Abstract: In order to improve the contact quality of Hindley worm gears, a dependent linear motion along the axis of the basic member is added to the linear cutting tools besides its rotation when the Hindley worm is cut, i.e. the single degree of freedom motion of the linear cutting tools is changed into two degrees of freedom one. So a new method of manufacturing enveloping worm and a new type of enveloping worm gears, which is called two degrees of freedom linear cutting tools enveloping worm gears, are obtained. The mathematical model of meshing analysis of the worm gears is built and the formula of calculating the helical parameter of the linear cutting tools motion is given. The affecting regularities of the number of the thread of the worm and the helical parameter of the linear cutting tools motion on the undercutting line, the addendum thickness of the side tooth, the contact pattern, the length of the double line contact pattern on the worm and the micro contact quality on the worm gear are studied. A pair of worm gears is manufactured on a normal hob machine. The contact pattern test of the worm gears is carried out to verify the theoretical calculation results. The worm gears can be used with up to six threads of the worm; better contact quality and transmission performance than those of Hindley worm gears can be obtained by selecting suitable helical parameter of the linear cutting tools motion, and which has practical value.

Key words: Degrees of freedom, Tooth contact analysis, Verification, Worm gears, Innovation approaches, Knowledge model, Manufacturing planning design, Ontology