Abstract:
This paper
studies first the conjugate action on the transverse plane and
calculate (Xp, Yp) the point on transverse path of contact out
of (Xp, Yp, Zp) the point on space path of contact. Then studies
the normal contact condition of rack and helical gear in the
plane normal to the tooth trace of rack and passing through
pitch point in order to get Zp. Consequently we get the three-dimensional
coordinates of contact point in fixed space as follows; Xp=－Yptanγ＝－Ytanγ(1)Yp＝Y(2)Zp=Xptanβ1＝－Yptanγtanβ1=h1λ1(3)Where,
Y, γ＝ordinate, gradient angle in transvers eplane of auxiliary
rack profile meshed with given helical gear1, β1, h1, λ1=helix
angle, reduced to a plane gearing. If gear 1 is a helical gear,
we must calculate Zp and λ1 with the above formulae. After
determination (Xp, Yp, Zp) of the contact point, with the aid of
screw motion and coordinate transformation, we can calculate the
profile of mating helical gear in a very simple way. A hob
design problem is used as an example and have been proven
exactly by actual cutting. This paper also determines the point
on line of contact on the rack-tooth surface with the same
method.
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