F. Viadero

Kinematic design of double-wishbone suspension systems using a multiobjective optimisation approach

This paper is focused on the kinematic design of double-wishbone suspension systems in vehicles, which is tackled using a multiobjective dimensional synthesis technique. The synthesis goal is to optimise an RSSR–SS linkage, subject to some constraints involved in the dynamic behaviour of vehicles. The synthesis method is based on gradient determination using exact differentiation to obtain the elements in the Jacobian matrix. These characteristics make the method adapt well to the optimum design of vehicle suspension systems. The method is capable of handling equality and inequality constraints, thus, the usual ranges of values may be imposed on the functional parameters. The formulation presented is easy to implement and the solutions obtained demonstrate the accuracy and robustness of the method.

Effect of cracks and pitting defects on gear meshing

The development of vibration-based condition monitoring techniques, especially those focused on prognosis, requires the development of better computational models that enable the simulation of the vibratory behaviour of mechanical systems. Gear transmission vibrations are governed by the so-called gear mesh frequency and its harmonics, due to the variable stiffness of the meshing process. The fundamental frequency will be modulated by the appearance of defects which modify the meshing features. This study introduces an advanced model to assess the consequences of defects such as cracks and pitting on the meshing stiffness and other related parameters such as load transmission error or load sharing ratio. Meshing forces are computed by imposing the compatibility and complementarity conditions, leading to a non-linear equation system with inequality constraints. The calculation of deformations is subdivided into a global and a local type. The former is approached by a finite element model and the latter via a non-linear Herztian-based formulation. This procedure enables a reduced computational effort, in contrast to conventional finite element models with contact elements. The formulation used to include these defects is described in detail and their consequences are assessed by a quasi-static analysis of a transmission example.

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.

Enhancement of Mechanical Engineering Degree through student design competition as added value. Considerations and viability

ABSTRACT This paper proposes using a student design competition as a learning tool in the Mechanical Engineering Degree for enhancing the general competences and motivation of the students, transferring theoretical knowledge to practical situations and bringing together all courses involved under a common framework. This constitutes an added value that the in-person universities should offer to their students as a consequence of the Bologna process and the raising of open online resources for self-learning. In order to assess the viability of this proposal, a pilot competition design activity (CDA) is presented using project-based learning methods during a Mechanism Theory course for sophomore students. Meanwhile, 27 participants of a 45-student course from a European university took part in the pilot CDA, which consisted of redesigning the motorbike rear suspension used in a student design competition. Participants also completed mid-term and final exams as well as a survey to get their perception of this activity. Based on the success of the pilot CDA, the authors are planning to implement the proposal, including similar CDAs in other Mechanical Engineering courses to use the competition as a link between them and to encourage students to participate on the competition.

Planetary gear profile modification design based on load sharing modelling

In order to satisfy the increasing demand on high performance planetary transmissions, an important line of research is focused on the understanding of some of the underlying phenomena involved in this mechanical system. Through the development of models capable of reproduce the system behavior, research in this area contributes to improve gear transmission insight, helping developing better maintenance practices and more efficient design processes. A planetary gear model used for the design of profile modifications ratio based on the levelling of the load sharing ratio is presented. The gear profile geometry definition, following a vectorial approach that mimics the real cutting process of gears, is thoroughly described. Teeth undercutting and hypotrochoid definition are implicitly considered, and a procedure for the incorporation of a rounding arc at the tooth tip in order to deal with corner contacts is described. A procedure for the modeling of profile deviations is presented, which can be used for the introduction of both manufacturing errors and designed profile modifications. An easy and flexible implementation of the profile deviation within the planetary model is accomplished based on the geometric overlapping. The contact force calculation and dynamic implementation used in the model are also introduced, and parameters from a real transmission for agricultural applications are presented for the application example. A set of reliefs is designed based on the levelling of the load sharing ratio for the example transmission, and finally some other important dynamic factors of the transmission are analyzed to assess the changes in the dynamic behavior with respect to the non-modified case. Thus, the main innovative aspect of the proposed planetary transmission model is the capacity of providing a simulated load sharing ratio which serves as design variable for the calculation of the tooth profile modifications.

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.

Applications of dynamic measurements to structural reliability updating

The present paper proposes a method for updating the assessment of reliability. It is based on the formulation of additional events. Note is made of the existence of changes in the dynamic behavior of a system due to perturbation of the basic design variables. An additional event is formulated based on a comparison between the natural frequencies of a system obtained by a theoretical (analytic or numerical) method and those obtained from an experimental modal analysis. Given the differences between theoretical and experimental values, a corrective factor is then introduced in the form of a new random variable. The characteristic values of this new variable are determined. Finally the effectiveness of the method is illustrated by an example.

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.