Highest Point Of Single Tooth Contact Research Articles

Optimization of spur gear pairs for aerospace applications

Abstract High power applications at high speed create contact problems, increase heat sink values and transmission error (TE) during gear meshing. Hence, analyzing the gear mesh including helix angle effect, the optimization in terms of contact pressure and the transmission error reduction are all crucial for high-speed applications. In this study, meshing characteristics including helix angle based on different approaches, optimization of spur gears pairs in terms of the transmission error and contact stresses obtained from improved analytical method besides transmission design tools are all investigated for high-speed aerospace applications. Results reveal that significant transmission error reduction could be achieved by applying tip relief starting from the highest-point of single tooth contact for spur gears in aerospace applications. Hence, the need for higher contact ratio by helix angle inclusion for smoother transmission could be compensated by using tip-relief modified spur gears in gearbox since the heat sink values also need to be minimized by using relatively lower contact ratio. Results obtained from the improved analytical method by directly considering gear geometry including gear foundation effects based on direct deformation–summation approach are found in between AGMA (American Gear Manufacturers Association) standard and ISO (International Organization for Standardization) standard results.

Experimental investigation of spur gear strength using photoelasticity

In this work, the maximum stresses, which are developed in the crucial toe section of spur gears being in contact and subjected to loading at the Highest Point of Single Tooth Contact (HPSTC), are numerically and experimentally studied. The results indicate that the deviation between the methods considered increase with increasing number of teeth of the gear, while the teeth number of the pinion remains constant. In addition it is shown that the deviations remain within acceptable limits.

Analytical solution to bending and contact strength of spiral bevel gears in consideration of friction

Friction is not considered in the calculation of load capacity for spiral bevel gears according to either ISO or AGMA gear standard, and friction effects on the bending, contact and shear of the gears have rarely been discussed. In this regard, the present work establishes analytical solutions to calculate bending and contact strength for spiral bevel gears incorporating friction on the tooth surface, which are verified by ISO gear standard and finite element method (FEM). The bending strength is calculated based on Lewis cantilever beam approximation, utilizing the modified normal force and the friction component. The modified normal force is derived at the highest point of single tooth contact (HPSTC) in the normal equivalent gear. Follow Hertz contact theory, the contact strength is calculated when the modified normal force and the friction component are exerted at the lowest point of single tooth contact (LPSTC) in the normal equivalent gear. The calculated bending and contact stresses agree well with those obtained from the FEM analysis while considering the influence of friction. Both theoretical predictions and FEM analysis have shown that friction has a crucial effect on load capacity of a spiral bevel gear drive, and that it exerts stronger influence on the bending strength (compared with the contact strength). When friction coefficients become larger (with the same input torque), the bending stress considering only the modified normal force decreases at HPSTC, whereas it increases if both the modified normal force and the friction component are included. In comparison, the contact stress will increase at LPSTC under both scenarios. Furthermore, it is illustrated that shear strength check of the tooth is necessary as large friction occurs in the contact zone. This developed analytical solution can be well applied to the determination of load capacity of spiral bevel gears, especially under harsh working conditions or in the demand for higher performance.

FEA-based design study of a gear tooth crack-growth monitoring sensor for high-reliability powertrains

In this paper, a sensing layout for the real-time in-situ monitoring of the length of a gear root crack is presented, suitable for use in powertrains where high reliability is expected. The sensing layout is based on the principle that electrical potential difference measurements between different positions on a tooth will be affected by a propagating crack and may be used to characterise the crack parameters. Mechanical finite element analysis (FEA) of spur gear teeth loaded at their highest point of single tooth contact (HPSTC) was performed and the location of the critical cross-section as well as the crack path was determined. Two measuring electrodes were placed in selected positions over the gauge area of a spur gear tooth and their readings were associated with the actual position of the crack tip by means of electrostatic FEA on cracked tooth geometries. The optimum position of the two measuring electrodes was determined by means of parametric simulation studies of the electrical field. With only two current electrodes and two sensing electrodes, the developed sensing array is simpler and more accurate than Boolean-type crack gauges using multiple wires.

COMPARISON BETWEEN NIEMANN’S AND FINITE ELEMENT METHOD FOR THE ESTIMATION OF MAXIMUM ALLOWABLE STRESS OF MESHING SPUR GEAR TEETH AT HIGHEST POINT OF SINGLE TOOTH CONTACT

Purpose of this study is the consideration of loading and contact problems encountered at rotating machine elements and especially at toothed gears. The later are some of the most commonly used mechanical components for rotary motion and power transmission. This fact proves the necessity for improved reliability and enhanced service life, which require precise and clear knowledge of the stress field at gear tooth. This study investigates the maximum allowable stresses occurring during spur gear tooth meshing computed using Niemann’s formulas at Highest Point of Single Tooth Contact (HPSTC). Gear material, module, power rating and number of teeth are considered as variable parameters. Furthermore, the maximum allowable stresses for maximum power transmission conditions are considered keeping the other parameters constant. After the application of Niemann’s formulas to both loading cases, the derived results are compared to the respective estimations of Finite Element Method (FEM) using ANSYS software. Comparison of the results derived from Niemann’s formulas and FEM show that deviations between the two methods are kept at low level for both loading cases independently of the applied power (either random or maximum) and the respective tangential load.

Increasing the Strength of Standard Involute Gear Teeth with Novel Circular Root Fillet Design

In this study the idea of spur gear teeth with circular instead of the standard trochoidal root fillet is introduced and investigated numerically using BEM. The strength of these new teeth is studied in comparison with the standard design by discretizing the tooth boundary using isoparametric Boundary Elements. In order to facilitate the analysis the teeth are treated as non-dimensional assuming unitary loading normal to the profile at their Highest Point of Single Tooth Contact (HPSTC), so that non-dimensional stress vs. Contact ratio diagrams are plotted. The analysis demonstrates that the novel teeth exhibit higher bending strength (up to 70%) in certain cases without affecting the pitting resistance since the geometry of the load carrying involute is not changed. The circular fillet design is particularly suitable in gear with a small number of teeth (pinions) and these novels gears can replace their existing counterparts in any mechanism without any alterations. Finally the geometry of the generating tool (i.e. rack) is determined in order to be able to cut these teeth using a generating method (i.e. hobbing).

Direct calculation of AGMA geometry factor J by making use of polynomial equations

The available sources and procedures for determination of AGMA geometry factor J are tables, charts and semi-analytical methods. When computerized gear design is considered, usage of tables requires a number of interpolations; usage of charts requires curve fitting; and usage of semi-analytical methods needs a numerical algorithm and may have convergence problems. As an alternative to these, polynomial equations for direct calculation of AGMA geometry factor J are derived for external spur gears. Thus, it is made possible to evaluate the J factor easily and with minimum process time. J factors are determined being independent of the highest point of single tooth contact (HPSTC). Derived equations can be used to calculate the tooth root stresses corresponding to loads acting on any point on the involute tooth profile. Thus, cases where the center distance is increased for providing backlash or for operating the gears at a desired exact center distance can easily be handled by determining the corresponding new HPSTC. A computer program is developed to demonstrate the usage of the derived equations. The method can also be used for determination of the J factors for gears with non-standard proportions.