Adhesion is the grip/force of attachment produced by friction between wheels and rails, keeping wheels from slipping, and applies a limit on useful TE for a given axle-load. Real coefficient of adhesion: μ = Tmax/W, where Tmax = maximum tractive effort transmittable to the wheel, W = effective load on the driving axle. Real max. value of μ for steel-on-steel is 0.44 (44%) in the most ideal case. Since Tmax = μW, increasing Tmax needs more weight on the driving wheel — but axle-load is capped by the track, so the number of axles has to increase instead (with curvature limiting how far this can go).
Wheel-Slip Phenomenon & Bad Effects
Real slip formula: Slip = (δV/V) × 100%, where δV is the difference between the wheel's peripheral speed and the true vehicle (track) speed V. Real bad effects of wheel slip: damaged gears (damaged gear profiles lead to further oscillation modes), damaged bearings, cracks in bogie frames/supports/fixtures, excessive wheel wear and rail-burns.
Real Factors Affecting Adhesion
- Effect of speed: friction (and hence adhesion) is maximum at start and reduces with speed. Real SNCF formula: μas = μar × (8+0.1V)/(8+0.2V), where μas = coefficient of adhesion at start, μar = its value at speed V. Real Curtius & Kniffler formula: μar = 7.5/(V+44) + 0.16.
- Rail condition & weather: wet rails reduce adhesion; oily rails reduce it drastically. A thin dust film stuck to the wheel-rim reduces steel-on-steel adhesion value; dry leaves and coal dust also reduce adhesion. Moderate-to-heavy rain is better than drizzle for adhesion. Sanding helps, but the sand must be fine, dry, and fall on the rail-head. Real other causes of reduced adhesion: unevenness of rail-wheel contact from worn-out rail/wheel, loose track packing, warp in wheel-rim, wheel-diameter difference, irregular wheel-tread profile, track-level variation, and less contact area at points/crossings and on curves.
- Reduction on curves: the angle subtended between the wheel flange and the rail's gauge face is called the 'angle of attack'. Real fact: increasing this angle by just 1 degree on curves REDUCES adhesion by half.
Real Weight-Transfer Formulas (Mechanical Factors)
Real variables: M = mass of locomotive at centre of gravity, T = tractive effort exerted by the motor at each driving axle, L = bogie centre distance, l = bogie wheel centre distance, H = height of drawbar coupling above rail level, h = height at which TE is exerted by the bogie on the locomotive body.
| Real Axle | Real Weight Formula |
|---|---|
| Leading axle of leading bogie | M/4 − 2T(H−h)/L − 2Th/l |
| Trailing axle of leading bogie | M/4 − 2T(H−h)/L + 2Th/l |
| Leading axle of trailing bogie | M/4 + 2T(H−h)/L − 2Th/l |
| Trailing axle of trailing bogie | M/4 + 2T(H−h)/L + 2Th/l |
| Maximum weight transfer | ± [2T(H−h)/L + 2Th/l] |
Weight-transfer effect reduces as bogie wheel-centre distance increases, but curve/point/crossing safety limits how far this distance can be adjusted; in bogies with nose-suspended motors, wheel-centre distance is fixed by driving-wheel diameter and TM dimensions. Reducing 'h' helps the axle-to-axle weight transfer within a bogie but worsens bogie-to-bogie transfer. Real magnitudes: weight transfer between the axles of a conventional bogie is of the order of 15 to 20% of the loco's adhesive weight, while bogie-to-bogie weight transfer is only 1 to 3%. So overall, reducing 'h' decreases weight transfer considerably.
- Real methods to reduce weight transfer: (a) Vertical coupling between bogies — since weight transfer at the trailing axle of the leading bogie and the leading axle of the trailing bogie are exactly opposite, vertical resilient coupling between bogies cancels the reactions out. (b) Low traction bar — brings the point of application of tractive effort virtually down (reducing 'h'); real fact: this design feature is used in the bodies of WAM1, WAG and WAG4 locomotives of Indian Railways.
| Real Mechanical Component | Real Important Factors |
|---|---|
| Body Reaction | Height of drawbar & centre-pivot; gap between loading points on front/rear bogie; secondary suspension |
| Bogie Reaction | Direction of TM noses; height of centre pivot; primary suspension |
| TM Nose Reaction | Diameter of wheel; gap between TM nose and axle-centre; direction of noses |
Real Suspension System by Loco Class
| Real Loco Class | Real Bogie Type / Key Real Specs |
|---|---|
| WAM4, WAG5 (Co-Co trimount) | Side bearers 40% load, centre pivot 60% load; 4 snubbers per bogie; equalizing beams (2 different sets — one each between end-axles and middle axle); motor axle-hung nose-suspended; ONLY primary suspension; unequal wheel base (1702+2108mm) |
| WAG7 (high-adhesion bogie) | 4 side bearers per bogie carry 100% load equally divided; centre pivot carries ONLY TE/BE, no vertical load; equal wheel base 3800mm (1900+1900mm); primary+secondary suspension; TM axle-hung nose-suspended; lateral dampers between body and bogie; leading/trailing axle-box bearings have rubber thrust pads. Real primary suspension: equalizers hung directly on end axle-boxes, supported on the middle axle-box via a link+compensating beam, ensuring equal vertical-load distribution across all 3 axles (unlike WAG5's 2 different equalizer-beam sets) |
| WAP1, WAP4 (flexi-coil bogies) | Primary + secondary suspension; provision of bolster; secondary suspension has lateral friction dampers; primary suspension with helical springs; bolster supported on springs on the bogie frame; low traction-bar design |
| WAP5, WAG9 (3-phase loco bogies) | Primary + secondary suspension, both with springs+dampers; lateral dampers; yaw dampers; WAP5's motors are FULLY suspended; WAG9's motors are axle-hung nose-suspended |
Real Electrical Factors Affecting Adhesion
- Effect of TM performance characteristics: the steepness of the TE-vs-Speed curve of a TM decides how fast wheel-slip gets arrested. TE at any speed is normally kept below the max. adhesive limit, but if the adhesive limit drops (dew/oil on rails) the wheels start slipping and speed rises, causing TE to fall. If this fall in TE is rapid enough (steep TE-speed curve), it may drop below the NEW (reduced) adhesive limit and arrest the slip; a less steep curve lets slipping continue longer.
- Effect of TM combination in series/parallel: wheel-slip on one axle raises that TM's speed → increases back-EMF → reduces current. If TM groups are in SERIES, the current-reduction in the slipping TM also reduces current in the other TMs series-connected with it, spreading slipping to additional TMs — whereas TMs in PARALLEL are unaffected by one TM's slip. Real conclusion: a 6-P (6 parallel) combination gives better adhesion than a 2S-3P combination.
- Method of traction control: rheostatic control (DC locos) or tap-changer control (AC locos) causes sudden large TE variation in discrete steps, dropping the average TE well below the adhesive maximum. More steps reduce this variation and bring average TE closer to maximum. Real conclusion: continuous step-less control, as provided in 3-phase locos, achieves better adhesion.
- Use of the ZQWC switch (real weight-transfer compensation switch): TM torque is proportional to field flux × armature current. Using ZQWC diverts part of a TM's field through a shunting resistor, weakening the TM's torque/TE. This weakens fields on OFF-LOADED axles while overloaded-axle TMs work at full strength — distributing total loco TE so the TE-to-weight ratio is more or less equal across all axles, relieving offloaded axles from unduly strained ratios and reducing wheel-slip probability; for the same limiting adhesion-utilisation-factor, higher TE becomes obtainable from the locomotive overall.
- Real circuit detail (Circuit for Weight Transfer Compensation Switch): a spring-loaded switch named 'ZQWC' is provided on the LP's desk. The LP is expected to press and hold it until the train starts rolling while starting on up-gradients — pressing operates a relay 'QWC', which operates shunting contactors to shunt the fields of the desired TMs depending on direction of motion. The LP must release the switch the moment the locomotive begins rolling — the circuit is only relevant BEFORE back-EMF gets established.
- Enginemanship: the LP's skill affects adhesion while in motion — a sudden TE increase may exceed the Kinematic Coefficient of Adhesion, causing slipping and auto-regression (temporary TE reduction). Negotiating a gradient with the necessary attacking speed and timely sander use helps maintain proper adhesion.
- Bogie design; Selection of TM characteristic; Arrangement of TMs in series or parallel; Field weakening of slipping TMs; Enginemanship; Stepless control; Sanding; Creep control.
Real Slip-Slide / Creep Control
Maximum tractive or braking effort is obtained when each powered wheel rotates at an angular velocity such that its actual peripheral speed is slightly HIGHER (motoring) or slightly LOWER (braking) than the true vehicle/ground/track speed. The difference between wheel speed and track speed is called 'slip speed' or Creep. This system maximises available rail adhesion so the vehicle accelerates/decelerates better under poor rail conditions.
| Real Slip-Control Method | Real Working Principle & Loco Examples |
|---|---|
| Doppler radar-based control | Measures vehicle speed independently and individual axle speed; controls slip by permitting the wheel to slip at a fixed rate above vehicle speed. Real examples: WAG-6A, WDG-4. |
| Delta-N control | Estimates reference speed, obtains TE feedback, permits slip till TE is maximum. Real examples: WAG-6B and C, WAG-9, WAP-5. |
There's a relatively low limit value of slip speed at which peak tractive/braking effort is realised — real term 'maximum creep speed' — a variable depending on track speed and rail conditions. As long as maximum creep speed isn't exceeded, slip speed is normal and the vehicle operates in a stable microslip/creep mode. If adhesion is reduced/lost, wheels may slip excessively beyond the max. creep speed — characterised by spinning axle-wheel sets (motoring) or sliding/skidding sets (braking) — continuously monitored, detected, and corrected immediately.
- 1. Measuring actual vehicle velocity and computing wheel rotational velocity/acceleration expected for that vehicle velocity. 2. Measuring actual wheel velocity and deriving actual wheel acceleration. 3. Determining if actual wheel velocity varies from computed wheel velocity by more than a selected first minimum value — if so, generating a wheel slip/slide signal.
- 4. Computing (in response to the slip/slide signal) a difference between actual and computed wheel acceleration. 5. Summing a value representing this computed difference with the torque-request signal, adjusting motor torque to correct the slip/slide condition.
- 6. Determining if actual wheel velocity varies from computed velocity by more than a SECOND minimum value (greater than the first) — if so, substantially reducing the torque-request signal until the variation drops below the 2nd minimum value. 7. Inhibiting modification of the torque-request signal until vehicle velocity exceeds a minimum threshold value.
- 8. The first minimum value includes a slip value AND a slide value; the method compares actual wheel velocity to each, generating respective wheel-slip and wheel-slide signals. 9. Determining whether the vehicle is in propulsion or braking mode, and enabling the corresponding one of the slip/slide signals.