuations of the speed and load, the apparent defect frequency fluctuation and amplitude fluctuation is generated. The mathematical model and the analysis results are verified by the experiment, which will provide the theoretical basis for the fault diagnosis of the gear shaft-bearing system.