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Special Design Problems in Gear Drives
Published in Stephen P. Radzevich, Dudley's Handbook of Practical Gear Design and Manufacture, 2021
The tooth profile in involute gears is the involute of the base circle. Figure 9.1, where 1 is the base circle and 2 is its involute, demonstrates the features of the involute. The most important feature is that in each point of the involute, the normal to it is tangent to the base circle. The length of arc ab of the base circle equals the length of line segment bc. Angle θ is denoted “invα” and called involute function. It is one of the parameters used often in the gear geometry calculations. From Figure 9.1 we can see that θ = φ – α. Since: φ=ab0.5db=bc0.5db=tanα,rad,θ=invφ=tanφ−φ,rad.
A Simplified Approach for Involute Gear Tooth Flank Generation
Published in Stephen P. Radzevich, Theory of Gearing, 2018
The tooth flank of a gear in a perfect parallel-axes gearing is a kind of involute surface. Gears with tooth flanks, G and P, designed to fulfill Equation 6.35, are referred to as involute gears for parallel-axes gear pairs. The term involute is because the transverse section of the gear tooth flank is an involute of a circle; that is, the involute tooth profile is developed from a base circle of a diameter, db.g, for a gear and from a base circle of a diameter, db.p, for a mating pinion, correspondingly. Once a type of transverse section of a gear tooth flank is known (this is an involute of a circle), simplified approaches can be used for the generation and further analyses of tooth flank geometry of involute gears.
Power transmission systems
Published in Mike Tooley, Lloyd Dingle, Engineering Science, 2020
The gear teeth profile is involute; this geometric profile is the curve generated by any point on a taut thread as it unwinds from a base circle. Once the gear teeth have been cut to this involute shape they will, if correctly spaced, mesh without jamming. It is interesting to note that this is the only shape where this can be achieved. The gear teeth involute profile is extended outwards beyond the pitch circle (the point of contact of intermeshing teeth) by a distance called the addendum. Similarly, the tooth profiles are extended inwards from the pitch circle by an identical distance called the dedendum. When we refer to the diameter of gear wheels, we are always referring to the pitch diameter.
Influence of tip modification on performance characteristics of involute spur gears
Published in Australian Journal of Mechanical Engineering, 2020
Wasiq A.M. Abdul, Timothy L. Krantz, Iqbal Shareef
For this study, a spur gear design previously used in gear durability research at NASA Glenn Research Center is used as an example design, for which pressure angle was 20°. The gear pair is a 1:1 ratio gear pair for a power recirculation gear tester. The gear design specification is provided in Table 1. The most commonly used pressure angles for spur involute gears are 14.5°, 20° and 25°, although other values are chosen for certain gearing applications. In general, the higher the pressure angle, the greater is the gear load carrying capacity, and a smaller number of teeth can be adopted without undercutting. But the higher the pressure angle, the greater is the separating force and the potential for larger dynamic effects and resulting noise. On the other hand, with lower pressure angles, one can reduce or eliminate undercutting and improve gear meshing while reducing dynamic stresses and noise. But lower pressure angles require higher number of teeth to avoid undercutting and decrease the maximal power transmission capacity of optimised gears. In general, a 20° pressure angle in involute profiles reduces risk of undercutting, reduces interference due to increased pressure angle compared to 14.5° and the tooth becomes slightly broader at the root. A pressure angle of 20° is a commonly selected good compromise design choice for many, but not all, gear applications as discussed in Dudley (1984).
Modeling and experimental verification of cutting forces in gear tooth cutting
Published in Machining Science and Technology, 2018
Gears are widely used in industry to transmit power or rotary motion while maintaining an intended torque and angular velocity ratio together with smooth motion and high efficiency. To achieve these favorable conditions, most of the gears have their tooth form based on involute curve. As the gear tooth flanks have a complex and precise shape, special attention is paid to gear during its manufacturing. Although a variety of gear forming methods such as casting, stamping, rolling, forging, extrusion, powder metallurgy, and machining are commercially available, gears should be produced by machining to achieve the desired dimensions, shape and surface finish. In practice, gear machining process can be performed by milling, broaching, hobbing, shaping and rack cutting. Of these methods, gear milling can be used for production of all types of external gears, performed on a conventional milling machine, and is economical and suitable for the production of replacement gears, small lot production, roughing and finishing operations.