Analytical calculation models for mesh stiffness and backlash of spur gears under temperature effects

The temperature has a great contribution to the mesh stiffness and backlash of the gear pair. Presence of thermal deformation caused by temperature will complicate the gear teeth interaction. In this paper, the thermal time-varying stiffness model and thermal time-varying backlash model are proposed with the consideration of tooth profile error and total thermo-elastic deformation consists of the teeth deformation, teeth contact deformation, and gear body-induced deformation. The key parameters of thermo-elastic coupling deformation affected by temperature are calculated. Based on the proposed models, the influencing mechanism of temperature on the tooth profile error, mesh stiffness, total deformation, and backlash are revealed. The effects of shaft radius and torque load on the thermal stiffness and thermal backlash are studied. The proposed thermal stiffness and backlash calculation model are proven to be more comprehensive and the correctness is validated.

Understanding the Thermal Time Constants of GaN HEMTs through Model Order Reduction Technique

This paper described a comparison between a numerical Finite Element Analysis (FEA) and an analytical approach in order to extract the thermal time constants and the thermal resistances of simple but realistic structures. Understanding the complex contribution of multidimensional thermal spreading, the effect of multiple layers, and the correlation with the heat source length is mandatory due to the severe mismatch of thermal expansion in different epitaxial layers and high operating temperatures. This is especially true on GaN HEMT (High Electron Mobility Transistor) with the continuous decrease of the gate length and the increase of the power density. Moreover, in this paper, we extracted the time constants with a Model Order Reduction (MOR) technique based on the Ritz vector approach with inputs coming from the FE matrices. It was found that the time constants obtained by an analytical solution and a model order extraction from FEA were exactly the same. This result validated the idea that our MOR technique provides the real time constants and resistances for our device structures and in this case unified the analytical world with the numerical one.

Thermal Niche for Seed Germination and Species Distribution Modelling of Swietenia macrophylla King (Mahogany) under Climate Change Scenarios

Swietenia macrophylla is an economically important tree species propagated by seeds that lose their viability in a short time, making seed germination a key stage for the species recruitment. The objective of this study was to determine the cardinal temperatures and thermal time for seed germination of S. macrophylla; and its potential distribution under different climate change scenarios. Seeds were placed in germination chambers at constant temperatures from 5 to 45 °C and their thermal responses modelled using a thermal time approach. In addition, the potential biogeographic distribution was projected according to the Community Climate System Model version 4 (CCSM4). Germination rate reached its maximum at 37.3 ± 1.3 °C (To); seed germination decreased to near zero at 52.7 ± 2.2 °C (ceiling temperature, Tc) and at 12.8 ± 2.4 °C (base temperature, Tb). The suboptimal thermal time θ150 needed for 50% germination was ca. 190 °Cd, which in the current scenario is accumulated in 20 days. The CCSM4 model estimates an increase of the potential distribution of the species of 12.3 to 18.3% compared to the current scenario. The temperature had an important effect on the physiological processes of the seeds. With the increase in temperature, the thermal needs for germination are completed in less time, so the species will not be affected in its distribution. Although the distribution of the species may not be affected, it is crucial to generate sustainable management strategies to ensure its long-term conservation.

Assessing the ability of the growing degree-day metric to explain variation in size-at-age and duration-to-moult of lobsters and crabs

Environmental temperature directly controls the rate at which ectotherms grow and develop. The growing degree-day metric (GDD, °C∙d) scales time by temperature to create a thermal time scale relevant to ectothermic organisms. Here we assess the ability of GDD to model size-at-age and duration-to-moult in 15 datasets (9 size-at-age, 6 duration-to-moult) comprising 7 species of lobsters and crabs. We applied generalized linear models to assess the ability of GDD vs. “calendar” time to explain growth and development observations within and across trials. Best-fit models included GDD with fewer parameters in 6 of 9 size-at-age and 5 of 6 duration-to-moult datasets, and a better fit to the data in 6 of 9 size-at-age datasets. Our results show that the individual growth of lobster and crab species can be modelled using thermal time models. Such models can be used to identify thermal tolerance limits, predict growth under varying temperature conditions and disentangle temperature effects from those of other factors affecting individual growth and development, resulting in improved growth models for field conditions including fisheries management.

Thermal Time Requirements for Maize Growth in Northeast China and Their Effects on Yield and Water Supply under Climate Change Conditions

Northeast China (NEC) is a region sensitive to climate change. However, the adoption of long-season maize cultivars in NEC has caused a substantial yield increase under climate change conditions. It is important to determine whether such cultivar adoptions are effective throughout the whole NEC to sustainably increase grain yield. In this study, phenological observations and meteorological data at six sites from 1981 to 2018 were used to detect thermal time (TT) trends during the maize growing period. TT, as a parameter for measuring changes in maize cultivars, was used in the crop simulation model CERES-Maize to examine the variations in maize yield produced with different cultivar × climate combinations in different decades. In NEC, both TTs from emergence to anthesis and from anthesis to physiological maturity showed significant increasing trends from 1981 to 2018. Simulation results for humid areas revealed that adopting longer-season cultivars during 2000–2018 caused yield increases, ranging from 6.3% to 13.3%, compared with the 1980s. However, for stations in semi-humid areas, maize grain yield showed a decrease or a small increase (from −12.7% to 8.0%) when longer-season cultivars were adopted during 2000–2018. For semi-humid areas, decreasing trends in the ratios of rainfed yield to no water-stress yield (Yrainfed/Yno water-stress) and lower Yrainfed/Yno water-stress values during 2000–2018 indicated a growing sensitivity of maize production to water, which was attributed to changes in TT and precipitation. Our results indicate that, for the semi-humid area, maize yield was limited by water after introducing cultivars with higher TT requirement under climate change conditions. Therefore, securing food supplies will depend on increases in water-use efficiency levels and other adaptive strategies, such as varietal diversification, drought-resistant varieties, conservation tillage and irrigation.