BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

88 Florin Popa et al.
In this figure, I is the reduced moment of inertia of the rotating elements
of the propulsion engine, I' is the drive wheels reduced moment of inertia, and
I'' is the reduced moment of inertia of the gearbox and main gear elements.
To study the movement of rigid, in the initial phase is necessary to
generate equivalent mechanical model of the propulsion system, which involves
calculating in different points the reduced masses of the real system and the
corresponding reduced loads (Cheng et al., 2009). Thus, the mechanical
equivalent of automotive car propulsion systems assembly is replaced by an
equivalent mass, resulting in the model in Fig. 2, whose degree of freedom is
given by the angle of rotation.
Fig. 2 – The mechanical equivalent of automotive powertrain assembly.
2. Mathematical Model
Considering the reduction point at the motor shaft level, the mass
moment of inertia, I, of the reduced mass is calculated according to the
equivalent kinetic energy criterion, by means of the relation
n
2 n
2
r
j
⎛ ω
j ⎞ ⎛ vi
⎞
∑ I
j
⎜
⎟ + mi
⎜ ⎟
j= 1` ω i=
1 ω
I = ∑
⎝ ⎠
where: I j – is mass moment of inertia of the rotating j mass; ω j – angular velocity
of the j mass; m i – mass of the i element moving translational; v i – speed
of the m i mass; n r – number of rotating masses; ω angular velocity of low
mass I (usually equal to the angular velocity of the shaft to which they reduce).
The mathematical model of evolution of the mechanical equivalent of
automotive powertrain assembly is provided as a starting point total energy
conservation of I mass condition, so that:
2
I( φ) ω ( φ)
d = ⎡M m( ωχ ,
1, χ2,..., χp) −M r(
ωψ ,
1, ψ2,..., ψ ⎤dφ
2 ⎣
q ) ⎦
, (2)
and equivalent simplified form is
ω 2 dI dω
+ I = Mm
−M
r, (3)
2 dφ
dt
which is actually a mathematical model of mass movement I reduced its axis.
⎝
⎠
(1)