Page 548 - Cam Design Handbook

THB16 9/19/03 8:04 PM Page 536

536 CAM DESIGN HANDBOOK

• Circular-arc—see Chap. 14
• Circular-arc with straight line (tangent cam)—see Chap. 15
• High-order polynomial curve
• Composite cam designs
• Polydyne cam (rarely used)
The polynomial equation is the most popular method for blending the ramp and main
event. The units of the characteristic curve equation are inches and degrees. Let us relate
these units to the time base employed throughout the book. If we let
N = cam speed, rpm
The follower characteristics at the cam are
(
Displacement lift)
y = inches
Velocity
1
˙
y = ¥ velocity, in sec = in deg
6 N
Acceleration
Ê 1 ˆ 2
˙˙ y = ¥ acceleration, in sec = in deg 2
2
Ë 6 N ¯
Jerk
Ê 1 ˆ 3 3
y =
˙˙˙ ¥ jerk, in sec = in deg 3
Ë 6 N ¯
In Fig. 16.5 we see the characteristic curves of an automobile camshaft (from software
DESINE) with a constant velocity ramp. Figure 16.6 shows diesel intake valve curves.
In these diesel curves it should be noted that the acceleration and jerk curve shape
and maximum values are acceptable since diesels run at about one-half the speed of
automobiles.

16.5 CAMSHAFT PROFILE GEOMETRY

In this section we investigate the camshaft geometric relationships:
• Cam profile
• Cam profile curvature
• Hertz stresses
• Follower linkage relationship

The cam profile or contour must first be established to determine the curvature of all
points for an acceptable minimum radii of curvature for both fabrication and the Hertz
stresses. In Chap. 9 the mathematical relationship for Hertz stresses was presented.
It is to be noted that the cam and valve have different displacement, velocity, acceler-
ation, and jerk curves (except for direct-acting systems). This phenomenon is because of
the linkage angularity and oscillations.