MadSci Network: Engineering

Re: Calculation of variation in kinetic friction of wheel bearings

Date: Wed Aug 30 23:59:05 2000
Posted By: Arnold Anderson, Staff, Tribology/Friction systems, retired (Ford Scientific Laboratory)
Area of science: Engineering
ID: 965402611.Eg

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.   (Aerodynamics)
archive-hyper/hardcore-bicycle-science.199710/0032.html  (Chain efficiency)
archive-hyper/hardcore-bicycle-science.199709/0076.html   (Human 

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