Page 61 - Mechanical Engineers' Handbook (Volume 2)

50 Input and Output Characteristics

maximum power from the battery, so that the load resistance must be R V /i R .At
sc
o
L
oc
this operating point, the equivalent resistor within the battery (representing the internal losses
in the battery) is dissipating exactly as much power as is being delivered to the load.
If we want maximum power delivery, impedance should match the load to the source,
but if we want to minimize power delivery from a source, then impedance mismatching is
the key. Impedance matching assures that the source and load will divide the power equally;
all other impedances will result in less power transfer.

4.5 An Unstable Energy Exchange: Tension-Testing Machine
Although tensile studies of material properties require only a simple test apparatus, it is not
simple to interpret the data from such tests. The problem is that the tensile test machine and
3
the specimen can interact in an unstable way. Almost any desired stress–strain curve can
be obtained in a given material by a suitable choice of the test machine’s elastic compliance
compared to the specimen.
A tensile test involves the interaction between two springs, one that represents the spec-
imen and the other combined with a velocity source that represents the testing machine.
Figure 10 shows this simple model. While the testing machine is linearly elastic and does
not yield, the test specimen is not elastic. It undergoes a large plastic deformation in a typical
load–elongation test. Normally in such a test, the specimen is to be elongated at a constant
cross-head velocity (v). The test machine, however, is not a velocity source as is commonly
supposed; that source is really in series with a spring (K) representing the elastic deforma-
tions of the testing machine structure between the source of the motion and the jaws of the
machine.
In the course of a test, the specimen undergoes an elongation ( ) comprised of both
elastic and plastic displacements. The test machine undergoes only an elastic displacement
( ) given by F/K, where F is the load applied to the specimen by the machine at a given
cross-head displacement (y), which is really the sum of both the specimen ( ) and the
machine ( ) displacements. Figure 11 shows the components of this force–displacement
situation.
The cross-head velocity of the test machine is made up of two components as well:

Figure 10 Simple model of a tensile-testing machine.