Many clients before talking with us ask us how our system CaDOD-100 behaves in its catenary, for that we have had to make reports, we are going to publish them here on our website:
Comparison of the static and dynamic behavior of the PAC110 Delachaux profile with Innoviria CaDOD-100 device.
This report shows the comparison of the results of mathematical models of finite elements for two different systems of Rigid catenary: Profile PAC110 of Delachaux with and without Innoviria CaDOD-100 device. In addition to this comparison, the comparative of a representative case of the MM14 profile of Metro Madrid is presented at the end of the report.
1.- Content of the report
The report includes a brief description of the Innoviria CaDOD-100 device, the comparison of the static stiffness behavior, the comparison of the natural frequencies of resonance, the comparison of the dynamic behavior before the passage of a standard pantograph, the effect of the increase in temperature and , to finish, the effect of improvement in the static rigidity of the MM14 profile of Metro Madrid.
2.- Description of the CaDOD-100 device
The CaDOD-100 device, which is shown in figure 1, consists of 4 parts essentially:
- a normally hollow and light profile that is positioned parallel to the catenary profile and above it at a controlled height (hereinafter referred to by the letter “H”),
- two supports that allow connecting the ends of the upper hollow profile with the catenary profile (hereinafter referred to as “L”), and
- an adjustment system that allows to precompress the upper hollow profile to properly elevate and align the rigid catenary profile.
Figure 1: CaDOD-100 device on profile PAC110 by Delachaux
Figure 2: Preload necessary in Innoviria CaDOD-100 device
To complete the description of the device, figure 2 shows the necessary forces of precompression to align a profile PAC110 placed in all the spans of 10 meters of a canton of 300 meters in total length. The figure shows how the necessary preload depends on the height at which the upper hollow profile of the CaDOD-100 is positioned. At a lower height, a higher preload is necessary. The calculations shown in the figure have been made for a length of invention L = 5.2 meters and a hollow profile of 80 x 80 x 2 mm in aluminum.
3.- Comparison of the stiffness in the center of the span
Figure 3: Rigidity in center of span for different sections of the CaDOD-100
Figure 3 shows the vertical rigidity of the center of bay number 18 in a canton of 300 meters with spans of 10 m. The figure shows in black the stiffness value for the PAC 110 profile. Also shown in blue and red is the stiffness variation for the PAC 110 profile with CaDOD-100 of L = 5.2 m in length installed with three different tubes of square section ( 100x100x2mm, 80x80x2mm and 60x60x2mm).In the figure it is observed that:
- The Innoviria CaDOD-100 device placed on the Delachaux profile increases its rigidity in all its configurations of different heights, from 46% for a device height of 0.1 m to 388% for a height of 0.5 m.
- No significant influence on stiffness is observed for the variation of the three different sections of the upper tube of the device.
Figure 4: Rigidity in center of span for different lengths of the Innoviria CaDOD-100
Figure 4 shows the vertical stiffness that the same vain 18 has in its center for a canton of 300 meters with spans of 10 m. The stiffness value for the PAC 110 profile is again observed, as well as the variation of stiffness for the PAC 110 profile with CaDOD-100 where the section of the tube is now kept constant at 80x80x2mm and the length of the device is modified with measures of 3.2, 5.2 and 7.2 meters. It is observed that:
- The variation of the length of the absorber CaDOD-100 significantly influences the rigidity, presenting a higher value in the case of length 5.2 meters, compared to the other cases studied.
- Increasing or decreasing the length of the CaDOD-100 device in the same proportion does not modify the final stiffness in that same proportion.
- There is, therefore, an optimum for the length value of the invention. This maximum is in accordance with other parameters of the absorber CaDOD-100.
4.- Comparison of natural frequencies
In the field of dynamics, the natural frequencies of mechanical systems are a fundamental element to know the behavior of the system under study when it is subjected to variable loads over time. The natural frequencies are related to the rigidity that a system presents during its deformation phase in the vibration. It is also known that in the vibratory phenomena of mechanical systems most of the energy in play is absorbed by the modes with the lowest natural frequencies. This last aspect is the reason that the rigid catenary present oscillations at low frequencies that last over time and take time to muffle.
Figure 5: Comparison of natural frequencies
Figure 5 shows the first 30 natural frequencies for the same canton as in the previous sections. It is observed that:
- The Innoviria absorbers CaDOD-100 placed on the PAC 110 profile increase the natural frequencies in all its height configurations.
- The modes with the smallest values, which are the most influential in the final vibratory response, are those that increase the most.
5.- Comparison of responses in time before the passage of a pantograph
This section shows the response of the canton modeled during the interaction of a standard pantograph (UNE-EN-50318) circulating at 110 km / h. The contact forces between the table and the contact wire, the oscillations of the catenary and the oscillations of the hollow profile of the absorber CaDOD-100 while the pantograph covers the entire section are shown. 
Figure 6: Comparison of contact forces
Figure 6 shows the contact force between the pantograph and the catenary for the same situations presented in the previous sections, that is, for the PAC110 profile and for the PAC110 with CaDOD-100 devices installed at different heights. All the vertical axes show force values in Newtons and the horizontal axes correspond to the position that the pantograph has at all times along the canton. In all cases, the standard deviation of the forces has been noted, which are related to the wear of the contact wire. It is observed that:
- In all cases, a greater excitation is generated at the entrance of the pantograph in the canton, a phenomenon that is also identified in reality.
- The standard deviation in the contact force of the PAC110 profile with absorbers CaDOD-100 show significantly lower values for all heights.
- For an absorber CaDOD-100 height of H = 0.1 m the contact force is reduced by 35% and for a height H = 0.3 m the reduction reaches 52%.
- The improvement in the life of the contact wire and the pantograph could be considerable .
Figure 7: Comparison of the oscillations in the center of span 18
Figure 7 shows, for the same conditions and with the same interpretation of its axes as in the previous case, the vertical oscillation of the center of bay 18. It is observed that:
- In all cases the PAC110 when the Innoviria CaDOD-100 device is installed decreases the oscillations.
Figure 8, on the next page, shows in the same circumstances as the previous two the oscillation of the center of the absorber CaDOD-100 placed in span 18 of the section. It is observed that:
- As the height of the device decreases, the oscillation increases, since it must work more in order to control the vibration of the PAC 110.
Figure 8: Comparison of the oscillation in the center of the Innoviria CaDOD-100 device
6.- Study of the effect of temperature
The rigid catenary is installed mostly in tunnels, where the temperature can increase substantially. Using the canton models of the previous sections, the study has been contemplated for two representative cases of the PAC110 profile with absorbers CaDOD-100 installed in two heights: at 0.3 meters (as a representative case) and at 0.1 meters height (as a limit case). Figures 9 and 10 show the results of the contact force and the oscillation of the center of the third bay of the canton. It is observed that:
- There are no substantial differences in the analyzes between the temperature of 20º and 60º.
- It is not expected that the temperature is therefore no problem.
Figure 9: Contact forces. Effect of temperature
Figure 10: Oscillation in center of span 3. Effect of temperature
7.- Comparison of profiles PAC110 and MM14
Once the behavior between the PAC110 and PAC110 systems with Innoviria CaDOD-100 has been compared, it seems interesting to ask how the MM14 profile behaves.
Figure 11: Stiffness in the center of the span for the profile PAC110, MM14 and PAC 110 with CaDOD-100
Figure 11 shows the stiffness in the center of the span for the profile PAC110, MM14 and PAC 110 with CaDOD-100 at different heights. It is observed that:
- The MM14 profile shows greater rigidity than the PAC 110, as expected since it has an inertia 72% greater than the PAC 110.
- The PAC 110 profile with Innoviria CaDOD-100 has much higher values than the MM14 profile. The PAC 110 profile with CaDOD-100 at H = 0.3 m almost duplicates the rigidity of the MM14 profile.
Figure 12: Natural frequencies. Comparison with profile MM14
Figure 12 shows the natural frequencies for the profile PAC110, MM14 and PAC 110 with Innoviria absorbers placed at 0.3 meters height. It is observed that:
- The MM14 profile shows higher frequencies than the PAC 110, as expected since it has an inertia 72% greater than the PAC 110.
- The PAC 110 profile with Innoviria absorbers presents frequency values in low modes up to 21% higher than the MM14 profile.
8.- Conclusions of the studies
From the comparative study presented, according to the results of the mathematical models developed, for profiles PAC110, MM14, PAC110 with Innoviria CaDOD-100 absorbers, we can conclude that:
- In all cases , for the static and dynamic behavior , whenever the Innoviria CaDOD-100 device is incorporated, the behavior is improved, reducing the contact forces and the vibrations of the catenary. The decrease in contact force reduces contact wire wear and wear on pantograph tables. The decrease of the vibration in the catenary improves the contact of the pantographs that travel in second position for units in double or even triple configuration.
- The incorporation of the Innoviria CaDOD-100 absorber on the PAC110 profile offers greater static rigidity than the MM14 profile.
- The incorporation of the Innoviria CaDOD-100 absorber on the PAC110 profile offers higher natural frequencies than those with the MM14 profile.
- The temperature does not substantially affect the vibrations or the contact forces.
Rigid Catenary Innovation Solution 