1. Användning av andraderivator av Spårlägesparameterar
för Värdering av Spårlägeskvaliten
Martin Li
Trafikverket,
Underhåll / Ban o vägssystem / Spårsystem
78189, Borlänge, Sweden
Transportforum 2012, 11-12 januari I Linköping
1 2012-01-10

2. On the Use of Second-Order Derivatives of Track
Irregularity for Assessing Track Geometry Quality
Martin Li1 , Ingemar Persson2 , Jan Spännar1 and Mats Berg3
1. Swedish Transport Administration (Trafikverket), Borlänge, Sweden
2. AB DEsolver, Optand, Sweden
3. KTH, Rail Vehicles, Stockholm, Sweden
22nd IAVSD Symposium
14-19 August 2011
Manchester, UK
The paper has been reviewed and accepted for publication on the journal Vehivle
system Dynamics (VSD)
2 2012-01-10

3. Background
• Measuring and assessing track geometry quality play an
important role for safety control and track maintenance.
• By using a modern track recording car (TRC), track
geometry data including longitudinal level, alignment,
gauge, cross level and twist, are routinely collected and
assessed.
• Current standards and assessment methods are based
on the track geometry data alone, by comparing isolated
defects with predefined limit values and by computing
their standard deviations
• But it is the dynamic responses of vehicle and track that
are relevant to safety, maintenance costs and ride
comfort.
3 2012-01-10

4. Track recording car (TRC) in Sweden
STRIX
Infranord SWE owns 1 pcs.
principal Track record. veh. at TRV.
New Track record. veh. is planned for 2010
(IMV 200 Infranord) delayed until 2011/12?
4 2012-01-10

5. TRV Limit Values (BVF 587.02)
5 2012-01-10

6. On-track test results: low correlation between Q-force and LL
[5] T. Karis, Track Irregularities for High-Speed Trains, Master Thesis, KTH, 2009
6 2012-01-10

7. Not easy to detect
Alert! > 9 mm
Short waved irregularity
No forces….
High forces !!
7 2012-01-10

8. Motivations of using the derivatives of longitudinal level (LL2)
• Only using amplitudes of isolated defects and standard deviations is
neither sufficient for vehicle dynamics nor efficient for track maintenance
• Without taking into account wavelength and defect shape, the correlation
between amplitudes of isolated defects and wheel-rail force is low
• Enhanced assessment can be made by Vehicle Response Analysis
(VRA), e.g., Pupil by ProRail and VRA-method by DB. However, we
observe:
– VRA method tends to be very expensive and complex to use
– Difficult to consider all vehicle types and all speed ranges
– Most importantly, although the VRA-results are good, eventually, it is the track
sections and defects that need to be inspected and identified so that
appropriate correction maintenance can be taken.
• Question: are the derivatives of track defects (LL2) useful?
8 2012-01-10

9. Theoretical study: SDOF model
The dynamic equation can be written as Transfer function from LL to z
The wheel-rail contact force can be calculated as
Note: it is LL2 not LL that contributes directly to the dynamic force due to unsprung mass.
9 2012-01-10

10. Gensys simulation results
LL
LL2
Q_dyn
• A modified regional passenger train
• Vehicle model has been developed and verified by the Green train project at KTH [12]
• Speed: V= 220 km/h
10 2012-01-10

11. Gensys simulation results:
• The correlation coefficient for Q_dyn – LL is only 0.17
• The correlation coefficient for Q_dyn – LL2 is increased to 0.63
11 2012-01-10

12. Simulation results for three theoretical track defects
(A) Single cosine, 10 m
wavelength, ballast
settlement
(B) Sinusoidal and triangle,
standard defect in
S&Cs ([8])
(C) Harmonic function, 3 m
wavelength, initial rail
defect
• Same amplitude: 4 mm
• Different wavelength
and shape
• Different second-order
derivatives
• Different dynamic track
forces
12 2012-01-10

13. Summary
• Current methods of assessing track geometry quality based on amplitudes
of isolated defects and standard deviations are neither effective for planning
track maintenance nor sufficient for evaluating vehicle dynamics
• Theoretical study, simulation results and PSD analysis in this study
demonstrate that the second-order derivatives of longitudinal level (LL2)
can be used to enhance the assessment of vertical track geometry quality.
• Advantages of using LL2:
– wavelength and shape of track defects are considered
– easy to use.
• LL2 cannot and shall not replace the Vehicle Response Analysis (VRA)
– When VRA is available, LL2 is useful to further characterise the track defect type
– When VRA is not available, LL2 provides an effective analysis of track defects
that potentially may result in severe vehicle responses
13 2012-01-10

14. ‘Good’: normal track ’Bad’ : track shifted after a test run
Both amplitude and 2nd derivatives are big!
Thank you for your attention!
14 2012-01-10