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      Gleason Spiral Bevel Gears Calculation

      View: 2913205/03/2017  

      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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