A. Fernandez del Rincon

A Model Of Spur Gears Supported ByBall Bearings

In this work a model of a 2D spur gear transmission is described for analysis of tooth contact forces and deformations. Assuming the position of each wheel is known, the contact points between gears are obtained taking into account the geometric description of the tooth profiles including profile errors and relief modifications. Then the deformation in each contact point is separated into a global and a local term combining a finite element model and an analytical formulation originating from Hertzian contact theory. The proposed procedure does not need new element meshing for each angular position thus obtaining an important computational advantage. Afterwards, a non-linear system of equations is obtained and solved for each gear position in order to calculate the meshing contact forces. The model can include the possibility of bidirectional single-flank or double-flank action as well as friction forces in the out-of-action line. Once the contact forces are known, it is possible to use the procedure in the calculation of loaded transmission error and meshing stiffness. Furthermore, each gear is supported by ball bearings that are included in the model taking into account their clearance and their variable stiffness due to the change in the number of balls supporting the load. This variable bearing compliance modifies the gear centre distance and as a consequence the transmission error during a turn. Using this methodology a numerical example is presented where the static behaviour of a spur gear transmission is described and analysed. Special attention is focused on the influence of load level on the final loaded transmission error.

Defect Simulation in a Spur Gear Transmission Model

This article describes a two-dimensional model for the analysis of the transmission error and dynamic performance of a spur gear transmission supported by bearings including defects. Knowing the position of each wheel and profiles geometry, including errors and roundings, contact points are determined.Meshing forces and associated deformations are then calculated, simplifying the deformation computation by means of its subdivision in structural and local deformations. The application of this procedure improves the results and reduces the computational effort. The model supports the possibility of contact on both flanks of the teeth simultaneously and it also takes into account the variable number of bearing elements. Finally, an application example of this method is presented, highlighting the effect of cracks, surface defects and tooth gear profile errors on the transmission error.

A Dynamic Model For The Study Of GearTransmissions

In this work a previous model developed by the authors for the quasi-static analysis of spur gear transmissions supported by ball bearings was modified extending its capabilities to dynamic analysis. The model combines a finite element and an analytical formulation achieving sufficient accuracy and computational efficiency to make dynamic analysis feasible. Non-linearity associated with the contact among teeth was included, taking into account the flexibility of gears, shafts and bearings. Furthermore, parametric excitations originating both from gear and bearing supports, as well as clearance, were also taken into account. An example of a simple transmission is presented providing several results obtained using the proposed model. Nevertheless, in spite of its usefulness, particularly in the case of variable torque loads, and its improved capabilities compared with other procedures, this approach still requires a high computational effort. As a consequence in those cases where the transmission operates under stationary conditions the formulation could be simplified by using a pre-calculated value for each the gear tooth stiffness as a function of the angular position. Once again, the original model is useful, taking advantage of its computational efficiency in the calculation of these stiffness coefficients throughout a meshing period. The improved model is applied to the same transmission and the consequences of a misleading calculation of the stiffness coefficients are shown. Then, it was used to study the vibratory behaviour under different levels of applied torque, showing the modifications suffered by the orbits, meshing contact forces and particularly the spectra obtained for bearing forces.

Modeling Run in Process in External Gear Pumps

In this work, the authors have developed a mathematical model that simulates the run in of external gear pumps, as an useful tool in the optimization of this time-consuming process. The model calculates the wear profile of the case by enveloping the tip circle of the gears concerning all the run in steps. For each step, the positions of the gear centers are obtained by the equilibrium between pressure forces and torques due to the pressure distribution, meshing forces and hydrodynamic journal bearing reactions. The pressure distribution depends on the clearance between case and gears, so for each run in step, since the positions of the gear centers change, the pressure distribution is recalculated considering the wear profile obtained in the previous step. Besides, the model also estimates the quantity of material taken away in each step and it shows the effects of modifications in the run in parameters (time, pressure and speed). In particular, the simulation results indicate that a meaningful reduction of run in global time, can be obtained by increasing the duration of the steps that remove the greater part of material and by decreasing the duration of the other steps. This model is used by TRW Automotive Italia S.p.A. (section Automotive Pumps, Ostellato, Italy) to improve the run in process with good reduction in manufacturing-time.Copyright

Efficiency Analysis of Shifted Spur Gear Transmissions

A quasi-static analysis of a shifted spur gear transmission is presented in this work. With this study, the influence of the profile modifications and the dissipative effects on the efficiency is assessed. Among the dissipative effects, friction between teeth in presence of lubricant is studied in this work, because of its important effect on power losses in the operating conditions used. Friction forces have been implemented by means of a Coulomb’s model with a variable friction coefficient (VFC). One VFC formulation have been developed derived from the well-known Niemann formulation and compared with a second one developed by Hai Xu. The final aim is to assess the impact on the efficiency of both the frictional effect and the profile shifting.

Modulation Sidebands of Planetary Gear Set

In this paper a torsional model of planetary gear set test bench is developed. This bench is composed by two identical planetary gears connected by a common shaft. A tri axial accelerometer is mounted in both rings. The mechanism leading to modulation sidebands is modelled. Time histories are characterized by a periodic fluctuation. Spectra showed sidebands around the mesh frequency and its harmonics. Simulation is achieved to demonstrate amplitude modulation and rich sidebands that agree well with the experimental results.

Efficiency Analysis of Shifted Spur Gears

An efficiency study of spur gears with profile modifications is presented. One of the objectives of this proposal is to make a comparison between efficiency values obtained by an advanced load contact model and reference values obtained from literature. Moreover, two methodologies for calculating the efficiency are presented: a “Numerical method” and an “Analytical method”. For the same gear pair, different efficiency values are obtained using each method. The differences among efficiency values are discussed and comparisons between both methodologies are made.

Test Bench for the Analysis of Dynamic Behavior of Planetary Gear Transmissions

In this paper a back-to-back test bench for experimental characterization of planetary gear transmissions is described. Some considerations related to the design of this kind of devices as well as the compromises and general features of the proposed design are presented. Particular attention is given to the instrumentation layout and the alternatives foreseen for measurement. In the last chapter, some results are presented in order to show the capabilities of the bench configuration.

Application of a Inter-University Competition on the Enhancement of Engineering Degrees

Within the frame of an innovative teaching project call of the University of Cantabria (Spain), authors have taken advantage of their experience on an inter-university competition (whose main goal is the design and construction of a motorbike among other tasks) in order to apply it on the Mechanical Engineering and Industrial Technologies degrees. The main idea of this experiment is to include a specific activity in each course which were related to this specific competition, using problem and project based learning techniques with the aim of studying some aspects of the analysis and design of components for the motorbike. Two courses, Applied Mechanics and Mechanisms Theory, have participated in this experiment. In the first one, it was proposed a problem about friction of the motorbike’s tires, which were modelled as rigid multibody system. In the second one, an open-ended project about the redesign of the rear suspension system of the University of Cantabria original motorbike that took part in the 2010 competition was proposed. Both activities were eligible for students. Results show that the students that took part in the proposed activities pass the courses in a more easy and satisfactory way.

Simulation Tool for Motorbike Prototype Design

This paper shows the development of a motorcycle simulation tool built at the University of Cantabria (UC) whose main aim is to support design tasks for future teams that will take part in the interuniversity competition MotoStudent. The tool has been implemented in a commercial multi-body software (MBS) in order to extend the model in a near future. Besides, the tool makes use of customized menu and user interfaces to have easy and quick use by non-especially trained engineers in MBS. The tool has been evaluated by comparison with a widely proved model and used to improve the UC 2010 prototype planar dynamics.