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374 CAM DESIGN HANDBOOK

is no force reversal at the operating speed. For spring-loaded open-track cam systems to
be fully effective in eliminating backlash the spring must be applied not just to the fol-
lower but also at a point in the output transmission that affects all significant clearances.
In summation, the complete action of the roller follower as it rides on the cam is unknown
as it rolls, slides, and impacts the cam surface during its cycle of operation.

12.3.5.3 Spring Surge. For open-track cam-follower systems, the force loading com-
pression spring has the basic function of keeping the cam and follower in contact. At high
speeds, a phenomenon occurs that may seriously reduce the effective force of the spring,
allowing the follower to leave the cam, even though considerable surplus spring force was
provided. This is called spring surge. It is a torsional wave transmitted through the wire
up and down the spring at the natural frequency of the spring. It has been found to be a
state of resonance at the natural frequency of the spring with the cam high-amplitude har-
monics. Preventing spring surge is simple. In general, the lower the harmonic number, the
higher are the vibratory amplitudes. Therefore, the natural frequency of the spring should
be high enough so that if resonance occurs it will be with higher harmonic numbers and
vibratory amplitudes will be kept to a minimum. The harmonic number should be 11 or
higher. However, a ratio as low as 9 may be used with good follower dynamics and a
smooth acceleration curve. In modeling the system, it is common practice to consider that
the weight of the spring substituted should be one-third the total spring weight. The phe-
nomenon of “jump” exists for high-speed springs as well as the linkages. For further dis-
cussion of the subject of spring surge, see Jehle and Spiller (1929).

12.4 CAM DRIVE DYNAMICS—
ELASTIC CAMSHAFT

12.4.1 Introduction to Elastic Camshaft
The power input of almost all mechanisms and machinery is transmitted torsionally from
an electric motor to the output where it performs its function. In this book, the output is
a cam-follower system. Also, every torsional motion has a rotating mass or flywheel that
is generally located near the cam and support bearing. The flywheel provides stability to
the system and, depending on its size, aims to control fluctuations in speed as energy surges
through the system.
In this section, torsionally elastic camshafts are discussed with a selection of diverse
kinds of compliant shafts and followers. We will explore the dynamic phenomena of the
total machine performance. The model system takes into account cam shaft compliance
and leads to a set of nonlinear equations owing to the fact that the driving cam function
is no longer a known function. For more on torsionally compliant cam-follower systems,
see Koster (1975a and b).

12.4.2 Single-Degree-of-Freedom Torsional System

In high-speed camera studies of cam-driven systems, Rothbart (1961) observed a phe-
nomenon that was termed “shaft windup.” This phenomenon arose under the conditions
of a high inertia load, a large pressure angle, and a flexible drive shaft. Although the power
input end of the shaft rotates at a constant speed, the speed of the cam itself fluctuates as
it twists due to the time-varying torque. During this period, the follower is at first reluc-
tant to move and later moves slower than intended. Beyond the instant of maximum torque,