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.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°
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 2 shows the calculations for spiral bevel gears in the Gleason system
Table 2 The calculations for spiral bevel gears in the Gleason system
|Pinion (1)||Gesr (2)|
|1||Shaft angle||∑||Set Value||90 deg|
|3||Normal pressure angle||αn||20 deg|
|4||Mean spiral angle||βm||35 deg|
|5||Number of teeth and spiral hand||z||20 (L)||40 (R)|
|6||Transverse pressure angle||αt||23.95680|
|8||Reference cone angle||σ1|
|10||Facewidth||b||It should be less than 0.3R or 10m||20|
|12||Dedendum||hf||1.888m – ha||2.2365||3.9915|
|13||Dedendum angle||θf||tan^-1( hf / R )||1.90952|
|15||Tip angle||σa||σ + θa||29.97024|
|16||Root angle||σf||σ – θf||24.65553|
|17||Tip diameter||da||d + 2ha cos σ||66.1313||121.4959|
|18||Pitch apex to crown||X||R cos σ – ha sin σ||58.4672||28.5041|
|20||Inner tip diameter||di||46.1140||85.1224|
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