Page 269 - Tribology in Machine Design

254 Tribology in machine design

helium is sometimes used. It is characterized by low vapour pressure and it
can remain in the liquid state for a wide range of temperatures, providing
efficient wetting.

7.2.8. Friction torque caused by temperature increase
Temperature does not uniformly affect friction torque. With an increase in
temperature to 100 C -120 °C, friction torque decreases, which is explained
by the decrease in the viscosity of the lubricant. An increase in temperature
beyond 100 C 140 °C causes an appreciable increase in the contact
component of the friction torque as a result of changes in the geometric
dimensions of individual components of the bearing. There are no
analytical models which can be used to estimate the effect of temperature on
friction torque. The majority of the expressions mentioned in this section
contain a well-founded constant friction coefficient, varying over large
intervals depending on the working conditions, though for approximate
analysis of less important bearing units it is probably sufficient to use an
average value chosen for a particular load and rotational speed. Thus, the
friction coefficient,/, for self-aligning ball-bearings is usually taken as 0.001,
for cylindrical roller-bearings 0.0011, for thrust ball-bearings 0.0013, for
deep groove ball-bearings 0.0015, for tapered roller-bearings 0.0018, and
needle roller-bearings 0.0045.

7.3. Deformations in In addition to knowing the stresses set up within the components of rolling
rolling-contact bearings bearings by the external loads (for information on contact stress please refer
to Chapter 3), knowing the amount that the bearing components will
elastically deform under a given load is important.
The normal approach, <5, of two bodies in point contact is

where K(a) is a complete elliptic integral of the first order, 0 a and 0 b are the
elastic constants for the two bodies in contact and are the functions of the
modulus of elasticity E and the Poisson ratio and a is the one of the contact
area semiaxes. Using known relationships from contact mechanics (see
Chapter 3) eqn (7.20) can be rearranged to yield

where E(a) is a complete elliptic integral of the second order and R is the
equivalent radius of the contacting bodies.
The compressive deformation in line contact cannot be simply expressed.
Palmgren gives an expression for the approach between the axis of a finite-
length cylinder compressed between two infinite flat bodies and a distant