Ernesto Rocca

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.

A feasibility study on elastokinematic parameter identification for a multilink suspension

Abstract In this paper an algorithm for the kinematic analysis of a multilink suspension taking joint compliance into account is presented. The analysis can be pro. tably used in an identi. cation procedure to determine elastokinematic parameters starting from experimental data. The proposed identification algorithm is based on the solution of a typical non-linear least-squares problem. Inorder to test the feasibility of this procedure, a multilink suspension, modelled by a multibody dynamics code, is employed as the experimental data source. Some joint stiVness values are determined to provide an example of the algorithms application.

Dynamic Behaviour of Tilting-Pad Journal Bearings

The dynamic behaviour of a rigid rotor on tilting-pad journal bearings system is analysed for balanced and unbalanced rotors. The study mainly regards a two-pad journal bearing symmetric with respect to the external static load. Both linear and non-linear behaviours have been analysed, with particular reference to the stability of the journal and pads equilibrium positions in the case of balanced or slightly unbalanced rotors, and to the stability of their synchronous motions in the case of considerable unbalance.

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.

Instability Threshold of a Rigid Rotor-Tilting Pad Journal Bearings System

The stability of a rigid rotor supported on radial tilting pad journal bearings is analysed. This study has been tackled both for small unbalance values by linearising the equations of motion, and also in the case where, because of the high unbalance value, the rotor axis describes orbits with an amplitude such that the systems non-linearity cannot be ignored. In both cases the systems stable operation maps have been obtained and verified through numerical integration of the differential equations of motion.

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.

Elasto-Kinematic Characteristics of Car Suspensions with Magneto-Rheological Bushings

The paper reports a feasibility study of car suspensions equipped with an innovative bushing composed by an elastomer having magneto-rheological characteristics in order to improve the performances in terms of handling and comfort. The analysis focuses on the effects produced by the variations in stiffness due to the magneto-rheological effect on the elastomeric material of the bushing. This magneto- rheological effect is designed to act on the performances of the vehicle particularly during the transients of the dynamic behavior. The performances can be achieved by acting on the characteristics of the suspension bushing on the car body.