Project summary at time of proposal (reduced to 200 words): A curve squeal model will be developed which will include excitation due to lateral and other components of creepage and including flange contact. Stability will be determined using a linearised frequency domain model while the amplitude will be determined using a time-domain model. Detailed wheel and track dynamics will be included making use of existing component models.

The forces at the wheel-rail contact will be studied using standard vehicle dynamics packages. The excitation of squeal depends on the negative slope of the force-creepage curve in the region beyond the range normally considered for adhesion. this is dependent on the contact conditions, calculated by the curving model, but is also known to depend on other factors which will be determined experimentally using test rigs.

A roughness growth model will be developed, taking account of the high frequency dynamics of both the wheel and the track, together with a model for the wear taking place under creepage conditions. Measurements of squeal noise under carefully controlled conditions in the laboratory are required to validate the model of squeal noise excitation. Measurements of wear and roughness growth will be made on the roller rig or the twin disc rig at MMU.

Curving behaviour: To provide inputs to curve squeal calculations, standard vehicle dynamics packages have been used to establish the contact forces, contact patch positions and creepages. These have been studied in detail for the example of a class 158 DMU in a range of curving situations. In addition, a user-defi ned routine has been produced to allow a falling creep force/creepage behaviour to be introduced into Simpack.

A dedicated steady state curving program has also been implemented in Matlab to allow direct integration with the curve squeal models.

Squeal Modelling: As proposed, two approaches have been taken to the modelling of curve squeal. These are each based on the understanding of the process as a positive feedback system in which the negative slope of the force-creepage relationship gives rise to instability.

In the first approach the system is analysed by treating the process as a control loop. In this way the stability can be examined by studying the open loop gain. A frequency domain model has been developed in which the creep force / creepage relationship is linearised around the steady creepages determined from the curving behaviour. As well as the excitation due to lateral creepage, that due to other components of creepage have been included including the possibility of flange contact. Detailed wheel and track dynamic behaviour is also included. This model can be used to study the propensity of a specific wheel (and vehicle) design to squeal in various curve confi gurations (radii, cant and speed).

In the second approach, a time-domain model has been developed which includes the non-linearity at the contact zone. This allows the analysis to be extended to include determination of the amplitude of the limit cycle and hence the results can be used to predict vibration amplitudes and radiated noise levels.

Comparison of the two approaches shows good agreement in most cases but reveals that in marginal cases the frequency domain approach can over-estimate the instability. this model allows the stick- slip behaviour to be investigated in detail. This approach can be used to study the amount of wheel damping required to overcome squeal. A small amount of work still remains to be completed within a related PhD project to include the spin component of creepage in the time domain model.

The excitation of squeal has been shown to depend strongly on the negative slope of the force-creepage curve in the region beyond the range normally considered for adhesion. It is apparent that predictions of squeal behaviour are very sensitive to the precise form of this friction curve. Study of the literature and discussions with industry contacts have revealed that very little information exists.

Validation Testing: Use has been made of three test rigs for validation of the squeal model, each of which has been modified for the purpose. Two of these rigs have also been used to measure creep force relationships which has provided valuable data.

A rig at ISVR has previously been used for rolling noise research. It comprises a reduced scale wheel rolling on a circular track of diameter 3 m. This rig was modifi ed to allow the yaw angle and lateral position of the wheel to be adjusted. Accelerometers are mounted on the wheel and their signals are transmitted using a specially devised radio telemetry system, commercial systems having an insuffi cient bandwidth. Results of a series of tests in which these parameters were varied showed good qualitative agreement with the stability model. However, there was considerable variability in the results as the wheel ran around the track due to subtle changes in the wheel and rail profiles. A limitation of this rig is that the quasi-static forces, and hence the force/creepage relationship, cannot be measured.

Through part-funding from an RAE Global Research Award one of the researchers spent 6 months at TNO in the Netherlands where an existing rig for curve squeal was available. this had the facility to measure the force/creepage relationship for lateral creepage (yaw angle). It was modified within the project to allow the introduction of longitudinal in combination with this. A series of tests was conducted which showed that the effects of combined creepage could be predicted by considering the resultant in the saturation model. The presence of longitudinal creepage therefore limited the occurrence of squeal. Four friction modifier treatments were tested on this rig, only one of which demonstrated the required high positive friction characteristics. Their relative durability was also assessed.

The main validation work was carried out on a twin disc rig at MMU by researchers from both partners. New rollers were designed and installed to represent a wheel and the rail. The rig was also modified to allow the yaw angle, lateral contact position and normal load to be adjusted. The rail roller was instrumented with an array of strain gauges to monitor the vertical and lateral contact forces and thus measure the friction characteristics. The location of these strain gauges was determined from a detailed FE study. Accelerometers were mounted on the wheel and rail roller and their signals were transferred using a system of slip rings.

Although the inherent variability of the force/creepage relationship is still an issue, results from the test rig agree well with both the stability and time domain squeal models. the model identifies the correct family of modes to be excited, but which of these modes is excited in a particular situation is found to be very sensitive to the details of the mode shape. This aspect may be exploitable for future optimisation of wheel design to reduce squeal. The amplitude of vibration and radiated noise is correctly predicted by the time-domain model. The lateral contact spring has been shown to be an important component of the model which was subsequently added to the time domain model.

A damping treatment was added to the wheel and the tests repeated. It was found that the amount of damping added was insuffi cient to prevent squeal, and this was confirmed by the model. the model could in future be used to optimise the placement of damping treatments to prevent squeal. Roughness growth modelling has been carried out in two phases using two complementary techniques. ISVR developed an initial frequency domain model to predict rail roughness initiation and growth on tangent track. This used a novel wavenumber based approach for predicting the high frequency interaction forces in the presence of several wheels. This represented the dynamics of a periodically supported track in terms of an expansion in the spatial harmonics of the sleeper spacing. the contact forces for a sequence of moving wheels are obtained and converted to the time domain. A two- dimensional contact model was then used to calculate the wear associated with each of these wheel forces as a function of position on the track. the model predicted a realistically shaped spectrum of roughness that emerges from an initially smooth rail. Results for multiple train passages indicated that the wavelength fi xing mechanisms depend on both the track structure and the wheel spacings. The effects of rail pad stiffness and train speed were also studied.

This work was taken further by MMU who developed the model using a time-domain approach and a three-dimensional contact model. With this model, the non-linearity of the contact zone dynamics which cannot be considered by the frequency domain model can be taken into account. Due to the presence of roughness on the rail, the normal problem of wheel/rail contact is non-Hertzian and the tangential problem is therefore non-steady due to the varying contact geometry. The non-steady effect can also come from varying normal load due to the interaction of wheel and rail. Using the Variational Method, MMU have developed a three-dimensional contact model to fully take account the non- Hertzian and non-steady effect. The non-Hertzian effect was first investigated by simulating a wheel rolling over various sinusoidal roughness with constant and varying normal force. It was shown that the contact geometry due to roughness has significant influence on solutions of the normal and tangential contact. It was demonstrated that the maximum wear occurs near the crest of the roughness and therefore roughness does not grow. It was shown that the non-Hertzian effect is the dominant factor on the wear for wavelength range of 30 ~ 100mm. With Hertzian contact, the wear is influenced by the normal force and therefore roughness growth is possible. To further understand the influence of choice of the contact model on wear calculation, simulations have been carried out using four methods: (1) Hertzian and steady; (2) non-Hertzian and steady; (3) Hertzian and non-steady and (4) non-Hertzian and non- steady.

It was found that a constant phase angle exists between steady and non-steady solutions. When the roughness wavelength is long, the non-Hertzian effect becomes less significant. Simulation with non-Hertzian contact always predicts wear to be almost in-phase with roughness. The analysis demonstrated that the choice of contact model is significant in the wear calculation for corrugation studies and an inappropriate model could give incorrect predictions for roughness growth. For wave- lengths between 30 and 100 mm (and amplitude 10 �m), the non-steady and non-Hertzian contact should be used.

The non-Hertzian and non-steady contact model were combined with a time-domain wheel/track interaction model. Various sinusoidal roughness and wheel velocities were considered. Differential wear was found to be mostly in-phase with the initial roughness giving no growth of roughness for both driven and free wheels. For the case of broad-band roughness, the wheel/rail force spectrum was influenced by wheel speeds and track dynamics. The wear spectrum was found to be almost independent of both the wheel speed and initial roughness spectrum and a decrease in roughness was again found. This was also believed to be due to the non-Hertzian contact, which leads to more wear for shorter and deeper roughness than longer and shallow roughness. No validation measurements of roughness growth were possible within the timescales of the project. However, the ISVR rig has been identified as suitable for such tests in the future should the opportunity arise.

• A vehicle dynamics package (Simpack) has been modified to implement an enhanced (falling) friction characteristic. Studies of typical curving behaviour have produced the contact forces, creepages and contact positions for input to the squeal model (Objective 2).
• A dedicated steady-state curving model has been produced for integration with the curve squeal model (Objective 2).
• A frequency-domain prediction model has been developed for assessing the propensity to curve squeal that includes not only lateral motion but also longitudinal and spin motion, making it suitable for predicting the effects of flange contact. This can be used for studying the effects of wheel shape design, damping treatments and vehicle suspension parameters for different curves and cant deficiency (Objective 2).
• A time-domain model for curve squeal has been developed which allows the amplitude of squeal noise to be predicted (Objective 2).
• Tests on the ISVR test rig show good qualitative agreement with the squeal model (Objective 3).
• A series of tests has been carried out on a twin disc rig at TNO in Delft. The rig was modified to study the effect of longitudinal creep. A range of proprietary friction modifiers was tested and their effect on squeal noise measured (Objective 3).
• An existing twin-disc rig at MMU has been modified to allow measurement of contact characteristics for a range of yaw angles. Measurements of squeal noise show good agreement with the squeal models (Objective 3).
• A frequency-domain based model for roughness growth has been developed which includes varying track support stiffness and longitudinal creepage and a 2D contact and wear model (Objective 1).
• A time-domain wheel/track interaction model has been developed and combined with a 3D contact model for roughness growth prediction (Objective 1).
• Predictions of roughness growth in response to an initial sinusoidal irregularity have been produced and have been shown to be significantly influenced by the choice of contact model (Objective 1).

• Thompson, D.J., Monk-Steel, A.D., Jones, C.J.C., Allen, P.D., Hsu, S.S., Iwnicki, S.D. (2003). Railway noise: curve squeal, roughness growth, friction and wear. RRUK Report A3/1(prepared for RSSB)

• Hsu, S.S., Huang, Z.Y., Iwnicki, S.D., Thompson, D.J., Jones, C.J.C., Xie, G., Allen, P.D. (2007). Experimental and theoretical investigation of railway wheel squeal. Proc. IMechE Vol. 221-1 Part F: J. of Rail & Rapid Transit. pp. 59-74.
• Huang, Z.Y., Thompson, D.J., Jones, C.J.C. (2006). A general model for wheel/rail curve squeal. Proc. 9th International Conference on Recent Advances in Structural Dynamics, Southampton, paper 34, 11pp.
• Monk-Steel, A.D., Thompson, D.J., de Beer, F.G., Janssens, M.H.A. (2006). An investigation into the influence of longitudinal creepage on railway squeal noise due to lateral creepage. Journal of Sound and Vibration 293, 766-776.
• Sheng, X., Thompson, D.J., Jones, C.J.C., Xie, G., Iwnicki, S.D., Allen, P.D., Hsu, S.S. (2006). Simulations of roughness growth on railway rails. Journal of Sound and Vibration 293, pp. 819-829.
• Xie, G., Iwnicki, S.D. (2006). Calculation of wear on a corrugated rail using a three-dimensional contact model. CM2006 Brisbane.
• Blanchard, A. (2005). Measurement of railway curve squeal noise on ISVR’s 1/5 scale railway. MSc dissertation, ISVR, University of Southampton.
• Sheng, X., Jones, C.J.C., Thompson, D.J. (2005). Responses of infinite periodic structures to moving or stationary harmonic loads. Journal of Sound and Vibration 282, 125-149. ISSN 0022-460X.
• Xie, G., Allen, P.D., Iwnicki, S.D., Alonso, A., Thompson, D.J., Jones, C.J.C., Huang, Z.Y. (2005). The introduction of falling friction coefficients into curving calculations for studying curve squeal noise. 19th IAVSD Conference, Milan, Aug 2005.
• Janssens, M.H.A., Monk-Steel, A. (2004). Test of friction modifiers for squeal noise abatement using the TNO roller rig for squeal noise studies. TNO contract report DGT-RPT-040037.
• Monk-Steel, A.D., Thompson, D.J., de Beer, F.G., Janssens, M.H.A. (2004). An investigation into the influence of longitudinal creepage on railway squeal noise due to lateral creepage. Proc. Eighth International Workshop on Railway Noise, Buxton, 711-720.
• Sheng, X., Thompson, D.J., Jones, C.J.C. (2004). Interactions between a moving wheel and a periodically supported rail. Proc. Institute of Acoustics 26(2), 80 – 91. ISSN 0309-8117
• Sheng, X., Thompson, D.J., Jones, C.J.C. (2004). Interactions between multiple moving wheels and a railway track. ISVR Technical Memorandum 930.
• Sheng, X., Thompson, D.J., Jones, C.J.C. (2004). Modelling rail roughness growth on tangent tracks. ISVR Technical Memorandum 929.
• Sheng, X., Thompson, D.J., Jones, C.J.C., Xie, G., Iwnicki, S.D., Allen, P.D., Hsu, S.S. (2004). Simulations of roughness growth on railway rails. Proc. Eighth International Workshop on Railway Noise, Buxton, England, Sept 2004, pp. 333-344.
• Thompson, D.J., Jones, C.J.C. (2004). Noise and vibration. Freight Transport Review, Autumn 2004, 91-92. ISSN 1474-6506.

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