Bevel-Gear  Formulas.  The  following  formulas  may  be
referred  to  in  solving  the  exercises  on  bevel  gears :


All  the  formulas  in  which  the  subscripts  g  for  "  gear  "  and  p  for
"  pinion  "  are  not  used,  apply  to  both  the  gear  and  the  pinion.  We  may
indicate  that  a  formula  applies  to  the  gear  or  to  the  pinion  by  adding
the  proper  subscripts,  as  in  the  following  cases :

D»=j?         D»  =  T?

^d  rd

The  result  found  from  the  formula  for  d  is  actually  the  dedendum
plus  the  clearance,  but  in  bevel  gears  we  treat  this  as  the  dedendum.
If  the  machinist  uses  formed  cutters  and  the  correct  indexing,  the
thickness  on  the  pitch  line  at  the  large  end  of  a  tooth  will  be  correct.  This
measurement  is  usually  checked  with  a  table  of  chordal  thicknesses.
BEVEL-GEAR  FORMULAS


101


Illustrative  Problem.    Make  the  calculations  for  the  pair  of
-7J  bevel  gears  shown  below  in  which  Ng  =  48  and  Np  =  24.
(1)  tan  Kg  =     a.  =        =  2.0000,  and  hence  Kg  =  63°  26'.
JNp      24

Kp  =  90°  -  Kg  =  90°  -63°  26'  =  26°  34'.
Hence    Dp    of    gear    is
4"  and  Z)p  of  pinion


is  2".
=  4


•>  v  0  8Q44


Hence  D0  of  gear  is  4.075"  and  D0  of  pinion  is  2.149".
Dp  4

~  2  sin  Ky  ~  2  x  0.8945  5  '

Hence  R  for  both  gear  and  pinion  is  2.236".
=  0.1798.  Hence  Wg  and  Wp  are  each  0.180".
(5)  W  =  =


(6)  a  =       =       =  0.0833.   Hence  ag  and  ap  are  each  0.083".
(7)  d  =


=  0.0964.   Hence  dg  and  dp  are  each  0.096".
