Assessing the safety of the embedding system of the guide rail of the Padova Metrobus

The Metrobus is part of the recent public transport strategy of Padova. It is based on an innovative design developed by the Lohr Group, specialist in the design and creation of passenger and goods transport systems. The Metrobus is a new generation of light urban tramways, where the axle on pneumatic tyres replaces the railway boogie. The guiding of the bus is provided by a roller “V” system linked to a single guide rail which is level with the roadway, thus assuring accuracy of the route whilst avoiding wear and noise, avoiding also weighing on the rail, and mechanically impossible to derail. The uniqueness of the solution of Padova’s Metrobus in connection with the common Lohr design, is the material which is used to embed the guide rail: a polyurethane resin matrix and inert black rubber composite.

Figure 1 - Guiding system of Padova’s Metrobus.

This paper deals with the assessment of the safety of such embedded guide rail structure design, with respect to loads induced by the Metrobus itself and by the traffic as well as related to environmental conditions and ageing factors. The mechanical properties of the system are first determined by solving an identification-type reverse engineering problem on the available data coming from laboratory and in site tests. Then various FE analyses are carried out on highly non-linear models (ANSYS) including investigation on the dynamic answer of the system to impact forces from road traffic (LS-DYNA).

Figure 2 – Implantation system of the track to the groove.

The Padova Metrobus is an electric powered public passenger vehicle on tires expressly designed for operating on a dedicated rail line. Padova’s Metrobus adopts an innovative automatic embedding system of guide rail using two couples of contrast wheels; the first couple is positioned in front of the axis wheel, the second couple behind it. This system imposes the axis wheel automatically on the rail path (Figure 1).

The rail is located in an u-shaped channel obtained from concrete slabs casted onto the road pavement. The concrete slabs form the base on which the Metrobus wheels run (Figure 2).

The rail embedding in the channel is granted by a composite material compound set up (millimeter hard rubber parts in polyurethane resin matrix).

Figure 3 - 2-D static analysis: model and results

Figure 4 – Lateral load case - Lateral displacement and directional stress

This rather new set-up, has been successfully used in other similar light urban tramways. The uniqueness of the Padova system is the choice of material which was used to embed the rail into the channel: a polyurethane resin matrix and inert black rubber composite, named CONCRESIVE®.

The suggested choice of the designers (and the construction company) was to cut vibrations and noise. Moreover, it was particularly low-cost and easy and fast to carry out. The local authorities responsible for safety and layout solutions of rail-based systems, however, pointed out a number of objections and reservations. For instance, the lack of pre-existing experience or sufficient data on the reliability of the solution with respect to the ageing of the material. On the other hand though, the public was pushing for a fast solution to improve the transport system.
In this context, computational models were considered to examine various scenarios and to offer a forum to all parties involved, to document and discuss various solutions, and to reach the ‘best’ solution, with reliable safety margins.
Both engineering simplified models were used (beam on Winkler soil) and advanced fully 3/D FE models (ANSYS), as well as fast dynamic impact simulations (LS-DYNA).

Summary description of the work performed

The objective of the study was to evaluate the coherence and safety of the system from an engineering point of view. In this light the following steps were carried out:

Tab. 1 - CONCRESIVE® material properties

Tab. 2 – Experimental vs numerical results.

a) Identification of the composite material properties, using best curve fitting techniques based on experimental test results against reference FE models.
b) Setting up of simplified common engineering practice models, such as ‘beam on Winkler soil’ type models, to involve the size and the hierarchy of the problems, and to guide the choice of more advanced FE-based models.
c) Setting up of 2/D and 3/D models (ANSYS) with progressive refinement, to investigate the stress and deformation states with respect to the static-equivalent loading conditions.
d) Virtual proving ground simulations to evaluate the dynamic answer of the system to impulsive loads due to unordinary traffic situations, e.g. heavy truck tire passage on the rails.

Figure 5 – VPG model for LS-DYNA simulation

CONCRESIVE® material data and material model characterization
The material model adopted for the resin is Mooney-Rivlin. Properties are determined by solving the identification problem stated on available data and reference FE models.
The main properties quoted by the producer of the resin are reported in the following table 1:

The identification problem was based on three series of test cases, referring to a vertical point load, a shear point load, and an axial load respectively, and by recording the entire load/displacement histories, up to the ultimate strength. Fully FE 3/D models were used on the simulation side (ANSYS 20-noded isoparametric elements with 14-points integration rule). The reverse-engineering-like identification problem was solved as if it were a direct optimization problem, using modeFRONTIER to drive the search. The difference between measured and computed data is negligible, as shown in table 2.

Design loads
The following design loads were taken into account:

• Loads corresponding to normal and extreme working conditions.
  
• Loads due to the crossing of traffic on the rail systems (both normal and exceptional, with reference to the planned route).

Results
Analytical beam-on-Winkler soil approach

The beam of the Winkler soil reference model was based on a Winkler constant of 20 N/mm2 per unit length, roughly corresponding to a 20 Mpa Young’s modulus of the resin. By solving the differential equations with the above values with respect to, for instance, a point load, one can obtain the maximum deflection as well as the wave length of deformation, respectively:

where


The latter is particularly useful to drive the choice of the portion of the system to be taken into account in the refined FE models.
For instance, a vertical point load di 30000 N produces a max deflection of 1.4457 mm, and the wave length of 491.884 mm (having assumed a second moment of 1.47 ´ 106 mm4 and a width of 150 mm for the rail)

2-D model approach
Various 2-D models were considered. The one shown in figure 1 was used to estimate the consistency of the analytical model mentioned above. The comparison suggests a Winkler constant of 19.47 N/mm2 which is quite close to the one estimated in engineering data.

Figure 6 – LS-DYNA simulations: Stress and tirerail contact force	Figure 7 - Some of the results

Fully 3-D model approach
Various fully 3-D models were used to investigate the static answer (or quasi static, that is including dynamic amplification factors as suggested by different standards) to different loading conditions.

Virtual proving ground (LS-DYNA) approach
Virtual proving ground simulations are performed to evaluate the dynamic answer of the system to impact loads, such as heavy truck tire passage on the rail. This approach was also used to discuss the reliability of the dynamic amplification factors used in the static-equivalent analyses described above.
VPG pre-processor code was used to translate and to import the LS-DYNA input file. VPG tools were used also to set up the FE model of the truck tire FEM model, to tune it and set up simulation conditions.
Exceptional loads considered are related to heavy truck (19 tons) passage on the rail system. The axle load on single tire is 3750 kg.
Tire dimension, load and pressure data are:
Type: 254/80R20
Axle load x tire: 3750 Kg
Tire-road contact area 250*250 mm2
Inflating pressure: 8 atm
Velocity condition: uniform speed 50 Km/h
Some results are shown in figure 7

Conclusions
Today, the Padova Metrobus has successfully completed its testing phase and is in service. Although the methods and procedures outlined in this paper are quite common in the FE community, the fact that public bodies and safety agencies based their decisions on numerical models makes this a unique case history.

Marco Perillo - EnginSoft
info@enginsoft.it