BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI - Universitatea ...

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Bul. Inst. Polit. Iaşi, t. LVI (LX), f. 2, 2010 163
3. Dynamic Mathematical Models
For both systems from Fig. 1 we can use the following model:
V0
Q = S ⋅ v + a ⋅ p + ⋅
E
dp
dt
dv
(5) M ⋅ + b ⋅ v + F = p ⋅ S .
dt
(6) V = ∫Q ⋅ dt .
(7) ∫ ⋅ = dt v .
x RD
In the last relations we have the following supplementary parameters: v-
instant speed of the CH engine, a- linear coefficient of the lost oil which are in
direct ratio with pressure, t-time, xRD-real movement in dynamic regime.
To find the real movement, in dynamic regime, we must simulate the
equation on a computer program. We consider the same data like in the case of
the static regime, in advance we know M = 200 kg and the values of a and b
coefficients. When the V quantity of oil is inserted we presume that the system
is in balance. The time which the system is in charge with the V oil quantity is
established as well as we obtain a movement theoretical equal with that we have
on the previous step (t = 2 s). The simulating chart in the simplified way is
presented in Fig. 2.
Fig. 2.a – The simulating chart.
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