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This paper addresses the effect of manufacturing errors such as eccentricity and planet pin positioning errors on the quasi-static behavior of a 3 planet planetary transmission, taking into account different configurations regarding the bearing condition of the sun gear shaft. The aim of the paper is to shed light on some untouched aspects of the load sharing behavior of planetary transmissions, such as the effect of radial positioning errors of the planets when different pressure angles are used, and the impact of the different loadings per planet on the actual load per tooth. A modeling approach is employed, and physical explanations and simplified graphs are provided to help understand the behavior of the transmission when the sun is allowed to float and errors are introduced. The model used, developed by the authors and presented and validated in previous works, hybridizes analytical solutions with finite element models in order to compute the contact forces. The results obtained show that the teeth loads are much lower than expected compared to the planet uneven loads, both in the non-defected and defected transmission, and that radial positioning errors have non-negligible effect on the load sharing ratio under certain operating conditions.

Traditional procedures to calculate efficiency on gear transmissions generally consider sliding friction as the only dissipative effect, and what is more, they are based on the usage of constant friction coefficients. Although this approach gives acceptable efficiency values depending on the transmission application, the utilisation of a variable friction coefficient provides more reliable results of the friction behavior. Within this framework, the influence of the choice of the friction coefficient on the efficiency of shifted spur gears is assessed in this study. The Niemann ′ s friction coefficient formulation, which is constant and commonly applied to traditional approaches, was implemented in this proposal, in order to compare it with two hybrid formulations, which are based on Elastohydrodynamic Lubrication fundamentals and capable to reproduce the friction coefficient in dry contact, boundary, mixed and fluid film conditions of lubrication. These friction coefficient formulations are dependent on the load applied in the conjunction, therefore an enhanced load sharing allows for a better modelling of sliding friction, not only because it depends directly on the normal forces, but due to the friction coefficient load dependence. In this regard, the Load Contact Model previously developed by the authors, which considers the deflections of the adjacent teeth and shifting profile to calculate the load sharing and the friction coefficient, is used, allowing for efficiency values with a high level of accuracy. The efficiency results obtained when hybrid formulations are implemented provides lower values than those determined including Niemann ′ s formulation. Furthermore, there is a shifting profile which makes optimal the efficiency. This shift factor depends on the implemented friction coefficient formulation, concluding the remarkable importance of the friction coefficient choice.

This paper presents a planar spur gear planetary transmission model, describing in great detail aspects such as the geometric definition of geometric overlaps and the contact forces calculation, thus facilitating the reproducibility of results by fellow researchers. The planetary model is based on a mesh model already used by the authors in the study of external gear ordinary transmissions. The model has been improved and extended to allow for the internal meshing simulation, taking into consideration three possible contact scenarios: involute-involute contact, and two types of involute-tip rounding arc contact. The 6 degrees of freedom system solved for a single couple of gears has been expanded to 6 ? 3n degrees of freedom for a planetary transmission with n planets. Furthermore, the coupling of deformations through the gear bodies' flexibility has been also implemented and assessed. A step-by-step integration of the planetary is presented, using two typical configurations, demonstrating the model capability for transmission simulation of a planetary with distinct pressure angles on each mesh. The model is also put to the test with the simulation of the transmission error of a real transmission system, including the effect of different levels of external torque. The model is assessed by means of quasi-static analyses, and the meshing stiffness values are compared with those provided by the literature.

A model for the assessment of the energy efficiency of spur gears is presented in this study, which considers a shifting profile under different operating conditions (40 -600 Nm and 1500 -6000 rpm). Three factors affect the power losses resulting from friction forces in a lubricated spur gear pair, namely, the friction coefficient, sliding velocity and load sharing ratio. Friction forces were implemented using a Coulomb ′ s model with a constant friction coefficient which is the wellknown Niemann formulation. Three different scenarios were developed to assess the effect of the shifting profile on the efficiency under different operating conditions. The first kept the exterior radii constant, the second maintained the theoretical contact ratio whilst in the third the exterior radii is defined by the shifting coefficient. The numerical results were compared with a traditional approach to assess the results.

A comparison between transfer path analysis and operational path analysis methods using an electric vehicle is presented in this study. Structure-borne noise paths to the cabin from different engine and suspension points have been considered. To realise these methods, two types of test have been performed; operational tests on a rolling road and hammer tests in static conditions. The main aim of this work is assessing the critical paths which are transmitting the structure-borne vibrations from the electric vehicle's vibration sources to the driver's ear. This assessment includes the analysis of the noise contribution of each path depending on the frequency and vehicle speed range and moreover, the assessment of the path noise impact for harmonic orders which arise due to the physical components of the electric vehicle. Furthermore, the applicability of these methods to electric vehicles is assessed as these techniques have been extensively used for vehicles powered with internal combustion engines

Abstract. This work describes a non-linear dynamic model for the study of the vibration signals generated by gear transmissions. The developed model considers both the parametric excitations due to the variable compliance of bearings and gears, can handle changes in the transmitted torque and allows the integration of the dynamic equations quickly and accurately. This model has been developed previously by the authors to assess the profile deviations on the dynamic behavior of gear transmissions and its influence on the transmitted torque. It also includes the presence of gear defects as cracks and pitting during the calculation of meshing forces. In this paper, the model has been enhanced in order to include two common defects such as index errors and run out or eccentricity errors. Index errors occur as a result of a non-uniform angular distribution of the tooth profiles along the pitch circle. Run out appears due to the displacement of the geometric center of the gear with respect to the center of rotation of the shaft on which it is mounted. Although both errors are caused by different reasons, sometimes they have been confused because of their similitudes. The procedure for including both kinds of errors in the model is described and simulations under several transmitted torques are presented. The results are assessed and compared focusing the attention on certain transmission parameters and magnitudes as transmission error, load forces in the tooth flanks and demodulation techniques on the resulting vibratory signals.

In this proposal, the effect of the friction coefficient on the efficiency of spur gears with tip reliefs was analysed. For this purpose, the efficiency values using an average friction coefficient along the mesh cycle were compared with those obtained implementing an enhanced friction coefficient formulation, which is based on elastohydrodynamic lubrication fundamentals. In this manner, it can be established the differences between both formulations in the efficiency and friction coefficient values, as well as the advantages of using this enhanced friction coefficient with respect to formulations implemented in traditional approaches of efficiency calculation. In addition to studying the impact of the friction coefficient choice on efficiency, the profile modifications influence on the friction coefficient and efficiency was also assessed. In this regard, three tip relief case studies were set out; pinion tip reliefs, driven wheel tip reliefs and profile modifications in both gears. From the results, it was inferred that the choice of friction coefficient formulation clearly influences the efficiency in gear transmissions with tip reliefs, obtaining discrepancies between both formulations with regard to which tip relief case study provides the lowest efficiency values.