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Gleason Spiral Bevel Gears Calculation

View: 2848405/03/2017  

Changzhou  Baoxin Gleason Spiral Bevel Gears  Calculation

A spiral bevel gear is one with a spiral tooth flank as in Figure 1. The spiral is generally consistent with the curve of a cutter with the diameter dc. The spiral angle β is the angle between a generatrix element of the pitch cone and the tooth flank. The spiral angle just at the tooth flank center is called the mean spiral angle βm. In practice, the term spiral angle refers to the mean spiral angle.

Fig.4.12 Spiral Bevel Gear (Left hand)
Fig.1 Spiral Bevel Gear (Left-hand)

All equations in Table 2 are specific to the manufacturing method of Spread Blade or of Single Side from Gleason. If a gear is not cut per the Gleason system, the equations will be different from these.

The tooth profile of a Gleason spiral bevel gear shown here has the tooth depth h = 1.888m; tip and root clearance c = 0.188m; and working depth hw = 1.700m. These Gleason spiral bevel gears belong to a stub gear system. This is applicable to gears with modules m > 2.1.

Table 1.8 shows the minimum number of teeth to avoid undercut in the Gleason system with shaft angle Σ = 90° and pressure angle αn = 20°.

Table 1.8 The minimum numbers of teeth to prevent undercut β=35°
Table 4.18 The minimum numbers of teeth to prevent undercut

If the number of teeth is less than 12, Table 1.9 is used to determine the gear sizes.

Table 1.9 Dimentions for pinions with number of teeth less than 12
Table 4.19 Dimentions for pinions with number of teeth less than 12

Table 2 shows the calculations for spiral bevel gears in the Gleason system

Table 2 The calculations for spiral bevel gears in the Gleason system

No.ItemSymbolFormulaExample
Pinion (1)Gesr (2)
1Shaft angleSet Value90 deg
2Modulem3
3Normal pressure angleαn20 deg
4Mean spiral angleβm35 deg
5Number of teeth and spiral handz20 (L)40 (R)
6Transverse pressure angleαtTable 4.20 The calculations for spiral bevel gears in the Gleason system 623.95680
7Reference diameterdzm60120
8Reference cone angleσ1


σ2

Table 4.20 The calculations for spiral bevel gears in the Gleason system 826.56505
deg
63.43495
deg
9Cone distanceRTable 4.20 The calculations for spiral bevel gears in the Gleason system 967.08204
10FacewidthbIt should be less than 0.3R or 10m20
11Addendumha1


ha2

Table 4.20 The calculations for spiral bevel gears in the Gleason system 113.42751.6725
12Dedendumhf1.888m – ha2.23653.9915
13Dedendum angleθftan^-1( hf / R )1.90952
deg
3.40519
deg
14Addendum angleθa1
θa2
θf2
θf1
29.97024
deg
1.90952
deg
15Tip angleσaσ + θa29.97024
deg
65.34447
deg
16Root angleσfσ – θf24.65553
deg
60.02976
deg
17Tip diameterdad + 2ha cos σ66.1313121.4959
18Pitch apex to crownXR cos σ – ha sin σ58.467228.5041
19Axial facewidthXbTable 4.20 The calculations for spiral bevel gears in the Gleason system 1917.35658.3479
20Inner tip diameterdiTable 4.20 The calculations for spiral bevel gears in the Gleason system 2046.114085.1224

 

All equations in Table 2 are also applicable to Gleason bevel gears with any shaft angle. A spiral bevel gear set requires matching of hands; left-hand and right-hand as a pair.

(4) Gleason Zerol Bevel Gears
When the spiral angle bm = 0, the bevel gear is called a Zerol bevel gear. The calculation equations of Table 4.16 for Gleason straight bevel gears are applicable. They also should take care again of the rule of hands; left and right of a pair must be matched. Figure 4.13 is a left-hand Zerol bevel gear.

Fig. 1.3 Left-hand zerol bevel gear
Fig. 4.13 Left hand zerol bevel gear


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