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

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

Multiple carbon accounting to support just and effective climate policies

Negotiating reductions in greenhouse gas emission involves the allocation of emissions and of emission reductions to specific agents, and notably, within the current UN framework, to associated countries. As production takes place in supply chains,increasingly extending over several countries, there are various options available in which emissions originating from one and the same activity may be attributed to different agents along the supply chain and thus to different countries. In this way, several distinct types of national carbon accounts can be constructed. We argue that these accounts will typically differ in the information they provide to individual countries on the effects their actions have on global emissions; and they may also, to varying degrees, prove useful in supporting the pursuit of an effective and just climate policy. None of the accounting systems, however, prove 'best' in achieving these aims under real-world circumstances; we thus suggest compiling reliable data to aid in the consistent calculation of multiple carbon accounts on a global level

Public Preferences for Forest Ecosystem Management in Japan with Emphasis on Species Diversity

We carried out online choice experiments (CE) to investigate what value Japanese individuals assign to rare versus familiar species in forest ecosystem, and to determine how preference heterogeneity arises. CE attributes comprised a forestry charge as the price attribute and rare versus familiar species of animals or plants as the good to be valued. Species numbers in a 5 km-mesh forest area were evaluated without the use of species names to focus purely on responses to numerical changes. Positional effects were also tested to validate results regarding alternatives and attributes other than the price attribute. A random parameter logit model was adopted to capture preferences for species diversity. After confirming that no positional effects existed, we found that (1) rare animals were valued more highly than rare plants, (2) familiar plants were assigned a positive value, but familiar animals were not assigned significant value at the mean parameter estimate, and (3) preference heterogeneities existed for all species. The sources of preference heterogeneity were analyzed with a latent class model having principal components of environmental attitudes. The influence of such attitudes was shown to be significant and suggested that attention should be paid to belief systems rather than solely demographics