Pressure Angle

Pressure Angle

The angle between the tooth profile and a radial line at its pitch point. In involute teeth it is often described as the angle between the line of action and the line tangent to the pitch circle.
In a spur gear, in which only one direction of cross-section needs to be considered, the general term pressure angle may be used without qualification.
In helical gears the pressure angle may be specified in the transverse, normal, or axial plane.

Whereas:
From Gear Data
z₁ = number of teeth in pinion (14)
z₂ = number of teeth in gear (61)
M_n = normal module (8)
ß = helix angle (15°)
a_n = pressure angle normal (20°)
profile shift coefficient x₁ (0.3)
................................x₂ (0.0)
a_w = centre distance (314mm)

Formula:

Transverse Pressure Angle: a_t
= atan(tan(a_n)/cos(ß))
= atan(tan(20)/cos(15))
= atan(0.36397/0.965925)
= atan(0.3768097)
= 20.647°

Working Transverse Pressure Angle: a_wt (a working example of this calculation can be found at SAP)
= acos(((z₁+z₂)/(2*a_w))*(M_n/cos(ß))*cos(a_t))
= acos(((14+61)/(2*314))*(8/cos(15))*cos(20.6469))
= acos(((14+61)/(2*314))*(8/0.965925)*0.935771)
= 22.242874º

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