Renato Brancati

A gear rattle model accounting for oil squeeze between the meshing gear teeth

Abstract In this paper a non-linear one-degree-of-freedom model for analysis of gear rattle vibrations in automotive manual transmissions is presented. In order to take into account the damping effects owing to the oil in the gap between two teeth of a meshing gear, a simple one-dimensional model for the oil-film squeeze effects is proposed. The squeeze model assumes that the damping force is proportional to the oil viscosity and to the extension of the oil film in the plane of curvature of the teeth, which may depend on the lubrication conditions (dry sump, splash, bath). The results provided from several numerical simulations, carried out with reference to helical involute tooth pairs, confirm the capability of oil in reducing the high-frequency vibrations subsequent to the impact between the teeth. In particular, the influence exerted by oil viscosity and gap extension on the rattle characteristics is investigated through the analysis of the transient response of the driven gear by imposing a harmonic motion to the driving gear.

Journal Orbits and Their Stability for Rigid Unbalanced Rotors

With reference to a rigid symmetrical unbalanced rotor on lubricated journal bearings and adopting the short bearing theory, synchronous orbits and orbits with a 1/2 component described by the journal are determined as approximated solutions of the system of non-linear motion equations. The method also makes it possible to evaluate the stability of the above solutions and thus of the journal orbital motion. For different values of dimensionless unbalance of the rotor, examples of orbits thus obtained are given and, in the modified Sommerfeld number-stability parameter plane, the stability areas of the solutions are identified, in particular, the area of stability of the small synchronous orbits corresponding to the stable operating condition of the rotor-bearings system.

Non-linear stability analysis of a rigid rotor on tilting pad journal bearings

This paper describes a method for conducting non-linear stability analysis on the synchronous motion of the journal axis and tilting pads in a system consisting of a symmetrical rigid rotor mounted on tilting pad journal bearings with two pads. The method makes it possible to obtain the limit curves separating the stable operating condition, characterized by the above motion, from the so-called unstable one characterized by motions of the pads and journal with a fundamental frequency equal to one half the rotor angular speed. A variational method is used to carry out stability analysis on the synchronous solution of the non-linear equations of motion, obtained in an approximated analytical form using a particularized harmonic balance method.

On the stability of periodic motions of an unbalanced rigid rotor on lubricated journal bearings

A theoretical investigation is carried out on the orbital motions of a symmetrical, unbalanced, rigid rotor subjected to a constant vertical load and supported on two lubricated journal bearings. In order to determine the fluid film forces, the short bearing theory is adopted.A method is illustrated that makes it possible to determine the analytical equation of the orbit as an approximated solution of the system of non-linear differential equations of motion of the journal axis. A procedure is also described for evaluating the stability of the solution found. Diagrams of the curves delimiting, in the working plane of the rotor σ-mσ, the areas of stability of the various periodic solutions determined are provided.Finally, the results obtained are compared and combined with those provided by a direct integration of the motion equation made using the Runge-Kutta method.

A Vibration Isolator Based on Magneto-Rheological Elastomer

The paper presents an investigation about a magneto-rheological elastomeric (MRE) pad to be adopted as seismic semi-active isolator for lightweight structures. MRE pad may change its stiffness if immersed in a magnetic field. This characteristic allows to real time shift the fundamental frequency of the isolated structure. In this way it is possible to drive away the structure fundamental frequency from the exciting frequencies and therefore to reduce accelerations induced by the ground motion. The isolator includes a ball transfer unit (BTU) to sustain the vertical load so that MRE pad must only exert horizontal restoring forces and it may have a slender geometry without concern regarding buckling.

Feasibility study of the Hilbert transform in detecting the gear rattle phenomenon of automotive transmissions

This paper describes the feasibility analysis of a methodology based on the Hilbert transform in order to detect the gear rattle phenomenon of automotive transmissions. The technique adopts the Hilbert transform to analyze experimental signals of the relative angular motion of gears starting from high-resolution optical encoder measurements. By this procedure it is possible to evaluate the severity of impacts occurring between the teeth of unloaded gears, by examining the root mean square value of the signal. The Hilbert transform is largely adopted in the detection of gear defects, such as tooth cracks, but it has not yet been used to detect gear rattle. This feasibility study highlights the capability in discriminating between impacts occurring on the two different sides of the tooth. The method puts in evidence the influence of oil lubricant between the teeth in reducing the severity of the impacts, by comparing many experimental tests performed with two different oils for transmission gears. Moreover, in order to evaluate the reliability of the proposed methodology some comparisons are conducted with a metric based on the fast Fourier transform, often adopted in this field, to highlight the goodness and simplicity of the technique based on the Hilbert transform.

Recent investigations on robot mechanics at D.I.M.E.

Recent investigations in robot mechanics at Dipartimento di Ingegneria Meccanica per l’Energetica of the University of Naples Federico II (D.I.M.E.) are here reported. In general, the aim of these investigations is to obtain trajectories and paths from the end effector of a robot with the highest possible accuracy. In particular, these investigations consider the influence of circumferential backlash and transmission elasticity on the accuracy of a trajectory, and the possibility of obtaining more accurate paths via optimum positioning and orientation of the paths in the work space. The investigations were carried out both through simulation and experimentally; the simulations were performed using the ADAMS and Matlab-Simulink computer programs while the experiments involved use of an industrial robot and a prototype designed and built at D.I.M.E.

Experimental Measurement of Underactuated Robotic Finger Configurations via RGB-D Sensor

Underactuated robotic systems need suitable experimental methods able to measure their small and low-weight component dynamics. Depth sensors represent a valuable strategy to develop quantitative approaches to study the behavior of these systems. Here, an experimental application of markerless vision technique is proposed employing the low-cost and low-resolution Kinect depth sensor to compute the kinematics of an underactuated robotic finger.

Experimental vibro-acoustic analysis of the gear rattle induced by multi-harmonic excitation

The paper reports a wide vibro-acoustic experimental investigation of the gear rattle phenomenon induced by multi-harmonic excitation. The analysis is performed by using different measurement techniques which allow some of the significant parameters in this type of investigation to be acquired on a specific test rig: the angular rotations of the gears by using encoders; the accelerations obtained from a triaxial accelerometer; the sound pressure level determined by employing both acoustic microphones; the correct evaluation of the acoustic sources by utilizing a p–v sound intensity probe. Performance indices were adopted to compare the dynamic behaviours of the system with respect to some parameters, such as the speed of the pinion, the fluctuations in the speed of the pinion and the lubrication conditions. The results of the comparative analysis show very good agreement between the vibro-acoustic measurements and the results from the encoder-based method; this has helped us to interpret the physical behaviour of the gear pair with respect to the impacts occurring between the teeth during the different phases of the phenomenon. Moreover, the study indicates interesting aspects of the effects of multi-harmonic excitation on the rattle phenomenon, with particular attention to the influence of lubrication on the reduction in the rattle noise.

Wavelet Analysis of Gear Rattle Induced by a Multi-harmonic Excitation

The paper reports a feasibility study for the detection of automotive gear rattle induced by multi-harmonic excitation through the use of a wavelet multi-resolution analysis. The analysis adopts experimental data coming from a helical gear pair under unloaded conditions. The excitation of gear rattle is of periodic type with two harmonic components, which is similar to the excitation of an actual automotive I.C. engine. The dynamic behavior of the gear pair has been analyzed by varying the second order harmonic amplitude of the excitation, for two mean speed values. The analysis gives useful information to develop an index of performances based on the wavelet theory that could be adopted for comparative analyses with respect to the severity of the tooth impacts occurring during the rattle phenomenon.