Page 358 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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the lubricant film is composed of a series of horizontal layers that can slide relative to
each other, that is, laminar flow. The lubricant layers adjacent to the surfaces A and B
have identical velocities to these surfaces. Intermediate layers have velocities following
a linear velocity gradient, as shown in Figure 12.4.
Neglecting inertial force and gravity, experimental results indicate that the shear stress
in the fluid is proportional to the rate of shearing strain u/ y [4, 5]. This is Newton’s
law of viscous flow and is expressed as
u
= (12.1)
y
where
–dynamic viscosity, also called absolute viscosity, measured in Pa s;
u
–the rate of shearing strain, or velocity gradient.
y
12.2.3.2 Viscosity of Lubricants
The viscosity of lubricants is a measure of internal frictional resistance of fluid. Com-
monly used viscosities are dynamic viscosity and kinematic viscosity.
(1) Dynamic viscosity,
Three physical units are used to describe dynamic viscosity, that is, SI metric
units, C.G.S. units and imperial (FPS) units. The dynamic viscosity is measured
−2
by Newton-second per square metre (N sm ), or Pascal-second (Pa s) in SI
units. To give a direct feel for dynamic viscosity, the viscosity of water at room
temperature is about 1 mPa s, while honey has a viscosity of 1500 mPa s [4]. The
unit of dynamic viscosity in C.G.S system is dyne-second per square centimetre
−2
(dyn s cm ) or poise (P). It has been customary to use centipoise (cP) in analysis for
convenience, where 1cP = 10 −2 P. In imperial units, dynamic viscosity has units of
2
pound force-second per square inch (lbf s/in ), called a reyn in honour of Osborne
Reynolds. The conversions of these units are listed in Table 12.1.
(2) Kinematic viscosity,
In many situations, it is convenient to use kinematic viscosity rather than dynamic
viscosity. Kinematic viscosity is defined as

= (12.2)

Table 12.1 Conversion factors for dynamic viscosity.

To
To convert from SI units (N s m ) C.G.S units (cP) Imperial units (lbf s in )
−2
−2
Multiply by

−2
SI metric units (N s m ) 1 10 3 1.45 × 10 −4
C.G.S units (cP) 10 −3 1 1.45 × 10 −7
−2
Imperial units (lbf s in ) 6.9 × 10 3 6.9 × 10 6 1