Vibration, like noise, is an extremely complex issue, and so it may help to start by saying what vibration is not. Although low frequency airborne noise from sources such as heavy lorries, trains or aircraft can have perceptible effects on buildings – rattling windows, shaking walls etc – and this is described by many people as vibration, this is really a mistake for the term ‘vibration’ that is really restricted to the displacement of the ground or of structures due to the propagation of energy waves through the ground and contiguous structures.
These energy waves can take several forms; broadly speaking, some waves spread out in all directions through the earth in a similar manner to the way that sound waves travel through the air. As the ground is more dense and more structurally complex than air, the waves may be more difficult to propagate initially than sound waves, but once started they may travel considerable distances.
The earth consists of numerous pockets and layers of material of different density and of outcrops of solid rock, so these underground waves (sometimes called ‘body waves’) may undergo distortion and reflection as they pass through these various materials and interfaces. Other waves of vibration travel on the surface in a manner similar to the surface ripples generated by a stone being dropped into a pool of water. These different waves will almost certainly travel at different speeds and be attenuated at different rates. Thus, the vibration may appear in unexpected places and in different frequencies, making vibration more difficult to predict.
Going underground or flying high
If trams or light rail vehicles are running on or above the surface then the effects of surface waves are important, and in subways or tunnel sections the underground body waves are the most important. These underground waves are particularly effective in transmitting to adjacent buildings. Vibration waves in structures will depend on the materials from which the structures are built, the flexibility of joints and the resilience of the foundation fixings. Structures made of stone or brick (such as 19th Century railway viaducts) can be very good at dissipating wave energy, whereas more modern structures made from reinforced concrete or steel can be distressingly good transmitters of noise.
Some readers may remember that the initial viaduct structures of the Docklands Light Railway (UK) had the rails mounted on a thin concrete deck, which was directly affixed to steel girders for the longer spans, the whole structure being supported by relatively tall, thin columns. Whilst this structure may have been economical in the use of materials it did result in the unwanted effect of responding to the noise and vibration effects of passing trains, transmitting the effects over
Defining the challenge
The measurement of vibration relates to the movement of the surface that is vibrating. This can be measured in units of velocity in metres per second (m/s) or acceleration (m/s2). The decibel scale can be used for measurement of vibration as well as noise, with all the complications of scales and the weighting of curves.
Naturally, the sensitivity of a person – or a delicate piece of recording or measuring machinery – will depend to a greater or lesser extent on the direction of position at the time and the dampening effect of surface treatments, wall coverings, flooring, carpets etc. Vertical vibration of a floor is perceived differently by a standing person, a person sitting on an upholstered chair and a person lying down; similarly, sensitive equipment will benefit from careful mounting within the structure.
So having established what vibration is there are two important issues to consider; how can its generation be minimised on our new urban rail system? And how can we mitigate the effects of vibration generated? As with any medical treatment, prevention is better than cure.
Most vibration is caused by the wheels of a tram rolling along the rail, the slip-skip effect as wheels round a curve, the grinding caused by flanges interacting with rail gauge faces and the hammer blows generated by wheels passing over discontinuities of the rail head (either at turnouts or at unwelded rail joints). Secondary effects may be created by friction brakes, gearboxes and transmissions and prime movers – as anyone who has felt a typical North American diesel locomotive with a massive, slow-revving diesel engine pass by can testify.
The first thing to recognise is that newly-installed rails are not planar, nor do they have a smooth rail head. The rollers at the mill will suffer from wear and slight eccentricity and this will impose a wave form and surface roughness on the railhead. Outdoor storage of new rails – which will lack the work-hardening effects of trains passing over them – can lead to surface pitting and corrosion
and the laying of the track with the welding of rail joints can result in a very rough running surface. It is therefore important to ensure that rails are ground smooth and to a uniform railhead profile before regular service commences.
The most difficult problem to deal with in tram track is rail corrugation; a frequently occurring rail wear pattern that arises mostly in curves. Causes are seen to be diverse and complex; however one of the inhibitors for corrugation is the use of continuously-supported track with high vertical resiliency and high or low horizontal resilience.
The wheel issue
Wheels will come from the manufacturer turned true, but again they will be ‘green’ and lack work-hardening. Cars used during commissioning and testing of the system will suffer damage from running over irregular track and may also suffer tread damage from slipping and sliding whilst the slip protection controls are being tuned up.
So, again it is important to ensure that all cars have uniform, truly circular wheels before commercial operation is commenced. If everything is then set up correctly the wheels and rails should inter-react to create work-hardened surfaces.
As the problems of slip/skip with fixed wheels on a rigid axle were discussed last issue, it is only necessary to say that the same solutions to vibration issues are relevant; individually motored wheels, limited slip differentials, etc, can all contribute to minimising the problem.
Similarly, gauge face engagement can be reduced by effective transitioning into curves, an effective flange root shape for the wheel, sufficient cant wherever possible, gauge widening on extreme curves and good driver training to ensure that curves are passed at the optimum speed to ensure that the wheels ride on the wheel/rail interface ‘sweet spot’. The overall design of the car, location of bogies or trucks in relation to body overhang and suitable fixed wheelbases can also help to mitigate nosing and intermediate bogie slop across the gauge, resulting in flange engagement.
The first step in minimising vibration is to allow for resilience in the wheel – this is usually created by having a non-metallic element in the wheel between the tread unit and the hub. Nowadays this is normally a rubber element either used in shear (as in the original PCC wheel) or in compression (as in the Bochum wheel). The resilient wheel will give some cushioning to the wheel/rail interaction and can be effective against very short pitch corrugation when specially designed to inhibit resonance frequencies that initiate corrugation.
The rails are most resistant to corrugation when they have a high vertical resiliency and horizontal frequencies that take the rail out of the corrugation frequency zone. Corrugation can be very aggressive, growing over a longer length of railhead with each passage of a car, and the depth of the corrugations can grow exponentially once established. Excessive corrugation can only be cured by eliminating the cause: e.g. force factor; excessive disparity of wheel diameters, etc. Rail grinding is a short-term measure and by removing the work-hardened surface of the rail will promote a rapid return of the problem.
Secondary mitigation measures have included the installation of track on floating slabs at sensitive locations, but these can be expensive and complex to install. There must also be a question as to their long-term effectiveness – a single breakdown in the resilient support or a contact between slab and a solid element bedded in the ground could cause a ‘vibration bridge’ to negate the value of the installation.
Of course one major issue worthy of careful consideration is the reduction of the overall mass of the tramcar. Less mass means less energy transmitted to the track and structure as the car moves along the track, and could form part of a virtuous circle of improvements in tramway performance. The reasons for weight growth are various – many of them are driven by an over-cautious approach to safety concerns. It will be of considerable value to the industry if the issue of weight is approached systematically and ruthlessly – every gram saved is a step forward. As a lecturer of mine was wont to say many years ago, “If mass is the answer you asked the wrong b—- question”.
From a feature originally published in Tramways & Urban Transit – April 2015 issue (927).