Gear transmission dynamic: Effects of tooth profile deviations and support flexibility

In this work a non-linear dynamic model of spur gear transmissions previously developed by the authors is extended to include both desired (relief) and undesired (manufacture errors) deviations in the tooth profile. The model uses a hybrid method for the calculation of meshing forces, which combines FE analysis and analytical formulation, so that it enables a very straightforward implementation of the tooth profile deviations. The model approach handles well non-linearity due to the variable meshing stiffness and the clearances involved in gear dynamics, also including the same phenomena linked to bearings. In order to assess the ability of the model to simulate the impact of the deviations on the transmission dynamics, an example is presented including profile deviations under different values of transmitted torque. Several results of this example implementation are presented, showing the model's effectiveness.This paper has been developed in the framework of Project DPI2006-14348 funded by the Spanish Ministry of Science and Technology

Guaranteed Detection of the Singularities of 3R Robotic Manipulators

The design of new manipulators requires the knowledge of their kinematic behaviour. Important kinematic properties can be characterized by the determination of certain points of interest. Important points of interest are cusps and nodes, which are special singular points responsible for the non-singular posture changing ability and for the existence of voids in the workspace, respectively. In practice, numerical errors should be properly tackled when calculating these points. This paper proposes an interval analysis based approach for the design of a numerical algorithm that finds enclosures of points of interest in the workspace and joint space of the studied robot. The algorithm is applied on 3R manipulators with mutually orthogonal joint axes

Non-stationary dynamic analysis of a wind turbine power drivetrain: Offshore considerations

This paper presents a multi-body model for studying the non-stationary dynamic behaviour of a wind turbine power drivetrain. The model includes some offshore considerations, such as the extra degrees of freedom and boundary conditions that installation on an offshore floating platform can add. The studied problem is an offshore implementation, with seafloor depths of the order of a hundred metres, making it necessary to use a floating platform. Special attention is paid to the characteristics of the combined offshore buoy support and detailed model of the power train, in order to assess the impacts of buoy movement on forces on gears and bearings. A multi-body analysis code was used to develop the model, and a conventional wind turbine set-up was implemented as an example. Gearbox dynamic behaviour was simulated for common manoeuvres such as a start-up and an emergency stop, and the results are presented and discussed.The authors like to thanks the company Apia XXI for supporting part of the research presented by the Project DINAER. Moreover, some parts of the developments presented have been made in the framework of Project DPI2006-14348 funded by the Spanish Ministry of Science and Technology

Enhanced model of gear transmission dynamics for condition monitoring applications: Effects of torque, friction and bearing clearance

Gear transmissions remain as one of the most complex mechanical systems from the point of view of noise and vibration behavior. Research on gear modeling leading to the obtaining of models capable of accurately reproduce the dynamic behavior of real gear transmissions has spread out the last decades. Most of these models, although useful for design stages, often include simplifications that impede their application for condition monitoring purposes. Trying to filling this gap, the model presented in this paper allows us to simulate gear transmission dynamics including most of these features usually neglected by the state of the art models. This work presents a model capable of considering simultaneously the internal excitations due to the variable meshing stiffness (including the coupling among successive tooth pairs in contact, the non-linearity linked with the contacts between surfaces and the dissipative effects), and those excitations consequence of the bearing variable compliance (including clearances or pre-loads). The model can also simulate gear dynamics in a realistic torque dependent scenario. The proposed model combines a hybrid formulation for calculation of meshing forces with a non-linear variable compliance approach for bearings. Meshing forces are obtained by means of a double approach which combines numerical and analytical aspects. The methodology used provides a detailed description of the meshing forces, allowing their calculation even when gear center distance is modified due to shaft and bearing flexibilities, which are unavoidable in real transmissions. On the other hand, forces at bearing level were obtained considering a variable number of supporting rolling elements, depending on the applied load and clearances. Both formulations have been developed and applied to the simulation of the vibration of a sample transmission, focusing the attention on the transmitted load, friction meshing forces and bearing preloads.The authors would like to acknowledge Project DPI 2013-44860 funded by the Spanish Ministry of Science and Technology and Project PRX14/00451 funded by the Spanish Ministry of Education, Culture and Sports

Efficiency analysis of spur gears with a shifting profile

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 well-known 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.The authors would like to acknowledge Project DPI2013-44860 funded by the Spanish Ministry of Science and Technology and the COST ACTION TU 1105 for supporting this research

Advanced model for the calculation of meshing forces in spur gear planetary transmissions

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.The authors would like to acknowledge Project DPI2013-44860 funded by the Spanish Ministry of Science and Technology

Dataset used in article "A 2-dimensional guillotine cutting stock problem with variable-sized stock for the honeycomb cardboard industry"

<p>The dataset presented is part of the one used in the article "A 2-dimensional guillotine cutting stock problem with variable-sized stock for the honeycomb cardboard industry" by P. Terán-Viadero, A. Alonso-Ayuso and F. Javier Martín-Campo, published in International Journal of Production Research (2023), doi: <a href="https://doi.org/10.1080/00207543.2023.2279129">10.1080/00207543.2023.2279129</a>. </p><p>In the paper mentioned above,  two mathematical optimisation models are proposed for the Cutting Stock Problem in the honeycomb cardboard sector. This problem appears in a Spanish company and the models proposed have been tested with real orders received by the company, achieving a reduction of up to 50% in the leftover generated. </p><p>The dataset presented here includes six of the twenty cases used in the paper (the rest cannot be presented for confidentiality reasons). For each case, the characteristics of the order and the solution obtained by the two models are provided for the different scenarios analysed in the paper.</p><p> </p><p>*Version 1.1 contains the same data but renamed according to the instances name in the final version of the article.<br>*Version 1.2 adds the PDF with the accepted version of the article publised in International Journal of Production Research (2023), doi: <a href="https://doi.org/10.1080/00207543.2023.2279129">10.1080/00207543.2023.2279129</a>. </p&gt