Ahmed Hammami

Modal Analysis of Spur Gearbox with an Elastic Coupling

Coupled shafts are considered as the main source of vibration in rotating systems. In this work, a mechanical system composed of an electric motor, an elastic coupling and one stage spur gear is investigated to analyze dynamic behavior of elastic coupling, its influence on the natural frequencies, the vibrations, and the response of the system. A lumped parameter model of the corresponding system is developed to identify the natural frequencies and vibration modes. In addition, distributions of modal kinetic and strain energies are studied.

Planet Load Sharing Behavior During Run Up

The objective of this paper is to study the effects of meshing phase between planets and the planet position error on the load sharing behavior in planetary gear set during run up regime. These effects will be studied numerically and will be validated experimentally through a back-to-back planetary gear test bench by comparing strains in the pinhole of each planet.

Effect of Gravity of Carrier on the Dynamic Behavior of Planetary Gears

This work investigates the effect of gravity of carrier on the dynamic behavior of back to back planetary gears in a stationary condition. A tridimensional lumped parameter model is developed in order to study this phenomenon. The gravity of carriers has an effect on the distance between gears and it is included in the model through sun-planets and ring-planets mesh stiffness which influence on the dynamic response of gear. Numerical results are correlated with the experimental results obtained from a back-to-back planetary gear test bench, this test bench is composed of two identical planetary gears sets: reaction gear, where the ring is free and test gear where the ring is fixed. They are connected through two rigid shafts. A fix external load was applied through an arm attached to the free reaction ring. Data Acquisition System acquired signals from accelerometers mounted on the carrier and the ring. The signal processing was achieved using LMS Test.Lab software.

Load Sharing Behavior in Planetary Gear Set

The objective of this paper is to study the effects of meshing phase between planets, the effects of the gravity of carrier and the planet position error on the load sharing behavior in planetary gear set. These effects will be studied numerically under the stationary condition and will be validated experimentally by a back-to-back planetary gear test bench. In this test bench, strain gauges are installed on each planet’s pin hole in order to compare strains in the pinhole of each planet.

Dynamic Behavior of Back to Back Planetary Gear in Presence of Pitting Defects

The diagnosis of rotating machinery such as planetary gearbox running under operating condition is a complex task. Depending on their nature, the defects can be classified into teeth, geometrical or bearing defects. This paper studies the dynamic behavior of a back-to-back spur planetary gear running in stationary condition in the presence of teeth defects. This damage is the pitting and it is located in one tooth of the sun gear. An experimental test is performed by the measurement of the instantaneous accelerations on a test gear. The tests are carried out under a fixed load and speed. The presence of the tooth pitting defect activates repeated-like transient in ring’s vibration displacement because of phase change and amplitude reduction of the mesh stiffness when the damage tooth comes into contact. The Fast Fourier Transform (FFT) is used to transform the time signal into the frequency domain for signature analysis. The acceleration spectra show the influence of damage both in frequency and amplitude. The frequency of pitting which is the frequency of rotation of the test sun and the frequency of rotation of the motor appears along of frequency bandwidth. Moreover, the impulses of the defect tooth with the planets become important in amplitude.

Dynamic Behavior of Spur Gearbox with an Elastic Coupling Under Acyclism Regime

For many researchers and industrials the dynamic behavior of gearbox remains a paramount concern. In fact the diagnosis as well as the improvement of efficiency of gearbox is an ultimate goal for users such as machine builders, aeronautic and automotive manufacturers or energy producers. We should remind that the dynamic behavior of a gearbox depends on its design parameters and is also influenced by the engine operating conditions as well as the type of driving unit. A single stage spur gearbox is considered in this paper to investigate its dynamic behavior under acyclism regime. In fact the studied spur gear is powered by a four strokes four cylinders diesel engine using an elastic coupling modeled by Nelson and Crandell approach [7]. A numerical model is proposed taking into account the excitations induced by the motor torque fluctuation as well as the load variation and the fluctuation of meshing stiffness cased by acyclism regime. The implicit Newmark algorithm is used to investigate dynamic response of the studied system and the obtained results show the significant influence of both acyclism effect and elastic coupling on it.

Transfer Path Analysis of Planetary Gear with Mechanical Power Recirculation

Planetary gears can transmit higher power density levels because they use multiple power paths formed by each planet branches. In order to study the propagation of vibration between components of planetary gear test bench with mechanical power recirculation, an approach to the classical transfer path analysis (TPA) method is used to improve vibration control of planetary gear test bench. This approach termed Global Transmissibility Direct Transmissibility (GTDT) avoids the drawbacks of the classical TPA which are decoupling of the active part in the measurements of the Frequency Response Functions (FRFs) of source-receiver paths and the difficult measurement of the operational forces. The Global Transmissibility Direct Transmissibility (GTDT) is two steps method: the first step is the measurements of transmissibility which requires no disassembly tests and the second step is the measurement of the operational responses which is easier than measurement of the operational forces. In fact, tri-axial accelerometers are mounted in each component of the back-to-back planetary gear test bench and the transfer functions (frequency response functions, FRFs) are measured using hammer impact test in order to measure the global transmissibilities. Then, the direct transmissibilities are computed from the global transmissibilities. Finally, reconstructed operation responses are shown in the partial path contribution (PPC) plots to compare the vibration level of each component and to know its contribution in the transfer of vibration.

Dynamic Behavior of Spur Gearbox with Elastic Coupling in the Presence of Eccentricity Defect Under Acyclism Regime

In this paper, the effect of eccentricity defect on the dynamic behaviour of one stage spur gearbox running under acyclism regime is studied. In fact, acyclism regime is generated by a combustion engine motor which produced fluctuations of load and speed. The motor torque is periodic and it modeled in the force’s vector. The rotational speed of the Diesel engine is a harmonic function and it generates a periodic fluctuation of the gear meshing stiffness function. This driven motor is joined to the gearbox through an elastic coupling in which the model of Nelson and Crandall is adopted. The eccentricity defect is introduced in the pinion. This defect produces an additional potential energies and kinetic energy and it is modelled through additional forces. The equation of motion is obtained using Lagrange formalism and the algorithm of Newmark is used to compute the dynamic response of the studied system and the Wigner–Ville distribution shows the dynamic behaviour of the gearbox under this cyclo-stationary regime. Results show the variability of the meshing frequency and its harmonics which excites the system. Also, natural frequencies are observed in the spectrum and Wigner–Ville distribution of the dynamic signal. Nevertheless, these methods fail to detect the frequencies of eccentricity and acyclism.

Instrumentation of Back to Back Planetary Gearbox for Dynamic Behavior Investigation

The objective of this chapter is to investigate experimentally the dynamic behavior of back-to-back two stages planetary gear under stationary and non stationary conditions. Instrumentation layout for measurement is presented. In order to get signal from carriers, a developed instrumentation is showed: connections are achieved between accelerometer and acquisition system through a hollow slip ring. After that, series of measurements are achieved to study the dynamic behavior of carriers under stationary condition and the influence of the run up regime in the dynamic behavior of carriers.

Back to back planetary gearbox: Influence of non-stationary operating conditions

Planetary gears operate frequently in non stationary conditions. In this paper, a variable input speed excites a back to back planetary gearbox. In order to understand its dynamic behaviour, a torsional model is developed. A suitable change in the mesh stiffness functions is operated in the model. Using the Short Time Fourier Transform, an amplitude-frequency modulation is observed in the non-stationary condition. An extensive experimental study of the back to back planetary gear is performed in order to validate numerical results.