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T-139 16.1  Forces In A Spur Gear Mesh The spur gear's transmission force Fn ,  which  is  normal  to  the  tooth  sur- face,  as  in  Figure  16-1,  can  be  re- solved into a tangential component, Fu , and  a  radial  component,  Fr.    Refer  to Equation (16-1). The  direction  of  the  forces  ac- ting   on   the   gears   are   shown   in Figure 16-2.  The tangential compo- nent  of  the  drive  gear,  Fu1,  is  equal to  the  driven  gear's  tangential  com- ponent,  Fu2,  but  the  directions  are opposite.  Similarly, the same is true of the radial components. Fu = Fn cosab ü ï ý             (16-1) ï Fr = Fn sinab þ 16.2   Forces In A Helical Gear Mesh The  helical  gear's  transmission force, Fn, which is normal to the tooth surface,   can   be   resolved   into   a tangential   component,   F1,   and   a radial component, Fr . F1 = Fn cosan ü ï ý             (16-2) ï Fr = Fn sinan þ The  tangential  component,   F1, can  be  further  resolved  into  circular subcomponent,  Fu,  and  axial  thrust subcomponent, Fa. Fu = F1 cosb ü ï ý             (16-3) ï Fa = F1 sinb þ Substituting   and   manipulating the above equations result in: Fa = Fu tanb ü ï ý             (16-4)      tanan ï Fr = Fu –––––– ï           cosb þ ab Fu Fn Fr Fig. 16-1     Forces Acting on a Spur Gear Mesh Fr1 Fr2 Fu2 Fu1 Fr1 Fr2 Fu1 Fu2 Drive Gear Driven Gear Fig. 16-2     Directions of Forces Acting         on a Spur Gear Mesh b an Fa F1 Fu F1 Fn Fr Fig. 16-3     Forces Acting on a       Helical Gear Mesh