From Gear Data
Mn = normal module (8)
z1 = number of teeth in gear 1 (14)
z2 = number of teeth in gear 2 (61)
ß = helix angle (15º)
an = normal pressure angle (20º)
da1 = tip diameter of gear 1 (136.75mm)
da2 = tip diameter of gear 2 (521.21mm)
aw = centre distance (314mm)
Calculated
at = transverse pressure angle (20.6469º)
db1 = base diameter gear 1 (108.504mm)
db2 = base diameter gear 2 (472.765mm)
awt = working transverse pressure angle (22.242874º)
Pt = transverse pitch (26.019mm)
ga = length of path of contact (32.475mm)
Formula:
Calculation
sequence:
1. Transverse pressure Angle: at
= atan(tan(an)/cos(ß)
= atan(tan(20)/cos(15)
= atan(0.363970/0.965925)
= 20.6469º
2a. Base Diameter Pinion:
db1
= Mn*(z1/cos(ß))*cos(at)
= 8*(14/cos(15))*cos(20.6469)
= 8*(14/0.965925)*0.935771
= 108.504mm
2b.
Base Diameter Gear:
db2
= Mn*(z2/cos(ß))*cos(at)
= 8*(61/cos(15))*cos(20.6469)
= 8*(61/0.965925)*0.935771
= 472.765mm
3. Working Transverse Pressure Angle:
awt
= acos(((z1+z2)/(2*aw))*(Mn/cos(ß))*cos(at))
= acos(((14+61)/(2*314))*(8/cos(15))*cos(20.6469))
= acos(((14+61)/(2*314))*(8/0.965925)*0.935771)
= 22.242874º
4. Transverse Pitch:
Pt
= (Mn*Pi)/cos(ß)
= (8*3.141592)/cos(15)
= (8*3.141592)/0.965925
= 26.019mm
5. Length of Path of Contact:
ga
= 0.5*[sqr(da22-db22)+sqr(da12-db12)-(db1+db2)*tan(awt)]
= 0.5*[sqr(521.212-472.7652)+sqr(136.752-108.5042)-(108.504+472.765)*tan(22.242874)]
= 0.5[sqr(48152.6862)+sqr(6927.444484)-581.269*0.408965]
= 0.5*(219.437203+83.23186-581.269*0.408965)
= 32.475mm
6. Arc of Action:
= ga/cos(at)
= 32.475/cos(20.6469)
= 32.475/0.935771
= 34.704