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Table 7-1 presents equations for a profile shifted screw gear pair. When the normal coefficients of profile shift is given by the expression: x
n 1 = x
n 2 =0, the equations and calculations are the same as for standard gears. Standard screw gears have relations as follows: W W
t T = W tan B ( 7-8 )where d
w 1 = d
1 , d
w 2 = d
2

º »

( 7-7 )
T = axial thrust load, and
t w 1 = B
1 , B
w 2 = B
2

¼

W = transmitted load. The direction of the thrust load is related to the hand of the gear and the direction of rotation. This is depicted in Figure 7-3a Figure 7-3b 7.3 Axial Thrust Of Helical Gears Figure 7-1 . When the helix angle is larger than about 20°, the use of double helical gears with opposite hands ( In both parallel-shaft and crossed-shaft applications, helical gears develop an axial thrust load. This is a useless force that loads gear teeth and bearings and must accordingly be considered in the housing and bearing design. In some special instrument designs, this thrust load can be utilized to actuate face clutches, provide a friction drag, or other special purpose. The magnitude of the thrust load depends on the helix angle and Figure 7-3a ) or herringbone gears ( Figure 7-3b ) is worth considering. More detail on thrust force of helical gears is presented in SECTION 16 . Table 7-1 The Equations for a Screw Gear Pair on Nonparallel and Nonintersecting Axes in the Normal System Example Pinion Gear ItemSymbolFormulaNo. 1 2 3 4 5 6 7 8 9101112 1314151617 18 192021 m
n 3 20° 20° 30° 15 (R) 24 (L) 18.0773 36.9504 A
n B z
1 , z
2 z ––––– cos z
v 3 B A A tan
–1 cos

SCREW GEARS (Crossed Helical Gears) - 11708 (

tan ––––– A
n t B

)

21.1728° 22.7959° 0.4 0.20.0228415 22.9338° 24.2404° 26.0386°0.5597767.1925 47.8880 83.1384 44.6553 76.6445 49.1155 85.2695 20.4706° 30.6319°51.1025° 4.0793 3.47936.6293 56.0466 90.0970 42.7880 76.8384 Normal ModuleNormal Pressure AngleHelix AngleNumber of Teeth & Helical HandNumber of Teeth of an Equivalent Spur GearRadial Pressure AngleNormal Coefficient of Profile Shift Involute Function x
n 2tan A

(

–––––––– x
n 1 + x
n 2 wn inv A
wn n z
v 1 + z
v 2

)

+ inv A
n Normal Working Pressure AngleRadial Working Pressure AngleCenter Distance Increment FactorCenter DistancePitch DiameterBase DiameterWorking Pitch DiameterWorking Helix AngleShaft AngleAddendumWhole DepthOutside DiameterRoot Diameter A
wn Find from Involute Function Table A tan
–1 cos

(

––––––– A
wn tan
wt B 1 cos

)

ya 2 cos

(

z
v 1 + z
v 2

)(

––––––– – 1 A
n –– A
wn

) (

2cos ––––––– + ––––––– + z
1 z
2 x B 2cos B y
1 2

)

m
n ––––– cos zm dd
n B
b d cos A
t d 2 a ––––––– d
1 w 1 x d
1 + d
2 2a ––––––– d d
2 w 2 x d
1 + d
2 B tan
–1

(

––– tan
w w d d B

)

3 B
w 1 + B
w 2 or B
w 1 – B
w 2 h
a 1 (1 + y – x
n 2 ) m
n h
a 2 (1 + y – x
n 1 ) m
n hd [2.25 + y – ( x
n 1 + x
n 2 )] m
n a d + 2 h
a d
f d
a – 2 h

T31