SECTION 10 TOOTH THICKNESS There are direct and indirect methods for measuring tooth thickness. In general, there are three methods: ¥ Chordal Thickness Measurement ¥ Span Measurement ¥ Over Pin or Ball Measurement 10.1 Chordal Thickness Measurement This method employs a tooth caliper that is referenced from the gear's outside diameter. Thickness is measured at the pitch circle, See Figure 10-1. 10.1.1 Spur Gears Table 10-1 presents equations for each chordal thickness measurement. 10.1.2 Spur Racks and Helical Racks The governing equations become simple since the rack tooth profile is trapezoid, as shown in Table 10-2. 10.1.3 Helical Gears The chordal thickness of helical gears should be measured on the normal surface basis as shown in Table 10-3. Table 10-4 presents the equations for chordal thickness of helical gears in the radial system. 10.1.4 Bevel Gears Table 10-5 shows the equations of chordal thickness for a Gleason straight bevel gear. Table 10-6 presents equations for chordal thickness of a standard straight bevel gear. If a standard straight bevel gear is cut by a Gleason straight bevel cutter, the tooth angle should be adjusted according to: tooth angle (º) = 180º ( s + h1tana) (10-1) pRe 2 This angle is used as a reference in determining the circular tooth thickness, s, in setting up the gear cutting machine. Table 10-7 presents equations for chordal thickness of a Gleason spiral bevel gear. The calculations of circular thickness of a Gleason spiral bevel gear are so complicated that we do not intend to go further in this presentation. 10.1.5 Worms and Worm Gears Table 10-8 presents equations for chordal thickness of axial module worms and worm gears. Table 10-9 contains the equations for chordal thickness of normal module worms and worm gears. 10.2 Span Measurement Of Teeth Span measurement of teeth, Sm, is a measure over a number of teeth, Zm, made by means of a special tooth thickness micrometer. The value measured is the sum of normal circular tooth thickness on the base circle, Sbn and normal pitch, Pen (Zm - 1). 10.2.1 Spur and Internal Gears The applicable equations are presented in Table 10-10. Figure 10-4 shows the span measurement of a spur gear. This measurement is on the outside of the teeth. For internal gears the tooth profile is opposite to that of the external spur gear. Therefore, the measurement is between the inside of the tooth profiles. 10.2.2 Helical Gears Tables 10-11 and 10-12 present equations for span measurement of the normal and the radial systems, respectively, of helical gears. 366

There is a requirement of a minimum blank width to make a helical gear span measurement. Let bmin be the minimum value for blank width. See Figure 10-5. Then bmin = Sm sinbb + Db (10-5) where bb is the helix angle at the base cylinder, bb = tan-1 (tanb cosat) = sin-1(sinb cosan) (10-6) From the above, we can determine that Db > 3 mm to make a stable measurement of Sm 10.3 Over Pin (Ball) Measurement As shown in Figures 10-6 and 10-7, measurement is made over the outside of two pins that are inserted in diametrically opposite tooth spaces, for even tooth number gears; and as close as possible...

For odd number of teeth: (10-13) In measuring a standard gear, the size of the pin must meet the condition that its surface should have the tangent point at the standard pitch circle. While, in measuring a shifted gear, the surface of the pin should have the tangent point at the d + 2xm circle. The ideal diameters of pins when calculated from the equations of Table 10-13 may not be practical. So, in practice, we select a standard pin diameter close to the ideal value. After the actual diameter of pin dP is determined, the over pin measurement dm can be calculated from Table 10-14. Table 10-15...