Page 69 - Cam Design Handbook

THB3 8/15/03 12:58 PM Page 57

MODIFIED CAM CURVES 57

3.2 FUNDAMENTALS

In this section, the fundamental conditions for shaping and combining curves are
presented, and typical combinations of simple curves are shown. It is not practical to
show all the possibilities, but it should be noted that any combination of sections of basic
curves may be utilized to fulfill design requirements. The control conditions are:

• The sum of the displacements of the combining sectors shall equal the total rise of the
follower.
• The sum of angles rotated of the combining sectors shall equal the total cam angle.
• The velocities at each sector junctions shall be equal.
• High-speed action requires that acceleration at all sector junctions be equal, that is,
having no discontinuity in the acceleration and no infinite jerk value. Also, the acceler-
ation curve should have the lowest maximum value with the value of jerk not too large.
• Sometimes special design requirements dictate the proportions of the acceleration curve.
An example may be the controlling of the ratio of positive and negative acceleration
periods and shapes. An asymmetrical acceleration curve, with the maximum positive
acceleration larger than the negative maximum acceleration (ratio about 3:1) would be
a good choice for spring-loaded high-speed cams. Smaller springs, larger cam curva-
tures, and longer surface life result.

On rare occasions limitations in the available manufacturing facilities may dictate the
cam profile developed. For convenience, we have presented Fig. 3.2, which gives a com-
parison of important cam curves. Note that the velocity, acceleration, and jerk curves pre-
sented in this figure are all normalized (i.e., they have a unit total displacement h in a unit
cam displacement b).
To illustrate terminology we see that the trapezoidal acceleration curve (discussed later)
is a continuous function whereas its derivative (jerk curve) has many discontinuities. Note
that continuity of the jerk curve is of little value due to the usual tolerance limitations of
cam profile machine tool fabrication.

3.3 MODIFIED CONSTANT VELOCITY CURVE

In Chap. 2, we saw that the simplest curve is the constant velocity curve. It has a straight-
line displacement at a constant slope. It also has the smallest cam for a given rise and
provides a long stroke action. In this section we will blend any acceptable curve at the
dwell ends for proper rise. The cycloidal curve or parabolic curves have been utilized
depending on the cam speed, mass of the follower, and work performed by the machine.
As an example let us combine the parabolic motion curve blended with the straight-
line displacement curve.
EXAMPLE A cam having a rigid heavy-mass follower rotates at 300rpm with a total DRD
rise of 4 inches in 130 degrees of cam movement. As a preliminary study, use a parabolic
curve modified with the constant velocity curve. The action is as follows: (a) for the first
40 degrees a positive parabolic curve acceleration; (b) for the next 30 degrees a straight-
line displacement; and (c) for the last 60 degrees a negative parabolic curve accelera-
tion. Find the ratio of accelerations, and plot all characteristic curves indicating pertinent
values.