An investigation on secondary force contacts of tooth pairs in conventional harmonic drives with involute toothed gear set

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Abstract
Originally fixed and uniform circular pitches of flex spline (FS) teeth of a ‘Strain Wave Gearing’ or ‘Harmonic Drive’ (HD) experience variations in pitch lengths when teeth move on ‘strain wave generating’ oval-shaped cam. This is due to varying root deformations of teeth. In case of teeth with widely used involute profile, away from the contacts on line of action through pitch point, they definitely experience force closeness to or separation from the circular spline’s (CS) originally conjugate tooth. We have estimated the deformed pitch distances at no load considering that FS teeth remain rigid while the rim deforms. The geometry of the oval-shaped pitch curve which is parallel to the elliptical outer profile of the cam is also defined. Similarly to maintain an elliptical pitch curve of FS, the oval cam is also defined. Both cases of tooth mesh of undeformed FS with CS and tooth mesh of deformed FS with CS, with involute teeth, are considered to find out tooth positions. Geometries of involute teeth profiles in mesh are examined and compared considering oval-shaped (on deformation) base drum of FS, whereas the base circle of the CS remained circular.

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