Calculation of the Effective Length and the Run-Out Length of Helical Gears

Based on theoretical analysis, through applying the Lagrange multiplier method and solving a quartic equation of one variable, the analytic expression of the effective length of a helical gear fitted with a cylindrical rack is derived; then the correctness is verified by the SolidWorks software. Based on theoretical analysis, and through solving a quartic equation with one variable, the analytic expression of distance between the farthest end of hobbing and the plane perpendicular to the workpiece axis and containing the shortest distance line between the hobbing axis and the workpiece axis is derived, this distance is the hobbing run-out length of a helical gear. Then the correctness is verified by SolidWorks software. These two expressions provide an important basis for design of the helical gear related mechanical products.