Traction Rolling Stock Operation PDF

___________________________________________________________________________ 6. Tractive Effort and Train Resistance 6.0 General Concepts about Force (Tractive Effort), Power & Speed : 6.0.1 Force : The application of force to a mass will cause it to accelerate as govern...

___________________________________________________________________________ 6. Tractive Effort and Train Resistance 6.0 General Concepts about Force (Tractive Effort), Power & Speed : 6.0.1 Force : The application of force to a mass will cause it to accelerate as governed by one of Newton's laws of motion. The relationship is that the force necessary, is the product of the mass and acceleration. Force = Mass x Acceleration ( Tractive Effort is a type of Force, causing a loco or train to move) 6.0.2 Energy : The energy consumed in moving an object over a distance is the product of the force required and the distance. Energy = Force x Distance 6.0.3 Power : Power is the rate of energy usage, or energy per unit time. Power = Energy/Time = (Force x Distance) / Time = Force x (Distance / Time) = Force x Speed or HP = TE x Speed 6.1 TRACTIVE EFFORT Tractive Effort (TE) is the force applied to the rail by the wheel of the train to cause movement. The size of this force is determined by the characteristic of the power equipment installed on the train, and how the driver uses it. TE is a function of speed for a particular setting of control. A typical TE-vs.-Speed Curve for a locomotive is shown on Fig.1 next page. The starting TE is shown constant up to 20 mph, therefore in this speed range, from relationship of F = m x a , as TE (or Force) is constant, the acceleration will be constant. As a result of this, speed will build up uniformly with time as shown in Fig.2. This is the region of Maximum Tractive Effort, limited by adhesion. Above this speed, TE falls, and in consequence, the acceleration will start to fall and speed will not build up so quickly. The plot of speed with time, now starts to take shape of a curve as shown in Fig 3. Fig.1 – Tractive Effort versus Speed Curve Traction Rolling Stock : OPERATION. 150 ___________________________________________________________________________ Fig.2 & 3 - Speed versus Time Curves 6.2 Maximum Power at Rail : In the example given, the maximum TE of the unit is 100kN, and hence the maximum power may be calculated as follows: Speed in m/s = {(speed in mph) / 2.2} = 20/2.2 = 9.1 m/s Power = Force x Speed = 100kN x 9.1 m/s = 910kW upto 20mph. As this is the power needed to actually move the train it is strictly referred to as the Maximum Power at Rail as shown below in Fig.4. Traction Rolling Stock : OPERATION. 151 ___________________________________________________________________________ Fig. 4 – Power – vs. –Speed Curve In reality, the total power drawn from the supply will be greater than 910kW, due to the need for additional auxiliary loads and due to losses in the conversion process. It is highly unlikely that the equipment is capable of running at this power level continuously, and for all types of services. Again, for reasons of rating, the characteristic of the equipment will not follow the curve of maximum power at top speed, as indicated by the dip from 70mph onwards in Figs 1 & 4. Consequently a continuous power rating will often also be quoted. Continuous Power rating may be derived from a number of factors based around the equipment characteristic and will include assumptions of proportion of time; coasting is done at a lower tractive effort demand by driver. 6.3 Types of tractive effort: As, TE = loco weight x adhesion. It may be noted that horsepower isn’t a part of the calculation for TE. 6.3.1 Starting Tractive Effort - is the amount of tractive effort that must be produced by the motive power to start moving a train from a dead stop without slipping the wheels. 6.3.2 Continuous Tractive Effort - is the amount of tractive effort required to keep a train in motion continuously for long term without slipping the wheels or overheating the traction motors & transmission. 6.3.3 Short Term Tractive Effort for X minutes - is the amount of tractive effort required, for short term (for prescribed X minutes), say to climb a grade. This will generally not exceed 120% of the Continuous TE for the prescribed short period of time. It is limited by overheating of the traction motors, of other power & transmission equipments on the locomotive. 6.4 Increase of Speed and Balancing Speed:- As the DC motor starts to turn, the interaction of the magnetic fields inside it causes it to generate a voltage internally. This "back emf" opposes the applied voltage and the current that flows is governed by the difference between the two. Traction Rolling Stock : OPERATION. 152 ___________________________________________________________________________ So, as the motor speeds up, and the internally generated voltage rises, the effective voltage falls, less current is forced through the motor and thus the torque falls. In order to continue accelerating the train, notches are further increased, each notch increases the effective voltage and thus increasing the current and torque for a little bit longer until the motor again catches up. This can be felt by a jerk of acceleration as the torque suddenly increases in response to the new surge of current. Fig.5-Intersection of TE-vs-Speed Curve, with Train Resistance Curve The motor naturally stops accelerating at any notch-position, when the drag or Resistance of the train (increasing with speed) matches the torque produced by the motors. This is called the “Balancing Condition”. Balancing Speed is the maximum speed for the given load, on that gradient & curvature, and is the speed at the intersection-point of TE-Speed curve & Train Resistance-Speed curve. Force available to accelerate the train is the difference between TE and train resistance. 6.5 TRAIN RESISTANCE : It is the resistance offered to start or run a train of given load at a given speed and on a given gradient. Train Resistance during run is normally given by:- R = a + bv + cv2, where v = speed The factors a, b and c characterise the particular train, with "a" being the static friction,”b” is due to mechanical considerations, and ”c” is air resistance. It is normally expressed as the Specific Resistance in kg/ton, which is the force or TE required for starting or running a loco or train, per ton weight of loco or train. Types of train-resistances are:- 1. Resistance to start (a loco or loco+train) on straight level track. 2. Resistance to run at a given speed on straight level track. 3. Resistance due to gradient. 4. Resistance due to track-curvature. 6.5.1 Calculation of Train Resistance & Tractive Effort : (RDSO's Technical Circular TC 27 vide Lr.No.EL/3.1.39/1 dt.27.7.98) (A) Starting Resistance of Train or TE required to start a Train is given by :- TE = T1x (Load Wt.) + T2 x (Loco Wt.) + T3 x (Train Wt.)+ T4 x (Train Wt.) Where, T1= Starting Resistance of load in kg/ton. Traction Rolling Stock : OPERATION. 153 ___________________________________________________________________________ = 4 kg/ton for BOXN wagon & 6 kg/ton for BOX wagon. T2= Starting Resistance of loco = 6 kg /ton T3= Grade Resistance in kg/ton T4= Curve Resistance in kg/ton (B) Running Resistance of train or TE required to run a train at a given speed "V“ in kmph , is given by :- Here, T3 & T4 remain the same as for starting the train, while T1 & T2 on run are given by :- T1= 0.6438797+ 0.01047218 V + 0.00007323 V2 (for BOXN load) T2= 0.647 + (13.17/ A) + 0.00933 V + (0.057 / AN) V2 (for loco) Where A = Axle-Load of Loco in ton and N = No. of Axles in Loco 6.5.2 Effect of gradient on train-resistance : If the train was travelling vertically upwards or on Grade 1 in 1 (G=1), it would incur the full effect of gravity. The acceleration due to gravity is constant. Mathematically, it is known as “g” and its value is 9.81 m/s2. For example, for a 150 tonne (150 x 1000 kg) train, the gravitational force acting on it is: Force = Mass x Acceleration = 150 x 1000 x 9.81 = 1471 500 N = 1471.5 kN. (This is also weight of train given by mg) Such a high TE is required to lift the train vertically upwards on 1:1 (G=1) gradient. Now, since luckily no gradient is that steep, so the gravitational resistance practically encountered isn't nearly so great. While it's not completely accurate, for the gradients encountered by trains, it suffices to divide the weight by the gradient to obtain the value for this resistance. For example, if the above train were to climb a 1 in 200 gradient or G=200, the resistance due to gravity would be :- TG = 1471.5/200 = 7.3575 kN Therefore TE required for a train of weight "W", to overcome a gradient of “1 in G“is given by:- TG = [ W / G ] Or, Specific Grade Resistance = (1/G)..in kg/ton The train's speed remains constant at the point where the torque of the motor, governed by the effective voltage, equals the drag or train-resistance at the balancing speed. If the train starts to climb a grade, the speed reduces because drag is greater than torque. But the reduction in speed causes the back voltage to decline and thus the effective voltage rises - until the current forced through the motor produces enough torque to match the new drag. As long as the train produces Tractive Effort, greater than the overall train resistance, the train will accelerate. In the example shown in Fig.5 above, the balancing speed is 95 mph on the level, but it is 75 mph on a 1 in 100 gradient, as it will reduce on increasing up-gradient. 6.5.3 Effect of curvature on train-resistance : Tractive Effort required to overcome curve-resistance of S0 curve is given by :- TC = 0.4 X S X W, where W= Weight of train in tons Traction Rolling Stock : OPERATION. 154 ___________________________________________________________________________ If instead of degree of curve, the radius of curvature (R) is given in m., then :- S0 = [1746 / R ] So, Specific Curve Resistance = T4 = 0.4 x S…..in kg/ton 6.5.4 Effect of Gear Ratio on Tractive Effort : A gearbox links the traction motor shaft to the train axle, in order to step down the high rotational speed of motors to the required speed of axles! Since power = force x speed; as the speed at axle is reduced, the force or torque at the axle is increased. Consequently, re-gearing is often used as a means of obtaining a revised traction characteristic to suit alternative service patterns. The effect of changing gear-ratio is to change the train speed at which full load can be applied. Therefore: 1. Increasing the gear ratio reduces the minimum speed (hence increases torque) at which a given locomotive can operate safely, e.g. gear ratio of about 4 (16:65, 18:64 or 17:77) is used in Goods 2. Reducing the gear ratio, increases the maximum speed at which a given locomotive can operate without mechanical damage to the motors, e.g. a gear- ratio of about 3 or (21:58) is used on Coaching Locos. 6.5.5 Effect of Wheel Diameter on Tractive Effort : As the wheels wear down, the tractive effort characteristic will change! A change in the wheel diameter is effectively a change of gear ratio, and consequently as the wheels get smaller the starting TE will increase. However, as this also means that the axle speed becomes higher for any given train speed, the TE at higher speeds will fall off more rapidly. When train performance is being predicted, it is normal to assume the average half-worn wheel diameter. 6.5.6 Effect of Field Shunt on TE & Speed : The DC motor can be made to run faster than the basic "balancing speed" achieved whilst in the full parallel configuration with full voltage applied. This is done by "field shunting". An additional circuit is provided in the motor field to weaken the current flowing through the field. The weakening is achieved by placing a resistance in Traction Rolling Stock : OPERATION. 155 ___________________________________________________________________________ parallel with the field. This has the effect of forcing the armature to speed up to restore the balance between its magnetic field and that being produced in the field coils. It makes the train go faster but at less power. ----------------------------- Traction Rolling Stock : OPERATION. 156