Stress calculation on bevel gears with FEM influence vectors

In order to be able to carry out an optimal gear design with the aim of cost reduction and the careful handling of resources, load capacity is an important criterion for the evaluation of a gear. For the calculation of the flank and root load capacity, a precise loaded tooth contact analysis (LTCA) is necessary. With LTCA software like BECAL, influence numbers are used to calculate the deformation of the gear. These influence numbers are calculated with a BEM-module and considered for calculating the local root stress. This method simplifies the coupling stiffness in tooth width direction with a decay function and neglects the influence of local differences in tooth stiffness. In this publication, this simplification shall be questioned and evaluated.Therefore, a new method for calculating stress with FEM influence vectors is presented. This method enables the calculation of full stress tensors at any desired location in the gear with the efficiency of the influence number method. Additionally, the influence of local stiffness variations in the gear is taken into account. Various gear examples show the influence of material connections at the pinion root and the influence of the rim thickness of a wheel on the root stress. To validate the accuracy and the time efficiency of the new calculation method and to compare the results to current state-of-the-art simulations, a well-documented series of tests from the literature is recalculated and evaluated.

Stress and stem allomorphy in the Romance perfectum: emergence, typology, and motivations of a symbiotic relation

Perfective stem allomorphy and stress are morphological traits which interact in complex ways in Romance verbal inflection. This article surveys the whole range of variation of these traits across Romance varieties, typologizes the observed interactions between the two, and examines attested and unattested possibilities. A comparison between the modern-day and the original Latin systems suggests that there is a strong pan-Romance bias against having verbs with a concrete combination of properties: perfective root-stress and no perfective stem alternation. This is a combination of traits that would have frequently resulted in diagonal syncretisms between past and present given the phonological changes attested in the daughter languages. Homophony avoidance (and the adaptive-discriminative role of morphology more generally) are therefore argued to motivate the observed bias.

Minimum friction losses in wind turbine gearboxes

Improving the mechanical efficiency is not the most important objective in the design of wind turbine gearboxes since the available wind energy is abundant and costless. The most important criteria for dimensioning the gearbox are the fatigue strength—bending and pitting—, noise emission, vibrations, and maintenance requirements. Nevertheless, mechanical losses increase the lubricant temperature and induce thermal stresses, which increases wear and cracking risk. This means that friction losses should be reduced as much as possible, but always regarding the contact and tooth-root stress levels, as well as the other operating parameters which should be kept for ensuring the required operating conditions.In this paper, a study on the variation of the friction losses with the tooth shift coefficients is presented. All the other geometrical parameters—number of teeth, tooth height, pressure angle, helix angle, face width, and center distance—are unalterable, since all of them have been chosen according to more important design requirements. In addition, to keep the contact and tooth-root stress levels, the shift coefficients of the sun, planets and ring are calculated in such a way that the transverse contact ratios are kept, and therefore the critical load points for bending and pitting are also unchanged. The radial clearance is also kept in order to allow the proper evacuation of the lubricant. Finally, all the geometrical constraints (undercut, pointing, root interference, secondary interference, backlash) are also imposed. With all these restrictions, the optimal shift coefficients for all the gears are calculated to minimize the friction losses.

Pepper Plants Leaf Spectral Reflectance Changes as a Result of Root Rot Damage

Symptoms of root stress are hard to detect using non-invasive tools. This study reveals proof of concept for vegetation indices’ ability, usually used to sense canopy status, to detect root stress, and performance status. Pepper plants were grown under controlled greenhouse conditions under different potassium and salinity treatments. The plants’ spectral reflectance was measured on the last day of the experiment when more than half of the plants were already naturally infected by root disease. Vegetation indices were calculated for testing the capability to distinguish between healthy and root-damaged plants using spectral measurements. While no visible symptoms were observed in the leaves, the vegetation indices and red-edge position showed clear differences between the healthy and the root-infected plants. These results were achieved after a growth period of 32 days, indicating the ability to monitor root damage at an early growing stage using leaf spectral reflectance.

Square root stress-sum index for graphs

The stress of a vertex is a node centrality index, which has been introduced by Shimbel (1953). The stress of a vertex in a graph is the number of geodesics (shortest paths) passing through it. In this paper, we introduce a new topological index for graphs called square root stress sum index using stresses of vertices. Further, we establish some inequalities, prove some results and compute stress-sum index for some standard graphs.

A numerical investigation on the hybrid spur gears: Stress and dynamic analysis

In this study, the effect of rim thickness of hybrid gears on the root stress, joint stress, tooth stiffness, natural frequency, and dynamic behavior are examined numerically. Hybrid gears consist of two materials, which are steel for the teeth-rim and hub regions of gear, carbon fiber reinforced plastic (CFRP) for the web region. Adhesive bonding is assumed for the joining of steel and composite materials. FE method is used to evaluate tooth root stress, joint stress, tooth deformation, and the natural frequency of hybrid gears. The adhesive is defined by cohesive zone modeling (CZM). Moreover, 2-DOF dynamic analyses are implemented to obtain dynamic factors and static transmission error. According to results, hybrid gears have substantial potential to reduce the mass of gear transmission systems with no adverse effect on root stress and dynamic factor if the design parameters are appropriately selected. Besides, rim thickness is found as a critical parameter for the hybrid gears since when its value changes from 0.5xm to 3xm, the root stress decreases 10% while the tooth stiffness and torque capacity increase 20% and 65%, respectively.

Compact Design of High-Contact-Ratio Spur Gears

This study presents a computer simulation for the dynamic design of compact high-contact-ratio spur gear transmissions. High contact ratio gears have the potential to produce lower dynamic tooth loads and minimum root stress but they can be sensitive to tooth profile errors. The analysis presented in this work was performed by using the NASA gear dynamics code DANST (Dynamic Analysis of Spur Gear Transmissions). In the analysis, the addendum ratio (addendum/diametral pitch) was varied over the range 1.30 to 1.40 to obtain a contact ratio of 2.00 or higher. The constraints of bending stress limit and involute interference provide the main criteria for this investigation. Compact design of high-contact-ratio gears with different gear ratios and pressure angles was investigated. Comparison of compact design between low-contact-ratio and high-contact-ratio gears was conducted. With the same operating parameters, high-contact-ratio gears appear to have much more compact design than low-contact-ratio gears. For compact design of high-contact-ratio gears, a diametral pitch of 6.00 appears to be the best choice for an optimal gear set.