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T-55 Table 6-4 presents the inverse calculation of items 5 to 9 of Table 6-3. Table 6-4     The Calculation of a Shifted Helical Gear in the Radial System (2) The  transformation  from  a  radial  to  a  normal  system  is  described  by  the  following equations:           xt ü xn = ––––––– ï         cosb ï ï mn = mt cosb ý    (6-12) ï ï an = tan –1 (tanat cosb ) þ 6.10.3  Sunderland Double Helical Gear A  representative  application  of  radial  system  is  a  double  helical  gear,  or  herringbone  gear,  made with the Sunderland machine.  The radial pressure angle, at, and helix angle, b, are specified as 20° and 22.5°,  respectively.    The  only  differences  from  the  radial  system  equations  of  Table  6-3  are  those  for addendum and whole depth.  Table 6-5 presents equations for a Sunderland gear. Center Distance Center Distance Increment Factor Radial Working Pressure Angle Sum of Coefficient of Profile Shift Normal Coefficient of Profile Shift 109 0.33333 21.39752° 0.34462 0.34462        0 ax y awt xt1 + xt2 xt1 , xt2 No. Item Symbol Formula Example 1 2 3 4 5 ax         z1 + z2 –––  – –––––––– mt            2           (z1 + z2) cosat cos–1[–––––––––––––]            (z1 + z2) + 2y (z1 + z2)(inv awt – inv at ) –––––––––––––––––––––               2tanan Table 6-5     The Calculation of a Double Helical Gear of SUNDERLAND Tooth Profile              xt1 + xt2 2 tanat (––––––) + invat               z1 + z2 Find from Involute Function Table z1 + z2     cosat –––––– (–––––– – 1)      2       cosawt   z1 + z2 (–––––– + y )mt       2 zmt d cosat    db ––––– cosawt (0.8796 + y – xt2) mt (0.8796 + y – xt1) mt [1.8849 + y – (xt1 + xt2)]mt d + 2ha da – 2h Radial Module Radial Pressure Angle Helix Angle Number of Teeth Radial Coefficient of Profile Shift Involute Function           awt Radial Working Pressure Angle Center Distance Increment Factor Center Distance Standard Pitch Diameter Base  Diameter Working Pitch Diameter Addendum Whole Depth Outside Diameter Root Diameter mt a t b z1, z2 xt1, xt2 inv awt awt y ax d db dw ha1 ha2 h da df 3 20° 22.5°       12            60   0.34462        0 0.0183886 21.3975° 0.33333 109.0000    36.000     180.000   33.8289    169.1447   36.3333    181.6667     3.639        2.605 5.621    43.278     185.210    32.036     173.968   1   2   3   4   5   6   7   8   9 10 11 12 13 14 15 16 Example   Pinion    Gear Item Symbol Formula No.