Дөңгелеу кедергісінің физикасы

Force resisting the motion when a body rolls on a surface

Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body (such as a ball, tire, or wheel) rolls on a surface. It is mainly caused by non elastic effects; that is, not all the energy needed for deformation (or movement) of the wheel, roadbed, etc., is recovered when the pressure is removed. Two forms of this are hysteresis losses (see below), and permanent (plastic) deformation of the object or the surface (e. g. soil). Note that the slippage between the wheel and the surface also results in energy dissipation. Although some researchers have included this term in rolling resistance, some suggest that this dissipation term should be treated separately from rolling resistance because it is due to the applied torque to the wheel and the resultant slip between the wheel and ground, which is called slip loss or slip resistance. In addition, only the so called slip resistance involves friction, therefore the name "rolling friction" is to an extent a misnomer. Analogous with sliding friction, rolling resistance is often expressed as a coefficient times the normal force. This coefficient of rolling resistance is generally much smaller than the coefficient of sliding friction. Any coasting wheeled vehicle will gradually slow down due to rolling resistance including that of the bearings, but a train car with steel wheels running on steel rails will roll farther than a bus of the same mass with rubber tires running on tarmac/asphalt. Factors that contribute to rolling resistance are the (amount of) deformation of the wheels, the deformation of the roadbed surface, and movement below the surface. Additional contributing factors include wheel diameter, load on wheel, surface adhesion, sliding, and relative micro sliding between the surfaces of contact. The losses due to hysteresis also depend strongly on the material properties of the wheel or tire and the surface. For example, a rubber tire will have higher rolling resistance on a paved road than a steel railroad wheel on a steel rail. Also, sand on the ground will give more rolling resistance than concrete. Sole rolling resistance factor is not dependent on speed.

In the broad sense, specific "rolling resistance" (for vehicles) is the force per unit vehicle weight required to move the vehicle on level ground at a constant slow speed where aerodynamic drag (air resistance) is insignificant and also where there are no traction (motor) forces or brakes applied. In other words, the vehicle would be coasting if it were not for the force to maintain constant speed. This broad sense includes wheel bearing resistance, the energy dissipated by vibration and oscillation of both the roadbed and the vehicle, and sliding of the wheel on the roadbed surface (pavement or a rail). But there is an even broader sense that would include energy wasted by wheel slippage due to the torque applied from the engine. This includes the increased power required due to the increased velocity of the wheels where the tangential velocity of the driving wheel(s) becomes greater than the vehicle speed due to slippage. Since power is equal to force times velocity and the wheel velocity has increased, the power required has increased accordingly. The pure "rolling resistance" for a train is that which happens due to deformation and possible minor sliding at the wheel road contact. For a rubber tire, an analogous energy loss happens over the entire tire, but it is still called "rolling resistance". In the broad sense, "rolling resistance" includes wheel bearing resistance, energy loss by shaking both the roadbed (and the earth underneath) and the vehicle itself, and by sliding of the wheel, road/rail contact. Railroad textbooks seem to cover all these resistance forces but do not call their sum "rolling resistance" (broad sense) as is done in this article. They just sum up all the resistance forces (including aerodynamic drag) and call the sum basic train resistance (or the like). Since railroad rolling resistance in the broad sense may be a few times larger than just the pure rolling resistance reported values may be in serious conflict since they may be based on different definitions of "rolling resistance". The train's engines must, of course, provide the energy to overcome this broad sense rolling resistance. For tires, rolling resistance is defined as the energy consumed by a tire per unit distance covered. It is also called rolling friction or rolling drag. It is one of the forces that act to oppose the motion of a driver. The main reason for this is that when the tires are in motion and touch the surface, the surface changes shape and causes deformation of the tire. For highway motor vehicles, there is some energy dissipated in shaking the roadway (and the earth beneath it), the shaking of the vehicle itself, and the sliding of the tires. But, other than the additional power required due to torque and wheel bearing friction, non pure rolling resistance doesn't seem to have been investigated, possibly because the "pure" rolling resistance of a rubber tire is several times higher than the neglected resistances.

For pneumatic tires on hard pavement, it is reported that the effect of diameter on rolling resistance is negligible (within a practical range of diameters).

"Applied torque" may either be driving torque applied by a motor (often through a transmission) or a braking torque applied by brakes (including regenerative braking). Such torques results in energy dissipation (above that due to the basic rolling resistance of a freely rolling, i. e. except slip resistance). This additional loss is in part due to the fact that there is some slipping of the wheel, and for pneumatic tires, there is more flexing of the sidewalls due to the torque. Slip is defined such that a 2% slip means that the circumferential speed of the driving wheel exceeds the speed of the vehicle by 2%. A small percentage slip can result in a slip resistance which is much larger than the basic rolling resistance. For example, for pneumatic tires, a 5% slip can translate into a 200% increase in rolling resistance. For trains climbing up a grade, this slip is normally 1.5% to 2.5%. Slip (also known as creep) is normally roughly directly proportional to tractive effort. An exception is if the tractive effort is so high that the wheel is close to substantial slipping (more than just a few percent as discussed above), then slip rapidly increases with tractive effort and is no longer linear. With a little higher applied tractive effort the wheel spins out of control and the adhesion drops resulting in the wheel spinning even faster. This is the type of slipping that is observable by eye—the slip of say 2% for traction is only observed by instruments. Such rapid slip may result in excessive wear or damage.

Rolling resistance greatly increases with applied torque. At high torques, which apply a tangential force to the road of about half the weight of the vehicle, the rolling resistance may triple (a 200% increase). This is in part due to a slip of about 5%. The rolling resistance increase with applied torque is not linear, but increases at a faster rate as the torque becomes higher.

The rolling resistance coefficient, Crr, significantly decreases as the weight of the rail car per wheel increases. For example, an empty freight car had about twice the Crr as a loaded car (Crr=0.002 vs. Crr=0.001). This same "economy of scale" shows up in testing of mine rail cars. The theoretical Crr for a rigid wheel rolling on an elastic roadbed shows Crr inversely proportional to the square root of the load.

For pneumatic tires, the direction of change in Crr (rolling resistance coefficient) depends on whether or not tire inflation is increased with increasing load. It is reported that, if inflation pressure is increased with load according to an (undefined) "schedule", then a 20% increase in load decreases Crr by 3%. But, if the inflation pressure is not changed, then a 20% increase in load results in a 4% increase in Crr. Of course, this will increase the rolling resistance by 20% due to the increase in load plus 1.2 x 4% due to the increase in Crr resulting in a 24.8% increase in rolling resistance.

When a vehicle (motor vehicle or railroad train) goes around a curve, rolling resistance usually increases. If the curve is not banked so as to exactly counter the centrifugal force with an equal and opposing centripetal force due to the banking, then there will be a net unbalanced sideways force on the vehicle. This will result in increased rolling resistance. Banking is also known as "superelevation" or "cant" (not to be confused with rail cant of a rail). For railroads, this is called curve resistance but for roads it has (at least once) been called rolling resistance due to cornering.

Rolling friction generates sound (vibrational) energy, as mechanical energy is converted to this form of energy due to the friction. One of the most common examples of rolling friction is the movement of motor vehicle tires on a roadway, a process which generates sound as a by product. The sound generated by automobile and truck tires as they roll (especially noticeable at highway speeds) is mostly due to the percussion of the tire treads, and compression (and subsequent decompression) of air temporarily captured within the treads.

The rolling resistance of steel wheels on steel rail of a train is far less than that of the rubber tires wheels of an automobile or truck. The weight of trains varies greatly; in some cases they may be much heavier per passenger or per net ton of freight than an automobile or truck, but in other cases they may be much lighter. As an example of a very heavy passenger train, in 1975, Amtrak passenger trains weighed a little over 7 tonnes per passenger, which is much heavier than an average of a little over one ton per passenger for an automobile. This means that for an Amtrak passenger train in 1975, much of the energy savings of the lower rolling resistance was lost to its greater weight. An example of a very light high speed passenger train is the N700 Series Shinkansen, which weighs 715 tonnes and carries 1323 passengers, resulting in a per passenger weight of about half a tonne. This lighter weight per passenger, combined with the lower rolling resistance of steel wheels on steel rail means that an N700 Shinkansen is much more energy efficient than a typical automobile. In the case of freight, CSX ran an advertisement campaign in 2013 claiming that their freight trains move "a ton of freight 436 miles on a gallon of fuel", whereas some sources claim trucks move a ton of freight about 130 miles per gallon of fuel, indicating trains are more efficient overall.