with displacement (e.g. as in a
rubber pad), the spring is called a hard spring. If it decreases with
displacement (e.g. as in a Belleville spring), the spring is called a soft
spring.
ENERGY STORAGE - This is the area under the force-deflection curve of the
spring. It represents the strain energy stored in the spring (Units: in-lbs, or
ft-lbs, etc.).
PRELOAD - A spring used in equipment may or may not have a rest (on the shelf)
position in which it has its natural, free, or unstretched length. If its
rest-position length is not its free length, the spring is in tension or
compression. The amount of this tension or compression is called the preload.
When measured in force units, it is a preload force; when measured in deflection
from free position, it is a preload deflection.
ELASTIC MODULUS (E) AND SHEAR MODULUS (G) - These are material properties, which
characterize material compliance in tension or in compression (E) and in shear
(G). They are defined as the ratio of stress to strain, where strain refers to
the change in length (or deformation) per unit length. E involves tensile or
compressive stress and G involves shear stress. Units: lbs/inē. In many
practical applications, E and G can be regarded as constants, within a limit of
material stress known as the proportional limit. Metals loaded below the
proportional limit are examples. Rubber and plastics, however, usually have no
well defined proportional limit.
2.4 Damping, Friction and
Energy-Dissipation Characteristics
STATIC FRICTION, SLIDING FRICTION, COULOMB DAMPING - These are all terms used
for the frictional resistance encountered when one body slides relative to
another, e.g. a weight dragged on the ground. The frictional force is
approximately proportional to the contact force between the two bodies and
opposed to the direction of relative motion. The constant of proportionality, m,
is known as the coefficient of friction. It a 10 lb weight is dragged along a
horizontal floor with a coefficient of friction, = 0.2, the frictional
resistance is 0.2 x 10 = 2 lbs. Sometimes a distinction is made between the
value of the coefficient of friction when motion is just impending (starting
friction) and the value during motion (kinetic friction). The coefficient of
friction in the latter case is generally somewhat lower. Table 2 shows typical
values of the coefficient of friction for various materials and operating
conditions.
VISCOUS DAMPING - If a body moves relative to a second body, viscous damping
refers to a resisting force, which is proportional to the relative velocity
between the two bodies and opposes the direction of relative velocity between
them. The constant of proportionality is known as the coefficient of viscous
damping, c. Units: lbs per unit velocity, i.e. lbs/(in/sec). Such damping is
encountered, for example, in hydraulic dashpots and devices, which meter a
liquid through an orifice. The more viscous the fluid, the greater the damping.
If c = 0.5 lbs/(in/sec) and the body moves through a viscous fluid at 10 in/sec,
the viscous damping force is 0.5 x 10 = 5 lbs. Typical example: hydraulic door
closers.
CRITICAL DAMPING - Value of damping constant just sufficiently high in a
mass-spring-damping system so as to prevent vibration.
DAMPING RATIO - The ratio of the damping constant to the critical damping
constant for that system.
2.5 Vibration
Characteristics of Mechanical Systems
MATHEMATICAL MODEL - An idealized representation of the real mechanical
system, simplified so that it can be analyzed. The representation often consists
of rigid masses and dashpots. Hopefully, the representation is sufficiently
realistic so that the results of the analysis correspond reasonably closely to
the behavior of the physical system from which it was derived.
T201