Numerical Modeling and Evaluation of Involute Curve Length of a Spur Gear Tooth to Maintain Constant Velocity Ratio While in Motion

Numerical modeling and values of the involutes curve length for a spur gear has been carried out using polar coordinate principles and application of calculus theorems. A set of values for base radius of the gear were considered from 10mm, 20mm, 30mm, 40mm and 50mm. The study also considered a pressure angle of 10°, 20°, 30°, 40°, and 50° for this set of values. The result of the length of involutes curve obtained at a pressure angle of 10° showed a significant increase in the length of the curve generated as the base radius increases that is at10° and for the set of the base radius values, the length obtained are:0.1555mm,0.311mm,0.4665mm,0.622mm and 0.7775mm. The result also revealed that at higher pressure angle of 50°, a better length of the curve was equally generated as seen from the plot.That is at 50° and with the base radius of 10mm, 20mm, 30mm, 40mm, and 50mm, the corresponding length of involutes are 7.1014mm, 14.203mm, 21.3045mm, 28.406mm and 35.5075mm. This equally validate the direct proportionality of length of curve as the square of tan a from equation.