# Electromechanical modelling of a bogie

IMMC

#### Modelling and analysis of a bogie driven by inductive motors

The application considered here is a subway bogie designed by Bombardier Transport for the city of Caracas (Venezuela). Unlike a classical bogie, this one (on the left figure) has an articulated chassis separated into two longitudinal parts assembled by a central joint allowing for left/right relative pitch. Actually, this joint is made out of rubber and six relative degrees of freedom (d.o.f.) exist between the two parts of the chassis.

Two three phase induction motors are coupled with the axles by means of reducers. These motors (blue elements in the right figure) are supported by the chassis at two specific locations:

• at the back of the motor, a pin comes out of the motor and is introduced in a bushing (rubber joint) crimped in the chassis,
• at the front of the motor, a rod connects the latter with the chassis by means of another rubber bushing.

Subway bogies are commonly driven by DC-motors, but in this case, the motor manufacturer proposed to replace them by three phase inductive motors. The latter are characterized by important torque oscillations when starting and Bombardier's engineers were worried about possible additional vibrations of the chassis, due to these torque oscillations. Indeed, additional vibrations could lead to fatigue issues, which should be avoided. The main objective in studying this bogie was thus to analyze the influence of the torque oscillations during starting of the bogie.

To achieve this goal, a strongly-coupled electro-multibody model was developed at UCL (via the ROBOTRAN program extension) using an original Lagrange formulation, involving both mechanical and electrical generalized coordinates. An illustrative result is shown below: the time history of the vertical force in a motor pin bushing (left figure) when the bogie is accelerated from rest (electrical torque in the right figure): for both motors, we assumed a U/F control from 0 to 50 Hz (0 to 290 V ) over 10 seconds. That corresponds to a typical subway acceleration of approximately 1.1 m/s2.

Fortunately, after comparing the results with those obtained with classical DC-motors, we could not conclude for significant additional vibrations induced on the chassis of the bogie, when introducing three phase actuators.