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

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.

Evidence of secondary tooth contact in harmonic drive, with involute toothed gear pair, through experimental and finite element analyses of stresses in flex-gear cup

“…As already mentioned earlier, following the Routh et al's 4 investigation, it is to be noted that at no load the secondary contacts due to tooth interference occur at all four quadrants. Tooth pair contacts for the considered HD are estimated as shown in Appendix 2.…”

“…Apparently, there are some other contacts along the periphery, which are also sharing the load. In an earlier investigation, 4 theoretical evidences are presented regarding secondary contacts in HDs with involute toothed gear pair.…”

“…General working principles and kinematics of HD are well explained by many researchers. [3][4][5][6] In an earlier investigation, it is already presented that the secondary tooth contact is inevitable in HDs with involute toothed gear pair at the least. 3,4 The tooth contact analysis in HDs is complex due to flexion of FG.…”

“…When the cam is inserted inside FG cup, the oval-shaped pitch curve of the FG, mating with pitch circle of RG, is not an ellipse. 3,4 However, the pitch length at the inner surface of the FG cup remains unaltered. As the FG teeth are on very thin rim, all tooth roots bend but remain perpendicular on the tangent at the inner midpoint of the respective tooth (refer to Figure 25].…”

“…They are symmetric but opposite in direction resulting in nullifying the torque, but contributing stresses in FG cup. Routh et al 4 established a method of estimating such interferences and the intensity of secondary contacts. In the present investigation, the stresses in the FG cup is first examined due to cam insertion only and then the change in state of stresses due to meshing of the RG next.…”