Cam Design Considerations
Pressure Angle
The commonly used cam motion acceleration profiles, such as modified-trapazoidal, modified-sine and 4-5-6-7 polynomial , all begin and end with a zero velocity. The accelerations of these begin in one direction and pass through zero to the opposite direction. The velocity is at a maximum where that occurs, (at 50% for almost all of them). Cam-follower pressure angle is roughly at a maximum at this point of maximum velocity. However, given a zero acceleration at that same position, the inertial response is zero. Therefore, cam wear does not occur at the point of maximum pressure angle.
This fact should weigh in your decision on how to select an acceleration profile. Maximum acceleration is often the primary factor to consider because, besides its' having a direct relation to the maximum force that will occur at the follower, it may be the limiting factor in some other aspect of the system's overall design intent, (such as one that requires the output motion to not exceed the value of acceleration due to gravity for example).
For plate cams, it is also worth considering, for symmetrical motions, that whatever maximum accelerated force the cam will produce in the positive direction, a spring or other return force device must be able to supply that same amount in the negative direction, (at the end of a rise or beginning of a fall). If it does not, the follower will leave the cam surface and cause major wear where the follower 'lands' back onto the cam.
The maximum pressure angle is better viewed upon as a relative indication
of the effect of the pressure angle that is occurring at the point of maximum
positive acceleration. Though that pressure angle is less than
that found at maximum velocity, the inertial reaction force presented between
the cam follower and the cam surface is proportional to the acceleration
multiplied by the secant of that pressure angle. Therefore,
with pressure angle in direct relation to velocity, it makes sense to initiate
the highest acceleration early in the motion and reduce it as the velocity
increases. Such is the aim of the Modified Sine acceleration
profile which is often chosen to minimize wear.
Harmonic / Modified-Trapezoidal Motion
As the name 'Harmonic' suggests, the formula is periodic; it is based upon a simple cosine function. Recalling elementary calculus, the derivative, (velocity), of the cosine position formula will be a sine function and the derivative of that, (acceleration), will, again, be a cosine function. This 3rd order function, being a cosine, (equaling one at zero), indicates that the highest acceleration occurs right at the beginning and at the end of the motion. The transition from a dwell condition to an 'instantaneous' high acceleration, being discontinuous, requires that the 'instantaneous' change of resultant force be absorbed by the compliance of the follower system.
To get a 'feel' for the effects of acceleration and jerk, hang a small weight on one end of a long thin rubber band. Holding the other end of the rubber band with your hand, resting it over the edge of a table, try to move it up a given amount and stop without having any left-over periodic motion. (If you can do this - you have excellent 4th order motor skills!) If you were to simulate a harmonic motion, the weight will end up bouncing quite a lot.
In a high speed system, this is exactly the effect you do not want. An indication to use harmonic motion is when there is a transition from a motion moving in one direction directly to a motion moving in the opposite direction. In the simple case, where both motions are identical in segment degrees and stroke, the deceleration value of the the first motion will match the acceleration value of the second motion. This complimentary acceleration attribute is very desirable. If there were only two motions on the cam and each were 180 degrees, the harmonic profile would be a simple circle eccentric to the shaft by the amount of stroke.
However, if there is also a dwell on the cam, something other than harmonic is needed for the motion in advance of the dwell as well as the one succeeding it. This where a split motion formula is useful. One common formula combines the modified trapezoidal profile with harmonic in either order. A 'mod-trap' motion would commence after the dwell and transition to a harmonic. The next motion would start with a harmonic then transition back to the mod-trap allowing a smooth transition back to the dwell.
Currently, we are limited to offering symmetrical 50% - 50% mod-trap/harmonic
motion in either order. Therefore, stroke and segment degrees
of the two back-to-back motions must be the same. This constraint
has, thus far, not presented any hardship in designing the machine cam
motions we typically need. If your application has a need for the more
complex asymmetrical combination, we would be most interested in hearing
about it.
More to come ..... please check back in the future.
Due to a lack of customer interest, our earlier plan to release free cam design software has been put on indefinite hold. We will actively pursue the idea in the future if conditions change to justify it.