page_title: Adhesion railway
section_title: Forces on wheels, creep
hierarchical_section_title: Adhesion railway / Forces on wheels, creep
caption_attribution_description: English: When a tractive force (torque M {\displaystyle M} ) is applied on a railway wheel, a small difference arises between the forward velocity V {\displaystyle V} and circumferential velocity &#x03C9; R {\displaystyle \omega R} . The relative difference is the "creepage" &#x03BE; {\displaystyle \xi } . It is resisted by the friction force F w {\displaystyle F_{w}} on the wheel.
context_page_description: An adhesion railway relies on adhesion traction to move the train. Adhesion traction is the friction between the drive wheels and the steel rail. The term "adhesion railway" is only used when there is need to distinguish adhesion railways from railways moved by other means, e.g. by a stationary engine pulling on a cable attached to the cars, by railways which are moved by a pinion meshing with a rack, etc.
  There are the good forces, e.g. the traction force, the braking forces, the centering forces, all of which contribute to stable running. There are the bad forces which increase costs by requiring more fuel consumption and increasing maintenance that is needed to address fatigue damage, wear on rail heads and on the wheel rims, and rail movement from traction and braking forces.
  The interface between the wheel and the rail is a specialist subject with continual research being done.
context_section_description: The behaviour of vehicles moving on adhesion railways is determined by the forces arising between two surfaces in contact. This may appear trivially simple from a superficial glance but it becomes extremely complex when studied to the depth necessary to predict useful results.
  The first error to address is the assumption that wheels are round.  A glance at the tyres of a parked car will immediately show that this is not true: the region in contact with the road is noticeably flattened, so that the wheel and road conform to each other over a region of contact.  If this were not the case, the contact stress of a load being transferred through a line contact would be infinite.  Rails and railway wheels are much stiffer than pneumatic tyres and tarmac but the same distortion takes place at the region of contact. Typically, the area of contact is elliptical, of the order of 15 mm across.
  The distortion in the wheel and rail is small and localised but the forces which arise from it are large. In addition to the distortion due to the weight, both wheel and rail distort when braking and accelerating forces are applied and when the vehicle is subjected to side forces. These tangential forces cause distortion in the region where they first come into contact, followed by a region of slippage. The net result is that, during traction, the wheel does not advance as far as would be expected from rolling contact but, during braking, it advances further. This mix of elastic distortion and local slipping is known as "creep" (not to be confused with the creep of materials under constant load). The definition of creep in this context is:
  In analysing the dynamics of wheelsets and complete rail vehicles, the contact forces can be treated as linearly dependent on the creep (Joost Jacques Kalker's linear theory, valid for small creepage) or more advanced theories can be used from frictional contact mechanics.
  The forces which result in directional stability, propulsion and braking may all be traced to creep.  It is present in a single wheelset and will accommodate the slight kinematic incompatibility introduced by coupling wheelsets together, without causing gross slippage, as was once feared.
  Provided the radius of turn is sufficiently great (as should be expected for express passenger services), two or three linked wheelsets should not present a problem.  However, 10 drive wheels (5 main wheelsets) are usually associated with heavy freight locomotives.
caption: A torque 
    
      
        
          M
        
      
      {\displaystyle M}
    
   applied on the axle causes creepage: difference between forward velocity 
    
      
        
          V
        
      
      {\displaystyle V}
    
   and circumferential velocity 
    
      
        
          ω
          R
        
      
      {\displaystyle \omega R}
    
  , with resulting creep force 
    
      
        
          
            F
            
              w
            
          
        
      
      {\displaystyle F_{w}}
    
  .
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