Table 4. Equations of Power Transmission

in the MATLAB-Simulink§R

environment. Such model is

accurateliy described in Tonoli et al. (2006).

The present section briefly describes the modeling ap- proach and its use for the design od the test bench.

Fig. 4. Analysis of torque requirements for CS electric motor: in black, torque needed for operating the BDS; in light blue, torque needed to overcome the electric motor inertia; in red, resulting torque.

tem) shown in Fig. 3 corresponds to the case when the crankshaft powers the BDS. In such situation the BSG can act only as an alternator and generates a torque according to its speed. The role of the two motors can be exchanged, for example, when simulating an engine start- stop function.

From the electrical point of view, the voltage imposed to the CS electric motor by the corresponding inverter is the input to the system.

The modeling of each subsystem of the BDS was kept as simple as possible by using lumped parameters of inertia, stiffness and damping. The  model  described  in Tonoli et al. (2006) was extended to a 5 pulleys configuration obtaining the lumped-parameter model of Fig. 2 that will be used to describe the system’s dynamics and to define the performance specifications of the test rig.

Table 4 provides the equations that describe the dynamic behavior of each subsystem. The two electric motors were modeled using a dq-axis representation, including the ef- fects of resistance, inductances and electromotive force.

3.2 ICE behavior reproduction

The performances of the motor are given by rated and maximum values of speed and torque and by the band- widths reachable with current and velocity control loops. Consequently it was important to define such specifica- tions, taking into account the desired reference values and dynamics, the layout characteristics and the additional inertia of the electric motor.

The definition of the required specifications took the fol- lowing steps. Firstly, the required speed was derived by the operating speed values of the real ICE, which arrives to 6000 rpm. Secondly, the crankshaft speed imposed by the ICE to the crankshaft pulley was measured on an engine test cell. Amplitude and phase of the main harmonics were identified analitically by implementing a curve fitting procedure, using the formula in (1) as suggested by Genta and Morello (2009).

4

ωi = ωmean + . nAncos(ωmeant + φn) (1)

n=1

As a first result, this identification process indicated the required bandwidth needed for speed and current control loops when running at different reference speed values.

Then, the identified speeds were given as a reference to the speed loop of the simulator that allowed the computation of the torque that the CS electric motor needs to provide. The analysis was performed for different electric motors available on the market, including their inertia values into the simulator. In Fig. 4 is shown the analysis of torque re- quirements at different speeds for the selected motor which has a low inertia value. In black is indicated the torque component needed for operating the BDS, in light blue the torque needed to overcome the electric motor inertia and in red the resulting torque that the motor will need to finally provide. As clearly highlighted by Fig. 4, the main contribution to the overall torque is required to overcome the electric motor inertia. This consideration allows to study the torque requirements taking into account only such contribution and motivated a design of the shafts with minimum inertia properties.