|MadSci Network: Engineering|
Question: Calculation of variation in kinetic friction of wheel bearings From: Steve Pearson Grade: grad (science) City: London, State/Prov.: Hampstead Country: England Area: Engineering Message ID Number: 965402611.Eg I would like to know if it is at all possible to determine the changes in the kinetic friction of a wheel bearing from just having rotational displacement and time data of the wheel. The scenario is one similar to having a cycle on stands and starting to pedal. The amount of "thrust force" on the wheel bearings change as a factor of the force applied to the wheel through the chain & pedals. This change will vary the wheel kinetic friction. I can determine the kinetic friction of the freewheeling wheel by tracking the displacement and time. If I then plot these values, the slope gives the acceleration, all I need to do then is multiply by the wheel inertia F=m*a. Your question cannot be answered, using the information you supplied. Perhaps a few comments on wheel frictional losses are in order. You mentioned a cycle wheel, with chain and pedals, so I have assumed you are primarily concerned about a bicycle. Bicycles are one of the world's most efficient devices for transport (roughly equaled only by freight barges). However, bicycle mechanical friction losses are greatest from the tires, then the chain drive, and then the wheel and pedal crank bearings. Air drag losses can be larger than the tire drag losses. Tire losses are largely determined by the pressure in the tire and the surface upon which they roll. Inflation pressure puts the tire cords in tension. Relaxation of this tension at the ground contact is what supports the load. When tension from inflation pressure is less than the load, you have a flat tire. Tire drag losses result from the flexing of the tire carcass and tread as it passes through the road contact. I found no current data on bicycle tire drag losses, as a function of pressure. When I last measured this (over 50 years ago), tire rolling friction power loss varied approximately with the 3.8 power of the inflation pressure. It also varied with speed, sidewall temperature, and tread temperature. Bicycle wheel bearings vary in design, but each wheel usually is fitted with a pair of shielded and caged ball bearings, lubricated with a light grease or heavy oil. Friction of such ball bearings is largely from contact between the balls and their cages. Without cages, friction results from ball-to-ball rubbing. The rolling friction of the balls to support a load is small. Losses from the grease or oil are generally small, excepting for speeds and temperatures that are uncommon in bicycles. Back to your question. With good wheel displacement/time data sets, you can get the velocity from the first derivative (the slope of wheel displacement versus time), and the deceleration from the second derivative (the slope of velocity versus time). The real question here is what does this data tell you? If the bicycle is on a stand, and the tires do not support any load, the major friction probably is from air drag. The freewheeling unit and the wheel bearing drag losses of the rear wheel can be separated, by testing with, and without, the freewheeling unit. If the front and rear wheels use the same bearings, the freewheeling unit loss can be inferred from the difference between the front and rear wheel frictional losses. You mentioned the 'thrust' force. I think that you will find that the ball bearings have such low losses that you will not be able to measure this thrust force effect. Remember, ball sliding provides most of the friction loss in the wheel bearings. A few web sites follow. You may find these useful on friction losses in bicycles. http://damonrinard.com/aero/formulas.htm (Aerodynamics) http://cyclery.com/lists/hardcore-bicycle-science/hardcore-bicycle-science- archive-hyper/hardcore-bicycle-science.199710/0032.html (Chain efficiency) http://cyclery.com/lists/hardcore-bicycle-science/hardcore-bicycle-science- archive-hyper/hardcore-bicycle-science.199709/0076.html (Human biomechanics)
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