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Several methodologies for the mesh stiffness calculation in spur gears have been found in the literature, in the last decades. Based on a bibliographical analysis and the research activities of the authors, attention has been devoted to three methodologies, which appeared as the most employed and cited. A critical review of such methodologies, FE-based method, hybrid analytical-FE method, and analytical approach, has been undertaken, highlighting some crucial aspects regarding the mesh stiffness estimation process. Within this framework, useful information related to the critical choice of parameters needed for the implementation of the methods are presented, in order to provide further guidelines for their application. Furthermore, the methods are compared in terms of results accuracy and computational time for full blank and lightweight gears. This comparison leads to useful guidelines regarding the definition of the most suitable approach depending on the specific requirements. Finally, two variants of an examined hybrid method are presented. They are based on linear, nonlinear FE analyses and analytical formulation. Their purpose is to compare the use of different analytical formulations against the FE formulation for the computation of the local deformation of gear teeth.

The mathematical model for evaluating the dynamic behavior of linear vibratory feeders is presented and discussed. The model is based on the Eksergian's equation of motion, with the aim at taking into account the effects of the main design parameters without unnecessarily increasing the complexity of the model. Deep emphasis is given to the procedure for the estimation of the external excitations applied to the driveline by proposing two procedures. The first one gives birth to a transcendent equation system, while the second procedure, based on more restrictive hypotheses regarding the geometry of the feeder, leads to a linear system. A dedicated experimental campaign for characterizing the dynamic behavior of a real machine is conducted under different operational conditions. Measured data are compared with simulated results obtained by applying both models; the experimental validation highlights the satisfactory quality of the model estimation, both in terms of torsional oscillations of the driveline and the global frame vibrations.

Noise and vibration control in mechanical systems has become ever more significant for automotive industry where the comfort of the passenger compartment represents a challenging issue for car manufacturers. The reduction of piston slap noise is pivotal for a good design of IC engines. In this scenario, a methodology has been developed for the vibro-acoustic assessment of IC diesel engines by means of design changes in piston to cylinder bore clearance. Vibration signals have been analysed by means of advanced signal processing techniques taking advantage of cyclostationarity theory. The procedure departs from the analysis of the Continuous Wavelet Transform (CWT) in order to identify a representative frequency band of piston slap phenomenon. Such a frequency band has been exploited as the input data in the further signal processing analysis that involves the envelope analysis of the second order cyclostationary component of the signal. The second order harmonic component has been used as the benchmark parameter of piston slap noise. An experimental procedure of vibrational benchmarking is proposed and verified at different operational conditions in real IC engines actually equipped on cars. This study clearly underlines the crucial role of the transducer positioning when differences among real piston-to-cylinder clearances are considered. In particular, the proposed methodology is effective for the sensors placed on the outer cylinder wall in all the tested conditions.

The gear fault diagnosis on multistage gearboxes by vibration analysis is a challenging task due to the complexity of the vibration signal. The localization of the gear fault occurring in a wheel located in the intermediate shaft can be particularly complex due to the superposition of the vibration signature of the synchronous wheels. Indeed, the gear fault detection is commonly restricted to the identification of the stage containing the faulty gear rather than the faulty gear itself. In this context, the paper advances a methodology which combines the Empirical Mode Decomposition and the Time Synchronous Average in order to separate the vibration signals of the synchronous gears mounted on the same shaft. The physical meaningful modes are selected by means of a criterion based on Pearson’s coefficients and the fault detection is performed by dedicated condition indicators. The proposed method is validated taking into account simulated vibrations signals and real ones.

Driveline components connected to internal combustion engines can be critically loaded by dynamic forces due to motion irregularity. In particular, flexible couplings used in engine test rig are usually subjected to high levels of torsional oscillations and time-varying torque. This could lead to premature failure of the test rig. In this work an effective methodology for the estimation of the dynamic behavior of highly flexible couplings in real operational conditions is presented in order to prevent unwanted halts. The methodology addresses a combination of numerical models and experimental measurements. In particular, two mathematical models of the engine test rig were developed: a torsional lumped-parameter model for the estimation of the torsional dynamic behavior in operative conditions and a finite element model for the estimation of the natural frequencies of the coupling. The experimental campaign addressed torsional vibration measurements in order to characterize the driveline dynamic behavior as well as validate the models. The measurements were achieved by a coder-based technique using optical sensors and zebra tapes. Eventually, the validated models were used to evaluate the effect of design modifications of the coupling elements in terms of natural frequencies (torsional and bending), torsional vibration amplitude, and power loss in the couplings.

Heavy duty wheels are used in applications such as automatic vehicles and are mainly composed of a polyurethane tread glued to a cast iron hub. In the manufacturing process, the adhesive application between tread and hub is a critical assembly phase, since it is completely made by an operator and a contamination of the bond area may happen. Furthermore, the presence of rust on the hub surface can contribute to worsen the adherence interface, reducing the operating life. In this scenario, a quality control procedure for fault detection to be used at the end of the manufacturing process has been developed. This procedure is based on vibration processing techniques and takes advantages of the results of a lumped parameter model. Indicators based on cyclostationarity can be considered as key parameters to be adopted in a monitoring test station at the end of the production line due to their not deterministic characteristics.

The development of a zero-dimensional model for analysing pressure phenomena in multiple stage external gear pumps is addressed in the present work. The tandem pump is composed of two coaxial stages: the high pressure one, made by spur gears, and the low pressure one, made by helical gears. The two stages have common shafts and a common case. The oil pressure course around the gearpair, as well as the suction/delivery pressure ripple, is estimated for both stages. Attention is focused on the description of the modelling approach: an original method is developed to model the helical gears and their effects on the determination of the geometrical parameters. The lumped parameter (LP) model takes advantage of a Computational Fluid Dynamic (CFD) model applied to different pump regions in order to estimate several internal flow features. Measured delivery pressure ripple and volumetric efficiency are used to evaluate the model reliability under different working conditions.

So far, the study of gear contacts in lightly loaded gears by means of vibration analysis has not been sufficiently addressed in the literature. Indeed, the complex nature of the physical phenomena involved makes the vibration analysis extremely challenging. This paper deals with the development and the validation of an approach for the contact pattern assessment in straight bevel gears within a pass/fail decision process. The proposed methodology is based on blending vibration-based condition indicators with classification algorithms in order to discriminate proper contact patterns from improper ones. Specifically, three different classification algorithms have been investigated: the Naive Bayes classifier, the weighted k-Nearest Neighbors classifier and a novel classifier proposed by the authors. The classifier accuracies are evaluated with a MC cross-validation that includes an extended experimental campaign consisting of more than one hundred different straight bevel gear pairs. The results show that the proposed classifier is superior to the other considered classifiers in terms of average accuracy. Finally, this manuscript proposes an original methodology that provides a reliable and quick assessment of the contact pattern in straight bevel gears considering different speeds, gear parameters and surface finish.

This paper addresses the use of first- and second-order cyclostationary (CS1 and CS2) tools to process the vibration signals picked up from internal combustion (IC) engines during cold tests. This type of analysis is needed in order to detect and diagnose irregular operations for quality control purposes. The effectiveness of indicators such as Mean Instantaneous Power (MIP), Degree of Cyclostationarity ( D C S α ) and Indicator of Cyclostationarity ( I C S n x ) in detecting assembly faults has been tested on real signals concerning three faulty conditions: inverted piston, connecting rod with incorrectly tightened screws, connecting rod without one bearing cap. In the past several authors have mainly used cyclostationary metrics for diagnostics purposes in rolling bearings and gear systems. Moreover, a signal model, qualitatively reproducing the features of actual cold test signals, has been formulated and used in order to preliminarily study the influence of signal parameters on the Indicators of Cyclostationarity. The results indicate that the cyclostationary tools – mainly CS2 tools – are effective in detecting and diagnosing all tested faulty conditions. In particular, indicator I C ⌢ S 2 x is highly sensitive to faults and it is suitable as pass/fail tool in quality control at the end of the engine assembly line. As a further second-order cyclostationary metric, the MIP is effective for detection, as well for fault identification, since it is able to localize regular and fault events within the engine cycle. In addition D C S α effectively characterizes the CS2 periodicities, giving the cyclic order distribution. Since these CS2 tools require a moderate computation cost, they can be considered ready for on-line industrial applications.

Classical design optimization procedures rely on the application of optimization algorithms upon system simulations. These algorithms need a large number of samples to converge on the optimal point. Hence design optimization needs large simulation time since each simulation has to be performed many times. In this paper an original and useful methodology to study and optimize mechanical systems is presented. The proposed methodology combines different techniques such as design of experiments, response surface models and evolutionary algorithms leading to larger time reduction with respect to the classical design optimization approach. On the one hand the proposed methodology gives the optimal combination of variables and on the other hand provides important results to understand the influence of each input to the system outputs. Moreover, a robust design process has been carried out in order to consider the manufacturing tolerances of the real mechanical system and assess their effect on the system performance. The results offer important information and design insights that would be very difficult to obtain without such a procedure. In order to demonstrate the methodology effectiveness, two case studies have been accounted: the optimization of the vibration level of a vane pump and a gear pump. To simulate the dynamical behaviour of the two pumps, mathematical models have been used. These models have been developed and validated by the authors in previous works. The mathematical models include the main important phenomena involved in the pumps operation and they have been validated on the basis of experimental data. The main operational and geometrical input variables have been taken into account in the optimization procedure of such pumps.

The monitoring of rolling element bearings through vibration-based condition indicators plays a crucial role in the modern machinery. The kurtosis is a very efficient indicator being sensitive to impulsive components within the vibration signature that often are symptomatic of localized faults. In order to improve the diagnostic performance of the kurtosis, blind deconvolution algorithms can be exploited in order to detect bearing faults and, most importantly, their position. In this scenario, this paper focuses on the development of a novel condition indicator specifically designed for the damage assessment in rolling element bearings. The proposed indicator allows to track the bearing degradation process taking into account three different possible positions: outer race, inner race, and rolling element. This indicator fits real-time monitoring procedures allowing for the automatic detection and identification of the bearing fault. The validation of the proposed indicator has been carried out by means of both simulated signal and a run-to-failure experiment. The results highlight that the proposed indicator is able to detect more efficiently the fault occurrence and, most importantly, quicker than other established techniques.

This work concerns external gear pumps for automotive applications, which operate at high speed and low pressure. In previous works of the authors (Part I and II, [1] , [2] ), a non-linear lumped-parameter kineto-elastodynamic model for the prediction of the dynamic behaviour of external gear pumps was presented. It takes into account the most important phenomena involved in the operation of this kind of machine. The two main sources of noise and vibration are considered: pressure pulsation and gear meshing. The model has been used in order to foresee the influence of working conditions and design modifications on vibration generation. The model experimental validation is a difficult task. Thus, Part III proposes a novel methodology for the validation carried out by the comparison of simulations and experimental results concerning forces and moments: it deals with the external and inertial components acting on the gears, estimated by the model, and the reactions and inertial components on the pump casing and the test plate, obtained by measurements. The validation is carried out by comparing the level of the time synchronous average in the time domain and the waterfall maps in the frequency domain, with particular attention to identify system resonances. The validation results are satisfactory global, but discrepancies are still present. Moreover, the assessed model has been properly modified for the application to a new virtual pump prototype with helical gears in order to foresee gear accelerations and dynamic forces. Part IV is focused on improvements in the modelling and analysis of the phenomena bound to the pressure distribution around the gears in order to achieve results closer to the measured values. As a matter of fact, the simulation results have shown that a variable meshing stiffness has a notable contribution on the dynamic behaviour of the pump but this is not as important as the pressure phenomena. As a consequence, the original model was modified with the aim at improving the calculation of pressure forces and torques. The improved pressure formulation includes several phenomena not considered in the previous one, such as the variable pressure evolution at input and output ports, as well as an accurate description of the trapped volume and its connections with high and low pressure chambers. The importance of these improvements are highlighted by comparison with experimental results, showing satisfactory matching.

This paper proposes an experimental methodology for the analysis of the lubrication regime and wear that occur between vanes and pressure ring in variable displacement vane pumps. The knowledge of the lubrication regime is essential for the improvement of the performance of high pressure vane pumps by reducing wear, increasing the volumetric efficiency and decreasing maintenance costs. Tests using pressure rings of different materials were carried out in order to identify the best material in terms of wear and friction. The proposed methodology is based on Archard's law and takes advantage of wear experimental measurements, an empirical model for the estimation of contact pressure forces and hardness standard tests. The results of the analysis state that low wear and reduced friction can be obtained if elasto-hydrodynamic lubrication between vanes and pressure ring is established. Results have been also verified by an analytical elasto-hydrodynamic model.

Before marketing external gear pumps are subjected to a running in process to increase their efficiency. However, this is one of the most time-consuming tasks of the entire manufacturing process. Therefore, a mathematical model for optimizing the running in process can be a useful tool for time-to-market reduction. In particular, in this paper a model for the analysis of the dynamic behaviour of external gear pumps, developed by the authors in previous works, is modified and used for simulating the running in process. The modified model is presented and validated via experimental data. A good correlation between simulation and test results guarantees the effectiveness of the model in determining the amount and the distribution of the removed material during the running in process. A meaningful reduction (16%) of the global running in time has been achieved with the introduction of a modified running in process drawn from simulation results.

The inertia properties of an engine to be mounted on complex mechanical systems (e.g., cars, boats, etc.) are usually evaluated by considering the engine like a rigid-body (RB). These properties are mainly employed to design the geometry and the stiffness of the engine support, so as to build the dynamic model of the mechanical system the engine has to be mounted on. In this paper, two different techniques for measuring the RB inertia properties are compared: one in the time domain and the other in the frequency domain. The time-domain technique is based on the measurement of the oscillation period of a trifilar pendulum; whilst, the frequency-domain technique is based on the measurement of the Frequency Response Function (FRF) of the softly suspended RB. These techniques are applied to estimate the RB inertia properties both of an engine block and of a marine diesel engine. Eventually, their pros and contras are highlighted.

The present paper addresses the development of a lumped parameters model used to analyze the dynamic behavior of a so-called tandem gear pump. The pump is composed of two coaxial stages, both with external gears: a high pressure stage with spur gears and a low pressure one with helical gears. In particular, the paper deals with the modelling and the analysis of the phenomena bound to the pressure distribution around the gears, since they have the most important effect in the dynamic behavior of the pump. The pressure variation in the inlet and outlet chambers, the variable pressure in the trapped volume as well as the pressure evolution from the low to the high pressure chamber is estimated based on the Euler’s approach. The model is developed in Matlab environment. Attention is particularly focused on the description of the methodology adopted for modelling the low-pressure stage, constituted by helical gears, and its influence on the calculation of the pump geometrical parameters. The results provided by the numerical model are compared with experimental measurements in terms of outlet pressure ripple and volumetric efficiency under different working conditions. The results of the validation can be considered satisfactory. Predicted pressure ripple is shown and the effects of interconnections between stages are analyzed studying the outlet pressure ripple in the frequency domain as well.Copyright © 2015 by ASME

This work concerns external gear pumps for automotive applications, which operate at high speed and low pressure. In previous works of the authors (Part I and II, [1] , [2] ), a non-linear lumped-parameter kineto-elastodynamic model for the prediction of the dynamic behaviour of external gear pumps was presented. It takes into account the most important phenomena involved in the operation of this kind of machine. The two main sources of noise and vibration are considered: pressure pulsation and gear meshing. The model has been used in order to foresee the influence of working conditions and design modifications on vibration generation. The model׳s experimental validation is a difficult task. Thus, Part III proposes a novel methodology for the validation carried out by the comparison of simulations and experimental results concerning forces and moments: it deals with the external and inertial components acting on the gears, estimated by the model, and the reactions and inertial components on the pump casing and the test plate, obtained by measurements. The validation is carried out comparing the level of the time synchronous average in the time domain and the waterfall maps in the frequency domain, with particular attention to identify system resonances. The validation results are satisfactory globally, but discrepancies are still present. Moreover, the assessed model has been properly modified for the application to a new virtual pump prototype with helical gears in order to foresee gear accelerations and dynamic forces. Part IV is focused on improvements in the modelling and analysis of the phenomena bound to the pressure evolution around the gears in order to achieve results closer to the measured values. As a matter of fact, the simulation results have shown that a variable meshing stiffness has a notable contribution on the dynamic behaviour of the pump but this is not as important as the pressure phenomena. As a consequence, the original model was modified with the aim at improving the calculation of pressure forces and torques. The improved pressure formulation includes several phenomena not considered in the previous one, such as the variable pressure evolution at input and output ports, as well as an accurate description of the trapped volume and its connections with high and low pressure chambers. The importance of these improvements are highlighted by comparison with experimental results, showing satisfactory matching.

The paper presents a methodology for noise and vibration analysis of gear pumps and its application to an external gear pump for automotive applications. The methodology addresses the use of a combined numerical model and experimental analyses. The combined model includes a lumped-parameter model, a finite-element model and a boundary-element model. The lumped-parameter (LP) model regards the interior parts of the pump (bearing blocks and gears loaded by the pressure distribution and the driving torque), the finite element (FE) model regards the external parts of the pump (casing and end plates), while the boundary element (BE) model enables the estimation of the emitted noise in operational conditions. Based on experimental evidences, attention has been devoted to the modelling of the pump lubricant oil: the fluid-structure interaction between the oil and pump casing was taken into account. In the case of gear pumps all these important effects have to be considered in the same model in order to take their interactions into account. The model has been assessed using experiments: the experimental accelerations and acoustic pressure measured in operational conditions have been compared with the simulated data coming from the combined LP/FE/BE model. The combined model can be considered a very useful tool for design optimisation. (C) 2013 Elsevier Ltd. All rights reserved.

The free vibrations of circular cylindrical shells partiallyloaded by a distributed mass and rested on an elastic bed are studied in this paper. Both the mass-load and the elastic bed are assumed to be applied on limited arcs and with arbitrary distributions in circumferential direction,while they are considered to be uniformly distributed in longitudinaldirection on the entire shell length. Therefore, the problem is notaxisymmetric. The solution is obtained by using the development of theflexural mode shapes in a Fourier series, whose coefficients are determinedby rendering the Rayleigh quotient stationary, so a Galerkin equation isobtained. The proposed method is independent of the boundary conditionsat the shell ends. The results are satisfactorily compared to FEM results.Finally, the influence of the mass-load and of the bed stiffness on thenatural frequencies and mode shapes of a simply supported shell is shownand discussed.

Two models for the estimation of the pressure evolution in high pressure variable displacement vane pumps are proposed: a lumped parameter model and an empirical model. The former has full physical meaning and allows to simulate the behavior of a wide pump range, the latter, based on experimental measurements, can be applied only to a single family of pumps. Both the models can simulate the pressure evolution around the rotor in working conditions. These results are important for the structural design of the pump. Moreover, these models are the first element of a combined model aimed at the dynamic simulation of this type of pump, as a tool for vibro–acoustical optimization.Copyright © 2013 by ASME

Vane pumps exhibit pressure ripple in the pressure evolution trend during a complete shaft rotation. Pressure ripple can determine oscillating forces within the system leading to vibration and noise generation. In this context, this paper is focused on the experimental measurement of the pressure evolution in vane pumps by using two different methodologies. Results of measurements are shown, highlighting advantages and disadvantages of both methodologies. In the first method a pressure transducer is directly facing the volume between two vanes, in the second method the sensor is located inside an external chamber where the oil is transferred via a duct suitably designed in the rotor shaft. Briefly, the first method gives better results in terms of pressure evolution but involves some practical problems in the setup: the measurements exhibit pressure offsets strongly dependent on the tightening torque used for sensor mounting and negative pressure values in the low pressure region. The second method is simpler to set up but the results are influenced by the dynamical behavior of the measurement duct carrying oil. In order to avoid resonances of this duct, a vibro-acoustical finite element (FE) model of the oil cavity has been developed. The numerical frequency response functions obtained by the FE model have been used in order to optimize the geometry of the measurement duct, reducing the effects of the resonances of the oil ducts. It is shown that, using this improved methodology, the dynamical components of the measured pressure are not significantly influenced by the frequency response of the measurement duct when the outlet pressures is higher than 50 bar, while for lower outlet pressure the first resonance of the measurement duct is close to the main vane harmonics.

This work addresses the elastodynamic modeling of vibratory bowl feeders and its experimental verification. The bowl feeder mainly consists of a bowl connected to a base by three or four inclined leaf springs. The springs constrain the bowl so that its vertical displacement causes a coupled rotation around its vertical symmetry axis. The feeder is actuated by electromagnets, while rubber mounts are positioned under the base for reducing the vibration transmission to the floor. The developed model is a linear lumped-parameter model for the prediction of the dynamic behavior of bowl feeders. The model has been experimentally verified by means of modal analyses and operational accelerations. Model parameters, such as the stiffness and damping of rubber mounts, leaf spring stiffness and time-varying excitation, have been experimentally estimated. The proposed model can be used for the analysis of feeder dynamics and for evaluating the effects of changes in design and operational parameters in terms of bowl and base vibration and dynamic forces transmitted to the floor.

In this work a combined model for the vibro-acoustic analysis of an external gear pump for automotive applications is presented and experimentally assessed. The model includes a lumped-parameter model, a finite-element model and a boundary-element model. The lumped-parameter (LP) model regards the interior parts of the pump (bearing blocks and gears), the finite element (FE) model regards the external parts of the pump (casing and end plates), while the boundary element (BE) model estimates the noise generation in operational conditions. Attention has been devoted to the inclusion of the oil effect inside the pump casing: the fluid-structure interaction between oil and pump casing was taken into account. The model has been assessed using experiments: the experimental accelerations and acoustic pressure measured in operational conditions have been compared with the simulated data coming from the combined LP/FE/BE model. Eventually, model results and limitations are presented.Copyright © 2013 by ASME

This work presents a wide number of results about the influence that variations in terms of operational and design parameters play on the dynamic behavior of external gear pumps. These results are obtained by using a non-linear lumped-parameter kineto-elastodynamic model developed and experimentally assessed with the aim of including all the important dynamic effects. On the one hand, the effects of variations in the operational parameters—namely output pressure, rotational speed and oil viscosity—are analysed; on the other hand, the effects of modifications of some design parameters are shown: clearances and relief groove dimension. The results in terms of gear eccentricity, pressure evolution, pressure forces, gear accelerations and variable forces exciting the pump casing enlighten the dynamic behavior of gear pumps and give useful indications for design improvements and vibration and noise reduction. As regards specifically gear accelerations as well as forces exciting the casing, they strongly increase with both output pressure and rotational speed, but variations in rotational speed in the operational range give lower effects. Conversely, the modifications of the clearances give negligible effects, while the relief groove dimension is very important: the larger the relief grooves are, the higher the gear accelerations and forces exciting the casing become.

This work addresses the topic of external gear pumps for automotive applications, which operate at high speed and low pressure. In previous works of the authors, a hybrid lumped-parameter/finite-element model has been developed, in order to foresee the pump dynamic behaviour in terms of gear and casing acceleration. The model includes the main important phenomena involved in the pump operation and it has been validated on the basis of experimental data. In this research, an original optimization process has been applied to such a hybrid model in order to reduce the pump vibration level, i.e. the acceleration of the external casing. The set up of the optimization process comprises a single objective (case accelerations) and some operational and geometrical input variables (oil viscosity, oil Bulk modulus, relief groove dimension and radial clearance in the journal bearings). This paper compares three optimization methodologies for the optimization of the pump vibration level. In particular common optimization processes based on simulations are compared with a combined analysis based, firstly, on Design Of Experiments (DOE) and Response Surface Modelling (RSM) and, secondly, on the application of evolutionary algorithms to reach the optimal variable combination. The different methodologies are compared in terms of time efficiency and accuracy in the solution. Finally, a robust design process has been carried out in order to consider the manufacturing tolerances of the real pump and assess their effect on the performance of the component. The results offer important information and design insights that would be very difficult to obtain without such procedures.

A non-linear lumped kineto-elastodynamic model for the prediction of the dynamic behaviour of external gear pumps is presented. It takes into account the most important phenomena involved in the operation of this kind of machines. Two main sources of noise and vibration can be considered: pressure and gear meshing. Fluid pressure distribution on gears, which is time-varying, is computed and included as a resultant external force and torque acting on the gears. Parametric excitations due to time-varying meshing stiffness, the tooth profile errors (obtained by a metrological analysis), the backlash effects between meshing teeth, the lubricant squeeze and the possibility of tooth contact on both lines of action were also included. Finally, the torsional stiffness and damping of the driving shaft and the non-linear behaviour of the hydrodynamic journal bearings were also taken into account. Model validation was carried out on the basis of experimental data concerning case accelerations and force reactions. The model can be used in order to analyse the pump dynamic behaviour and to identify the effects of modifications in design and operation parameters, in terms of vibration and dynamic forces. Part I is devoted to the calculation of the gear eccentricity in the steady-state condition as result of the balancing between mean pressure loads, mean meshing force and bearing reactions, while in Part II the meshing phenomena are fully explained and the main simulation results are presented.

A non-linear lumped kineto-elastodynamic model for the prediction of the dynamic behaviour of external gear pumps is presented. It takes into account the most important phenomena involved in the operation of this kind of machines. Two main sources of noise and vibration can be considered: pressure and gear meshing. Fluid pressure distribution on gears, which is time-varying, is computed and included as a resultant external force and torque acting on the gears. Parametric excitations due to time-varying meshing stiffness, the tooth profile errors (obtained by a metrological analysis), the backlash effects between meshing teeth, the lubricant squeeze and the possibility of tooth contact on both lines of action were also included. Finally, the torsional stiffness and damping of the driving shaft and the non-linear behaviour of the hydrodynamic journal bearings were also taken into account. Model validation was carried out on the basis of experimental data concerning case accelerations and force reactions. The model can be used in order to analyse the pump dynamic behaviour and to identify the effects of modifications in design and operation parameters, in terms of vibration and dynamic forces. Part I is devoted to the calculation of the gear eccentricity in the steady-state condition as a result of the balancing between mean pressure loads, mean meshing force and bearing reactions, while in Part II the meshing phenomena are fully explained and the main simulation results are presented.

In the context of full automation of manufacturing processes, it is important to develop predictive maintenance methodologies in every industrial field. This paper presents experimental tests carried out on some components of high-performance automatic machines. The aim is to assess and compare the effectiveness and reliability of different condition monitoring methodologies based on vibration analysis. A methodology based on recovery of the acceleration pattern of the final actuator of the mechanism under consideration seems to be particularly promising. It allows the working conditions to be judged, directly comparing the recovered output member acceleration with the functional requirements which, for this kind of mechanism, are mainly relative to the motion law. A lumped parameter model of the same mechanism is presented and its application for diagnostic purposes is shown.

A combined lumped/finite element model of a portion of the desmodromic valve train of a racing motorbike engine was developed and validated in order to simulate the elastodynamic behaviour of such a particular timing system. The model includes the lumped parameter model of the belt transmission that drives the camshafts, the finite element model of the camshafts, and the lumped parameter model of two cam-valve mechanisms (one for each camshaft). The procedure to validate the model, based on experimental tests carried out on a test bench described here, is presented and discussed. The comparison between the numerical results and the experimental data shows that the effectiveness of the model is satisfactorily achieved. It will be possible, in a further study, to add the other cam-valve mechanisms and the missing external forces, in order to obtain a complete system model. Some possible applications of the presented model are provided in order to show how the overall model could be employed to perform both design optimisation and diagnostics.

This work deals with valve motion measurements on cylinder heads of Ducati racing motorbikes, by means of high speed laser Doppler vibrometer. The experimental apparatus is described and some measurement results are presented.The results confirm that the effects of the dynamic phenomena are very important, especially at high speeds, and that thedynamic response gets worse with the increment of backlashes in the cam kinematic pairs. In addition, the measurements make it possible to analyse the valve bumping phenomena. The information retrieved from measurements provides insight into the cam system dynamics and helps the development of elastodynamic predictive models.Keywords: valve train, laser Doppler vibrometer, motorbike engine, test bench. 1. INTRODUCTION Nowadays tests on the dynamic performances of valve trains in reciprocating engines are becoming more and more important. In fact, this kind of devices operates at very high speed and, as a consequence, it is not possible to neglect theeffects of link elastic flexibility and mass distribution, as well as the effects of backlashes and friction in joints, on thedynamic response of the mechanism. In particular, the valve motion can be so affected by the above mentioned effects,that it may fail to perform its tasks adequately, e.g. leading to alterations of the engine's fluid dynamics. In addition, highaccelerations and dynamic stress levels take place and may cause serious functional troubles, such as wear, fatigue andbreakage of mechanical components (see Fig. 1 and 2).This work deals with a desmodromic valve train of the twincylinder 'L' engine of Ducati racing motorbikes. This timing

A lumped-parameter model of a motorbike engine’s desmodromic valve train is developed for the simulation of the dynamic behaviour of such an uncommon train. The model takes into account several non-linear effects and is highly time-varying. The estimation of the model parameters is discussed and the effectiveness of the model is assessed by a comparison with experimental results. The model is employed to predict the magnitude of forces, impacts and bounces, and to detect unacceptable dynamic phenomena; thus, it may be used as a tool both in design optimization and diagnostics.

This paper deals with gear condition monitoring based on vibration analysis techniques. The detection and diagnostic capability of some of the most effective techniques are discussed and compared on the basis of experimental results, concerning a gear pair affected by a fatigue crack. In particular, the results of new approaches based on time-frequency and cyclostationarity analysis are compared against those obtained by means of the well-accepted cepstrum analysis and time-synchronous average analysis. Moreover, the sensitivity to fault severity is assessed by considering two different depths of the crack. The effect of transducer location and processing options are also shown. In the case of the experimental results considered in this paper, the power cepstrum is practically insensitive to the crack evolution. Conversely, the spectral correlation density function is able to monitor the fault development and does not seem to be significantly influenced by the transducer position. Analysis techniques of the time-synchronous average, such as the ‘residual’ signal and the demodulation technique, are able to localise the damaged tooth; however, the sensitivity of the demodulation technique is strongly dependent on the proper choice of the filtering band and affected by the transducer location. The wavelet transform seems to be a good tool for crack detection; it is particularly effective if the residual part of the time-synchronous averaged signal is processed.

This paper assesses and compares the effectiveness and reliability of different vibration analysis techniques for fault detection and diagnostics in cam mechanisms used in high performance automatic packaging machines. Firstly, the results of the application of widely used techniques are given and their limitations are delineated. Secondly, the application of the wavelet transform is proposed, since the vibrations of this kind of machine are highly non-stationary. Finally, an inverse filtering technique is used to recover the actual output link motion from the casing vibration, in order to enable condition monitoring and diagnostics to be carried out through the analysis of the mechanism motion.

The influence of Poisson's ratio upon the free vibrations of free-edge circular plates is studied, both when in vacuum and in contact with liquid. In the latter case, the liquid-structure interaction is evaluated by applying the added virtual mass approach. The frequency and mode shape parameters, as well as the non-dimensionalized added virtual mass incremental (NAVMI) factors are given for modes having up to seven nodal diameters and five nodal circles and the full range of possible Poisson's ratios.

Vibration analysis is the most common means of gear monitoring and diagnostics. Gear vibration is affected by faults but the signal is usually picked up at the case, where it is also affected by the structural response. An appropriate filtering function is therefore proposed to recover the torsional gear vibration from the case vibration signal. The restored gear vibration can then be used with greater confidence than case vibration both for particular diagnostics purposes like crack detection and for more general objectives. This technique and its possible advantages in fatigue crack detection are illustrated in the paper.

In this paper, the bulging modes (i.e., modes where the walls oscillate moving the liquid) of the flexible bottom annular plate of an otherwise rigid annular cylindrical container are studied. The tank has a vertical axis and is partially filled with liquid, so that the free surface of the liquid is orthogonal to the tank axis. The volume occupied by the liquid is delimited by two coaxial rigid cylinders and the liquid deformation potential is obtained by using variables separation. First, by using the simplifying hypothesis that the mode shapes of the plates in contact with the liquid (wet modes) are the samein vacuo, the approach based on the non-dimensionalized added virtual mass incremental (NAVMI) factor is applied, so that all numerical computations can be made non-dimensional. Second, the accuracy of this method is checked by using the Rayleigh-Ritz method, which removes the restrictive hypothesis on the wet mode shapes. Finally, several experimental modal analyses were performed on two different test tanks filled with different water levels in order to verify the accuracy of the theoretical results.