OT: My brain is failing me again. Help with numerical / mechanical problem required.

[Harald]

I have the following problem and don't really find a way to solve it:

For a given cam I have the lift versus the rotation angle as numerical values. Which looks something like this:


If a cam runs on a flat surface tappet it is possible to reduce or increase the base circle and the lobe by the same amount, or in other words shift the curve in the picture down or up. If the distance between the surface of the tappet and the center of the cam is also change accordingly, the lift does not change. Edit: After thinking about this again, that is wrong. But at leas the difference is not that big. And when grinding a cam nobody really compensates for that.
So far this is pretty straight forward. Now we get to the more difficult part. If a roller tappet is used instead of a flat tappet this is not the case anymore.


Firstly, to get the same lift, the lobe profile has to be different. This is because the contact point between the cam and the tappet isn't static anymore. It moves along the roller. Again, I have (or at least can measure) the cam profile.
And secondly, because the contact point is moving, it is not possible anymore to simply shift the curve up and down without changing the lift.
Now my question is, given the numerical cam profile data and the diameter of the roller, how do I calculate the new cam profile for a reduced base circle?

Sorry for the OT. But I think you guys appreciate a challenge and I appreciate your help :)

Cheers,
Harald

Edited: 27 June 2013, 4:14 p.m. after one or more responses were posted

[Mark Storkamp]

I've never done any cam design myself, but I have run across a book that looks pretty thorough in its treatment of the subject. You can download it from a link on this page:

http://www.camcoindex.com/indfaq.htm

[Harald]

Thank you. I will have a look at that, maybe it helps.

[Bruce Larrabee]

Please explain why you say that the lift differs between the two designs. It seems to me that the actual lift is the same. The time it takes to reach the maximum lift would be slightly slower with the roller design you show.

[Harald]

You are right, the maximum lift is the same. Also the minimum lift (0) is the same. But the ramps might be different. Or in other words at cam angles between minimum and maximum lift there will be a difference.
At min and max lift the contact point of the cam and the roller is on the line connecting the centers (of rotation) of the roller and the cam. But in between min and max the contact point moves away from that line. Now I think that the contact point for a given cam angle will be in a different position if the size of the cam is changed. If this is the case, that would result in a different lift at that angle, too.

Hope this clarifies what I mean.

Cheers,
Harald