BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI - Universitatea ...

Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 2, 2010 127
phase (AP) between current ant voltage. Using the numerical values u[tk] and
i[tk] of the voltage and the current, the numerical evolution of the AEP can be
described by calculus (based on Eq. (1), as average value on the period T) with:
(2)
n⋅(
l+
1)
n⋅(
l+
1)
3
3
P[ tl
] ≈ ∑(
u[
tk
] ⋅i[
t k]
⋅ Δ t)
= ⋅ ∑(
u[
tk
] ⋅i[
t k])
,
T
n
k=
n⋅l+
1
k=
n⋅l+
1
where: P[tl] is the numerical value of the AEP (tl=l·T, l=1,2….m, m values for a
registration of m·T total duration), n=T/Δt, Δt is the reciprocal of the sampling
rate for u[tk] and i[tk], tk=k·Δt. If Δt→0 then in Eq (2) the symbol ≈ becomes =.
The sampling rate of AEP is equal with frequency f value (50 s -1 ). Using the
effective values U[tl] and I[tl] (the amplitudes of the voltage and current divided
by square root of 2), the AP and REP (reactive electric power Q) are given by:
(3)
P[
tl
]
ϕ [ tl
] ≈ arccos
and Q[ tl
] ≈ 3⋅U
[ tl
] ⋅ I[
tl
] ⋅sin(
ϕ[
tl
]) .
3⋅U
[ t ] ⋅ I[
t ]
l
l
The experimental research was done on a Romanian lathe SNA 360 (used as
MS, see Fig. 1) with the kinematics of the main shaft gearbox described in Fig.
Fig. 2 – Overview on the kinematics of the SNA 360 lathe main shaft
gearbox used as MS in experimental research.
2. An asynchronous EDM with 5.5 KW and 1440 rpm (speed in rotations per
minute) is used to drive it. Two different configurations of the gearbox were
used (see Kd1 and Kd2), each one is able to actuate the main spindle (shaft) Ms
on 1000 rpm or 1600 rpm.