The Green rings of pointed tensor categories of finite type

In this paper, we compute the Clebsch-Gordan formulae and the Green rings of connected pointed tensor categories of finite type.Comment: 14 page

Profile modification to minimize spur gear dynamic loading

An analytical computer simulation program for dynamic modeling of low-contact-ratio spur gear systems is presented. The procedure computes the static transmission error of the gears operating under load and uses a fast Fourier transform to generate the frequency spectrum of the static transmission error at various tooth profile modifications. The dynamic loading response of an unmodified (perfect involute) gear pair was compared with that of gears with various profile modifications. Correlations were found between various profile modifications and the resulting dynamic loads. An effective error, obtained from frequency domain analysis of the static transmission error of the gears, gave a very good indication of the optimum profile modification to reduce gear dynamic loading. Design curves generated by dynamic simulation at various profile modifications are given for gear systems operated at various loads. Optimum profile modifications can be determined from these design curves for improved gear design

The PDFLattice2017 workshop: a summary report

The workshop on Parton Distributions and Lattice Calculations in the LHC era (PDFLattice2017) was hosted at Balliol College, Oxford (UK), from 22$^{\rm nd}$ to 24$^{\rm th}$ March 2017. The workshop brought together the lattice-QCD and the global-fit physicists who devote their efforts to determine the parton distribution functions (PDFs) of the proton. The goals were to make the two communities more familiar between each other, review developments from both sides, and set precision targets for lattice calculations so that they can contribute, together with the forthcoming experimental input, to the next generation of PDF determinations. This contribution summarises the relevant outcome of the workshop, in anticipation of a thorough white paper.Comment: 5 pages, 1 figure, contribution to the proceedings of the XXV Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2017

Effect of extended tooth contact on the modeling of spur gear transmissions

In some gear dynamic models, the effect of tooth flexibility is ignored when the model determines which pairs of teeth are in contact. Deflection of loaded teeth is not introduced until the equations of motion are solved. This means the zone of tooth contact and average tooth meshing stiffness are underestimated and the individual tooth load is overstated, especially for heavily-loaded gears. The static transmission error and dynamic load of heavily-loaded, low-contact-ratio spur gears is compared with this effect both neglected and included. Neglecting the effect yields an underestimate of resonance speeds and an overestimate of the dynamic load

Computer-aided design of high-contact-ratio gears for minimum dynamic load and stress

A computer aided design procedure is presented for minimizing dynamic effects on high contact ratio gears by modification of the tooth profile. Both linear and parabolic tooth profile modifications of high contact ratio gears under various loading conditions are examined and compared. The effects of the total amount of modification and the length of the modification zone were systematically studied at various loads and speeds to find the optimum profile design for minimizing the dynamic load and the tooth bending stress. Parabolic profile modification is preferred over linear profile modification for high contact ratio gears because of its lower sensitivity to manufacturing errors. For parabolic modification, a greater amount of modification at the tooth tip and a longer modification zone are required. Design charts are presented for high contact ratio gears with various profile modifications operating under a range of loads. A procedure is illustrated for using the charts to find the optimum profile design

Influence of linear profile modification and loading conditions on the dynamic tooth load and stress of high contact ratio gears

A computer simulation for the dynamic response of high-contact-ratio spur gear transmissions is presented. 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 examines various profile modifications under realistic loading conditions. The effect of these modifications on the dynamic load (force) between mating gear teeth and the dynamic root stress is presented. Since the contact stress is dependent on the dynamic load, minimizing dynamic loads will also minimize contact stresses. It is shown that the combination of profile modification and the applied load (torque) carried by a gear system has a significant influence on gear dynamics. The ideal modification at one value of applied load will not be the best solution for a different load. High-contact-ratio gears were found to require less modification than standard low-contact-ratio gears. High-contact-ratio gears are more adversely affected by excess modification than by under modification. In addition, the optimal profile modification required to minimize the dynamic load (hence the contact stress) on a gear tooth differs from the optimal modification required to minimize the dynamic root (bending) stress. Computer simulation can help find the design tradeoffs to determine the best profile modification to satisfy the conflicting constraints of minimizing both the load and root stress in gears which must operate over a range of applied loads

Effect of operating conditions on gearbox noise

Low contact ratio spur gears were tested in the NASA gear noise rig to study the noise radiated from the top of the gearbox. The measured sound power from the gearbox top was obtained from a near field acoustic intensity scan taken at 63 nodes just above the surface. The sound power was measured at a matrix of 45 operating speeds and torque levels. Results are presented in the form of a spectral speed map and as a plot of sound power versus torque (at constant speed) and as sound power versus speed (at constant torque). Because of the presence of vibration modes, operating speed was found to have more impact on noise generation than torque level. A NASA gear dynamics code was used to compute the gear tooth dynamic overload at the same 45 operating conditions used for the experiment. Similar trends were found between the analytical results for dynamic tooth overload and experimental results for sound power. Dynamic analysis may be used to design high quality gears with profile relief optimized for minimum dynamic load and noise

Effect of contact ratio on spur gear dynamic load

A computer simulation is presented which shows how the gear contact ratio affects the dynamic load on a spur gear transmission. The contact ratio can be affected by the tooth addendum, the pressure angle, the tooth size (diametral pitch), and the center distance. The analysis presented was performed using the NASA gear dynamics code, DANST. In the analysis, the contact ratio was varied over the range 1.20 to 2.40 by changing the length of the tooth addendum. In order to simplify the analysis, other parameters related to contact ratio were held constant. The contact ratio was found to have a significant influence on gear dynamics. Over a wide range of operating speeds, a contact ratio close to 2.0 minimized dynamic load. For low contact ratio gears (contact ratio less than 2.0), increasing the contact ratio reduced the gear dynamic load. For high contact ratio gears (contact ratio = or greater than 2.0), the selection of contact ratio should take into consideration the intended operating speeds. In general, high contact ratio gears minimized dynamic load better than low contact ratio gears

Dynamic analysis of spur gears using computer program DANST

DANST is a computer program for static and dynamic analysis of spur gear systems. The program can be used for parametric studies to predict the effect on dynamic load and tooth bending stress of spur gears due to operating speed, torque, stiffness, damping, inertia, and tooth profile. DANST performs geometric modeling and dynamic analysis for low- or high-contact-ratio spur gears. DANST can simulate gear systems with contact ratio ranging from one to three. It was designed to be easy to use, and it is extensively documented by comments in the source code. This report describes the installation and use of DANST. It covers input data requirements and presents examples. The report also compares DANST predictions for gear tooth loads and bending stress to experimental and finite element results