BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI - Universitatea ...

54 Silviu Berbinschi et al
with u variable parameter, measured along the profile and a constant value
depending the profile form.
The Σ profile family is on form:
(2) ( )
Fig. 4 – Straight lined profile.
ξ = 0;
Σ η = ucosϕ − asinϕ + R ϕ;
ϕ
ζ = usinϕ + acos ϕ −R
,
with ϕ variable parameter.
The
specifically enveloping condition, in the “in-plane generation trajectory”
methods is:
(3)
or
(4)
cosϕ
−usinϕ
− acosϕ
+ Rrp
= ,
sinϕ ucosϕ − asinϕ
u = R sinϕ
.
The equations
assembly (2) and (4), for u variable between limits
umin
=−0.5⋅ Rrp ; umax = 0.5⋅Rrp , for a hexagonal shaft, represent the rack-gear
tool’s profile reciprocally enwrapping with the shaft’s profile.
In Table 2 are presented the tool’s profile coordinates determined by the
analytical
method [6], [7].
In Figure 5 are presented the profiles form and the errors obtained at
profiling, regarding the coordinates
transformation:
rp
rp
rp