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The pitch diameter, d for the pinion and D for the gear, is the diameter of the pitch circle; it is measured in inches or in millimeters The module m is the ratio of the theoretical pitch diameter to the number of teeth N The module is the metric index of tooth sizes and is always given in millimeters The diametral pitch Pd is the ratio of the number of teeth on a gear to the theoretical pitch diameter It is the index of tooth size when US customary units are used and is expressed as teeth per inch The addendum a is the radial distance between the top land F and the pitch circle B in Fig 91 The dedendum b is the radial distance between the pitch circle B and the root circle D in Fig 91.

The whole depth h t is the sum of the addendum and dedendum The clearance circle C in Fig 91 is tangent to the addendum circle of the mating gearThe distance from the clearance circle to the bottom land is called the clearance c Backlash is the amount by which the width of a tooth space exceeds the thickness of the engaging tooth measured on the pitch circle Undercutting (see distance u in Fig 91) occurs under certain conditions when a small number of teeth are used in cutting a gear Table 91 lists all the relations described above Additional terminology is shown in Fig 92 Here line OP is the line of centers connecting the rotation axes of a pair of.

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Rectangular emission volumes are the easiest way to go and are often enough for what you need. However, sometimes you do not want that. It might be nicer to be able to have the particles fill a spherical volume.

9.3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

FIGURE 9.1 Terminology of gear teeth. A, addendum circle; B, pitch circle; C, clearance circle; D, dedendum circle; E, bottom land; F, top land; G, flank; H, face; a = addendum distance; b = dedendum distance; c = clearance distance; p = circular pitch; t = tooth thickness; u = undercut distance.

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meshing gears. Line E is the pressure line, and the angle is the pressure angle. The resultant force vector between a pair of operating gears acts along this line. The pressure line is tangent to both base circles C at points F. The operating diameters of the pitch circles depend on the center distance used in mounting the gears, but the base circle diameters are constant and depend only on how the tooth forms were generated, because they form the base or the starting point of the involute profile.

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

// a random position around my position -(BBPoint)newParticlePosition { if (!sphericalEmissionVolume) return BBPointMake(BBRandomFloat(emitVolumeXRange),BBRandomFloat(emitVolumeYRange),BBRandomFloa t(emitVolumeZRange));

FIGURE 9.2 Layout drawing of a pair of spur gears in mesh. The pinion is the driver and rotates clockwise about the axis at O. A, addendum circles; B, pitch circles; C, base circles; D, dedendum circles; E, pressure line; F, tangent points; P, pitch point; a, initial point of contact; b, final point of contact.

Line aPb is the line of action. Point a is the initial point of contact. This point is located at the intersection of the addendum circle of the gear with the pressure line. Should point a occur on the other side of point F on the pinion base circle, the pinion flank would be undercut during generation of the profile. Point b of Fig. 9.2 is the final point of contact. This point is located at the intersection of the addendum circle of the pinion with the pressure line. For no undercutting of the gear teeth, point b must be located between the pitch point P and point F on the base circle of the gear. Line aP represents the approach phase of tooth contact; line Pb is the recess phase. Tooth contact is a sliding contact throughout the line of action except for an instant at P when contact is pure rolling. The nature of the sliding is quite different during the approach action and the recess action; bevel-gear teeth, for example, are generated to obtain more recess action, thus reducing wear. Instead of using the theoretical pitch circle as an index of tooth size, the base circle, which is a more fundamental distance, can be used. The result is called the base pitch pb. It is related to the circular pitch p by the equation pb = p cos (9.5)

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