Adhesion

Before we move to EMU vs Locomotives (Powerhead) approach to power a train, a study of adhesion is inescapable. This is the concept on which we pay heavy premium when we opt for EMU architecture over Powerheads (loco hauled, push-pulls).

Lack of appreciation of this concept, which is also traction agnostic, can lead to incorrect selection of architecture to offer a service. While eminently avoidable by appreciation of just the basics, this mistake can substantially push up the cost of acquisition of rolling stock and its O&M.

So what is adhesion?

Friction between wheel tread and the rail head is called adhesion by railwaymen. There are theoretical approaches to model adhesion, however, that can be left in the able hands of the researchers. We can however, limit ourselves to what practicing engineers and designers have agreed on and which has been consistent with the repeated measurements across continents.

When rotational speed of wheel disagrees with the vehicle speed

As the wheel rolls on the rail, one notices that we are dealing with multiple speeds (that of each wheel disc, that of the wheelset, that of the bogie, that of the locomotive). Again, we limit ourselves to basics for brevity.

So, one speed of our interest is that of the vehicle and the other one is the speed we derive from wheel diameter and its rotational speed (each rotation of the wheel should advance the wheel, by distance that equals one circumference).

If the speed derived from wheel diameter and that of the vehicle are not same, wheel either slips (i.e. spinning faster than required for the vehicle speed) or is sliding (i.e. wheel is spinning slower than needed for the vehicle speed).

Slide is straightforward to understand. Say we brake a fast car, wheels lock while the car skids, i.e. car still keeps moving while losing steering control. Wheel slip is akin to driving on a sandy beach-wheels spin faster while the car moves slower.

Note: For sake of brevity we refer motive power as locomotive, concepts apply identically to EMU as well, unless specifically mentioned.

Wheel Slip

Wheel slip will happen only when the locomotive is in traction, i.e. when locomotive wheels are being driven.

We define wheel slip speed of ith wheel as, difference between circumferential speed of ith wheel and the vehicle speed. If we divide slip speed by vehicle speed, we get slip. This is also expressed as percentage.

Basic physics tells us that the tangential force at the contact patch (between wheel and the rail) is product of coefficient of friction (μ) and the weight at the contact patch (if our locomotive has 6-axles, it has 12 wheels, so entire weight of the locomotive comes on the 12 contact patches).

It so happens that coefficient of adhesion and the weight at the contact patch changes as the locomotive runs. Again for sake of brevity we can assume that weight on contact patch remains constant. However, even in simple calculations we can not take coefficient of adhesion (μ) as constant. μ depends on the slip speed, conditions of rail surface, train speed and the temperature of contact area.

Question is, is adhesion at its maximum value when slip is zero? Slip is zero when we derive linear speed from wheel diameter and the rotational speed of the wheel, we get vehicle speed.

It is unfortunately not so.

Adhesion-Slip Speed Characteristics

Now we introduce second curve (we introduced first one in Comparing Locomotives here). This characteristic curve gives relationship between adhesion coefficient (μ) and slip or slip speed. Note that this curve is traction agnostic.

Few things readily standout:

1. You need some slip for adhesion to be available. What it means? 'Zero-slip' driving is a mirage, there has to be certain amount of slip for traction forces to be transferred.
2. The curve has stable and unstable regions-we operate EMUs and locos in the stable region.

Following is the 'settled wisdom' of designers:

1. It is important to note that, part of the stable region where we operate the loco/EMU is design choice optimised for service demands.
2. Loco adhesion controller will typically operate in [b], i.e. in the region where the adhesion is maximum. Note this will require the wheel to have maximum slip in stable region-penalty paid to access this part of the characteristic is wear and loss of energy. This hence becomes a consideration in the design of wheel discs for locomotives.
3. An EMU will sacrifice maximum adhesion value to optimise on energy and wheel-rail wear. Thus, an EMU will be typically found operating in [a] which is the linear region in stable part of the characteristics.
4. While a powerhead (loco) will be seen working between 30-40% adhesion, EMU platform will be working between 15-20%. EMUs make up for working at low adhesion value by having more driving wheels.

What adds to the challenge is the fact that the adhesion curve keeps changing as wheels move. The family of curves, as drawn in Fig-B gives the envelope of possibilities.

The shape of these curves can be generalised.

1. We can spot linear-nonlinear or stable-unstable regions in most of the curves.
2. Further, one notes that the peak adhesion will shift towards lower slip speed as friction (adhesion) value increases.

Corollary, as wheel-rail contact deteriorates, the peak falls and will occur at higher value of slip speed (shifts to right). Higher slip will lead to loss of energy and wear of wheel and the rail.

Maximum Friction (adhesion) to Vehicle Speed Value

This is arrived using Curtius-Kniffler equation:

For dry rail-wheel conditions:

For wet rail-wheel conditions:

Values returned by the equations above are taken as nominal and we derive an envelope of +15% and -45% about this nominal value of adhesion.

The maximum value of adhesion reduces as speed increases. This equation has no dependence on weight of the vehicle.

Concluding

We need certain amount of wheel slip for traction forces to be dispatched. Amount of slips we permit in EMU is way less than that a locomotive gets designed about. EMU makes up for this by having more driving wheels.

To illustrate, a 16 coach Amrit Bharat has two WAP5 on each end. WAP5 will typically weigh 80 tons and gives about 258 kN of pull at the draw bar. This translates as required adhesion value of 33%. While Vande Bharat will need about 16% adhesion. Amrit Bharat has 8 driving axles, while a Vande Bharat has 32 driven wheel sets-this makes Vande Bharat deliver speed and pickup even though it works on low adhesion like any other EMU train.

If we look at WAP7, then needed adhesion would be 27%. While a WAG9 will need 38% (which is about maximum adhesion value seen in Fig-D, which is 15% above nominal dry conditions).

Point to ponder: If we run a 130 kmph service, would Amrit Bharat give better all weather performance with WAP7s instead of WAP5s as P7 will need lower adhesion and still dispatch higher tractive effort due to four additional driving wheel sets?

As an aside:

Experience shows that WAP7, a passenger locomotive, which needs just 27% adhesion also encounters wheel slip in first showers-more on this in a later post. This shows that achieving even 27% is also not a given.

Contd... where we discuss what is the implications for loco hauled and EMU architecture.

References:

1. Author's notes.
2. Pichlík, P., & Zdeněk, J. (2014). Overview of slip control methods used in locomotives. Transactions on Electrical Engineering, 3(2), 38-43.