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A mathematical model to quantify dynamic forces in the powertrain of torque regulated movable bridge machineries

K. Sektani, A. Tsouvalas, A. Metrikine

Faculty of Civil Engineering and Geosciences, Delft University of Technology, the Netherlands (

The reassessment of existing movable bridges in The Netherlands has created the need for acceptance or rejection criteria to assess whether the machineries meet certain design demands. However, the existing design code NEN 6786:2001 Rules for the design of movable bridges defines a limit state design, meant for new machineries, which is based on simple linear spring-mass models. These models, as first proposed by Stroosma in 1980, are valid as long as damping is negligible and the externally applied loads, such as motor and braking torques, are assumed to be constant. However, observations show that these assumptions lead to a more stringent reassessment of existing bridges. As a result, existing bridge machineries do not confirm the model predictions and should unduly be replaced.

In fact, the powertrain of movable bridges are nonlinear systems consisting of many mechanical components, such as, couplings, shafts, gears and push-pull rods, with significant damping. Besides, the excitation of externally applied torques by motors and brakes are time-dependent and smooth.

In this paper, a model is developed that overcomes the limitations of the existing modelling approach. First, the classical semi-definite model is amended by an extra term which accounts for damping, using three load cases: opening from closed position, acceleration or deceleration and braking. The model gives an upper bound of the peak forces or torques occurring in the powertrain during normal operations and emergency braking. Subsequently, we discuss a novel nonlinear discrete model that allows one to deal with the time-dependency of the externally applied torques, such as, torque-speed characteristics of electric motors and braking torque characteristics.

Key words: Movable bridge dynamics, bridge machinery, powertrain, electric motors and brakes