Determination of Tooth Profile Curve of Helical Pinion and Rack Gears to Achieve Non-constant Transmission Ratio

Abstract

AbstractThis paper discusses a determination scheme of spatial tooth profile curvatures of helical pinion and rack gears to achieve a desired non-constant transmission ratio, called variable rack and pinion. In the scheme, a meshing kinematics is firstly considered. This problem is determined by a base circle and involute tooth profile of a pinion gear, a pitch point namely an instantaneous center between the rack and pinion gears and a line of action which is tangential to the base circle and passes through the pitch point. On each transverse plane along the pinion’s rotation axis, the rack gear’s profile is obtained as a locus of crossing points of the involute curve and line of action. To solve this problem, a scheme targeted on the spur gears previously proposed by the authors has been extended. In this scheme, the generation of involute helix and variation of cross-sectional tooth shape on each transverse plane are considered. In case of variable rack and pinion, the pitch point determined by a target transmission ratio with respect to the pinion gear’s rotation angle is not constant. Accordingly, the obtained rack gear’s profile becomes uneven and thus the geometrical conditions of it should be evaluated to avoid undesirable profiles such as not being smooth or causes self-interference. Thus, two of five previously proposed conditions have been modified to deal with the variation between each transverse tooth profile. After eliminating unsuitable combinations of design parameter values that result in undesirable meshing conditions, remaining solutions can be obtained as candidate of practical design. The authors picked up one of them in a numerical example and fabricated test pieces of a helical gear, constant- and non-constant rack gears that mesh with the common pinion gear. Result of a driving experiment using those test pieces shows that output stroke of those two gears agree with a target curve, and therefore demonstrates the feasibility of the proposed approach.KeywordsHelical rack and pinion gearTooth profile generationNon-constant ratioMotion and power transmission