Adhesion

Last updated on April 5th, 2015 at 06:13 am

Rolling of wheel

In the fig 1 above, we all know F_r is very less as compared to F_s for the same weight but why and how much? This is because coefficient of friction, in case of rolling,  is very small as compared to sliding. Again why? For understanding this, it is important to calculate the speed at the point of contact when linear and rotational motion of wheel is taking place. It is calculated by taking vectorial sum of speeds at each point as given in Fig 2 above.

Let Linear and angular speed is V and ω respectively with wheel radius r.  Vectorial sum of speed at the top and bottom is ωr+V and ωr-V. V is approximately equal to rω, therefore speed at the point of contact is almost zero unless there is difference between V and rω. When relative motion between two surfaces is almost negligible, theory of friction does not explain the phenomenon about what is happening at the point of contact. Rolling resistance is the term coined to account for the energy loss at the point of contact instead rolling friction.

It is difficult to perceive almost nil speed at the point of contact. It can better be understood that if there is a rotational speed at the point of contact then it will be grinding the rail, situation similar to wheel slipping.

There are many theories given to explain the action taking place at the point of contact and summarized as follows:

Coulomb in 1781

• Two famous Laws based on experimental studies
  • Resistance to rolling is directly proportional to the load
  • Resistance to rolling is inversely proportional to the diameter of the roller

Later studies showed these laws are only approximation but used commonly for first approximation

Reynolds (1876)

• Rolling friction is due to the slip/creep taking place within the contact area

Heathcote (1921)

• Surface speed of different points of a rolling sphere is different but travel the same distance on the surface.
• Lubrication has negligible effect on rolling resistance but increases micro slip

Tomlinson (1929)

• Molecular Theory of Friction: The rolling friction is due to the hysteresis in adhesion between the atoms of the roller and the surface. He suggested that when roller rolls over a surface, the atoms are pulled from their equilibrium position, which on reaching a critical distance flick back to their original position. The hysteresis in this process leads to energy dissipation, resulting in rolling friction.

Bikerman (1949)

• Surface roughness can have a significant effect on rolling friction only if it has a significant magnitude (height of hills) in comparison with the radius of the roller ( of the order of 0.1% of the roller radius)

Eldredge and Tabor (1955)

• Main cause of rolling friction was the energy dissipation due to plastic deformations which reduces with each traversal. After a large number of traversals, the predominant reason for rolling friction becomes elastic hysteresis, since no plastic deformation takes places

Rolling resistance

Rolling resistance thus accounts for hysteresis loss during elastic deformation and sliding friction during micro-slip of 0.1 to 0.2% [difference between rolling and linear speed (rω-v)]. When rw-V is high than wheel is said to be slipping and sliding friction causes erosion of material from rail and energy loss. Rolling resistance is also expressed in terms of the factor (µ_r) which when multiplied with its weight (W) gives Force (Fr) requires to start the rolling action and is called coefficient of rolling resistance on lines similar to coefficient of friction.

Rolling resistance is very small of the order of 0.0001 as compared to sliding friction around 0.73-0.75 between two steel bodies.   This is how Physics explains why rolling is easier then sliding. Rolling resistance of rail road vs road is as follows:

Rail Road                                                      0.0001-.0002

Truck Tire on asphalt                              0.006-.01

Ordinary car tires on concrete            0.01-.015

Car tires on solid sand                             0.08

Car tire on loose sand                              0.2-0.4

This also explains the main reasons for higher efficiency of rail transport as compared to Road. Efficiency is slightly lost due to prevailing sliding friction between flange and inner face of rail i.e. the factor b which does not exists in road transport of the equation a+bv+cv² and higher tare weight per unit carrying capacity which is not so inroad transport.

Adhesion

It is important to note that in case of traction wheel, tractive effort is transferred to rail due to sliding friction in relation to micro-slip. Tractive effort vs. micro-slip characteristics is as given in Fig 3.

It may be seen that when tractive effort is increased, slip increases in proportion. Maximum Tractive effort is attained when micro-slip is around 1.5% and is the maximum value of sliding friction which can be converted into adhesive weight responsible for transfer of tractive effort. Thereafter, capability of transferring TE reduces with increase in micro-slip. Sliding friction in laboratory condition between steel and steel is around 0.73 of which only maximum 0.42 is converted into adhesion due to practical surface conditions of rail and wheel. Coefficient of adhesion when multiplied with weight gives adhesive weight. Wheel slip starts when Tractive effort is more than adhesive weight.

Tractive effort control for best adhesion

It is not possible to attain maximum adhesion in Tap changer control system due to its inability to touch the peak adhesion and likely occurrence of wheel slipping associated with auto-regression during progression in steps. This results in average tractive effort to be lower than maximum adhesion available (Fig3). Tractive effort is reapplied manually in steps which again find difficulty to touch the maximum level and therefore, maximum adhesion is limited to 0.35 in tap changer locomotive of WAG7 class of locomotive with high adhesion bogie. Zone A in the above figure demonstrate TE control in Tap changer locomotive.

When tap changer locomotive works with auto-regression control isolated, the working will be in zone B where TE will get applied in excess to adhesion, with excess energy lost in heat due to sliding friction between rolling wheel and stationary rail.

With advanced power electronics and its control, it is possible to work at maximum limit of adhesion (Zone C) where wheel slip is detected by comparing sudden change in acceleration and speed with reference values and corrective action taken to reduce tractive effort till such time acceleration and speed normalises. Condition of improved adhesion is sensed automatically and TE restored without loss of time. A typical characteristic phenomenon happening is depicted in Fig 4 giving detection and correction cycle during time period from O to C are in the following range

Fig 4

OA:      Detection of slip on any axle and slip condition recorded after 5msec.

AB:       Reduction of Traction motor current starts with a time constant of about 50msec.

BC:       1. Holding level of torque is maintained to stop the slip condition for a period of about 1sec.

              2.  Holding level is   decided by in built  programme depending upon severity of slip

    3. When slip condition is no more existing, Tractive Effort is reapplied with a time constant of 1sec.

This arrangement ensures application of tractive effort to match the adhesion available (Ref. DMRC Project Re-adhesion)

Control of Traction Motor for best Adhesion

Three phase Induction Motor:

For detection of wheel slip within 5msec means less than quarter of one cycle rotation. This is not possible by conventional method. Rotor current is produced by the same air gap flux therefore both are dependent on each other. In a three phase induction motor, Torque dynamics will be limited by the dynamics of the flux, which has large time constant (300ms). To improve the torque dynamics, the torque and flux producing components of the stator current space vector i_sq and i_dq must be decoupled. On decoupling, the torque will have dynamics as that of the stator currents (10ms) which is generally faster by 20-50 times. De-coupling of the torque producing and the flux producing components of the stator current to achieve high dynamic performance in torque control is done by the method called Vector Control or Field Oriented Control. This control is similar to separately excited DC series motor in which armature current and field is controlled separately.

The object of vector control or FOC is to separately control the magnitude of the two components of stator current called id(Flux controlling component) and i_q (Torque controlling component). The approach is

Convert three phase motor current into two phase motor current by phase transformation. The current vector in the stationary frame is converted as iα and iβ. Based on an assumed position of the momentary rotor flux, this vector is decomposed into a flux generating component Id and a torque generating component Iq (Park d-q reference frame). The required voltage to the stator of the motor can be expressed in the same reference frame by means of the 2 dimensions of the vector: U_sd and U_sq.  These vectors are first transformed into the stator voltages U_α  and U_β  and then again into three phase control voltages. These voltages are the basis for a switching pattern to control the power electronics.

Separately Excited DC Series Motor:

WAG6A,B&C Thyristor control locomotives are provided with separately excited DC series motor, with slip slide control where adhesion of 38% could be attained. The armature and field current can be controlled independently which are responsible for Torque and air gap field.

WAG9HI locomotive:

This is new development on WAG9 class  with higher weight and IGBT power devices  is planned for provision of radar control to measure linear speed accurately as a reference speed to help in improving the adhesion further. There is individual control of motors and it is possible to control TE of each motor in case of drop in adhesion.

Weight Transfer:

As per BHEL documents (Ref 2), steady state weight transfer between each bogie(L-95% & T-105%) and  each axle (L-97% & T-103%) of the same bogie are worked out and tractive effort is controlled accordingly. This helps in applying tractive effort in relation to adhesive weight reducing wheel slip probability. In tap changer locos, reduction of TE during start on leading wheels is reduced by field weakening but not very effective.

Dynamic Weight Transfer:

Weight transfer during start redistributes locomotive weight on each axle depending on the reactions and couples acting as mentioned in para 4.3. In case of a wheel slips in this condition, it momentarily disturbs weight transfer creating condition of wheel slip for other axles also. With advanced microprocessor control it is possible to identify the transient condition of weight transfer on each axle and reduce or increase the TE as required. (Ref.3 )

Review of Tractive control of Tap changer locomotive

Tap changer locomotive will continue to be with us for another 35 years even if the manufacturing is likely to be stopped in a year or two. A review of the auto-regression control to contain the tractive effort within adhesive weight is required which presently is based on cut in and cut out of relay Q_d. During auto-regression, holding current cannot be decided precisely but in steps. This can therefore be set at each one step regression for a time period of 1 sec. This will prevent auto regression of more than one notch at a time thus giving early opportunity of using restored adhesive weight.

References:

1. DMRC Project Re-adhesion

2. BHEL manual on Inverter Control

3. Development of Re-adhesion Control Method considering Axle-weight transfer of Electric Locomotive by Michihiro Yamashita QR of RTRI Vol 52 No. 1 Feb 2011