Mismatched gearing composed of hourglass worm and spur gear: Meshing theory, tooth contact simulation, comprehensive design

Abstract

The ideology of non-specific mismatched drive is expounded, and its meshing theory is investigated by taking a new-type worm gearing composed of planar enveloping hourglass worm and spur involute gear as an example. The contact equations for determining the instantaneous contact points are established and its equivalent form containing only one unknown are obtained by artificial elimination, thereby realizing the datum point, the contact endpoints can be calculated more concisely. A comprehensive design method is proposed to avoid edge contact and guarantee the center locating of bearing contact area. On this basis, an effective mismatched scheme for the worm gearing is obtained. Simulation of tooth contact indicates that the scheme can simultaneously ensure: (a) no curvature interference; (b) respectable carrying capacity; (c) reasonable kinematic errors. Additionally, the influence of some mismatched parameters on meshing property is discussed, which provides references for the matching and selection of parameters. The developed mismatched strategies and meshing theory discussed in this paper can be extended to other types of complicated point-contact spatial gearing as well.