Rolling resistance

The rolling resistance (also the rolling friction and rolling friction ) is the force produced during the rolling of a wheel or roller body and the movement in the opposite direction. Since the rolling resistance is approximately proportional to the normal force, as a characteristic value of the rolling resistance coefficient, is formed ( also the rolling resistance coefficient, rolling friction, etc.).

The values ​​for the rolling resistance coefficient is compared with the appropriate values ​​for sliding friction is considerably smaller. Therefore have roller bearings ( eg ball bearings) compared to plain bearings in terms of friction advantages.

The rolling resistance coefficient depends not only on the material pairing also on the geometry from ( radius of the rolling body).

The force that must be overcome in order ( for example, a wheel ) to move a body from rest into rotating motion is called rolling resistance.

Basics

During the rolling of both the rolling body and the base (the road ) is deformed. The deformation is carried out both on the rolling elements themselves and the rolling body and that at the contact point or the contact line. Essentially, this is indeed an elastic deformation, but there are processes added, causing a loss of energy. These are example of sliding friction when rolling the tire off-center parts or cornering, the flexing in the tire rubber or plastic processes in the subsurface ( driving on sand, gravel or crushed stone operations in the track bed ). Examples:

  • Combination steel wheel - rail on the railroad. In the accompanying picture the rail surface is elastically deformed by the wheel, when moving the rail material is compressed in the direction of travel. Here, a mountain piled up in front of the wheel. Since the rail material moves only slightly shaped, the mountain is continuously rolled through the wheel and paving behind the wheel again. When slipping the material is strongly pressed due to the large surface pressure. The more often a track is traveled, the more can break parts of the surface, which is recognizable by matt or rough surfaces as a result of compression and relaxation. A side effect is the liegte in a compliant ballast bed rail-tie combination that has a damping effect. Since the wheel is located in the "valley" of the impression point during the trip, it must be continually renewed even in horizontal distance. It migrates with while driving, resulting in a corresponding loss of energy. But the effect is smaller than that of the above. Moreover friction during cornering because of the rigid axles.

Even if a rubber-tired vehicle on soft ground, such as loose sand driving, driving becomes more onerous, the narrower the tire, ie the deeper they thereby sink into the sand. Off-road vehicles such as mountain bikes, etc. therefore have rather wide tires.

  • Combination tire road surface, in which, conversely, the deformation of the tire is usually greater than that of visible ( fixed ) road. An increased air pressure in the tire reduces rolling resistance, because it reduces the flexing and the contact area. This also facilitates the turning, but it has a negative effect on the roadholding and ride comfort, so that usually a compromise is necessary. Even with bicycles is the rolling resistance on a hard surface, such as Asphalt, the lower, the harder you inflate the tires. Bicycles for solid surfaces, such as Racing bikes, so tend to have more narrow tires and go with a similarly high Reifeninnnendruck such as trucks.
  • The roles of so-called medicine balls specially requires great strength. This is achieved in that they possess not only a relatively heavy, but also plastic, within certain limits filling that constantly deformed during rolling and this requires additional energy. It often occurs as a result of continuous stress to material fatigue and parts are removed. This is called pitting (English: pitting ).

Rolling resistance coefficient

The deformation during rolling, the contact force between the body and base asymmetric ( Fig. 1). The replacement of the contact forces due to static equivalent individual forces results in a normal force FN, which is shifted by the distance d to the front, and a frictional force F against the direction of movement ( Fig. 2).

From the equilibrium conditions for the following rollers at constant speed

The quotient is the rolling resistance coefficient cR (deprecated also: coefficient of rolling resistance, rolling friction ):

This gives the expression for the rolling friction FR the form

The rolling resistance coefficient is a dimensionless ( unit -free ) number, which depends on material properties and geometry of the rolling body ( For tires greatly from air pressure). Typical numerical values ​​of the rolling resistance coefficient will be around one to two orders of magnitude below those of the coefficient of sliding friction.

Typical rolling resistance coefficients cR

Limits of the theory

The relationship described above is a simplified model, which is sufficient for most of the calculations in the art. The dependence of skin friction of the other variables ( contact force, speed, etc. ) is not considered.

Furthermore, the described model does not consider the possible influence of another substance which may be present at the interface between the rolling elements and rolling body ( fluid or lubricant ). Examples are grease on the rail or water on the road. In such a case is referred to the mixed friction.

Extreme values ​​for velocities and temperatures as well as any chemical effects at the contact points can not be detected with this model.

For more information

  • "Tyre changing technical and climatic aspects, " Schmidt / Dr.Schlender ( tire technology on 109 pages processed, PDF, 1.62 MB, archive, PDF; 1.7 MB)
  • Popov, Valentin L.: Contact mechanics and friction. A teaching and application book by nanotribology to numerical simulation, Springer- Verlag, 2009, 328 pp., ISBN 978-3-540-88836-9.
  • Tribology
  • Physical size
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